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Enthalpies of formation of liquid and solid binary alloys based on 3d metals
Physiea B 152 (1988) 303-346 North-Holland, Amsterdam
ENTHALPIES OF FORMATION OF LIQUID AND SOLID BINARY ALLOYS BASED ON 3d METALS
V. ALLOYS OF NICKEL A.K. NIESSEN and A.R. MIEDEMA Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands
F.R. de BOER Natuurkundig Laboratorium, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands
R. BOOM Research Laboratories, Hoogovens-Groep, 1970 CA IJmuiden, The Netherlands Received 12 July 1988
Continuing the papers on alloys based on either Sc, Ti, V, Cr, Mn, Fe or Co we review in the present paper, on the basis of the model developed by Miedema and co-workers, enthalpies of formation of ordered binary intermetallic compounds of Ni with arbitrary metal partners. The enthalpy effects are also examined for liquid Ni alloys. The calculated values agree quite satisfactorily with the available experimental data for binary systems of Ni with a transition metal, except where Ni is the minority partner in alloys with the much more electropositive metals like Y, La and Ti, in which case the model tends to overestimate the enthalpy effects. A formalism is suggested to improve the predictions in these cases.
In the binary systems where Ni is alloyed with a non-transition metal differences are sometimes observed between predicted and experimentally determined enthalpies. These discrepancies are analysed taking into consideration information on all 3d metals. The limitations of the model will become clear for Ni alloys in particular.
1. Introduction
In recent papers [ 1-4 ] it has been demonstrated that the existing experimental information on the enthalpy of formation of alloys in binary systems based on Sc, Ti, V, Cr, Mn, Fe and Co can be reproduced within the experimental uncertainties by means of a semi-empirical model, which has been introduced extensively in [ 5 ]. In the present paper we compare predicted and experimental enthalpy effects that occur upon the formation of solid or liquid alloys based on Ni. The use of the model to predict enthalpy effects of Ni alloys and the comparison of the predicted values with experimental data are of particular interest since Ni is widely used in metallurgy and electronic devices, while moreover, for no other metal than Ni so much experimental thermodynamic infor-
marion is available. It is particularly interesting to compare enthalpy effects for alloys of Co and Ni; although Ni and Co have about the same model parameters, some differences in alloying behaviour may be expected between Ni and Co since the d band may become completely filled upon alloying Ni. In combination with the previous papers [ 1-4 ] in this series the present paper covers all the alloys of 3d transition metals and in fact the majority of experimental data on alloys containing at least one transition metal. Therefore it is appropriate to evaluate in this paper to what extent the experimental data and the most recently published version of the calculated enthalpy values [ 4,6 ] do agree. As in the previously published papers [ 1-4 ] of this series, our aim in this paper is to present a
0921-4526/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
304
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
Table Ni-Ia C a l c u l a t e d v a l u e s for the h e a t o f f o r m a t i o n , A H for , o f c o m p o u n d s o f five different c o m p o s i t i o n s , the limiting p a r t i a l h e a t s o f solution, A H °, a n d the h e a t o f m i x i n g for a statistically o r d e r e d liquid at the e q u i a t o m i c c o m p o s i t i o n , A H mix, in kJ ( m o l e o f a t o m s ) - l , for b i n a r y nickel s y s t e m s N i - M w h e r e M is a t r a n s i t i o n m e t a l o r a n o b l e m e t a l . A v a i l a b l e p h a s e - d i a g r a m i n f o r m a t i o n has b e e n a d d e d (¶).
~ t_tfo~
AH
I . d t l l calc
M
NiM 5
NiM 2
NiM
Ni2M
NisM
¶
°
AHmi~
AH
°
Ni in M
NiM
M in Ni
Sc
- 21
- 42
- 57
- 53
- 29
- 130
- 39
- 180
Ti
-20
-40
-52
-46
-25
- 126
-35
- 154
V
- 11
-22
-27
-23
- 12
-69
-18
-75
Cr
-4
-8
-10
-8
-4
-27
-7
-27
Mn
-5
- 10
- 12
- 10
-5
-33
-8
-33
Fe
-1
-2
-2
-2
-1
-6
-2
-6
Co
0
0
0
0
C
0
C-
-1
0
-I
Ni Y
- 15
-31
-44
-45
-26
- -
-97
-31
- 162
Zr
-26
-53
-72
-68
-38
- -
-165
-49
-237
Nb
-17
-34
-45
-40
-22
- -
-107
-30
-136
Mo
-4
-9
- 11
- 10
-5
- -
-27
-7
-32
Tc
0
+1
+1
+!
0
C
+2
+1
+3
Ru
0
+1
+1
+1
0
+
+2
0
+2
RJa
(C+)
-3
- 1
-4
- 1
- 1
- 1
- 1
- 1
Pd
0
0
0
0
0
La
- 13
-26
-38
-39
-24
- -
-81
-27
- 146
Hf
-23
-46
-63
-59
-33
- -
-145
-42
-204
Ta
-17
-33
-44
-39
-21
- -
-105
-29
-133
W
-2
-4
-5
-4
-2
- -
-ll
-3
-14
Re
+1
+3
+3
+3
+2
+
+8
+2
+10
Os
+1
+2
+2
+2
+1
+
+5
+1
+6
Ir
-1
-2
-2
-2
-1
C
-5
-2
-7
Pt
-3
-5
-7
-6
-3
C-
-17
-5
-22
Th
- 19
-39
-56
- 58
-35
- -
- 122
-39
-218
U
- 16
- 31
-42
-40
-22
- 98
-29
- 140
Pu
- 14
- 28
- 37
- 34
- 19
-88
- 25
- 118
Cu
+2
+4
+5
+4
+2
C
+ 14
+4
+ 14
Ag
+9
+ 18
+23
+20
+ I1
+
+56
+ 15
+68
Au
+4
+8
+11
+10
+5
(C+)
+25
+7
+33
complete collection of the published experimental thermodynamic data on Ni systems. In addition, we present the known binary phase diagrams, making it possible to compare predictions with phase-diagram information in a qualitative way for those systems on which no thermodynamic data are available in the literature, as will be shown in sec. 2.
C
0
0
0
Since the model parameters depend on the electronic configuration, the formation of atomic magnetic moments of varying magnitude might be expected to be a disturbing factor in the prediction of the stability of Ni compounds as well. However, for Cr and Mn [2] and also for Fe [3 ] and Co [ 4 ] it has turned out that the dependence of the model parameters upon the magnetic state is not
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
305
Table N i - l b Calculated values for the heat o f formation, A H for , o f c o m p o u n d s o f five different compositions, the limiting partial heats o f solution, A H "°, and the heat o f mixing for a statistically ordered liquid at the equiatomic composition, A H mix, in k J ( m o l e o f a t o m s ) - I , for binary nickel systems N i - M w h e r e M is a non-transition metal. Available phase-diagram information has been added (¶). A T• ."/ ~for c M
NiM 5
NiM 2
NiM
- -° AH Ni2M
Ni5M
¶
Ni in M
A H m~
A H- - °
NiM
M in Ni
Li
0
+1
+1
+1
0
+
+3
+1
+3
Na
+16
+32
+46
+44
+23
(+)
+100
+32
+140
K
+20
+39
+59
+68
+41
(+)
+123
+45
+235
Rb
+20
+39
+59
+71
+46
+ 123
+47
+259
Cs
+ 20
+ 39
+ 59
+ 74
+ 51
+ 122
+ 48
+ 284
Be
-4
-8
-9
-7
-3
-
-19
-4
-15
Mg
-3
-6
-8
-8
-4
-
-13
-4
-16
Ca
-4
-7
-10
-11
-6
-37
Sr
0
- 1
- 1
Ba
0
0
0
-2
-22
-7
- 1
-
-3
- 1
-6
0
+
+1
0
+1
0
Zn
-10
-19
-23
-20
-10
--
-34
-9
Cd
-3
-6
-8
-7
-4
-
+7
+2
+9
0
+1
+1
+1
+1
--
+28
+8
+40
-9*
-55*
Hg
B
+2
-23
-33
-27
- 14
- -
AI
- 19
-37
-48
-42
-22
- -
Ga
- 14
-28
-37
-34
- 18
In
-4
-9
-12
-12
-7
T1
+ 1
+3
+4
+4
+2
+
+5
+
--
C
+113
+54
+21
+9
Si
+8
- 17
-33
-32
- 18
Ge
+8
-9
-20
-21
-12
Sn
-8
- 16
-22
-23
Pb
+1
+1
+2
+2
N
+203
+ 103
+36
+ 10
P
- 13
-42
-61
-56
-30
As
- 17
-35
-47
-44
-25
- -
Sb
-7
-14
-20
-21
-13
- -
Bi
- 1
-3
-4
-4
~2
-
strong and that in practice the alloying properties of these metals can be described with unique values of the model parameters. Clearly no problems are expected for Ni alloys in this respect. In the phase diagrams presented in figs. 1 and 2 the most recent information has been included either in the phase diagram itself or in the references attached to the diagrams. Where no
...
-36
-82
-22
-97
-53
- 15
-69
+5
+2
+8
+41
+ 13
+67
...
+51"
+50*
-86
-23
-98
- -
-41
- 11
-51
- 13
- -
- 13
-4
-21
+!
+
+40
+13
+73
+4
+
...
+86*
+50*
...
-26*
- 134"
-65
-19
-93
-4
-1
-7
+31
+ 10
+58
complete phase diagram was available, as much partial information as possible has been included, for example the existence of compounds or the solubility at certain temperatures. Temperatures are indicated in units of lO3 °C. Calculated enthalpy values are presented in tables Ni-Ia and Ni-Ib for binary solid compounds of five different compositions and for binary liquid
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
306
nickel-based [1]
[1.2,31 1.5
....
~.-~-~
[ 1,2,4,5,6]
.
A
,.o~ O.
-
I
I
~
i|
1
Sc
Ni
O.
Ti
[I] N
1.5
[I_,7, 8]
Ni
V
oJ
Ni
'T?'o
,131
~c.,, ~-w--~
I
I
Cr
,i
[ 2 . 1 2 ] ~ co i-~ r~.z c~ z>:+,.>,.-
Ni
\
;;
Y
Ni
[1,2.~1
Zr
~
x
Nb
I~,2]~
o~"
o.
Ni
zzz~zz
,~
Ni
3.0-
[ I~_a~'17]
~.o
z ~
2°1-
10 Ni
- ~
•~ r ,
~e-_~~,.~
05 Th
Ni
Ni
Hf
~l
Jr
~
0.51 1 U
Ni
[1,2] ~
I
,.oF=q--r~ I
"T='Lo
Mo
[1'191~
Ni
To
,
l
[;J
w
Ni
~
% = ~
II I d l
I Ni
Pu
Ni
a
Fig. I. Binary phase diagrams of nickel with 3d-, 4d- and 5d-transition metals, noble metals and actinides. Temperatures (103 °C) are plotted vertically, the atomic concentration of Ni horizontally. Numbers between brackets are the references of experimental
307
A.K. Niessen et al. I Enthalpies of formation of Ni alloys
binary ph~e diillr=m,~ [1._9 ]
,=
1.0~"~-~,N,)
[1,10.11,/~]
[1 ]
I
•
Ni
-Co,Ni }
0.5 Mn
Ni
~,,
[1,2_.1
~°r't:-.
I
Fe
2^J ~-~"~ ~~"~[1]
(Tel 1.0 Tc
Ni
~.oI'~,,I:
1'I-/; ~
-,
"~--q "1
Re
Ni
q
Ru
Ni
1"0t
1Ot
i
i/ Ni
(Cu,Ni)
,.oF Ni
Ag
lAg) + (Ni)
Ni
''"Ni'
175
i
1
!
0.5
Ni
Pd
/
Ir
201 ,t L1 "L2 L * (Nil
[1]
.~,.<,.,,,.~o.il
Rh
2.
Os
[ 1,2,151
1.01" at low temp.
2.ol"-. I /,o,, ', ',,----~,q
1.5i
I
2.0
[1 231
[!, 20, 21,221
0.51 Cu
I
,or ,
Ni
Co
Ni
"]
o.si
Ni
Pt
Ni
------t
(pLN,)/
/(~'~',"~
I Ni
[1'2~'1 . 0 ~ (Au,Ni}
Au
Ni
b cited work; if more numbers are indicated, the dial-am has been reproduced from the underlined reference. (a) nickel and elements with less than five d electrons per atom and Co) nickel and elements with more than four d electrons per atom.
308
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
nickel-based
2o[ [ [2,2__5] _~
[ 1,2_] 2'0f / ' t ' i L 2 " ' " 1.0 / / ?>1200% ~I L +(Ni)
I
o.or
I
[i
Ni
\ Be
[1]
Q,2; 2.0
solubility of Ni in Na at 600"C 0 20 ppm No
1.0 Ni
0.0 N
[1]
Ni
11,2]
solubility of Ni
~
in K at 1055 °C 58 ppm K
Ni
[t.26.27] Z z
1.0
~._u~
10 Ni
0o
Co
Ni
Hm
Zn
[1. 28]
[2]
2° I
z~-
Ji
10
i
no i n f o r m a t i o n
Rb
Ni
Ni
0,0 Sr
i
Ni
Cd
Ni
[1,29]
[1.2]
1-01
/ ~/~---'~ no information Cs
Ni
10Iv,/-- L * INi) rI (Bo)*(Ni) 0.0 ~
Bo
0.5 f ~ . ...~-
Ni
0.0 !
Hg
en
r,~
/'1 !
Ni
II Fig. 2. Binary phase diagrams of nickel with non-transition metals ranged according to increasing valence. Temperatures (10 3 °C) are plotted vertically, the atomic concentration of Ni horizontally. Numbers between brackets are the references of cited experimental
A.E. Niessen et al. / Enthalpies of formation of Ni alloys
309
binary phase diagrams [1.2, 3 0 , 3 1 ,32]
1.01
0s| •
[1.37] 2.0
IC)+ L
1.0
(C)+ (Ni)
[1]
+'~.+_+.,
0.0
B
Ni
C
[1, 331 1.5
Ni
~'~.----,
10
I .j,n~:~ =I
~ununv+ ~ ._,,*,e+,, z
05 Ni
Si
[1,_2.34. 3.5] ~ ~ ~'~./TA
[11
1+f 1.0
1.0
~ .~.~~ ~z z
Ni
[1, 3.~8,3g)
._I 1.bl~
0.5 AI
N
Ni
..T.,r~em Q.z t----
o..,'~+-, ..~,
,, i i
0.5 P
Ni
[1_,40] 1.5
._
i
[1]
oJ
~sl-
<+",,,~.~<-"' -J
1.0
z z~.~:~
.-
.<- " ~
¢.~
1.0 0+0 ~
'
~
Ga
IIH
05
Ni
[!. 3.__6] c ~- -/ ~ c
Ge
Ni
As
[!.~3,~
[I]
" ¢:::'~ c
Ni
1.5 ~;~ z Z z z
1+0
0.0 In
Ni
1.0
1.0~
0.5
0.5
0.0 Sn
[i]
00
Sb
Ni
[i]
[!.4; ,+.2]
+ (Nil
(Tll+INi)
0.0" TI
Ni
ooi
0.0[ Ni
Pb
Ni
Bi
I
a Ni
work; if more numbers are indicated, the diagram has been reproduced from the underlined reference. (a) nickel and elements with less than three p electrons per atom and (b) nickel and elements with more than two p electrons per atom.
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
310
Table Ni-II Comp arison of experimental and calculated values for the heat of formation, A H for, of nickel compounds. Published experimental A,~ for values for the entropy of formation, ~ A.~for exp, have been added. The units for A H f°r and - - e x p are kJ (mole of atoms) - l and J (K mole of atoms) - l , respectively. System
Compound
A ~ -m- for exp
At-/'for Lx~~ calc
Ni-Ti
NiTi 2
- 27 298 K - 29 1202 K 28 298 K
- 40
- 34 298 K 34 298K - 32 (AG) 1300 K - 37 (AG) 1320 K 34 1450-1475 K 33 298 K
- 52
- 35 298 K - 54 1100-1300 K - 44 (AG) 1300 K - 41 (AG) 1320 K 43 1513 K 35 298 K
- 37
- 2 1 (AG) 1320 K
- 17
A.~ for ~ exp
-
NiTi
-
Remarks
1
calorim.
3,4
assessm.
117-19
calorim.
1
calorim.
118 28
emf 1150-1350 K calorim.
-
- 12 1100-1300 K
6 3-5
assessm.
117-19
calorim.
1
e mf
7
e mf
28
emf 1150-1350 K calorim.
-
6 3,4
assessm.
-
Ref.
calorim.
e mf
-
Ni3Ti
Method
117,19
Ni-V
NiV 3
Ni-Cr
Ni20Cr80
+ 8.0 1100-1500 K
- 5
+ 8.1 1100-1500 K
assessm,
boe sol. soln
8
Nis0Cr50
+ 6.4 1550 K
- 10
+ 9.3 1550 K
assessm,
foe sol. soln
1
Ni60Cr40
+ 3.6 1073-1448 K + 3.6 1100-1500 K +5 1123-1273 K
- 9
assessm,
foe sol. soln
11
assessm,
foe sol. soin
8
e mf
foe sol. soln
107
+ 0.6 1523 K +8 1123-1273 K
- 6
calorim,
foe sol. soln
17
emf
foe sol. soln
107
- 14 1050 K 14 1023 K 11 (AG ra) 1050 K
- 12
assessm,
sol. soln
1
emf 950-1150 K emf 950-1348 K
sol. soln
12
sol. soln
98
Ni7sCr25
Ni-Mn
NisoMnso
-
-
emf 1150-1350 K
+ 8.2 1100-1500 K +9 1123-1273 K
+9 1123-1273 K + 3.7 1050 K +4 1023 K
6
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table N M I
(continued)
System
Compound
Ni-Fe
NisoFeso
AH~,
AH~[ c
- 3.9 1200 K -3.7 ~-1200 K -4.6 1223-1373 K -2.4 1273 K
- 2
^.~ _ _ ~for p
+5.0 ~-1200 K
+ 6.3 1273 K
- 1.3
1273 K -5 1473 K -3.2 1523 K - 5.4 1550-1700 K
xs) 1573 K -5 ~-1370 K -3.6 T unknown
- 2.5 ( A G
Ni-Co
Nis0Cos0
+ 0.0 1400 K
+5.1 0
+0.6 1600 K
+6.5 1600 K
+0.9
Method
Remarks
calorim. +
sol. soln
1
assessm. assessm.
sol. soin
15
e mf
sol. s o l n
e mf 1173-1373 K e mf 1023-1423 K yap. press.
sol. soln
13
sol. soln;
2O
see also[21,22] sol. soln
16
calorim.
sol. soln
17
yap. press.
sol. soln
10
equilibr.
sol. soln
9
calorim.
2
assessm.
sol. soln; from A H mix sol. soln
calorim.
sol. soln
vap. press. 1480-1720 K calorim.
sol. soln; see also [ 24 ] sol. soln; from A H mix
~- 1780 K Ni-Y
311
NiY3
- 33 887-1224 K -19 298 K
- 23
- 35 887-1224 K -30 298 K
- 37
-35 887-1224 K -37 298 K
-44
- 31 887-1224 K -39 298 K
- 45
-29 88%1224 K -37 298 K
- 37
- 28 887-1224 K -35 298 K
- 34
Ni4Y
- 25 887-1224 K
- 30
NisY
- 34 298 K
- 26
Ni2Y 3
NiY
Ni2Y
Ni3Y
NiTY2
- 8.6 887-1224 K
emf calorim.
- 6.8 887-1224 K
e mf calorim.
-5.1 887-1224 K
e mf calortm.
- 2.5 887-1224 K
e mf calorim.
- 1.7 887-1224 K
e mf calorim.
- 1.6 887-1224 K
e mf calorim.
- 1.6 887-1224 K
e mf calortm.
Ref.
106
14
1
23 25
100 112-13 100 112-13 100 112-13 100 112-13 100 112-13 100 112-13 100 102-04
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
312 Table Ni-II System
(continued) Compound
A f°r ~ -/-- / exp
AH~[ c
31 298 K -21 887-1224 K
NilTY 2
Ni-Zr
- 16
- 37 298 K - 37 1230 K
- 53
- 49 298 K - 72 1300 K - 52 1405 K
- 72
Nil0Zr7
- 52 298 K
- 73
Ni2Zr
- 70 1300 K
- 68
Ni3Zr
- 67 1300 K
- 55
NiTZr 2
- 46 298 K
- 50
NiZr
Method
Remarks
calorim.
- 13 887-1224 K 19 298 K
NiZr 2
A.K' r°r ~ exp
Ref. 112-13
- !.5 887-1224 K
emf
100
-0.9 887-1224 K
emf
100
calorim.
112-13
calorim.
29
calorim,
+ 1.7 1300 K
see a l s o [ 115 ]
4,27
calorim.
29
emf
30
calorim,
see also [ 115 ]
4,27
calorim.
29
- 0.3 1300 K
emf
30
- 8.4 1300 K
emf
30
calorim.
29
calorim,
- 4 0
see a l s o [ 115 ]
4,27
1670 K NisZr
- 35 298 K - 48 1300 K
- 38 - 6.0 1300 K
calorim.
29
emf
30
calorim,
- 3 2
see a l s o [ 115 ]
4,27
1479 K Ni-Nb
NiNb
- 23 298 K - 35 (AG) 1220 K -42 1250 K
- 45
- 32 298 K 40 (AG) 1220 K -39 1250 K 24 1273 K
- 32
- 1.0 973 K 2.7 1073-1183 K -2.8 1193-1348 K + 8.2 1323 K
- I1
Ni3Nb -
Ni-Mo
NiMo
calorim.
- 5.2 1250 K
emf 1050-1370 K emf
1 32 51 a/o N i
caiorim.
+ 1.7 1250 K + 0.5 1273 K
+ 1.3 1073-1183 K + 1.0 1193-1348 K + 9.0 1323 K
31 1
emf 1050-1370 K emf 1273-1373 K emf 1050-1370 K
32 31,33 34
calorim.
48 a/o N i
35
emf
54 a/o N i
38
emf
54 a/o N i
38
emf 1223-1373 K
37
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-II System
313
(continued) Compound
A/-/ f°r - - - exp
AH~[ c
A,~ 'f°r ~ exp
+0.2 1473 K +0.8 1573 K - l.l
Method
Remarks
Ref.
calorim.
49 a/o Ni
36
calorim.
48 a/o Ni
35
assessm.
48 a/o Ni
114
298 K Ni3Mo
Ni4Mo
- 2.6 1073-1183 K + 8.0 1323 K
- 8
- 0.6 I073-I133 K + 7.3 1323 K 3.7 298 K
- 7
+ 1.1 1100 K + 3.9 1400 K + 1.9 unknown
- 1
+ 1.2 1073-1183 K + 9.6 1323 K
emf
38
emf 1223-1373 K
37
+ 2.9 1073-1133 K + 9.2 1323 K
emf
38
emf 1223-1373 K assessm.
37
-
Ni-Rh
NisoRhs0
T
+ 8.3 1100 K + 8.4 1400 K
emf 920-1370 K emf 870-1530 K calorim,
assessm,
Ni-Pd
Nis0Pds0
-0.5 1273 K
0
Ni-La
NiLa 3
- 13 298 K
- 19
calorim.
NiLa
- 15 298 K 28 298 K - 25 298 K
- 38
calorim.
Ni t.4La
- 29 298 K
- 40
Ni2La
- 20 298 K 30 298 K -23 1095 K
- 39
- 21 298 K - 28 298 K -26 1080 K
- 33
- 26 298 K -24 1035 K
- 30
- 21 298 K - 21, - 22 298 K - 26, - 27 298 K
- 24
+ 0.0 298
-
Ni7La 2
NisLa
sol. soln
39
sol. soln
41
sol. soln
40
sol. soln
I
42 52 a/o Ni
43
estimate
44
calorim.
42
e mf 805-950 K
44
caiorim.
45
e mf 947-1068 K calorim,
44
K
+ 0.3 298 K
- 0.8 298 K
-
Ni3La
+ 7.6 1273 K
114
- 0.6 298 K
+ 0.0 298 K
da t a for La N i 5 used from [ 43 ]
109
calorim.
43
emf 1124-1193 K calorim,
44
e mf 1023-1134 K calorim,
da t a for La N i 5 used from [ 43 ]
109 44
da t a for L a N i 5 used from [ 43 ]
109
calorim.
43
calorim.
46,93
calorim.
103-05
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
314 Table Ni-II System
(continued) Compound
A / / f °e xrp
~-"
AH~c
- 28 298 K - 24 298 K - 26 298 K - 27 298 K Ni-Hf
Ni-Ta
+ 0.7 298 K
Method
Remarks
Ref.
calorim.
19
emf 1104-1194 K calorim.
44
+ 0.6 298 K
calorim.
42 AS from C_ f r o m [ 95 ] e
26
NiHf 2
- 47 298 K
- 46
0.0 298 K
assessm.
116
NiHf
- 65 298 K
- 63
0.0 298 K
assessm.
116
Nil0Hf7
- 63 298 K
- 63
0.0 298 K
assessm.
116
NisHf2
- 57 298 K
- 54
0.0 298 K
assessm.
116
N i T H f2
- 52 298 K
-44
0.0 298 K
assessm.
116
NisHf
-42 298 K
- 33
0.0 298 K
assessm.
116
Ni2Ta
- 39 1173-1323 K 20 1240-1320 K - 36 1700 K
- 39
+ 1.0 1173-1323 K + 9.9 1240-1320 K
- 29 i 173-1323 K -20 1220-1320 K
- 31
-
Ni3Ta
Ni-W
A'K' f°r
emf emf
47 see also [ 85 ]
48
calorim.
97
+ 3. i 1173-1323 K +6.4 1220-1320 K
emf
47
emf
see also [ 85 ]
48
NiW
- 1.0 T unknown
- 5
+ 1.2 T unknown
assessm.
99
Ni4W
- 6.2 298 K 2.5 T unknown
- 2
+ 0.3 298 K + 1.1 T unknown
emf 1073-1273 K assessm.
49
-
99
Ni-Pt
Nis0Pt5o
- 9.3 298 K
- 7
+ 5.4 1625 K
assessm,
Ni-Th
Ni3Th 7
- 28 973 K
- 35
- 1.4 973 K
emf 841-1141 K
50
NiTh
- 45 973 K
- 56
- 2.4 973 K
emf 841-1141 K
50
Ni2Th
- 45 973 K
- 58
- 3.2 973 K
emf 841-1141 K
50
NisTh
- 43 973 K
- 35
- 7.1 973 K
emf 841-1141 K
50
NilTTh2
- 25 973 K
- 22
- 1.8 973 K
emf 841-1141 K
50
NiU 6
-21 1000 K
- 14
- 10 1000 K
emf 1073-1173 K
51
NiTU 5
- 55 1000 K
- 43
- 23 1000 K
emf 1073-1173 K
51
Ni-U
sol. soln
1
A.K. Niessen et aL / Enthalpies of formation of Ni alloys Table Ni-II
System
(continued)
Compound
AHfor - - - exp
Ni2U
- 54 1000 K - 32 1023 K
- 40
Ni77U23 6-phase
- 54 1000 K
- 30
NiTaU22 8-phase
- 53 1000 K
NisU
AH~[ c
51
- 29
- 19 1000 K
emf 1073-1173 K
51
-46 1000 K -44 1000 K - 30 1023 K
-22
- 16 1000 K - 16 1000 K
emf 1073-1173 K emf 1073-1173 K
-12
52
82 a/o Ni
+ 1.8 973 K + 2.0 1273 K + 2.4 1173-1373 K +2.3 1350 K
+5
+ 7.6 1150 K +8 293 K
+ 11
- 2 9 (AG) 1100 K - 26 298 K
-5
- 4 1 (AG)
-9
-1.2 951-1097 K + 4.7 973 K +4.8 1273 K
+ 8.6 1150 K
51 51
calorim.
NisoCuso
NiB¢
Ref.
emf 1073-1173 K
Ni-Cu
Ni5B¢21
Remarks
- 19 1000 K
-8.8 951-1097 K
Ni-B¢
- 19 1000 K
Method
51
NitTPU 2
NisoAUs0
A.~ for ~ exp
emf 1073-1173 K calorim.
Ni-Pu
Ni-Au
315
52
emf
ref. st. < P u >
53
assessm,
sol. soln; see also [ 89 ] sol. soln
1
emf 1173-1373 K emf
37
sol. soln
106
yap. press,
sol. soln
108
assessm,
sol. soln
1
caiorim,
sol. soln
54
assessm.
20 a/o Ni
1
calorim.
55
assessm.
1
calorim.
55
calorim.
1
1100 K
- 42 298 K Ni-Mg
NiMg 2
Ni2M8
Ni-Ca
- 13 298 K - 13 923-1033 K
- 6
- 18 298 K - 21 923-1033 K
- 8
+ 0.4 923-1033 K
vap. press,
ref. st. < Mg >
calorim.
56 1
- 4.2 923-1033 K
yap.press,
ref. st. < Mg >
56
Ni2Ca
-19 900-1150 K
-11
-9.7 900-1150 K
emf
ref. st. < C a >
94
Ni3Ca
- 16 1050-1350 K
-9
-7.1 1050-1350 K
emf
ref. st. < C a >
94
NiTCa 2
- 14 1050-1350 K
--8
--6.0 1050-1350 K
emf
ref. st. < C a >
94
NisCa
- 10 1050-1350 K
-6
-3.7 1050-1350 K
emf
ref. st. < C a >
94
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
316 Table Ni-II
(continued)
System
Compound
A ~ -H- for
Ni-Zn
NiZn 8
- 6.4 355 K 12 (AG) 623 K
- 7
- 15 355 K 18 (AG) 623 K - 18 753 K
- 11
e x p
-
NisZn21 v-phase -
-
2
AH~c
-
NiZn 3 yl-phase -
~
e x p
-3.5 973 K
- 14
- 19 355 K 22 (AG) 623 K - 22 753 K 27 773 K 20 905 K - 27 973 K
- 23
- 16 1100 K (AG) 1100 K - 18 1100 K 18 (AG) 1113 K
- 23
-2.5 753 K
-
-
-
NiZn //-phase -
-
1
9
ref. st. < Z n >
emf 973-1153 K assessm.
59 58
20 a/o Ni; ref. st. < Z n > ref. st. < Z n >
59
f r o m [ 58 ]; ref. st. < Z n > ref. st. < Z n >
90
25 a/o N i
57
61 1
vap. press, 993-1113 K
ref. st. {Zn}
60
calorim.
26 a/o N i
58
vap. press, 623-873 K emf 693-873 K vap. press,
ref. st. < Z n >
59
23 a/o Ni; ref. st. < Z n > f r o m [ 58 ]; 26 a/o Ni; ref. st. < Z n >
57
calorim.
- 2.8 753 K
-
vap. press. 623-873 K emf 693-873 K yap. press,
Ref.
58
calorim.
1
- 16 355 K 20 (AG) 623 K 19 753 K 22 773 K
Remarks
calorim.
-3.4 753 K
-
NiZn f/t-phase
Method
vap. press, 623-873 K
773 K -18 973 K 15 (AG) I100K 15 (AG) 1113 K
-
A.~ for
yap. press, 623-873 K emf 693-873 K vap. press,
90
58 ref. st. < Z n >
59
ref. st. < Z n >
57
f r o m [ 58 ]; ref. st. < Z n > ref. st. < Z n >
90
+ 0.2 905 K - 6.9 973 K
vap. press,
62
emf 973-1153 K
ref. st. < Z n >
61
+ 2.1 1100 K
vap. press, 1054-1150 K assessm,
ref. st. < Z n >
62
ref. st. < Z n >
1
calorim,
ref. st. < Z n >
63
vap. press, 971-1113 K
ref. st. {Zn}
60
Ni69Zn31
- 6.2 (AG xs) 1067 K
- 19
vap. press,
sol. soln; ref. st. < Z n >
Ni75Zn25
- 8.5 355 K 14 773 K
- 15
calorim,
sol. soln
58
yap. press,
f r o m [ 58 ]; sol. soln; ref. st. < Z n > ref. st. < Z n >
90
-
-
- 8.5 II00K 12 (AG) 1200 K
calorim, - 15
vap. press,
sol. soln; ref. st. {Zn}
110
63 91
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table N i - I I
(continued)
System
Compound
A for - - -I-4 exp
AH~[ c
Ni-Hg
NiHg 4
- 9.1 298 K -8.7
+ 1
443-505 K
N i - B
A.g' for ~ exp
- 15 298 K - 13
Method
Remarks
Ref.
emf 293-503 K y a p . press,
ref. st. < H g >
64
ref. st. < H g >
65
443-505 K
NiHg 3
- 7.2 298 K
+ 1
- 11 298 K
emf 293-503 K
ref. st. < H g >
64
NiHg 2
-7.2 298 K
+ 1
- 13 298 K
emf 293-503 K
ref. st. < H g >
64
NiB
- 50 298 K
- 33
calorim.
A H selected in [ 117]; see a l s o [ 119 ]
66
- 20 1385 K 23 298 K Ni4B 3
Ni2B
Ni3B
Ni-AI
317
NiAI 3
- 45 298 K
NiAI
Ni3AI
- 32
67
assessm.
88
26 298 K
- 4.2
assessm,
A H selected in [ 117]; see a l s o [ 119 ] monoclinic
- 26 298 K
- 3.9
assessm,
orthorhombic
- 23 1385 K 21 298 K
- 27
- 22 298 K
- 21
- 38 298 K 38 298 K - 56 980 K - 33 (AG)
- 28
1127
Ni2A13
- 3.7
calorim.
calorim.
66
88
88
calorim.
67
+ 0.2
assessm.
88
- 1.9
assessm.
88
assessm.
I
assessm.
117-19
+ 8.2 980 K
emf 933-1030 K emf
29 % Ni; ref. st. < A I >
69 68
K
- 57 298 K 57 298 K -70 298 K
- 43
- 59 298 K 59 298 K -67 980 K - 63 298 K -67 II00K - 71 1023 K
- 48
-41 298 K
-33
+4.3
+ 1.4 980 K
assessm.
1
assessm.
117-19
emf
39 % N i
69
assessm.
1
assessm.
117-19
emf 933-1030 K not given
51 a/o Ni; ref. st. < AI >
calorim,
ref. st. < A I >
70
calorim. assessm.
69
71,72 52
73 a/o N i
1
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
318 Table Ni-II System
(continued) Compound
A t- 4" f eox p r
AH~r~[c
A,q efor xp ~
38 298 K - 3 5
+ 0.5 980 K
Ref. 117-19
assessm.
77 a/o Ni
emf 633-1030 K
ref. st. < AI >
1 69
Ni3Ga7
- 34 300 K
- 25
calorim.
39,73
Ni2Ga 3
- 45 300 K
- 33
calorim.
39,73
NiGa
- 38 300 K 47 298 K - 43 1023 K - 43 1223 K
- 37
calorim.
39,73
calorim.
74
- 36 300 K 45 298 K
- 37
- 23 300 K 28 298 K - 33 1223 K
- 27
Ni3In 7
-21 673 K
Ni21n 3
Ni3Ga2
Ni3Ga
Ni-In
Remarks
assessm.
298 K - 47 980 K Ni-Ga
Method
Niln
Nil3In 9
Ni2In
e-phase Ni3In
- 2.9 1223 K
caiorim,
ref. st. < G a >
92
emf 1073-1273 K
ref. st. < G a >
75
calorim.
39,73
calorim.
74
calorim.
39,73
calorim.
74
- 5.2 1223 K
emf 1073-1273 K
ref. st. < G a >
75
-8
- 10 673 K
emf 633-943 K
ref. st. < I n >
76
-25 673 K - 23 850 K - 26 1060 K
- 10
- 10 673 K - 7.6 850 K
emf 633-943 K emf 633-943 K calorim,
ref. st. < I n >
76
ref. st. < I n >
76
ref. st. < I n >
77
-25 673 K - 22 850 K - 25 1060 K
- 12
emf 633-943 K emf 633-943 K calorirn,
ref. st. < I n >
76
ref. st. < In >
76
ref. st. < In >
77
- 17 850 K - 20 1060 K
- 13
emf 633-943 K calorim,
ref. st. < In >
76
ref. st. < In >
77
- 17 760 K 12 800 K 18 1060 K
- 12
ref. st. < I n >
78
see also [ 79 ]
1
calorim,
h i g h - T phase; ref. st. < I n >
77
- 13 673 K - 14 760 K
- 10
emf 633-943 K emf 663-873 K
ref. st. < I n >
76
ref. st. < I n >
78
- 10 673 K - 6.7 850 K
- 2.7 850 K
-4.9 760 K +0.9 800 K
- 12 - 3.8 673 K -4.2 760 K
emf 663-873 K assessm,
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-II System
(continued) Compound
f°r -A- f'/" - exp
AH~c
- 8.4 800 K - 13 850 K - 16 1060K Ni-C
Ni3C
A.q' f°r ~ exp + 2.2 800 K - 3.6 850 K
+ 8.5 298-1000 K
+7
+ 1.8 298-1000 K
+ 9.4 298 K
Ni-Si
Remarks
assessm,
see also [ 79 ]
1
emf 633-943 K calorim,
ref. st. < In >
76
ref. st. < I n >
77
assessm.
Ref.
87 117
NiSi 2
-31 298 K
-17
-0.7 298 K
a$~sm.
see also [ 2 ]; assessed AH selected in [ 117]; see also [ 119]
80
NiSi
-45 298 K
-33
-2.1 298 K
a$~sm.
see also [ 2 ]; assessed AH selected in [ 117]; see also [ 119 ]
80
calorim.
101
- 46 298 K
- 35
a&sessm.
see also [ 2,119 ]
80
- 48 298 K < - 36 (AG) 1273-2073 K
- 32
asse$sm.
see also [ 119]
80
Ni5Si 2
- 42 298 K
Ni3Si
Ni3Si 2 Ni2Si
equifibr. + phase d i a g r .
96
- 29
as~sln.
80
- 36 298 K
- 26
a$~sm.
31 (AG) 1273-2073 K
- 18
equifibr. + phase diagr.
NiGe
- 32 330 K
- 20
calorim.
Ni2G¢ 8"-phase
- 27 1060 K -29 1060 K -30 330 K -37 298 K -30 1060 K
- 21
calorim.
-21
calorim.
-21
calorim.
- 25 330 K -31 1060 K
- 17
- 25 1060 K -34 1023 K -34 298 K
-
Ni5Si
e'-phase e-phase
Ni3Ge
Ni-Sn
Method
assessm.
-42 298 K
Ni-Ge
319
Ni3Sn4
< -
calorim. calortm.
20
77 a/o Ni
80 96
39,73 high-T phase; 58 a/o Ni high-T phase; 61 a/o Ni high-T phase; 64 a/o Ni AH selected in[ll7] high-T phase; 64 a/o Ni
81 81 39,73 82 81
calonm.
76 a/o Ni
39,73
calorim.
76 a/o Ni
81
calorim.
ref. st. < S n >
81
calorim. ~$m.
52 117-19
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
320 Table Ni-II System
(continued) Compound
f°r -A- /-4 ,xp
Ni3Sn 2
-31 293K -39 298K -32 1060K -39 1023K
- 24
-23 293K -26 1060K -26 298K
-19
Ni3Sn
AH~[ c
A.~' f°r ~ exp
Method
Remarks
1
caionm. caiorim. calonm.
Ref.
A H selected in [ 117,119] ref. st. < Sn >
82 81
calorlm.
52
caionm.
1
caiorim.
ref. st. < Sn >
81 117-19
assessm.
Ni3N
+0.2 292K
+6
calorim,
Ni-P
NiP 3
-41 298K 39 298K
- 28
assessm.
117
assessm.
119
-48 298K -43 298K
- 42
assessm.
117
assessm.
119
-57 298K 51 298K
- 62
assessm.
117
assessm.
119
62 298K 55 298K
- 56
assessm.
117
assessm.
119
-62 298K -56 298K
- 50
assessm.
117
assessm.
119
55 298K -67 298K
- 45
assessm.
117
assessm.
119
36 298K
- 47
-
NiP 2
Ni6P 5
-
Ni2P
-
-
NisP 2
Ni3P
Ni-As
NiAs
-
-
A H selected in [ 117 ]; see also [ i 19 ]
calorim.
34 298K -
Ni-Sb
calorim.
ref. st. (NE)
83
Ni-N
84
NiSb 2
-26 298K
- 14
calorim.
32 a/o N i
NiSb
-42 298K
- 20
calorim.
A H selected in [ 117]; see also [ 119 ]
- 3 2
298K -33 1060K
calorim. calorim,
82
1
82
1
see also [ 111 ]
86
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-II System
Ni-Bi
321
(continued) Compound
AH~,
Ni3Sb
- 18 298 K - 18 1060K
- 18
- 3.9 298 K
- 4
NiBi
AH~[ c
^.~ exp for - - - -
Method
Remarks
calorim.
77 a/o Ni
calorim.
alloys. For the liquid alloys the two limiting enthalpies of solution are shown together with the heat of mixing of a regular mixture at equiatomic concentration. The reference states are those of the pure solid metals for the solid compounds while for the liquid alloys reference is made to the pure liquid metals. In these tables the information on each of the phase diagrams shown in figs. 1 and 2 is summarized characteristically by one of the following symbols: - - three or more compounds stable at low temperatures (indicating that AH f°r is large and negative); one or two compounds stable at low temperatures (indicating that AH f°r is negative); c - continous solid solubility at high temperatures and one or more ordered alloys at low temperatures (indicating that AH ~or is negative but closer to zero than in the foregoing cases); c continous solubility at all temperatures or a large solid solubility at low temperatures for at least one of the constituents if the crystal structure is different for the two constituent metals (indicating that AH f°r is approximately zero); c+ continous solubility at high temperatures and a miscibility gap at low temperatures (indicating that AH f°r is small, but positive); + no compounds and both solubilities smaller than 10 "/o (indicating that AH f°~ is posifive); ? the available information is contradictory. In a few cases it has been impossible to distinguish clearly one of these characteristics; the most probable one is then placed between brackets. This
calorim.
Ref. 1 86
AH selected in [ 117]; see also [ 119 ]
82
applies particularly to the simple quotations:>, which have been denoted by (+) since these quotations may indicate that no compounds exist in such binary systems. Although these symbols correlate with the sign of the enthalpy of formation, a numerical value of this enthalpy cannot be assigned to them.
2.
Nickel alloys
Table Ni-Ia and table Ni-Ib make it possible to compare in a qualitative way the predicted values for the enthalpy effects in solid and liquid alloys Table 1 Qualitative comparison o f AH ~[c at equiatomic composition in kJ (mole o f atoms) - l with phase-diagram information System
AH ~ c
Phase-diagram information
Ni-Sc Ni-Cd Ni-Ir Ni-Sr Ni-Ba Ni-Tc Ni-Ru Ni-Li Ni-Os Ni-Pb Ni-Re Ni-TI Ni-Ag Ni-Na Ni-K Ni-Rb Ni-Cs
- 57 - 8 - 2 - 1 0 + 1 +1 + 1 +2 +2 +3 +4 + 18 +46 + 59 + 59 + 59
five compounds two compounds solid solubility one compound no compounds; liquid immiscibility solid solubility solid solubility o f Ni and Ru no compounds; liquid immiscibility solid solubility no compounds; liquid immiscibility solid solubility no compounds; liquid immiscibility no compounds, liquid immiscibility very slight solubility in {Na} very slight solubility in {K} no information no information
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
322
Table Ni-III Comparison o f experimental and calculated values for the enthalpy of alloying o f liquid nickel alloys: the heats of solution AH°{Ni}, AHO{M} and the heat o f mixing A H e M ~. The reference states are those o f {Ni} and {M}; the heat o f fusion, AH fuse, used in a required conversion o f the reference state is g~ven. The unit o f all enthalpy values shown is kJ (mole o f atoms) - t . X
A/~°{Ni}
Sc
- 130
AHeM } - 39
AH°{M}
Method
- 180 147
prediction calorim. (1873 K)
-
Ti
- 126
-35
- 154 -207 183 - 184 ( - 190) - 188 -
( - 105) - 113
-44 -38 -38
- 1 4 8
V
Cr
-69
- 18
- 27
- 7 -4.3
- 33 (-31) (-36)
-
32
- 35 -36 -64 -6
Fe
(-18) 10 -
(-8.6) (-6.3)
- 8 - 11 -2.6 - 6.0
-
10
-
23
- 18 --2 -4.2 -2.1 -7.5 -4.2 +3.9 -5.8 -4.2 -5.2
assessm. (1823-1973 K)
- 134,- 180
assessm. (1873 K)
-75 - 107 -70,-95 (-73)
lm~lletioa calorim. (1873 K) assessm. 0873 K) assessm. (1873 K)
- 27 - 14 -37 (-9.2) 14 +0.2 (-2.3) ( - 15) - 7 . 9 , - 11
prediction calorim. (1873 K) calorim. (1950 K) yap. press. (1873 K) yap. press. (1873 K) vap. press. (1873 K) emf (1873 K) assessm. (1823-1873 K) assessm. (1873 K)
-
Mn
~edietion calorim. (1786-1803 K) calorim. (1873 K) calorim. (2000 K) yap. press. (1748-1973 K) assessm. (1100-2000 K)
- 33 (-49) (-23) <0
-
49
- 53 -47 -77 0 -6 (-21) (-41) -34 (-20) (-21) (-21)
prediction calorim. (1773 K) yap. press. (1310-1900 K) emf ( 1573 K)
emf (1683 K) equilibr. ( 1743-1893 K) equilibr. 0843 K) equilibr. (1893 K) assessm. (1200-1800 K) assessm. (1873 K) prediction calorim. (1773 K) calorim. (1803 K) calorim. (1813-1853 K) calorim. (1839 K) calorim. (1873 K) calorim. (1873 K) calorim. (1873 K) calorim. (1873 K)
Remarks
Ref.
168 A H ~ se : 15 A H ~ : 15 AH mix at 55 a/o Ni values at 1873 K A H ~ : 17.6; A H ~ : 16.2 AGo xs at 1873 K; AH~f~ : 15
189 3 4 5 178-79 184 6
AH(/se : 21 A~-o xs A H ~ r : 17 A H ~ r : 17 A~o xs AGo xs; AH~er : 17 A~-O xs A~o xs at 1873 K see also [ 12,176]
values at 1750 K AG xs; value at 50 % N i derived from AG ~fvln} AG xs A~'o xs A~-o,~
46 a/o Ni, 5 a/o C
3 6 184 3 8 7 10 131 11 184 6 9 142 13
133 132 132 132 156 6,184 136 30 14 16 15 17 18 136
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-III
X
(continued)
A/~°{Ni} +9.1
-6.9 - 10 (-76) ( - 10) -30
-6.5 -1.1 -6.5 -5.4
-4 -5.6
( - 30) - 18 ( - 10)
AH ~ v l }
AH°{M}
-6.4
-5 -3.0 -4.6 -33 -4.4 - 10 -2.8
-16 -32 (-140) (-23) -45 - 14 -14 - 11 -24 -24
-2.2 -2 -2.7 -9.5 -5.6 -4.9
-46 (-20) - 16
7.5
- 2.8
-6.5, - 8.8 (-9.5) -6.5 -6.5
-5.1 -2.7
16, - 2 2 (-27) -14
- !3
- 5.0
- 25
- 10
- 5.0
-
-
Co
- 16 -
0
0
-1
0
( + 1.2)
+ 0.4
25 0 -I
( + 1.2)
+0.3 ( + 1.3)
+0.4
-~0 +2.4 - 12 (+8.4) +3.3
"0 +0.6 -4.6 -0.4
(+
1.7)
~-0 +2.4 - 13 (-0)
+0.8
+3.3
-12 -9.9 Y Zr
Method
Remarks
yap. press. (1630-1870 K)
values at 1833 K; AG xs; value at 5__0a/o Ni derived from AG ~qi} value at 1873 K AG xs at 1873 K values at 1873 K
yap. yap. yap. yap. yap. yap. yap. yap. yap. yap. yap. vap. yap. yap. X-ray
press. (1750-1900 K) press. (1750-1900 K) press. (1773-1923 K) press. (1783-1873 K) press. (1800-1950. K) press. (1820-1950 K) press. (1825-1895 K) press. (1825-1930 K) press. (1873 K) press. (1873 K) press. (1873 K) press. (1873 K) press. (2174-2500 K) press. (2178-2558 K) (1833
assessm. (1873 assessm. (1873 assessm. (1873 assessm. (1873 assessm.
K) K) K) K)
calorhn. (1780 K) calorim. (1813 K) yap. press. (1480-1875 K) yap. press. (1773-1873 K) yap. press. (1873 K) yap. press. (1873 K) yap. press. (2174-2500 K) assessm. (1600-1900 K) assessm. (1873 K) assessm. (1873 K)
- 162
la~iaioa calorim. (1923 K)
- 165
-49
-237 - 202 -166
calorim. (1873 K) assessm. (1823-1973 K)
136
- 134
AG xs values at 2326 K
AG-°'s at 1873 K AG xs; see also [ 27,31,32 ] see also [ 163 ]
Ago xs
165
23 23 25 28 174 22 26 29 10 21 24 164 20 19 36 184 I 6 12 33 34 35 135 134
la~etim
(-48)
-
AG xs
assessm.
-11
- 30
values at 1873 K values at 1873 K AG xs at 1873 K value at 1873 K
assessm.
- 31
- 107
Ref.
K)
assessm. (1783-1973 K) assessm. (1873 K)
-97 ( - 17)
- 162,-220 Nb
323
values at 1800 K ; see also [40]
AGXS AH- / ~~ : 17.6; M 16.2
A~OXS
170 21 164 41 177-79 184 188
42 6 H f ~~ : 16.9 A~'o xs at 1873 K; AHf~ e : 16.9
assessm. (1873 K)
p~llceee calorim. (1873 K)
38 37 39
AH~:
26
3 184
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
324 Table Ni-III X
(continued) AH°{Ni} -
Mo
- 27
Pd
La
Hf
54
W
Pt
U
-26
AH°{M}
Method
Remarks
- 155
assessm. (1400-2800 K)
AH~ AH~
- 7
- 18
-4.4
0 +4.9 >0 (+4) +4.7 +5.0
0 +2.3 >0 +2.0 + 1.2 +2.3
- 32 -39
prediction solub. (1737-1973 K)
- 18
assessm. (1500-2800 K)
0 +5.3 >0 (+5) + 12 +5.0 + 8 . 1 , + 11
: 17.6; 22.9
178-80
A~-o xs at 1873 K; A H ~ o : 24.3 A H [ ~ : 17.6; AHk~oo 24.3
187 178-80
prediction calorim. (1873 K) vap. press. (1400-1873 K) e m f (1833-1973 K) assessm. (1873 K) assessm. (1873 K) asseasm. (1873 K)
see also [ i 84 ]
45 6
47
43 46
AG xs
44 1
-27 - 28
-146 - 172
prediction calorim. (1376 K)
AH~:
- 145
-42
- 58
- 204 -214 -216 - 293
wmlietion calorim. (1873 K) assessm. (1873 K) assessm.
A H ~ : 24 A H ~ : 26 AG xs
3 6 i 43
-29
-
133 -150 - 149
lmNlietion calorim. (1873 K) assessm. (1873 K)
A H ~ a : 32 A H ~ a : 31
3 6
-
105
-11
-3
-14 - 62
l~rt~lietion equilibr. 0873-1973 K) assessm. (1600-3700 K)
+40
+ 1.0
- 32
+ 16
-2.4
(+38) - 35
- 17 + 5.6
- 5 + 1.4 - 14
- 98
- 29
- 22 + 5.6
-
140
-44 Cu
Ref.
-81 - 54
- 167 Ta
AHeM }
+ 14 -2.5 + 5.4 + 11
+4
( + 1.6) ( + 15) + 17 (+5)
+ 2.8 -i.6 +4.3 +4.3 +2.3
+ 12
+ 3.0
- 3.5
- 2.9
+ 14
+ 11 + 17 + 17 (+8) + 12
assessm. (1873 K) assessm. (3000 K)
15.1
A~-o xs at 1873 K; A H ~ : 35 A H ~ : 17.6; A/-/~ 30.5 A ~ - o xs
AGXS; A H ( ~ :
178-80 184
46
prediction vap. press. (1733-2223 K) yap. press. (1877-1893 K)
values at 2073 K AG xs at 1877 K
prediction calorim. (1423 K)
AH~iSc~ : 17
prediefloa calorim. (1373 K) calorim. (1385 K) calorim. (1473 K) calorim. (1580 K) calorim. (1728 K) calorim. (1733-1763 K) calorim. (1748 K) calorim. (1753 K) yap. press. (1800-1873 K) ¢mf (1373-1673 K)
48
A H { ~ : 16.9 A H ~ : 15.1 A H ~ , ~ : 17.6
AG xs AG xs at 1673 K; A H { , ~ : 17.5
176
49 137
50
64 54,144 52,53 123 15 14 37 51 56 60
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-III X
(continued) A/7°{Ni}
AH~M}
AH°IM}
( - 67)
Ag
+0.9 +9.8 + 9.8
+ 1.4
( + 13) + 9.9
+3.5 + 2.9
+ 56 +75 + 100
+ 3.0
+ 15
+ 10 + 12 + 12 + 12, + 16 ( + 15) + 13 + 68
>0 Au
K Be
emf (1393-1523 K)
value at 1523 K; AH~e~ : 17
assessm. assessm. assessm. assessm. assessm. assessm. assessm.
(1200-1800 K) (1473 K) (1823 K) (1823 K) (1873 K)
la'ediefion solub. (1268-1638 K) solub. phase diagr,
+ 33
( + 14)
+2.9
(+8)
vap. press. (1600-1820 K)
(+2.1) ( + 12) ( + 14) + 15 ( - 7.1) (+8.0)
+0.8 + 3.6 +2.8 + 2.3 - 3.0 +2.2
(+3.8) ( + 10) ( + 14)
+3 +47 +40 + 100 +71 + 16
+1
+3
+ 100 - 11 -8.0 + 18 +6.1 +3.4 +0 + 13
+32
+ 123 +42
+ 45
-19
-4
+ 140
+ 235 -15
-74 Mg
Remarks
+7 +2.2 (+3.5) +2.2
>0 Na
Method
+ 25 (+8.0) + 12 ( + 18)
+7.0 Li
325
-13 -56
-4
-16
pcedietioa calorim. (1369 K) calorim. (1378 K) calorim. (1383 K)
Ref.
see also [ 32,58,59 ] AG xs; see also [ 32,57 ] A~o xs
AH~t~e~ : 17.6 liquid immiscibility
141 156 61 1 184 6 55 166 62 63 2
yap. press. (1600-1820 K) yap. press. (1600-1920 K) yap. press. (1623 K) emf 0400-1500 K) equilibr. (1523-1608 K) assessm. (1369 K) assessm. 0733 K)
AH~e~ : 17.5 AH~'et : 15.1 AH mix at 42 a/o Ni; A H ~ : 16.9 values at 1732 K; see also [ 68 ] AG xs at 1732 K values at 1820 K AG xs values at 1450 K AG xs at 1608 K AH~]~e~: 17.5 AG °xs
145 65 67 70 71 l 184
la~lletion solub. (923-1153 solub. (953-1153 solub. (973-1223 solub. (813-1098 solub. (873-1473 phase diagr,
AH~e~ : 17.5 AH{]~e~ : 17.5 AH~e~ : 17.5 AH~e~ : 17.5 AH~e~ : 17.5 liquid immiscibility
73 73 73 73 155 147,155
K) K) K) K) K)
la~lietltea solub. (473-873 K) solub. (505-783 K) solub. (719-873 K) solub. (719-873 K) solub. (873-1273 K) solub. (973-1187 K) solub.
AH~e~ : AH{~e~ : AH~e~ : AH~e~ : AH~: AH~e~ : AH~e~ :
lwedktiea solub. (933-1343 K)
AH~
wedktioa equilibr. (1623 K) ln'edlktlea calorim. (981 K, II20 K)
72 138 64 69
17.5 17.6 17.5 17.5 17.5 17.5 17.5
73 146 74 73 158 73,159 161-62
: 17.5
73
AG°~; AH~e~ : 17.6
148 77,140
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
326 Table Ni-III X
(continued) AH°{Ni}
AH~M}
AH°{M}
-42 (-38)
-14 ( - 10)
- 22 - 17
- 7
- 37 - 13
- 13
-0.9
+ 1 + 16
Ba
0
-8.0 ( - 7.4) - 7,8, - 11 + 1
>0 Zn
- 9 <0
- 36 -60...-52 (-26)
+7 <0
+2
+9
+ 28
+ 8
-
Cd
Hg
34
+ 40
+39 - 9
- 55
-25 - 12
- 101 (-73)
- 82 157 - 157 - 155 - 157 - 160 - 154 -166
- 22
- 97
-
-146
( - 138)
-49
- 136
- 50 -25
-22 - 151 -156
vap. press. (923-1023 K)
A~-o xs at AH~ : values at AH~e~ : A~-o xs at
assessm. (923-1123 K ) assessm. (1000 K ) lm~lletloa calorim. (1120 K) yap. press. (1737-1766 K) e m f (1050-1350 K)
assessm. (1750 K) assessm. (I 750 K) assessm. (1873 K)
(-5.4) ( - 32)
- 148 - 162
(-22) ( - 109)
Ref. 1000 K; 17.5 1373 K; 17.5 1023 K
A~-o xs
1,75 76 184 1
A~'o xs at 1753 K AG xs at 1200 K and at 45 a/o Ni; AH~[~¢~ : 17.5; A H ~ aa : 8.5 AG xs AG-* xs
77,140 66 157
1 184 6
predietion solub. (1073-1473 K) phase diagr,
AH~e~ : 17.5 liquid immiscibility
lm~dletlon yap. press. (ll00-1300 K) yap. press. 0 7 4 8 K)
AG xs AG"°xs
79 78
prediction vap. press. (823 K)
A~-o xs
173
155 i 47,155
prediction
solub. (373-483 K) solub. (667-1023 K)
+ 5
Al
Remarks
e m f (973-1423 K)
-42 Ca
Method
AH[,~¢~ : 17 AH~: 17
80 81
prediction
calorim. (1838 K) yap. press. (1400-1750 K) assessm. (1873 K) prediction calorim. (948 K) caiorim. (952 K) calorim. (1000 K) calorim. (1023 K) calorim. 0 0 3 0 K) calorim. (1100 K) calorim. (1158 K) calorim. (1173 K) calorim. (1773 K) calorim. (1873 K) calorim. (1923 K) yap. press. (1750-2100 K) e m f (1100 K) equilibr. 0 8 7 3 K) assessm. (1173 K)
A H mix at 1600 K AG-°xs
AH~ AH~ AH~ AH~e~ AH~ AH~ AH[,~ AH~:
: : : : : : :
17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5
AG xs at 54 a/o Ni; value at 2000K AG xs AH~e~ : 17.5
82 191 184
86,149 139 88 85 190 84,87 167 150 89 3,90 83 91 92 93 160
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-III X
(continued) AH°{Ni}
AH~}
A/-~°{M} -
( - 70)
- 15
129,- 174 ( - 30) 133 -
In
+5 35 33 (-27) (-15)
+2
-
TI
+41 - 86 ( - 112)
( - 113) ( - 150) - 136 ( - 112) (-80) (-77)
-4.5 >0
(-15)
+!3 >0
+67
- 23 - 54 -56
- 98 ( - 188)
-54 -52
(-188)
-67 -54 -26 -36
(-200) (-148) (-142) 188 -
145
- 13 -49
129
-55
(-55)
-28
- 41 - 78 (-79) (-65) (-69) (-75) - 37
- 11
-
-
-
Ge
Sn
Method
Remarks
Ref.
assessm. (1873 K) assessm. (1873 K) assessm. (1873 K)
A~o xs
6 175 184
calorim. (1090 K) calorim. (1096 K) calorim. (1096 K) yap. press. (1248 K) assessm,
A H ~ : 17.5 AH~e~ : 17.5 AH~e~ : 12.6 AG ~ liquid immigcibility
186 94 95 96 151
phase diagr,
liquid immiscibility
2
+8
-
Si
327
( - 300) - 173 - 188 138, - 187 (-74) - 51
-38 -32 -26 -29
( - 117) (-53) ( - 132)
(-55)
-19
-32 -29 (-71)
- 13 -77...-66 -69...-61 -66 -59 -71...-67 -63 -60...-62 -61
-4
-21
lwe&ktlea calorim. (293 K,1873 K) calorim. (1400 K) calorim. (1750-1950 calorim. (1773 K) calorim. (1773-1823 calorim. (1793 K) calorim. (1873 K) emf (1753-1883 K) emf (1753-1883 K) emf (1753-1883 K) equilibr. (1853 K) asseum. (1773-1873 assessm. (1823-1873 assessm. (1873 K) assessm. (1873 K) assessm. (1873 K)
K) K) max. AH value AG ~ at 1753 K AG xs at 1883 K value at 1818 K AG~i } at 50 a/o Ni K) K)
l~¢~lctieo calorim. (1274 K) calorim. (1288 K) calorim. (1773 K) vap. press. (1623 K) yap. press. (1640-1920 K) equilibr. (1723 K) equilibr. (1723 K) assessm. (1723 K) assessm. (1873 K) lredlettoo calorim. (523-773 calorim. (621-770 calorim. (623 K) calorim. (623 K) calorim. (623-743 calorim. (698 K) calorim. (773-832 calorim. (775 K)
AH~e~ : 17.5; AH[[~e : 50.5
K) K)
K) K)
AG ° n at 1873 K see also [ 101,103 ]
AH~t~e~: 17.5 AH~e~ : 17.5 AG~; AH~e~ : 17.5 values at 1870 K AG °xs &G°~
AH~e~ : AH[]~e~ : AH[]~e~ : AH~: AH{~e~ : AH~el : AH~e~ : AH~e~ :
17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5
100 183 15 89 98 97 99 104 104 104 102 185 184 105 6 175 171 106 107 109 108 110 111 184 175 153 i18 117 154 115 127 112-13 150
328
A.K.
Table Ni-III X
N i e s s e n et
(continued) A/~° {Ni} -57 - 59 -57 -70 -56 -54 -53 -55 (-45) (-42) -42 -24 -70
AH ~M}
-20 -19 - 13 - 15
A/~°{M}
(-80) (-94) (-25) (-97) -26
Pb
+40 +9.0 + 36 8.9
+ 13
+ 73
+ 10 + 1.7 + 18 + 8.9 +8.8 + 42
Bi
+ 31 (+4)
- 19 + 10 +2.7
Remarks
calorim. (883 K) calorim. (910 K) calorim. (913 K) calorim. (914 K) calorim. (1023 K) calorim. (1078-1093 K) calorim. (1095 K) calorim. (ll00 K) calorim. (1580 K) calorim. (1773 K) vap. press. (1573 K) vap. press. (1573-1623 K) assessm. (600 K) assessm. (1573 K)
AH~e~ : AH~iSe~ : AH~: AH~el : AH~e~ : AH~e~ : AH~e~ : AH~i~e~ :
prediction calorim. (823 K) yap. press. (1703-1783 K) emf (973-1373 K)
Ref. 17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5
AG xs AG xs at 1573 K AH~: 17.2 A~o xs AH~Se~ : 17.5 A~o xs at 1750 K value at 1273 K; AH~e~ : 17.5 A H ~ : 17.5 AH~'~ : 17.5 AH~e~ : 17.5 A H ~ : 17.5 AH~'e~ : 17.5
120 114 116,121 119 85 94 182 122 123 124 126 125 152 184 127 181 172
A~o xs liquid immiscibility
73 73 169 73 128 63 184 2
- 93 (-96)
prediction yap. press. (1273-1423 K)
A~-o xs at 1423 K
129
+ 58 (+20)
lm~lietion emf (970-1170 K)
AG xs, evaluated at 1773 K
130
+ 5.2 - 65
Method
solub. (597-823 K) solub. (600-755 K) solub. (643-1000 K) solub. (645-1026 K) solub. (645-1517 K) solub. assessm. (1873 K) phase diagr,
>0 As
al. / Enthalpies of formation of Ni alloys
based on Ni with the available phase diagram information obtained from fig. 1 and fig. 2 and "translated" into qualitative information as described in sec. 1. In general the predictions are qualitatively in accordance with the information emerging from phase diagrams as can also be seen in tables Ni-Ia and Ni-Ib. This conclusion is confirmed by the additional information given in table 1 for the Ni-based systems whose phase diagrams are known, at least partly, in the absence of any useful experimental numerical thermodynamic information in the solid phase. By means of table Ni-II the experimentally observed enthalpies or free enthalpies of formation
which have been reported in the literature can be compared quantitatively with the predicted enthalpies of formation, while the predicted and observed formation enthalpies for liquid Ni alloys are collected in table Ni-III. In fig. 3 and fig. 4 this comparison is made more explicitly for ordered compounds by displaying the data from for vs ,Air-/" for plot. In fig. 3 table Ni-II in a AF']" ---exp ~,. ~¢ formation-enthalpy values of Ni compounds with transition metals are shown and in fig. 4 the formation-enthalpy values are presented for Ni compounds with non-transition elements. On the basis of fig. 3 and fig. 4 more or less similar conclusions can be arrived at for ordered
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
100
100
T
_AHfor "'exp
ii.'!J, /
/
/
/
,.for - AMcalc
-
Fig. 4. A H ~ [ versus A H ~ [ c (kJ (mole of atoms) -l) of ordered compounds of Ni with non-transition metals.
I&H C
/ /
/
5~
for I _&Hexp
50
/
!
/*
- ~Hfc°~
/
I/ i.i
for versus A H ~ foc (kJ (mole ofatoms)- 1) ofordered Fig • 3 , AHex p . . . . . . . . compounds of Nt with transttion metals, mcludmg actmtde, noble and alkaline earth metals.
100
~for -AMex p
5O
50
50
l
329
--)Ni-AI
/-"
/
//
/
/
/
/
Z
Z
z
/
,/
/
"
/
\
S
/,,
Ni_Sb~~~N/i/-Ga
/ //
Ni-ln /
^l_ifor
-'~f 'calc
~V
5()
forp and AH~.~[ fo c for some Ni-based Fig. 5. Comparison o f AHex systems indicating that the scatter in fig. 4 is caused, at least partly, by an incorrectly described concentration dependence of AH ~c-
-AHcalc
Fig. 6. Scheme to explain the loop-like curves as given in fig. 5 with the dependence of A H ~ [ c and A/4"for ---- exp on concentration.
330
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
Ni compounds as for the Co-based compounds; see [ 4 ]. In these figures A H r°r values are indicated by dots and AG r°r values by + signs, while the corresponding AG r°~ and A H f°r points have been connected by a line and an arrow pointing from A/.-/for towards A~r°r If one compound has been -- exp ~ v exp" subject o f more than one independent observations reported in the literature, the various experimental points have been connected by a drawn line, indicating the accuracy of the experimental data. Within the experimental uncertainty there is a fair agreement between prediction and experiment, certainly if ~A/4for values are not accepted -" cxp for ordered compounds with improbably large A.~ror exp values and the corresponding AG f°~ values are considered instead as a better alternative. In the following, more quantitative, discussion the thermodynamic properties o f a Ni-based alloy will occasionally be compared with those belonging to a similar alloy, but based on Co instead o f on Ni with the same partner metal, in order to elucidate some peculiar resemblances or differences in behaviour of these alloys of the two elements which are so similar as far as the values o f q~', n ws and V are concerned. F r o m the distribution of the points in fig. 3 and fig. 4, we may conclude that experiment and prediction agree satisfactorily. For Ni compounds with non-transition metals (fig. 4), in particular, we note that the experimental values tend to be more negative than the predicted ones while the rather wide scatter of the points suggests that the predicted concentration dependence is not confirmed by the experimental values, similar as for Co based alloys [ 4 ]. The latter is illustrated in fig. 5 where the points representing compounds in one and the same binary system are connected according to concentration. The meaning o f these loops can be understood from the schematically given difference in concentration dependence o f the predicted AH f°r and A- /-4 -f o r cxp in fig. 6. F r o m fig. 5 and fig. 6 it will be clear that, at least partly, the scatter shown in fig. 4 is related to an incorrectly predicted concentration dependence of A H r°r for these particular compounds. In sec. 4 we shall
come back to this point. For Ni compounds with other transition metals (fig. 3) there is indeed a satisfactory agreement, except for a number of cases with a strongly negative ,_.,,^ r~rfOrme.This set will contain the cases where the predicted enthalpy is overestimated due to a complete filling o f the d band at alloying. The general conclusions about the predicted enthalpies of Ni alloys are that we understand qualitatively the deviations for Ni with transition metals, and that further discussion is needed on the alloys with non-transition metals.
3. Alloys with Ni as minority element The more detailed discussion on the Ni-based systems with transition metals will firstly be concerned with the differences between predicted and experimentally observed enthalpies of formation if Ni is surrounded by more electropositive metals like La and Ti. In the model [ 5 ] it is proposed that the enthalpy o f formation contains two terms, a negative contribution stemming from the difference in ~b" and a positive one arising from the difference in n ws. The first contribution can be seen as arising from a charge transfer proportional to A~" over a difference in potential of -A~b'. However, the atomic cell with the highest electron potential ~b" can accept only a limited amount o f charge without drastic changes in the electronic configuration. Conversely, the atomic cell with the smaller electronegativity like Na or Ca cannot lose more than one or two valence electrons. The change in electronic configuration is reflected in a change o f the model parameters: if q~" is plotted versus Z, the number o f atomic valence electrons, ~" changes abruptly at the end of each d series, see fig. 7. Since there are several indications [ 7,8] that one electron will be transferred by a difference in potential of about 2 V, the empty d-electron states in Ni (about 0.5 electron per Ni atom) may be occupied upon alloying with a majority o f the partner metal which possesses a q~" such that l#*Ni -- (~" > 1 V.
A.K. Niessen et aL / Enthalpies of formation of Ni alloys
Iv] 5.0
/
3d series
./"'"
4.0 5
4d series 6
4
\
/
10
15
Fig. 7. ~* in r e l a t i o n to Z , the n u m b e r o f a t o m i c valence electrons for the three t r a n s i t i o n m e t a l series.
In view of the large differences in electronegativity in the systems of Ni with the transition metals Sc, Ti, V, Y, Zr, Nb, La, Hf, Ta, Th, U and Pu, these changes in electronic configuration may occur in the solid and the liquid state if Ni is sufficiently surrounded by these electron-donating metals. This effect is seen as a systematic deviation of the heat of solution, the prediction being too negative. Table Ni-III contains information about this aspect for the Ni-based systems with Ti, Y, La and U in the liquid phase. In the solid phase formationenthalpy values have been reported for Ti, V, Y, Zr, Nb, La, Ta and Th compounds with reasonably low concentrations of Ni (table Ni-II). The system Ti-Ni is very conclusive concerning this effect: in the liquid state (table Ni-III) the experimental heat of solution of Ni in liquid Ti appears to be less negative than the calculated one
331
and in the solid phase ~.a.,tAt/f°rcalc< ----expA/4f°rNiTi2 and NiTi (table Ni-II). As expected this effect is not present for NiaTi. It is also not observed for NiV3 since ¢ ' s i - ~b'v < 1 V. A large asymmetry is observed in the heat of solution in the liquid state for Ni-Y, but no conclusion can be drawn from solid-state data. Calorimetric measurements on Ni-Nb alloys indicate that here too a reduced enthalpy of formation is encountered: as expected, for the more Ni-rich compound Ni3Nb there is good agreement between calculation and experiment. Although the scatter of the experimental data is often large for Ni-Zr compounds the reduced formation enthalpy can be traced in the Ni-Zr system, too. The effect is also clearly observed in the Ni-La system, both in the solid phase and in the liquid phase. The data for Ni-Ta compounds could perhaps support the conclusion, too; unfortunately the data scatter widely. The trend is found indeed for Ni-Th, in particular, if one takes the AG f°r values in the solid phase for the latter system. The necessary reduction of ,~for '~,, ~c of Ni-based alloys with other transition metals appears to be well established if Ni is the minority partner in a relatively electropositive surrounding. If Ni is the minority partner the reduction of the enthalpy of alloying means a reduction of the negative contribution Air/for •~,, c~ ionic of aH~Ic: A r t for l i calc
--
a r J r for, ionic art zal~ calc -t- ~
for, pos calc ,
(1)
where (2) Upon accepting charge the electronegativity will drop more than average (Ni being the last one in the series of 3d-transition metals) leading to a lower value of the proportionality constant P. For AO" < 1 V this reduction is not present, but for larger values of AO" a drastic change may occur for alloys poor in Ni, as indeed can be observed if the experimental negative part, AF/for,ioaic calculated according to A/4" for, ionic "'exp
=
A r T for a r _ r for, pos - - - - exp - - za~, calc
(3)
A.K. Niessen et aL / Enthalpies of formation of Ni alloys
332
is plotted in relation to the calculated ionic part, AH~[; i°"~c. In fig. 8 where these quantifies related to one mole Ni have been plotted it is surprising that the observed trend is towards a constant reduction, independent of the magnitude of AH[.~6i°nic, or which is equivalent, independent of A~b" at larger A~," values. For Ni alloys with Mn and V it is expected, and observed, that the enthalpy is not reduced since the charge transfered to Ni is too small //
j'/ /./
300 //'/
i200 .x L I
"r 10C <1
~oo
20OAHo~~.
300
[k J/mole Ni
for or po$ Or lOmC Fig. 8. The quantity (AHex p - AHfe0~tc ) versus AHf~tc " for binary systems where Ni is the minority partner in a c o m p o u n d with a transition metal in kJ (mole N i ) - L
In the next section a quantitative correction is presented accounting for limitations in transfer of charge to metals at the end of a transition-metal series. This correction scheme is applied to Ni in this paper, but this formalism can be applied similarly to alloys of either Pd or Pt, elements of the same column as Ni in periodic table.
4. Proposed corrections for Ni, Pd and Pd
This means that for large A~* it is no longer required that Ni is the minority partner. For the examples given in table 2 at least half an electron is expected to be transferred to each Ni atom, and it should be noted that in some compositions Ni is indeed not the minority partner; for the given compositions, both in the liquid and the solid phase, the value of 30 kJ (mole Ni) -1 is a reasonable estimate. Since a discontinuity of ~* (Z) can also be expected for the 4d- and 5d-series (fig. 7) the same phenomenon can be expected to occur for Pd and Pt. Unfortunately, the experimental information is relatively scarce. From recent free-enthalpy measurements [ 9 ] on Pd-rich Y alloys one might estimate a value of 90 kJ (mole Pd) -1 at larger values for fPvd. Atb*, where f~d is the degree to which Pd atoms are surrounded by dissimilar neighbours (Y). The large reduction for Pd is confirmed in experiments on Pd compounds with rare-earth metals by means of a dynamic differential calorimetric method [10,11] and is also consistent with the more steep drop in ~b" when going from Pd to Ag as compared with the drop in ~b* for Ni to Cu or Pt to Au in fig. 7. For Pt-based alloys there is an experimental value for equiatomic compounds of Pt with rare-earth metals [12] (the same kind of calorimetry as above), and further some values [ 13-17] for compounds very rich in Pt. The reduction of the formation-enthalpy effect for Pt compounds is without any doubt smaller than for Pd compounds. The correction to the predicted formationenthalpy effect accounting for a limited charge transfer can also be calculated by means of the following scheme. For alloys of two transition metals the ionic term of the enthalpy of alloying of the alloy ABn (per mole A) is written as ~t
The predictions can be improved by assuming that if more than about half an electron is transferred to a Ni atomic cell upon alloying, the enthalpy will be changed by about 30 kJ (mole Ni) -1. In order to decide whether more than the charge of half an electron is transferred to the Ni atoms one has to take into account the magnitude of A~b* and the degree to which Ni atoms are surrounded by dissimilar neighbours.
AH for, ionic (per mole A) ~
-
AZ A~
2
(4)
where AZ is the charge transferred per A atom (in units of electronic charge) that is assumed to be proportional to both AO" and f ~ such that f ~ is the degree to which A atoms are surrounded by dissimilar neighbours (B). With the charge transfer the difference in ~* is equalized and the
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
333
Table 2 The reduction of A H ~ [ c, AH corr, where AH corr = A H ~ [ e - AH f°e~rin kJ (mole Ni) - I if the d band in Ni becomes completely filled upon alloying of Ni and X. Predicted values for the enthalpy of fo-l~nation ( AH~t°[c)corr are also shown according to the formalism given in sec. 4 with ( A~b*max )0 = 1.05 V. X
CNi
A~b"
f~i
Ti Ti Y Y Y Y Y Zr
0.33 0.50 0.25 0.40 0.50 0.67 0.75 0.33
1.40 1.40 2.00 2.00 2.00 2.00 2.00 1.75
Zr
0.50
1.75
Nb Nb Nb La La La La La Ta Th Th Th
0.50 0.50 0.75 0.25 0.50 0.50 0.67 0.75 0.33 0.30 0.50 0.67
1.15 1.15 l.l 5 2.03 2.03 2.03 2.03 2.03 1.15 1.90 1.90 1.90
0.95 0.83 0.99 0.96 0.92 0.70 0.53 0.96 0.88 0.84 0.84 0.41 0.99 0.98 0.93 0.73 0.56 0.96 0.98 0.92 0.72
AH~ - 28 - 34 - 19 -30 -37 - 39 - 37 - 37 - 52 -23 - 35 - 32 - 13 - 15 - 25 - 20 - 21 - 39 - 28 - 45 - 42
AH~[e
AH corr
( AH~[c )corr
- 40 - 52 -23 -37 -44 - 45 - 37 - 53 - 72 -45 - 45 - 32 - 19 - 38 - 38 - 39 - 33 - 39 - 35 - 56 - 58
36 36 16 18 14 9 0 48 40 44 20 0 24 46 26 29 9 0 23 22 24
- 37 - 51 -8 - 12 - 19 - 36 - 37 - 41 - 61 -45 - 45 - 32 -3 - 9
-
- 9 26 33 33 22 35 50
a v e r a g e p o t e n t i a l o v e r w h i c h t h e c h a r g e is t r a n s -
Now AZ remains constant with further increasing
f e r r e d is A O ' / 2 . T h e r e f o r e
AO',
but
the
effective
difference
in
potential
AO'ar for the transferred charge becomes
AH for, ionic (per mole A) oc
_ f A ( A~* )2 2 . (5)
In the case of a limitation of the charge transferred due to the electronic configuration, of the electropositive
atom
(e.g. N a )
either
or of the
e l e c t r o n e g a t i v e a t o m (e.g. N i ) , A Z will b e p r o p o r tional
to
Ao"
for fA
=
1 until
A Z m ~ is r e a c h e d a t ( A 0 " m ~ ) 0 assumption
a
A~b*eff =
Hence tion
band
allows
for
some
v a l u e f o r A Z is
additional
(A0"m~)0
in
the
formalism
is o b t a i n e d
However, iff A <
as a
1 then AZ
the
it
of
charge
transfer,
O----
~r_r for, ionic ~'achargelimit
_--
A H for, ionic
the
ratio
without reads
in
of
limitacase
AZma x
Aw*eff "~
(8a)
AZ A~*
or
A Z m ~ is r e a c h e d
O =
(A~b*max) (2A~b* - A~b'max) ( A(~" )2
t
( A~b max ) 0 / f A .
i.e.
parameter
at
A~b max =
@,
A~" > a#'max,
best-fit parameter. =
for
charge
t r a n s f e r . H o w e v e r , t h i s s i m p l i f i c a t i o n is a c c e p t a b l e because
value
(7)
maximum
r e a l i s t i c , f o r N i i t is a n o v e r s i m p l i f i c a t i o n s i n c e t h e s-d
the
A~btmax ).
A H f°r,i°uic ( p e r m o l e A ) w i t h a n d
While for Na the
of a rigid maximum
A~b'max + 2 (A~b* -
(6)
a n d b y i n s e r t i n g eq. (6)
(8b)
334
A.K. Niessen et al. I Enthalpies of formation of Ni alloys
=
[
( A~b max ) 0
4
2
1
( A~b max ) 0
4
,,+"
"
(8c)
ilc"):4
In table 2 this correction is applied for those Ni-based alloys for which experimental information on AHror ---cxp is available in table Ni-II, using ( A~b'max) 0 = 1.05 V as best-fit parameter. In combination with the approximation between f ~ • A~b" and AZ, as given in [ 18 ] this corresponds to AZm~x is about 0.5 e per Ni atom. For Pd and Pt we have estimated that (A~b'max)0 = 1.15 V for Pd and ( A~b*m~x) 0 = 1.00 V for Pt, respectively.
5. Alloys of a transition metal and a non-transition metal
In this section the enthalpy of formation for binary alloys of a non-transition metal and a transition metal, in the solid state as well as in the liquid phase, will be discussed in more detail. Some discrepancies between the predicted and experimental enthalpy effects upon alloying a non-transition metal and a transition metal have already been mentioned in the previous section and in other papers of this series. Now the discussion is not limited to the alloys based on Ni, but covers in principle all alloys of a non-transition metal and a transition metal. For 3d-transition metals other than Ni this information is readily available in [ 1-4,19 ]; experimental information on alloys containing 4d- or 5d-transition metals [ 19 ] is less abundant than for 3d metals. For alloys of two transition metals we have previously shown that the contact-interaction model [ 5 ] yields an expression for AH r°r with two terms: AHf°r c~ f ( c S )
x [ _,, (,,+-)
x
Q (,,,,
cells (f]) and the molar surface area of the two constituent metals (V~ 3, V~ 3)
(9)
where f (c s) is a function of the surface concentration c s. We can express [ 5 ] f (c s) in the atomic concentration of one constituent (CA), the degree to which A atoms are surrounded by B atomic
[
tlO/
Expression (9) does not only apply to binary systems of transition metals, but also to systems of two non-transition metals. There is little doubt that such a description based on contactinteraction also applies in the case of alloys of a non-transition metal and a transition metal. The convincing agreement between predicted and observed enthalpy effects on the formation of a binary alloy of Co or Ni with another transition metal confirms the adequacy of the assumption that the energy effects upon alloying are generated at the interfaces of dissimilar atomic cells. Further support is found in fig. 9, where all available thermodynamic data [ 19 ] on compounds of transition metals with other transition metals have been collected. Those compounds are indicated for which it can be expected that the predicted charge transfer is reduced, as for example in NiLus. For a few compounds with the AuCu 3 structure the experimental enthalpy of formation is exceptionally large, presumably due to an additional contribution if some Brillouin zones are filled upon alloying. Taking into consideration that there is an uncertainty of 2 to 5 kJ (mole of atoms) -L in the predicted values and an uncertainty of about the same magnitude in the experimental results, the agreement between predicted and experimental values is very conclusive. A good agreement is also observed in the liquid state (fig. 11). The experimental values plotted in these figures were obtained solely by calorimetry. In fig. l0 and fig. 12 the thermodynamic data for alloys of a transition metal and a nontransition metal are analysed along the same lines as in fig. 9 and fig. 11. The scatter is much larger in fig. 10 than in fig. 9: 30 to 50 kJ (mole of atoms) -1 instead of l0 to 15 kJ (mole of atoms) -1. The way the points scatter in fig. 12 differs markedly from that in fig. 10. The predicted enthalpy of solution appears to be insufficiently negative in fig. 12 (liquid phase) while in fig. 10 (solid phase) the points scatter
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
335
i t
kJ
i
- &Hexp
for -AHex p
2O0
20(3
/'.
/. •
• HIPt3 /
t 10C
]1
"+'+Z /+
Y:
,,
//"I',
i']
•
•
I I
,,"
"~:/:" °.
/
..,o+
~" +//
- AHcalc
t¢
=
Fig. 9. Comparison of predicted and experimental AH for for compounds of a transition metal with another transition metal (e) or with a noble metal (&). One type of discrepancy is indicated by x; if sufficiently electropositive atoms surround a Ni, Pd or Pt atom, AH ~ c is too negative (e.g. in La3Ni ) since the d bands of the electronegative metal tend to be fully occupied upon alloying. The experimental values were obtained exclusively by calorimetry (taken from chapter III in [ 19 D.
t, i-icalc
=
Fig. 10.. Comparison o f A H ~ rP and A H ~ c for compounds of . . . a transmon metal (including the noble metals) and a polyvalent non-transition metal. The experimental values were obtained by calorimetry (taken from chapter III in [ 19 ]).
oo[l-,xo
T-• --o Hex p
//
300
IkJ7 1 Lm--gi~J
[&]
2O0
200
l
100
~
i /
/.
,-
,o,
0he'.
•
~).'.,~.. ~" .,,. .~.~.. • . . . / .
.: ..~. ~fi" ix
"
,4 / •
UPd3
:~
//1
/
• ///:.
./
/
100 / . . " " . . / : ' ~ " * v'" /" ~ y~:." ,/
~:
•
"/// /.
/
/
;~
.."
// /
x •
;
.
,~:.'~ ..
x,
-'Hca~
100
r kJ]200
"
i
-100
; ~//~
~/~
%1
r
L~I
-I0-'56m'.-~"-"
' ~ 0 0 /1/ / / /
//100
I kJ I
300
[moleJ
-100[ Fig. I I. Comparison of predicted and experimental A H °, the enthalpy of solution in the liquid phase of a transition metal and another transition metal (e) or a noble metal (A). As in fig. 9, some deviating points with Ni, Pd or Pt as solute metal are indicated by x (problem of full d bands). The experimental values were obtained by calorimetry (taken from chapter I l l in []9D.
Fig. 12. Comparison of AH"° ~p and A/~°calc for liquid alloys of a transition metal and a polyvalent non-transition metal (C, N and P are excluded). The experimental values were observed by calorimetry (taken from chapter III in [ 19 D. The dashed lines indicate that the scatter in fig. 12 is comparable to that fig. 10. The scatter in values of AH f°r is expected to be about 0.375 times that for the enthaipy of solution.
336
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
more evenly around the line where the predicted value is equal to the observed value. By means of fig. 5 we already indicated that for solid alloys with non-transition metals the concentration dependence of ~.,AUr°~c~ is not described correctly. In order to compare the predicted and the experimental concentration dependence of the enthalpy of formation more information is required than has been provided in fig. 5. A fairly complete survey on the concentration dependence of A/./ror _..~,p can readily be obtained from the phase diagrams by searching systematics in the concentration range where compounds tend to be present. For instance, if AHfor --exp as a function of concentration is asymmetric with the more negative values in the nontransition metal range, one expects to find compounds predominantly in that range. In our analysis we have divided the concentration range in eleven equal intervals and have counted the number of times a compound stable at low temperatures is found in each interval of the available binary phase diagrams of one nontransition metal with all transition metals, noble metals and Th, Pu and U. The number of compounds in each interval is then divided by the total number of compounds involved in this analysis, defining in this way a probability to observe a compound in an interval. The result of this procedure is shown in fig. 13 for all non-transition metals. The probability to find a compound is definitely not spread over the concentration range in a statistical way. In general the compounds cluster at compositions rich in the non-transition metal. This appears to be very pronounced for Be and Mg, and also for the other divalent metals Zn, Cd and Hg. The trend is very much the same as for Be and Mg: the smaller the molar volume the more asymmetric the number of compounds is distributed over the concentration intervals. The asymmetry observed in the occurrence of compounds in Zn-based phase diagrams is consistent with the quantitative information on the concentration dependence of AHfor ~ exp in the Co-Zn system, noted in [4]. For the trivalent non-transition metals the distribution of the compounds resembles only for M-based compounds that for the divalent metals. The pronounced asymmetry as for Be and Zn is not
observed for the tetravalent and pentavalent non-transition metals, however, the probability to find a compound at a certain concentration appears to be not a statistical one. Note that the diagrams for B, C, Si, Ge, N and P have to be considered with some care since in the pure state these elements have an enhanced stability with respect to the hypothetical metallic state, and the metallic character of compounds rich in these elements may be disputable. The strongly varying numbers of the compounds at lower concentrations of the non-transition metal, e.g. the pronounced minimum in the occurrence of Sn-based compounds around c = 0.6, are statistically significant. How complicated this matter in fact is will be illustrated in fig. 14 where we compare the compound occurrence in those systems where B is alloyed with d metals from different rows in the periodic system. One observes a striking difference between Sc, Y and La from the first row of transition metals, Cr, Mo and W from the middle row and Ni, Pd en Pt from the last row. For compounds based on C and N a similar behaviour is observed. In conclusion we note that the asymmetry in the number of compounds, which we now prefer to interprete as being related to an asymmetrical concentration dependence of the so-called R term, is certainly more pronounced for the metals with the smaller molar volumes (Be and Zn) than for others. The varying numbers of the compounds at lower concentrations of the non-transition metal may have some significance, indicating that the variation of the R term upon concentration does not have to be a monotonic function. It is appropriate to recall here the reasoning to introduce the R term. For alloys of a transition metal and a non-transition metal an equally important energy contribution, the so-called R term, has to be added to the two terms in eq. (4) that describes the enthalpy of formation of an alloy of two transition metals: AHf°r oc f ( c S ) x
[
-
x R].
(11)
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
30%
B
C
AI
Si
337
N
wt 20% 10%
30%
Mg
2O%
N
10% 0 Zn
30%
Ga
Ge
As
Jt
20%
10%
Cd
30%
In
Sn
Sb
TI
Pb
Bi
2O%
10% ~:~I~ii!i!i!~iiiii
Hg
3O% 20% 10% 0
0
0.5CA_.,. " 0
0.5CA_,,. 0
0.5CA ---,,.- 0
0.5CA
Fig. 13. The probabifity of finding compounds in binary systems of transition metals and the polyvalent non-transition metals in one of eleven equal ranges of concentration.
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
338
100%
7=2
t
W 5O%
015 c B " 1 60%
Z=3
Z=4
Z=5
Z=6
Z=7
Z=8
Z=9
Z=IO
W
50%
W 25%
0
0.5 CB --"'- 1
0
0 . 5 c B --,,,--1
0
0.5 c 8 --"~1
0
0.5 c B ---,'--1
Fig. 14. The probability o f finding c o m p o u n d s in binary systems o f transition metals and boron in one o f eleven equal ranges o f concentration for three groups o f transition metals as partner metals. Note the large differences between these groups.
Whereas much attention has been paid in [ 5 ] to the physical meaning o f each o f the first two terms in eq. 6, the third term, the R term, has been introduced without much argumentation. Since about the same additional energy is required in the liquid as in the solid phase, and since in the liquid phase it is very improbable that an additional contribution to the formation enthalpy can be ascribed to effects owing to the tilling o f Brillouin zones o f particular crystal structures, the o r i o n has to be sought in the fact that different types o f metals are combined: here a metal with p-type electron wave functions is combined with a metal with mainly d-type wave functions. Adopting the contact-interaction as essential, it has been assumed that the concentration dependence o f the R term is similar to that o f the first two
terms [ 5 ]. It is an intentional choice to treat the third term, too, as an atomic interfacial energy, independent of concentration, which leads, however, to some controversial aspects. Relation (6) is oversimplified: A H ° {^} in {B} and A H ° is} i, {A} cannot differ in sign. But there are some examples showing such a change in sign, e.g. in the Co - S n , Cr - S n , U - Pb, M n - Sb and R u - Bi systems. The exceptional occurrence o f different signs for the enthalpies o f solution in these phase systems implies that relatively large differences may occur in the numerical experimental values o f both terminal enthalpies of solution (larger than predicted by means o f the variation in V~ 3) for systems with equal sign for both enthalpies o f solution. In the solid phase such an asymmetry will lead to an asymmetric distrib-
A.K. Niessen et aL / Enthalpies of formation of Ni alloys
339
a "'=a
R"ffiO.73 R
l
i • ::':" , / :
•
I :.:.:::-
,oo. •
,oo
I . . ...
•
•
:
"
,
I
,
100
-~Hcal -o ,c------~ 200
-
./:•'~ ;o.O -~Hc~1c---,,,..
1
200
-100 Fig. 15. The effect of the inclusion of the reduction factor for the R term in the liquid phase for fiquid solutions of a transition metal and a non-transition metal for which AH ° has been determined by calorimetry. The scatter is more evenly distributed around the line where A/7 ° exp = AH° calc without this reduction factor (at right) if the transition metal belongs to one at the end of the d series (o) and with the reduction factor taken into account (left figure) if the d metal (,t,) is situated at the begin of the d series in the periodic system.
urion of compounds in phase systems. For instance, if A H ~ as a function of concentration is asymmetric with the more negative values in the non-transition metal range, one will find compounds predominantly in that range. Fig. 5 and the distribution of compounds with concentration (fig. 13) make clear that the concentration dependence of ALrror ,~--~1c is indeed insufficiently accounted for by f(c s). A possible orion of the incorrectly predicted concentration dependence could be found in the R term. The introduction of R as a constant that is included between brackets in eq. 6 is in fact a too crude approximarion. Unfortunately, at present we have not found a formalism for the R term, either based on physical insight or purely empirical, in which the observations can be treated quantitatively. Perhaps one should have two, in principle independent, relations for AHf°r: one based on the solution of a transition metal in a non-transition metal and the other for the reversed situation. This idea is qualitatively very attractive since it opens the
possibility for a change in sign of the two terminal heats of solution, compounds in the solid phase and liquid immiscibility in the liquid phase and a concentration dependence largely differing from eq. (6). Unfortunately, we are unable to introduce such a scheme without including many more fully empirically determined parameters. Since the introduction of more empirical parameters means a complete loss of simplicity we have not modified the model. The only difference in the treatment of the ¢nthalpy effects in the solid and liquid phase is the reduction of the R term in the liquid state. The advantage of keeping this reduction factor is that the predicted sign to be ascribed to phase systems in the solid phase and in the liquid phase may differ for one and the same binary. If the emphasis of the analysis is on the sign of the formationenthalpy effects of phase systems one prefers that the uncertainty is proportional to AH ° {A}i°{S}, while the choice of neglecting the reduction factor might be a more constant spread of the uncertainty in some cases as is demonstrated in fig. 15.
340
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
The calorimetrically determined enthalpies of solution AH ° for solutions based on either Ti, V, Cr, Mn or Fe, Co, Ni (as collected in chapter III) are plotted versus the predicted AH °. Indeed, for Fe-, Co- and Ni-based solutions one could prefer no reduction, in contrast to the solutions with Ti up to Mn. We conclude that the quantitative information on the enthalpies of formation does not always support a reduced value of the R term for liquid alloys. Data for individual systems of 3d metals for which both the heat of solution in the liquid phase and the heat of formation for compounds rich in the respective solvent metal have been measured support this conclusion, too. The enthalpy effect in the liquid phase arises in principle from the same mechanisms as in the solid phase. However, the environment of the solute atom may be more variable; if heats of solution are measured in the situation of a high-meltingpoint solute metal (e.g. Ni) and a low-meltingpoint solvent (e.g. Sn) clustering of the solvent atoms around the solute atoms may occur. This preferential surrounding of the solute atoms by the solvent atoms produces negative contributions to both the alloying enthalpy and the entropy. The complication of cluster formation may well be more serious for liquid alloys of a transition metal and a non-transition metal. The R term in liquid alloys possibly favours (or requires) local ordering, strongly affecting the entropy of formation. This ordering will depend on temperature; hence a temperature-dependent enthalpy of solution may occur as reported for Ni in Sn (table Ni-III). At least the thermodynamic properties of liquid solutions of transition metals in low-melting non-transition metals can be very complex!
6. Conelmioas In this paper we have presented an extensive comparison of experimental and model values for enthalpy effects in alloys containing Ni. Apart from the benefit of reporting such a large collection of data, we have demonstrated the usefulness of comparing model predictions with experiments: it focusses attention to the limitations of the model.
The main limitation of the model appears to be the fact that no distinction is made between the electrons with various kinds of wave functions. This is encountered in the reduction of the enthalpy at the end of each transition-metal series if the d band becomes fully occupied upon alloying with a more electropositive metal. The latter can be overcome by applying the formalism sketched in this paper. This limitation is also encountered if atomic cells of a transition metal and a non-transition metal, either in the solid or in the liquid phase become first neighbours. The description of the additional energy required in the model is too crude. The concentration dependence of the enthalpy of formation for alloys of such metal combinations, if interpreted in terms of relation (5), would imply at least a different value of R at each side of the binary phase diagram and stronger variations of RIP than used at present.
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344
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ENTHALPIES OF FORMATION OF LIQUID AND SOLID BINARY ALLOYS BASED ON 3d METALS
V. ALLOYS OF NICKEL A.K. NIESSEN and A.R. MIEDEMA Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands
F.R. de BOER Natuurkundig Laboratorium, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands
R. BOOM Research Laboratories, Hoogovens-Groep, 1970 CA IJmuiden, The Netherlands Received 12 July 1988
Continuing the papers on alloys based on either Sc, Ti, V, Cr, Mn, Fe or Co we review in the present paper, on the basis of the model developed by Miedema and co-workers, enthalpies of formation of ordered binary intermetallic compounds of Ni with arbitrary metal partners. The enthalpy effects are also examined for liquid Ni alloys. The calculated values agree quite satisfactorily with the available experimental data for binary systems of Ni with a transition metal, except where Ni is the minority partner in alloys with the much more electropositive metals like Y, La and Ti, in which case the model tends to overestimate the enthalpy effects. A formalism is suggested to improve the predictions in these cases.
In the binary systems where Ni is alloyed with a non-transition metal differences are sometimes observed between predicted and experimentally determined enthalpies. These discrepancies are analysed taking into consideration information on all 3d metals. The limitations of the model will become clear for Ni alloys in particular.
1. Introduction
In recent papers [ 1-4 ] it has been demonstrated that the existing experimental information on the enthalpy of formation of alloys in binary systems based on Sc, Ti, V, Cr, Mn, Fe and Co can be reproduced within the experimental uncertainties by means of a semi-empirical model, which has been introduced extensively in [ 5 ]. In the present paper we compare predicted and experimental enthalpy effects that occur upon the formation of solid or liquid alloys based on Ni. The use of the model to predict enthalpy effects of Ni alloys and the comparison of the predicted values with experimental data are of particular interest since Ni is widely used in metallurgy and electronic devices, while moreover, for no other metal than Ni so much experimental thermodynamic infor-
marion is available. It is particularly interesting to compare enthalpy effects for alloys of Co and Ni; although Ni and Co have about the same model parameters, some differences in alloying behaviour may be expected between Ni and Co since the d band may become completely filled upon alloying Ni. In combination with the previous papers [ 1-4 ] in this series the present paper covers all the alloys of 3d transition metals and in fact the majority of experimental data on alloys containing at least one transition metal. Therefore it is appropriate to evaluate in this paper to what extent the experimental data and the most recently published version of the calculated enthalpy values [ 4,6 ] do agree. As in the previously published papers [ 1-4 ] of this series, our aim in this paper is to present a
0921-4526/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
304
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
Table Ni-Ia C a l c u l a t e d v a l u e s for the h e a t o f f o r m a t i o n , A H for , o f c o m p o u n d s o f five different c o m p o s i t i o n s , the limiting p a r t i a l h e a t s o f solution, A H °, a n d the h e a t o f m i x i n g for a statistically o r d e r e d liquid at the e q u i a t o m i c c o m p o s i t i o n , A H mix, in kJ ( m o l e o f a t o m s ) - l , for b i n a r y nickel s y s t e m s N i - M w h e r e M is a t r a n s i t i o n m e t a l o r a n o b l e m e t a l . A v a i l a b l e p h a s e - d i a g r a m i n f o r m a t i o n has b e e n a d d e d (¶).
~ t_tfo~
AH
I . d t l l calc
M
NiM 5
NiM 2
NiM
Ni2M
NisM
¶
°
AHmi~
AH
°
Ni in M
NiM
M in Ni
Sc
- 21
- 42
- 57
- 53
- 29
- 130
- 39
- 180
Ti
-20
-40
-52
-46
-25
- 126
-35
- 154
V
- 11
-22
-27
-23
- 12
-69
-18
-75
Cr
-4
-8
-10
-8
-4
-27
-7
-27
Mn
-5
- 10
- 12
- 10
-5
-33
-8
-33
Fe
-1
-2
-2
-2
-1
-6
-2
-6
Co
0
0
0
0
C
0
C-
-1
0
-I
Ni Y
- 15
-31
-44
-45
-26
- -
-97
-31
- 162
Zr
-26
-53
-72
-68
-38
- -
-165
-49
-237
Nb
-17
-34
-45
-40
-22
- -
-107
-30
-136
Mo
-4
-9
- 11
- 10
-5
- -
-27
-7
-32
Tc
0
+1
+1
+!
0
C
+2
+1
+3
Ru
0
+1
+1
+1
0
+
+2
0
+2
RJa
(C+)
-3
- 1
-4
- 1
- 1
- 1
- 1
- 1
Pd
0
0
0
0
0
La
- 13
-26
-38
-39
-24
- -
-81
-27
- 146
Hf
-23
-46
-63
-59
-33
- -
-145
-42
-204
Ta
-17
-33
-44
-39
-21
- -
-105
-29
-133
W
-2
-4
-5
-4
-2
- -
-ll
-3
-14
Re
+1
+3
+3
+3
+2
+
+8
+2
+10
Os
+1
+2
+2
+2
+1
+
+5
+1
+6
Ir
-1
-2
-2
-2
-1
C
-5
-2
-7
Pt
-3
-5
-7
-6
-3
C-
-17
-5
-22
Th
- 19
-39
-56
- 58
-35
- -
- 122
-39
-218
U
- 16
- 31
-42
-40
-22
- 98
-29
- 140
Pu
- 14
- 28
- 37
- 34
- 19
-88
- 25
- 118
Cu
+2
+4
+5
+4
+2
C
+ 14
+4
+ 14
Ag
+9
+ 18
+23
+20
+ I1
+
+56
+ 15
+68
Au
+4
+8
+11
+10
+5
(C+)
+25
+7
+33
complete collection of the published experimental thermodynamic data on Ni systems. In addition, we present the known binary phase diagrams, making it possible to compare predictions with phase-diagram information in a qualitative way for those systems on which no thermodynamic data are available in the literature, as will be shown in sec. 2.
C
0
0
0
Since the model parameters depend on the electronic configuration, the formation of atomic magnetic moments of varying magnitude might be expected to be a disturbing factor in the prediction of the stability of Ni compounds as well. However, for Cr and Mn [2] and also for Fe [3 ] and Co [ 4 ] it has turned out that the dependence of the model parameters upon the magnetic state is not
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
305
Table N i - l b Calculated values for the heat o f formation, A H for , o f c o m p o u n d s o f five different compositions, the limiting partial heats o f solution, A H "°, and the heat o f mixing for a statistically ordered liquid at the equiatomic composition, A H mix, in k J ( m o l e o f a t o m s ) - I , for binary nickel systems N i - M w h e r e M is a non-transition metal. Available phase-diagram information has been added (¶). A T• ."/ ~for c M
NiM 5
NiM 2
NiM
- -° AH Ni2M
Ni5M
¶
Ni in M
A H m~
A H- - °
NiM
M in Ni
Li
0
+1
+1
+1
0
+
+3
+1
+3
Na
+16
+32
+46
+44
+23
(+)
+100
+32
+140
K
+20
+39
+59
+68
+41
(+)
+123
+45
+235
Rb
+20
+39
+59
+71
+46
+ 123
+47
+259
Cs
+ 20
+ 39
+ 59
+ 74
+ 51
+ 122
+ 48
+ 284
Be
-4
-8
-9
-7
-3
-
-19
-4
-15
Mg
-3
-6
-8
-8
-4
-
-13
-4
-16
Ca
-4
-7
-10
-11
-6
-37
Sr
0
- 1
- 1
Ba
0
0
0
-2
-22
-7
- 1
-
-3
- 1
-6
0
+
+1
0
+1
0
Zn
-10
-19
-23
-20
-10
--
-34
-9
Cd
-3
-6
-8
-7
-4
-
+7
+2
+9
0
+1
+1
+1
+1
--
+28
+8
+40
-9*
-55*
Hg
B
+2
-23
-33
-27
- 14
- -
AI
- 19
-37
-48
-42
-22
- -
Ga
- 14
-28
-37
-34
- 18
In
-4
-9
-12
-12
-7
T1
+ 1
+3
+4
+4
+2
+
+5
+
--
C
+113
+54
+21
+9
Si
+8
- 17
-33
-32
- 18
Ge
+8
-9
-20
-21
-12
Sn
-8
- 16
-22
-23
Pb
+1
+1
+2
+2
N
+203
+ 103
+36
+ 10
P
- 13
-42
-61
-56
-30
As
- 17
-35
-47
-44
-25
- -
Sb
-7
-14
-20
-21
-13
- -
Bi
- 1
-3
-4
-4
~2
-
strong and that in practice the alloying properties of these metals can be described with unique values of the model parameters. Clearly no problems are expected for Ni alloys in this respect. In the phase diagrams presented in figs. 1 and 2 the most recent information has been included either in the phase diagram itself or in the references attached to the diagrams. Where no
...
-36
-82
-22
-97
-53
- 15
-69
+5
+2
+8
+41
+ 13
+67
...
+51"
+50*
-86
-23
-98
- -
-41
- 11
-51
- 13
- -
- 13
-4
-21
+!
+
+40
+13
+73
+4
+
...
+86*
+50*
...
-26*
- 134"
-65
-19
-93
-4
-1
-7
+31
+ 10
+58
complete phase diagram was available, as much partial information as possible has been included, for example the existence of compounds or the solubility at certain temperatures. Temperatures are indicated in units of lO3 °C. Calculated enthalpy values are presented in tables Ni-Ia and Ni-Ib for binary solid compounds of five different compositions and for binary liquid
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
306
nickel-based [1]
[1.2,31 1.5
....
~.-~-~
[ 1,2,4,5,6]
.
A
,.o~ O.
-
I
I
~
i|
1
Sc
Ni
O.
Ti
[I] N
1.5
[I_,7, 8]
Ni
V
oJ
Ni
'T?'o
,131
~c.,, ~-w--~
I
I
Cr
,i
[ 2 . 1 2 ] ~ co i-~ r~.z c~ z>:+,.>,.-
Ni
\
;;
Y
Ni
[1,2.~1
Zr
~
x
Nb
I~,2]~
o~"
o.
Ni
zzz~zz
,~
Ni
3.0-
[ I~_a~'17]
~.o
z ~
2°1-
10 Ni
- ~
•~ r ,
~e-_~~,.~
05 Th
Ni
Ni
Hf
~l
Jr
~
0.51 1 U
Ni
[1,2] ~
I
,.oF=q--r~ I
"T='Lo
Mo
[1'191~
Ni
To
,
l
[;J
w
Ni
~
% = ~
II I d l
I Ni
Pu
Ni
a
Fig. I. Binary phase diagrams of nickel with 3d-, 4d- and 5d-transition metals, noble metals and actinides. Temperatures (103 °C) are plotted vertically, the atomic concentration of Ni horizontally. Numbers between brackets are the references of experimental
307
A.K. Niessen et al. I Enthalpies of formation of Ni alloys
binary ph~e diillr=m,~ [1._9 ]
,=
1.0~"~-~,N,)
[1,10.11,/~]
[1 ]
I
•
Ni
-Co,Ni }
0.5 Mn
Ni
~,,
[1,2_.1
~°r't:-.
I
Fe
2^J ~-~"~ ~~"~[1]
(Tel 1.0 Tc
Ni
~.oI'~,,I:
1'I-/; ~
-,
"~--q "1
Re
Ni
q
Ru
Ni
1"0t
1Ot
i
i/ Ni
(Cu,Ni)
,.oF Ni
Ag
lAg) + (Ni)
Ni
''"Ni'
175
i
1
!
0.5
Ni
Pd
/
Ir
201 ,t L1 "L2 L * (Nil
[1]
.~,.<,.,,,.~o.il
Rh
2.
Os
[ 1,2,151
1.01" at low temp.
2.ol"-. I /,o,, ', ',,----~,q
1.5i
I
2.0
[1 231
[!, 20, 21,221
0.51 Cu
I
,or ,
Ni
Co
Ni
"]
o.si
Ni
Pt
Ni
------t
(pLN,)/
/(~'~',"~
I Ni
[1'2~'1 . 0 ~ (Au,Ni}
Au
Ni
b cited work; if more numbers are indicated, the dial-am has been reproduced from the underlined reference. (a) nickel and elements with less than five d electrons per atom and Co) nickel and elements with more than four d electrons per atom.
308
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
nickel-based
2o[ [ [2,2__5] _~
[ 1,2_] 2'0f / ' t ' i L 2 " ' " 1.0 / / ?>1200% ~I L +(Ni)
I
o.or
I
[i
Ni
\ Be
[1]
Q,2; 2.0
solubility of Ni in Na at 600"C 0 20 ppm No
1.0 Ni
0.0 N
[1]
Ni
11,2]
solubility of Ni
~
in K at 1055 °C 58 ppm K
Ni
[t.26.27] Z z
1.0
~._u~
10 Ni
0o
Co
Ni
Hm
Zn
[1. 28]
[2]
2° I
z~-
Ji
10
i
no i n f o r m a t i o n
Rb
Ni
Ni
0,0 Sr
i
Ni
Cd
Ni
[1,29]
[1.2]
1-01
/ ~/~---'~ no information Cs
Ni
10Iv,/-- L * INi) rI (Bo)*(Ni) 0.0 ~
Bo
0.5 f ~ . ...~-
Ni
0.0 !
Hg
en
r,~
/'1 !
Ni
II Fig. 2. Binary phase diagrams of nickel with non-transition metals ranged according to increasing valence. Temperatures (10 3 °C) are plotted vertically, the atomic concentration of Ni horizontally. Numbers between brackets are the references of cited experimental
A.E. Niessen et al. / Enthalpies of formation of Ni alloys
309
binary phase diagrams [1.2, 3 0 , 3 1 ,32]
1.01
0s| •
[1.37] 2.0
IC)+ L
1.0
(C)+ (Ni)
[1]
+'~.+_+.,
0.0
B
Ni
C
[1, 331 1.5
Ni
~'~.----,
10
I .j,n~:~ =I
~ununv+ ~ ._,,*,e+,, z
05 Ni
Si
[1,_2.34. 3.5] ~ ~ ~'~./TA
[11
1+f 1.0
1.0
~ .~.~~ ~z z
Ni
[1, 3.~8,3g)
._I 1.bl~
0.5 AI
N
Ni
..T.,r~em Q.z t----
o..,'~+-, ..~,
,, i i
0.5 P
Ni
[1_,40] 1.5
._
i
[1]
oJ
~sl-
<+",,,~.~<-"' -J
1.0
z z~.~:~
.-
.<- " ~
¢.~
1.0 0+0 ~
'
~
Ga
IIH
05
Ni
[!. 3.__6] c ~- -/ ~ c
Ge
Ni
As
[!.~3,~
[I]
" ¢:::'~ c
Ni
1.5 ~;~ z Z z z
1+0
0.0 In
Ni
1.0
1.0~
0.5
0.5
0.0 Sn
[i]
00
Sb
Ni
[i]
[!.4; ,+.2]
+ (Nil
(Tll+INi)
0.0" TI
Ni
ooi
0.0[ Ni
Pb
Ni
Bi
I
a Ni
work; if more numbers are indicated, the diagram has been reproduced from the underlined reference. (a) nickel and elements with less than three p electrons per atom and (b) nickel and elements with more than two p electrons per atom.
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
310
Table Ni-II Comp arison of experimental and calculated values for the heat of formation, A H for, of nickel compounds. Published experimental A,~ for values for the entropy of formation, ~ A.~for exp, have been added. The units for A H f°r and - - e x p are kJ (mole of atoms) - l and J (K mole of atoms) - l , respectively. System
Compound
A ~ -m- for exp
At-/'for Lx~~ calc
Ni-Ti
NiTi 2
- 27 298 K - 29 1202 K 28 298 K
- 40
- 34 298 K 34 298K - 32 (AG) 1300 K - 37 (AG) 1320 K 34 1450-1475 K 33 298 K
- 52
- 35 298 K - 54 1100-1300 K - 44 (AG) 1300 K - 41 (AG) 1320 K 43 1513 K 35 298 K
- 37
- 2 1 (AG) 1320 K
- 17
A.~ for ~ exp
-
NiTi
-
Remarks
1
calorim.
3,4
assessm.
117-19
calorim.
1
calorim.
118 28
emf 1150-1350 K calorim.
-
- 12 1100-1300 K
6 3-5
assessm.
117-19
calorim.
1
e mf
7
e mf
28
emf 1150-1350 K calorim.
-
6 3,4
assessm.
-
Ref.
calorim.
e mf
-
Ni3Ti
Method
117,19
Ni-V
NiV 3
Ni-Cr
Ni20Cr80
+ 8.0 1100-1500 K
- 5
+ 8.1 1100-1500 K
assessm,
boe sol. soln
8
Nis0Cr50
+ 6.4 1550 K
- 10
+ 9.3 1550 K
assessm,
foe sol. soln
1
Ni60Cr40
+ 3.6 1073-1448 K + 3.6 1100-1500 K +5 1123-1273 K
- 9
assessm,
foe sol. soln
11
assessm,
foe sol. soin
8
e mf
foe sol. soln
107
+ 0.6 1523 K +8 1123-1273 K
- 6
calorim,
foe sol. soln
17
emf
foe sol. soln
107
- 14 1050 K 14 1023 K 11 (AG ra) 1050 K
- 12
assessm,
sol. soln
1
emf 950-1150 K emf 950-1348 K
sol. soln
12
sol. soln
98
Ni7sCr25
Ni-Mn
NisoMnso
-
-
emf 1150-1350 K
+ 8.2 1100-1500 K +9 1123-1273 K
+9 1123-1273 K + 3.7 1050 K +4 1023 K
6
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table N M I
(continued)
System
Compound
Ni-Fe
NisoFeso
AH~,
AH~[ c
- 3.9 1200 K -3.7 ~-1200 K -4.6 1223-1373 K -2.4 1273 K
- 2
^.~ _ _ ~for p
+5.0 ~-1200 K
+ 6.3 1273 K
- 1.3
1273 K -5 1473 K -3.2 1523 K - 5.4 1550-1700 K
xs) 1573 K -5 ~-1370 K -3.6 T unknown
- 2.5 ( A G
Ni-Co
Nis0Cos0
+ 0.0 1400 K
+5.1 0
+0.6 1600 K
+6.5 1600 K
+0.9
Method
Remarks
calorim. +
sol. soln
1
assessm. assessm.
sol. soin
15
e mf
sol. s o l n
e mf 1173-1373 K e mf 1023-1423 K yap. press.
sol. soln
13
sol. soln;
2O
see also[21,22] sol. soln
16
calorim.
sol. soln
17
yap. press.
sol. soln
10
equilibr.
sol. soln
9
calorim.
2
assessm.
sol. soln; from A H mix sol. soln
calorim.
sol. soln
vap. press. 1480-1720 K calorim.
sol. soln; see also [ 24 ] sol. soln; from A H mix
~- 1780 K Ni-Y
311
NiY3
- 33 887-1224 K -19 298 K
- 23
- 35 887-1224 K -30 298 K
- 37
-35 887-1224 K -37 298 K
-44
- 31 887-1224 K -39 298 K
- 45
-29 88%1224 K -37 298 K
- 37
- 28 887-1224 K -35 298 K
- 34
Ni4Y
- 25 887-1224 K
- 30
NisY
- 34 298 K
- 26
Ni2Y 3
NiY
Ni2Y
Ni3Y
NiTY2
- 8.6 887-1224 K
emf calorim.
- 6.8 887-1224 K
e mf calorim.
-5.1 887-1224 K
e mf calortm.
- 2.5 887-1224 K
e mf calorim.
- 1.7 887-1224 K
e mf calorim.
- 1.6 887-1224 K
e mf calorim.
- 1.6 887-1224 K
e mf calortm.
Ref.
106
14
1
23 25
100 112-13 100 112-13 100 112-13 100 112-13 100 112-13 100 112-13 100 102-04
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
312 Table Ni-II System
(continued) Compound
A f°r ~ -/-- / exp
AH~[ c
31 298 K -21 887-1224 K
NilTY 2
Ni-Zr
- 16
- 37 298 K - 37 1230 K
- 53
- 49 298 K - 72 1300 K - 52 1405 K
- 72
Nil0Zr7
- 52 298 K
- 73
Ni2Zr
- 70 1300 K
- 68
Ni3Zr
- 67 1300 K
- 55
NiTZr 2
- 46 298 K
- 50
NiZr
Method
Remarks
calorim.
- 13 887-1224 K 19 298 K
NiZr 2
A.K' r°r ~ exp
Ref. 112-13
- !.5 887-1224 K
emf
100
-0.9 887-1224 K
emf
100
calorim.
112-13
calorim.
29
calorim,
+ 1.7 1300 K
see a l s o [ 115 ]
4,27
calorim.
29
emf
30
calorim,
see also [ 115 ]
4,27
calorim.
29
- 0.3 1300 K
emf
30
- 8.4 1300 K
emf
30
calorim.
29
calorim,
- 4 0
see a l s o [ 115 ]
4,27
1670 K NisZr
- 35 298 K - 48 1300 K
- 38 - 6.0 1300 K
calorim.
29
emf
30
calorim,
- 3 2
see a l s o [ 115 ]
4,27
1479 K Ni-Nb
NiNb
- 23 298 K - 35 (AG) 1220 K -42 1250 K
- 45
- 32 298 K 40 (AG) 1220 K -39 1250 K 24 1273 K
- 32
- 1.0 973 K 2.7 1073-1183 K -2.8 1193-1348 K + 8.2 1323 K
- I1
Ni3Nb -
Ni-Mo
NiMo
calorim.
- 5.2 1250 K
emf 1050-1370 K emf
1 32 51 a/o N i
caiorim.
+ 1.7 1250 K + 0.5 1273 K
+ 1.3 1073-1183 K + 1.0 1193-1348 K + 9.0 1323 K
31 1
emf 1050-1370 K emf 1273-1373 K emf 1050-1370 K
32 31,33 34
calorim.
48 a/o N i
35
emf
54 a/o N i
38
emf
54 a/o N i
38
emf 1223-1373 K
37
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-II System
313
(continued) Compound
A/-/ f°r - - - exp
AH~[ c
A,~ 'f°r ~ exp
+0.2 1473 K +0.8 1573 K - l.l
Method
Remarks
Ref.
calorim.
49 a/o Ni
36
calorim.
48 a/o Ni
35
assessm.
48 a/o Ni
114
298 K Ni3Mo
Ni4Mo
- 2.6 1073-1183 K + 8.0 1323 K
- 8
- 0.6 I073-I133 K + 7.3 1323 K 3.7 298 K
- 7
+ 1.1 1100 K + 3.9 1400 K + 1.9 unknown
- 1
+ 1.2 1073-1183 K + 9.6 1323 K
emf
38
emf 1223-1373 K
37
+ 2.9 1073-1133 K + 9.2 1323 K
emf
38
emf 1223-1373 K assessm.
37
-
Ni-Rh
NisoRhs0
T
+ 8.3 1100 K + 8.4 1400 K
emf 920-1370 K emf 870-1530 K calorim,
assessm,
Ni-Pd
Nis0Pds0
-0.5 1273 K
0
Ni-La
NiLa 3
- 13 298 K
- 19
calorim.
NiLa
- 15 298 K 28 298 K - 25 298 K
- 38
calorim.
Ni t.4La
- 29 298 K
- 40
Ni2La
- 20 298 K 30 298 K -23 1095 K
- 39
- 21 298 K - 28 298 K -26 1080 K
- 33
- 26 298 K -24 1035 K
- 30
- 21 298 K - 21, - 22 298 K - 26, - 27 298 K
- 24
+ 0.0 298
-
Ni7La 2
NisLa
sol. soln
39
sol. soln
41
sol. soln
40
sol. soln
I
42 52 a/o Ni
43
estimate
44
calorim.
42
e mf 805-950 K
44
caiorim.
45
e mf 947-1068 K calorim,
44
K
+ 0.3 298 K
- 0.8 298 K
-
Ni3La
+ 7.6 1273 K
114
- 0.6 298 K
+ 0.0 298 K
da t a for La N i 5 used from [ 43 ]
109
calorim.
43
emf 1124-1193 K calorim,
44
e mf 1023-1134 K calorim,
da t a for La N i 5 used from [ 43 ]
109 44
da t a for L a N i 5 used from [ 43 ]
109
calorim.
43
calorim.
46,93
calorim.
103-05
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
314 Table Ni-II System
(continued) Compound
A / / f °e xrp
~-"
AH~c
- 28 298 K - 24 298 K - 26 298 K - 27 298 K Ni-Hf
Ni-Ta
+ 0.7 298 K
Method
Remarks
Ref.
calorim.
19
emf 1104-1194 K calorim.
44
+ 0.6 298 K
calorim.
42 AS from C_ f r o m [ 95 ] e
26
NiHf 2
- 47 298 K
- 46
0.0 298 K
assessm.
116
NiHf
- 65 298 K
- 63
0.0 298 K
assessm.
116
Nil0Hf7
- 63 298 K
- 63
0.0 298 K
assessm.
116
NisHf2
- 57 298 K
- 54
0.0 298 K
assessm.
116
N i T H f2
- 52 298 K
-44
0.0 298 K
assessm.
116
NisHf
-42 298 K
- 33
0.0 298 K
assessm.
116
Ni2Ta
- 39 1173-1323 K 20 1240-1320 K - 36 1700 K
- 39
+ 1.0 1173-1323 K + 9.9 1240-1320 K
- 29 i 173-1323 K -20 1220-1320 K
- 31
-
Ni3Ta
Ni-W
A'K' f°r
emf emf
47 see also [ 85 ]
48
calorim.
97
+ 3. i 1173-1323 K +6.4 1220-1320 K
emf
47
emf
see also [ 85 ]
48
NiW
- 1.0 T unknown
- 5
+ 1.2 T unknown
assessm.
99
Ni4W
- 6.2 298 K 2.5 T unknown
- 2
+ 0.3 298 K + 1.1 T unknown
emf 1073-1273 K assessm.
49
-
99
Ni-Pt
Nis0Pt5o
- 9.3 298 K
- 7
+ 5.4 1625 K
assessm,
Ni-Th
Ni3Th 7
- 28 973 K
- 35
- 1.4 973 K
emf 841-1141 K
50
NiTh
- 45 973 K
- 56
- 2.4 973 K
emf 841-1141 K
50
Ni2Th
- 45 973 K
- 58
- 3.2 973 K
emf 841-1141 K
50
NisTh
- 43 973 K
- 35
- 7.1 973 K
emf 841-1141 K
50
NilTTh2
- 25 973 K
- 22
- 1.8 973 K
emf 841-1141 K
50
NiU 6
-21 1000 K
- 14
- 10 1000 K
emf 1073-1173 K
51
NiTU 5
- 55 1000 K
- 43
- 23 1000 K
emf 1073-1173 K
51
Ni-U
sol. soln
1
A.K. Niessen et aL / Enthalpies of formation of Ni alloys Table Ni-II
System
(continued)
Compound
AHfor - - - exp
Ni2U
- 54 1000 K - 32 1023 K
- 40
Ni77U23 6-phase
- 54 1000 K
- 30
NiTaU22 8-phase
- 53 1000 K
NisU
AH~[ c
51
- 29
- 19 1000 K
emf 1073-1173 K
51
-46 1000 K -44 1000 K - 30 1023 K
-22
- 16 1000 K - 16 1000 K
emf 1073-1173 K emf 1073-1173 K
-12
52
82 a/o Ni
+ 1.8 973 K + 2.0 1273 K + 2.4 1173-1373 K +2.3 1350 K
+5
+ 7.6 1150 K +8 293 K
+ 11
- 2 9 (AG) 1100 K - 26 298 K
-5
- 4 1 (AG)
-9
-1.2 951-1097 K + 4.7 973 K +4.8 1273 K
+ 8.6 1150 K
51 51
calorim.
NisoCuso
NiB¢
Ref.
emf 1073-1173 K
Ni-Cu
Ni5B¢21
Remarks
- 19 1000 K
-8.8 951-1097 K
Ni-B¢
- 19 1000 K
Method
51
NitTPU 2
NisoAUs0
A.~ for ~ exp
emf 1073-1173 K calorim.
Ni-Pu
Ni-Au
315
52
emf
ref. st. < P u >
53
assessm,
sol. soln; see also [ 89 ] sol. soln
1
emf 1173-1373 K emf
37
sol. soln
106
yap. press,
sol. soln
108
assessm,
sol. soln
1
caiorim,
sol. soln
54
assessm.
20 a/o Ni
1
calorim.
55
assessm.
1
calorim.
55
calorim.
1
1100 K
- 42 298 K Ni-Mg
NiMg 2
Ni2M8
Ni-Ca
- 13 298 K - 13 923-1033 K
- 6
- 18 298 K - 21 923-1033 K
- 8
+ 0.4 923-1033 K
vap. press,
ref. st. < Mg >
calorim.
56 1
- 4.2 923-1033 K
yap.press,
ref. st. < Mg >
56
Ni2Ca
-19 900-1150 K
-11
-9.7 900-1150 K
emf
ref. st. < C a >
94
Ni3Ca
- 16 1050-1350 K
-9
-7.1 1050-1350 K
emf
ref. st. < C a >
94
NiTCa 2
- 14 1050-1350 K
--8
--6.0 1050-1350 K
emf
ref. st. < C a >
94
NisCa
- 10 1050-1350 K
-6
-3.7 1050-1350 K
emf
ref. st. < C a >
94
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
316 Table Ni-II
(continued)
System
Compound
A ~ -H- for
Ni-Zn
NiZn 8
- 6.4 355 K 12 (AG) 623 K
- 7
- 15 355 K 18 (AG) 623 K - 18 753 K
- 11
e x p
-
NisZn21 v-phase -
-
2
AH~c
-
NiZn 3 yl-phase -
~
e x p
-3.5 973 K
- 14
- 19 355 K 22 (AG) 623 K - 22 753 K 27 773 K 20 905 K - 27 973 K
- 23
- 16 1100 K (AG) 1100 K - 18 1100 K 18 (AG) 1113 K
- 23
-2.5 753 K
-
-
-
NiZn //-phase -
-
1
9
ref. st. < Z n >
emf 973-1153 K assessm.
59 58
20 a/o Ni; ref. st. < Z n > ref. st. < Z n >
59
f r o m [ 58 ]; ref. st. < Z n > ref. st. < Z n >
90
25 a/o N i
57
61 1
vap. press, 993-1113 K
ref. st. {Zn}
60
calorim.
26 a/o N i
58
vap. press, 623-873 K emf 693-873 K vap. press,
ref. st. < Z n >
59
23 a/o Ni; ref. st. < Z n > f r o m [ 58 ]; 26 a/o Ni; ref. st. < Z n >
57
calorim.
- 2.8 753 K
-
vap. press. 623-873 K emf 693-873 K yap. press,
Ref.
58
calorim.
1
- 16 355 K 20 (AG) 623 K 19 753 K 22 773 K
Remarks
calorim.
-3.4 753 K
-
NiZn f/t-phase
Method
vap. press, 623-873 K
773 K -18 973 K 15 (AG) I100K 15 (AG) 1113 K
-
A.~ for
yap. press, 623-873 K emf 693-873 K vap. press,
90
58 ref. st. < Z n >
59
ref. st. < Z n >
57
f r o m [ 58 ]; ref. st. < Z n > ref. st. < Z n >
90
+ 0.2 905 K - 6.9 973 K
vap. press,
62
emf 973-1153 K
ref. st. < Z n >
61
+ 2.1 1100 K
vap. press, 1054-1150 K assessm,
ref. st. < Z n >
62
ref. st. < Z n >
1
calorim,
ref. st. < Z n >
63
vap. press, 971-1113 K
ref. st. {Zn}
60
Ni69Zn31
- 6.2 (AG xs) 1067 K
- 19
vap. press,
sol. soln; ref. st. < Z n >
Ni75Zn25
- 8.5 355 K 14 773 K
- 15
calorim,
sol. soln
58
yap. press,
f r o m [ 58 ]; sol. soln; ref. st. < Z n > ref. st. < Z n >
90
-
-
- 8.5 II00K 12 (AG) 1200 K
calorim, - 15
vap. press,
sol. soln; ref. st. {Zn}
110
63 91
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table N i - I I
(continued)
System
Compound
A for - - -I-4 exp
AH~[ c
Ni-Hg
NiHg 4
- 9.1 298 K -8.7
+ 1
443-505 K
N i - B
A.g' for ~ exp
- 15 298 K - 13
Method
Remarks
Ref.
emf 293-503 K y a p . press,
ref. st. < H g >
64
ref. st. < H g >
65
443-505 K
NiHg 3
- 7.2 298 K
+ 1
- 11 298 K
emf 293-503 K
ref. st. < H g >
64
NiHg 2
-7.2 298 K
+ 1
- 13 298 K
emf 293-503 K
ref. st. < H g >
64
NiB
- 50 298 K
- 33
calorim.
A H selected in [ 117]; see a l s o [ 119 ]
66
- 20 1385 K 23 298 K Ni4B 3
Ni2B
Ni3B
Ni-AI
317
NiAI 3
- 45 298 K
NiAI
Ni3AI
- 32
67
assessm.
88
26 298 K
- 4.2
assessm,
A H selected in [ 117]; see a l s o [ 119 ] monoclinic
- 26 298 K
- 3.9
assessm,
orthorhombic
- 23 1385 K 21 298 K
- 27
- 22 298 K
- 21
- 38 298 K 38 298 K - 56 980 K - 33 (AG)
- 28
1127
Ni2A13
- 3.7
calorim.
calorim.
66
88
88
calorim.
67
+ 0.2
assessm.
88
- 1.9
assessm.
88
assessm.
I
assessm.
117-19
+ 8.2 980 K
emf 933-1030 K emf
29 % Ni; ref. st. < A I >
69 68
K
- 57 298 K 57 298 K -70 298 K
- 43
- 59 298 K 59 298 K -67 980 K - 63 298 K -67 II00K - 71 1023 K
- 48
-41 298 K
-33
+4.3
+ 1.4 980 K
assessm.
1
assessm.
117-19
emf
39 % N i
69
assessm.
1
assessm.
117-19
emf 933-1030 K not given
51 a/o Ni; ref. st. < AI >
calorim,
ref. st. < A I >
70
calorim. assessm.
69
71,72 52
73 a/o N i
1
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
318 Table Ni-II System
(continued) Compound
A t- 4" f eox p r
AH~r~[c
A,q efor xp ~
38 298 K - 3 5
+ 0.5 980 K
Ref. 117-19
assessm.
77 a/o Ni
emf 633-1030 K
ref. st. < AI >
1 69
Ni3Ga7
- 34 300 K
- 25
calorim.
39,73
Ni2Ga 3
- 45 300 K
- 33
calorim.
39,73
NiGa
- 38 300 K 47 298 K - 43 1023 K - 43 1223 K
- 37
calorim.
39,73
calorim.
74
- 36 300 K 45 298 K
- 37
- 23 300 K 28 298 K - 33 1223 K
- 27
Ni3In 7
-21 673 K
Ni21n 3
Ni3Ga2
Ni3Ga
Ni-In
Remarks
assessm.
298 K - 47 980 K Ni-Ga
Method
Niln
Nil3In 9
Ni2In
e-phase Ni3In
- 2.9 1223 K
caiorim,
ref. st. < G a >
92
emf 1073-1273 K
ref. st. < G a >
75
calorim.
39,73
calorim.
74
calorim.
39,73
calorim.
74
- 5.2 1223 K
emf 1073-1273 K
ref. st. < G a >
75
-8
- 10 673 K
emf 633-943 K
ref. st. < I n >
76
-25 673 K - 23 850 K - 26 1060 K
- 10
- 10 673 K - 7.6 850 K
emf 633-943 K emf 633-943 K calorim,
ref. st. < I n >
76
ref. st. < I n >
76
ref. st. < I n >
77
-25 673 K - 22 850 K - 25 1060 K
- 12
emf 633-943 K emf 633-943 K calorirn,
ref. st. < I n >
76
ref. st. < In >
76
ref. st. < In >
77
- 17 850 K - 20 1060 K
- 13
emf 633-943 K calorim,
ref. st. < In >
76
ref. st. < In >
77
- 17 760 K 12 800 K 18 1060 K
- 12
ref. st. < I n >
78
see also [ 79 ]
1
calorim,
h i g h - T phase; ref. st. < I n >
77
- 13 673 K - 14 760 K
- 10
emf 633-943 K emf 663-873 K
ref. st. < I n >
76
ref. st. < I n >
78
- 10 673 K - 6.7 850 K
- 2.7 850 K
-4.9 760 K +0.9 800 K
- 12 - 3.8 673 K -4.2 760 K
emf 663-873 K assessm,
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-II System
(continued) Compound
f°r -A- f'/" - exp
AH~c
- 8.4 800 K - 13 850 K - 16 1060K Ni-C
Ni3C
A.q' f°r ~ exp + 2.2 800 K - 3.6 850 K
+ 8.5 298-1000 K
+7
+ 1.8 298-1000 K
+ 9.4 298 K
Ni-Si
Remarks
assessm,
see also [ 79 ]
1
emf 633-943 K calorim,
ref. st. < In >
76
ref. st. < I n >
77
assessm.
Ref.
87 117
NiSi 2
-31 298 K
-17
-0.7 298 K
a$~sm.
see also [ 2 ]; assessed AH selected in [ 117]; see also [ 119]
80
NiSi
-45 298 K
-33
-2.1 298 K
a$~sm.
see also [ 2 ]; assessed AH selected in [ 117]; see also [ 119 ]
80
calorim.
101
- 46 298 K
- 35
a&sessm.
see also [ 2,119 ]
80
- 48 298 K < - 36 (AG) 1273-2073 K
- 32
asse$sm.
see also [ 119]
80
Ni5Si 2
- 42 298 K
Ni3Si
Ni3Si 2 Ni2Si
equifibr. + phase d i a g r .
96
- 29
as~sln.
80
- 36 298 K
- 26
a$~sm.
31 (AG) 1273-2073 K
- 18
equifibr. + phase diagr.
NiGe
- 32 330 K
- 20
calorim.
Ni2G¢ 8"-phase
- 27 1060 K -29 1060 K -30 330 K -37 298 K -30 1060 K
- 21
calorim.
-21
calorim.
-21
calorim.
- 25 330 K -31 1060 K
- 17
- 25 1060 K -34 1023 K -34 298 K
-
Ni5Si
e'-phase e-phase
Ni3Ge
Ni-Sn
Method
assessm.
-42 298 K
Ni-Ge
319
Ni3Sn4
< -
calorim. calortm.
20
77 a/o Ni
80 96
39,73 high-T phase; 58 a/o Ni high-T phase; 61 a/o Ni high-T phase; 64 a/o Ni AH selected in[ll7] high-T phase; 64 a/o Ni
81 81 39,73 82 81
calonm.
76 a/o Ni
39,73
calorim.
76 a/o Ni
81
calorim.
ref. st. < S n >
81
calorim. ~$m.
52 117-19
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
320 Table Ni-II System
(continued) Compound
f°r -A- /-4 ,xp
Ni3Sn 2
-31 293K -39 298K -32 1060K -39 1023K
- 24
-23 293K -26 1060K -26 298K
-19
Ni3Sn
AH~[ c
A.~' f°r ~ exp
Method
Remarks
1
caionm. caiorim. calonm.
Ref.
A H selected in [ 117,119] ref. st. < Sn >
82 81
calorlm.
52
caionm.
1
caiorim.
ref. st. < Sn >
81 117-19
assessm.
Ni3N
+0.2 292K
+6
calorim,
Ni-P
NiP 3
-41 298K 39 298K
- 28
assessm.
117
assessm.
119
-48 298K -43 298K
- 42
assessm.
117
assessm.
119
-57 298K 51 298K
- 62
assessm.
117
assessm.
119
62 298K 55 298K
- 56
assessm.
117
assessm.
119
-62 298K -56 298K
- 50
assessm.
117
assessm.
119
55 298K -67 298K
- 45
assessm.
117
assessm.
119
36 298K
- 47
-
NiP 2
Ni6P 5
-
Ni2P
-
-
NisP 2
Ni3P
Ni-As
NiAs
-
-
A H selected in [ 117 ]; see also [ i 19 ]
calorim.
34 298K -
Ni-Sb
calorim.
ref. st. (NE)
83
Ni-N
84
NiSb 2
-26 298K
- 14
calorim.
32 a/o N i
NiSb
-42 298K
- 20
calorim.
A H selected in [ 117]; see also [ 119 ]
- 3 2
298K -33 1060K
calorim. calorim,
82
1
82
1
see also [ 111 ]
86
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-II System
Ni-Bi
321
(continued) Compound
AH~,
Ni3Sb
- 18 298 K - 18 1060K
- 18
- 3.9 298 K
- 4
NiBi
AH~[ c
^.~ exp for - - - -
Method
Remarks
calorim.
77 a/o Ni
calorim.
alloys. For the liquid alloys the two limiting enthalpies of solution are shown together with the heat of mixing of a regular mixture at equiatomic concentration. The reference states are those of the pure solid metals for the solid compounds while for the liquid alloys reference is made to the pure liquid metals. In these tables the information on each of the phase diagrams shown in figs. 1 and 2 is summarized characteristically by one of the following symbols: - - three or more compounds stable at low temperatures (indicating that AH f°r is large and negative); one or two compounds stable at low temperatures (indicating that AH f°r is negative); c - continous solid solubility at high temperatures and one or more ordered alloys at low temperatures (indicating that AH ~or is negative but closer to zero than in the foregoing cases); c continous solubility at all temperatures or a large solid solubility at low temperatures for at least one of the constituents if the crystal structure is different for the two constituent metals (indicating that AH f°r is approximately zero); c+ continous solubility at high temperatures and a miscibility gap at low temperatures (indicating that AH f°r is small, but positive); + no compounds and both solubilities smaller than 10 "/o (indicating that AH f°~ is posifive); ? the available information is contradictory. In a few cases it has been impossible to distinguish clearly one of these characteristics; the most probable one is then placed between brackets. This
calorim.
Ref. 1 86
AH selected in [ 117]; see also [ 119 ]
82
applies particularly to the simple quotations:
2.
Nickel alloys
Table Ni-Ia and table Ni-Ib make it possible to compare in a qualitative way the predicted values for the enthalpy effects in solid and liquid alloys Table 1 Qualitative comparison o f AH ~[c at equiatomic composition in kJ (mole o f atoms) - l with phase-diagram information System
AH ~ c
Phase-diagram information
Ni-Sc Ni-Cd Ni-Ir Ni-Sr Ni-Ba Ni-Tc Ni-Ru Ni-Li Ni-Os Ni-Pb Ni-Re Ni-TI Ni-Ag Ni-Na Ni-K Ni-Rb Ni-Cs
- 57 - 8 - 2 - 1 0 + 1 +1 + 1 +2 +2 +3 +4 + 18 +46 + 59 + 59 + 59
five compounds two compounds solid solubility one compound no compounds; liquid immiscibility solid solubility solid solubility o f Ni and Ru no compounds; liquid immiscibility solid solubility no compounds; liquid immiscibility solid solubility no compounds; liquid immiscibility no compounds, liquid immiscibility very slight solubility in {Na} very slight solubility in {K} no information no information
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
322
Table Ni-III Comparison o f experimental and calculated values for the enthalpy of alloying o f liquid nickel alloys: the heats of solution AH°{Ni}, AHO{M} and the heat o f mixing A H e M ~. The reference states are those o f {Ni} and {M}; the heat o f fusion, AH fuse, used in a required conversion o f the reference state is g~ven. The unit o f all enthalpy values shown is kJ (mole o f atoms) - t . X
A/~°{Ni}
Sc
- 130
AHeM } - 39
AH°{M}
Method
- 180 147
prediction calorim. (1873 K)
-
Ti
- 126
-35
- 154 -207 183 - 184 ( - 190) - 188 -
( - 105) - 113
-44 -38 -38
- 1 4 8
V
Cr
-69
- 18
- 27
- 7 -4.3
- 33 (-31) (-36)
-
32
- 35 -36 -64 -6
Fe
(-18) 10 -
(-8.6) (-6.3)
- 8 - 11 -2.6 - 6.0
-
10
-
23
- 18 --2 -4.2 -2.1 -7.5 -4.2 +3.9 -5.8 -4.2 -5.2
assessm. (1823-1973 K)
- 134,- 180
assessm. (1873 K)
-75 - 107 -70,-95 (-73)
lm~lletioa calorim. (1873 K) assessm. 0873 K) assessm. (1873 K)
- 27 - 14 -37 (-9.2) 14 +0.2 (-2.3) ( - 15) - 7 . 9 , - 11
prediction calorim. (1873 K) calorim. (1950 K) yap. press. (1873 K) yap. press. (1873 K) vap. press. (1873 K) emf (1873 K) assessm. (1823-1873 K) assessm. (1873 K)
-
Mn
~edietion calorim. (1786-1803 K) calorim. (1873 K) calorim. (2000 K) yap. press. (1748-1973 K) assessm. (1100-2000 K)
- 33 (-49) (-23) <0
-
49
- 53 -47 -77 0 -6 (-21) (-41) -34 (-20) (-21) (-21)
prediction calorim. (1773 K) yap. press. (1310-1900 K) emf ( 1573 K)
emf (1683 K) equilibr. ( 1743-1893 K) equilibr. 0843 K) equilibr. (1893 K) assessm. (1200-1800 K) assessm. (1873 K) prediction calorim. (1773 K) calorim. (1803 K) calorim. (1813-1853 K) calorim. (1839 K) calorim. (1873 K) calorim. (1873 K) calorim. (1873 K) calorim. (1873 K)
Remarks
Ref.
168 A H ~ se : 15 A H ~ : 15 AH mix at 55 a/o Ni values at 1873 K A H ~ : 17.6; A H ~ : 16.2 AGo xs at 1873 K; AH~f~ : 15
189 3 4 5 178-79 184 6
AH(/se : 21 A~-o xs A H ~ r : 17 A H ~ r : 17 A~o xs AGo xs; AH~er : 17 A~-O xs A~o xs at 1873 K see also [ 12,176]
values at 1750 K AG xs; value at 50 % N i derived from AG ~fvln} AG xs A~'o xs A~-o,~
46 a/o Ni, 5 a/o C
3 6 184 3 8 7 10 131 11 184 6 9 142 13
133 132 132 132 156 6,184 136 30 14 16 15 17 18 136
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-III
X
(continued)
A/~°{Ni} +9.1
-6.9 - 10 (-76) ( - 10) -30
-6.5 -1.1 -6.5 -5.4
-4 -5.6
( - 30) - 18 ( - 10)
AH ~ v l }
AH°{M}
-6.4
-5 -3.0 -4.6 -33 -4.4 - 10 -2.8
-16 -32 (-140) (-23) -45 - 14 -14 - 11 -24 -24
-2.2 -2 -2.7 -9.5 -5.6 -4.9
-46 (-20) - 16
7.5
- 2.8
-6.5, - 8.8 (-9.5) -6.5 -6.5
-5.1 -2.7
16, - 2 2 (-27) -14
- !3
- 5.0
- 25
- 10
- 5.0
-
-
Co
- 16 -
0
0
-1
0
( + 1.2)
+ 0.4
25 0 -I
( + 1.2)
+0.3 ( + 1.3)
+0.4
-~0 +2.4 - 12 (+8.4) +3.3
"0 +0.6 -4.6 -0.4
(+
1.7)
~-0 +2.4 - 13 (-0)
+0.8
+3.3
-12 -9.9 Y Zr
Method
Remarks
yap. press. (1630-1870 K)
values at 1833 K; AG xs; value at 5__0a/o Ni derived from AG ~qi} value at 1873 K AG xs at 1873 K values at 1873 K
yap. yap. yap. yap. yap. yap. yap. yap. yap. yap. yap. vap. yap. yap. X-ray
press. (1750-1900 K) press. (1750-1900 K) press. (1773-1923 K) press. (1783-1873 K) press. (1800-1950. K) press. (1820-1950 K) press. (1825-1895 K) press. (1825-1930 K) press. (1873 K) press. (1873 K) press. (1873 K) press. (1873 K) press. (2174-2500 K) press. (2178-2558 K) (1833
assessm. (1873 assessm. (1873 assessm. (1873 assessm. (1873 assessm.
K) K) K) K)
calorhn. (1780 K) calorim. (1813 K) yap. press. (1480-1875 K) yap. press. (1773-1873 K) yap. press. (1873 K) yap. press. (1873 K) yap. press. (2174-2500 K) assessm. (1600-1900 K) assessm. (1873 K) assessm. (1873 K)
- 162
la~iaioa calorim. (1923 K)
- 165
-49
-237 - 202 -166
calorim. (1873 K) assessm. (1823-1973 K)
136
- 134
AG xs values at 2326 K
AG-°'s at 1873 K AG xs; see also [ 27,31,32 ] see also [ 163 ]
Ago xs
165
23 23 25 28 174 22 26 29 10 21 24 164 20 19 36 184 I 6 12 33 34 35 135 134
la~etim
(-48)
-
AG xs
assessm.
-11
- 30
values at 1873 K values at 1873 K AG xs at 1873 K value at 1873 K
assessm.
- 31
- 107
Ref.
K)
assessm. (1783-1973 K) assessm. (1873 K)
-97 ( - 17)
- 162,-220 Nb
323
values at 1800 K ; see also [40]
AGXS AH- / ~~ : 17.6; M 16.2
A~OXS
170 21 164 41 177-79 184 188
42 6 H f ~~ : 16.9 A~'o xs at 1873 K; AHf~ e : 16.9
assessm. (1873 K)
p~llceee calorim. (1873 K)
38 37 39
AH~:
26
3 184
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
324 Table Ni-III X
(continued) AH°{Ni} -
Mo
- 27
Pd
La
Hf
54
W
Pt
U
-26
AH°{M}
Method
Remarks
- 155
assessm. (1400-2800 K)
AH~ AH~
- 7
- 18
-4.4
0 +4.9 >0 (+4) +4.7 +5.0
0 +2.3 >0 +2.0 + 1.2 +2.3
- 32 -39
prediction solub. (1737-1973 K)
- 18
assessm. (1500-2800 K)
0 +5.3 >0 (+5) + 12 +5.0 + 8 . 1 , + 11
: 17.6; 22.9
178-80
A~-o xs at 1873 K; A H ~ o : 24.3 A H [ ~ : 17.6; AHk~oo 24.3
187 178-80
prediction calorim. (1873 K) vap. press. (1400-1873 K) e m f (1833-1973 K) assessm. (1873 K) assessm. (1873 K) asseasm. (1873 K)
see also [ i 84 ]
45 6
47
43 46
AG xs
44 1
-27 - 28
-146 - 172
prediction calorim. (1376 K)
AH~:
- 145
-42
- 58
- 204 -214 -216 - 293
wmlietion calorim. (1873 K) assessm. (1873 K) assessm.
A H ~ : 24 A H ~ : 26 AG xs
3 6 i 43
-29
-
133 -150 - 149
lmNlietion calorim. (1873 K) assessm. (1873 K)
A H ~ a : 32 A H ~ a : 31
3 6
-
105
-11
-3
-14 - 62
l~rt~lietion equilibr. 0873-1973 K) assessm. (1600-3700 K)
+40
+ 1.0
- 32
+ 16
-2.4
(+38) - 35
- 17 + 5.6
- 5 + 1.4 - 14
- 98
- 29
- 22 + 5.6
-
140
-44 Cu
Ref.
-81 - 54
- 167 Ta
AHeM }
+ 14 -2.5 + 5.4 + 11
+4
( + 1.6) ( + 15) + 17 (+5)
+ 2.8 -i.6 +4.3 +4.3 +2.3
+ 12
+ 3.0
- 3.5
- 2.9
+ 14
+ 11 + 17 + 17 (+8) + 12
assessm. (1873 K) assessm. (3000 K)
15.1
A~-o xs at 1873 K; A H ~ : 35 A H ~ : 17.6; A/-/~ 30.5 A ~ - o xs
AGXS; A H ( ~ :
178-80 184
46
prediction vap. press. (1733-2223 K) yap. press. (1877-1893 K)
values at 2073 K AG xs at 1877 K
prediction calorim. (1423 K)
AH~iSc~ : 17
prediefloa calorim. (1373 K) calorim. (1385 K) calorim. (1473 K) calorim. (1580 K) calorim. (1728 K) calorim. (1733-1763 K) calorim. (1748 K) calorim. (1753 K) yap. press. (1800-1873 K) ¢mf (1373-1673 K)
48
A H { ~ : 16.9 A H ~ : 15.1 A H ~ , ~ : 17.6
AG xs AG xs at 1673 K; A H { , ~ : 17.5
176
49 137
50
64 54,144 52,53 123 15 14 37 51 56 60
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-III X
(continued) A/7°{Ni}
AH~M}
AH°IM}
( - 67)
Ag
+0.9 +9.8 + 9.8
+ 1.4
( + 13) + 9.9
+3.5 + 2.9
+ 56 +75 + 100
+ 3.0
+ 15
+ 10 + 12 + 12 + 12, + 16 ( + 15) + 13 + 68
>0 Au
K Be
emf (1393-1523 K)
value at 1523 K; AH~e~ : 17
assessm. assessm. assessm. assessm. assessm. assessm. assessm.
(1200-1800 K) (1473 K) (1823 K) (1823 K) (1873 K)
la'ediefion solub. (1268-1638 K) solub. phase diagr,
+ 33
( + 14)
+2.9
(+8)
vap. press. (1600-1820 K)
(+2.1) ( + 12) ( + 14) + 15 ( - 7.1) (+8.0)
+0.8 + 3.6 +2.8 + 2.3 - 3.0 +2.2
(+3.8) ( + 10) ( + 14)
+3 +47 +40 + 100 +71 + 16
+1
+3
+ 100 - 11 -8.0 + 18 +6.1 +3.4 +0 + 13
+32
+ 123 +42
+ 45
-19
-4
+ 140
+ 235 -15
-74 Mg
Remarks
+7 +2.2 (+3.5) +2.2
>0 Na
Method
+ 25 (+8.0) + 12 ( + 18)
+7.0 Li
325
-13 -56
-4
-16
pcedietioa calorim. (1369 K) calorim. (1378 K) calorim. (1383 K)
Ref.
see also [ 32,58,59 ] AG xs; see also [ 32,57 ] A~o xs
AH~t~e~ : 17.6 liquid immiscibility
141 156 61 1 184 6 55 166 62 63 2
yap. press. (1600-1820 K) yap. press. (1600-1920 K) yap. press. (1623 K) emf 0400-1500 K) equilibr. (1523-1608 K) assessm. (1369 K) assessm. 0733 K)
AH~e~ : 17.5 AH~'et : 15.1 AH mix at 42 a/o Ni; A H ~ : 16.9 values at 1732 K; see also [ 68 ] AG xs at 1732 K values at 1820 K AG xs values at 1450 K AG xs at 1608 K AH~]~e~: 17.5 AG °xs
145 65 67 70 71 l 184
la~lletion solub. (923-1153 solub. (953-1153 solub. (973-1223 solub. (813-1098 solub. (873-1473 phase diagr,
AH~e~ : 17.5 AH{]~e~ : 17.5 AH~e~ : 17.5 AH~e~ : 17.5 AH~e~ : 17.5 liquid immiscibility
73 73 73 73 155 147,155
K) K) K) K) K)
la~lietltea solub. (473-873 K) solub. (505-783 K) solub. (719-873 K) solub. (719-873 K) solub. (873-1273 K) solub. (973-1187 K) solub.
AH~e~ : AH{~e~ : AH~e~ : AH~e~ : AH~: AH~e~ : AH~e~ :
lwedktiea solub. (933-1343 K)
AH~
wedktioa equilibr. (1623 K) ln'edlktlea calorim. (981 K, II20 K)
72 138 64 69
17.5 17.6 17.5 17.5 17.5 17.5 17.5
73 146 74 73 158 73,159 161-62
: 17.5
73
AG°~; AH~e~ : 17.6
148 77,140
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
326 Table Ni-III X
(continued) AH°{Ni}
AH~M}
AH°{M}
-42 (-38)
-14 ( - 10)
- 22 - 17
- 7
- 37 - 13
- 13
-0.9
+ 1 + 16
Ba
0
-8.0 ( - 7.4) - 7,8, - 11 + 1
>0 Zn
- 9 <0
- 36 -60...-52 (-26)
+7 <0
+2
+9
+ 28
+ 8
-
Cd
Hg
34
+ 40
+39 - 9
- 55
-25 - 12
- 101 (-73)
- 82 157 - 157 - 155 - 157 - 160 - 154 -166
- 22
- 97
-
-146
( - 138)
-49
- 136
- 50 -25
-22 - 151 -156
vap. press. (923-1023 K)
A~-o xs at AH~ : values at AH~e~ : A~-o xs at
assessm. (923-1123 K ) assessm. (1000 K ) lm~lletloa calorim. (1120 K) yap. press. (1737-1766 K) e m f (1050-1350 K)
assessm. (1750 K) assessm. (I 750 K) assessm. (1873 K)
(-5.4) ( - 32)
- 148 - 162
(-22) ( - 109)
Ref. 1000 K; 17.5 1373 K; 17.5 1023 K
A~-o xs
1,75 76 184 1
A~'o xs at 1753 K AG xs at 1200 K and at 45 a/o Ni; AH~[~¢~ : 17.5; A H ~ aa : 8.5 AG xs AG-* xs
77,140 66 157
1 184 6
predietion solub. (1073-1473 K) phase diagr,
AH~e~ : 17.5 liquid immiscibility
lm~dletlon yap. press. (ll00-1300 K) yap. press. 0 7 4 8 K)
AG xs AG"°xs
79 78
prediction vap. press. (823 K)
A~-o xs
173
155 i 47,155
prediction
solub. (373-483 K) solub. (667-1023 K)
+ 5
Al
Remarks
e m f (973-1423 K)
-42 Ca
Method
AH[,~¢~ : 17 AH~: 17
80 81
prediction
calorim. (1838 K) yap. press. (1400-1750 K) assessm. (1873 K) prediction calorim. (948 K) caiorim. (952 K) calorim. (1000 K) calorim. (1023 K) calorim. 0 0 3 0 K) calorim. (1100 K) calorim. (1158 K) calorim. (1173 K) calorim. (1773 K) calorim. (1873 K) calorim. (1923 K) yap. press. (1750-2100 K) e m f (1100 K) equilibr. 0 8 7 3 K) assessm. (1173 K)
A H mix at 1600 K AG-°xs
AH~ AH~ AH~ AH~e~ AH~ AH~ AH[,~ AH~:
: : : : : : :
17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5
AG xs at 54 a/o Ni; value at 2000K AG xs AH~e~ : 17.5
82 191 184
86,149 139 88 85 190 84,87 167 150 89 3,90 83 91 92 93 160
A.K. Niessen et al. / Enthalpies of formation of Ni alloys Table Ni-III X
(continued) AH°{Ni}
AH~}
A/-~°{M} -
( - 70)
- 15
129,- 174 ( - 30) 133 -
In
+5 35 33 (-27) (-15)
+2
-
TI
+41 - 86 ( - 112)
( - 113) ( - 150) - 136 ( - 112) (-80) (-77)
-4.5 >0
(-15)
+!3 >0
+67
- 23 - 54 -56
- 98 ( - 188)
-54 -52
(-188)
-67 -54 -26 -36
(-200) (-148) (-142) 188 -
145
- 13 -49
129
-55
(-55)
-28
- 41 - 78 (-79) (-65) (-69) (-75) - 37
- 11
-
-
-
Ge
Sn
Method
Remarks
Ref.
assessm. (1873 K) assessm. (1873 K) assessm. (1873 K)
A~o xs
6 175 184
calorim. (1090 K) calorim. (1096 K) calorim. (1096 K) yap. press. (1248 K) assessm,
A H ~ : 17.5 AH~e~ : 17.5 AH~e~ : 12.6 AG ~ liquid immigcibility
186 94 95 96 151
phase diagr,
liquid immiscibility
2
+8
-
Si
327
( - 300) - 173 - 188 138, - 187 (-74) - 51
-38 -32 -26 -29
( - 117) (-53) ( - 132)
(-55)
-19
-32 -29 (-71)
- 13 -77...-66 -69...-61 -66 -59 -71...-67 -63 -60...-62 -61
-4
-21
lwe&ktlea calorim. (293 K,1873 K) calorim. (1400 K) calorim. (1750-1950 calorim. (1773 K) calorim. (1773-1823 calorim. (1793 K) calorim. (1873 K) emf (1753-1883 K) emf (1753-1883 K) emf (1753-1883 K) equilibr. (1853 K) asseum. (1773-1873 assessm. (1823-1873 assessm. (1873 K) assessm. (1873 K) assessm. (1873 K)
K) K) max. AH value AG ~ at 1753 K AG xs at 1883 K value at 1818 K AG~i } at 50 a/o Ni K) K)
l~¢~lctieo calorim. (1274 K) calorim. (1288 K) calorim. (1773 K) vap. press. (1623 K) yap. press. (1640-1920 K) equilibr. (1723 K) equilibr. (1723 K) assessm. (1723 K) assessm. (1873 K) lredlettoo calorim. (523-773 calorim. (621-770 calorim. (623 K) calorim. (623 K) calorim. (623-743 calorim. (698 K) calorim. (773-832 calorim. (775 K)
AH~e~ : 17.5; AH[[~e : 50.5
K) K)
K) K)
AG ° n at 1873 K see also [ 101,103 ]
AH~t~e~: 17.5 AH~e~ : 17.5 AG~; AH~e~ : 17.5 values at 1870 K AG °xs &G°~
AH~e~ : AH[]~e~ : AH[]~e~ : AH~: AH{~e~ : AH~el : AH~e~ : AH~e~ :
17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5
100 183 15 89 98 97 99 104 104 104 102 185 184 105 6 175 171 106 107 109 108 110 111 184 175 153 i18 117 154 115 127 112-13 150
328
A.K.
Table Ni-III X
N i e s s e n et
(continued) A/~° {Ni} -57 - 59 -57 -70 -56 -54 -53 -55 (-45) (-42) -42 -24 -70
AH ~M}
-20 -19 - 13 - 15
A/~°{M}
(-80) (-94) (-25) (-97) -26
Pb
+40 +9.0 + 36 8.9
+ 13
+ 73
+ 10 + 1.7 + 18 + 8.9 +8.8 + 42
Bi
+ 31 (+4)
- 19 + 10 +2.7
Remarks
calorim. (883 K) calorim. (910 K) calorim. (913 K) calorim. (914 K) calorim. (1023 K) calorim. (1078-1093 K) calorim. (1095 K) calorim. (ll00 K) calorim. (1580 K) calorim. (1773 K) vap. press. (1573 K) vap. press. (1573-1623 K) assessm. (600 K) assessm. (1573 K)
AH~e~ : AH~iSe~ : AH~: AH~el : AH~e~ : AH~e~ : AH~e~ : AH~i~e~ :
prediction calorim. (823 K) yap. press. (1703-1783 K) emf (973-1373 K)
Ref. 17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5
AG xs AG xs at 1573 K AH~: 17.2 A~o xs AH~Se~ : 17.5 A~o xs at 1750 K value at 1273 K; AH~e~ : 17.5 A H ~ : 17.5 AH~'~ : 17.5 AH~e~ : 17.5 A H ~ : 17.5 AH~'e~ : 17.5
120 114 116,121 119 85 94 182 122 123 124 126 125 152 184 127 181 172
A~o xs liquid immiscibility
73 73 169 73 128 63 184 2
- 93 (-96)
prediction yap. press. (1273-1423 K)
A~-o xs at 1423 K
129
+ 58 (+20)
lm~lietion emf (970-1170 K)
AG xs, evaluated at 1773 K
130
+ 5.2 - 65
Method
solub. (597-823 K) solub. (600-755 K) solub. (643-1000 K) solub. (645-1026 K) solub. (645-1517 K) solub. assessm. (1873 K) phase diagr,
>0 As
al. / Enthalpies of formation of Ni alloys
based on Ni with the available phase diagram information obtained from fig. 1 and fig. 2 and "translated" into qualitative information as described in sec. 1. In general the predictions are qualitatively in accordance with the information emerging from phase diagrams as can also be seen in tables Ni-Ia and Ni-Ib. This conclusion is confirmed by the additional information given in table 1 for the Ni-based systems whose phase diagrams are known, at least partly, in the absence of any useful experimental numerical thermodynamic information in the solid phase. By means of table Ni-II the experimentally observed enthalpies or free enthalpies of formation
which have been reported in the literature can be compared quantitatively with the predicted enthalpies of formation, while the predicted and observed formation enthalpies for liquid Ni alloys are collected in table Ni-III. In fig. 3 and fig. 4 this comparison is made more explicitly for ordered compounds by displaying the data from for vs ,Air-/" for plot. In fig. 3 table Ni-II in a AF']" ---exp ~,. ~¢ formation-enthalpy values of Ni compounds with transition metals are shown and in fig. 4 the formation-enthalpy values are presented for Ni compounds with non-transition elements. On the basis of fig. 3 and fig. 4 more or less similar conclusions can be arrived at for ordered
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
100
100
T
_AHfor "'exp
ii.'!J, /
/
/
/
,.for - AMcalc
-
Fig. 4. A H ~ [ versus A H ~ [ c (kJ (mole of atoms) -l) of ordered compounds of Ni with non-transition metals.
I&H C
/ /
/
5~
for I _&Hexp
50
/
!
/*
- ~Hfc°~
/
I/ i.i
for versus A H ~ foc (kJ (mole ofatoms)- 1) ofordered Fig • 3 , AHex p . . . . . . . . compounds of Nt with transttion metals, mcludmg actmtde, noble and alkaline earth metals.
100
~for -AMex p
5O
50
50
l
329
--)Ni-AI
/-"
/
//
/
/
/
/
Z
Z
z
/
,/
/
"
/
\
S
/,,
Ni_Sb~~~N/i/-Ga
/ //
Ni-ln /
^l_ifor
-'~f 'calc
~V
5()
forp and AH~.~[ fo c for some Ni-based Fig. 5. Comparison o f AHex systems indicating that the scatter in fig. 4 is caused, at least partly, by an incorrectly described concentration dependence of AH ~c-
-AHcalc
Fig. 6. Scheme to explain the loop-like curves as given in fig. 5 with the dependence of A H ~ [ c and A/4"for ---- exp on concentration.
330
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
Ni compounds as for the Co-based compounds; see [ 4 ]. In these figures A H r°r values are indicated by dots and AG r°r values by + signs, while the corresponding AG r°~ and A H f°r points have been connected by a line and an arrow pointing from A/.-/for towards A~r°r If one compound has been -- exp ~ v exp" subject o f more than one independent observations reported in the literature, the various experimental points have been connected by a drawn line, indicating the accuracy of the experimental data. Within the experimental uncertainty there is a fair agreement between prediction and experiment, certainly if ~A/4for values are not accepted -" cxp for ordered compounds with improbably large A.~ror exp values and the corresponding AG f°~ values are considered instead as a better alternative. In the following, more quantitative, discussion the thermodynamic properties o f a Ni-based alloy will occasionally be compared with those belonging to a similar alloy, but based on Co instead o f on Ni with the same partner metal, in order to elucidate some peculiar resemblances or differences in behaviour of these alloys of the two elements which are so similar as far as the values o f q~', n ws and V are concerned. F r o m the distribution of the points in fig. 3 and fig. 4, we may conclude that experiment and prediction agree satisfactorily. For Ni compounds with non-transition metals (fig. 4), in particular, we note that the experimental values tend to be more negative than the predicted ones while the rather wide scatter of the points suggests that the predicted concentration dependence is not confirmed by the experimental values, similar as for Co based alloys [ 4 ]. The latter is illustrated in fig. 5 where the points representing compounds in one and the same binary system are connected according to concentration. The meaning o f these loops can be understood from the schematically given difference in concentration dependence o f the predicted AH f°r and A- /-4 -f o r cxp in fig. 6. F r o m fig. 5 and fig. 6 it will be clear that, at least partly, the scatter shown in fig. 4 is related to an incorrectly predicted concentration dependence of A H r°r for these particular compounds. In sec. 4 we shall
come back to this point. For Ni compounds with other transition metals (fig. 3) there is indeed a satisfactory agreement, except for a number of cases with a strongly negative ,_.,,^ r~rfOrme.This set will contain the cases where the predicted enthalpy is overestimated due to a complete filling o f the d band at alloying. The general conclusions about the predicted enthalpies of Ni alloys are that we understand qualitatively the deviations for Ni with transition metals, and that further discussion is needed on the alloys with non-transition metals.
3. Alloys with Ni as minority element The more detailed discussion on the Ni-based systems with transition metals will firstly be concerned with the differences between predicted and experimentally observed enthalpies of formation if Ni is surrounded by more electropositive metals like La and Ti. In the model [ 5 ] it is proposed that the enthalpy o f formation contains two terms, a negative contribution stemming from the difference in ~b" and a positive one arising from the difference in n ws. The first contribution can be seen as arising from a charge transfer proportional to A~" over a difference in potential of -A~b'. However, the atomic cell with the highest electron potential ~b" can accept only a limited amount o f charge without drastic changes in the electronic configuration. Conversely, the atomic cell with the smaller electronegativity like Na or Ca cannot lose more than one or two valence electrons. The change in electronic configuration is reflected in a change o f the model parameters: if q~" is plotted versus Z, the number o f atomic valence electrons, ~" changes abruptly at the end of each d series, see fig. 7. Since there are several indications [ 7,8] that one electron will be transferred by a difference in potential of about 2 V, the empty d-electron states in Ni (about 0.5 electron per Ni atom) may be occupied upon alloying with a majority o f the partner metal which possesses a q~" such that l#*Ni -- (~" > 1 V.
A.K. Niessen et aL / Enthalpies of formation of Ni alloys
Iv] 5.0
/
3d series
./"'"
4.0 5
4d series 6
4
\
/
10
15
Fig. 7. ~* in r e l a t i o n to Z , the n u m b e r o f a t o m i c valence electrons for the three t r a n s i t i o n m e t a l series.
In view of the large differences in electronegativity in the systems of Ni with the transition metals Sc, Ti, V, Y, Zr, Nb, La, Hf, Ta, Th, U and Pu, these changes in electronic configuration may occur in the solid and the liquid state if Ni is sufficiently surrounded by these electron-donating metals. This effect is seen as a systematic deviation of the heat of solution, the prediction being too negative. Table Ni-III contains information about this aspect for the Ni-based systems with Ti, Y, La and U in the liquid phase. In the solid phase formationenthalpy values have been reported for Ti, V, Y, Zr, Nb, La, Ta and Th compounds with reasonably low concentrations of Ni (table Ni-II). The system Ti-Ni is very conclusive concerning this effect: in the liquid state (table Ni-III) the experimental heat of solution of Ni in liquid Ti appears to be less negative than the calculated one
331
and in the solid phase ~.a.,tAt/f°rcalc< ----expA/4f°rNiTi2 and NiTi (table Ni-II). As expected this effect is not present for NiaTi. It is also not observed for NiV3 since ¢ ' s i - ~b'v < 1 V. A large asymmetry is observed in the heat of solution in the liquid state for Ni-Y, but no conclusion can be drawn from solid-state data. Calorimetric measurements on Ni-Nb alloys indicate that here too a reduced enthalpy of formation is encountered: as expected, for the more Ni-rich compound Ni3Nb there is good agreement between calculation and experiment. Although the scatter of the experimental data is often large for Ni-Zr compounds the reduced formation enthalpy can be traced in the Ni-Zr system, too. The effect is also clearly observed in the Ni-La system, both in the solid phase and in the liquid phase. The data for Ni-Ta compounds could perhaps support the conclusion, too; unfortunately the data scatter widely. The trend is found indeed for Ni-Th, in particular, if one takes the AG f°r values in the solid phase for the latter system. The necessary reduction of ,~for '~,, ~c of Ni-based alloys with other transition metals appears to be well established if Ni is the minority partner in a relatively electropositive surrounding. If Ni is the minority partner the reduction of the enthalpy of alloying means a reduction of the negative contribution Air/for •~,, c~ ionic of aH~Ic: A r t for l i calc
--
a r J r for, ionic art zal~ calc -t- ~
for, pos calc ,
(1)
where (2) Upon accepting charge the electronegativity will drop more than average (Ni being the last one in the series of 3d-transition metals) leading to a lower value of the proportionality constant P. For AO" < 1 V this reduction is not present, but for larger values of AO" a drastic change may occur for alloys poor in Ni, as indeed can be observed if the experimental negative part, AF/for,ioaic calculated according to A/4" for, ionic "'exp
=
A r T for a r _ r for, pos - - - - exp - - za~, calc
(3)
A.K. Niessen et aL / Enthalpies of formation of Ni alloys
332
is plotted in relation to the calculated ionic part, AH~[; i°"~c. In fig. 8 where these quantifies related to one mole Ni have been plotted it is surprising that the observed trend is towards a constant reduction, independent of the magnitude of AH[.~6i°nic, or which is equivalent, independent of A~b" at larger A~," values. For Ni alloys with Mn and V it is expected, and observed, that the enthalpy is not reduced since the charge transfered to Ni is too small //
j'/ /./
300 //'/
i200 .x L I
"r 10C <1
~oo
20OAHo~~.
300
[k J/mole Ni
for or po$ Or lOmC Fig. 8. The quantity (AHex p - AHfe0~tc ) versus AHf~tc " for binary systems where Ni is the minority partner in a c o m p o u n d with a transition metal in kJ (mole N i ) - L
In the next section a quantitative correction is presented accounting for limitations in transfer of charge to metals at the end of a transition-metal series. This correction scheme is applied to Ni in this paper, but this formalism can be applied similarly to alloys of either Pd or Pt, elements of the same column as Ni in periodic table.
4. Proposed corrections for Ni, Pd and Pd
This means that for large A~* it is no longer required that Ni is the minority partner. For the examples given in table 2 at least half an electron is expected to be transferred to each Ni atom, and it should be noted that in some compositions Ni is indeed not the minority partner; for the given compositions, both in the liquid and the solid phase, the value of 30 kJ (mole Ni) -1 is a reasonable estimate. Since a discontinuity of ~* (Z) can also be expected for the 4d- and 5d-series (fig. 7) the same phenomenon can be expected to occur for Pd and Pt. Unfortunately, the experimental information is relatively scarce. From recent free-enthalpy measurements [ 9 ] on Pd-rich Y alloys one might estimate a value of 90 kJ (mole Pd) -1 at larger values for fPvd. Atb*, where f~d is the degree to which Pd atoms are surrounded by dissimilar neighbours (Y). The large reduction for Pd is confirmed in experiments on Pd compounds with rare-earth metals by means of a dynamic differential calorimetric method [10,11] and is also consistent with the more steep drop in ~b" when going from Pd to Ag as compared with the drop in ~b* for Ni to Cu or Pt to Au in fig. 7. For Pt-based alloys there is an experimental value for equiatomic compounds of Pt with rare-earth metals [12] (the same kind of calorimetry as above), and further some values [ 13-17] for compounds very rich in Pt. The reduction of the formation-enthalpy effect for Pt compounds is without any doubt smaller than for Pd compounds. The correction to the predicted formationenthalpy effect accounting for a limited charge transfer can also be calculated by means of the following scheme. For alloys of two transition metals the ionic term of the enthalpy of alloying of the alloy ABn (per mole A) is written as ~t
The predictions can be improved by assuming that if more than about half an electron is transferred to a Ni atomic cell upon alloying, the enthalpy will be changed by about 30 kJ (mole Ni) -1. In order to decide whether more than the charge of half an electron is transferred to the Ni atoms one has to take into account the magnitude of A~b* and the degree to which Ni atoms are surrounded by dissimilar neighbours.
AH for, ionic (per mole A) ~
-
AZ A~
2
(4)
where AZ is the charge transferred per A atom (in units of electronic charge) that is assumed to be proportional to both AO" and f ~ such that f ~ is the degree to which A atoms are surrounded by dissimilar neighbours (B). With the charge transfer the difference in ~* is equalized and the
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
333
Table 2 The reduction of A H ~ [ c, AH corr, where AH corr = A H ~ [ e - AH f°e~rin kJ (mole Ni) - I if the d band in Ni becomes completely filled upon alloying of Ni and X. Predicted values for the enthalpy of fo-l~nation ( AH~t°[c)corr are also shown according to the formalism given in sec. 4 with ( A~b*max )0 = 1.05 V. X
CNi
A~b"
f~i
Ti Ti Y Y Y Y Y Zr
0.33 0.50 0.25 0.40 0.50 0.67 0.75 0.33
1.40 1.40 2.00 2.00 2.00 2.00 2.00 1.75
Zr
0.50
1.75
Nb Nb Nb La La La La La Ta Th Th Th
0.50 0.50 0.75 0.25 0.50 0.50 0.67 0.75 0.33 0.30 0.50 0.67
1.15 1.15 l.l 5 2.03 2.03 2.03 2.03 2.03 1.15 1.90 1.90 1.90
0.95 0.83 0.99 0.96 0.92 0.70 0.53 0.96 0.88 0.84 0.84 0.41 0.99 0.98 0.93 0.73 0.56 0.96 0.98 0.92 0.72
AH~ - 28 - 34 - 19 -30 -37 - 39 - 37 - 37 - 52 -23 - 35 - 32 - 13 - 15 - 25 - 20 - 21 - 39 - 28 - 45 - 42
AH~[e
AH corr
( AH~[c )corr
- 40 - 52 -23 -37 -44 - 45 - 37 - 53 - 72 -45 - 45 - 32 - 19 - 38 - 38 - 39 - 33 - 39 - 35 - 56 - 58
36 36 16 18 14 9 0 48 40 44 20 0 24 46 26 29 9 0 23 22 24
- 37 - 51 -8 - 12 - 19 - 36 - 37 - 41 - 61 -45 - 45 - 32 -3 - 9
-
- 9 26 33 33 22 35 50
a v e r a g e p o t e n t i a l o v e r w h i c h t h e c h a r g e is t r a n s -
Now AZ remains constant with further increasing
f e r r e d is A O ' / 2 . T h e r e f o r e
AO',
but
the
effective
difference
in
potential
AO'ar for the transferred charge becomes
AH for, ionic (per mole A) oc
_ f A ( A~* )2 2 . (5)
In the case of a limitation of the charge transferred due to the electronic configuration, of the electropositive
atom
(e.g. N a )
either
or of the
e l e c t r o n e g a t i v e a t o m (e.g. N i ) , A Z will b e p r o p o r tional
to
Ao"
for fA
=
1 until
A Z m ~ is r e a c h e d a t ( A 0 " m ~ ) 0 assumption
a
A~b*eff =
Hence tion
band
allows
for
some
v a l u e f o r A Z is
additional
(A0"m~)0
in
the
formalism
is o b t a i n e d
However, iff A <
as a
1 then AZ
the
it
of
charge
transfer,
O----
~r_r for, ionic ~'achargelimit
_--
A H for, ionic
the
ratio
without reads
in
of
limitacase
AZma x
Aw*eff "~
(8a)
AZ A~*
or
A Z m ~ is r e a c h e d
O =
(A~b*max) (2A~b* - A~b'max) ( A(~" )2
t
( A~b max ) 0 / f A .
i.e.
parameter
at
A~b max =
@,
A~" > a#'max,
best-fit parameter. =
for
charge
t r a n s f e r . H o w e v e r , t h i s s i m p l i f i c a t i o n is a c c e p t a b l e because
value
(7)
maximum
r e a l i s t i c , f o r N i i t is a n o v e r s i m p l i f i c a t i o n s i n c e t h e s-d
the
A~btmax ).
A H f°r,i°uic ( p e r m o l e A ) w i t h a n d
While for Na the
of a rigid maximum
A~b'max + 2 (A~b* -
(6)
a n d b y i n s e r t i n g eq. (6)
(8b)
334
A.K. Niessen et al. I Enthalpies of formation of Ni alloys
=
[
( A~b max ) 0
4
2
1
( A~b max ) 0
4
,,+"
"
(8c)
ilc"):4
In table 2 this correction is applied for those Ni-based alloys for which experimental information on AHror ---cxp is available in table Ni-II, using ( A~b'max) 0 = 1.05 V as best-fit parameter. In combination with the approximation between f ~ • A~b" and AZ, as given in [ 18 ] this corresponds to AZm~x is about 0.5 e per Ni atom. For Pd and Pt we have estimated that (A~b'max)0 = 1.15 V for Pd and ( A~b*m~x) 0 = 1.00 V for Pt, respectively.
5. Alloys of a transition metal and a non-transition metal
In this section the enthalpy of formation for binary alloys of a non-transition metal and a transition metal, in the solid state as well as in the liquid phase, will be discussed in more detail. Some discrepancies between the predicted and experimental enthalpy effects upon alloying a non-transition metal and a transition metal have already been mentioned in the previous section and in other papers of this series. Now the discussion is not limited to the alloys based on Ni, but covers in principle all alloys of a non-transition metal and a transition metal. For 3d-transition metals other than Ni this information is readily available in [ 1-4,19 ]; experimental information on alloys containing 4d- or 5d-transition metals [ 19 ] is less abundant than for 3d metals. For alloys of two transition metals we have previously shown that the contact-interaction model [ 5 ] yields an expression for AH r°r with two terms: AHf°r c~ f ( c S )
x [ _,, (,,+-)
x
Q (,,,,
cells (f]) and the molar surface area of the two constituent metals (V~ 3, V~ 3)
(9)
where f (c s) is a function of the surface concentration c s. We can express [ 5 ] f (c s) in the atomic concentration of one constituent (CA), the degree to which A atoms are surrounded by B atomic
[
tlO/
Expression (9) does not only apply to binary systems of transition metals, but also to systems of two non-transition metals. There is little doubt that such a description based on contactinteraction also applies in the case of alloys of a non-transition metal and a transition metal. The convincing agreement between predicted and observed enthalpy effects on the formation of a binary alloy of Co or Ni with another transition metal confirms the adequacy of the assumption that the energy effects upon alloying are generated at the interfaces of dissimilar atomic cells. Further support is found in fig. 9, where all available thermodynamic data [ 19 ] on compounds of transition metals with other transition metals have been collected. Those compounds are indicated for which it can be expected that the predicted charge transfer is reduced, as for example in NiLus. For a few compounds with the AuCu 3 structure the experimental enthalpy of formation is exceptionally large, presumably due to an additional contribution if some Brillouin zones are filled upon alloying. Taking into consideration that there is an uncertainty of 2 to 5 kJ (mole of atoms) -L in the predicted values and an uncertainty of about the same magnitude in the experimental results, the agreement between predicted and experimental values is very conclusive. A good agreement is also observed in the liquid state (fig. 11). The experimental values plotted in these figures were obtained solely by calorimetry. In fig. l0 and fig. 12 the thermodynamic data for alloys of a transition metal and a nontransition metal are analysed along the same lines as in fig. 9 and fig. 11. The scatter is much larger in fig. 10 than in fig. 9: 30 to 50 kJ (mole of atoms) -1 instead of l0 to 15 kJ (mole of atoms) -1. The way the points scatter in fig. 12 differs markedly from that in fig. 10. The predicted enthalpy of solution appears to be insufficiently negative in fig. 12 (liquid phase) while in fig. 10 (solid phase) the points scatter
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
335
i t
kJ
i
- &Hexp
for -AHex p
2O0
20(3
/'.
/. •
• HIPt3 /
t 10C
]1
"+'+Z /+
Y:
,,
//"I',
i']
•
•
I I
,,"
"~:/:" °.
/
..,o+
~" +//
- AHcalc
t¢
=
Fig. 9. Comparison of predicted and experimental AH for for compounds of a transition metal with another transition metal (e) or with a noble metal (&). One type of discrepancy is indicated by x; if sufficiently electropositive atoms surround a Ni, Pd or Pt atom, AH ~ c is too negative (e.g. in La3Ni ) since the d bands of the electronegative metal tend to be fully occupied upon alloying. The experimental values were obtained exclusively by calorimetry (taken from chapter III in [ 19 D.
t, i-icalc
=
Fig. 10.. Comparison o f A H ~ rP and A H ~ c for compounds of . . . a transmon metal (including the noble metals) and a polyvalent non-transition metal. The experimental values were obtained by calorimetry (taken from chapter III in [ 19 ]).
oo[l-,xo
T-• --o Hex p
//
300
IkJ7 1 Lm--gi~J
[&]
2O0
200
l
100
~
i /
/.
,-
,o,
0he'.
•
~).'.,~.. ~" .,,. .~.~.. • . . . / .
.: ..~. ~fi" ix
"
,4 / •
UPd3
:~
//1
/
• ///:.
./
/
100 / . . " " . . / : ' ~ " * v'" /" ~ y~:." ,/
~:
•
"/// /.
/
/
;~
.."
// /
x •
;
.
,~:.'~ ..
x,
-'Hca~
100
r kJ]200
"
i
-100
; ~//~
~/~
%1
r
L~I
-I0-'56m'.-~"-"
' ~ 0 0 /1/ / / /
//100
I kJ I
300
[moleJ
-100[ Fig. I I. Comparison of predicted and experimental A H °, the enthalpy of solution in the liquid phase of a transition metal and another transition metal (e) or a noble metal (A). As in fig. 9, some deviating points with Ni, Pd or Pt as solute metal are indicated by x (problem of full d bands). The experimental values were obtained by calorimetry (taken from chapter I l l in []9D.
Fig. 12. Comparison of AH"° ~p and A/~°calc for liquid alloys of a transition metal and a polyvalent non-transition metal (C, N and P are excluded). The experimental values were observed by calorimetry (taken from chapter III in [ 19 D. The dashed lines indicate that the scatter in fig. 12 is comparable to that fig. 10. The scatter in values of AH f°r is expected to be about 0.375 times that for the enthaipy of solution.
336
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
more evenly around the line where the predicted value is equal to the observed value. By means of fig. 5 we already indicated that for solid alloys with non-transition metals the concentration dependence of ~.,AUr°~c~ is not described correctly. In order to compare the predicted and the experimental concentration dependence of the enthalpy of formation more information is required than has been provided in fig. 5. A fairly complete survey on the concentration dependence of A/./ror _..~,p can readily be obtained from the phase diagrams by searching systematics in the concentration range where compounds tend to be present. For instance, if AHfor --exp as a function of concentration is asymmetric with the more negative values in the nontransition metal range, one expects to find compounds predominantly in that range. In our analysis we have divided the concentration range in eleven equal intervals and have counted the number of times a compound stable at low temperatures is found in each interval of the available binary phase diagrams of one nontransition metal with all transition metals, noble metals and Th, Pu and U. The number of compounds in each interval is then divided by the total number of compounds involved in this analysis, defining in this way a probability to observe a compound in an interval. The result of this procedure is shown in fig. 13 for all non-transition metals. The probability to find a compound is definitely not spread over the concentration range in a statistical way. In general the compounds cluster at compositions rich in the non-transition metal. This appears to be very pronounced for Be and Mg, and also for the other divalent metals Zn, Cd and Hg. The trend is very much the same as for Be and Mg: the smaller the molar volume the more asymmetric the number of compounds is distributed over the concentration intervals. The asymmetry observed in the occurrence of compounds in Zn-based phase diagrams is consistent with the quantitative information on the concentration dependence of AHfor ~ exp in the Co-Zn system, noted in [4]. For the trivalent non-transition metals the distribution of the compounds resembles only for M-based compounds that for the divalent metals. The pronounced asymmetry as for Be and Zn is not
observed for the tetravalent and pentavalent non-transition metals, however, the probability to find a compound at a certain concentration appears to be not a statistical one. Note that the diagrams for B, C, Si, Ge, N and P have to be considered with some care since in the pure state these elements have an enhanced stability with respect to the hypothetical metallic state, and the metallic character of compounds rich in these elements may be disputable. The strongly varying numbers of the compounds at lower concentrations of the non-transition metal, e.g. the pronounced minimum in the occurrence of Sn-based compounds around c = 0.6, are statistically significant. How complicated this matter in fact is will be illustrated in fig. 14 where we compare the compound occurrence in those systems where B is alloyed with d metals from different rows in the periodic system. One observes a striking difference between Sc, Y and La from the first row of transition metals, Cr, Mo and W from the middle row and Ni, Pd en Pt from the last row. For compounds based on C and N a similar behaviour is observed. In conclusion we note that the asymmetry in the number of compounds, which we now prefer to interprete as being related to an asymmetrical concentration dependence of the so-called R term, is certainly more pronounced for the metals with the smaller molar volumes (Be and Zn) than for others. The varying numbers of the compounds at lower concentrations of the non-transition metal may have some significance, indicating that the variation of the R term upon concentration does not have to be a monotonic function. It is appropriate to recall here the reasoning to introduce the R term. For alloys of a transition metal and a non-transition metal an equally important energy contribution, the so-called R term, has to be added to the two terms in eq. (4) that describes the enthalpy of formation of an alloy of two transition metals: AHf°r oc f ( c S ) x
[
-
x R].
(11)
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
30%
B
C
AI
Si
337
N
wt 20% 10%
30%
Mg
2O%
N
10% 0 Zn
30%
Ga
Ge
As
Jt
20%
10%
Cd
30%
In
Sn
Sb
TI
Pb
Bi
2O%
10% ~:~I~ii!i!i!~iiiii
Hg
3O% 20% 10% 0
0
0.5CA_.,. " 0
0.5CA_,,. 0
0.5CA ---,,.- 0
0.5CA
Fig. 13. The probabifity of finding compounds in binary systems of transition metals and the polyvalent non-transition metals in one of eleven equal ranges of concentration.
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
338
100%
7=2
t
W 5O%
015 c B " 1 60%
Z=3
Z=4
Z=5
Z=6
Z=7
Z=8
Z=9
Z=IO
W
50%
W 25%
0
0.5 CB --"'- 1
0
0 . 5 c B --,,,--1
0
0.5 c 8 --"~1
0
0.5 c B ---,'--1
Fig. 14. The probability o f finding c o m p o u n d s in binary systems o f transition metals and boron in one o f eleven equal ranges o f concentration for three groups o f transition metals as partner metals. Note the large differences between these groups.
Whereas much attention has been paid in [ 5 ] to the physical meaning o f each o f the first two terms in eq. 6, the third term, the R term, has been introduced without much argumentation. Since about the same additional energy is required in the liquid as in the solid phase, and since in the liquid phase it is very improbable that an additional contribution to the formation enthalpy can be ascribed to effects owing to the tilling o f Brillouin zones o f particular crystal structures, the o r i o n has to be sought in the fact that different types o f metals are combined: here a metal with p-type electron wave functions is combined with a metal with mainly d-type wave functions. Adopting the contact-interaction as essential, it has been assumed that the concentration dependence o f the R term is similar to that o f the first two
terms [ 5 ]. It is an intentional choice to treat the third term, too, as an atomic interfacial energy, independent of concentration, which leads, however, to some controversial aspects. Relation (6) is oversimplified: A H ° {^} in {B} and A H ° is} i, {A} cannot differ in sign. But there are some examples showing such a change in sign, e.g. in the Co - S n , Cr - S n , U - Pb, M n - Sb and R u - Bi systems. The exceptional occurrence o f different signs for the enthalpies o f solution in these phase systems implies that relatively large differences may occur in the numerical experimental values o f both terminal enthalpies of solution (larger than predicted by means o f the variation in V~ 3) for systems with equal sign for both enthalpies o f solution. In the solid phase such an asymmetry will lead to an asymmetric distrib-
A.K. Niessen et aL / Enthalpies of formation of Ni alloys
339
a "'=a
R"ffiO.73 R
l
i • ::':" , / :
•
I :.:.:::-
,oo. •
,oo
I . . ...
•
•
:
"
,
I
,
100
-~Hcal -o ,c------~ 200
-
./:•'~ ;o.O -~Hc~1c---,,,..
1
200
-100 Fig. 15. The effect of the inclusion of the reduction factor for the R term in the liquid phase for fiquid solutions of a transition metal and a non-transition metal for which AH ° has been determined by calorimetry. The scatter is more evenly distributed around the line where A/7 ° exp = AH° calc without this reduction factor (at right) if the transition metal belongs to one at the end of the d series (o) and with the reduction factor taken into account (left figure) if the d metal (,t,) is situated at the begin of the d series in the periodic system.
urion of compounds in phase systems. For instance, if A H ~ as a function of concentration is asymmetric with the more negative values in the non-transition metal range, one will find compounds predominantly in that range. Fig. 5 and the distribution of compounds with concentration (fig. 13) make clear that the concentration dependence of ALrror ,~--~1c is indeed insufficiently accounted for by f(c s). A possible orion of the incorrectly predicted concentration dependence could be found in the R term. The introduction of R as a constant that is included between brackets in eq. 6 is in fact a too crude approximarion. Unfortunately, at present we have not found a formalism for the R term, either based on physical insight or purely empirical, in which the observations can be treated quantitatively. Perhaps one should have two, in principle independent, relations for AHf°r: one based on the solution of a transition metal in a non-transition metal and the other for the reversed situation. This idea is qualitatively very attractive since it opens the
possibility for a change in sign of the two terminal heats of solution, compounds in the solid phase and liquid immiscibility in the liquid phase and a concentration dependence largely differing from eq. (6). Unfortunately, we are unable to introduce such a scheme without including many more fully empirically determined parameters. Since the introduction of more empirical parameters means a complete loss of simplicity we have not modified the model. The only difference in the treatment of the ¢nthalpy effects in the solid and liquid phase is the reduction of the R term in the liquid state. The advantage of keeping this reduction factor is that the predicted sign to be ascribed to phase systems in the solid phase and in the liquid phase may differ for one and the same binary. If the emphasis of the analysis is on the sign of the formationenthalpy effects of phase systems one prefers that the uncertainty is proportional to AH ° {A}i°{S}, while the choice of neglecting the reduction factor might be a more constant spread of the uncertainty in some cases as is demonstrated in fig. 15.
340
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
The calorimetrically determined enthalpies of solution AH ° for solutions based on either Ti, V, Cr, Mn or Fe, Co, Ni (as collected in chapter III) are plotted versus the predicted AH °. Indeed, for Fe-, Co- and Ni-based solutions one could prefer no reduction, in contrast to the solutions with Ti up to Mn. We conclude that the quantitative information on the enthalpies of formation does not always support a reduced value of the R term for liquid alloys. Data for individual systems of 3d metals for which both the heat of solution in the liquid phase and the heat of formation for compounds rich in the respective solvent metal have been measured support this conclusion, too. The enthalpy effect in the liquid phase arises in principle from the same mechanisms as in the solid phase. However, the environment of the solute atom may be more variable; if heats of solution are measured in the situation of a high-meltingpoint solute metal (e.g. Ni) and a low-meltingpoint solvent (e.g. Sn) clustering of the solvent atoms around the solute atoms may occur. This preferential surrounding of the solute atoms by the solvent atoms produces negative contributions to both the alloying enthalpy and the entropy. The complication of cluster formation may well be more serious for liquid alloys of a transition metal and a non-transition metal. The R term in liquid alloys possibly favours (or requires) local ordering, strongly affecting the entropy of formation. This ordering will depend on temperature; hence a temperature-dependent enthalpy of solution may occur as reported for Ni in Sn (table Ni-III). At least the thermodynamic properties of liquid solutions of transition metals in low-melting non-transition metals can be very complex!
6. Conelmioas In this paper we have presented an extensive comparison of experimental and model values for enthalpy effects in alloys containing Ni. Apart from the benefit of reporting such a large collection of data, we have demonstrated the usefulness of comparing model predictions with experiments: it focusses attention to the limitations of the model.
The main limitation of the model appears to be the fact that no distinction is made between the electrons with various kinds of wave functions. This is encountered in the reduction of the enthalpy at the end of each transition-metal series if the d band becomes fully occupied upon alloying with a more electropositive metal. The latter can be overcome by applying the formalism sketched in this paper. This limitation is also encountered if atomic cells of a transition metal and a non-transition metal, either in the solid or in the liquid phase become first neighbours. The description of the additional energy required in the model is too crude. The concentration dependence of the enthalpy of formation for alloys of such metal combinations, if interpreted in terms of relation (5), would imply at least a different value of R at each side of the binary phase diagram and stronger variations of RIP than used at present.
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341
[ 24 ] J. Tomiska, L. Erd~lyi, A. Neckel and H. Nowotny, Z. Metallkd. 68 (1977) 734. [ 25 ] K.M. Friederich, S. J6usson, F. Aldinger and G. Petzow, Z. Metallkd. 71 (1980) 584. [26] S. Budurov, G. Wassilew and N. Nentschew, Z. Metallkd. 65 (1974) 681. [ 27 ] A.J. Morton, Acta Metall. 27 (1979) 863. [ 28 ] A.J. Goldschmidt and M.J. Walker, J. Appl. Cryst. 2 (1969) 273. [29] A. Baranski and Z. Galus, Electroanal. Chem. and Interracial Electrochem. 46 (1973) 289. [ 30] J.-D. Sch6bel and H.H. Stadelmaier, Z. Metalikd. 56 (1965) 856. [ 31 ] A.S. Sobolev and T.F. Fedorov, Inorg. Mater. 3 (1967) 643. [ 32 ] K.I. Portnoi, V.M. Romashov, V.M. Chubarov, M.Kh. Levinskaya and S.E. Salibekov, Poroshk. Met. 7 (1967) 15 and Chem. Abstr. 66 (1967) 119482. [ 33 ] A. Taylor and N.J. Doyle, J. Appl. Cryst. 5 (1972) 201. [34] S. Martosudirdjo and J.N. Pratt, Thermochim. Acta 17 (1976) 183. [ 35 ] P. Feschotte and P. Eggimann, J. Less-Common Met. 63 (1974) 15. [36] K.J. Best and T. G6decke, Z. Metallkd. 60 (1969) 659. [ 37 ]L.D. Lucas, M&m. Sci. Rev. M6tall. 66 (1969) 747. [ 38 ] E.B. Badtiev, O.S. Petrushkova and L.A. Panteleimonov, Vesta. Mosk. Univ., Ser. 2, 15 (1974) 367. [39] L.F. Lutskaya and P.V. Gel'd, Inorg. Mater. 13 (1977) 315. [40] M. Ellner, T. G6decke and K. Schubert, J. LessCommon Met. 24 (1971) 23. [41 ] E.M. Rybalkin and B.P. Burylev, Termodin. Svoistva Rasplavov, Mater. Konf. (1969) 225 and Chem. Abstr. 74 (1971) ! 16523. [42] B.P. Burylev and E.M. Rybalkin, Tr. Krasnodar. Politekh. Inst. 63 (1974) 108 and Chem. Abstr. 83 (1975) 16547 [43] S. Heinrich, H.U. Rexer and K. Schubert, J. LessCommon Met. 60 (1978) 65. [ 44 ] O. Kubaschewski, Iron Binary Phase Diagrams (Springer, Berlin, 1982). [ 45 ] P. Villars and L.D. Calvert, Pearson's Handbook of Crystallographic Data for lntermetallic Phases (American Society for Metals, Ohio, 1985).
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342
A.K. Niessen et al. / Enthalpies of formation of Ni alloys
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343
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