Enthalpies of formation of liquid and solid binary alloys based on 3d metals

Physica 1OlB (1980) 294-319 0 North-Holland Publishing Company

ENTHALPIES

OF FORMATION

OF LIQUID AND SOLID BINARY ALLOYS BASED ON 3d METALS

I. ALLOYS OF SCANDIUM, TITANIUM AND VANADIUM

F.R. DE BOER Natuurkundig Laboratorium, Universiteit van Amsterdam, 1018 XE Amsterdam, The Netherlands

Valckenierstraat 65,

R. BOOM Research Laboratories, Hoogovens IJmuiden

B. V., 1970 CA IJmuiden,

The Netherlands

A.R. MIEDEMA Philips Research Laboratories, 5600 MD Eindhoven,

The Netherlands

Received 29 February 1980

Model predictions are presented for heats of formation of binary intermetallic compounds of SC, Ti or V with arbitrary metal partners, and for heats of mixing and solution of the corresponding liquid alloy systems. Predicted values are compared with the existing experimental data as well as with qualitative information derived from phase diagram information. A complete set of binary phase diagrams based on SC, Ti or V is presented in schematic form. Differences between experimental and calculated enthalpy values are discussed.

as on SC, Ti and V systems, may serve several purposes. Firstly there is the direct applicability, but secondly the data present the basic information from which the best-fit values for the model parameters +* (electronegativity) and nws (electron density) have been derived. Recently a number of authors have quite successfully used these model parameters to characterize metals in relation to problems different from heats of alloying (e.g. [4]). In the study of these new problems the question may arise as to what extent slight changes in the values of ro P osed to improve the description of G* andn,,p the problem, can be accepted. Agreement between calculated values for heats of formation, based upon the “better” $J* and n, values, and the thermodynamic information from which the original values for $* and n,, have been derived, will be decisive. It has only recently become possible to compare the empirically derived 4’ and nws values with theoretical expectations for parameters of this type. For example, Moruzzi et al. [5] have derived, by means of self-consistent band structure calculations, values

1. Introduction In a recent paper [3] we argued that the existing experimental information on heats of formation in binary systems based on transition metals can be reproduced by means of a simple semi-empirical model. This enables us to predict heat effects on alloying for any alloy system. Since these heat effects provide basic information in connection with a variety of metallurgical problems, it is of interest to make the predicted values available in tabular form. In the present paper, the first of a series on the alloys of 3d metals, we will treat solid and liquid binary alloys based on scandium, titanium or vanadium. In addition to the prediction of alloying enthalpies we presed an extensive set of experimental data with the aim of achieving completeness. However, in view of the fact that part of the experimental information has only been published in reports or journals of limited accessibility, completeness will never be achieved in practice. Presentation of a collection of experimental data 294

F.R. de Boer et al. / Enthalpies of formation of Se, Ti and V alloys

295

tropositive metals like SC, Ti and V will be discussed later on in this paper by way of illustration.

2. Scandium alloys

I”,_$ l-

Li
Nay

/

Mg

sr

Rb OK /" / Olf 1

, 10 P,, CdC.

100

Fig. 1. Comparison of the empirically derived values for the electron density at the boundary of an atomic cell, nw, and the value of the interstitial charge density, pout, as obtained

from self-consistent band structure calculations by Moruzzi et al. [ 51. Metals up to atomic number 49 (In) are included. The two quantities are plotted on a logarithmic scale; the lie drawn corresponds to a linear relation between nws and Pout. nws is expressed in the density units of table I of ref. [31,Pout in electrons/(Bohr radius)3. Filled points are transition metals, open points represent non-transition metals and half-open points the boundary cases Ca, Sr, Cu and Ag.

for the interstitial charge density pout for all metals up to atomic number 49 (In). As shown in fig. 1, there is a linear relationship between calculated values of pout and the empirically derived values of n,. However, some metals show a deviation from the general relation; in a discussion of these deviations the actual set of data on which the value of nws is based is of direct interest. In the calculations of the heats of formation the coefficients of the ionic term (a$~*)~ and the electron density mismatch term (A~z$)~ are taken the same for large groups of metal combinations. As a consequence, differences between predicted and experimental AH values may show up that are to some extent systematic, e.g. in relation to the position of the metals involved in the Periodic Table. Such differences may give some idea about the direction in which predictions will deviate for related systems on which no experimental information is available. In this way the accuracy of the tabulated predictions can be improved on an individual basis. Alloys of electronegative metals like Pd with elec-

In tables Sc-Ia, b we have collected calculated values for the enthalpy of formation of binary alloy systems based on scandium. Presented are the heat of formation, &Or, of solid intermetallic compounds of five different compositions (ScMS, ScM2, SCM, Sc2M and ScsM), the two limiting partial heats of solution, &, for liquid alloys (SC in M and M hi SC), and the heat of mixing, Aff”‘“, of a regular mixture of SC and M at the equiatomic concentration. For the compounds the reference states are the pure metals in the solid state, for the liquid alloys the reference states are the pure liquid metals. Throughout this paper it is assumed that enthalpies of formation and mixing are temperature-independent. Experimental information on heats of alloying of scandium alloys is scarce, which makes it difficult to compare the calculations and the results of experiments. An idea about the reliability of the calculations can be obtained from a comparison with qualitative information derived from phase diagram information. In the handbooks on phase diagrams of binary alloys [ 1,221 a number of systems based on SC are missing. The published phase diagrams have been sketched in figs. 2 and 3; additional references updating the handbook information are included in figs. 2 and 3. If experimental information on the phase diagrams from different authors agrees only partially, we have preferably followed the most recent publication in drawing figs. 2 and 3. If no diagram is known, then other available partial information, like the existence of compounds or the occurrence of a miscibility gap in the liquid state, is depicted in figs. 2 and 3. In order to make it possible to compare the predicted heats of formation and the phase diagram information, we have introduced in tables Sc-Ia, b a column in which the characteristics of the phase diagrams of fig. 2 have been “translated” into qualitative information about the heat of formation by means of the following symbols: - one or more compounds that are stable at low temperatures (indicating that Lwf” is negative);

296

F.R. de Boer et al. / Enthalpies of formation of SC, Ti and V alloys

Table Sc-Ia Calculated values for the heat of formation, AHfor , o.f compounds of five different compositions, the limiting partial heats of solution, fl, and the integral heat of mixing, Ap lx, kJ/mole of atoms, for binary scandium alloys. Phase diagram information, if available, has been added for the solid systems M

,for SCM,

ScM2

SCM

Sc2M

+I

Sc5M

Phase diagram inform.

A9

Af@=

Ai?

SC in M

SCM

M in SC

+25 +33 +3 -40 -53 -140 -180

+6 +I +1 -8 -12 -30 -38

+20 +25 +2 -28 -39 -99 -129

+3 +13 +69 +45 -162 -185 -251 -353

+1 +3 +16 +10 -39 -44 -61 -86

+4 +12 +60 +38 -141 -159 -221 -320

+21 +11 +68 +39 -150 -162 -255 -354

+8 +4 +16 +9 -31 -39 -62 -89

+35 +16 +59 +34 -135 -142 -229 -331

-0

+11 -3

-0 +4 -1

-0 +11 -3

-141 -131 -292

-30 -33 -15

-103 -128 -300

Ti V Cr Mn Fe co Ni

+4 +5 +1 -6 -9 -23 -29

+8 +11 +1 -12 -11 -43 -56

+6 +8 +1 -9 -13 -32 -41

+3 +4 +o -5 -6 -16 -21

c+

+10 +1 -12 -16 -41 -53

Y Zr Nb MO Tc Ru Rh Pd

+1 +2 +11 +I -26 -30 -42 -51

+1 +4 +21 +14 -50 -51 -19 -109

+1 +5 +24 +16 -5-I -65 -91 -128

+1 +4 +19 +12 -45 -50 -10 -101

+1 +2 +10 +6 -22 -25 -35 -51

C C + +

La Hf Ta W Re OS Ir Pt

+4 +3 +11 +6 -24 -26 -41 -51

+9 +5 +21 +12 -46 -50 -19 -111

‘+ll +6 +24 +14 -54 -58 -93 -133

+10 +5 +19 +11 -43 -45 -12 -106

+6 +3 +9 +5 --22 -23 -36 -54

CO C + +

Th U Pu

-0 +3 -1

-0 +5 -1

-0 +I -1

-0 +5 -1

-0

CO

cu Ag Au

-23 -22 -47

-41 -42 -91

-44 -50 -113

-33 -40 -93

solid solubility and one or more ordered alloys (indicating that AHror is negative but closer to zero than above); C continuous solid solubility, also at low temperatures (indicating that &Or is approximately zero); Co continuous solubility at high temperatures for one type of phase, and one or both solid solubilities larger than 10 a/o in the low temperature phases; no ordered phases;

C- continuous

+ + -

_ _ _

_ _

+3 -1 -16 -20 -48

-

no compounds and one or both solid solubilities larger than 10 a/o (indicating that &Or is approximately zero); l same as 0, but the solid solubility decreases strongly with decreasing temperature to values below 10 a/o (indicating &Or to be small but positive); CO continuous solid solubility in a high temperature phase and a solid solubility in the low temperature situation which is larger than 10 a/o for one or both phases but decreases strongly with decreasing temperature;

0

F.R. de Boer et al. / Enthalpies of formation of SC, Ti and Valleys

297

Table Sc-Ib For caption see Ia M

&ffor

ScMS

ScM2

SCM

Li Na K Rb cs

+9 +20 +29 +31 +32

+16 +40 +58 +62 +64

+18 +51 +83 +90 +95

+14 +45 +84 +95 +105

+7 +24 +49 +57 +67

Be

-4

-4 -8

+29 -46 -45 -52

+36 +40 -52 -55 -65

-3 -6 +23 +34 +39 -41 -46 -56

-1 -3 +13

Hg

-3 -3 +10 +13 +14 -25 -23 -21

+19 +23 -20 -24 -29

B Al Ga In Tl

-43 -32 -30 -23 -21

-12 -59 -57 -46 -42

-70 -68 -69 -58 -53

-49 -53 -56 -50 -41

-24 -21 -29 -26 -25

C Si Ge Sn Pb

-10 -18 -24 -32 -28

-70 -64 -68 -64 -56

-66 -80 -85 -81 -73

-44 -63 -68 -71 -65

-22 -31 -34 -31 -35

N As Sb Bi

+10 -55 -41 -32

-163 -106 -82 -63

-184 -130 -106 -83

-127 -107 -95 -76

-63 -55 -51 -41

Mg Ca Sf Ba Zn Cd

-6 +19 +26

+26

Sc2M

C+ continuous solid solubility at high temperatures and miscibility gap at low temperatures (@ small positive); + no compounds and both solid solubilities smaller than 10 a/o (Lwf”’ positive). It can already be seen from tables ScJIa, b that there is a good agreement between both the sign and the numerical values of AH and the general appearance of the phase diagrams. In order to get a better overall picture we have produced table SC-II. Even the intermediate case of AHrof positive but small is reflected in the phase diagram information. It depends on the size difference between the SC atoms and the atoms of the partner metal whether small

ScsM

Phase diagram inform.

AHO

AHmm’x

fG?

SC in M

SCM

M in SC

+54 +125 +181 +192 +201

+12 +35 +58 +64 +70

+45 +151 +306 +357 +415

-

-8 -14

-

+61 +82 +89 -130 -120 -142

-1 -3 +17

-5 -13 +78 +I18 +141 -108 -124 -158

_ -

_ _ _ _ -

.. . -162 -153 -114 -101 .. . -249 -241 -166 -142 .. . -300 -219 -160

+24 +28 -29 -30 -37 . .. -38 -38 -30 -21 ... -51 -57 -45 -40 . .. -11 -61 -46

. .. -140 -147 -129 -120 ... -202 -210 -193 -177 . .. -304 -269 -209

or appreciable solid solubility can occur. The solid solubilities are indeed small in the SC-V and Sc-Cr systems (large size differences), while solubilities are appreciable in alloys of SC with Ti, Y, Zr, La, Hf and Th. In view of the positive value predicted for the heat of formation of Sc-Hf alloys, immiscibility in the solid state is likely to exist, though it has not yet been reported. Phase diagram information is still lacking for alloys of Sc with alkaline and alkaline-earth metals, For these systems the calculated values for the heats of formation and mixing are strongly positive, so that one cannot prepare alloys of this type, since both solid and liquid immiscibility are to be expec-

F.R. de Boer et al. / Enthalpies of formation of SC, Ti and V alloys

298

11.701

\

lizi

1.5

'\

'\

.@

c- p

1.0

Ill.221

2.0 .#

/ a

:

\ I

TI

SC

1.5

151

V*

-

IV) + (a-54 1.0I!?!??4 V

I

SC

11.23.261

10 M Cr

SC

[l 1

2.0 I

2.0 1.5

. .

a SC

'

2

a SC

<

5.C

Ru

SC

1.5

\

2

1.0 Nb

'\

1 I

\'

2

1.0

31sfm

alloys

MO

1.0 H Zr

I1 1

M _

2.0

---

P

25

1.5

\

1.0 no

---_

llL.221 2.0 '\

I

P0

1.0M Y

111

[l 1

I

15

&# _

SC

Mn

SC

Rh

SC

Pd

SC 1221

[II

L-l no alloys

Hf

La

SC

111

SC

W

SC

Re

SC

ill

(Y 8 s: L OS

.-Ta

1, N

&=,

L

XL%

SC

Ir

Pt

Fig. 2. Binary phase diagrams of SC with 3d, 4d and Sd transition metals. Temperatures (10’ ’ C) are plotted vertically, the atomic concentration of SC is plotted horizontally. Numbers between brackets are references to experimental work; if more numbers are indicated, thesketched diagram is reproduced from the underlined reference.

F.R. de Boer et al. / Enthalpies of formation of Sc, Ti and V alloys

SC

Th

299

SC

4 111

0.5 Au

SC

u

1.5

11.721

mJ

Ill

1.5

PJ 9 m-mN x;:

I

11.10.241

E

IO

x

05

I

4

1.0 0.5

m

x

0.0

In

SC

SC

I

St-l

SC

Pb

11 1

Ly 6

2

As

5C

Sb

BI

Fig. 3. Binary phase diagrams of SC with actinides, noble metals and the other metals ranged according to increasing valence. For SC with the alkali and the alkaline earth metals and for SC with Tl no information is available.

F.R. de Boer et al. / Enthalpies of formation of SC, Ti and V alloys

300

Table SC-II Qualitative comparison of calculated LVifor values (kJ/mole of atoms) with phase diagram information A@c(ScM)

M

Phase diagram information

AH> 14

Nb, MO, Ta, W

No intermediate phases; very small solid solubility

o
V,Cr

No intermediate phases; very small solid solubilities (there is a relatively large size difference) No intermediate phases; large solid solubilities (here the size differences are less important)

0 < aH< 14

Ti, Y, Zr, La, Hf, Th

AH<-4

Ma, Fe, Co, Ni, Tc, Ru, One or more intermetallic compounds Rh, Pd, Re, OS, II, Pt, Cu, Ag, Au, Be, Mg, Zn, Cd, Hg, B, Al, Ga, In, C, Si, Ge, Sri, Pb, N, As, Sb, Bi

ted. Also on the SC-Tl system no phase diagram information is available; due to the large negative AH$& values a number of compounds may be expected to exist in this system. Experimental values of the heat of formation are known for ScN, ScAs and ScSb, the latter two having been obtained in direct reaction calorimetry (see table SC-III). There is reasonable agreement for the nitride and the arsenide, whereas for ScSb the cal-

Table SC-IV Comparison of experimental heats of solution A@ of liquid scandium systems with calculated values, kJ/mole of atoms. Heats of fusion AHfuse from ref. 2

Ta W

71 75

32 36

39 39

59 34

culated value is 30 percent more negative than the result of Chua and Pratt [8]. Bowersox [9] published values for the heats of solution of solid Ta and W in liquid SC, derived from solubility data; regular mixture behaviour was assumed. As shown in table SC-IV, the heat of solution of liquid W and Ta in liquid SC can be obtained by subtracting the heat of fusion of the elements (taken from Hultgren et al. [2]) from the experimental values. The limiting eYexp values have been taken equal to the values at the saturation concentration. Given the accuracy of determinations of maximum solubilities, the agreement between calculation and experiment is satisfactory. The SC-U system has been reported to show extensive liquid immiscibility [ 11. The calculated value of ,Fix is indeed positive, although not very large (ma;: = +4 kJ/mole of atoms). If excess terms in the entropy of mixing can be neglected, this AL#E value at the equi-atomic concentration leads to a critical demixing temperature of about 700 K. The fact that the heat of formation (calculated) of SC with U is of the same order of magnitude as that of SC with Ti, Zr and Hf, makes it likely that some solid solubility will also exist in the SC-U system.

Table SC-III Comparison of experimental and calculated values for the heat of formation of scandium compounds, kJ/mole of atoms System

Compound

SC-N

ScN

SC-AS

ScAs

Sc-Sb

ScSb

9 9

Ufor exp

for mca1c

Method

-157 -136 (700-730K) -66 (764-889K)

-184 -130 -106

Remarks

Ref.

estim. calorim.

6,130 7

calorim.

8

F.R. de Boer et al. / Enthalpies of formation of SC, Ti and V alloys

3. Titanium

alloys

In tables Ti-Ia, b we have collected calculated values for the enthalpies of formation, mixing and solution of binary alloys containing titanium. In the same way as for SC, the partner metals are divided into groups according to the positions of the metallic elements in the Periodic Table. For nearly all Ti-based binary systems there are phase diagrams available in the handbooks by Hansen and Anderko, Elliott and Shunk [l], and in the recent one by Moffatt [22]. All these diagrams, supplemented with recent information, are presented schematically in figs. 4 and 5; if no phase diagram is known, then other information like the existence of intermetallic compounds is depicted in figs. 4 and 5. For Ti with Rb and Cs there is no information at all. For these two systems the heats of alloying are predicted to be large and positive; miscibility gaps will occur in both the solid and the liquid state. Qualitatively the model predictions agree perfectly well with the phase diagrams. For those metal combinations for which AH is predicted to be positive (Ti with SC, Y, Nb, La, Ta, Th, Li, Na, K, Mg and Ca) no compounds have been reported. A quantitative comparison of experimental and calculated Lwf”’ values is made in table Ti-II; on the whole the agreement is satisfactory. The alloys for which the difference between experimental and calculated values is rather large can be divided into three groups. One group consists of the compounds TiNi, TizNi and TiPd and is characterized by the fact that the partner metal is the last one of a transition metal series and that it is the minority metal (present up to 50%). If the more electropositive metals (like Ti) are alloyed with much more electronegative metals like Ni, Pd and Pt, there is a considerable charge transfer. Therefore the 3d-shell of the more electronegative metal is filled and the metal becomes isoelectronic with its right-hand neighbour in the Periodic Table. Since the electronegativity as a function of the position in the Periodic Table shows a steep fall at the end of a transition metal series (e.g. Ni + Cu, Pd + Ag, Pt + Au -+ Hg), the resistance against charge transfer in these situations is greater than normal. As a consequence the negative term in the heat of formation will be diminished relative to the average case. With respect to Ti compounds one observes that the

301

experimental values of the heat of formation of TiNi, TiNiZ and TiPd are less negative than calculated. For Ti-poor alloys the increased resistance against charge transfer and the corresponding effect on M is less important, since the charge transfer per atom of the electronegative partner metal is reduced. For the corresponding systems of SC a similar difference between calculated and experimental values is to be expected, i.e. ScZNi, ScNi, ScPd, ScsPdZ, Sc4Pd, ScPt and SczAu. This argument, in reduced form;may also correct predictions for vanadium systems (below). The Ti-Sn compounds form a second group of compounds for which there is a discrepancy between calculated and experimental heats of formation. For these compounds the experimental values have been determined by a calorimetric method in which compounds are formed by magnesium (thermite) reduction of Ti- and Sn-chlorides (Savin [46]). The author states that the Lwfor values have to be considered as estimates, since side-reactions can seriously influence the result. In the Ti-Hg system too the calculated heats of formation differ considerably from the experimental results. At this moment we have no explanation for these large differences; we may conclude that our model predictions for intermetallic compounds with mercury should be treated with some reserve. Also given in table Ti-II are the experimental values for the entropy of formation. Unfortunately, due to the fact that most A$Or values have been determined by direct reaction calorimetry and not by AG methods, there is little information about entropy effects. The limited number of experimentally determined aSfor values can be highly inaccurate, since A,Sfo’ is obtained from the temperature dependence of AGforin a limited temperature range on the assumption that &Or and asf”l are temperatureindependent. It is clear that predictions of aSfor are quite relevant, because AGfo’ rather than &” is the important thermodynamic quantity. We shall treat entropies of formation later. In table Ti-III the available experimental information on heats of mixing and solution for binary liquid Ti systems is compared with calculated enthalpy values. Thermodynamic properties of the liquid binaries Fe-Ti, Ni-Ti and Pd-Ti have been determined by the vapour pressure method in combination with mass spectrometry [51,54,55,58] .‘The

F.R. de Boer et al. / Enthalpies of formation of SC, Ti and V alloys

302

Table Ti-Ia Calculated values for the heat of formation, Aff for, of compounds of five different compositions, the limiting partial heats of solution, A@, and the integral heat of mixing AHm’Ix , kJ/mole of atoms, for binary titanium alloys. Phase diagram information, if available, has been added, for the solid systems M

ufor TiMs

TiMz

TiM

TiZM

TiSM

Phase diagram inform.

A@

AHmix

IG?

Ti in M

TiM

M in Ti

c+

+20

V Cr Mn Fe co Ni

-1 -6 -1 -13 -23 -27

-3 -11 -14 -25 -42 -51

-3 -13 -16 -28 -41 -58

-3 -10 -12 -22 -36 -45

-1 -5 -6 -11 -18 -22

Co C-

-9 -38 -46 -82 -140 -110

-2 -9 -11 -19 -32 -39

-8 -32 -39 -10 -115 -140

Y Zr Nb MO Tc RU Rh Pd

+6 -0 +1 -3 -27 -31 -31 -46

+13 -0 +3 -5 -52 -59 -71 -88

+17 -0 +4 -6 -64 -71 -86 -109

+16 -0 +3 -5 -52 -58 -71 -91

+9 -0 +2 -3 -21 -30 -36 -41

+ C Co Co -

+40 -0 +9 -16 -169 -191 -231 -283

+12 -0 +2 -4 -42 -41 -51 -12

+58 -0 +10 -16 -169 -187 -221 -293

La Hf Ta W Re OS II Pt

+14 +o +1 -4 -21 -28 -40 -50

+28 +o +3 -8 -53 -55 -16 -98

+39 +o +3 -9 -65 -61 -93 -122

+38 +o +3 -8 -54 -55 -78 -104

+22 +o +1 -4 -28 -28 -40 -54

+ C co c+ -

+87 +1 +8 -25 -170 -171 -246 -313

+21 +o +2 -6 -43 -45 -62 -81

+136 +1 +9 -26 -175 -178 -250 -337

Th U Pu

+3 -1 -0

+1 -3 -0

+9 -3 -1

+9 -3 -0

+5 -2 -0

+ c.

+21 -9 -1

+6 -2 -0

+30 -10 -2

_ _ _

-78 -55 -210

SC

cu Ag AU

+3

-13 -9 -34

+6

-24 -17 -66

+8

-21 -21 -85

+I

-21 -18 -14

Fe-Ti system is found to be regular, while the calculated values indicate a small asymmetry. In the Ni-Ti system pronounced irregularities in AGm” are found at compositions corresponding to NiTi and NisTi [58]. This is in good agreement with the calculated AH values, which are asymmetrical and strongly negative in the Ni-rich region. The experimental AH”“” values for liquid PdTi and PdsTi [5 l] agree very well with the calculated values. The heats of mixing of Al-Ti alloys [66] and the heat of solu-

+4

-11 -10 -39

+6

-18 -14 -56

+25

-61 -60 -241

tion of Ti in Si [67] have been determined by isothermal calorimetry; the experimental values agree well with the calculated values. Heats of solution of Ti in liquid Ge have been measured by solution calorimetry up to 0.4 a/o Ti [113]. Peyzulayev et al. [59, 601 report an activity coefficient y = 1 for the Ti-Zr system, indicating an ideal alloying behaviour which is also predicted (w$ = 0 kJ/mole). Mills and Kinoshita [53] determined activities of liquid Ti-V alloys and found small positive deviations from

F.R. de Boer et al. / Enthalpies of formation of Sc, Ti and Valloys

303

Table Ti-Ib For caption see Ia

M

ufo’

TiMS Li Na K Rb CS Be

+19

+32 +39 +40 +41

Phase diagram inform.

Ai?

AHmix

aiso

Ti in M

TiM

M in Ti

+116 +199 +246 +253 +251

+30 +60 +86 +91 +96

+115 +287 +500 +561 +641

-39 +40 +121 +144 +152 -82 -54 -65

-8 +11 +38 +41 +51 -20 -15 -18

-25 +47 +189 +256 +294 -80 -65 -84

TiM2

TiM

Ti2M

TiSM

+36 +64 +I9 +81 +82

+44 +88 +116 +121 +123

+36 +83 +128

+

+139 +148

+18 +46 +80 +91 +103

-14 +13 +54 +66 +71 -42 -34 -39

-10 +11 +53 +69 +I6 -34 -30 -36

-5 +6 +30 +41 +41 -18 -16 -20

+ + + +

-55 -56 -52 -34 -25

-21 -29 -21 -18 -14

-

+ +

-13

Hg

-8 +5 +19 +23 +24 -18 -13 -15

B Al Ga In Tl

-42 -28 -24 -14 -10

-13 -55 -41 -21 -19

-15 -61 -60 -36 -26

C Si Ge Sn Pb

-12 -15 -16 -23 -16

-19 -61 -54 -46 -32

-81 -82 -14 -62 -44

-56 -69 -64 -58 -42

-28 -35 -33 -32 -24

-

N As Sb Bi

+30 -48 -31 -20

-130 -94 -61 -40

-168 -121 -83 -55

-122 -106 -19 -54

-61 -51 -45 -31

-

Mg Ca Sr Ba Zn Cd

+10 +39

+46 +49 -35 -26 -30

Raoult’s law, indicating small negative excess entropies and/or small positive enthalpies of mixing. From the calculations a small negative value for AI@“ is found, so that excess entropies should be responsible for the deviation from ideality. Johnson [61] published a value for the partial molar excess free enthalpy of solution,-A~“*xs, of Pu in Ti; neglecting excess entropies gives AcoPXS= s. However, experimental and calculated values do agree in sign but not in magnitude, so that excess entropies may be important in the Pu-Ti system. From solubility measurements flPexp values have been derived for Ti in Mg ([63,

_ _

_ _ _

-

-

.. . -135 -109 -46 -22 ... -222 -182 -100 -58 .. . -246 -143 -11

. .. -34 -29 -13 -1 ... -54 -46 -29 -17

... -137 -124 -62 -31 .. . -211 -188 -139 -87

..* -67 -42 -24

... -293 -208 -121

681, good agreement with mScalc) and for Ti in L,i and Ca [ 1,62,63]. The latter values are much smaller than predicted; one must realize, however, that @9exp values derived from extremely small solubilities are highly, inaccurate. The solubilities of Ti in Na and K have been reported to be very small [ 1,62, 651, indicating large positive heats of solution which, according to the calculations, should indeed occur for all T&alkali metal systems. There are indications that La and Ti are immiscible in the liquid state [ 11, in agreement with the calculated positive AR”“‘” value.

F.R. de Boer et al. / Enthalpies of formation of Sc, Ti and V alloys

304

11.701 1.5

/

/

kE4 N.

‘\

’

/

2.0

\

1.0

a

P _-_

1.0

:

Ti

SC

TI

V

Cr

Ti

un

Ti

Fe

[I.23 2.0

15

1.0

P

Zr

Ti

Nb

TI

Rh

Ti

Pd

Ti

W

Ti

Re

co

TI

Ni

TI

Y

Ti

MO

Ti

TC

TI

RU

Ti

Ta

Ill

M -_

[1.2_21 2.0

k P

1.0

a

La

Ti

Hf

Fig. 4. Binary

phase diagrams

of Ti with 3d, 4d and Sd transition

metals.

Ti

F.R. de Boer et al. / Enthalpies of formation of Sc, Ti and V alloys 2.0 t-

Il.le.Lll

I 15

Ti

Th

PU

Ti

CU

Ti

4

Ti

K

TI

Be

Ti

1.0

0.0

Ti

AU

Li

Ti

0.0

00 No

Ti

Ill

2.0 r

I

1.0

1.0

0.0

05

-C-._-----

M9

Ti

Co

TI

Cd

TI

4

Ti

0.5

Sr

Ti

Ba

Ti

Zn

Ti

e

TI

Al

TI

Go

Ti

Sn

Ti

Bi

Ti

Ill 1.5

Ti4Pb

1.0

+

P

Ti,Pb?+i

t

Pb

,

: Ti

N

TI

As

Ti

Sb

TI

Fig. 5. Binary phase diagrams of Ti with actinides, noble metals and the other metals ranged according to increasing valence.

F.R. de Boer et al. / Enthalpies of formation of Sc, Ti and V alloys

306

Table Ti-II Comparison of experimental and calculated values for the heat of formation, tifor, of titanium compounds (kJ/mole of atoms). Published values for the entropy of formation, ASfor , have been added (J/K mole of atoms) aHfor

tifor

ASfor

Method

Remarks

Ref.

-3

-

vap. press.

111

-11

_

sol. soln; reg. sol. model assumed

System

Compound or alloy

Ti-V

TkoV50

;12773-1998 K)

Ti-Cr

TiCr2

-3 (AC) (1523 K) -9 -20 (298 K) -35 (298 K) -44 (AC) (1300 K) -34 (298 K) -32 (AC) (1300 K) -27 (298 K) +3 (1844-1900

Ti-Fe

TiFe

Ti-Ni

TiNi

TiNi

TizNi Ti-Mo

Ti-Pd

TisoMoso

TiPd3 TiPd

Ti-Ir

TiIr3 TiIr

Ti-Pt

TiPtg TiPt3

Ti-Cu

TiCu4 TiCu TizCu

Ti-Hg

TiHg

Ti3Hg

C&Z

exp

Cv

-28

-

vap. press. (1523-1653 not given calorim.

-41

-

calorim.

2

emf

48

calorim.

2

emf

48 2

-58

-

-45

_

calorim.

-6

_

vap. press.

-67

-

vap. press. (1821-2036 vap. press. (1710-1965 vap. press. (1850-2100 vap. press. (1850-2100 emf

42 K) 43 2

K)

-56 (AC) (1873 K) -67 (AC) (1873 K) -59 (AC) (2000 K) -83 (AC) (2000 K) -42 (1150-1300 K) -85 (1150-1400 K) -23 (773 K) -19 (773 K) -26 (AC) (773 K) -1 (<573 K) -2 (>573 K) -3 (523-673 K)

-109 -58 -93 -34 -76

-6.0 (1150-1300 -8.4 (1150-1400

-16 -27 -21 -39

-29

(7”,3 K) 0 (773 K) +6.1 (<573 K) +3.0 (>573 K) -0.4 (523-673 K)

K) K) K) K)

sol. soln; reg. sol. model assumed ref. st . liq . Ti and Pd ref. st. liq. Ti and Pd see also ref. 45 see also ref. 45

112

57 51 50 50 44

K) emf

44

metal-hydrogen equil. (773 K) ,>

120

K)

120

I, vap. press. l

,

>I

120 exp. refer to solid Hg 3, >,

37 37 37

F.R. de Boer et al. / Enthalpies of formation of Sc, Ti and V alloys

301

Table T&II (continued) *for

System

Compound or alloy

&$yp

Ti-B

TiBz

-93 (298 K)

-13

Ti-Al

TiA13

-31 (298 K) -38 (298 K) -36 (890-1010 K) -25 (298 K) -24 (890-1010 K) -93 (298 K) -45 (298 K) -60 (923 K) -59 (298 K) -65 (298 K) -19 (923 K) -80 (298 K) -12 (298 K) -17 (923 K) -15 (298 K) -115 * (1093 K) -94 * (1093 K) -92 * (1093 K) -50 * (1093 K) -169 (298 K)

-42

calorim.

2

-61

calorim.

2

TiAl

Ti3Al

Ti-C

TiC

Ti-Si

TiSi2

TiSi

TigSig

Ti-Sn

Ties”5 Ti5Sn3 TiZSn Ti3Sn

Ti-N

TiN

talc

Asfor

exn

Method

Remarks

Ref.

-4.6 (298 K)

calorim.

AS from CP analysis

2

emf.

-2.9

(890-1010

K)

-3.8 (890-1010 -6.0 (298 K)

-61

-82

-14

emf K) calorim.

52 2

calorim.

-50

-81

exp. refer to solid Al

exp. refer to solid Al AS from CP analysis

52 2

calorim.

2

calorim.

46

calorim.

41

calorim.

2

calorim.

46

calorim.

41

calorim.

2

calorim.

46

calorim.

41 exp. refer to solid Sn ,,

46

-63

calorim.

-61

calorim.

-58

calorim.

3,

46

-48

calorim.

I,

46

-168

* Must be regarded as estimate due to experimental uncertainties.

-48 (298 K)

calorim.

AS from CP analysis

46

2

F.R. de Boer et al. / Enthalpies of formation of SC, Ti and V alloys

308

Table Ti-III The heat of mixing and solution of liquid titanium alloys (kJ/mole of atoms): comparison of experimental and calculated values. Standard states: pure liquid elements M V Fe

Ni

fl

exp T:

-9 -82

-41 -67 -55 -46 -190

ZI Pd

Aqgc~c

,ylmix exp

AH!%

+o * -10 -23

-2 -19

-38

-39

&hexp

ASIcalc -8 -70

-41 -66

* * -170 0*

-0 -283

0*

-0 -72

-105

-140

Li

small solub. +15, +35

+116

+30

-0 -293 +136 -2 +115

Na K

small solub. small solub. +17, +45 +41

k199 +246 +40

+60 +86 +11

+287 +500 +47

+26 -115 -188 -154

+121 -135 -222 -182

+87 -1

La Pu

Mg Ca Al Si Ge

-56

*

liq. imm.

-30 C-67)

+27 -0

+38 -34 -54 -46

0*

-18

-100

*

+189 -137 -211 -188

Ref. 53 54 55 56 57 58 59,60 51 1 61 1,62 63 65 62,64 63 68 63 66 2,67 113

* AGXSor A@“. ( ) extrapolated value.

4. Vanadium

alloys

In tables V-Ia, b we have collected calculated values for the alloying enthalpies of binary vanadium alloys. For the majority of the V-based binary systems phase diagrams have been published in the handbooks (Hansen and Anderko, Elliott, and Shunk [ 11, Moffat [22]). The binary phase diagrams are presented in figs. 6 and 7. For V with Ag, K, Na, Rb, Cs, Ca, Sr, Ba, and Tl, there is no information. For these nine systems the heats of alloying are predicted to be large and positive, ranging from &SC = +16 kJ/mole for “VAg” to +123 kJ/mole for “VRb”. A quantitative comparison of experimental and calculated values of AH for solid compounds is made in table V-II; agreement is quite satisfactory. We note that for VseTise, VseCrse, VseFese, and V6eA14e the experimental values refer to solid solutions, whereas the calculated values are for the ordered compounds. Near the equiatomic composition

AH:& for the statistical solid solution and AHzc for the ordered compound differ by a factor of 1.5 [3] ; in addition there can be an elastic size mismatch contribution, which contributes more positively to AHfor for the solid solution than to AHfor for the ordered alloy. For VsNi the calculated value appears to be too negative: here we have the situation of a compound in which the electronegative minority metal is one at the end of a transition metal series. As explained in section 3, in this situation one may expect AHcalc values to be too negative. Similar devia. tions are to be expected at the V-rich side of the V-Pd, Pt, Au systems. In the V-Ge system the values tend to be less negative than the experAH% imental data. It is remarkable, however, that the experimental values for A,Yp are large and negative; in fact, AGZ, agrees quite well with &Gf,. Probably, therefore, the deviations in the V-Ge system are caused by inaccuracies in the determination of the temperature dependence of AGgp. It can be seen in table V-Ib that for V-C, V-Si, V-Ge and

F.R. de Boer et al. / Enthalpies of formation of Sc, Ti and V alloys

V-N the &czc values change sign with composition. This is due to the fact that under normal conditions C, Si, Ge and N are not metals. To account for the transformation from the diamond structure (C, Si, Ge) into a more conventional metallic structure and from molecular into metallic nitrogen we have introduced transformation energies. The change in sign in the V-N system prevents the existence of compounds at the N-rich side of this system. The problem of the stability of transition metal nitrides has been treated in detail by Bouten and Miedema [108]. In table V-III we compare experimental values for heats of mixing and solution of liquid V systems with calculated values. Calorimetric data are available for V in liquid Si, Ge, and U and for the V-Sn system. For V-Si the agreement is perfect, but for V in U there is a large discrepancy which, in our opinion, is due to experimental inaccuracy. The V-Sn system is a special case since a change in sign of A/!!?$$ has been observed (V in Sn: t29 kJ/mole; Sn in V: -67 kJ/mole). The calculated values apparently represent the average value. Knudsen cell activity data and information on AGxS are available for the Fe-V system; the experimental data show a large scatter. For the remaining alloy systems in table V-III the experimental information consists of solubility or miscibility data, from which the enthalpy values have been derived. Finally, we compare in table V-IV the qualitative alloying behaviour of vanadium with phase diagram information; only systems for which AH!& for the equiatomic compound lies in between -6 and +6 kJ/ mole are included. The critical situation is reflected in the systems of V with Pb, In, and Cd. Compounds of the VaM composition have been prepared, whereas A@& > 0. V&r, however, is reported to be metastable at normal pressure [75]. One may also note, that although &c& < 0 for V-Bi, no compounds have been reported yet.

5. Discussion Differences between the empirically predicted enthalpy values and the experimental ones can partly be attributed to the fact that the proportionality constants in our three-term description have been

309

given the same value for widely different alloy systems. Further, we do not consider structuredependent energy terms in detail. For the proportionality constant P (of the charge transfer term) and Q (of the density mismatch term) we only distinguish between transition and non-transition metals. Also, the coefficient of the hybridization term R (for alloys consisting of a d and a p metal) is treated as a contact interaction term independent of structure and only varying with the valence of the p metal. As noted in section 3, the value of P may be lower than average if electropositive metals (like SC and Ti) are combined with the electronegative metals at the right-hand side of a series of transition metals Ni, Pd and Pt (and Au). The fact that electronegativities of the elements tend to fall steeply beyond the elements Ni, Pd and Pt(Au) makes the resistance against charge transfer larger than average (P is reduced). The predictions do not take this effect into account; therefore, for alloys of SC and Ti (and many other electropositive metals) with Ni, Pd and Pt, that are rich in the first metal, it is likely that the predicted values for the enthalpies of formation will generally be too negative. A second quite general source of differences between calculated and experimental values will be the way the R term has been introduced. Without doubt this hybridization term involves special orientation of the non-spherical part of the p electron wave functions of the polyvalent non-transition metals with respect to that of the d electron wave functions of the transition metal partner. Apparently, for a given d metal + p metal alloy system there are always a number of combinations of compositions and crystal structures for which d and p metal wave functions combine properly, thus giving rise to a large (negative) R term. Crystal structures or compositions for which the hybridization term is not large simply cannot exist. One must conclude therefore that there is some additional uncertainty in the predictions of enthalpies of alloying if the R term is large. The problem manifests itself quite clearly in the experimental observation that in liquid alloy systems, in which there is a large R term and in which moreover AHmix is near zero, the integral heat of mixing may change sign as a function of concentration of the liquid alloy. The origin of this is that in the liquid, too, the R term (found to be about 73% of that in ordered compounds) requires considerable ordering.

F.R. de Boer et al. / Enthalpies of formation

310

of SC, Ti and V alloys

Table V-Ia Calculated values for the heat of formation, &Yfor , of compounds of five different compositions, the limiting partial heats of solution, &, and the integral heat of mixing mmrx, kJ/mole of atoms, for binary vanadium alloys. Phase diagram information, if available, has been added for the solid systems M

SC

Ti

Al!P VM5

VM2

VM

V2M

V5M

+4 -1

+8 -3

+11 -3

+10 -3

+5 -1

Phase diagram inform.

2

Ai?0

V in M

VM

Co

+25 -8

-2

+

-+I

M in V +33 -9

Cr Mn Fe co Ni

-1 -0 -5 -9 -12

-2 -1 -9 -18 -23

-3 -1 -11 -21 -27

-2 -1 -9 -17 -22

-1 -0 -4 -8 -11

C cc_ _

-8 -3 -29 -58 -75

-2 -1 -7 -14 -18

-8 -3 -28 -53 -69

Y Zr Nb MO Tc Ru Rh Pd

+9 -2 -1 -0 -13 -15 -18 -21

+17 -4 -2 -0 -25 -30 -35 -41

+24 -5 -2 -0 -32 -31 -44 -53

+24 -5 -2 -0 -27 -32 -38 -46

+14 -3 -1 -0 -14 -17 -20 -24

+ C C _ _

+54 -12 -6 -0 -80 -94 -112 -131

+17 -3 -2 -0 -21 -25 -29 -35

+85 -16 -7 -0 -89 -104 -123 -152

La Hf Ta W Re OS Ir Pt

+18 -1 -1 -0 -13 -14 -21 -21

+36 -2 -1 -1 -26 -28 -41 -53

+51 -3 -2 -1 -34 -35 -51 -68

+52 -3 -1 -1 -29 -30 -45 -60

+31 -1 -1 -1 -15 -16 -23 -32

+ _ cC _ _ _ _

+112 -1 -4 -3 -84 -88 -129 -167

+36 -2 -1 -1 -23 -23 -34 -46

+191 -9 -4 -3 -97 -99 -147 -200

Th U Pu

+4 +o +3

+9 +1 +5

+12 +1 +6

+12 +1 +6

+I +o +3

+

+21 +2 +16

+9 +1 +4

+45 +3 +19

cu Ag Au

+3 +8 -11

+5 +15 -22

+6 +19 -29

+5 +17 -26

+2 +9 -14

+

+16 +48 -69

+4 +13 -19

+15 +51 -89

If the heats of solution are large and negative this ordering will always be present. Experimentalists tend to speak of “molecular ordering in the liquid”, excess entropies generally being large and negative. However, if the heat of mixing (including the average R value) were to come out positive the local order in the liquid would be less. Hence if predicted values of the heat of mixing come out positive one can expect the real values to be even more positive. In the inter-

0

+

+ -

(11

mediate case of aflmix near zero the result is difficult to predict. A large R term will be associated with a small entropy of mixing. Predictions for small heats of mixing would imply a proper evaluation of the competing terms in a free energy calculation, which is not done in our model. It will be clear that a change of sign of the enthalpy of mixing with alloy composition can easily occur. In fact for any alloy system with an R term and an enthalpy of mixing near zero

F.R. de Boer et al. / Enthalpies of formation of SC, Ti and V alloys

311

Table V-Ib For caption see Ia M

Lwf”’

“MS

-

VM2

VM

V2M

V5M

Phase diagram inform.

sip V in M

VM

MinV

+ [II

+140 +230 +265 +268 +268

+31 +13 +96 +100 +103

+143 +344 +552 +614 +681

-23 +a2 +134 +151 +163 -6 +32 +34

-5 +23 +43 +53 +51 -2

-16 +103 +224 +296 +336 -6 +42 +4a

-

Li Na K Rb cs

+22 +37 +42 +43 +43

+44 +14 +85 +85 +85

+55 +104 +126 +128 +129

+45 +101 +144 +152 +I58

+23 +56 +90 +101 +112

Be

-9 +24 +43 +50 +52 -11 +1 +2

-10 +31 +61 +73 +I1 -13 +2 +3

-1 +28 +62 +85 -11 +2 +3

-4 +15 +36 +48 +54 -6 +1 +2

+

Hg

-5 +12 +21 +25 +26 -5 +1 +1

B Al Ga In Tl

-26 -16 -11 +1 +6

-41 -32 -21 +1 +11

-51 -40 -28 +2 +I6

-38 -34 -25 +2 +15

-19 -18 -13 +1 +9

+

C Si Ge Sn Pb

+15 +1 +3 -7 +1

-43 -29 -19 -14 +3

-53 -41 132 -19 +4

-38 -43 -31 -19 +4

-19 -23 -11 -11 +2

_ _ _ -

-121 -10 -3 +48

N AS Sb Bi

+83 -27 -11 -2

-45 -54 -22 -3

-93 -11 -31 -5

-14 -66 -31 -5

-31 -36 -18 -3

+

-122 -25 +33

Mg Ca Sr Ba Zn Cd

+I8

we expect anomalous behaviour; for instance, the. enthalpy of mixing can have a much stronger temperature dependence than in normal situations. Apart from offering a possibility to make reasonable estimates of alloying enthalpies for practical purposes, there is also an interest in the predicted values from the theoretical side. Recently a number of theorists [ 121-I 261 have tackled the problem of alloy cohesion. In theoretical work it is important to find trends by doing a series of calculations in which the metals involved are varied systematically (Fe with all other 3d metals [123], Rh with all 4d metals [ 124-

+ [II

.. . -61 -29 +40 +11 ...

...

+9 +10 .. . -16 -8 +12 +21 . .. -31 -19 -1 +15 . .. -35 -8 +10

.. . -68 -36 +59 +109 .. . -128 -80 -4 +80 .. . -162 -40 +51

125 1, trends in M with increasing difference in atomic number of the constituent metals taken from a given series of transition metals [ 124,126], alloys of Pt with 3d metals or Zr with Sd metals [ 1251). The systematics of such theoretical approaches are usually not covered by the availability of experimental data. However, in view of the fact that our empirical values for the heats of formation are in good agreement with hundreds of experimental data, our predictions may serve as the “experimental” reference to verify the reliability of the assumptions or approximations made in theoretical work. In order to illu-

F.R. de Boer et al. / Enthalpies of formation of Sc, Ti and V alloys

312

il.731

[lJ.2_2.8_71

2.0

1.5

2.0

u

l,ol

c+V

(6-t4n.V)

10

1.0

ia-Scl + (VI

lIII--d +

I

15

,

,$,

)

I’1

;

2.0

:

1.5

CO

V

Ni

V

Ma

V

TC

V

L2

M ’

10

+

(P-La)

LO

:

\

IL

L*tv)

1.0

IYl*lVl

P

\

\

/’

Y

V

M Zr

V

Nb

V

RU

V

Rh

V

Pd

V

Il.221

\ 3.0

‘\\

20

+

1.0 V

Hf

V

/0’

‘A

:

\

3.0

\

15

+ (V)

, r;l >”

20

L1*L2

1

(Liq.Lak(V) -

,

Ill

2.0 L,

1.0

:-‘\

I

I

2.01

III

a::;

Ta

V

1w.v

. .

\

\

\

20’

‘\

1

i:-_

10

W

V

25

Fig. 6. Binary phase diagrams of V with 3d, 4d and Sd transition

m 11.741

H z \ z,

metals.

\

I I

I -

Re

V

F.R. de Boer et al. / Enthalpies of formation of Sc, Ti and V alloys

[l I 15

/

r1.121

20

I

ILA /

/

/

/

/.

,

1.0

1.0

, [~.22,103,1fl]

C*

2.0

L +v

1.5 1.0

u

I

Th

V

u

V

,

2.0

Lt+L2

//’

Y

lot

313

w

O.Om

1.0

L *(VI ICU)*IV) I

1

CU

V

0.0 AU

V

I221

Ill

2.0 L_

lrl 2

3 >

-9 3

L + (VI

wgl + IV1 V

[ll

u;rl

I? I I 1.0

20 533n *_--1.0

, I

0.5

Al

' ‘I

I 'I II

(VI

II II

V

Ga

2.0 1.5

ll.s_21

V

Zn

2.0 '

si;,$

1.5

2.0

3 f

El 4

V

Be

3.0

:

1.0

0

sl >

[ll

\

Ll l L2

12J.751 L1+L2

Cd

V

1.0 I3

V

c

V

Si

V

As

V

' ?

L +w

V

0.0;_1 In

V

V

Pb

V

5, g

, -_ I

1.0 / 0.5 , ml Sn

1221

L

0.5

Sb

IBi) + IV)

00 V

L + IV)

Bi

V

Fig. 7. Binary phase diagrams of V with actinides, noble metals and the other metals ranged according to increasing valence.

F.R. de Boer et al. / Enthalpies of formation of SC, Ti and V alloys

314

Table V-II Comparison of experimental and calculated values for the heat of formation, AHfor, of vanadium compounds (kJ/mole of atoms). Published values for the entropy of formation, Asfor , have been added (J/K mole of atoms) System

Compound or alloy

V-T1

Vdko

V-C1 V-Fe

+2 (1773-1998

mfor talc

-3

-3

VsoFe50

vco3 v25c075 V55Co45 V9oCot 0

V-Ni

V3Ni

V-Al

VA13 V5A18

V60A’40 v-c

vc

V-Si

VSi2

V&

$76-1748 +o (1450-1800 -5 (1600 K) -6 (1665 K) ,“,,O K) -8 (1273 K) -8 (1665 K) -9 (1400 K) -14 (973 K) -9 (1473 K) -11 (1473 K) -2 (1473 K) -7 (900 K) -28 (298 K) -23 (298 K) -38 (933-1040 -22 (298 K) -54 (298 K) -42 (960-1033 -42 (298 K) -50 (298 K) -40 (298 K) -51 (960-1033

ASfor exp

Method

Remarks

Ref.

vap. press.

sol. soln; reg. sol. model assumed sol. soln

111

K)

vsoc’so

VFe

v-co

tifor exp

K) -11 K)

+6.8 (1376-1748 +10.9 (1450-1800 +7.2 (1600 K) +3.9 (1665 K) +6.9 (1600 K) +5.0 (1273 K) +2.0 (1665 K) +4.7 (1600 K)

vap. press. vap. press. K)

sol. soln; ref.st. o-Fe sol. soln; ref.st. T-Fe sol. soln; ref.st. S-Fe sol. soln; ref.st. or-Fe c-phase; ref.st. y-Fe o-phase; ref.st. y-Fe a-phase; ref.st. or-Fe ref.st. fee Co

2

-14

calorim. + assessm. vap. press. + phase diagr. calorim. + assessm. calorim. + assessm. vap. press. + phase diagr. calorim. + assessm. calorim.

-14

calorim.

-21

calorim.

-5

calorim.

-16

calorim.

80

-24

calorim.

2

-36

calorim.

2

-11

-2.6 (933-1040

K)

emf K)

-38 -53 -29 K)

-45 K)

2

K)

calorim. -3.3 (298 K) +4.1 (960-1033 -2.6 (298 K)

-2.5 (298 K) -4.8 (960-1033

calorim.

sol.soln; ref.st. fee Co o-phase; ref.st. fee Co sol. soln; refst. fee Co

81 106 78 81 106 78 115 115 115 115

exp. refer to solid Al sol. soln

52

AS from Cr, analysis

2

2

emf

99

assessm.

76

calorim.

96

assessm.

105

emf

99

K)

K)

F.R. de Boer et al. /En thalpiesof formation of Sc, Ti and V alIoys

315

Table V-II (continued) System

Compound or alloy V&3

V3Si

V17Ge31

V-Ge

VrlCes V&e3 V&e V-N

VN “2N

&$OT

ASfor =P

exp

-58 (298 K) -59 (298 K) -49 (298 K) -38 (298 K) -41 (298 K) -27 (940-1170 K) -47 (940-1170 K) -48 (940-1170 K) -45 (940-1170 K) -109 (298 K) -88 (298 K)

Method

-44

-1.3 (298 K) -32 -0.8 (298 K) -3.9 (940-1170 -9.4 (940-l 170 -9.3 (940-1170 -11.6 (940-1170

-21 -34 -33 -25

Remarks

assessm.

76

calorim.

96

assessm.

105

assessm.

76

assessm.

105

emf

98

emf

98

emf

98

emf

98

K) K) K) K)

-93

vap. press. (1900-2412 calorim.

-74

77 K) 79

Table V-III The heat of mixing and solution of liquid vanadium alloys (kJ/mole of atoms): Comparison of experimental and calculated values. Standard states: pure liquid elements M Ti Fe

Y Zr La U Pu Cu Ag Li Na K Mg Si Ge Sn Bi

* AGXS

fl

v

exp

-57 -26 * -42 * -80 *
small solub. small solub. small solub. +65 +23 -130 -68 +29 +27 or AcxS.

( ) extrapolated value.

A@$@lC -8 -29

AHg

qz

+o*

-2 -7

-7.5

mijti exp

I),calc

UM

-9 -28 -27 *

+54 -12 +112 +2 +I6 +16 +48 +140 +230 +265 +82 -121 -70 -3 +33

-4.5 * liq. imm. liq. imm.

liq. imm. liq. imm.

C-25) -5.1

Ref.

(-92 *) +17 -3 +36 +1 +4 +4

+85 -16 +191 +3 +19 +15

+13 +37 +73 +96

+57 +143 +344 +522

+23 -31 -19 -1 +10

+103 -128 -80 -4 +57

(-67)

Ref. 53 101 56 57 106 1 60 1,103 85 86,102 100 1,103 1 1,62 64 65 63 63 67 113 104 63

F.R. de Boer et al. / Enthalpies of formation of Se, Ti and V alloys

316

Table V-IV Qualitative comparison of calculated AHfor values (kJ/mole of atoms) with phase diagram information System

Af&c

v-Pu v-cu V-Pb V-Hg V-In V-Cd v-u V-MO V-Mn V-W V-Ta V-Nb V-Cr V-Hf V-Ti V-Bi V-Zr

+6 +6 +4 +3 +2 +2 +1 -0 -1 -1 -2 -2 -3 -3 -3 -5 -5

(VM) no compounds; small solid solubility no compounds; small solid solubility V3Pb no compounds V3In exists; metastable at normal pressure V3Cd no compounds; max. sol. 12% V in U and 4% U in V cont. solid solubility cont. solid solubility T > 1100” C; ordering cont. solid solubility cont. solid solubility T > 1300°C; VZTa exists cont. solid solubility cont. solid solubility V2Hf cont. solid solubility T > 800°C no compounds known V2Zr

strate this application of our work we compare in fig. 8 a number of theoretical results for &Or of equiatomic compounds containing SC, Ti or V with the empirical predictions.

AH!&, [ kJlmole

otomsl

-

AH$~kJlmole

atoms]

Fig. 8. Comparison of the results of several theoretical calculations with the “experimental data” provided by the empirical model [ 3 ] x self-consistent local density formalism [ 121) 0 atomic cell approach [ 1221,~~ variational theory based upon band widths and band positions [ 1231.

6. Conclusion In this paper we have demonstrated that enthalpies of alloying for binary systems based on either SC, Ti or V, can be predicted with an accuracy which is of practical interest. In most cases in which there is a difference between experimental and calculated AH values the origin of this deviation can be explained. Although much experimental work has been performed, in particular on Ti and V systems, the availability of a complete set of predicted values can be of importance in connection with the metallurgy of these metals. In future papers in this series this will be demonstrated in a treatment of i) interfacial energies for solid-solid or solid-liquid bi-metallic interfaces; ii) solid solubilities in alloys of 3d metals; iii) the composition of the surface layer in dilute alloys; and iv) the stability of hydrides formed from intermetallic compounds with Sc, Ti or V. Although the scope of the present paper is restricted to a comparison of model values with experiments on binary systems, the availability of predicted enthalpy values is of great relevance for multicomponent systems. In theoretical metallurgy there is a tendency to

F. R. de Boer et al. /En thalpies of formation of Sc, Ti and V alloys

tackle the problems of multicomponent systems of technological importance by means of detailed computer calculations. In these computer calculations the present set of AH values may serve as input parameters [ 1091.

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