Binary common-ion alkali halide mixtures thermodynamic analysis of solid-liquid phase diagrams

Binary common-ion alkali halide mixtures thermodynamic analysis of solid-liquid phase diagrams

CALPHAD Printed Vo1.7, No.3, in the USA. pp. 211-218, 0364-5916/83 $3.00 + .OO (c) 1983 Pergamon Press Ltd. 1983 BINARY COMMON-ION ALKALI HALIDE ...

457KB Sizes 0 Downloads 60 Views

CALPHAD Printed

Vo1.7, No.3, in the USA.

pp. 211-218,

0364-5916/83 $3.00 + .OO (c) 1983 Pergamon Press Ltd.

1983

BINARY COMMON-ION ALKALI HALIDE MIXTURES THERMODYNAMIC ANALYSIS OF SOLID-LIQUID PHASE DIAGRAMS III. THREE SYSTEMS WITH LIMITED AND SIX SYSTEMS WITH NEGLIGIBLE SOLID MISCIBILITY APPLICATION OF THE EXTXD/SIVAMIN METHOD Harry

A.J. Oonk, Jacobus G. Blok and Joke A. Bouwstra

General Chemistry Laboratory, Chemical Thermodynamics Group University of Utrecht, Padualaan 8, Utrecht, The Netherlands ABSTRACT

Solid-liquid phase diagrams of three common-ion alkali halide mixtures showing limited solid miscibility and of six common-ion alkali halide mixtures with negligible solid miscibility have been analyzed using the EXTXD/SIVAMIN method. The results of the calculations follow the characteristics of the results (reported in part I) that were obtained for another set of systems with negligible solid miscibility. Introduction

The investigation, the results of which are presented in this series of papers, was carried out to check the significance of two recently developed methods for analyzing TX phase diagrams. The systems selected for the investigation all belong to the class of common-ion alkali halides which are of great importance from a theoretical as well as from a practical point of view. In part I (1) we presented the results for 15 systems with negligible solid miscibility, which were analyzed by the statistical EXTXD/SIVAMIN method. The results for 18 systems with complete subsolidus miscibility were reported in part II (2); these systems were analyzed by the LIQFIT method which is an iterative procedure of phase-diagram calculations in which the calculated liquidus is made to run through the experimental liquidus points. In this part we present the results of EXTXD calculations for the three systems (Li, Na)F; (Na, K)F and (Na, Rb)Cl, for which the degree of solid miscibility is known, and for the following six systems with negligible solid miscibility (Li, Cs)F; (Li, Cs)Cl; (Li, Cs)Br; (Na, Cs)Cl; (Na, Cs)Br and (Na, Cs)I. Formulation The excess properties for which numerical values can be derived from eutectic solid-liquid phase diagrams are the excess thermodynamic potentials of the components in the liquid state. The equations are the following ny liq(T,X,liq )= 7 AS; dT - RTln(l-X'liq) To1

!A; liq(T,Y'

T

+ RTln Y' sol +v : s"l(y~sol)

liq)= f AS; dT - RTln Y1liq To2

Received 26 January

+ RTln(l-X' sol) + uf: sol(x,sol) (1)

1983

211

(2)

HARRY A. J. OONR et al.

212

AS* stands for the entropy. change on melting, R stands for the gas constant and T for the thermodynamic temperature. The subscripts 1 and 2 refer to the components: in this paper the second component is the one with the larger non-common ion. To1 and To2 are the melting points of the pure components. The meaning of the various mole-fraction symbols follows from figure 1.

FIG 1

I X

I

,sol

X

lliq

Y

’lliq Y"sol

When solid miscibility can be neglected, calculations are made with the parts of these equations at the left-hand side of the stroke. The 'correction terms' at the right-hand side of the stroke are needed when solid miscibility cannot be ignored. In calculating these corrections, we make the assumption that the solid state can be described by one Gibbs energy function and that its excess part is given by GE "l(X)

= X(1-X) {G;O' + G;"(l-2X)]

,

(3)

sol

in which the coefficients G and GSol are independent of temperature. The values of these coeffic 4ents can'be calculated if for one temperature the extension of the region of demixing - the solubility of each of the components in the other - is known. In this model the excess thermodynamic potentials of the components in the solid state are given by

,( sol(x’sol) = (x-01)2 {G;”

+ ~;~~(3_4~,SO1))

(4

'O') = (1-Y'so1)2 {G;O' + G;01(1_4Y'Sol)]

(5

For the system (Li, Na)F the numerical values of the terms of the right-hand sides of Eqns (1) and (2) are, for the eutectic temperature and expressed in joule per 'mol., -4741 + 3789

-131 + 12

-9049

-698

+ 7218

+ 79

The calculations, the results of which are given in this paper, were made without taking into account heat-capacity influences.

213

BINARYCOMMON-IONALKALIHALIDEMIXTURES

Experimental information a. extent of solid miscibility For each of the three systems for which solid miscibility is taken into account experimental information on the extent of solid miscibility is available for at least one temperature. In any case we preferred data obtained by other techniques over the data that had been derived from cooling curves. A survey of the experimental information used as well as of the calculated excess Gibbs energy coefficients is given in Table 1. TABLE 1 ExperimentalInformation on Solid Miscibility and Calculated Energy Coefficients Expressed in Joule per Mol. system

(Li, Na)F

(Na,K)F (Na, Rb)Cl

solid state miscibility sol

T/K

X'

898 994 788

0.015 0.015 0.008

Y'

exp technique

ref.

sol

0.92 0.930 0.94

interdiffusion equilibration interdiffusion

Excess Gibbs

3 4 3

sol G1

sol G2

26180 29590 25630

5920 5990 6350

b. entropy of melting The entropy of melting values of the pure components, which we used for the calculations are given in part I (1) and part II (2). c. liquidus The sources of the experimental phase diagrams the number of experimental liquidus points (between melting point of pure component and eutectic point) of the left-hand as well as of the right-hand liquidus, the melting points of the pure components and the coordinates of the eutectic points are given in Table 2. Data input a. the systems with limited solid miscibility In the first place the compositions of the solid phases at the eutectic temperature were calculated making use of the calculated values of the two excess Gibbs energy coefficients. The solidi were then taken as the straight lines connecting the calculated points at the eutectic temperature and the melting points of the pure components. Next the initial slopes of the liquidi were calculated with the Van 't Hoff equation, taking into account the slopes of the solidi. Finally the liquidus curves were obtained by drawing "by eye" a smooth curve through the experimental liquidus points, making allowance for the calculated initial slope. For the EXTXD computations a dummy data set was read from the eye-fitted curves at regular temperature intervals. The corrections due to solid miscibility were introduced separately. Details of the data sets are given in Table 3.

214

BARRY A. J. OORlCet al.

TABLE 2 Experimental Phase Diagram Information system

ref. n

(Li, Na)F

left nright Tol'K

(Na, Bb)Cl

5 5 6

4 6 6

I 6 4

(Li, Cs)F (Li, CS)Cl (Li, Cs)Br

7 7 8

5 6 6

10 11 6

1 123

(Na,Cslcl (Na,Cs)Br

9 10 11

3 8 10

2 13 5

1071 1031

(Na,K)F

(Na, cs)I

notes table 2:

To2'K

1119.3 1267.5 1072

1267.5 1131.4 993

Teut'K

Keut

922 994 823

0.39 0.60 0.56

958 919 914

879 820

1,2 1,2 2,5

913 919 920

941

note

759 755 701

0.65 0.57 0.515

3 4

1. liquidus points to be read from a figure 2. compound formation 3. no data for mole fractions < 0.3 4. no data for mole fractions > 0.15 5. no data for mole fractions > 0.7

TABLE

3

Details of the Data Sets Used for the Computations system

left-hand liquidus

right-hand liquidus

range (K) intervals(K) range (K) intervals(K)

(Li,Na)F (Na,K)F (Na,Kb)Cl

930-1110 1010-1250 840-1040

10 10 10

930-1250 1010-1130 840- 990

10 10 10

(Li, Cs)F (Li, Cs)Cl (Li, Cs)Br

760-1080 660- 870 580- 800

20 10 20

760- 940 660- 900 580- 840

20 10 20

(Na, Cs)Cl (Na, Cs)Br (Na, Cs)I

760-1060 760- 960 710- 880

20 10 10

760- 900 760- 910 710- 880

20 10 10

b. the systems with negligible so.id miscibility Apart from the allowance for solid miscibility, the liquidus curves were constructed in the same manner as indicated above. In the case of (Na, Cs)Br and also in the case of (Na, Cs)I the melting points of the pure components, which possibly had been taken from other sources, were slightly corrected; 7 K or less. The melting points given in Table 2 are the corrected ones. A note concerning the transition in the solid state of CsCl has to be made. In the case of (Na, Cs)Cl the transition can be ignored as it is below the eutectic temperature. In the case of (Li, Cs)Cl the transition interferes with the solid-liquid equilibrium. However, we did not take it into account: the experimental data are of limited accuracy and do not reveal a change in the slope of the liquidus.

BINARYCOMMON-IONALKALIHALIDEMIXTURES

215

Results For the thermodynamic description of the liquid mixtures we adopt the in which the excess Gibbs energy takes the form of Redlich-Kister model, Eqn. (3) GE liq(T,X) = X(1-X) {Giiq(T) + G;iq(T)(1-2X) + G;iq(T)(1-2X)2 + ...I Furthermore we assume that in the temperature range considered the G coefficients (of which we drop the superscript liq) are linear functions of temperature Gi(T) = Hi(e) - T Si(0)

(7)

in which 0 is the mean temperature of the range and accentuates that the-Hi and S. constants are representative of the mean temperature of the range cbnsidered. In the EXTXD/SIVAMIN method in which the H. and S. coefficients act as the parameters to be adjusted, computations ar& made dith an increasing number of adjustable parameters in such a manner that the number of S parameters is either equal to or one less than the number of H parameters. The significance of the results follows not only from the standard deviation of the fit but above all from the degree of agreement between the experimental data and the calculated phase diagram, i.e. the phase diagram calculated with the computed H and S constants. In the following the degree of agreement between experimental data and calculated phase diagram is indicated with the quantities AT and Ax. AT is the mean temperature difference between original liquidus point and the calculated liquidus temperature corresponding to the mole fraction of the original point: ‘T

1 = ii

n C

abs(Tiexp - Ticalc)/K ,

(8)

i_l

where n is the number of original points. On the same lines A, is defined as 1" C abs(Xi - Xi *x = z i=l talc 1 exp

.

(9)

a. the three systems with limited solid miscibility The results of EXTXD calculations on the three systems with limited solid miscibility are given in Table 4. In each case the solutions with three and four adjustable parameters reproduce the phase diagram with great accuracy as follows from the AT values. The use of the weighted mean temperature instead of the unweighted mean temperatures, as we did in part I, reduces the dispersion in the calculated excess Gibbs energy coefficients G1(B) and G2(8). b. the six systemswithnegligible

solid miscibility

The results of EXTXD/ SIVAMIN calculations on the six systems with negligible solid miscibility are given in Table 5 and that for the solutions with two and with four adjustable parameters. It is to be assumed that for most of these systems the results lag behind the results obtained for other common-anion systems, such as the three considered above, of which the phase diagram data are of higher quality.

216

HARRY A. J. OONK et al.

In the case of the (Li, Cs) systems the significance of the results is further decreased owing to the fact that, as a consequence of compound formation, there is a gap in the data sets around X = 0.5. In this connection it may be mentioned that MTXD/SIVAMIN calculations based on Dergunov's (12 phase diagram for (Li, Cs)Cl yield G (6) values which are about 7 kJ mol- 1 less negative than the values given f&r (Li, Cs)Cl in Table 5 (see also part I, results obtained for six different data sets on (Li, K)Cl). TABLE 4 The Three Systems with Limited Solid Miscibility. Survey of Results of Computations. B values in kJ per mol; S values in J per K per mol; Standard Deviation of the Fit; Mean Temperature Difference; Mean Mole-Fraction Difference; Weighted Mean Temperature and Values of the Excess Gibbs Energy Coefficients for the Mean Temperature Expressed in kJ per mol. B.

S.

B,

(Li, Na)F - 6.05 -15.81 - 9.17 -17.71 -11.80 -20.69 -14.88 (Na,

0.22 - 2.07

S,

s.d.

- 2.33

55.3 22.3 14.1 9.5

- 6.94

51.7 21.6 9.9

2.31

44.4 38.0 19.2 17.0

A..

8/K

985

1.02 1.01

0.0019 0.0019

G,(8)

G,(8)

-6.05 -6.19 -6.09 -6.04

0.22 0.20

0.23 0.14 0.48 0.40

-0.60 -0.58

-3.11 -3.10 -2.95 -2.91

-0.30 -0.30

K)F

0.23 -

A_.

5.39

-12.79 - 1.80 (Na, Rb)Cl - 0.31 3.38 0.04 - 2.24

1040

54.9

- 5.31 -12.76 - 2.12

7.36 3.31 0.76

- 0.60 - 7.80

- 0.30 1.73

0.78 0.86

0.0021 0.0023

880 0.86 0.68

0.0021 0.0017

TABLE 5 The Six Systems with Negligible Solid Miscibility. Symbols have the Same Meaning as in Table 4. System (Li, Cs)F

(Li, CslCl

(Li, Cs)Br

(Na, Cs)Cl

(Na, Cs)Br

(Na, CslI

Survey of Results

s.d.

of Computations.

8/K

H1

sl

H2

s2

-37.97 -57.03

-28.75 -54.72

- 1.64

311 50

22.9 3.7

800

- 4.90

-40.26 -26.19

-27.81 - 6.86

7.34

229 40

12.5 3.3

720

2.73

-50.16 -51.53

-47.12 -48.29

-13.65

210 24

11.7 2.5

650

-10.87

- 8.86 -12.12

- 6.50 -10.55

5.28

40 28

1.0 1.3

820

4.50

-11.11 - 7.56

- 8.16 - 3.86

- 8.51

73 11

2.6 1.2

810

- 7.35

-26.73 -26.39

-27.28 -26.79

3.16

76 24

3.2 1.8

760

2.84

AT

The

Gl(8)

G2(8)

-14.97 -13.26

-3.59

-20.23 -21.25

-2.55

-19.53 -20.14

-2.00

- 3.53 - 3.47

0.17

- 4.50 - 4.44

-0.46

- 6.00 - 6.03

0.43

BINARY COLON-10~ ALKALI HALIDE MIXUPS

Discussion The results of the calculations reported in this paper are in agreement with and strengthen the conclusions arrived at in part I. Although the significance of the computed H and S values in the first place is of a mathematical nature (in that they permit an accurate calculation of the phase diagram) it cannot be ignored that the computed H and S values have a certain physical meaning. This is most clearly demonstrated by the H values obtained for the systems that display a large negative heat of mixing. In figure 2 the computed H values are suggestively plotted in an Hl versus T diagram and connected with the experimental values obtained by Kleppa and coworkers. It follows from figure 2 that the computed values are mutually consistent and, moreover, show a certain trend with respect to the experimental values. If we concentrate on the systems for which the computations are based on high-quality data sets (low values for AT) and take into account the intrinsic inaccuracy of the method, we could say that the mean trend shown in figure 2 points to a value for dHl/dT (which Is Cl,the first coefficient of the Redlich-Rister expression for the excess heat capacity) of about +25 J K-lmol-l. This estimate fits in with the value of +13 given by Hong (13) for (Li, K)F and also with the value of +9 which can be derived from the data given by Holm (14) and Hong (13) for the system (Li, Na)F. i?acleod(15), on the other hand, reports for (Li, Na)F heat of mixing values which become more negative with increasing temperature, corresponding to a value fox Cl of -17.

* *\"r \

ap

,Li,Rb

0

-40

Li,CS

* .

Li,K

Li,Na A-A *-

Na,Cs --*

Br

0

800

1000

FIG 2

Comparison of calculated and experimental Hl values.

1200

218

HARRY A. J. OONK et al.

References 1.

H.A.J. Oonk, J.G. Blok, B. van der Koot, N. Brouwer, Calphad, 2, 55 (1981).

2.

J.A. Bouwstra, H.A.J. Oonk, Calphad, 5, 11 (1982).

3.

J.M. Short, R. Roy, J. Am. Ceram. Sot., 47, 149 (1964).

4.

N.B. Chanh, J. Chim. Phys., 61, 1428 (1964).

5.

J.L. Holm, Acta Chem. Stand., 2,

6.

A.D. Pelton, S.N. Flengas, Can. J. Chem., 48, 3483 (1970).

I.

G.A. Bukhalova, D.V. Sementsova, Zh. Neorg. Khim., lo, 1886 (1965).

8.

1.1. Il'yasov, K.I. Iskandarov, M. Davranov, R.N. Berdieva, Russ. J. Inorg. Chem., Engl. Transl., 2, 135 (1975).

9.

I.G. Murgulescu, S. Sternberg, Z. Phys. Chem., 219, 114 (1962).

10.

1.1. Il'yasov, Ukr. Khim. Zh., 31, 930 (1965).

11.

1.1. Il'yasov, A.G. Bergman, Russ. J. Inorg. Chem., Engl. Transl., 2, 768 (1964).

12.

E.P. Dergunov, Zh. Fiz. Khim., S,

13.

K.C. Hong, O.J. Kleppa, J. Chem. Thermodynamics, 8, 31 (1976).

14.

J.L. Holm, O.J. Kleppa, J. Chem. Phys., 49, 2425 (1968).

15.

A.C. Macleod, J. Cleland, J. Chem. Thermodynamics, 7, 103 (1975).

638 (1965).

584 (1951).