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Assessment of thermodynamic functions of formation for rare earth silicides, germanides, stannides and plumbides
ELSEVIER
Journal of Alloys and Compounds 248 (1997) 233-245
Assessment of thermodynamic functions of formation for rare earth silicides, germanides, stannides and plumbides
A critical assessment has been made of the available data on thertnodynamic properlies of bhtary compounds of ktnhanii metals, scandium and yttrium tR) with IV group p elements (X&i. Ge, Sn and Pb). obtained mainly through the direct e.m.f and cakehnenk methods On the basis of the most reliable data the following empirical relation was derived which allows the cstlmatko of encopks or formation for the intennetallics (A,.51 by using the enthatpies of formation per mole of A,,,,+,,B,,,,+,, compotmd (A,& together with the melting CT,,,,) and boiling temperatures CT,,,) of the components I (1EA.B): A&,
= aR
mn (m +I#
Im+“,~lnn
3Tnl (3 Tb
f 3,H,. h
where A&=AJ-
WA+%JB);AH m-tn
,m
=AH-(mAm4+~LHB). , m+n
+
i;. =(T,,,, + T,,,a)12 and F,, =(T,,, +T,,,)/2; A,$, and A,H, are the entropy and enthalpy of melting of the comptments, respectively; m and n are stoichiotnetrlc coefficients of a binary A,B, compound; a and b are empirical coeBictents, and R is the gas constant. The calculated entropy values for the R-X intennetallics are in agreement with expethnental data avallabk. Keywords: Rare eanh-p element compoand: Enthalpy of fonn&o:
Entropy of formation: Empirical assessment
1. Introduction
enthalpies
of form&u. By contrast, the e.m.f.datacan be more exothermicdue to the possibleexistenceof oxygen impurities, which can form very stabk oxides. ‘l’hcsc effects should be cottshiered when comparing the ex-
During the last decade, there has been a great increase in the amount of tbermndynamic data for intermetallic rare earth-p element compounds. The mejorlty of available information (with very few exceptions) concerning thermodynamics of formation for R-IV-group p element intermetallics was obtained by two direct methods - e.m.f. and calorimetry. Combination of these data allows mote precise determination of entropies of formaticn for the
perimental results of the two methoda. UttforhtnateIy, the still remains incomplete owing hermodynamic infoematkn to the difficnltka of e.m.f. and cal&mehic measutemanta at high temperatures, which have been pointed out in a
compounds[l-3]. Both methodshave some advantages
recent paper by Colinet [4]. Ne~&&ss, the available data make it possibleto reveal some enthalpy-erttropy correlations.It mustbe pointedout that nowadaysit is very
and restrictions.
important
Errors
in caIorimettic
experiments
(dissn-
.
to search such empirkal
approaches
for reaBatic
mason of incompleteness of dissolution or combustion because of high thermodynamic stability of the com-
values for a system L the basis of o&r experinn&tl data for the same system. In a previous paper [5] the method for
pounds. This results in less exothermic values of the
empirical estimationof excess partid and integral entropies of mixing for the binary systemsby using experimental
*Conespwding author. u925-8388/97/$17.00 PII
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1997 Flscvler
S.A. All
dglns
-cd
mixing
enUtaIpy
datp,
melting
and
boiling
234
LT.
Wesinvic;
er ul. I Journal
of Alloys
40 m
and Ccmpounds
248 !199?)
.‘33-245
RF?)3
-36
40
Rsn 3
l -
40 &
-70 OD?
.
$0
0.08
. .
o!kT-x--
- 0.11
b
Fig. 1. Plots of the enthalpies of formation of some isostoic! iometric types of R-X compounds vs. atomic nunber of lanttsnides (a! and (rr enc vs. mdiudius of three-valent cation of rate earths (b) and (d): points are experimental values: lines are results of appmximatiott.
temperatures of the components, was proposed. In the present paper, it is shown that a similar approach is also applicable for empirical evaluation of thermodynamic functions of formation for the binary intermetallics such as silicides. germanides. stannides and plumbides of the rare earth metals.
2. Regularities COI”plldS
in thermodynamics
using correlations between different thermodynamh parameters, or observed regularities in the periodic t..ble. Thus, for enihalpies of lanthanide isostoichiometric clampounds there is a linear dependence on lanthaniae ato1.k number (N), or on the three-valent radius of rare earh cation (rr ). Such relationships for some Sn- and Pbcontaining compounds, for which thermodynamic prop etties have been studied rather extensively [6-561, are shown in Fig. I. The results of a least-squares analysis of this data are listed in Table 1. The values of radii for three-valent cations of the metals were taken from [57]. The dependencies A,H vs. N (Fig. 10 Fig. l(c)! and A,H vs. rr (Fig. l(b) Fig. l(d)) for RSn, and R,Sn, com-
of R-X
Generally, fundamental treatments for predicting such data is scarce, but rometimes good results can be obtained Table t
Resultsof least-quares analysis of A,H vs. N and A,H vs. r:’ depwkwies
for some isostoichiometric R-Sn and R-Pb compounds
Typ of compounds
Dependme
03&l
b+Ab
Standard deviation of A,H
Comlaion cafficien:
RSll,
4/l VS. N &$H vs. 1: A/ff YR. iv Ap vs. r; L$JI vs. N d/ff vs. 1: p vs. N A/i vs. r:* A/i vs. N A,n vs. r:
- 16S.7^15.9 52.2e 17.3 -208.OZ6.0 26.426.0 - 168.7~9.8 -4.3t10.4 - 155.928.9 66.3~5.6 - 175.4Z20.9 86.5+13.9
1.81+0.25 -1092Z18 2.14~O.IO - IOSSt63 1.65?0.16 -644211 1.76-cO.14 - 1163f59 tKEo.33 -1398215
3.8 4.3 0.8 1.7 1.5 3.1 1.9 1.8 3.6 2.5
0.916 -0.875 0.997 -0.993 0.978 -0.922 0.970 -0.Y85 0.9i36 - 0.989
fW4 R,Sn. m, m>
VT. Wifusiewic: et al. I Journal of Alloys and Compounds 248 (1997) W3-245 Table 2 The results of estim%ion of the enthalpies of fomution and their prediction confidcncc bands at toknncc 0.05 for R&B,, R,.Sn, nd P.!h, compmmds R
N
z-21Y La Ce R Nd F’m
Sm EU Gd Tb Dy Ho Er Tm Yb Lu
39 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
r:* “In
O.WOS 0.1071 0.1034 0.1013 0.0995 0.0979 0.0964 0.0950 0.0938 0.0923 O.WC8 0.0894 0.0881 0.0869 0.0858 0.0848
-A& RSll,
kJ ml-‘ R,S%
R,%
LitemNrc dats
vs. N
YS r;
Literature Cw
vs. N
63.Ok9.7 61.1-9.5 59.1+9.0 57.lk8.6 .55.1+8.4 53.027.6 51.0-6.8 49.0+6.0 47.1T5.6 45.0f4.6 430?4.0 41.1+3.8
46.7e6.0 64.8t9.5 60.8Z8.6 58.527.2 56.5=6.4 54.8-iS.5 53.1~5.4 5,.6-c5.C 50.3%5.0 48.7Z4.7 47.0~57 43.3-5.3 44.1+7.0
52.2% 1.2 161= 87.4t4.2 [S] 83.724.2 1181 80.0 I281 69.0 1171 68 1171 -
SO.SZ9.4
52.3Z2.1 181 62.5+2.1 [SJ-171 55.OZ2.1 [IS] 5a.s+3.s [I I] 64.3 [11.17.191 56.0 [11.17.20] 52.82 1.9 1211 5l.Of2.1 1221 45.0 [ 171 45.211.2 1241 43.0 [,7.2.5] 44.0Zl.0 t11.261 33.920.4 1231’ 39.0 [I71
37.0-3.8 34.924.2
41.6~8.5 40.5’9.0
-
IS. r:’
Li*RRIca
.5X2+1.2161 69.3+6586.6k4.2 86.8Z9.0 84.424.0 82.927.6 82.3Z3.8 80.7+7.0 80.2-3.8 78.8k6.6 78.023.8 77.126.6 759~3.8 75 5Z6.0 73.8’3.9 i4.OkS.a 71.6~4.0 72.825.8 69.524.2 71.225.9 67.424.2 69.626.2 65 354.5 6X1-6.4 63.1k4.8 66.7Z6.8 61.OZ5.0 6X527.2 58.9~5.2 65.5k7.3 56.7e5.6 63.228.0
vs. N
75.9~42 [8] 73.2Z4.2 (IS] 70.0 1171 63.623.4 1201 61.0 [17] 61.0 1171 59.0 1171 56.0 [I71
74.7239 73.1 f3.8 71.423.7 69.8?3.6 68.123.6 66.5Z3.5 64.8235 63.223.6 61.523.7 59.9233 58.2+3.9 56.6T4.0 54924.2 53.3k4.4 51.624.6
vs. r;* 51.3-TlO.8 62.6*5.0 7X327.7 70.926.4
69.s~5.8 69.4f5.3 67.425.0 66.424.6 6X5-+4.6 64.724.6 63.824.6 62.824.8 61.9Z5.1 61.1+24 60.3Z3.7 60.3zs.9 58.926.3
‘In the reuem works of [59.60] rhe existvlce of LuSn, and SC,% compounds was not confirmed.
pounds, as well as for RPb, and RPb?, show very similar slopes because the character of interatomic interaction is very similar for them systems. The crossing of A,H vs. r: lines for RsSn, and RsSn, intermetatlics. located between Sc and Y, confirms that for the Sc-Sn system the Sc,Sn, compound is the most stable. Such dependencies dlow the evaluation of unknown enthalpies for the compounds. According to a survey of R-Sn phase diagrams [58], the R,Sn, and R,Sn, compounds form in the majority of the systems while RPbz compounds exist in most of the R-W systems. However,
the information about enthalpies of formation for the above mentioned three isostoichiitric series of imetmemilii is scarce (see Fig. l(c) Fig. l(d)). Taking into account the similarities of RSn, and RPb, comPouuds (see Rg. l(a) Fig. l(b)), evaluation of missing data using both A,H vs. N and A$! vs. $ dcpmdmcies was carried out. Some results for stannides and plumhides 3re summarized in Table 2 and Table 3 respectively. The values cakukd using the dependence on N in most cases has a low confidence limit, but the iatter approach possibility to evaluate the -nthatpies of
Tabk 3 The results of estimation of the cnthalpies of fomuti0.l and their prediction confidence bands at cokrance 0.05 for RF%,
RPh
f9
LilcraIure data SC Y La CC R Nd Pm Sm Eu Gd Tb DY HO Er 7-m Yb LU
21 39 57 58 59 60 61 62 63 64 it 67 68 69 70 71
0.0730 0.0905 0.1071 0.1034 O.ILl. 0.099s 0.0979 i o.owd I 0.0950 V.0938 O.W23 0.0908 0.0894 O.OS81 0.0869 0.0858 0.0848
vs. N
YS. r;-
LikraNN &la
55.7+5.6 53.9e4.2 52.2Z3.6 50.5+2.2 48.7-2.7 46.9T2.5 4X222.3 43 4+i..3 41.6k2.6 39.922.6 38.123.6 36.424.0 34 624.4 32.824.8 3l.lZS.4
18.528.8 38.918.0 58.2~8.0 539~6.6 51.4z5.7 49.325.2 47.se4.a 45.124.4 44.124.0 42.7-4.0 41.o-c4.0 39.224 1 37.fe4.3 36.lT4.8 34.755.1 34.725.2 32.226.0
37.2=2.l 1281 64?2.; 1461 55.0 1461 34.120.3 [%I
. .
19.O.tO.5 1271’ 35.9-4.9 [9,28-30.461 56.4k3.4 [31-33.47.481 53.822.4 ]31.34.35.49] 53.8ZO.5 [XI] 5i.422.9 ]31.34.36.51] 48.1+1.6 43.2Z2.4 41.3-3.4 39.854.1 42.224.3 36.8Z2.9 35.5?1.3 35.4k2.0 37.0~2.0
I31.52.531 [31.54] [31$5] I31.381 ]31.39.40] [31.41] 131.42.431 [31] [31&l]
‘In the resent work of [MI] tbc eaisuacc of ScFb, compmd
was not confirmed.
VS. N
“1 r:
61.7k9.7 59.729.4 57.729.2 55.7+9.1 53.7T8.9 51.628.9
40.026.3 63.2~6.9 58.026.5 55.1 f6.3 52.6k6.2 50.3e6.1 48.326.1
47.8Z9.C 45.7k9.1 43.7z9.3 41.829.5 39.629.8 37.72 10.1
44.6?6.1 42526.2 40.426.3 38.5 26.4 36.6265 34926.7
33.7210.9
32.Ok7.0
236
scandiumand yttrium-based compounds. For the intermetallics of light lanthanides both methods give very similar results, whereas for the systems of heavy lanthanides the difference in the values may extend up to 6 kJ mol-‘. There is insufficient thermodynamic data available for R-Si and R-Ge compounds 161-961 to reveal similar regularities.
CT,,,, + T,,,,)12 melting
thermodynamic,physical or structural data is available, such methodsof approximation may be improved 1971. For instance by correlating between the excess partial entropy and enthalpy in liquid binary alloys [97-1071 Kubashewski has shown that a plot of ASzax vs 2AH,,,,,/(T,,, + Tb,z) (where AH,,,,, and AS’,“,, are the maximum absolute values
of integralenthalpyand excessentropy of alloy formation and Tb.,, Tb,2 are boiling temperaturesof the metal components)has a constantslope [98,99]. Similarly Chart et al. [97] have shown that plot of AH,,, vs A.$,,,,, for I50 solid and liquid solutions is a straight line within enthalpy values from -50 to 120 kJ 11101-l. Tanaka with co-authors [102-1071 using a solution model based on free volume have derived the following relationships between partial
enthalpy (J&a) and excess partial entropy (AS’,“) at infinite dilution in a binary A-B system with similar physico-chemicalpropertiesof the components:
where T,,, A and T,,, B are
the mc!ting points of components This correlation has provided better A and B iespectiveiv. results than the previous one due to using melting temperaNres. The solution model hased on the free volume theory
and Eq. (I) is applicablefor the entire concentrationrange taking into account positive. negative or zero values of molar entropy in very dilute solution [ 1071. shown that excess partial and integral in the full concentration range for the 3d transition metals with metalloids (B, be estimated from experimental mixing
enthalpy data, melting and boiling temperaturesof the components [S]. According to this work, the integral excess entropy (A,$“) and integral enthalpy (A,&) of mixing is given by the following expression: $
(‘y” b
+T,,,)12
temperatures
of
are the
I,“+.l~l,,t.
A$,,, = ah’A For estimating the entropy of formation for metallic alloys the regular solution model is more often used. It can only be a rough model because the excess entropy in the whole composition range is supposed to be zero. If other
A$‘” =6Rr(l -x)
F,,=(T,,,
relation exists between the enthalpies and entropies of formation for solid compounds, which can then be used to evaluate the entropy of formation for binary intermetallics. A least-squares regression analysis through the all statistically treated experimental data of investigated R-X sys-
of the approach and calcrdarion details
Receutly it was mixing entropies binary systems of C, Si and Ge) can
and boiling
and
tems [6-56,58,6]-961 resulted in the following best equations:
3. Assessmentof entropy 3.1. Background
where F,,, = the average
components.respectively: R is the gas constantand x 1s concentrationof a metalloid. In the present paper, it is announcedthat a similar
+ +A,“,
-b
(2)
+A,Hh
(m + n)’
(3)
OnA,,,S,,+ nA,S, ) A$,,, = A$ nf + n A
H rm
= A H I
_
@4J4 ~-
(4)
+ 4J&l
(5)
m + n
where A,S and A,H are entropy and enthalpyof formation per moleof A,,,, +“,B,,,, +“, compound(a mole of alloy), respectively;A,,$, and A,HA are the entropy and enthalpy of melting of the components,respectively; m and n are coefficients of a binary A,B, comthe stoichiometric pound; a and b are empirical coefficients, which apply for the compounds of rare earth metals with the same p element. So, the plots of (A,S,IR) vs (A,H,,,/F,,R) for Si,
Ge, Sn and Pb systemsare the straight lines. where
(‘5) Evidently, the first term of Eq. !3] and Eq. (2) are rather similar especially if rnn/(m+n)‘=x(l-x), but there are bigger differences in the second terms of these relations. The above mentioneddependenciesare shown in Fig. 2. Tbe parametersa and b with their error bands(toleranceis 0.05) and correlation coefficients for the systems under consideration
are summarized
in Table
4. The
data
for
melting and boiling temperatures.and entbalpiesof melting for the componentsused were taken from (1081. For simplicity the coefficientsa and b can be rounded off within the range of their error bands, and it is convenientto operatewith the parameterslisted in Table 5. As one can see, both empiricalcoefficientsfor germanides and plumbidesare then equal to unity. The correlation between available experimental and estimated
(by Eq. (3)-
Eq. (5)
using parameters
given
in
Table 4) entropiesof formation for R,X, compoundsis shown in Fig. 3. A least-squaresanalysisshows that these data are described by straight line A,S,,,,,=(0.4?0.3)+ A&, with correlationcoefficientR=0.916, the tolerance being0.05. Similarly using coefficientsfrom Table 5 leads and R = 0.906. Much of the to A&c = (0.620.6) + A&, discrepancy
between
experimental
and calculated
values
1
b
-140 1 . . . -140 -120 -100
. -#)
. do
. -40
. f -20
0 -rm 5 j -200
,,‘. +‘:
Fig. 3. lllustmtion of conformity between estirnwd (AS sm., ) and experimental one (A&.
,.,-’ ,.’ ..-- ,/-. c3-J ,’ ,.’ ,tk+ I’ -? Jo0 v y ;a00
_400
C
400
-so
form&
110”
,,:/ ..
1
may bc explained by large errors in measuring of the entropies of formation for the intermetalliis as one should that all literature entropy data were determined indirectly.
remember
4 -200
-100
0
3.2. Results and discussion 0 earth stannides The evaluated entropies of formation for rare earth-tin compounds iogether with appropriate literature data are collated in Table 6. The same values for the most investigated systems are presented graphiially in Fig. 4. 3.2. I. The rare
Obiously, unlike infomdon about enthalpicsof fomw -250 -zoo d
150
+m/aTb
-100
-50
0
, J n-&K-’
Fig. 2. Relaions between enlbalpy and entropy baed on Eq. (3k F& (5): a, for R-S compounds; b, for R-C& compounds; c. for R-8n compounds: d. for R-Pb compounds: points are experimental values: solid lines UC rcsul~sof linear appmximation:dotted lines an conlidence bands at tolerance 0.05.
Trble 4
tion of the compounds, the experimental data for the entropies are very scarce. Thus, the propo& approach is very useful either for thermodynamic analysis of the processes or for furdter stimulation of experimental investigation of likewise systems. The Sc-Sn and Lu-Sn compounds form with positive vahtes for entropy. For Y-G, Dy-Sn and Ho-% systems, the dependencies of entropy vs. concentration of Sn have a variable sign. For
Table b Statisfically treated experimental and estm~aled thermodynamic properties for the raie ranh srannides --____-____--
,ss, 181 18.10,
05 -4,=13
-94-15
the other presented systems, the process of intermetallics’ formation goes on with negative entropy, the minimum value generally corresponding to RsSn,. Taking into account the results given in Tables 2 and 6 one may say
57f19 6,120 * 3.lZZ.I 03t18 -33222 -24524 -22522 -99=29 -85219 -nit25 -IS*t*, -I4,226 -14557 -14w27 -,22r2.4 -74+,9 -,23z24 -IS.%27 - I1.9L2 5 -58f17 -78+20 -148226 -113123 -7 8I2.0 -104224 -125ttb -126fZ6 -10,*24 -741,0 -12,232 .. 10.0~3 I -24r2, -86S.O - 10 6S.2 -19t28 -7.5-24 - 12.952 9 - w.5t3., -*Liz,., -*se23 -6CE2.1 -62+21 -4.122.3 1.1+1.6 -2.2220 -5.4t2 4 lSt*O - IOZ2.7 *.4=2., -18t28 -2658 62?,8 -2.or2.6 -2 63.7 O.St24 4.1Z2.1 I *+2* l.4f2.3 31ZL.l -49225 - l2..%f,.0 -104~2.5 37f19 -0.9222 ^ _
that interaction between unlike atoms and ordering effects in R-Sn systems arise respectively with an increased radius of three-valent cations of rare earth metals. This is also reflexted in an increasing melting temperature of the
VT. Wirusiewicz ef al. I Jouvd
of Alloys and Compounds 248 (1997) 213-245
Fig. 4. Enthalpies (left scak: s juares) and entropks (right scak: cixks) of fmtion points are literature data: solid points are the results of prfon’ned assessmenl.
of R-X
most row.
3.2.2.
The rare
earth
systems in the same
stannides
The experimentat and evaluated thermodynamic values for R-Pb systems are summed up in Table 7. In the present calculations all available data [27-561 except data from [34] was used. Entropy values measured by Knudsen method [34] seem to give low values by a factor of 2 or 3 and are not consistent with later results. Possibly there was a lack of information concerning phase equilibria and
of the intcmw.tallii compmmds in some M
ervrh-tin syslem~: open
stoichiometries of existing compounds while these measurements were perfotmed. Although there are so11te more entropy data for R-Pb intermetallics in comparison with R-Sn ones in the literature, they arc fragmentary; most of the data corresponds to RPb, compounds. For this reason, in Fig. 5. the results for only four almost compkteiy cxperimentatly investigated systems are prrsewed. Both iitemture and estimated data for entropy of YPb, and LaPb, compounds formation demonstrate good agreement. The experimental entropy value for LuPb, is evidently doubtM. As it can he seen from the illustmtion, in Y-Pb. La-Pb and Yb-Pb
Table 7 St~tistadly treaed experimental and estimated themmdynamic properties for the rare eanh plumbides Conipound
-6,H. kJ mol ’ 419ris x5.9+4.9 37.222.1 60.222.1 66.9-fZ.l 56.4Z3.4 64.0’2.1 59.0+2. I 69.9Z2.0 72.2+2.1 55.0~4.1 58.016.5 53.5=0.5 55.0 50.4r2.9 52.626.2 47.5C4.8 50.3e6.1 48.1+1.6 C.8.3-f6.1 43.1 k2.4 39.lk5.2
44.6-6.1 39.824.1 42.224.3 40.426.3 36.8Z4.1 38.5+6.4 35.5e2.0 36.6?6.5 35.4-c-2.0 34.9-6.7 37.OT2.0 57.3+0.8 57.7zo.a 58.2+2.9 32.6+6.0 34.22tJ.3 44.c 41.0
-A,.% J mol.’ K-’ 0.8-c3.2 2.5x4.1
10.7’*-2.3
t2.7ZO.6 Il.4ZO.6 9.1 CO.8
7.723.4 13.5?0.8 2.0~0.5 0.2Zl.4 5.923.6 1.7t1.2 4.7zt.5 -
4.627.7
Tetnperttture. K
Ref.
-A,S,,,,,,, . J mol.’ Km
298 298-loo0 300 300 300 298-l 140 300 300 300 300 298-t 103 298-IMKi 298-983 298 298-973 298-IWO 298-1000 29X-1000 298-1073 298-IOLN? 29X-IO23 298-101 I 29% IOU0 298-873 298-1018 zss-IO00 ,$98-950 298- loo0 ,98-1035 298-IO00 298 298-1000 298 298 298 298 29%loo0 298-881 298 2598
1271 L9.28.301 I281 I281
2.2+2.1 2.22 1.9 2.72 1.9 10.4-CI.8 12.7el.7 Il.5ZO.7 13.8~0.8 15.4kO.8 I5.7-eO.8 16.5~0.9 ,1.9+0.7 I3 0to.s 11.3-‘0.7 I I .sr0.7 9.9to.7 10.9zo.9 9.320.7 10.01c_0.7 10.0+3.a 9.523.7 11.5Z2.7 4.72 t.2 6.0?2.0 4.5-cl.B 2.2~4.9 1.123.8 1.2?4.1 O.ZZ4.0 t .225.6 0.4e5.0 5.32 1.0 4.82 I.2 7.7?0.8 I5.R?I.O 15.9Zl.O 16.22 1.0 -2.3-cz.7 - I.lf2.5 3.922.6 O.I-cZ.7
1331 [3l-33.47.48) I331 1331 [331 1331 (35.491 This study [31.501 Ehimatron of [461 [3 I a34.36.5II This study This study This study 13152.531 This study [3 I.541 t31.37.551 This study [31.381 [31.39.‘wI This study 13lAll Thus study f31.42.431 This stud) 1311 Tnis study f31.441 WI WI WI This study 145.46.561 Estinwtion of 1461 Esdmation of 1461
‘Experimental value 1271 for Scab. was recalculated for the rompound SC&%, according lo the recent data 1601.
systems the R,Pb, compounds are most stahlr:, while in the Lu-Pb system the more stable one is Lu,Po,. Considering the common enthalpies of formation for some R-Sn and R-PI, compcurrds (see Fig. I), one may suppose the similar atomic interaction in both systems. 3.2.3. The rare earth silLides The assessed data for thermodynamics of R-S1 compounds [6l-811 ate listed in Table 8. This data shows more scatter than for the plumbides ind srmnides. Thus, for S&i, L&i,,,, GdSi, ., silicides, values of formation entbatpy according to v&ous authors differ by more than 20 kJ mol-‘. Only for Y-Si and Gd-Si systems is there reasonably complr?e experimental information (Fig. 6). while, the entropy data for yttrium silicides reveals enorm-
ous scatter. The discrepancies in entropies could be explahred by the narrow temperature range (820-920 K) of the relevant electromotive force measurements [66]; range of 100 K is insufficient to determine reliable entropy data [4]. Oxygen contamination of yttrium also might have drastic effects on the thermodynamic properties of yttriumrich silicides. Despite all these factors the data indicates that all investigated sillcides possess a very high thermodynamic stability. With increasing silicon content of the compounds, the values of the enthalpies and the entropies gradually decrease and approach minima near R,Si,. The rare earth germanides In Table 9 both experimental [Sl-961 and assessed data for the germanides are presented. The situation concerning
3.24.
241
0
il?5i?J -8
-20
+
i
-15 e
1 r‘ ‘9’40
-80 M Y
-20 % T -25
02
0.4 =m
Od
Od
1.0” m
L8
%
m
Table 8 Statistically cleated experimemal sod ebtimaled themwdynamic proper&s fw the mm earth srlicides Compocmd
A,H.kJmol
ScSi ScSi SC,%, YSi, Y,Si, Y ,Si, YSI Y,Si, Y,Si, LA, la.%, , LA,, CCS12 C& P&i. RSINdSi, ” GdSi , v GdSi, y Gd,Si, Gd$, GdSi GdSi Gd,Si, Gd,Si,
87.1?2.1 117.2 102.3~3.8 66023.4 74.2T3.8 44.2 69.158.0 7s.ot 12.0 92.1’6.7 56.8’c2.5 ‘Y I k4.6 t1.Y 60.5 72.5~3.3 61.521 7 78.121.9 89.023.4 82.3-c3.4 63.5k5.2 94.324.2 84 226.1 109.8+5.3 92.625.5 I15.6rtS.8 118.6-8.6
’
-A,S.kJmOl-’
TempcnNrc. K
Ref.
-A&,,.
14.5??.5
830-loo0 298 298-loo0 820-920 820-920 298 298-920 298-920 820-920 298 960-1060 298 298 298 298 298 920-1020 830-960 298 6f%700 298 780-910 298 600-725 780-910
161.631 f621 i61.641 164 WI I671 R&671 166.671 tw 1761 (701 1711 I761 176.801 i761 176.791 1721 I731 I%1 [731 WI t73.811 WI I741 1743
15.1+7.1 27.55.9 18.327.3 8.4+5.2 I I .524.6 -1.15.9 9.05t.6 Il.8Z4.4 18.OZ4.8 14.2Z2.5 30.8f4.7 15.5+2.7 16.2-2.6 18.422.8 13.923.7 19.823.3 26.3L3.4 18.2k3.2 10.3z3.4 22.6t3.1 18.623.1 28.4k3.4 21.223.1 30.4rt3.6 30.6f3.6
14.5+4.2 2.824.0 3.1 e4.5 -40 x3+5.0 8.Ok4.0 -5.627.8 28.4~4.6
2O.IZ3.4 23.0?5.7 25.925.7 32.127.0 38.227.8 39.4% 14.2
* kJ mo-’
242
LT.
Wirusiewic:
et al. I Journal
of
Alloys
and Compounds
248 (1397)
233-245
Fig. 6. Emhalpies (left scale; squares) and envopies (right scale: circles) of formation of the inwmetalbc compounds in Y-Si and Gd-Si systems: open points are literature data: sobd points are the results of performed assessment.
thermodynamicdata in R-Ge systems is similar to R-Si. For only 16 out of 100 germanidesof rare earths [Sl] there is data on enthalpy and entropy of formation:
moss refractory intermetallics,and R,Ge, to be as a rule the only congruently
compoundswere studiedby calorimetric methods[76,85]. In Fig. 7, the data for four almost completely investigated R-Ge systems are shown graphically. The experimental entropies for YGe, YGe,,, and LaGe, r [81,88] may be disputed as in the case of silicides. The empirically deduced entropy vatues for these compounds are much more negative as compared to experime-nal data. Experimental and estimated entropies of folmatiun
4. Conclusion
Some generalizationof experimentaldata for thermodynamic functions of formation for the binary compounds of rare earth metals with si!icon, germanium, tin and lead has heen perfcrmed. Empirical relations were derived, which have allowed the entropies of formation of the compounds to be assessed using enthalpies and values of
for other
germanidesare in agreement.The processof formation of RsGe, and R&e, intermetallizsis accompaniedby essen tially high exothermic effects and negative entropies in comparison with other compounds. As in all previous systems, the thermodynamic properties correlate with
melting and boiling temperaturesof pure components.The data of the entropies for the systems derived in this way are consistent with experimental ones where reliable thermodynamic information exists. Large scatter in experimentaldata on silicides and germanidesmakes further
phase diagrams, which prove those germanides to be the Tzbie 9 Stadstically treated experimentaland estimatedlhermodwamic for . .orouenieb . COillpGWld
-s&e,
s&e sc..Ge...
Jaw-’ K-’
A,/f.kJIlWl-’
-A,S.
71.521.6 99.9Z4.2 99.6k2.2 104.1f2.3 99.326.0 78.Ok3.7 9s.o+4.9 89.825.9 82.422.9 I16.4zt6.2 117.4t6.4
17.921.7 1s.j+2.3 19.122.4 19.3+:.6 12.623.3 4.4+5.4 2.4'5.7 1.123.4 17.6T5.5 15.4r5.0
68.1~1.0
73.422.3 75.6k1.9 70.4~2.3 81.7-tl.7 103.h~5.0 74.8ft.3 84.OZ3.2 104.o-c3.0 !15.3~5.5
WW
112.8Z7.0
13.5~5.0 9.324.5 10.525.2 17.2~8.5 22.1*10.1 19.0f12.9
melting compounds @I].
5 more
lhe rare eanh -eemmnidcs
Temperature,K
Ref.
-4L,m,,
897-975 830-loo0 825-990 850-1025 830-IO40 600-740 820-920 820-920 950-1060 950-1060
182.881 WI
900-1060
1811 I851
2.221.5 12.8-cZ.l 12.7+2.0 14.722.1 13.522.1 9.621.8 16.422.1 13.4Zl.9 11.721.6 18.012.0 18.8+2.0 6.421.4 6.I-cl.3 7.2+ 1.4 5.821.4 9.521.6 16.321.9 8.2~1.6 9.221.6 14.8Zl.9 17.9Z2.1 16.7+2.0
298 298 298 298 298 930-1050 298-960
298-860 298-860 760-850 8cQ-910
1831 ;83i 183.851 181.891 I891
I811 I81.911
[Sl.!J2]
I761
I761 I761 I761
ISIS41 I81 195.961
I81.95.%1 I8L95,%1 I81.951 I81.951
. J mol-l K-’
243
0 -20
4 %
‘40 1 aa 540
-lo’:
-1s -20 YP-r P
-100 -2s -120
/ m-
0.0 I.8
02
0.4
%a
t 0.0
01
,o* .
dr
Fig. 7. Emhalples (left scale; squares) and entropies (right scale: circlxs) of formation of the intermetallic compounds in some M systems: open paints are litenture data: solid points are the results of performed assessment.
experimental investigation of these systems necessary. It is also important to have farther investigation of thermodynamic functions of formation for europium and ytterbium germanides, where the rare earth metals, unlike to other
R-Ge
compounds,
are in a bivalent
state [ 1091.
Acknowledgments The authors are grateful to Dr. ML Ivanov for helpful discussion and comments on the manuscript.
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of Rure
and
Color
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245
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Journal of Alloys and Compounds 248 (1997) 233-245
Assessment of thermodynamic functions of formation for rare earth silicides, germanides, stannides and plumbides
A critical assessment has been made of the available data on thertnodynamic properlies of bhtary compounds of ktnhanii metals, scandium and yttrium tR) with IV group p elements (X&i. Ge, Sn and Pb). obtained mainly through the direct e.m.f and cakehnenk methods On the basis of the most reliable data the following empirical relation was derived which allows the cstlmatko of encopks or formation for the intennetallics (A,.51 by using the enthatpies of formation per mole of A,,,,+,,B,,,,+,, compotmd (A,& together with the melting CT,,,,) and boiling temperatures CT,,,) of the components I (1EA.B): A&,
= aR
mn (m +I#
Im+“,~lnn
3Tnl (3 Tb
f 3,H,. h
where A&=AJ-
WA+%JB);AH m-tn
,m
=AH-(mAm4+~LHB). , m+n
+
i;. =(T,,,, + T,,,a)12 and F,, =(T,,, +T,,,)/2; A,$, and A,H, are the entropy and enthalpy of melting of the comptments, respectively; m and n are stoichiotnetrlc coefficients of a binary A,B, compound; a and b are empirical coeBictents, and R is the gas constant. The calculated entropy values for the R-X intennetallics are in agreement with expethnental data avallabk. Keywords: Rare eanh-p element compoand: Enthalpy of fonn&o:
Entropy of formation: Empirical assessment
1. Introduction
enthalpies
of form&u. By contrast, the e.m.f.datacan be more exothermicdue to the possibleexistenceof oxygen impurities, which can form very stabk oxides. ‘l’hcsc effects should be cottshiered when comparing the ex-
During the last decade, there has been a great increase in the amount of tbermndynamic data for intermetallic rare earth-p element compounds. The mejorlty of available information (with very few exceptions) concerning thermodynamics of formation for R-IV-group p element intermetallics was obtained by two direct methods - e.m.f. and calorimetry. Combination of these data allows mote precise determination of entropies of formaticn for the
perimental results of the two methoda. UttforhtnateIy, the still remains incomplete owing hermodynamic infoematkn to the difficnltka of e.m.f. and cal&mehic measutemanta at high temperatures, which have been pointed out in a
compounds[l-3]. Both methodshave some advantages
recent paper by Colinet [4]. Ne~&&ss, the available data make it possibleto reveal some enthalpy-erttropy correlations.It mustbe pointedout that nowadaysit is very
and restrictions.
important
Errors
in caIorimettic
experiments
(dissn-
.
to search such empirkal
approaches
for reaBatic
mason of incompleteness of dissolution or combustion because of high thermodynamic stability of the com-
values for a system L the basis of o&r experinn&tl data for the same system. In a previous paper [5] the method for
pounds. This results in less exothermic values of the
empirical estimationof excess partid and integral entropies of mixing for the binary systemsby using experimental
*Conespwding author. u925-8388/97/$17.00 PII
SO9258388(96)02659-X
Q
1997 Flscvler
S.A. All
dglns
-cd
mixing
enUtaIpy
datp,
melting
and
boiling
234
LT.
Wesinvic;
er ul. I Journal
of Alloys
40 m
and Ccmpounds
248 !199?)
.‘33-245
RF?)3
-36
40
Rsn 3
l -
40 &
-70 OD?
.
$0
0.08
. .
o!kT-x--
- 0.11
b
Fig. 1. Plots of the enthalpies of formation of some isostoic! iometric types of R-X compounds vs. atomic nunber of lanttsnides (a! and (rr enc vs. mdiudius of three-valent cation of rate earths (b) and (d): points are experimental values: lines are results of appmximatiott.
temperatures of the components, was proposed. In the present paper, it is shown that a similar approach is also applicable for empirical evaluation of thermodynamic functions of formation for the binary intermetallics such as silicides. germanides. stannides and plumbides of the rare earth metals.
2. Regularities COI”plldS
in thermodynamics
using correlations between different thermodynamh parameters, or observed regularities in the periodic t..ble. Thus, for enihalpies of lanthanide isostoichiometric clampounds there is a linear dependence on lanthaniae ato1.k number (N), or on the three-valent radius of rare earh cation (rr ). Such relationships for some Sn- and Pbcontaining compounds, for which thermodynamic prop etties have been studied rather extensively [6-561, are shown in Fig. I. The results of a least-squares analysis of this data are listed in Table 1. The values of radii for three-valent cations of the metals were taken from [57]. The dependencies A,H vs. N (Fig. 10 Fig. l(c)! and A,H vs. rr (Fig. l(b) Fig. l(d)) for RSn, and R,Sn, com-
of R-X
Generally, fundamental treatments for predicting such data is scarce, but rometimes good results can be obtained Table t
Resultsof least-quares analysis of A,H vs. N and A,H vs. r:’ depwkwies
for some isostoichiometric R-Sn and R-Pb compounds
Typ of compounds
Dependme
03&l
b+Ab
Standard deviation of A,H
Comlaion cafficien:
RSll,
4/l VS. N &$H vs. 1: A/ff YR. iv Ap vs. r; L$JI vs. N d/ff vs. 1: p vs. N A/i vs. r:* A/i vs. N A,n vs. r:
- 16S.7^15.9 52.2e 17.3 -208.OZ6.0 26.426.0 - 168.7~9.8 -4.3t10.4 - 155.928.9 66.3~5.6 - 175.4Z20.9 86.5+13.9
1.81+0.25 -1092Z18 2.14~O.IO - IOSSt63 1.65?0.16 -644211 1.76-cO.14 - 1163f59 tKEo.33 -1398215
3.8 4.3 0.8 1.7 1.5 3.1 1.9 1.8 3.6 2.5
0.916 -0.875 0.997 -0.993 0.978 -0.922 0.970 -0.Y85 0.9i36 - 0.989
fW4 R,Sn. m, m>
VT. Wifusiewic: et al. I Journal of Alloys and Compounds 248 (1997) W3-245 Table 2 The results of estim%ion of the enthalpies of fomution and their prediction confidcncc bands at toknncc 0.05 for R&B,, R,.Sn, nd P.!h, compmmds R
N
z-21Y La Ce R Nd F’m
Sm EU Gd Tb Dy Ho Er Tm Yb Lu
39 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
r:* “In
O.WOS 0.1071 0.1034 0.1013 0.0995 0.0979 0.0964 0.0950 0.0938 0.0923 O.WC8 0.0894 0.0881 0.0869 0.0858 0.0848
-A& RSll,
kJ ml-‘ R,S%
R,%
LitemNrc dats
vs. N
YS r;
Literature Cw
vs. N
63.Ok9.7 61.1-9.5 59.1+9.0 57.lk8.6 .55.1+8.4 53.027.6 51.0-6.8 49.0+6.0 47.1T5.6 45.0f4.6 430?4.0 41.1+3.8
46.7e6.0 64.8t9.5 60.8Z8.6 58.527.2 56.5=6.4 54.8-iS.5 53.1~5.4 5,.6-c5.C 50.3%5.0 48.7Z4.7 47.0~57 43.3-5.3 44.1+7.0
52.2% 1.2 161= 87.4t4.2 [S] 83.724.2 1181 80.0 I281 69.0 1171 68 1171 -
SO.SZ9.4
52.3Z2.1 181 62.5+2.1 [SJ-171 55.OZ2.1 [IS] 5a.s+3.s [I I] 64.3 [11.17.191 56.0 [11.17.20] 52.82 1.9 1211 5l.Of2.1 1221 45.0 [ 171 45.211.2 1241 43.0 [,7.2.5] 44.0Zl.0 t11.261 33.920.4 1231’ 39.0 [I71
37.0-3.8 34.924.2
41.6~8.5 40.5’9.0
-
IS. r:’
Li*RRIca
.5X2+1.2161 69.3+6586.6k4.2 86.8Z9.0 84.424.0 82.927.6 82.3Z3.8 80.7+7.0 80.2-3.8 78.8k6.6 78.023.8 77.126.6 759~3.8 75 5Z6.0 73.8’3.9 i4.OkS.a 71.6~4.0 72.825.8 69.524.2 71.225.9 67.424.2 69.626.2 65 354.5 6X1-6.4 63.1k4.8 66.7Z6.8 61.OZ5.0 6X527.2 58.9~5.2 65.5k7.3 56.7e5.6 63.228.0
vs. N
75.9~42 [8] 73.2Z4.2 (IS] 70.0 1171 63.623.4 1201 61.0 [17] 61.0 1171 59.0 1171 56.0 [I71
74.7239 73.1 f3.8 71.423.7 69.8?3.6 68.123.6 66.5Z3.5 64.8235 63.223.6 61.523.7 59.9233 58.2+3.9 56.6T4.0 54924.2 53.3k4.4 51.624.6
vs. r;* 51.3-TlO.8 62.6*5.0 7X327.7 70.926.4
69.s~5.8 69.4f5.3 67.425.0 66.424.6 6X5-+4.6 64.724.6 63.824.6 62.824.8 61.9Z5.1 61.1+24 60.3Z3.7 60.3zs.9 58.926.3
‘In the reuem works of [59.60] rhe existvlce of LuSn, and SC,% compounds was not confirmed.
pounds, as well as for RPb, and RPb?, show very similar slopes because the character of interatomic interaction is very similar for them systems. The crossing of A,H vs. r: lines for RsSn, and RsSn, intermetatlics. located between Sc and Y, confirms that for the Sc-Sn system the Sc,Sn, compound is the most stable. Such dependencies dlow the evaluation of unknown enthalpies for the compounds. According to a survey of R-Sn phase diagrams [58], the R,Sn, and R,Sn, compounds form in the majority of the systems while RPbz compounds exist in most of the R-W systems. However,
the information about enthalpies of formation for the above mentioned three isostoichiitric series of imetmemilii is scarce (see Fig. l(c) Fig. l(d)). Taking into account the similarities of RSn, and RPb, comPouuds (see Rg. l(a) Fig. l(b)), evaluation of missing data using both A,H vs. N and A$! vs. $ dcpmdmcies was carried out. Some results for stannides and plumhides 3re summarized in Table 2 and Table 3 respectively. The values cakukd using the dependence on N in most cases has a low confidence limit, but the iatter approach possibility to evaluate the -nthatpies of
Tabk 3 The results of estimation of the cnthalpies of fomuti0.l and their prediction confidence bands at cokrance 0.05 for RF%,
RPh
f9
LilcraIure data SC Y La CC R Nd Pm Sm Eu Gd Tb DY HO Er 7-m Yb LU
21 39 57 58 59 60 61 62 63 64 it 67 68 69 70 71
0.0730 0.0905 0.1071 0.1034 O.ILl. 0.099s 0.0979 i o.owd I 0.0950 V.0938 O.W23 0.0908 0.0894 O.OS81 0.0869 0.0858 0.0848
vs. N
YS. r;-
LikraNN &la
55.7+5.6 53.9e4.2 52.2Z3.6 50.5+2.2 48.7-2.7 46.9T2.5 4X222.3 43 4+i..3 41.6k2.6 39.922.6 38.123.6 36.424.0 34 624.4 32.824.8 3l.lZS.4
18.528.8 38.918.0 58.2~8.0 539~6.6 51.4z5.7 49.325.2 47.se4.a 45.124.4 44.124.0 42.7-4.0 41.o-c4.0 39.224 1 37.fe4.3 36.lT4.8 34.755.1 34.725.2 32.226.0
37.2=2.l 1281 64?2.; 1461 55.0 1461 34.120.3 [%I
. .
19.O.tO.5 1271’ 35.9-4.9 [9,28-30.461 56.4k3.4 [31-33.47.481 53.822.4 ]31.34.35.49] 53.8ZO.5 [XI] 5i.422.9 ]31.34.36.51] 48.1+1.6 43.2Z2.4 41.3-3.4 39.854.1 42.224.3 36.8Z2.9 35.5?1.3 35.4k2.0 37.0~2.0
I31.52.531 [31.54] [31$5] I31.381 ]31.39.40] [31.41] 131.42.431 [31] [31&l]
‘In the resent work of [MI] tbc eaisuacc of ScFb, compmd
was not confirmed.
VS. N
“1 r:
61.7k9.7 59.729.4 57.729.2 55.7+9.1 53.7T8.9 51.628.9
40.026.3 63.2~6.9 58.026.5 55.1 f6.3 52.6k6.2 50.3e6.1 48.326.1
47.8Z9.C 45.7k9.1 43.7z9.3 41.829.5 39.629.8 37.72 10.1
44.6?6.1 42526.2 40.426.3 38.5 26.4 36.6265 34926.7
33.7210.9
32.Ok7.0
236
scandiumand yttrium-based compounds. For the intermetallics of light lanthanides both methods give very similar results, whereas for the systems of heavy lanthanides the difference in the values may extend up to 6 kJ mol-‘. There is insufficient thermodynamic data available for R-Si and R-Ge compounds 161-961 to reveal similar regularities.
CT,,,, + T,,,,)12 melting
thermodynamic,physical or structural data is available, such methodsof approximation may be improved 1971. For instance by correlating between the excess partial entropy and enthalpy in liquid binary alloys [97-1071 Kubashewski has shown that a plot of ASzax vs 2AH,,,,,/(T,,, + Tb,z) (where AH,,,,, and AS’,“,, are the maximum absolute values
of integralenthalpyand excessentropy of alloy formation and Tb.,, Tb,2 are boiling temperaturesof the metal components)has a constantslope [98,99]. Similarly Chart et al. [97] have shown that plot of AH,,, vs A.$,,,,, for I50 solid and liquid solutions is a straight line within enthalpy values from -50 to 120 kJ 11101-l. Tanaka with co-authors [102-1071 using a solution model based on free volume have derived the following relationships between partial
enthalpy (J&a) and excess partial entropy (AS’,“) at infinite dilution in a binary A-B system with similar physico-chemicalpropertiesof the components:
where T,,, A and T,,, B are
the mc!ting points of components This correlation has provided better A and B iespectiveiv. results than the previous one due to using melting temperaNres. The solution model hased on the free volume theory
and Eq. (I) is applicablefor the entire concentrationrange taking into account positive. negative or zero values of molar entropy in very dilute solution [ 1071. shown that excess partial and integral in the full concentration range for the 3d transition metals with metalloids (B, be estimated from experimental mixing
enthalpy data, melting and boiling temperaturesof the components [S]. According to this work, the integral excess entropy (A,$“) and integral enthalpy (A,&) of mixing is given by the following expression: $
(‘y” b
+T,,,)12
temperatures
of
are the
I,“+.l~l,,t.
A$,,, = ah’A For estimating the entropy of formation for metallic alloys the regular solution model is more often used. It can only be a rough model because the excess entropy in the whole composition range is supposed to be zero. If other
A$‘” =6Rr(l -x)
F,,=(T,,,
relation exists between the enthalpies and entropies of formation for solid compounds, which can then be used to evaluate the entropy of formation for binary intermetallics. A least-squares regression analysis through the all statistically treated experimental data of investigated R-X sys-
of the approach and calcrdarion details
Receutly it was mixing entropies binary systems of C, Si and Ge) can
and boiling
and
tems [6-56,58,6]-961 resulted in the following best equations:
3. Assessmentof entropy 3.1. Background
where F,,, = the average
components.respectively: R is the gas constantand x 1s concentrationof a metalloid. In the present paper, it is announcedthat a similar
+ +A,“,
-b
(2)
+A,Hh
(m + n)’
(3)
OnA,,,S,,+ nA,S, ) A$,,, = A$ nf + n A
H rm
= A H I
_
@4J4 ~-
(4)
+ 4J&l
(5)
m + n
where A,S and A,H are entropy and enthalpyof formation per moleof A,,,, +“,B,,,, +“, compound(a mole of alloy), respectively;A,,$, and A,HA are the entropy and enthalpy of melting of the components,respectively; m and n are coefficients of a binary A,B, comthe stoichiometric pound; a and b are empirical coefficients, which apply for the compounds of rare earth metals with the same p element. So, the plots of (A,S,IR) vs (A,H,,,/F,,R) for Si,
Ge, Sn and Pb systemsare the straight lines. where
(‘5) Evidently, the first term of Eq. !3] and Eq. (2) are rather similar especially if rnn/(m+n)‘=x(l-x), but there are bigger differences in the second terms of these relations. The above mentioneddependenciesare shown in Fig. 2. Tbe parametersa and b with their error bands(toleranceis 0.05) and correlation coefficients for the systems under consideration
are summarized
in Table
4. The
data
for
melting and boiling temperatures.and entbalpiesof melting for the componentsused were taken from (1081. For simplicity the coefficientsa and b can be rounded off within the range of their error bands, and it is convenientto operatewith the parameterslisted in Table 5. As one can see, both empiricalcoefficientsfor germanides and plumbidesare then equal to unity. The correlation between available experimental and estimated
(by Eq. (3)-
Eq. (5)
using parameters
given
in
Table 4) entropiesof formation for R,X, compoundsis shown in Fig. 3. A least-squaresanalysisshows that these data are described by straight line A,S,,,,,=(0.4?0.3)+ A&, with correlationcoefficientR=0.916, the tolerance being0.05. Similarly using coefficientsfrom Table 5 leads and R = 0.906. Much of the to A&c = (0.620.6) + A&, discrepancy
between
experimental
and calculated
values
1
b
-140 1 . . . -140 -120 -100
. -#)
. do
. -40
. f -20
0 -rm 5 j -200
,,‘. +‘:
Fig. 3. lllustmtion of conformity between estirnwd (AS sm., ) and experimental one (A&.
,.,-’ ,.’ ..-- ,/-. c3-J ,’ ,.’ ,tk+ I’ -? Jo0 v y ;a00
_400
C
400
-so
form&
110”
,,:/ ..
1
may bc explained by large errors in measuring of the entropies of formation for the intermetalliis as one should that all literature entropy data were determined indirectly.
remember
4 -200
-100
0
3.2. Results and discussion 0 earth stannides The evaluated entropies of formation for rare earth-tin compounds iogether with appropriate literature data are collated in Table 6. The same values for the most investigated systems are presented graphiially in Fig. 4. 3.2. I. The rare
Obiously, unlike infomdon about enthalpicsof fomw -250 -zoo d
150
+m/aTb
-100
-50
0
, J n-&K-’
Fig. 2. Relaions between enlbalpy and entropy baed on Eq. (3k F& (5): a, for R-S compounds; b, for R-C& compounds; c. for R-8n compounds: d. for R-Pb compounds: points are experimental values: solid lines UC rcsul~sof linear appmximation:dotted lines an conlidence bands at tolerance 0.05.
Trble 4
tion of the compounds, the experimental data for the entropies are very scarce. Thus, the propo& approach is very useful either for thermodynamic analysis of the processes or for furdter stimulation of experimental investigation of likewise systems. The Sc-Sn and Lu-Sn compounds form with positive vahtes for entropy. For Y-G, Dy-Sn and Ho-% systems, the dependencies of entropy vs. concentration of Sn have a variable sign. For
Table b Statisfically treated experimental and estm~aled thermodynamic properties for the raie ranh srannides --____-____--
,ss, 181 18.10,
05 -4,=13
-94-15
the other presented systems, the process of intermetallics’ formation goes on with negative entropy, the minimum value generally corresponding to RsSn,. Taking into account the results given in Tables 2 and 6 one may say
57f19 6,120 * 3.lZZ.I 03t18 -33222 -24524 -22522 -99=29 -85219 -nit25 -IS*t*, -I4,226 -14557 -14w27 -,22r2.4 -74+,9 -,23z24 -IS.%27 - I1.9L2 5 -58f17 -78+20 -148226 -113123 -7 8I2.0 -104224 -125ttb -126fZ6 -10,*24 -741,0 -12,232 .. 10.0~3 I -24r2, -86S.O - 10 6S.2 -19t28 -7.5-24 - 12.952 9 - w.5t3., -*Liz,., -*se23 -6CE2.1 -62+21 -4.122.3 1.1+1.6 -2.2220 -5.4t2 4 lSt*O - IOZ2.7 *.4=2., -18t28 -2658 62?,8 -2.or2.6 -2 63.7 O.St24 4.1Z2.1 I *+2* l.4f2.3 31ZL.l -49225 - l2..%f,.0 -104~2.5 37f19 -0.9222 ^ _
that interaction between unlike atoms and ordering effects in R-Sn systems arise respectively with an increased radius of three-valent cations of rare earth metals. This is also reflexted in an increasing melting temperature of the
VT. Wirusiewicz ef al. I Jouvd
of Alloys and Compounds 248 (1997) 213-245
Fig. 4. Enthalpies (left scak: s juares) and entropks (right scak: cixks) of fmtion points are literature data: solid points are the results of prfon’ned assessmenl.
of R-X
most row.
3.2.2.
The rare
earth
systems in the same
stannides
The experimentat and evaluated thermodynamic values for R-Pb systems are summed up in Table 7. In the present calculations all available data [27-561 except data from [34] was used. Entropy values measured by Knudsen method [34] seem to give low values by a factor of 2 or 3 and are not consistent with later results. Possibly there was a lack of information concerning phase equilibria and
of the intcmw.tallii compmmds in some M
ervrh-tin syslem~: open
stoichiometries of existing compounds while these measurements were perfotmed. Although there are so11te more entropy data for R-Pb intermetallics in comparison with R-Sn ones in the literature, they arc fragmentary; most of the data corresponds to RPb, compounds. For this reason, in Fig. 5. the results for only four almost compkteiy cxperimentatly investigated systems are prrsewed. Both iitemture and estimated data for entropy of YPb, and LaPb, compounds formation demonstrate good agreement. The experimental entropy value for LuPb, is evidently doubtM. As it can he seen from the illustmtion, in Y-Pb. La-Pb and Yb-Pb
Table 7 St~tistadly treaed experimental and estimated themmdynamic properties for the rare eanh plumbides Conipound
-6,H. kJ mol ’ 419ris x5.9+4.9 37.222.1 60.222.1 66.9-fZ.l 56.4Z3.4 64.0’2.1 59.0+2. I 69.9Z2.0 72.2+2.1 55.0~4.1 58.016.5 53.5=0.5 55.0 50.4r2.9 52.626.2 47.5C4.8 50.3e6.1 48.1+1.6 C.8.3-f6.1 43.1 k2.4 39.lk5.2
44.6-6.1 39.824.1 42.224.3 40.426.3 36.8Z4.1 38.5+6.4 35.5e2.0 36.6?6.5 35.4-c-2.0 34.9-6.7 37.OT2.0 57.3+0.8 57.7zo.a 58.2+2.9 32.6+6.0 34.22tJ.3 44.c 41.0
-A,.% J mol.’ K-’ 0.8-c3.2 2.5x4.1
10.7’*-2.3
t2.7ZO.6 Il.4ZO.6 9.1 CO.8
7.723.4 13.5?0.8 2.0~0.5 0.2Zl.4 5.923.6 1.7t1.2 4.7zt.5 -
4.627.7
Tetnperttture. K
Ref.
-A,S,,,,,,, . J mol.’ Km
298 298-loo0 300 300 300 298-l 140 300 300 300 300 298-t 103 298-IMKi 298-983 298 298-973 298-IWO 298-1000 29X-1000 298-1073 298-IOLN? 29X-IO23 298-101 I 29% IOU0 298-873 298-1018 zss-IO00 ,$98-950 298- loo0 ,98-1035 298-IO00 298 298-1000 298 298 298 298 29%loo0 298-881 298 2598
1271 L9.28.301 I281 I281
2.2+2.1 2.22 1.9 2.72 1.9 10.4-CI.8 12.7el.7 Il.5ZO.7 13.8~0.8 15.4kO.8 I5.7-eO.8 16.5~0.9 ,1.9+0.7 I3 0to.s 11.3-‘0.7 I I .sr0.7 9.9to.7 10.9zo.9 9.320.7 10.01c_0.7 10.0+3.a 9.523.7 11.5Z2.7 4.72 t.2 6.0?2.0 4.5-cl.B 2.2~4.9 1.123.8 1.2?4.1 O.ZZ4.0 t .225.6 0.4e5.0 5.32 1.0 4.82 I.2 7.7?0.8 I5.R?I.O 15.9Zl.O 16.22 1.0 -2.3-cz.7 - I.lf2.5 3.922.6 O.I-cZ.7
1331 [3l-33.47.48) I331 1331 [331 1331 (35.491 This study [31.501 Ehimatron of [461 [3 I a34.36.5II This study This study This study 13152.531 This study [3 I.541 t31.37.551 This study [31.381 [31.39.‘wI This study 13lAll Thus study f31.42.431 This stud) 1311 Tnis study f31.441 WI WI WI This study 145.46.561 Estinwtion of 1461 Esdmation of 1461
‘Experimental value 1271 for Scab. was recalculated for the rompound SC&%, according lo the recent data 1601.
systems the R,Pb, compounds are most stahlr:, while in the Lu-Pb system the more stable one is Lu,Po,. Considering the common enthalpies of formation for some R-Sn and R-PI, compcurrds (see Fig. I), one may suppose the similar atomic interaction in both systems. 3.2.3. The rare earth silLides The assessed data for thermodynamics of R-S1 compounds [6l-811 ate listed in Table 8. This data shows more scatter than for the plumbides ind srmnides. Thus, for S&i, L&i,,,, GdSi, ., silicides, values of formation entbatpy according to v&ous authors differ by more than 20 kJ mol-‘. Only for Y-Si and Gd-Si systems is there reasonably complr?e experimental information (Fig. 6). while, the entropy data for yttrium silicides reveals enorm-
ous scatter. The discrepancies in entropies could be explahred by the narrow temperature range (820-920 K) of the relevant electromotive force measurements [66]; range of 100 K is insufficient to determine reliable entropy data [4]. Oxygen contamination of yttrium also might have drastic effects on the thermodynamic properties of yttriumrich silicides. Despite all these factors the data indicates that all investigated sillcides possess a very high thermodynamic stability. With increasing silicon content of the compounds, the values of the enthalpies and the entropies gradually decrease and approach minima near R,Si,. The rare earth germanides In Table 9 both experimental [Sl-961 and assessed data for the germanides are presented. The situation concerning
3.24.
241
0
il?5i?J -8
-20
+
i
-15 e
1 r‘ ‘9’40
-80 M Y
-20 % T -25
02
0.4 =m
Od
Od
1.0” m
L8
%
m
Table 8 Statistically cleated experimemal sod ebtimaled themwdynamic proper&s fw the mm earth srlicides Compocmd
A,H.kJmol
ScSi ScSi SC,%, YSi, Y,Si, Y ,Si, YSI Y,Si, Y,Si, LA, la.%, , LA,, CCS12 C& P&i. RSINdSi, ” GdSi , v GdSi, y Gd,Si, Gd$, GdSi GdSi Gd,Si, Gd,Si,
87.1?2.1 117.2 102.3~3.8 66023.4 74.2T3.8 44.2 69.158.0 7s.ot 12.0 92.1’6.7 56.8’c2.5 ‘Y I k4.6 t1.Y 60.5 72.5~3.3 61.521 7 78.121.9 89.023.4 82.3-c3.4 63.5k5.2 94.324.2 84 226.1 109.8+5.3 92.625.5 I15.6rtS.8 118.6-8.6
’
-A,S.kJmOl-’
TempcnNrc. K
Ref.
-A&,,.
14.5??.5
830-loo0 298 298-loo0 820-920 820-920 298 298-920 298-920 820-920 298 960-1060 298 298 298 298 298 920-1020 830-960 298 6f%700 298 780-910 298 600-725 780-910
161.631 f621 i61.641 164 WI I671 R&671 166.671 tw 1761 (701 1711 I761 176.801 i761 176.791 1721 I731 I%1 [731 WI t73.811 WI I741 1743
15.1+7.1 27.55.9 18.327.3 8.4+5.2 I I .524.6 -1.15.9 9.05t.6 Il.8Z4.4 18.OZ4.8 14.2Z2.5 30.8f4.7 15.5+2.7 16.2-2.6 18.422.8 13.923.7 19.823.3 26.3L3.4 18.2k3.2 10.3z3.4 22.6t3.1 18.623.1 28.4k3.4 21.223.1 30.4rt3.6 30.6f3.6
14.5+4.2 2.824.0 3.1 e4.5 -40 x3+5.0 8.Ok4.0 -5.627.8 28.4~4.6
2O.IZ3.4 23.0?5.7 25.925.7 32.127.0 38.227.8 39.4% 14.2
* kJ mo-’
242
LT.
Wirusiewic:
et al. I Journal
of
Alloys
and Compounds
248 (1397)
233-245
Fig. 6. Emhalpies (left scale; squares) and envopies (right scale: circles) of formation of the inwmetalbc compounds in Y-Si and Gd-Si systems: open points are literature data: sobd points are the results of performed assessment.
thermodynamicdata in R-Ge systems is similar to R-Si. For only 16 out of 100 germanidesof rare earths [Sl] there is data on enthalpy and entropy of formation:
moss refractory intermetallics,and R,Ge, to be as a rule the only congruently
compoundswere studiedby calorimetric methods[76,85]. In Fig. 7, the data for four almost completely investigated R-Ge systems are shown graphically. The experimental entropies for YGe, YGe,,, and LaGe, r [81,88] may be disputed as in the case of silicides. The empirically deduced entropy vatues for these compounds are much more negative as compared to experime-nal data. Experimental and estimated entropies of folmatiun
4. Conclusion
Some generalizationof experimentaldata for thermodynamic functions of formation for the binary compounds of rare earth metals with si!icon, germanium, tin and lead has heen perfcrmed. Empirical relations were derived, which have allowed the entropies of formation of the compounds to be assessed using enthalpies and values of
for other
germanidesare in agreement.The processof formation of RsGe, and R&e, intermetallizsis accompaniedby essen tially high exothermic effects and negative entropies in comparison with other compounds. As in all previous systems, the thermodynamic properties correlate with
melting and boiling temperaturesof pure components.The data of the entropies for the systems derived in this way are consistent with experimental ones where reliable thermodynamic information exists. Large scatter in experimentaldata on silicides and germanidesmakes further
phase diagrams, which prove those germanides to be the Tzbie 9 Stadstically treated experimentaland estimatedlhermodwamic for . .orouenieb . COillpGWld
-s&e,
s&e sc..Ge...
Jaw-’ K-’
A,/f.kJIlWl-’
-A,S.
71.521.6 99.9Z4.2 99.6k2.2 104.1f2.3 99.326.0 78.Ok3.7 9s.o+4.9 89.825.9 82.422.9 I16.4zt6.2 117.4t6.4
17.921.7 1s.j+2.3 19.122.4 19.3+:.6 12.623.3 4.4+5.4 2.4'5.7 1.123.4 17.6T5.5 15.4r5.0
68.1~1.0
73.422.3 75.6k1.9 70.4~2.3 81.7-tl.7 103.h~5.0 74.8ft.3 84.OZ3.2 104.o-c3.0 !15.3~5.5
WW
112.8Z7.0
13.5~5.0 9.324.5 10.525.2 17.2~8.5 22.1*10.1 19.0f12.9
melting compounds @I].
5 more
lhe rare eanh -eemmnidcs
Temperature,K
Ref.
-4L,m,,
897-975 830-loo0 825-990 850-1025 830-IO40 600-740 820-920 820-920 950-1060 950-1060
182.881 WI
900-1060
1811 I851
2.221.5 12.8-cZ.l 12.7+2.0 14.722.1 13.522.1 9.621.8 16.422.1 13.4Zl.9 11.721.6 18.012.0 18.8+2.0 6.421.4 6.I-cl.3 7.2+ 1.4 5.821.4 9.521.6 16.321.9 8.2~1.6 9.221.6 14.8Zl.9 17.9Z2.1 16.7+2.0
298 298 298 298 298 930-1050 298-960
298-860 298-860 760-850 8cQ-910
1831 ;83i 183.851 181.891 I891
I811 I81.911
[Sl.!J2]
I761
I761 I761 I761
ISIS41 I81 195.961
I81.95.%1 I8L95,%1 I81.951 I81.951
. J mol-l K-’
243
0 -20
4 %
‘40 1 aa 540
-lo’:
-1s -20 YP-r P
-100 -2s -120
/ m-
0.0 I.8
02
0.4
%a
t 0.0
01
,o* .
dr
Fig. 7. Emhalples (left scale; squares) and entropies (right scale: circlxs) of formation of the intermetallic compounds in some M systems: open paints are litenture data: solid points are the results of performed assessment.
experimental investigation of these systems necessary. It is also important to have farther investigation of thermodynamic functions of formation for europium and ytterbium germanides, where the rare earth metals, unlike to other
R-Ge
compounds,
are in a bivalent
state [ 1091.
Acknowledgments The authors are grateful to Dr. ML Ivanov for helpful discussion and comments on the manuscript.
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