Calorimetric study of ternary liquid Al-La-Ni alloys

Journal of

ALLOYS

AND CONPOUNDS ELSEVIER

Journal of Alloys and Compounds 257 (1997) 234-244

Calorimetric study of ternary liquid Al-La-Ni alloys H. Feufel, F. Schuller, J. Schmid, F. Sommer* Max-Planck-lnst#ut flir Metallforschung and lnstitut fiir Metallkunde der Unh,ersitSt Stuttgart, Seestr. 75, D-70174 Stuttgart, Germany Received 7 January 1997

Abstract Enthalpies of mixing of ternary liquid A1-La-Ni alloys were determined at 1073 K by a calorimetric method along seven different isopleths. The heat capacity of liquid Alo.25Lao.TSand LaosNio.s alloys were measured using an adiabatic calorimeter. An association model was applied to calculate the thermodynamic functions of mixing of ternary liquid A1-La-Ni alloys using the model parameters of the three limiting binary systems. There are systematic deviations between measurement and calculation which indicate the presence of additional ternary interactions. © 1997 Elsevier Science S.A. Keywords: Enthalpy of mixing; Heat capacity; Association model calculation

1. Introduction Ternary A t - L a - N i alloys are known for their good glass-forming ability by rapid quenching from the liquid state [1] and for their ability for hydrogen storage in the solid state [2,3]. These alloys are therefore potential candidates for technological applications. Several investigations have been carried out on selected compositions in order to study crystal structures, magnetic properties, hydrogen storage etc. of A1-La-Ni alloys. Partial investigations of isothermal sections of the phase diagram [4] and the enthalpy of formation of some solid alloys [5,6] have been carried out. So far, there is, to our knowledge, neither a well defined phase diagram available for the A1-La-Ni system, nor any thermodynamic data for liquid alloys. The glass-forming ability of liquid alloys is directly correlated to their thermodynamic properties and the tendency to form associates in the liquid state [7]. An investigation of the thermodynamic behaviour of liquid AI-La-Ni alloys would therefore be helpful in understanding the glass-forming ability of these alloys. Therefore it was decided to study the composition dependence of the enthalpy of mixing and the temperature dependence of the heat capacity of liquid ternary AI-La-Ni alloys. In this paper, we present the results of calorimetric measurements of the heat capacity of liquid A10.2~La0.75 and Lao.sNio. 5 alloys and of the enthalpy of mixing of ternary liquid *Corresponding author. Tel.: +49 711 2095162; Fax: +49 711 1211280; e-mail: [email protected] 0925-8388/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. P l l S0925-838 8 ( 9 7 ) 0 0 0 2 4 - 8

A1-La-Ni alloys. Furthermore, association model calculations of the liquid binary bordering systems will be discussed in the light of the new Cp. The enthalpy of mixing of ternary liquid AI-La-Ni alloys is calculated on the basis of the model parameters of the binary systems. In a subsequent paper the results of the heat capacity measurements of ternary liquid AI-La-Ni alloys and a detailed discussion of our calculations taking also these results into account will be presented separately.

2. Experimental procedures The enthalpy of mixing was measured with a solution calorimeter using the isoperibolic procedure. The arrangement of the apparatus and the principal features have been described previously [8]. The alloy samples were prepared from A1 (purity 99.9%), La (purity 99.99%) and Ni (purity 99.99%). The La samples were prepared and stored m an argon glove box. The measurements were performed under pure argon gas at atmospheric pressure and constant temperature (1073 K) with continuous stirring throughout the experiment. 5aT(x) is measured by making successive additions of the third component from room temperature to a liquid binary alloy bath in the reaction crucible (alumina). The temperature change occurring during the dissolution process was determined by a Ni-NiCr thermopile situated directly below the reaction crucible. The enthalpy of reaction corresponds to the area under the AT vs. time curve. For each series of measurements, the

H. Feufel et al. / Journal of Alloys and Compounds 257 (1997) 234-244

calorimeter was calibrated by dropping molybdenum samples between the additions of the third element using the known heat content [9]. The standard deviation of the calibrations was in the order of _+3%. The heat capacities were measured using an adiabatic calorimeter. Details concerning the calorimeter set-up and the measurement procedure have been published previously [10]. The measurements are performed in the isothermic mode, which keeps the surroundings at a constant temperature during the measurement. The sample and the BN container are heated for a short time (2-4 s) and the associated small temperature increase AT (1-1.5 K) is measured within 10-20 s. From the electrical energy AQ supplied to an inner heater of the sample container the average specific heat of container and sample is given by

~-

-

--~ (1)

mo_~dxT

where m os is the mass of container, heater and sample. With this adiabatic calorimeter Cp of liquid alloys can be determined without any calibration procedure [10].

235

Table 2 Experimental values of the heat capacity of liquid La0.5oNi0.50 alloys T (K)

Cp (J moI -l K -l)

994 999 I015 1030 1039 1054 1065 1090 1115 I140 I165

46.5

44.1 45.5 46.5 45.0 42.6 42.4 43.9 41.5 43.5 43.0

temperature and the solid element at room temperature. This enthalpy difference of the pure element was calculated from the unary data compiled by Dinsdale [9]. Summing up the transformed heat effects of all the previous additions of the same series and dividing by the total amount of initial bath material plus all added third element results in _YSAH~ values given in column 6. The enthalpy of mixing of the respective ternary alloy can be obtained by adding the 2xH values of the binary bordering system AH ((xA/x B) = const, x c)

3. Results

AHG~:A/X B) The experimental results of the heat capacity measurements of liquid Alo.25La0.75 and La0.sNi0. 5 alloys are given in Table 1 and Table 2 respectively. The standard deviation of the obtained values is in the order of _+4%. The experimental results of the enthalpy of mixing of liquid A 1 - L a - N i alloys with constant concentration ratios are given in Tables 3-10. The "heat effect" given in column 3 of Tables 3 - 9 is the effect measured by adding the amount of solid element, given in column 2, from room temperature to the calorimetric bath at measuring temperature. The bath contains all "amounts" of the previous measurements of the same series. The corresponding concentration, given in column 5, is the concentration after the last addition of third element. For the calculations the measured heat effect has to be transformed by subtracting the enthalpy difference between the liquid pure element at calorimetric bath Table 1 Experimental values of the heat capacity of liquid AI0.:sLao 75 alloys T(K)

Cp (J mol-' K -t)

T (K)

Cp (J mol-' K -I)

830 835 840 845 850 860 865 870 875 880 885

39.8 41.2

890 895

38.0 38.5

41.6 40.1 41.4 39.8 38.6 37.5 38.1 36.1 36.9

900 905 910 930 950 960 1000 i030 1050

37.3 37.6 36.1 36.4 38.0 36.7 37.2 38.1 36.0

.

.

.

.

.

t. xc) = ( t

Xc)AH(
-

i

The binary starting values of each series of measurements are given in the first line respectively. For liquid A I - L a alloys the results of Lee and Sommer at 1200 K [11] and for liquid L a - N i alloys the results of Watanabe and Kieppa at 1376 K [12] were used. In Table 10 the experimental results of a different kind of solution experiment are given. Here, the respective components La and Ni were added simultaneously, starting with pure aluminium as bath material. The enthalpy of mixing can be calculated directly from the transformed heat effects. Figs. 5 and 6 show the results for two sections graphically, together with experimental points of intersection from different sections2 For each series of measurements the standard deviation of &H is increasing cumulatively with concentration, i.e. the values at lower concentrations of x c ( C = L a , Ni) have a higher accuracy than the ones at higher concentrations. The standard deviation of/_k/-/ for the last value measured for each series of measurements is in the order of +-2 kJ mol - ~. The AH values at points of intersection show the inner consistency of the experimental results.

4. Discussion An association model has been used to describe the concentration and temperature dependence of the enthalpy of mixing of the three basic binary liquid alloys. Within

H. Feufel et aL / Journal of Alloys and Compounds 257 (1997) 234-244

236

Table 3 Experimental values of the enthalpy change during dissolution of solid Ni of 298 K in liquid Alo ~LLao,8:Ni alloys at 1073 K and calculated enthatpies of mixing; standard states: AI(1), La(l), and Ni(1) Measured

Calculated

Starting amount real in g

mL. in g

0,1441

6.0017

Added amounts

Heat effect

Mole fraction

Enthalpy of mixing

AmNi in g

AQ in J

Ni

~YgM-/ in k3mol- t

AH in kJmol-

0.1500 0.1032 0.1053 0.2247 0.2434 0.2803 0.2638 0.3740 0.4031

-59.5 -40.5 -35.4 - 104.8 -90,5 -87.5 - 119.8 -82,3 -70,9

0.050 0.082 0.112 0.170 0,225 0.280 0,325 0.380 0.430

-3,19 -5.20 -7.01 - I1.00 - 14.40 - t7.55 -20.65 -23.32 -25,55

-9.9 - 12.6 - 14.3 - 15,8 - 19,2 --22.1 - 24.7 -27.35 -29.5 -31.2

Table 4 Experimental values of the enthalpy change during dissolution of solid Ni of 298 K in liquid Alo ~8Lao 8 : N i alloys at 1073 K and calculated enthalpies of mixing; standard states: At(I), La(l), and Ni(1) Measured

Calculated

Starting amount

Added amounts

Heat effect

Mole fraction

AQ in J

Ni

_Y'SAH, in kJmol - ~

AH in kJmol -

0.050 0.100 0.150 0.204 0.304 0.338

-3.26 -7.59 - 10.80 - 13.88 - 19.18 -20.91

16.13 - 18.6 -22,1 -24,5 -26.7 -30.4 -31.6

mAj in g

mr., in g

~m~, in g

0.2502

5.8681

. 0.1591 0,1768 0.1974 0.2398 0.5502 0.2235

.

. -66.9 -135.3 -83.6 -77.9 - 142.4 -53.8

Enthalpy of mixing

.

Table 5 Experimental values of the enthalpy change during dissolution of solid Ni of 298 K in liquid AIo.27Lao.7:Ni alloys at 1073 K and calculated enthalpies of mixing; standard states: AI(1), La(1), and Ni(1) Measured

Calculated

Starting amount m,l in g

mL~ in g

0.4309

5.9977

Added amounts

Heat effect

Mole fraction

AmNi

&Q in J

Ni

in g . 0.1793 0.1576 0.1280 0.1369 0.1480 0.2118 0.2949 0.3485 0.4963 0.2724

.

. -47.7 - 59.7 -53.0 - 64.4 -72.5 - 70.7 - 97.2 - 99.2 - 86.8 -47.7

.

Enthalpy of mixing X[SAHi in kJmol - J

AH in kJmol -

-2.76 - 5.24 -7.18 - 9,23 - 11,34 - 13.67 - 16.55 - 19.35 - 22.15 - 23.49

24.65 -26.2 - 27.7 -28.9 -30,2 -31.6 - 33.0 - 34.6 - 36.2 - 37.5 - 38.1

. 0.049 0.088 0.118 0,147 0.178 0.217 0.266 0.316 0,377 0.406

H. FeufeI et aI. / Journal of Alloys and Compounds 257 (1997) 234-244

237

Table 6 Experimental values of the enthalpy change during dissolution of solid Ni of 298 K in liquid AIo.97La0.o3-Ni alloys at 1073 K and calculated enthalpies of mixing; standard states: AI(1), La(1), and Ni(1) Measured

Calculated

Starting a m o u n t

A d d e d amounts

Heat effect

Mole fraction

AQ in J

Ni

mat in g

mL~ in g

AmNi in g

5.8353

0.9987

.

.

.

Enthalpy of mixing ,~8~xH i

AH

m kJmol - )

in kJmol -

.

:

-5.7

0.2499 0.2965

- 416.5 - 506.5

0.019 0.040

- 2.59 - 5.59

- 8.2 - 11.1

0.3038 0.2975

-558.7 -424.5

0.061 0.081

- 8.70 - 11.12

- 14.05 - 16.35

alloy melts with a strong compound forming tendency, chemical short range order (CSRO) occurs. This CSRO is subject to concentration and temperature dependencies. The association model given by Sommer [13] describes the relation between CSRO and the thermodynamic mixing quantities. It is assumed that the free atoms and the associates, characterized by a fixed stoichiometry, are in dynamic equilibrium that is governed by the law of mass action. For the enthalpy and entropy of mixing of binary liquid alloys, the following expressions result

AH _

?IAIKIBI creg m H

AIBI

. . [ _flA _ _IflAiBj creg ]'/ A I'AIB)

nB I~'/AIBj (-,reg 0 @- - H ~BI'AIBj "/- 12AiBj,~HAiB) A S = - R(nA,

in

ZAI

"~ nB~ I n ZB~

+

(3)

J'ZAiBjI n ZAiBj ) (4)

-t- rtAiBjAS°AiBj

where hA, and riB, moles of free atoms are in equilibrium

Table 7 Experimental values of the enthalpy change during dissolution of solid A1 of 298 K in liquid Lao.88Nio ,2-A1 alloys at 1073 K and calculated enthalpies of mixing; standard states: AI(1), La(1), and Ni(I) Measured

Calculated

Starting amount

Added amounts

Heat effect

Mole fraction

Enthalpy of mixing

mLa

mNi

Atom

in g

in g

AQ in J

Ni

in g 6.0000

0.3452 0.0696

- 144.2

0.050

- 4.46

0.0757 0.0524 0.0621 0.0929

- I50.9 -93.4 - 124.1 - 186.4

0.099 0.130 0.164 0.213

- 8.72 - 11.23 - 14.22 - I8.28

0.0898 0.1259 0.0558

- 184.4 - 257.3 - 102.0

0.255 0.300 0.320

-21.87 - 26.30 - 27.92

0.0898 0.0987

- 147.6 - 163.9

0.350 0.380

-30.12 -32.34

0.0698 0.0755 0.0523 0.0628 0.0907 0.0903 0.0729 0.1055 0.0930 0.0987 0.0727

-

0.050 0.099 0.130 0.164 0.210 0.250 0.280 0.319 0.350 0.380 0.400

-4.01 - 8.09 - 10.92 - 13.88 - I8.00 - 21.31 - 23.74 -26.82 -29.20 - 31.69 - 33.24

6.0009

~SAH,

AH

in

in kJmol- '

kJmol- i

0.3457 120.7 140.1 110.7 121.3 183.6 171.7 133.0 183.5 157.2 181.4 122.8

-7.9 -12.0 -15.8 -18.1 -

2 0 . 8

- 24.5 -

2 7 . 8

-31.8 -33.3 - 35.25 - 37.25 -7.9 -11.5 15.2 -18.0 - 20.5 -24.I5 27.24 29.45 -32.2 -34.35 -36.6 -38.0

H. Feufet et al. / Journal of Alloys and Compounds 257 (1997) 234-244

238

Table 8 Experimental values of the enthalpy c h a n g e during dissolution o f solid A1 o f 298 K in liquid Lao 75Nio.2:A1 alloys at 1073 K a n d calculated enthalpies o f mixing; standard states: AI(1), La(1), and Ni(l) Measured

Calculated

Starting a m o u n t

A d d e d amounts

H e a t effect

Mole fraction

~AH,

E n t h a l p y of mixing

AQ in J

Ni

in Idmol- '

AH in kJmol-

mL~ in g

.~nl,~i in g

Areal

5.9985

0.8452

. 0,0811 0.0461 0.0457 0.0966 0.0716 0.0717 0.0510 0,1403 0.1982

in g .

. - 144.2 - 150.9 - 93.4 - 124.1 - 186.4 - 184.4 - 257.3 - 102.0 - 147.6

.

. 0.050 0,076 0.100 0,148 0,180 0,210 0,230 0,280 0,341

16.2 - 19.9 - 22.2 - 24.3 -28.0 -30.25 -32.5 - 33.9 -36,8 -39.85

-4.49 - 7.24 - 9.72 - 14.16 - I6.95 - 19.67 - 21.39 -25.11 -29.17

Table 9 Experimental values of the enthalpy c h a n g e during dissolution of solid AI o f 298 K in liquid Lao65Nio,35-A1 alloys at 1073 K and calculated enthalpies of mixing; standard states: AI(1), La(1), a n d Ni(t) Measured

Calculated

Staving amount

Added amounts

H e a t effect

M o l e fraction

AQ

Ni

mL~ in g

mr9 in g

AreA1 in g

5.9975

1.3653

. 0.0751 0.0612 0.0625 0.0691 0.1235 0.0853 0.1842

.

. 0.1356

.

5.9881

1.3625

Enthalpy of mixing

in J

0.1314

0.2083 0.1843

. - 171.5 - 139.2 - 134.2 - 155.4 -251.1 - 162,1 - 330.2

.

. - 276.9 - 266.0 -421.2 - 395.9

.

XSAH,

AH

in kJmol - ~

in kJmol -

-3.82 - 6.70 -9.35 - 12.19 - 16.48 -19.04 -23.74

22.13 -24.9 -27.15 -29.15 -31.35 -34,55 -36,4 - 39,8

- 6.23 - I 1.44 - t8,47 - 23,94

22.0 - 26.7 -- 30.6 -35.85 -40.0

. 0.040 0.071 0.100 0.t30 0.179 0.210 0.269 . 0.070 0.130 0.210 0.269

Table 10 Experimental values of the enthalpy c h a n g e during dissolution o f a solid mixture o f the c o m p o s i t i o n Lao.,,~Nio,35 of 298 K in liquid Al-Lao.6~Ni o 35 alloys at 1073 K a n d calculated enthalpies o f mixing; standard states: AI(1), La(1), and Ni(1) Measured

Calculated

Starting a m o u n t

Added amounts

H e a t effect

Mole fraction

E n t h a l p y of mixing

real in

Z~mLa in

Am m in

AQ in

A1

AH in

g

g

g

J

0.3634 0.3861 0.3833 0.4009

0.0831 0.0874 0.0873 0.0913

- 603.2 - 614.4 - 587.0 -67t.2

kJmol -

7.0~7 0.985 0.969 0.954 0.939

- 2.8 - 5,65 - 8.3 - 11.15

H. Feufel et a[. ! JourJm[ of Alloys and Compounds 257 (1997) 234-244 with nA, Bj moles of associates with the composition AiBj ( i , j = 1 , 2 . . . n). ZA~, ZB~ and ZA,Bj are the mole fractions of the respective species in one mole of binary alloy. AH°A,Bj 0 and ASA~B, refer to the enthalpy and entropy of formation (-,reg represents the interaction parameter of the associates. ~k,t between the assumed species k and t. Within the model, the 0 o reg adjustable parameters zX/-/A~Bj and ASA~Bj and the Ck.z are assumed to be independent of temperature in a first step. Hence, the temperature dependence of the enthalpy and entropy of mixing are exclusively caused by the temperature dependence resulting from the law of mass action. The equilibrium value for nA,Bj is determined by (nAiB)")/AIB)/ri) (hA,

.TA,/n)i(nB, 7B,/n) "1

exp[-(2XHOA,B: - T2XS°A B )/RTJ

= KA/Bj

(5)

with KA,Bj the association constant, Yk the activity coefficient of the assumed species k, and n the overall number of moles. The activity coefficients of the different species can be expressed by the interaction parameter (., ~k.zreg• Thus Eq. (5) becomes a function of the five model parameters and can therefore be solved iteratively. The adjustable parameters are determined by fitting experimental data, e.g. AH, excess heat capacity ACp and activities a~, by the leastsquares method. The association model was already applied to binary liquid A1-La, A1-Ni and L a - N i alloys in recent studies. In these calculations an AltNi~, A12La 1 and La~Ni 2 stoichiometry was assumed for the association reactions [14,11,15]. The stoichiometries AI~Ni t and AIaLa I correspond to intermetallic compounds in the solid state with the same stoichiometry. With the new obtained heat capacity data from the present study, a recalculation of the model descriptions of the A1-La and L a - N i alloys was necessary. From the experimental values of the heat

239

capacity given in Tables 1 and 2 ACp was calculated using the heat capacities of the pure elements at their respective melting point [9]. Hereby, it is assumed that the heat capacity of the pure elements is constant with temperature in the undercooled state. For liquid A I - L a alloys only a small change in the model description was necessary to describe the additional data. The data set used for the calculations and the resulting model parameters of liquid A I - L a alloys are summarized in Table 11. In Fig. 1 the calculated composition dependence of 2xH at 1200 K is shown together with the experimental data of [11]. Fig. 2 shows the calculated temperature dependence of the heat capacity of liquid Alo.zsLao.75 alloy together with experimental results given in Table 1. For the calculation of liquid L a - N i alloys the set of parameters was fixed on the basis of the experimental AH values at 1376 K [12] and the heat capacity data of the present study. The obtained temperature dependence resulted in calculated heat capacities which were generally too low. Hence, it was assumed that the enthalpy and entropy of formation of the associates cannot not be regarded as independent of temperature for 0 0 liquid L a - N i alloys. If AHAII3/ ASAIBj are known at a temperature T I the following relationship for T < T I can be used [13]: o ACp.AiB)

~---

A + B*T + C T 2

(6)

B AH°,Bj(T) = 2x/-/°,B,(T~) + A ( T - Zl) -q- T (r2 -- z2)

C

(7)

+ T (r3 - T31) T AS° sj(T) = AS°A,sj(TI) + A In --f71+ B ( T - T~) C + -~- (T 2 - Z~)

(8)

The five model parameters of Eqs. (3)-(5) are determined

Table 11 Association model parameter of the binary systems (in kJ moI-') Associate

AI-La AlzLa~

A1-Ni AI~Ni~

AH°.Bj~

- I28.2

- 127.6

AS°Bj

- 0.0506

-0.029

C r~ AI,B I C~,g j "A~B C reg B I,AIB] Data used for fitting/Reference

- 98.1 -- 50.9 - 86.3 ~H at I200 K: [I1] AH at I920 K: [16] AHt.0 . at 1000 K: [17] AQ(T): present study

- 68.9 = 32.7 - 86.3 [I4]

La-Ni La~Ni2 : - 108.0 +0.2462'(T- 1376 K) -3.57810-~*(T: - 13762 K2)/2 + 1.310 -7 *(T3- 13763 K3)/3 - 0.O28 + 0.2462*In(T/1376 K) -3.57810-4*(T - I376 K) + 1.3 10-7*(T' - 1376" K2)/2 i - 86.0 -37.0 -47.0 /',H at 1376 K: [12] . ~xCp(T): present study

240

H. Feufel et al, / Journal of Alloys and Compounds 257 (1997) 234-244 10

5S*T

v_ o

-10 ¢5 .:3

-20

5G

-30

-40

-50 0

.i

.2

,3

AI

.4

,5

.6

.7

.8

.9

X~

1.0

La

Fig. 1. Integral enthalpy, entropy, and Gibbs energy of mixing of liquid and undercooled liquid AI-La alloys at 1200 K calculated using the association model; O, experimental results of [11]. Standard states: AI(1), La(I).

42

A

40

A

A

3B A

o

A A A

A

A

34

32

I=+I= 800

l~=Itnlr=ttrI1nttri+=rqlJr;t=tJl+llllq[l+tllllllIllll 900

1000

1100

1200

1300

1400

a'/x Fig. 2. Temperature dependence of the heat capacaty Cp of liquid and undercooled liquid Alo.2~Lao.Tsalloy calculated using the association model; (. . . . . -, mechanical mixture of the C~-values of the pure liquid and undercooled liquid components; ~, experimental results of the present study). Standard states: AI(1), La(1).

H. Feufel et al. / Journal of Alloys and Compounds 257 (1997) 234-244

in a first step at 1376 K. In a following trial and error process the temperature dependence of the associate formation at temperatures below 1376 K was fixed according to Eqs. (6)-(8) on the basis of the heat Capacity given in Table 2. The resulting model parameters are given in Table 11. In Fig. 3 the calculated composition dependence of dill at 1376 K, in Fig. 4 the calculated temperature dependence of the heat capacity of liquid Lao.sNio. 5 alloy are shown together with the respective experimental data. Provided that no additional ternary interaction occurs, the enthalpy and entropy of mixing of the ternary liquid alloys are given by the following expressions: AH = Crag AIl'Lal

A S = --R(r/AI t In ~,A11 + r/La I ln'ZLa ' + t2Ni I In ZNi, -t-?IAI2Lal In ZAI2La ~ + F/AIINiI in ZAI~NI ~ 0 + llLalNi2 In zLa,yi2) + tlAI2NilASAI2Nil

(AS°a,Ni2

"+ ,rlAllNitASAiiNit dr- F/LalNi2 o

+ B(T - T1) + -~- (T 2 - r~)

r-7

"JVA in T

)

(10)

where/2i (i=All,Lax,Ni~) is the number of moles of free atoms in equilibrium with/2AI2La~, nAi1Nil and nLaiNi~" moles of associates, zi (i=All, La~, Nil, AlzLat, AllNit, La~Ni:) is the mole fraction of the respective species in 1 mole of a ternary alloy. Ck.l r~g represents an interaction parameter between the assumed species k and l. The equilibrium values of the moles of associates are determined by three laws of mass action coming from the binary systems. These three equations in combination with Eqs. (9) and (10) have to be solved simultaneously by an iteration process. The calculated values of zM~/, the Gibbs energy AG and dis for the section (Lao.65Nio.35)~_xA1x and (Alo.zvLao.73),_xNi;~ are shown together with experimental AH data in Figs. 5 and 6. The experimental dill-values are much more negative then the calculated ones. This behaviour is even more evident in Fig. 7 where the difference between calculated and experimental as well as their

__nAl'nLal + (-,reg nAllnA12Lat t1 ~AI I'Al2Lal /7,

+ creg /2LalF/A12Lat ...}_ 0 La i,AI2La I tZ /2A12La I diHAl2 La I F/A11HAl 1Ni 1 -]- t"'reg -/'ZAI - 1F/Ni I "Jr- C reg ~All'Nil tZ All'AIlNit /2 q_ /--,reg l/Ni I ~/2AIINit 0 ~ N i I,AI i Ni l 12 "Jr-/2AI i Ni I A N A l t Nil + C reg __/ILal/2Nil + crLeagl,LatNi2 /2LalF/LalNi2 Lal'Nil /2 F/ -.~ c r e g /2Nil F/La INi2 ( Nit'LalNi2 t~ + 17LalNi2 ~HLaINi20

B + ACT- T~) +-~ (TZ- T~) +~c (T3- T3~))

241

(9)

I0

5 0

7 O


r.o

_

OO

-15

.z.

={

-20

<~

-25 -30 -35

i~llt+ilr

irllrrlelf

-40

0

La

.l

.'~

.3

rlt Irtllllfllll11+lllllllll .4

.5

XNi

.6

.7

.8

.9

1.0

Ni

Fig. 3. Integral enthalpy, entropy, and Gibbs energy of mixing of liquid and undercoolcdliquid La-Ni alloys at 1376 K calculatedusing the association model; <~, experimentalresults of [12]. Standard states: La(1), Ni(1).

242

H. Feufel et al. / Journal of Alloys and Compounds 257 (1997) 234-244

50

48

i,o

~.

A

A

44

42

40

TII

38

Iii

I1111111li

800

ii11

900

III

IIITII

I000

IIII11

III

Ill

1 I00

ii

II+I

1200

rlllll+Jllll111

1300

1400

T/K Fig. 4. Temperature dependence of the heat capacity C o Of liquid and undercooled liquid LaosNio 5 alloy calculated using the association model; (- - -, mechanical mixture of the Co-values of the pure liquid and undercooled liquid components; ~, experimental results of the present study). Standard states: La(]), Ni(1).

10

T o -10 <3 <3

-20

-30

-40

-50

0

.1

.2

I.,a0.65 N i 0.85

.3

.4

.5 xxz

.s

.7

.8

.9

z.o A1

Fig. 5. Integral enthalpy, entropy, and Gibbs energy of mixing of liquid and undercooled liquid (La o +sNio 35)1 ~At~ alloys at t073 K calculated using the association model; A, experimental results for the enthalpy at 1073 K; ['r'l, 0, O × from different sections. -Standard states: AI(I), La(1), Ni(1).

H. Feufel et al. / Journal of Alloys and Compounds 257 (1997) 234-244

10

.,

I,

1

4

l

,

I

,

1

4

1

,

l

,

L

[

,

,

'

I

'

'

I

'

'

I

a

l

243

'

I

l

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T I

[

I

LO -i0

-20

~ m

-30

m

AG

-40

-50

F I

,

T

O

I

~ ,

.1

I

I

,

.2

i

,

I

r

I

.3

I

I

.4

AI o.2~La O.Ta

~ !

I

I

,

.5

,

I

,

.6

xm

~ I

.7

~

I

I

.8

I

I

.9

1.

Ni

Fig. 6. Integral enthalpy, entropy, and Gibbs energy of mixing of liquid and undercooled liquid (Alo,7Lao 73),_~Nix alloys at 1073 K calculated using the association model; [~ experimental results for the enthalpy at 1073 K; ~, &, C)from different sections.Standard states as in Fig. 5.

extrapolated results are shown. There are systematic deviations between measurement and calculation. The maximum of the deviation is about - 8 kJmo1-1 and centres around the composition Alo3Lao.45Nio.25. This indicates the presence of additional ternary interactions that can be described by a ternary association reaction. The assumption of a ternary A12La3Ni 3 associate leads to a

Lfl

References

0.44" ,,Q,. _ ~

'~

\06

÷

0. / 0.8/("

AI /

,,

~ \.

0v? v

\x

--6"

""~_

...-4"

~-,'/

m o d e l description which allows us to describe the c o m position d e p e n d e n c e of M-/ for the present study and the temperature and c o m p o s i t i o n d e p e n d e n c e o f the heat capacity of ternary liquid A1-La-Ni alloys. A detailed description of these calculations together with the experimental heat capacity data of ternary liquid A1-La-Ni alloys will be published in a subsequent paper.

/

/ 0.2

/

0v6 ,

0s

Ni

×N

Fig. 7. Difference between the experimental and the calculated enthalpy of mixing of liquid and undercooled liquid AI-La-Ni alloys at 1073 K in kJ tool -] using the association model ( . - - . , from measurements; ---, extrapolated).

[1] A. Inoue, T. Zhang, T. Masumoto, J. Noncryst. Solids 156-158 (1993) 473-480. [2] R Dantzer, E. Orgaz, Int. J. Hydrogen Energy I1 (1986) 797-806. [3] R Dantzer, J. Less-Common Met. 131 (1987) 349-363. [4] A.Kh. Abramyan, Deposited Doe., VINITI 3782 (1979) 212-214. [5] C. Chatillion-Colinet, H. Diaz, J. Mathieu, A. Percheron-Guegan, J.C. Achard, Ann. Chim. Fr. 8 (I979) 657-663. [6] H. Diaz, A. Percheron-Guegan, J.C. Achard, C. Chatilton, J.C. Mathieu, Int. J. Hydrogen Energy 4 (1979) 445-454. [7] F. Sommer, in: Rapidly Quenched Metals, S. Steeb and H. Warlimont, (Eds.) Elsevier Science Publishers, Amsterdam, 1985, pp. 153161. [8] F. Sommer, in: Materials and Physical Chemistry in Liquid Metal Systems, H.M. Borgstedt, (Ed.) Plenum Press, New York, 1982, pp. 387-393. [9] A.T. Dinsdale, Calphad I5 (1991) 317-425. [10] M. Bienzle, F. Sommer, Z. Metallkd. 85 (1994) 766-770. [11] F. Sommer, M. Keita, H.G. Krull, B. Predel, J.J. Lee, J. LessCommon Met. 137 (1988) 267-275. [12] S. Watanabe, O.J. Kleppa, J. Cheml Thermodyn. 15 (I983) 633644.

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H. Feufel et al. / Journal of Alloys and Compounds 257 (1997) 234-244

[13] F. Sommer, J. Non-Crystalline Solids 117/118 (1990) 505-512. [14] U.K. Stolz, I. Arpshofen, F. Sommer, Z, Metallkd. 84 (1992) 552-556. [15] H. Feufel, M. Krishnaiah, F. Sommer, B. Predel, J. Phase Equilibria 15 (1994) 303-309,

[16] Y.O. Esin, S.E Kolesnikov, V.M. Baev, M.S. Petrushevskii, P.V. Geld, Russ, J. Phys. Chem. 55 (1981) 893-896. [17] V.A. Lebedev, V.I. Kober, I.F, Nichkov, S.R Raspopin, A.A. Kalinsovskii, Izv. Akad. Nauk SSSR, Met. 2 (1972) 69-71.