Binary p-dihalobenzene systems - correlation of thermochemical and phase-diagram data

Vol. 15, No. 3, pp. 225-234, Printed in the USA.

CALPHAD

0364-5916191 $3.00 + .oo (c) 1991 Pergamon Press plc

1991

BINARY P-DIHALOBENZENE SYSTEMS - CORRELATION THERMOCHEMICAL AND PHASE-DIAGRAM DATA

M.T. Calveta)

, M,A. Cuevas-Diartea) and

a)

Dcpartament

OF

, Y. Hagetb) , P.R. van der E&d&)

H.A.J. Oonkc)

de Cristal.lografia, Mineralogia i Dip&its Minerals, Facultat de Geologia, Marti i Franqu&s, s/n. E-08028 Barcelona

b)

Laboratoire de ~st~io~phie

et de Physique Cristalline, URA 144 au CNRS,

Universit& de Bordeaux I, 351, COWSde la Lib&ration, F-33405 Talence c)

Chemical Thermodynamics Group, Faculty of Chemistry, Utrecht University, Padualaan 8, NL-3584 CH Utrecht

(Presented at CALPHAD XIX, N~rdwijkerhout,

ABSTRACT

The Netherlands, June 1990)

The excess Gibbs energy difference between the liquid and the mixed crystalline state, having space group P21/a with Z=2, of binary p-dihalobenzene systems (halo = Cl, Br, I) can be represented, as a function of temperature and mole fraction of the second component (the one with the larger molar volume), by the formula AGE(T,X) =A(1 -3

X(1-X)fl+B(l-2X)]

The constant 8 is a characteristic temperature; for the family of p-dihalobenzene systems it has the value 500 K. The constant B, which is a measure of the asymmetry of the thermodynamic mixing properties of a system, can be given as B = 0.2. The other binary characteristic, the constant A, stands in relation to the coefficient of crystalline iso~mo~hism cm. The latter expresses the degree of geometrical similarity of the unit cells of the two pure com~nents. The relation between A and c;, is A = -62( l-em) kJ.mol-1

The five substances p-dichlorobenzene (ClCl), p-bromochlorobenzene (Cl&), p-chloroiodobenzene (CII), p-dibromobenzene

(BrBr) and p-bromoiodobenzene

(BrI) are members of the chemically coherent group of

substances: the pdihalobenzenes. At room temperature the substances crystallize in the space group P2t/a with _~_*_C_L*~~__~___~______________L___ Received 25 October 1990

225

MT. CALVET et

226

al.

Z=2 molecules per unit cell. With the exception of CICI, the crystal structures do not change when raising the temperature from room temperature to the melting point. The substance p-diiodobenzene has a different crystal structure and for that reason it is not taken into account in this study. The five substances include ten binary systems and from thermal analytical work it is known, for a long time, that the substances are miscible in the solid state. We refer to the work of Bruni and Gorni (1900) [l] on ClCl+ClBr, ClCl+BrBr and ClBr+BrBr; the work of Kiister (1905) [2] on ClCl+BrBr; Nagomow (1911) [3] on ClCl+ClI and BrBr+BrI; Kruyt (1912) [4] on ClCl+BrBr and, in particular, to the work of Campbell and Prcdan (1948) [5] on ClCl+ClBr; ClCl+BrBr and ClBr+BrBr. In all these cases one is dealing with an accurate determination of the liquidus curves; the positions of the solidus curves and the subsolidus characteristics, on the other hand, being less well defined, see also Oonk et al. [6]. In the research of our group of laboratories on molecular mixed crystals the p-dihalobenzenes represent a key group of chemically coherent substances. Molecular mixed crystal systems are studied by us by means of a variety of methods, which include thermal analysis, X-ray crystallography,

crystal physics, experimental

thermodynamics and thermodynamic phase-diagram analysis. The combined approach of various methods has proved to be very fruitful. This was demonstrated, in particular, by the results obtained for the group of substances composed of naphtbalene and its 2-derivatives [7]. In the case of the p-dihalobenzenes, on the other hand, the combined approach not only has problem solving aspects but also a number of problem generating, read confronting, aspects. As an example we may mention the system ClCl+BrBr, where from a thermodynamic point of view, complete miscibility at room temperature is expected, whereas X-ray experiments give evidence of demixing phenomena; see Haget et al. [8]. Comparable phenomena were also observed for ClCl+BrI, ClI+BrBr; ClBr+BrI and for ClI+BrI [9]. Before one can try to understand the conflicting behaviour of a part of the p-dihalo systems, one has to know, in a quantitative

manner, what would be “normal” for these systems. Normal in the context of

isomorphous substances that show a pronounced geometrical similarity, i.e. for substances that share a high value of E,,,, the coefficient of crystalline isomorphism [lo]. The scope of the investigation, which is reported in this paper, has been, then, to analyze the data of the five systems, which do not show demixing phenomena, in order to arxive at the formulation of the “normal” behaviour of the whole family of the ten p-dihalobenzene systems.

The experimental

data which we use in this investigation

are from thermal

analytical

work

[9] on pure substances and binary mixtures. They include liquidus temperatures and heats of melting as a function of composition. The liquidus temperatures of a given binary system, and the corresponding melting points and heats of melting of the pure components, were used to calculate, by means of the LIQFIT procedure [ 11,121, the excess Gibbs energy difference, AGE, between the liquid and solid state. For the latter we use the Redlich-Kister form with two coefficients: G=l_

GES“’E AGE = X(1-X)[AG,+(l-2X)AG,]

(1)

where the superscripts liq and sol refer to the liquid and solid states, respectively; X represents the mole fraction of the second component.

BINARY P-DIHALOSENZENE

In the LIQFIT temperature;

computations,

the adjustable

it implies that the calculated

The results of the LIQFIT computations energy difference

SYSTEMS - THERMOCHEMICAL

parameters

AG1

AND PHASE-DIAGRAM DATA

and AG2

were taken independent

values are valid for the mean temperature

of the solid-liquid

227

of

range.

are assembled in Table 1 as follows: in the sixth column the excess Gibbs

at X = 2, 1. m . the seventh column AGt and in the eighth column the quotient of AG2 and AG1; all

for the mean temperature of the solid-liquid range. The experimental

excess enthalpy difference is just given for the equimolar mixture; Table 1 fourth column;

it was derived, for a given system, from a plot of heat of fusion versus composition. At this place it must be stressed that the data given in Table 1 correspond

to a uniform treatment of all ten

systems. A treatment, therefore, in which - for the time being - any evidence for incomplete

solid-state miscibility

is ignored.

TABLE I The ten p-dihalobenzene

systems.

The asterisks refer to systems which do not show solid-state demixing phenomena. E, is the coefficient of crystalline isomorphism. AHE (kJ.mol-‘) represents the excess enthalphy difference between the liquid and the solid state for the equimolar mixture. Tmean(K) stands for the mean temperature of the solid-liquid region. AGE (kJ.mol-‘) is the excess Gibbs enerp difference of the equimolar mixture. AG1 (kJ.mol-‘) and AGz are the coefficients of the expression for AG , F@.(l). The last column gives AGE values (kJ.mol-‘) for the cquimolar mixture and valid for 323 K.

svstem No.

Em

LIOFIT results

AHE T mean

Comp’s

AGE

AG1

AGE 3

(X=+,

AG1

1* ClCl+ClBr

0.967

-0.22

329

-0.12

-0.49

0.34

2

ClCl+BrBr

-0.12

0.936

-1.09

338

-0.36

-1.45

0.46

-0.39

3* ClCl+ClI

0.879

-2.23

312

-0.72

-2.88

0.39

-0.67

4

ClCl+BrI

0.857

-1.99

312

-0.85

-3.41

1.11

-0.81

5* ClBr+BrBr

0.971

-0.13

346

-0.17

-0.68

0.03

-0.17

6* ClBr+ClI

0.915

-0.98

326

-0.33

-1.32

0.07

-0.34

7

ClBr+BrI

0.893

-1.96

340

-0.54

-2.16

0.57

-0.61

8

BrBr+ClI

0.946

-0.76

341

-0.11

-0.43

-0.54

-0.14

9* BrBr+BrI

0.925

-1.10

356

-0.29

-1.15

0.12

-0.36

10 ClI+BrI

0.980

-0.52

343

-0.05

-0.22

0.21

-0.08

228

MT. CALVET

et al.

In Figure 1 the equimolar excess Gibbs energy difference values, sixth column of Table 1, for the five “unsuspicious” systems are plotted against the equimolar excess enthalpy difference values from the fourth column of that table. It follows from Figure

1 that the AGE values

-3l3

are

considerably smaller than the AHE values, the proportionality factor beiig about $

AG~(X=I/Z) W.mol-’

AG~(x=$

= ~AH~(X=;)

-xi

(2)

The A@ and the AHE in this equation both are valid for the mean temperature of the solid-liquid region. The mean of the mean temperatures of the five systems is about 333 KTaking AHE independent of temperature, we now

-‘I3L!C!!?_ cl

write the evidence contained in Figure 1 in the following

-1

-2

.3

aHE(X.l/Z)

form

hJ.mol -I

AG~(x=~, 33313) = ~AH~(x=$

(3) &L-L

Substitution of this equality into the general thermodynamic reIation, AGE = AHE - TASE, gives rise to the following

equality AHE(X=;) - 333ASE(X=$ = +I-IE(X=$

ExcessGibbs energy differences derived from phase diagrams against experimental excess enthalpy differences.Thenumberingof the systemsfollows from Table 1.

(4)

where ASE is the excess entropy difference of the liquid and solid mixtures. We take ASE independent of temperature (as a consequence of taking AHE independent of temperature). The significance of Eqn.(4) is that the family of the five p-dihalobenzene systems is characterized by a constant ratio (Cl)of AHE and ASE, having the dimension of temperature and the value of 500 K. AHE(X=;) =9=5OOK

(5)

ASE(X=;) We will refer to 0 as the characteristic temperature of the family of substances. Its meaning is the following. If AHE and ASE would (indeed) be independent of temperature and, as a consequence A@ linearly dependent on temperature, then the change of AGE with temperature would be such that it becomes zero for T = 0. Apparently, therefore, the family of the (five) p-dihalobenzene systems is characterized by a characteristic temperature of 500 K. A comparable situation exists for the family of the common-anion alkali halide systems, where we found a characteristic temperature of about 2600 K [ 131.

BINARY P-DIHALOBENZENE

SYSTEMS - THERMOCHEMICAL

AND PHASE-DIAGRAM

DATA

229

Owing to the fact that for the systems considered the temperature range of interest is limited (let us say from O’C to lOO’C, which is just above the highest melting point of the members of the group), we will, indeed, take AHE and ASE independent of temperature. In addition we will assume that l!@.(S) is valid over the whole mole fraction range (and not just for X=$). Therefore we can write AGE(T,X) = (l- 3AHE(X) To start with, we used this equation to bring the AGE values, Table 1 sixth column, to 323 K. The choice of 323 K is a compromise between the mean temperature of the set of experimental data and the wish that the extrapolation does not blow up the absolute errors of the greater A@ values. The reason for extrapolating the A@ values to a common temperature lies in the circumstance that we want to relate these values to the coefficient of crystalline isomorphism. This is the subject of the following section. The AGE values valid for X=‘/2 and T=323K are given in the last column of Table 1. The combination of Eqn.( l), which contains the mole-fraction dependent part of AGE, and Eqn.(6), which contains the temperature dependent part of A@, gives rise to the following general excess function AGE(T,X) = A(l- :)X(1-X)[l

+ B(l-2X)]

(7)

The constant 8 represents a temperature which is characteristic for the family of systems. The constants A and B have - for the different members of the family - different values. In terms of the Redlich-Kister coefficients of Eqn.( l), A is given by

and B=!% AGt

(9)

The constant A, therefore, represents the magnitude of AGE and B is a measure of the asymmetry of the latter. In the following, the quantities A and B, read the binary properties A and B, will be brought into relation with the coefficient of crystalline isomorphism Ein The latter is a quantity which is defined by pure-component properties only.

TS PROP-

When studying the thermodynamic mixing properties of a series of mixed crystals, two principal factors have to be taken into account: the geometrical factor and the sort factor. The latter is related to the difference in chemical nature of the species that are mixed and within a group of chemically coherent substances it will play a minor part. The geometrical factor is related to the space, or rather the difference in space, needed by the different species; within a chemically coherent group of substances, such as the p-dihalobenzenes, it plays the dominant part.

M.T. CALVET et al.

230

The geometrical

factor can be quantified by the coefficient

of crystalline

measure of the similarity between the unit cells of the pure components. cells of the two pure components

are superimposed

Em is obtained

so as to maximize

overlapping part of which the volume is I-, and non-overlapping

isomorphism,

their overlap.

E,,, [lo], which is a

as follows. The two unit Then there will be an

parts of which the total volume is Am. Then Ed

is defined as &m=lA geometrical Furthermore,

2) C In

(10)

factor will correspond

to positive

excess Gibbs energies

of the mixed crystalline

solid state.

it can be expected that G Esol, the solid state excess Gibbs energy, will be greater the smaller the

value of E,. Within a group of chemically coherent substances that show solid state miscibility,

the excess Gibbs energy

of the liquid state of a pair of members usually is small. Therefore, lGEliql<< GEsol

(11)

and consequently

In other words, minus AGE will be close to @I. GEso* and E,,,, we will look for a relationship

And because it is to be expected that there is a relation between

between AGE and Em.

AGE versus E,,, In Figure 2 the values of AGE(X=$ derived from the phase diagrams by LIQFIT and brought to the uniform temperature of 323K are plotted against the coefficient of crystalline isomorphism,

cm.

mixing property p-dihalobenzenes

1.0 -

4

-~G~(x=1/2) 3

kJ.mol -1

7

0

0.5 -

pure camp’s property

-FIG 2 Excess Gibbs energy difference values, valid for T=323 K, derived from phase-diagram and thermochemical data, plotted against the coeffkient of crystalline isomotphism. Shaded circles: the “unsuspicious” systems. Open circles: the systems showing the puzzling demixing phenomena. The numbering follows from Table 1.

BINARY P-DIHALOBENZENE SYSTEMS - THERMOCHEMICAL AND PHASE-DIAGRAM DATA

The figure shows the expected

trend and, moreover,

it is seen that the two groups of five systems support one

between AGE and E,-,,,we arrive at the following

another. If we assume a linear relationship

231

expression

for the

constant A A -= kJ.mol-l

-62 (l-a,,,)

(13)

It can be expected that it is easier to replace a molecule by a smaller one than to replace it by a bigger one. In other words, the thermodynamic

mixing properties

of the mixed crystalline

energy, GEsol, will show a certain degree of asymmetty.In

state, such as the excess Gibbs

terms of the two-constant

function

GEso’ = X(1-X) [G;‘t + Gyt (1-2X)] of which Gsol is positive, see above, q1

(14)

will also be positive if the first component

is the one with the smaller

unit cell. From a phase-diagram

point of view, the choice of q’/Gy’,

as a measure of asymmetry

For instance, for the case where Gt and G2 are (positive and) independent demixing

in the solid state (i.e. temperature

determined

divided

of temperature,

by critical temperature

is a suitable one.

the reduced region of

versus mole fraction)

is fully

by the choice of G2/Gt. As an example, for G2/Gl= 0.5 the mole fraction of the critical point will be

X&302.

For the same ratio the critical temperature follows from Gl/RTc = 1.488.

In view of the fact that l@soll is expected to be about IAGEI, we will try to correlate the quotient (AG2/AGt) of the constants

of the excess Gibbs energy difference

function. In accordance

with the remarks made above,

AC2 and AGt should have the same sign. This is indeed the case, as follows from Table 1, eighth column (with the exception

of one of the “suspicious”

systems). However,

the AGt and AGdAGt

values, shown in Table 1,

were derived from the phase diagram by means of LIQRT in the mode of temperature-independent energies.

This implies that the AGdAGt

temperature AGdAGl

values not only are the result of asymmetry

on the excess Gibbs energies, values obtained

for the systems

see also reference

excess Gibbs

but also of the effect of

14, p.208. For that reason we concentrated

of which the components

on the

have melting points which are closely

together, such as the systems which have been numbered 3,6 and 9. There is some trend of increasing AGdAGt with decreasing E,,,. In view of the uncertainties,

however, it seems to be reasonable to use a constant value:

B +o., 1

The emirical formula The results obtained

above correspond

to the following

difference AGE(T,X)= A(1 - $X(1-X)[I+B(l-2X)] with

A = -62000 ( I-E~) J.mol-1 B = 0.2 8=5OOK.

empirical

relation

for the excess Gibbs energy

MT. CALVET et al.

232

Eqn.(l6) corresponds AHE

to the following expressions

for the excess enthalphy and excess entropy differences

= A X(1-X)[l+B(l-2X)]

(17)

ASE(X) = +X(1-X)[l+B(l-2X)]

(18)

The equimolar excess enthalpy difference contained in Eqn.( 17) is AHE

= -15500 (l-E,,,) J.mol-*

(19)

The straight line defined by Eqn.( 19) is shown in Figure 3 along with the original AHE(X=$) values from the fourth column of Table 1.

-1 -

6

FIG. 3 Excess enthalpy difference versus coefficient of crystalline isomorphism. Open and shaded circles and numbering as in Fig.2. Line: function given by Eqn(l9).

The “normal”

behaviour

of the family of binary p-dihalobenzene

systems

is reflected

by AGE(T,X),

Eqn.( 16) and the values of its constants. Although we started by saying that the normal behaviour of the group should be established observe, a posteriori,

by examining

import of this observation

of unsuspicious

systems

(numbered

1, 3, 5, 6, 9) we may

is twofold: for one part it is related to the lower boundary of the liquid single-phase

field of the phase diagram, diagram.

a subgroup

that the other subgroup of systems, as a whole, displays the same type of behaviour. The i.e. to the liquidus,

and for another part to the subliquidus

region of the phase

BINARY P-DIHALOBENZENE

As for the liquidus,

the following

SYSTEMS - THERMOCHEMICAL

can be remarked.

AND PHASE-DIAGRAM

Because liquidus data were used to set up the empirical

relation between AGEand Ed, we may expect that, on the average, the liquidus curves can be recalculated the emperical

relation - for the two subgroups

233

DATA

with the same precision.

- from

This aspect is treated in the following

paragraph. The subliquidus matters will be considered at the end of this section.

Br

Br

The key quantity in the relation between thermodynamic mixing properties

and the phase diagram

energy difference.

is the excess Gibbs

It is directly related to the equal-G curve [ 141,

which is a curve in the phase diagram

between

solidus

liquidus and for that reason reflects the main characteristics

and of the

T/K ’ I

phase diagram. In those cases where there is complete subsolidus miscibility

the solidus

changes in es01

and liquidus

are rather insensitive

and GE”q, provided

remains unchanged.

Therefore,

to

that AGE = GEti4 - GEsot

the empirical

relation for AGE

given above should reproduce the experimental

phase diagram if

354

-

GEtis is put equal to zero and GEsot to -AGE. An example of a phase diagram

calculated

under these conditions

Figure 4. It is the phase diagram absolute difference liquidus reflects

between experimental

temperatures

experimental

of system

calculated

the limitation

of the empirical

two-parameter

data.

I

I

1

no.9. The mean

for the compositions

of the experimental

I

-x

0

liquidus points and the

points is AT = 0.6 K (Besides,

uncertainty

I

is shown in

this value not only

relation

FIG 4 &

of the

but also the

For comparison:

the

The p-dibromobenzene + p-bromoiodobenzene system. Phase diagram calculated by means of the empirical relation along with part of the experimental solidus and Iiquidus points.

LIQFIT result gave AT = 0.3 K).

For the complete

set of systems the mean temperature

liquidus temperatures

difference

between experimental

liquidus points and the

calculated, still with GEtiq = 0, is about 1 K.

. . . .. solid mrscr&&y

mlete

If it is supposed

that the liquid binary state is an ideal mixture -and accordingly

GEsc’ = -AGE- then the

region of demixing in the solid state can be calculated from Eqn.(l6) and the values of the constants. The constant value of B=0.2 corresponds

to the following

demixing, the critical point: X&.377.

constant

mole fraction

coordinate

Next, the critical temperature, in terms of Em, is given by

T _ 4020(1-E,) ‘-

(20)

1+8.04(1-a&

And using this equation, the critical temperatures temperature.

The critical

This observation

temperature

of the ten p-dihalobenzene

corresponding

implies that the description

demixing phenomena.

of the top of the region of

to the lowest

systems all are found below room ~~

value (rzm = 0.857) is 267 K.

used in this paper, indeed, is incapable of explaining

the observed

MT. CALVET et

234

al.

In a sense the last remark is too categoric and that because of the fact that the excess Gibbs energies of the liquid mixtures have been ignored. If the latter would be. positive, then the experimental AGE (=GBhq - GEsc’l)values would result in higher GEsol values and, as a consequence, in higher critical temperatures. Although we do not expect that the deviant behaviour of the systems no. 2,4,7,8

and 10 can be related to the excess properties of the

liquid state, we cannot deny the desirability of the experimental determination of these properties.

The thermodynamic description which is followed in this paper and which, apart from the Gibbs function of the liquid state, is based on one Gibbs function for the solid state leads to a coherent excess Gibbs energy difference function. The latter permits a close reproduction of the liquidus curves, but fails to explain the puzzling demixing phenomena that have been observed in part of the p-dihalobenzene systems.

1.

G. Bruni and F. Gomi, Gazz. Chim. Ital. (II) 3,

2.

F. Ktister, Z. Physik. Chem. s,

3.

N.N. Nagomow, Z. Physik. Chem. D, 578 (1911).

4.

H.R. Kruyt, Z. Phys. Chem. B, 657 (1912).

5.

A.N. Campbell and L.A. Prodan, J. Am. Chem. Sot. a, 553 (1948).

6.

127 (1900).

65 (1905).

H.A.J. Oonk, M.T. Calvet, M.A. Cuevas-Diarte, Y. Haget, J.C. van Miltenburg and E.H. Teunissen, Thermochim. Acta J&j, 297 (1989).

7.

J.S. van Duijneveldt, N.B. Chanh and H.A.J. Oonk, Calphad, u, 83 (1989).

8.

c9F;Iet,

9.

M.T. Calvet, Thesis, University of Barcelona, 1990.

J.R. Housty, A. Maiga, L. Bonpunt, N.B. Chanh, M. Cuevas, E. Estop, J.Chim.Phys.,u,

197

10. Y. Haget, N.B. Chanh, A. Meresse and M.A. Cuevas-Diarte, Phase equilibrium data Proceedings, 1, 170 (1985).

11. J.A. Bouwstra, N. Brouwer, A.C.G. van Genderen and H.A.J. Oonk, Thermochim. Acra, J&97

(1980).

12. J.A. Bouwstra and H.A.J. Got&, Calphad, 4, 11 (1982).

13. H.A.J. Gonk, J.A. Bouwstra and P.J. van Ekeren, Calphad, JQ, 137 (1986). 14. H.A.J. Oonk, Phase Theory: The Thermodynamics

Comp., Amsterdam (1981).

of Heterogeneous Equilibria, Elsevier Sci. Publ.