Thermodynamic description of the Hg–Te binary system

Journal of Alloys and Compounds 494 (2010) 102–108

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Thermodynamic description of the Hg–Te binary system Wojciech Gierlotka Department of Chemical Engineering & Material Science, Yuan Ze University, # 135 Yuan-Tung Road, Chungli, Taoyuan 320, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 16 November 2009 Accepted 4 January 2010 Available online 11 January 2010 Keywords: Calphad Ionic liquid Phase diagram

a b s t r a c t The (Hg,Cd)Te is a traditional material for infrared optoelectronic devices. It is possible to tune its energy gap practically to any infrared wavelength by varying CdTe mole fraction. The (Hg,Cd) Te is using as an epitaxial layers which have been grown on CdTe substrate from pseudobinary Hg-rich and Te-rich solutions by PLE. The knowledge of the phase diagram of Hg–Cd–Te system as well as of the Cd–Hg, Hg–Te and Cd–Te systems is essential for understanding and planning technological processes. In this work the binary system Hg–Te has been modeled using ionic liquid, associate liquid and subregular models. Results of calculations were compared and discussed. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The (Hg,Cd)Te is a traditional material for infrared optoelectronic devices. It is possible to tune its energy gap practically to any infrared wavelength by varying CdTe mole fraction [1]. The (Hg,Cd) Te is using as an epitaxial layers which have been grown on CdTe substrate from pseudobinary Hg-rich and Te-rich solutions by PLE [2,3]. The knowledge of the phase diagram of Hg–Cd–Te system as well as of the Cd–Hg, Hg–Te and Cd–Te systems is essential for understanding and planning technological processes. The binary system Hg–Te has been described before using associate liquid model [4], however, taking into account available literature information about properties of liquid Me–Te systems it seems to be reasonable to describe the liquid phase by ionic liquid model [5]. In this work, the binary Hg–Te system was reoptimized and three different models for describing of the liquid phase were used. 2. Literature information The literature information about binary Hg-Te system is very limited. There is no experimental thermodynamic data about liquid phase. The thermodynamic properties of the liquid can be derived from ternary equilibria between gas, liquid and solid phases based on vapor pressure measurement. The pressure of the vapor was examined by Brebrick and Strauss [6], Sha et al. [7] and Su et al. [8] who used optical absorption method. The information is in agreement one other. Moreover, the mass spectrometry has been used by Goldfinger et al. [9] for determining the three phase equilibria

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vapor pressure. Liquidus line has been described by several papers. Brebrick and Strauss [6], Strauss [10], Vanyukov et al. [11], Asadov [12], Harman [13], Delwes and Lewis [14], Delves [15] and Dziuba [16] used cooling curves to obtain liquidus temperature. Generally speaking, for tellurium concentration smaller than 0.5 mole fraction all data agree one other; however, for mole fraction of Te higher than 0.5 data obtained by Dziuba [16] and Vanyukov et al. [11] shows higher temperature than obtained by others. Besides that, Delves [15] reported small miscibility gap in liquid phase for concentration of tellurium between 0.52 and 0.55 mole fraction at temperature 937 K. The solubility of HgTe intermetallic compound in mercury was examined by Pajaczkowska and Dziuba [17] for mole fraction of Te between 0.001 and 0.5. Thermodynamic properties of HgTe intermetallic compound were examinated by different methods. The standard enthalpy of formation at 273.15 K was obtained by Ratajczak and Terpilowski [18] who used electromotive force experiment and reported by Mills [19]. The dissociation pressure method was used by Sha et al. [7], Su et al. [8], Nasar and Shamsuddin [20] and Brebrick et al. [21]. Enthalpy of formation of HgTe at 298 K was measured by solution calorimetry by Rugg et al. [22]. Enthalpy of melting of HgTe was reported by Garbato and Ledda [23], Asadov [24] and Kulakov [25] based on DTA measurement. Temperature of melting of the HgTe intermetallic compound has been described by Strauss [10], Vanyukov et al. [11], Asadov [24], Szofran and Lehoczky [26], Blair and Newnham [27] and Ray and Spencer [28] based on DTA experiment. High pressure reflux has been used by Steininger [29]. One can say that all those information agree one other and described the temperature of melting of HgTe intermetallic compound as 943 ± 3K. The Hg–Te binary system has been modeled previously by Yang et al. [30] who used associate solution model for description of liquid phase.

W. Gierlotka / Journal of Alloys and Compounds 494 (2010) 102–108 Table 1 Crystal structure in Cu–Sb binary system [39].

Q =

Phase

Pearson’s symbol

Space group

Hg Te HgTe

hR1 hP3 cF8

¯ R3m P31 21 ¯ F 438

(4)

ionic 0 Gm = YHg−2 GHg

1

The binary Hg–Te system includes 5 phases: Rhombohedral A10 (Hg), Hexagonal A8 (Te), HgTe, liquid and gas. Description of the crystal structures is given in Table 1. The system shows 2 invariant reactions: eutectic reaction between liquid, solid Hg and intermetallic compound HgTe at temperature 233 K and another eutectic between liquid, solid tellurium and intermetallic compound at 684 K. Temperature of congruent melting of HgTe intermetallic compound is 943 K. In this work different thermodynamic models for liquid phase were used and result obtained by these models were compared and discussed. The Gibbs free energies of pure elements with respect to temperature 0 Gi (T ) = Gi (T ) − HiSER are represented by Eq. (1): Gi (T )=a+bT +cT ln(T )+dT 2 +eT −1 +fT 3 +iT 4 +jT 7 +kT −9

yj vj

j

where vi is the valency of ion i. The summation over i is made for all anions, summation over j is made for all cations. According to this model, the Gibbs free energy of the liquid phase can be expressed as:

3. Thermodynamic models

0



103

0 + YTe0 GHg

0

+2 T e 0 1

0 + YVa−2 GHg

1

+2 V a −2 1

+RT (YTe−2 ln YTe−2 + YTe−0 ln YTe−0 + YVa−1 ln YVa−1 ) +YTe−2 YTe0 LHg+2 :Te−2 ,Te0 + YTe−2 YVa−2 LHg+2 :Te−2 ,Va−2 +YTe0 YVa−2 LHg+2 :Te0 ,Va−2 +YTe−2 YTe0 YVa−1 LHg+2 :Te−2 ,Te0 ,Va−2 (5) Hg1 +2 Te1 −2

where represents a hypothetical, electrically neutral liquid compound HgTe. A hypothetical compounds Hg0 +2 Te1 0 and Hg1 +2 Va1 −2 are identical to pure Te and Hg respectively. The interaction parameters Li:j are functions of temperature and are described by linear equations: Li:j = A + BT

(1)

The 0 Gi (T ) data are referred to the constant enthalpy value of the standard element reference HiSER at 298.15 K and 1 bar as recommended by Scientific Group Thermodata Europe (SGTE) [31]. The reference states are: Liquid (Hg), Hexagonal A8 (Te). The 0 Gi (T ) expression may be given for several temperature ranges, where the coefficients a, b, c, d, e, f, i, j, k have different values. The 0 Gi (T ) functions are taken from SGTE Unary (Pure elements) TDB v.4 [31]. The solid Hg and Te were treated as pure components because there is no information about solubility of Te in solid Hg or Hg in solid Te. In this case, the Gibbs energies of Hg in Rhombohedral A7 structure and Te in Hexagonal structure were taken directly from SGTE Unary database [31].

+2 Te −2 1

(6)

Last two parameters G0

Hg0 +2 Te1 0 between Te0

and G0

Hg1 +2 Va1 −2

in Eq. (5)

containing interactions and Va−2 which are equivalent to free atoms Hg and Te in the association solution model [4], do not make significant contribution to Gibbs free energy. This lack of significance results from the fact that both Te0 and Va−2 cannot simultaneously be present in large concentration because the liquid salt Hg1 +2 Te1 −2 is very stable. Thus, Eq. (5) can be rewritten as Gibbs free energy of mixing: ionic 0 Gm = YTe−2 GHg

1

+2 Te −2 1

+ RT (YTe−2 ln YTe−2 + YTe−0 ln YTe−0

+YVa−1 ln YVa−1 ) + Gxs

(7)

3.1. Intermetallic compound HgTe The HgTe phase was treated as the line compound because the homogeneity range of it is negligible. In this case, the Gibbs energy is described as follow:

3.4. Associate liquid model

where GHSERHG and GHSERTE are Gibbs energies of mercury and tellurium in liquid and Hexagonal A8 structure, respectively.

The two-sublattices associate liquid model has been proposed by Sommer [4]. Similar to ionic liquid model, also this one was adopted for Me–Te systems previously [30,34]. In case of Hg–Te system the model includes HgTe specie. The Gibbs energy for one mole of atoms is given by the following formula:

3.2. Liquid phase

Gm

0 = a + bT + GHSERHG + GHSERTE GHgTe

(2)

Liquid

i

(8)

Excess Gibbs energy of liquid is described by the expression:

The ionic liquid model [5] has been used for Me–Te systems previously [32,33]. In case of Hg–Te system the model becomes (Hg+2)P (Te−2,Te,Va−v )Q where P and Q are the number of sites on the cation and anion sublattice, respectively. The stoichiometric coefficients P and Q vary with the composition in order to maintain electroneutrality yi (−vi ) + yv Q

Liquid

+ xHgTe 0 GHgTe

+xs GLiquid ]/(1 + 2xHgTe )

3.3. Ionic liquid model



Liquid

+ xTe 0 GTe

+RT (xHg ln xHg + xTe ln xTe + xHgTe ln xHgTe )

In this work three different models were using for describing the liquid phase: ionic liquid model, associate model and subregular model.

P=

Liquid

= [xHg 0 GHg

(3)

xs

GLiquid = xHg xHgTe

n 

i Liquid

L

(xHg − xHgTe )i

i=0

+xHgTe xTe

n 

i Liquid

L

(xHgTe − xTe )i

i=0

+xHg xTe

n  i=0

i Liquid

L

(xHg − xTe )i

(9)

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W. Gierlotka / Journal of Alloys and Compounds 494 (2010) 102–108

Fig. 1. Calculated Hg–Te binary system with ionic liquid model adapted to liquid phase.

Fig. 2. Calculated Hg pressure along liquidus line superimposed with Brebrick and Strauss [6] data. Ionic liquid model adapted to liquid phase.

3.5. Subregular model

than 0.5 mole fraction, the experimental points obtained by Dziuba [16] and Vanyukov [11] lay higher than calculated line. Better fit to Strauss’ [10] and Harman’s [13] data is reasonable because their results agree with invariant reaction L = Te + HgTe reported by Massalski [39]. For tellurium concentration smaller than 0.5 mole fraction all experimental information agree one other and calculation reproduces experiments well. Calculated partial pressure of Hg along liquidus line superimposed with experimental information obtained by Brebrick and Strauss [6] is shown in Fig. 2. The calculated line shows very good agreement with literature data. In next, Fig. 3 is shown calculated partial pressure of mercury along liquidus line compared with data obtained by Brebrick and Strauss [6], Goldfinger and Jeunehomme [9] and Sha et al. [7]. Generally speaking, the calculation agrees with experiment. Calculated partial pressure of Te2 superimposed with experimental data obtained by Brebrick and Strauss [6] is shown in Fig. 4. One can find slight difference between computed and measured value for low Te2 pressure. The calculation shows very good agreement with Brebrick and Strauss [6] data for higher pressure of Te2 . Calculated invariant reactions compared to literature data [39] are gathered in Table 3. From this table one can see that calculations and experiment agree each other. Calculated and published in literature enthalpies of formation of HgTe at 273.15 K are gathered in Table 4. This table shows that

The subregular model is widely used and commonly known. The Gibbs energy of the liquid phase is described as below: Liquid

Gm

Liquid

= xHg 0 GHg

+xHg xTe

Liquid

+ xTe 0 GTe

 n 

i Liquid

L

+ RT (xHg ln xHg + xTe ln xTe )



(xHg − xTe )i

(10)

i=0

Where the first term of Eq. (10) describes Gibbs energies of pure, liquid mercury and tellurium, the second term describes ideal mixing and the last one describes excess Gibbs energy. 3.6. Gas phase The gas phase was treated as a mixture of ideal gases. Gibbs energies of gaseous species have been taken from SGTE database [35]. 4. Optimization procedure The thermodynamic parameters for all phases in the system were optimized using ThermoCalc v. R software [36]. Results were checked additionally using Pandat v. 7 software [37]. For this optimization, thermodynamic data for the liquid (equilibrium vapor pressure) and HgTe phases, invariant reactions and liquidus data were used. Each piece of the selected information was given a certain weight based on personal judgment. The optimization was carried out step by step in agreement with the guideline given by Schmid-Fetzer et al. [38]. First, the optimization of the liquid phase using ionic liquid model was performed, and then the HgTe phase was assessed. All parameters were finally evaluated together to provide the best description of the system. After that the optimization of associate liquid and subregular liquid were conducted. During these optimizations the parameters of HgTe obtained in previous assessment were kept. The calculated interaction parameters are shown in Table 2. 5. Result and discussion Calculated phase diagram of the Hg–Te binary system is shown in Fig. 1. For this calculation ionic model was used. As can be seen from this figure, the liquidus line shows good agreement with experimental data. Only for tellurium concentration higher

Fig. 3. Calculated Hg pressure along liquidus line compared with experimental data. Ionic liquid model adapted to liquid phase.

W. Gierlotka / Journal of Alloys and Compounds 494 (2010) 102–108

105

Table 2 Gibbs free energies of pure components and parameters for Gibbs free energies of phases. Phase Rhombohedral A10

Temperature limit

Function

100.00 < T < 234.32

0

234.32 < T < 2000.00

Rhombohedral GHg

A10

= −10668.401 + 123.274598 × T − 28.847 × T × LN(T ) + .01699705 × T 2 −

2.4555667E − 05 × T 3 + 13330 × T −1 0 Rhombohedral A10 GHg = −11425.394 + 135.928158 × T − 30.2091 × T × LN(T ) − .00107555 × T 2 − 2.28298E − 07 × T 3 + 35545 × T −1

298.15 < T < 722.66

0 Hexagonal A8 GTe = −10544.679 + 183.372894 × T − 35.6687 × T × LN(T ) + .01583435 × T 2 − 5.240417E − 06 × T 3 + 155015 × T −1

722.66 < T < 1150.00

0 Hexagonal A8 GTe = +9160.595 − 129.265373 × T + 13.004 × T × LN(T ) − .0362361 × T 2 + 5.006367E − 06 × T 3 − 1286810 × T −1

1150.00 < T < 1600.00

0

Hexagonal GTe

HgTe

298.15 < T < 2000

0

HgTe GHg:Te

Ionic liquid

298.15 < T < 2000

0

Gionic 2+

298.15 < T < 2000

0

Gionic 2+

298.15 < T < 2000

0

ionic GTe = GLIQTE

298.15 < T < 2000

0 ionic L 2+ 2− Hg :Te ,Va

298.15 < T < 2000

1 ionic L 2+ 2− Hg :Te ,Va

= 7.65831183E + 04 − 7.77464035E + 01 × T

298.15 < T < 2000

0 ionic L 2+ 2− Hg :Te ,Te

= 1.26970275E + 04 + 2.15363026E + 00

Hexagonal A8

Associated liquid

Subregular

Functions

Hg Hg

A8

= −12781.349 + 174.901226 × T − 32.5596 × T × LN(T )

= −4.36475541E + 04 + 1.87483819E + 01 × T + GHSERTE + GHSERHG

:Te2−

= −9.91828353E + 04 + 6.64090416E + 01 + 2 × GHSERHG + 2 × GLIQTE

= GHSERHG

:Va

= 1.16317909E + 05 − 1.01856317E + 02 × T

298.15 < T < 2000

0

assoc GHgTe

liq

= −4.88957403E + 04 + 3.19311150E + 01 × T + GHSERHG + GLIQTE

298.15 < T < 2000

0

assoc GHg

liq

= GHSERHG

298.15 < T < 2000

0

assoc GTe

liq

298.15 < T < 2000

0 assoc liq LHg,HgTe

298.15 < T < 2000

1 assoc liq LHg,HgTe

= −3.11475750E + 04 + 2.95496291E + 01 × T

298.15 < T < 2000

0 assoc liq LHgTe,Te

= 2.77380688E + 03 + 6.75819448E + 00 × T

298.15 < T < 2000

0

298.15 < T < 2000

0

= GLIQTE = 5.73699121E + 04 − 4.95390551E + 01 × T

liq

GHg = GHSERHG

298.15 < T < 2000

liq GTe = GLIQTE 0 liq LHg,Te = −2.68277282E

298.15 < T < 2000

1 liq LHg,Te

200.00 < T < 234.32

GHSERHG = +82356.855 − 3348.19466 × T + 618.193308 × T × LN(T ) − 2.0282337 × T 2 + .00118398213 × T 3 − 2366612 × T −1

234.32 < T < 400.00

GHSERHG = −8961.207 + 135.232291 × T − 32.257 × T × LN(T ) + .0097977 × T 2 − 3.20695E − 06 × T 3 + 6670 × T −1

400.00 < T < 700.00

GHSERHG = −7970.627 + 112.33345 × T − 28.414 × T × LN(T ) + .00318535 × T 2 − 1.077802E − 06 × T 3 − 41095 × T −1

700.00 < T < 2000.00

GHSERHG = −7161.338 + 90.797305 × T − 24.87 × T × LN(T ) − .00166775 × T 2 + 8.737E − 09 × T 3 − 27495 × T −1

298.15 < T < 626.49

GLIQTE = −17554.731 + 685.877639 × T − 126.318 × T × LN(T ) + .2219435 × T 2 − 9.42075E − 05 × T 3 + 827930 × T −1

626.49 < T < 722.66

GLIQTE = −3165763.48 + 46756.357 × T − 7196.41 × T × LN(T ) + 7.09775 × T 2 − .00130692833 × T 3 + 2.58051E + 08 × T −1

722.66 < T < 1150.00

GLIQTE = +180326.959 − 1500.57909 × T + 202.743 × T × LN(T ) − .142016 × T 2 + 1.6129733E − 05 × T 3 − 24238450 × T −1

1150.00 < T < 1600.00

GLIQTE = +6328.687 + 148.708299 × T − 32.5596 × T × LN(T )

298.15 < T < 2000

Hexagonal GHSERTE = 0 GTe

assessed in this work standard enthalpy of formation of HgTe intermetallic compound agrees with experimental data. Fig. 5 shows calculated Hg–Te phase diagram with adopted associate solution model for liquid phase. Gibbs energy of HgTe intermetallic phase was taken from previous calculation, where ionic liquid model was used. In case of associate solution model one

Table 3 Temperatures of invariant reactions in Hg–Te binary system. Reaction

Experiment

Hg + HgTe = L L = HgTe HgTe + Te = L

T = 233 T = 943 T = 684

+ 04 + 8.17174658E + 00 × T

= −1.45191605E + 03 + 6.80494176E + 00 × T

Calculation Ionic liquid

Associated liquid

Subregular

T = 234 T = 944 T = 683

T = 234 T = 944 T = 683

T = 233 T = 942 T = 675

AB

can say that liquidus line is reproduced as well as in case of ionic liquid. Similar to previous calculation, for concentration of tellurium higher than 0.5 mole fraction liquidus line does not agree with Dziuba [16] and Vanyukov [11] data but Strauss [10] and Harman Table 4 Calculated and measured standard enthalpy of formation of HgTe. 0 H298 [kJ/mol]

Reference

−33.9 −31.8 −41.2 −43.802 −36.5 −43.69 −44.02 −43.648

[18] [19] [7] [8] [20] [21] [30] This work

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W. Gierlotka / Journal of Alloys and Compounds 494 (2010) 102–108

Fig. 7. Calculated Hg pressure along liquidus line compared with experimental data. Ionic liquid model adapted to liquid phase. Fig. 4. Calculated Te2 pressure along liquidus line superimposed with Brebrick and Strauss [6] data. Ionic liquid model adapted to liquid phase.

Fig. 5. Calculated Hg–Te system superimposed with experimental information. Associate solution model adapted to liquid phase.

Fig. 6. Calculated Hg pressure along liquidus line superimposed with Brebrick and Strauss [6] data. Associate liquid model adapted to liquid phase.

[13]. Next Fig. 6 shows blown up part of calculated partial pressure of Hg superimposed with Brebrick and Strauss [6] data for associate solution model. Fig. 7 shows calculated 3-phase equilibrium partial pressure of Hg compared to Goldfinger and Jeunehomme [9], Sha et al. [7] and Brebrick and Strauss [6] data. The calculation shows good agreement with experimental data. Fig. 8 exhibits calculated partial pressure of Te2 along liquidus line. The calculation reproduced well experimental data, only for low pressure of Te2 specie the calculation shows slightly smaller values than experiment. The last model which was used for description of the liquid phase was subregular solution model. Fig. 9 shows calculated phase diagram superimposed with experimental data. In this figure one can see that liquidus line for tellurium concentration higher than 0.5 mole fraction fits data obtained by Dziuba [16] and Vanyukov [11]. Better fit of Strauss’ [10] and Harman’s [13] data was impossible even higher order parameters were used. If higher order interaction parameters were added to calculations then liquidus line shows unwanted shape. Worse fitting was also obtained for liquidus line for tellurium concentration between 0 and 0.5 mole fraction. The calculated partial pressures of Hg and Te2 are shown in Figs. 10 and 11 respectively. Additionally, Fig. 12 shows blown up part of Fig. 10 superimposed with Brebrick and Strauss [6] data. Comparison between calculated and measured invariant reactions

Fig. 8. Calculated partial pressure of Te2 . The associate solution model adapted to liquid phase.

W. Gierlotka / Journal of Alloys and Compounds 494 (2010) 102–108

Fig. 9. Calculated Hg–Te binary system. Subregular model adapted to liquid phase.

107

Fig. 12. Calculated Hg pressure along liquidus line superimposed with Brebrick and Strauss [6] data. Subregular solution model adapted to liquid phase.

Taking into account results of modeling of liquid phase by different models it is easy to find that computed information obtained by ionic liquid model and associate solution model are very similar. Liquid modeled by subregular solution cannot reproduce proper liquidus line well and gives bigger differences between measured and calculated temperatures of invariant reactions. The result obtained from subregular model should not be surprise because in liquid phase one can find strong interaction between tellurium and mercury and subregular model is not able to reproduce it. Calculations made by either ionic liquid or associate liquid models show good agreement between computed and measured information; however, because of ionic behavior of tellurium in liquid phases [32,33] the ionic liquid model seems to be more suitable for description of Hg–Te binary system. 6. Summary Fig. 10. Calculated Hg pressure along liquidus line compared with experimental data. Ionic liquid model adapted to liquid phase.

is shown in Table 3. Calculated invariant reactions and temperature of melting of HgTe intermetallic compound are reproduced a little bit worse than those obtained from ionic and associate solution models.

The binary Hg–Te system was assessed and three different models were used for description of liquid phase: ionic liquid model, associate solution model and subregular solution model. Subregular solution model gives much bigger differences between measured and calculated temperatures of invariant reactions and liquids line. Inaccurate description of the system by subregular solution can be explained in view of strong interactions between Hg and Te in liquid phase. Associate solution and ionic liquid model described the system well and both can be used for modeling highordered systems; however, ionic liquid model better describes physical properties of liquid solutions of Te. References

Fig. 11. Calculated partial pressure of Te2 . The subregular solution model adapted to liquid phase.

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