CALJHAD Vol. 16. No. 2. ~9. 151-l 59, 1992 Printed in the USA.

0364493 6/92 $!KOO + .OO (c) 1992 Pergamon Press Ltd.

THERMODYNAMIC ANALYSIS OF THE Co-Si SYSTEM

Soon-Don Choi Depa~ent of ~etallurg~~l Engineering, Yeungnam Univ.,

Daedong, Kyongsan, Kyongbuk. KOREA

ABSTRACT: An evaluation of the thermodynamic and phase diagram data for the Co-Si system has been made to provide a set of self-consistent thermodynamic description for all the phases. ~edlich-Kister polynomials were used to describe the Gibbs energies of solution phases in the system. For the hcp and fee Co solid solutions, the magnetic contribution to the Gibbs energy was taken into account. Various types of thermodynamic data, including heat capacities for the intermediate phases and enthalpies and free energies of mixing for the liquid phase were analyzed simultaneously with the phase diagram data. The optimized parameter set gives a satisfactory description of the experimental data.

I. lntrg&&tg_g

Metallic silicides are of practical interest owing to their widespread uses as gate electrodes and interconnects. Recently, the silicides of cobalt show a promise for the future devices such as metal base transistors and permeable base transistors. For improving the properties of the materials, one needs self-consistent thermodynamic and phase diagram data. The simultaneous analysis of various kinds of experimental data provides the opportunity to detect the inconsistencies in the availabte information.

Thermodynamic data for 46 transition metal-silicon systems were reviewed in detail and assessed by Chart(l) in 1973. Later, Kaufman(2), without considering the existence of CogSi and magnetic ordering effect, presented an evaluation for the Co-Si

system. The evaluation of Kaufman was mainly based on the assessed thermodynamic data of Chart and phase diagram of Hansen and Anderko(3).

In the present work, a critical evaluation of all the available data has been made using the computer programs developed by Lukas. Henig and Zimmermann(4) and by us at the University of Wisconsin, Madison, Wt.

2.1 Phase diagram information The first systematic investigation of the Co-Si phase diagram was undertaken by

Lewkonja(5), using thermal and microscopic methods. In addition to the intermediate phases Co2Si, CoSi and CoSi2 reported earlier(6-8)‘ two more compounds CogSi, and

Reedwwl on 8 Novunba 1991

151

152 S.-D. CHOI

CoSi3 were found. In connection with a study of the Fe-Co-Si system, Vogel and

Rosenthal(S) re-determined the Co-Si phase diagram by means of thermal analysis and microscopic examination. The compound Co3Si2 was not found. Instead, Co2Si in the

form of two modifications and a silicide CogSi were introduced. Later, the existence of

CogSi was denied by Koster and Schmid(l0) but more recently confirmed by Boomgaard

and Carpay(l1) and Johnson, Rayson and Wright(12). The Co-Si phase diagram, as selected by Hansen and Anderko(B), was based on the work of Haschimoto(l3). CoSi3 was

not found in this investigation. The existence of CoSi, is doubtful, considering the

structures of the similar sub-iron group(Fe-Si and Ni-Si systems). It was found that there is negligibly small solid solubility of Co in Si(14).

Except for the CoCo2Si section, the Co-Si phase diagram is well established.

The data reported in the literature for the hcp->fcc transformation ( s-Co->a-Co) in cobalt-rich solid solutions differ considerably. According to Kijster and Schmid(lO), the

transformation is raised to 1 160°C, corresponding to a peritectoid reaction, a -

Co+Co2Si-e-Co. Even higher temperature was presented by Kijster, Warlimont and

Godecke(l5), giving rise to a peritectic reaction, a-Co+L-E-Co, at 1245°C. On the other hand, Haschimoto(l3) showed that the temperature of the transformation is increased

only up to about 755’C. Enoki, lshida and Nishizawa(l6) further studied the transformation. Their results are in good agreement with the data by Kijster, Warlimont and Godecke( 15).

Recently, lshida and Nishizawa(l7) presented a complete Co-Si phase diagram in “Binary Alloy Phase Diagrams(2nd ed.)“. Their selection was based on the data by Haschimoto(l3) for the Co2Si-Si section and the data by Enoki, lshida and Nishizawa(16)

and Kdster, Warlimont and Godecke(l5) for the CoCo2Si section, The Curie point values

selected are from the work by Haschimoto(l3). There are five intermediate phases and

three solution phases in the Co-Si system, namely CogSi, a-Co2Si, p-Co2Si, CoSi, CoSip,

E-CO, a-Co, and liquid.

2.2 Thermodynamic information Enthalpies of mixing of the liquid alloys were determined experimentally at

1 600°C by Oelsen and Middel(lB), who poured the liquid metals into a calorimeter near room temperature, measuring the heat evolved. As indicated by Hultgren et al.(19), the final state might not be in an equilibrium. Activities of silicon in the liquid alloys were determined using emf measurements by Schwerdtfeger and Engell(20) at 1400°, 1525”, 1580” and 1610°C for the whole composition range, and using equilibration

measurements by Bowles, Ramstad and Richardson(21) at 156OOC only for two compositions, 22.0 and 25.0 at.% Si. Both data are in accord with the activity data derived from the isothermal section of the Ag-Co-Si system by Martin-Garin, Ansara and Desre(22).

For the intermediate phases Co2Si, CoSi and CoSi2, heats of formation were

obtained by Oelsen and Middel(l8), using the above direct reaction calorimeter. The difference in the heat evolved by the liquid alloy and by pouring together the unmixed liquid metals is the heat of formation. The enthalpies and heat capacities were determined by Frolov et al.(23) for CopSi. by Kalishevich, Gel’d and Krentis(24) for CoSi,

and by Kalishevich, Gel’d and Putintsev(25) and Kalishevich, Gel’d and Krentis(26) for

THERMOOYNNAC ANALYSIS OF THE Co-Si SYSTEM 153

CoSi2. All these data were measured in a nonhermetic and vacuum-coated calorimeter.

This information also gives the heats of fusion for the compounds.

In enthalpies fusion for 1873K for

1973 Chart(l) reviewed and assessed all the earlier thermodynamic data. The and entropies of formation at 298K, heat capacity various cobalt silicides as well as the enthalpies the liquid alloys were listed in his assessment.

3. Thermodvw Mo&&

For a nonmagnetic pure element, the Gibbs free energy can be expressed as

equations and enthalpies of and entropies of mixing at

G=A+BT+CT(l-lnT+T2- ;E?- ;F? (1)

In this equation, the last four coefficients correspond exactly to those of the heat

capacity.

% I C + DT + ET-* + FT* (2)

The Gibbs free energy of a ferromagnetic material is described as the sum of two contributions, a magnetic and a nonmagnetic one. These contributions, when combined, for a solution phase give the following expression.

G - X,OG, + X,OG, + RT(X,In X,+X21n X2) + AGXs + AGmq (3)

where X, is the atomic fraction of a pure component i, OG, the molar Gibbs energy of the

pure component i in a hypothetical nonmagnetic state, AGXS the excess Gibbs energy,

AGmag the magnetic contribution to the Gibbs energy. The excess Gibbs energy is

represented by a Redlich-Kister polynomial equation of the form

AGXS ‘XrX2C (Ai-Bi)(XI-Xi)i i-0

Analytical expressions for the magnetic Gibbs energy were proposed separately by Chuang, Schimid and Chang(27), and by lnden(28). In the Lukas program, the following expression is included.

AGmae - RT In( p + 1) f(t), t- Tn, (9)

where T, is Curie temperature for the magnetic ordering, p a quantity related to the total

magnetic entropy, and f(t) a series expansion(29) of a nonlinear expression suggested by lnden(28). The parameters f3 and T, as a function of composition are described as

(6)

p=x,p;+xgf+x,x2~ Pf2fX,-x9’ i=O

(7)

154 S.-O. CHOI

The lattice stabilities of pure Co and Si according to Guillermet(30) and Chakrabarti and Lukas(31). respectively, are used in the present analysis. Some assessed data with an additional term of T7 in the SGTE(Scientific Group Thermodata Europe) data file were smoothly fitted to eq.(l) for the present purpose. Data for the metastable forms, Si(fcc) and Si(hcp), are taken from the data of Saunders, Miodownik and Dinsdale(32).

The intermediate phases Co,Si and CoSi, exhibiting a narrow homogenei~ range,

are treated as stoichiometric phases. The two modifications of Co,Si are considered as

one phase. Heat capacity equations of CoSi and CoSi, are adopted from the assessment of

Chart(l). From a least square fit of the heat contents of Frolov et al.(23), the heat capacity expression for Co,Si is obtained. Lacking any thermodynamic data of Co,Si,

Neumann-Kopp rule is assumed to obtain the heat capacity equation. In this case, the pure Co(hcp) in the hypothetical nonmagnetic state and the pure Si(diamond) are chosen as the reference states of the system. The applications of Neumann-Kopp rule of the heat capacity data of CoSi and CoSi, with the same reference states, give reasonable fits,

supporting the validity of the assumption made.

The input parameter values are tabulated in Table 1. In the input file, eight phases are included: liquid, Si(diamond), e-Co, a-Co, Co,Si, Co,Si and CoSi, The derived

variation of 3 with composition is obtained from the experimentaJ data of magnetic moments by Parson, Sucksmith and Thompson(33).

TABLE 1.

Input data for optimization.

S.tabi A B C D

~o(liquid) 13805.5 -118.93900 28.818799 &-Co(nonmag) 309.6 -108.27991 25.086180 a-Co(nonmag) 737.2 -107.66466 25.086100 Si(liquid) 43647.3 -68.84350 19.971920 Si(dia.) -8162.6 -114.39550 22.831751 Si( hcp) 41037.4 -93.59550 22.831751 Si(fcc) 42837.4 -92.59550 22.831751

c D CoSi, 23.62000 0.0062200 CoSi 24.58000 0.0060500 CosSi 21 S7710 0.0120060 Co,Si 24.52251 0.0049386

tic Transformation

T, = 1396.00X, - 1 842.72Xs,

P- 1.35Xr., - 2.80Xs,

E F -0.0012981 -394608. 4.4089E-06 0.0053095 -145054. l.O409E-06 0.0053095 -145054. l.O409E-06 0.0098630 -214393. -3.2817E-06 0.0038260 -353334. 2.1312E-08 0.0038260 -353334. 2.1312E-08 0.0038260 -353334. 2.1312E-08

E F -331000. O.OOOOE-00 -377000. O.OOOOE-00 -244300. O.OOOOE-00 -197124. 7.8599E-07

THERMODYNAMIC ANALYSIS OF THE Co-Si SYSTEM 155

In the optimization, all the available thermodynamic data for the liquid and intermediate phases are included. The phase diagram data are taken from the assessment of lshida and Nishizawa reported in ‘Binary Alloy Phase Diagram(2nd ed.)‘. A primary attempt was made by using the assessed data of Chart, together with the Co-Si phase diagram in ‘Binary Alloy Phase Diagrams”. The calculated eutectic temperatures were in significant disagreement with the experimental ones. It was concluded that the severe discrepancies are mainly due to the enthalpy data of Oelsen and Middel(18). Their measurements for many binary systems(for example, Ai-Ni, AI-CU AI-Fe, Sb-Zn, etc.) have been frequently found to be in error by Hulgren et al.(19). Good results are obtained by using the uncertainty limit of 10% as indicated by Chart.

Description of the liquid phase by the Redlich-Kister polynomial was found to require a large number of parameters. The final number of the Redlich-Kister parameters needed is eight. The optimization has been performed with 24 unknown parameters. The potential-composition diagram at a given temperature is constructed to verify the stability of all the phases. The optimized parameter values are listed in Table 2.

TABLE 2.

The optimized parameter values.

A B C D E F

Co(liquid) i-0 -200104.0 -47.13668 i-1 -40783.1 -3.33709 i-2 108723.5 50.43157 i-3 143143.5 73.63639

E-CO i-0 -147438.0 -1.78253 i-1 -45650.9 -35.84748

a-Co i-0 -148550.0 -3.41324 i-1 -46243.5 -37.58562

CoSi, -34409.3 -3.70000 0.036800 0.0018995 -47093. -3.6117E-07

CoSi -50124.2 -10.59740 0.621075 0.0014823 -127806. -5.3111 E-07

Co,Si -41040.1 9.36000 -2.757550 0.0071910 -29819. -7.0102E-07

Co,Si -19613.0 6.62800 0.000000 0.0000000 0. O.OOOOE-00

l reference state: solutbn phase I pure elements with the same structure as the solution phase intermediate phase - Co(hcp.nonmagnetb) and Si(diamond)

The phase diagram calculated from the optimized parameters is presented in Fig. 1, together with the selected experimental data points. The enlarged Co-rich region is also shown in Fig. 2. In Table 3, the calculated temperatures of the invariant equilibria are compared with those selected in ‘Binary Alloy Phase Diagrams(2nd ed.)“. The

equilibrium phase boundaries are well reproduced within 1.5 at.% and 5.8OC.

156 S.-D. CHOI

0 ”

GO. 10. 20. 30.

.- VI

G

1 I

0 Haschimato(l937) A Koster(1973) l Enoki(1990)

- calculated

c .-

tn

8

1 , I-

40. 50. 60. 1 I I I 1 I

70. 80. 90. 100.

co Atomic Percent Silicon Si

FIG. 1 The Calculated Phase Diagram.

I I

18.

FIG. 2 Enlarged Co-rich

region.

u”Atomic Percent Si I icon4

THERMODYNAMIC ANALYSIS OF THE Co-Si SYSTEM 157

TABLE 3.

Calculated and measured temperatures of the invariant equilibria.

reaction measured calculated

TN) xsi TV) x,

L=CoSi,+Si 1259.0

L-CoSi+CoSi, 1310.0

L=Co,Si+CoSi 1286.0

L+Co,Si-Co,Si 1214.0

L-e-Co+Co,Si 1204.0

Co.+e-Co+Co,Si 1193.0

a-Co+L-E-Co 1250.0 L=CoSi, 1326.0

L-CoSi ’ 1480.0 L=Co,Si 1334.0

0.775-0.667-l .OOO 1257.7 0.789-0.667-l .OOO

0.618-0.500-0.667 1315.8 0.631-0.500-0.667

0.397-0.333-0.500 1291.8 0.382-0.333-0.500

0.244-0.333-0.250 1210.0 0.248-0.333-0.250

0.231-0.184-0.250 1208.2 0.242-0.188-0.250

0.250-0.181-0.333 1189.9 0.250-0.188-0.333

0.165-0.214-0.175 1247.4 0.162-0.220-0.168 0.667 1324.0 0.667

0.500 1455.1 0.500 0.333 1330.7 0.333

In Fig. 3, the calculated enthalpies and partial molar free energies of Si for the liquid alloys are compared to the corresponding experimental values. Considering the scatter of the data, the experimental points are well represented by the calculated curves, although the experimental enthalpy data are somewhat less endothermic and then exothermic with concentration than the calculated values. However, even the calculated enthalpy values around the equiatomic composition, as the worst fits, fall within the scatter band(lO%) of the experimental values.

Curves : calculated 0 Oelsen. Middel A Schwerdtfeger

and Engell(1610°C)

FIG. 3 Calculated and measured thermodynamic data in

liquid Co-Si alloys.

70. 20. 40. 60. 80. 100.

Atomic Percent Silicon

158 S.-D. CHOI

In Table 4, the calculated and measured data such as the enthalpies and entropies of formation and the enthalpies of fusion are presented for various intermediate phases. For an easy comparison, the reference state of Co is not the hypothetical nonmagnetic but the pure hcp cobalt. The magnetic enthalpy and entropy expressions are obtained by the applications of Gibbs-Helmholtz relationship to eq.(l). The evaluated data are in satisfactory agreement with the experimental values.

TABLE 4. Calculated enthalpies and entropies of formation and enthalpies of fusion for the intermediate phases compared to experimental information.

measured calculated AH,(298K) AS,(298K) AHJT,,) AH,(298K) AS,(298K) AH,(T,,)

Co,Si -32900.0 -1.2 33400.0 -31320.0 -0.32 31180.0

CoSi -47500.0 -3.1 34600.0 -45190.0 -2.40 30550.0 CoSi, -37700.0 - 21300.0 -35770.0 0.63 20610.0

- ‘The subscripts f and m refer to formation and melting, respectively.

The study was carried out at the Department of Materials Science and Engineering at the University of Wisconsin during 1991 when the author was on leave from the Department of Metallurgical Engineering, KOREA. He wishes to thank the Ministry of Education of Korea for financial support and Professor Y. A. Chang for his interest in this work and his encouragement.

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THERMODYNAMIC ANALYSIS Of THE Co-Si SYSTEM

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