Experimental investigation and thermodynamic

Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 470–481 www.elsevier.com/locate/calphad

Experimental investigation and thermodynamic description of the Co–Si system Lijun Zhang, Yong Du ∗ , Honghui Xu, Zhu Pan State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, PR China Received 25 February 2006; received in revised form 24 May 2006; accepted 1 June 2006 Available online 30 June 2006

Abstract The Co–Si system is investigated via experiment and modeling. Based on the critical evaluation of the phase diagram data available in the literature, one key Co/Si diffusion couple and eight decisive alloys are prepared. The diffusion couple, which is annealed at 1323.15 K for 8 days, is first examined by scanning electron microscopy (SEM) with energy dispersive X-ray analysis (EDX), and then by electron probe microanalysis (EPMA) to determine homogeneity ranges of the phases. The alloys, which are annealed at 1373.15 K for 3 days and then water-quenched, are analyzed using X-ray diffraction (XRD), optical microscopy, differential thermal analysis (DTA), and EPMA. The thermodynamic optimization for the Co–Si system is then conducted by using the assessed literature data and the present experimental data. For (αCo) and (εCo), the magnetic contribution to the Gibbs energy is taken into account. The sublattice model is employed to describe βCo2 Si (the high-temperature form of the Co2 Si phase), αCo2 Si (the low-temperature form of the Co2 Si phase) and CoSi. A set of self-consistent thermodynamic parameters is finally obtained. Comprehensive comparisons show that the calculated phase diagram and thermodynamic properties agree well with the experimental ones. Significant improvements have been made, compared with the previous assessments. c 2006 Elsevier Ltd. All rights reserved.

Keywords: Co–Si phase diagram; Diffusion couple; Thermodynamic calculations; X-ray diffraction; Differential thermal analysis

1. Introduction The silicides of the transition metals with 3d electrons possess attractive properties, such as high thermal stability and excellent oxidation resistance, which make them potential candidates for high temperature structural application, high temperature furnace construction and for protective coatings [1,2]. Cobalt silicides (particularly CoSi2 ) show a great promise for applications as contacts and interconnects in very largescale integrated (VLSI) technology because of their very low resistivity and excellent lattice match with Si that allow for the epitaxial growth on silicon substrate [3]. The epitaxially grown cobalt silicides on Si have been used to fabricate a fast metalbased transistor. Chart [4] reviewed the thermodynamic data for 46 transition metal–silicon systems. Without considering the existence of ∗ Corresponding author. Tel.: +86 731 8836213; fax: +86 731 8710855.

E-mail address: [email protected] (Y. Du). URL: http://www.imdpm.net (Y. Du). c 2006 Elsevier Ltd. All rights reserved. 0364-5916/$ - see front matter doi:10.1016/j.calphad.2006.06.001

αCo3 Si and the magnetic contribution to the Gibbs energy, Kaufman [5] presented the computed Co–Si phase diagram. His assessment was mainly based on the thermodynamic data recommended by Chart [4] and the phase diagram of Hansen and Anderko [6]. Ishida et al. [7] performed an evaluation of the experimental phase diagram and thermodynamic data in the Co–Si system. Five intermediate phases (αCo3 Si, βCo2 Si, αCo2 Si, CoSi and CoSi2 ) and four solution phases ((αCo), (εCo), liquid and (Si)) were included in the assessment due to Ishida et al. [7]. The Co–Si system has been modeled carefully by Choi [8]. In the modeling of Choi [8], two modifications of the Co2 Si, viz. βCo2 Si and αCo2 Si, were regarded to be the same phase, and the intermediate phases with homogeneity ranges were treated as stoichiometric ones. Based on these simplifications, the modeling resulted in a relatively good description of the phase diagram and thermodynamic data under Lukas program [9] but led to one serious problem that the low-temperature stable phases, (αCo) and (εCo), appear again in the high-temperature region. This problem was detected by

L. Zhang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 470–481

Fig. 1. Calculated Co–Si phase diagram by Schmid-Fetzer [10] using PANDAT program [11], based on the parameters of Choi [8]. The unusual feature is that (αCo) and (εCo) appear again in the high temperature region.

Schmid-Fetzer [10] using PANDAT program [11], as shown in Fig. 1. Therefore, a thorough assessment of the Co–Si system is necessary in order to provide a reliable set of thermodynamic parameters for thermodynamic extrapolations to related ternary and higher order systems. The purpose of the present work is to obtain a self-consistent set of thermodynamic parameters for the Co–Si system by means of thermodynamic modeling coupled with key experiments. 2. Evaluation of literature information The experimental phase diagram and thermodynamic data available in the literature were reviewed by Ishida et al. [7]. The present assessment takes into account both the experimental data assessed by Ishida et al. [7] and those published later. All of the data are summarized in Table 1 and concisely categorized in the following. 2.1. Phase diagram information Using thermal analysis (TA) and microscopic methods, Lewkonja [12] systematically investigated the Co–Si phase diagram on the basis of earlier works [13–15], and reported the existence of five intermediate phases, viz. Co2 Si, CoSi, CoSi2 , Co3 Si2 and CoSi3 . Vogel and Rosenthal [16] re-determined the Co–Si phase diagram by means of TA and microscopic examination, and claimed the occurrence of a new silicide αCo3 Si. According to their work [16], Co2 Si exists in the two bimorphic phases, i.e. βCo2 Si (high-temperature form) and αCo2 Si (low-temperature form). The existence of αCo3 Si was denied by Köster and Schmid [17] but confirmed by both Boomgaard and Carpay [18], and Köster et al. [19]. In accordance with the metallographic and DTA observations by Boomgaard and Carpay [18], αCo3 Si is stable between 1443.15 and 1483.15 K, while Köster et al. [19] claimed that its stability range is from 1466.15 to 1487.15 K based on DTA measurements. The compounds Co3 Si2 and CoSi3 found by the earlier researcher [12] were not observed by subsequent investigators [16–19]. In addition, in view of the experimental work of Haschimoto [20] and the similarity

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among the Fe–Si, Co–Si and Ni–Si systems, the existence of CoSi3 was doubtful. In the Fe–Si and Ni–Si system, there is no corresponding compound which is compatible with CoSi3 reported by Lewkonja [12]. By means of the TA technique, Vogel and Rosenthal [16] constructed the Co–Si phase diagram from 15 to 50 at.% Si, Haschimoto [20] from the Co to the Si side, and Köster et al. [19] from 17 to 26 at.% Si. Liquidus data of Köster et al. [19] and Haschimoto [20] are used in the present optimization since these data are consistent with each other. Using electron probe microanalysis (EPMA), Enoki et al. [21] measured the (αCo)/(εCo) phase equilibria, and the results were in good agreement with those by Köster et al. [19]. Consequently, both data [19,21] are utilized in the present modeling. According to Köster et al. [19], (εCo) is stable up to the peritectic temperature of 1523.15 K and the maximum Si solubility in (εCo) is 18.4 at.% Si at the eutectic temperature (L ↔ Co2 Si+ (εCo)) of 1777.15 K. The solid solubility of Co in (Si) is negligible on the basis of work of Collins and Carlson [22] and Kitagawa and Hashimoto [23]. The homogeneity range of αCo2 Si was reported to be within the composition range of 33 to 33.6 at.% Si between 973.15 and 1273.15 K based on the metallographic observations by Frolov et al. [24]. Using TA, Vogel and Rosenthal [16] and Haschimoto [20] investigated the transformation behavior between αCo2 Si and βCo2 Si. Their data on the stability range of βCo2 Si agreed with each other. Using X-ray diffraction (XRD), Zelenin et al. [25] determined the homogeneity range of CoSi to be from 49 to 50.6 at.% Si in the temperature range of 1073.15–1273.15 K, and from 48.5 to 50.9 at.% Si at 1473.15 K. These values [16,20,24,25] are considered to be reliable and, therefore, employed in the present optimization. The Curie temperatures of the (αCo) were determined by Köster and Schmid [17] using the TA method, Köster et al. [19] employing DTA and dilatometry, Haschimoto [20] utilizing DTA, and Krentsis et al. [26] using the temperature plane wave method. All the data are used to derive the analytical expression of the Curie temperature as a function of composition. Martensitic transformation between (αCo) and (εCo) was subjected to the investigation by Köster and Schmid [17], Köster et al. [19], Haschimoto [20] and Krajewski et al. [27]. These data are employed to determine the (αCo)/(εCo) boundaries at low temperatures in the present optimization. 2.2. Thermodynamic information By means of the reaction calorimetry technique, Oelsen and Middel [28] measured the enthalpies of mixing of the liquid at 1873.15 K. Activities of Si in the liquid alloys at 1743.15, 1798.15, 1853.15 and 1883.15 K were determined by Schwerdtfeger and Engell [29] using the electron motive force (emf) method within the whole composition range. Bowles et al. [30] also measured activities of Si in the liquid alloys at 1833.15 K for two compositions (22.5 and 25 at.% Si) by measuring the equilibrium constant of the related chemical reaction. The activity data [29,30] are in agreement with

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Table 1 Summary of the phase diagram and thermodynamic data in the Co–Si system Reference

Experimental method

Quoted modea

[16] [19] [20] This work

TA DTA TA DTA

+

[20] This work [23] [16] [20]

TA EPMA Radiotracer method TA TA

+

Homogeneity of αCo2 Si

[24] [21] This work

Metallography EPMA EPMA

Homogeneity of CoSi

[25] This work

XRD EPMA

(αCo)/(εCo) phase equilibria

[19] [21] [28] [5] [28] [36] [37] [39] [40]

DTA EPMA Reaction calorimetry Model calculation Reaction calorimetry KREMS/KEMS HTDSC Miedema model Miedema model

+ + +

[29] [30] [31] [32] [24] [33] [34] [33] [35]

Emf measurement Measurement of equilibrium constant TA KEMS Adiabatic calorimetry Adiabatic calorimetry Adiabatic calorimetry Adiabatic calorimetry Adiabatic calorimetry

+ +

Type of data Liquidus: 15%–50% at.% Si 17%–26% at.% Si 0%–100% at.% Si Solidus in Co-rich region Solubility of Co in (Si) Homogeneity of βCo2 Si

Enthalpy of mixing of liquid Enthalpy of formation

Activity coefficient of Si in liquid Activity of Si in liquid Activity of Co in fcc phase Enthalpy increments of Co2 Si Enthalpy increments of CoSi Enthalpy increments of CoSi2 Heat capacities of CoSi Heat capacities of CoSi2

TA = Thermal analysis. DTA = Differential thermal analysis. EPMA = Electron probe microanalysis. XRD = X-ray diffraction. KREMS = Knudsen reaction effusion mass spectrometry. KEMS = Knudsen effusion mass spectrometry. HTDSC = High temperature direct synthesis calorimetry. emf = Electron motive force. a Indicates whether the data are used or not used in the parameter optimization: , used; , not used but considered as reliable data for checking the modeling; +, not used.

those at 1853.15 K of Martin-Garin et al. [31], which were derived from the isothermal section of the Ag–Co–Si system. Using Knudsen effusion mass spectroscopy, Lexa et al. [32] determined the activities of Co at 1463.15 K in the (αCo) phase and the activities of Si and Co at the same temperature in four two-phase regions, |(εCo) + (αCo)|, |(εCo) + αCo2 Si|, |αCo2 Si + CoSi| and |CoSi + CoSi2 |. All of the thermodynamic data are included in the present optimization. High-temperature enthalpy increments (HT K − H298 K ) of Co2 Si in the temperature range of 400–1800 K were measured by Frolov et al. [24] using adiabatic calorimetry. There is no low-temperature heat capacity data for Co2 Si. Employing the adiabatic calorimetry technique, Kalishevich et al. [33] measured the high-temperature enthalpy increments from room temperature up to 1850 K and low-temperature heat capacities

from 54 to 300 K for the compound CoSi. Following the same method, Kalishevich et al. [34,35] determined the hightemperature (500–1800 K) enthalpy increments and the lowtemperature (60–300 K) heat capacities of the compound CoSi2 . In addition, Kalishevich et al. [33,34] and Frolov et al. [24] measured enthalpies of melting for the compounds Co2 Si, CoSi and CoSi2 , respectively. In the present optimization, the measured high-temperature enthalpy increments [25,33–35] are utilized in the present optimization. Using the reaction calorimetry technique, Oelsen and Middel [28] obtained the enthalpies of formation for Co2 Si, CoSi and CoSi2 at 298.15 K. Subsequently, Lexa et al. [36] measured the enthalpies of formation and entropies of formation for the above three compounds, using Knudsen effusion mass spectrometry. Meschel and Kleppa [37] also


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Table 2 Summary of the phases and DTA signals for the samples in the Co–Si system annealed at 1373.15 K for 3 days No. Composition (at.% Si)

Phasea

DTA signal (K)b

1 2

12 20

1597, 1670 ≈1459, 1478, 1514, 1547–1621

3

29.6

4

40

5

60

6 7 8

66.67 72 86

(Co) (Co) + Co2 Si (Co) + Co2 Si Co2 Si + CoSi CoSi + CoSi2 CoSi2 CoSi2 + (Si) CoSi2 + (Si)

1464c , 1567–1602 1517, 1572 1585, 1623 1591 1535, 1570 1530, 1597

a Identified with XRD and metallography. b Obtained from DTA measurement with a heating rate of 5 K/min. c Very weak peak.

Fig. 2. Backscatter electron image of the Co/Si diffusion couple annealed at 1323.15 K for 8 days.

determined the enthalpies of formation of Co2 Si, CoSi and CoSi2 using high temperature synthesis calorimetry. The enthalpies of formation for the intermediate compounds were calculated theoretically by Kaufman [5], Machlin [38], Pasturel et al. [39] and Niessen et al. [40]. The experimentally measured enthalpy of formation values [28,36,37] are included in the present optimization. 3. Experimental procedure According to the assessment of Ishida et al. [7], further experimental work is of interest for the refinement of the Co–Si phase diagram. Thus, a diffusion couple and decisive alloys are prepared in the present work in order to provide accurate phase equilibrium data needed for thermodynamic modeling. 3.1. Preparation and characterization of Co/Si diffusion couple

Fig. 3. Calculated enthalpies of mixing for the liquid at 1873.15 K by means of the parameters obtained in the first step of this work (solid line) and Choi [8] (dashed line), compared with the experimental data [28]. The reference states are liquid Co and liquid Si.

Co pieces (purity 99.95 wt.%) and Si pieces (purity 99.99 wt.%) were used and cut into bars with approximate dimension of 5 × 4 × 12 mm3 . After they were carefully grounded and polished, they were bound together with Mo wires to make the Co/Si diffusion couple. The couple was sealed in an evacuated silica capsule under vacuum (1 Pa), annealed at 1323.15 K for 8 days in an L4514type diffusion furnace (Qingdao Instrument & Equipment Co. Ltd., China), and then water-quenched. After standard metallographic preparation, the microstructure observation and phase identification were performed via optical microscopy (Leica DMLP, Wetzlar, Germany) and scanning electron microscopy with energy dispersive X-ray (SEM/EDX) analysis (JSM-5600LV, JEOL, Japan). EPMA (JXA-8800R, JEOL, Japan) was employed to determine the homogeneity ranges of the observed phases. 3.2. Preparation and characterization of the alloys Eight key alloys, the nominal compositions of which were listed in Table 2, were prepared with Co pieces (purity

Fig. 4. Calculated Co–Si phase diagram according to the present work.

99.95 wt.%) and Si pieces (purity 99.99 wt.%) in an arc melting furnace (WKDHL-I, Opto-electronics Co. Ltd., Beijing, China)

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under high purity argon atmosphere using a non-consumable W electrode. The buttons were re-melted five times to improve their homogeneities. No chemical analysis for the alloys was conducted since the weight losses of alloys were all less than 0.5 wt.% during arc-melting. The alloy samples were sealed in evacuated silica capsules under vacuum (1 Pa), annealed at 1373.15 K for 3 days in the above mentioned diffusion furnace, and then water-quenched. The annealed samples were examined by means of optical microscopy, SEM/EDX microanalysis, and XRD analysis (Rigaku D/max2550VB, Japan) using Cu Kα1 radiation with Si as an internal standard. And the lattice parameters were calculated by means of the JADE program [41]. DTA (DSC404C, Netzsch, Germany) was used to measure phase transition temperatures. The measurements were performed between room temperature and 1825.15 K with heating and cooling rates of 5 K/min under an argon atmosphere. A Pt–Pt/Rh thermocouple was used. In the examined temperature range, the accuracy of the temperature measurement was estimated to be ±2 K. The liquidus was determined from the peak temperature of the final thermal effect on heating, and the invariant reaction temperatures from the onset of the other thermal effects during the heating step. In order to determine the homogeneity ranges of αCo2 Si and CoSi compounds at 1373.15 K, three key alloys, which are located in three two-phase regions, viz. |(εCo) + αCo2 Si|, |αCo2 Si + CoSi| and |CoSi + CoSi2 |, were prepared. After being carefully grounded and polished, the three annealed alloys were subjected to EPMA measurements. 4. Thermodynamic model 4.1. Unary phase The thermodynamic properties of pure elements Co and Si are taken from the SGTE-compilation by Dinsdale [42] and described by an equation of the form:

Table 3 Thermodynamic parameters for αCo2 Si, βCo2 Si and CoSi phases in the threestep treatment of the Co–Si systema

Co2 Si

CoSi

The third treatment

0 G Co2 Si Co,Si

0 G Co2 Si Co,Si

0 G αCo2 Si 0 G βCo2 Si Co,Si Co,Si

0 G Co2 Si Co,Co

0 G αCo2 Si 0 G βCo2 Si Co,Co Co,Co

0 G Co2 Si Si,Si

0 G αCo2 Si 0 G βCo2 Si Si,Si Si,Si

0 G Co2 Si Co,Si

0 G αCo2 Si 0 G βCo2 Si Si,Co Si,Co

0 L Co2 Si Co,Si :∗ 0 L Co2 Si ∗:Co,Si

0 L αCo2 Si 0 L αCo2 Si Co,Si :∗ Co,Si :∗ 0 L αCo2 Si 0 L βCo2 Si ∗:Co,Si ∗:Co,Si

0 G CoSi Co,Si

0 G CoSi Co,Si 0 G CoSi Co,Co 0 G CoSi Si,Si 0 G CoSi Si,Co 0 L CoSi Co,Si :∗ 0 L CoSi ∗:Co,Si

a In the first treatment, Co Si and CoSi are treated as stoichiometric 2 compounds. In the second treatment, a two-sublattice model is employed to describe Co2 Si and CoSi phases. In the third treatment, the two bimorphic phases of Co2 Si (high-temperature βCo2 Si and low-temperature αCo2 Si) are considered in the modeling. Both Co2 Si and CoSi are described by two-sublattice model.

0 L L ·x where 0 G Co Co + G Si · x Si denotes the mechanical mixing of the pure elements. R ·T ·[xCo ·ln xCo +xSi ·ln xSi ] corresponds to the contribution of the ideal entropy of mixing to the Gibbs Pn i,φ energy. xCo · xSi · i=0 L Co,Si (xCo − xSi )i denotes the excess i,φ

i,φ

+ E · T −1 + F · T 3 + I · T 7 + J · T −9 . (1) HiSER

Here is the molar enthalpy of the element i at 298.15 K and 1 bar in its standard element reference (SER) state, and T is the absolute temperature. The last two terms in Eq. (1) are used only outside the ranges of the melting point, I · T 7 for a liquid below the melting point and J · T −9 for solid phases above the melting point. 4.2. Solution phases

φ, and equal to L Co,Si = ai + bi · T . The interaction parameters ai and bi are to be optimized from the experimental phase diagram and thermodynamic data. H SER is the abbreviation of SER + x H SER . xCo HCo Si Si For the (αCo) and (εCo), the Gibbs energy is described by splitting it into a nonmagnetic contribution (0 G nmg ) and a magnetic one (∆ G mag ). The nonmagnetic contribution is described by Eq. (2), while the magnetic contribution by the Hillert–Jarl–Inden model [44,45]: ∆

The liquid, (αCo) and (εCo) phases are modeled as completely disordered solutions. The Gibbs energy of liquid is described by the Redlich–Kister (R–K) polynomial [43]:

i=0

The second treatment

Gibbs energy. L Co,Si is the ith R–K parameter of solution phase

G i (T ) − HiSER = A + B · T + C · T · ln T + D · T 2

L L G φ − H SER = 0 G Co · xCo + 0 G Si · xSi + R · T · [xCo · ln xCo + xSi · ln xSi ] n X i,φ + xCo · xSi · L Co,Si (xCo − xSi )i

The first treatment

(2)

G mag = RT ln(β φ + 1)g(τ φ )

(3)

in which τ is T /T ∗ , T ∗ the critical temperature for magnetic ordering (Curie temperature Tc for ferromagnetic materials or Néel temperature TN for antiferromagnetic materials), and β the average magnetic moment per atom of the alloy expressed in Bohr magnetons. The function g(τ ) is the polynomial derived by Hillert and Jarl [45]. Its complete description is given in Ref. [45].

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L. Zhang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 470–481 Table 4 Summary of the thermodynamic parameters in the Co–Si systema Liquid: (Co, Si)1 0LL Co,Si = −183 483.8 + 34.80023 · T 1LL Co,Si = −3219.5 − 15.28341 · T 2LL Co,Si = 34 241.7 3LL Co,Si = 15 579.7

(αCo)b : (Co, Si)1 Va1 0 L (αCo) = −166 661.9 + 29.94175 · T Co,Si 1 L (αCo) = −58 780.2 + 28.62343 · T Co,Si 0 TcαCo = −1943.6 Co,Si 0 β αCo = −2.95 Co,Si

(εCo)b : (Co, Si)1 Va0.5 0 L (εCo) = −199 795.7 + 35.01457 · T Co,Si 1 L (εCo) = 3322.1 + 9.000271 · T Co,Si 0 TcεCo = 0 Co,Si 0 β εCo = 0 Co,Si

αCo3 Si : Co0.75 Si0.25 0 G αCo3 Si −0.75 · 0 G hcp −0.25 · 0 G Diamond = −14 443.8 − 9.99743 · T c Si Co Co,Si

αCo2 Si : (Co, Si)2/3 (Co, Si)1/3 0 G αCo2 Si − 2 · H SER − 1 · H SER = −28 546.8 − 24.99165 · T − Co,Si Co Si 3 3 0.79442 · T · ln T − 0.015093 · T 2 − 1419 271.2 · T −1 0 G αCo2 Si − 0 G hcp = 5000c Co Co,Co 0 G αCo2 Si − 0 G Diamond = 5000c Si Si,Si 0 G αCo2 Si = 0 G αCo2 Si + 0 G αCo2 Si − 0 G αCo2 Si Si,Co Co,Co Si,Si Co,Si 0 L αCo2 Si = −23 521.8 ∗:Co,Si 0 L αCo2 Si = 2215.7 ∗:Co,Si

βCo2 Si:(Co, Si)2/3 (Co, Si)1/3 0 G βCo2 Si − 0 G αCo2 Si = 994.54 − 0.60720 · T Co,Si Co,Si 0 G βCo2 Si − 0 G hcp = 5000c Co,Co Co 0 G βCo2 Si − 0 G Diamond = 5000c Si,Si Si 0 G βCo2 Si = 0 G βCo2 Si + 0 G βCo2 Si − 0 G βCo2 Si Si,Co Co,Co Si,Si Co,Si 0 L βCo2 Si = −30 715.8 ∗ Co,Si : 0 L βCo2 Si = 63.546 ∗:Co,Si

CoSi: (Co, Si)0.5 (Co, Si)0.5 0 G CoSi −0.5 · H SER − 0.5 · H SER = −48 001.0 + 50.451 · T Co,Si Co Si − 10.582 · T · ln T − 0.010127 · T 2 − 389 369.9 · T −1 0 G CoSi − 0 G hcp = 5000c Co,Co Co 0 G CoSi − 0 G Diamond = 5000c Si,Si Si

Table 4 (continued) CoSi2 : Co1/3 Si2/3 0 G CoSi2 − 1 · H SER − 2 · H SER = −41 239.2 + 116.62481 · T Co,Si Co Si 3 3 − 20.17772 · T · ln T − 0.0043072 · T 2 − 63 420.2 · T −1

Diamond: (Si) a Temperature (T ) in Kelvin and Gibbs energy in J/mol atoms. Values for T c

are given in Kelvin (K) and β in Bohr magnetons, µB. b The magnetic contribution to the Gibbs energy is described by the Hillert–Jarl–Inden model [44,45]. c The underlined parameters are fixed during the optimization.

The parameters Tc and β are usually expressed as a function of composition. o Tc = xCo · TCo + xSi · TSio n X Co,Si + xCo · xSi · TCi (xCo − xSi )i

(4)

i=0 o o β = xCo · βCo + xSi · βSi n X + xCo · xSi · βiCo,Si (xCo − xSi )i .

(5)

i=0

4.3. Intermetallic compounds Lacking any thermodynamic data, αCo3 Si is modeled as a stoichiometric compound. The Gibbs energy of αCo3 Si per mole-formula is given by the following expression: 0

3 Si − 3 · H SER − H SER = A + B · T G αCo m Co Si

hcp

+ 3 · 0 G Co + 0 G Diamond (6) Si where A and B are the parameters to be evaluated in the course of optimization. Since there are experimental data on heat capacity (C p ) of CoSi2 in a wide temperature range, it is preferable to express its Gibbs energy relative to the SER state. The Gibbs energy of CoSi2 per mole-formula is expressed as: 2 − 2 · H SER − H SER = a + b · T + c · T · ln T G CoSi m Co Si

+ d · T 2 + e · T −1 .

The coefficients c, d and e can be obtained directly from the C p expression. In view of the reported homogeneity ranges [7], βCo2 Si, αCo2 Si and CoSi phases are described with two-sublattice models, (Co, Si)x (Co, Si)y , where the first sublattice is mainly occupied by Co, the second by Si and x, y denote the number of sites in each sublattice. The Gibbs energy of the φ phase (φ = βCo2 Si, αCo2 Si, or CoSi) per mole-formula can be expressed as follows: 0

φ

φ

φ

0 00 0 00 G = 0 G Co:Si · yCo · ySi + 0 G Co:Co · yCo · yCo φ

φ

0 G CoSi = 0 G CoSi + 0 G CoSi − 0 G CoSi Si,Co Co,Co Si,Si Co,Si

0 00 0 00 + 0 G Si:Si · ySi · ySi + 0 G Si:Co · ySi · yCo

0 L CoSi = 6995.6 Co,Si:∗

0 0 0 0 + x · RT · (yCo ln yCo + ySi ln ySi )

0 L CoSi ∗:Co,Si = −4396.1

(7)

00 00 00 00 + y · RT (yCo ln yCo + ySi ln ySi )

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A value of 5000 J/mol atom is assigned to the parameters

0Gφ 0 φ 0 αCo2 Si 0 hcp Co:Co and G Si:Si , i.e. G Co:Co − 3 · G Co = 15 000 and 0 G CoSi − 0 G Diamond = 5000. Si:Si Si φ φ The parameters 0 G Co:Co and 0 G Si:Si correspond to

the Gibbs energy needed to fill one sublattice with φ antistructure defects. The parameter 0 G Si:Co relates to the filling of both sublattices with antistructure defects. This φ latter parameter can be estimated by the equation 0 G Si:Co = 0Gφ 0 φ 0 φ Co:Co + G Si:Si − G Co:Si . In addition, the interaction between two species in one sublattice is assumed to be independent of occupation of the other sublattice. Thus, we adopt the following equations in the optimization:

Fig. 5(a). Calculated Co–Si phase diagram along with experimental data from the present work and the literature [16,19–21,24,25].

0 φ L Co:Co,Si

= 0 L Si:Co,Si = 0 L ∗ : Co,Si

φ

φ

0 φ L Co,Si:Co

= 0 L Co,Si:Si = 0 L Co,Si :∗ .

φ

φ

(9)

5. Results and discussion

Fig. 5(b). Enlarged Co-rich region along with the literature data [16,19,20] and present experimental data.

φ

φ

0 00 00 0 0 00 00 0 + yCo yCo ySi · L Co:Co,Si +ySi yCo ySi · L Si:Co,Si φ

0 0 00 + yCo ySi yCo · 0 L Co,Si:Co φ

0 0 00 0 + yCo ySi ySi · L Co,Si:Si + . . . j

(8)

where the parameter yi is the site fraction of the species i (i = Co or Si) on the sublattice j. The superscripts 0 and 00 denote the first and second sublattices of the presented φ model, respectively. 0 G Co:Si is the Gibbs energy of the ideal compound Cox Siy . Since C p values in a wide temperature range φ are available for αCo2 Si and CoSi, 0 G Co:Si corresponding to stoichiometric αCo2 Si and CoSi compositions can be expressed as an equation similar to Eq. (7). However, for the high temperature modification βCo2 Si with limited experimental βCo Si βCo Si 2 Si data, 0 G Co:Si2 can only be expressed as 0 G Co:Si2 − 0 G αCo Co:Si = A0 + B0 · T .

Fig. 2 shows the backscatter electron image of the Co/Si diffusion couple, which was annealed at 1323.15 K for 8 days. After interdiffusion, five phases, viz. CoSi2 , CoSi, Co2 Si, (εCo) and (αCo), are formed. This is in agreement with the assessed Co–Si phase diagram by Ishida et al. [7]. As shown in Fig. 2, the thicknesses of the CoSi and Co2 Si are larger than that of CoSi2 . This could be due to the fact that CoSi2 is a stoichiometric compound while CoSi and Co2 Si are intermediate compounds with certain homogeneity ranges. The homogeneity range of (εCo) determined by EPMA is 15.8–16.9 at.% Si at 1323.15 K. Table 2 summarizes the results obtained by XRD and DTA measurements. XRD data confirm all established Co–Si intermetallic phases and their crystal structures. The observed lattice parameters match closely with those assessed by Ishida et al. [7] and thus not presented here. With DTA measurements, which were found to be consistently reproducible, the general features of the Co–Si phase diagram established by Haschimoto et al. [20] are confirmed, but for the three-phase equilibrium temperatures some deviations are observed. The temperatures of peritectic reaction (L + (αCo) ↔ (εCo)) and eutectic reaction (L ↔ βCo2 Si+CoSi) are higher by 9 K and 13 K than those of Köster et al. [19] and Haschimoto [20], respectively. The peritectic reaction, (L + αCo2 Si ↔ αCo3 Si), was not observed by the present DTA measurement probably because of the slow reaction kinetics associated with this peritectic reaction. According to EPMA measurement, the homogeneity ranges of αCo2 Si and CoSi at 1373.15 K are 32.1 to 33.5 at.% Si and 49 to 51.7 at.% Si, respectively. Evaluation of the model parameters was attained by recurrent run of the PARROT program [46], which is based on a least square procedure. The step-by-step optimization procedure carefully described by Du et al. [47] was utilized in the present assessment. The experimental data selected from the literature as well as the present experimental results were employed in the optimization. In the assessment procedure,


Fig. 6. Calculated enthalpies of formation at 298.15 K, compared with the experimental data [28,36,37]. The reference states are hcp Co and diamond Si.

each piece of experimental information was given a certain weight. The weights were changed systematically during the assessment until most of the experimental data were accounted for within the claimed uncertainty limits. Because βCo2 Si, αCo2 Si and CoSi show certain homogeneity ranges, the optimization can be divided into three steps. In the first step, βCo2 Si and αCo2 Si were treated as the same phase, and all the intermediate phases were treated as stoichiometric compounds. Based on these simplifications for the thermodynamic models, the optimization started with liquid phase. At least a0 and a1 in Eq. (2) need to be introduced in order to make the excess enthalpy of Si-rich liquid independent of that of Co-rich liquid. The well-established liquidus line in the wide temperature and composition ranges makes it possible to optimize the parameters b0 and b1 . In the present work, it was found that the introduction of two additional parameters (a2 and a3 ) can improve the description for the liquid phase. For CoSi2 , CoSi and Co2 Si, C p expressions for the stoichiometric compounds can be derived from the measured enthalpy increment data. Thus, for the stoichiometric compounds, the coefficients c, d and e in Eq. (7) can be estimated from the C p expression directly. The coefficient a in Eq. (7) can be evaluated from the values of the enthalpy of formation and coefficient b in Eq. (7) from the measured phase diagram data. The obtained coefficients for the three intermediate compounds were subjected to further optimization. For (αCo) and (εCo) solid solutions, magnetic contributions to the Gibbs energy 0 were taken into account. According to Guillermet [48], TCo 0 (1396 K) and βCo (1.35 µB) of (εCo) phase are equal to those Co,Si of (αCo) phase. Tc0 and β0Co,Si of (αCo) in Eqs. (4) and (5) can be estimated from the experimental Curie temperatures and magnetic moments [49], and the estimated values are −1943.6 K and −2.95 µB, respectively. Due to the lack of Co,Si experimental data, Tc0 and β0Co,Si of (εCo) are assumed to zero. All the evaluated parameters obtained in this step are further refined in the subsequent optimization. In view of the comparison between parameters obtained in the first step of the present work and those of Choi [8],

477

Fig. 7. Calculated enthalpies of mixing for the liquid at 1873.15 K with the experimental data [28]. The reference states are liquid Co and liquid Si.

significant improvements have been made. For the description of the liquid phase, five parameters are introduced in this step but eight in Choi’s work [8]. For (αCo) and (εCo) phases, three parameters are adjusted for each of them in this step, compared with four in Choi’s work [8]. Although less parameters are used in the first step of the present optimization, a better fit to the experimental phase diagram and thermodynamic data is obtained. As one of the indications, Fig. 3 presents the calculated enthalpies of mixing for the liquid at 1873.15 K along with the experimental values. As shown in this figure, the present optimization yields a better agreement with the experimental data. In the second step, the homogeneity ranges of Co2 Si and CoSi phases were considered. In this step, two-sublattice models were employed to describe the two phases. During this step, first all the parameters obtained in the first step were fixed, and only interact parameters associated with Co2 Si and CoSi phases are evaluated on the basis of experimental homogeneity ranges. After that, all the parameters are optimized simultaneously. In the third step, two modifications, βCo2 Si and αCo2 Si, are considered. The parameters of Co2 Si obtained in the second step were considered to be those of αCo2 Si. For the high-temperature βCo2 Si, a two-sublattice model, (Co, Si)2 (Co, Si)1 , was also employed to describe its Gibbs energy. Because of the lack of experimental data, the expression 0 G βCo2 Si − 0 G αCo2 Si = A + B · T was employed in the 0 0 Co,Si Co,Si optimization of βCo2 Si phase. The details of the three-step treatment in the optimization process of Co–Si system are listed in Table 3. As mentioned in the section on evaluation of literature information, data concerning the martensitic transformation between (αCo) and (εCo) have been reported by several groups using various techniques [17,19,20,27]. Although these data do not provide direct information about the position of the equilibrium boundaries, they may be employed to locate the approximate position of the T0 line, where the Gibbs free energies of (α-Co) and (ε-Co) are equal. According to Kaufman and Cohen [50], the line can be bracketed from

478


Table 5 Summary of the invariant equilibria in the Co–Si system Temperature (K) Peritectic 1523.15 1514 1510 Eutectic 1477.15 1478 1475 Eutectic 1466.15 1464 1467 Peritectic

Composition (at.% Si) L 21.4

↔

23.2 αCo3 Si 25.0

↔

25.0

L ∼31 31.2

+

L 39.6 39.7

↔

1481.15 1511.15 1517 1511 Eutectic 1583.15 1584 1587 Eutectic

↔

34.3 ↔

63.5 ↔

L 33.3 33.3 33.3

↔

1605.15 1605.15 1600

L 50.0 50.0 50.0

↔

1733 1738 1730

L 66.7 66.7 66.7 66.7

↔

1599 1595 1591 1593

Congruent

TA = Thermal analysis. DTA = Differential thermal analysis. AC = Adiabatic calorimetry.

[16] [20] [18] [19] [This work]

TA TA DTA DTA Calculated

[7] [This work]

TA Calculated

[16] [20] [This work] [This work]

TA TA DTA Calculated


TA TA DTA Calculated

[20] [This work] [This work]

TA DTA Calculated


TA DTA Calculated

βCo2 Si 33.3 33.3 33.3

[16] [20] [This work]

TA TA Calculated

CoSi 50.0 50.0 50.0

[20] [33] [This work]

TA AC Calculated

CoSi2 66.7 66.7 66.7 66.7


TA AC DTA Calculated

βCo2 Si 36.0 35.8

↔

↔

+

αCo2 Si 34.0 34.1

CoSi 52.1

CoSi2 66.7 66.7

αCo2 Si ∼33 33.3 CoSi 50.0 49.1 49.1

+

CoSi 50.0 49.1 49.1

+

51.5

77.9

Congruent

αCo3 Si 25.0 25.0 25.0 25.0 25.0

αCo2 Si /

+

33.8

1532.15 1533 1533 Congruent

DTA DTA Calculated

18.6

34.6

βCo2 Si 35.7 35.1

L 77.5

32.2


(εCo) 18.1

βCo2 Si ∼32.6 33.3

37.8

L 61.8

DTA DTA Calculated

(εCo) 18.4

+

αCo2 Si 33.3 32.3 33.3 / 32.4

∼1593 1592

Eutectoid


αCo3 Si 25.0

15.9

18.9 +

1543.15 1559.15 1572 1577

DTA DTA Calculated

25.0

L 24.8 23.9 / 24.4 24.3

Eutectic


(εCo) 17.5

↔

13.1

1483.15 1485.15 1483.15 1487 1488 Peritectic

Method

(αCo) 16.5

+

20.9 L 23.1

Reference

CoSi2 66.7 66.7

+

(Si) 97.9 100.0


Fig. 8. Calculated activity of Si in liquid at 1853.15 K, compared with the experimental data [29,31]. The activity data at different temperatures (1743.15, 1798.15, 1883.15 K) are converted into the same temperature 1853.15 K exp cal (1853.15 K) − a cal (T ), where T via the function, aSi (Texp ) + aSi exp exp is Si exp the experimental temperature, aSi (Texp ) the measured activity value at the cal (1853.15 K) and a cal (T ) the calculated ones experimental temperature, aSi exp Si at 1853.15 K and the experimental temperature, respectively. The reference state is liquid Si.

Fig. 9. Computed activity of Co in the (αCo) phase at 1463.15 K with the experimental data [32]. The reference state is fcc Co.

479

reproduced by the modeling. Fig. 5(b) is the enlargement of the Co–Si phase diagram in the composition range of 10–40 at.% Si from 1423.15 to 1623.15 K. The calculated invariant equilibria are listed in Table 5. The differences between the calculated and the measured temperatures are less than 5 K. The inflections appearing in the (αCo) and (εCo) phase boundaries are traced to two phenomena. One is the magnetic contribution to the Gibbs energy, and the other is two kinds of phase transitions (diffusionless and diffusion controlled) associated with (αCo)/(εCo) transformation, as reported by Köster et al. [19]. Fig. 6 presents the comparison between the calculated enthalpies of formation at 298.15 K and the experimental data available in the literature [28,36,37]. These accurate experimental data are reasonably reproduced by the present thermodynamic parameters. Fig. 7 shows the calculated enthalpies of mixing for the liquid at 1873.15 K along with the experimental data [28], showing a good agreement. In Fig. 8, the calculated activity of Si in liquid at 1853.15 K is compared with the experimental data [29,31]. In order to compare the activity data at different temperatures in one diagram, the measured data are converted into the exp common temperature 1853.15 K via the function, aSi (Texp ) + cal cal aSi (1853.15 K) − aSi (Texp ), where Texp is the experimental exp temperature, aSi (Texp ) is the measured activity value at the cal (1853.15 K) and a cal (T ) experimental temperature, aSi exp Si are the calculated ones at 1853.15 K and the experimental temperature, respectively. The figure shows that the fit to the experimental data [29,31] is excellent. A comparison of the computed activity of Co in (αCo) at 1463.15 K with the experimental data [32] is made in Fig. 9, showing a reasonable agreement also. In Fig. 10(a)–(c), the calculated enthalpy increments for the compounds Co2 Si, CoSi and CoSi2 are compared with the experimental data [24,33,34], respectively. The agreement is good within the estimated experimental uncertainties, except for some deviation at temperatures close to the melting points of the compounds. Large experimental errors are expected when measurements are approaching the melting of the compounds. 6. Conclusions

transition temperature data obtained on cooling (“Ms”) and heating (“As”) as follows: T0 = (“As” + “Ms”)/2.

(10)

The line based on Eq. (10) may have a typical uncertainty (“As” − “Ms”)/4. The thermodynamic parameters finally obtained in the third step are listed in Table 4. The calculated Co–Si phase diagram according to the final modeling is presented in Fig. 4. The computation by means of the PANDAT program [11] indicates that the calculated phase diagram is a real stable one. Fig. 5(a) presents the calculated Co–Si phase diagram, compared with the experimental data from the literature data [16,19–21,24,25] and present work. As can be seen from this figure, all the reliable experimental values are well

• All the experimental phase diagram and thermodynamic data available for the Co–Si system have been critically evaluated. The Co–Si phase diagram has been checked via a Co/Si diffusion couple and eight decisive alloys. The annealed samples are characterized by using XRD, optical microscopy, DTA, SEM/EDX and EPMA. • Using a step-by-step optimization procedure, a consistent set of thermodynamic parameters has been obtained on the basis of the present experimental data as well as critically evaluated literature data. The comparison demonstrates that the calculated phase diagram and thermodynamic properties are in good agreement with the experimental ones. The present modeling yields a better description of the Co–Si system, compared with the previous modeling.

480


Fig. 10. Calculated HT − H298 K for the compounds along with the measured data [24,33,34]. (a) Co2 Si, (b) CoSi, (c) CoSi2 .

Acknowledgements The financial support from the National Outstanding Youth Science Foundation of China (Grant No. 50425103) and the National Natural Science Foundation of China (Grant No. 50571114) is acknowledged. One of the authors (Yong Du) acknowledges the Furong Chair Professorship Program released by Hunan Province of PR China for financial support. The donation of the Leica DMLP microscope from the Alexander von Humboldt Foundation is greatly appreciated. References [1] M.E. Schlesinger, Chem. Rev. 90 (1990) 607–628. [2] K.S. Kumar, C.T. Liu, JOM 45 (1993) 28–34. [3] S.P. Murarka, in: R.W. Eathader, S. Mantl, L.J. Schowalter, K.N. Tu (Eds.), Materials Reasearch Symposium Proceedings, vol. 320, Materials Society, Pitasburgh, 1993, p. 3. [4] T.G. Chart, High Temp.-High Press. 5 (1973) 241–252. [5] L. Kaufman, CALPHAD 3 (1979) 45–76. [6] M. Hansen, K. Anderko, Constitution of binary alloys, second edn, New York, USA, 1958, pp. 503–506. [7] K. Ishida, T. Nishizawa, M.E. Schlesinger, J. Phase Equilib. 12 (1991) 578–586. [8] S.-D. Choi, CALPHAD 16 (1992) 151–159.

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