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Thermodynamic analysis of crystallisation in amorphous solids
L
Journal of Alloys and Compounds 322 (2001) L17–L18
www.elsevier.com / locate / jallcom
Letter
Thermodynamic analysis of crystallisation in amorphous solids W. Sha* Metals Research Group, School of Civil Engineering, The Queen’ s University of Belfast, Belfast BT7 1 NN, UK Received 21 January 2001; accepted 6 March 2001
Abstract Thermodynamic modelling of the crystallisation products of amorphous solids has been carried out using the computer package Thermo-Calc. Systems investigated include Ni–B, Ni–P(–Sn), Fe–Ni–P, Fe–Ni(–Cr)–P–B and Ni–W–P. Excellent agreement between calculation and experimental results has been demonstrated. It is reasonable that good results are obtained by applying equilibrium calculations to what starts as a very non-equilibrium system. 2001 Elsevier Science B.V. All rights reserved. Keywords: Amorphous materials; Thermodynamic modelling
1. Introduction A significant advance in thermodynamic databases is the completion of SGTE (Scientific Group Thermodata Europe) SOLution database, SSOL [1]. In the present work, thermodynamic calculations for several amorphous systems have been carried out, and the results are compared with experimental data. The type of materials investigated is mainly amorphous coating produced using electroless or electrodeposition. The aim is to assess the viability of using thermodynamic calculation to evaluate the crystallisation products upon heating of the coating. Various authors have carried out a large amount of experimental work over the years to identify such products; it was envisaged that much of this could be replaced, or at least guided, with the much less laborious calculations. The calculations were conducted with Thermo-Calc version L [2].
2. Results and discussion The modelling starts with the most common electroless amorphous plating systems, Ni–B and Ni–P. These are well covered in literature, e.g. in the ASM Handbook [3]. In the present calculation, for Ni–B, a typical B content of 4 mass% was used. The result showed that the equilibrium *Fax: 144-28-9066-3754. E-mail address: [email protected] (W. Sha).
phases for temperatures ranging from 250 to 3758C are consistently 74 mol% Ni 3 B and almost pure Ni. This is in agreement with what was described in the ASM Handbook. In the case of Ni–P, for 6.8 mass% P, the equilibrium at 3008C consists of almost pure Ni and 48.6 mol% Ni 3 P, again in agreement with many published data. The ternary Fe–Ni–P system was investigated. Experimental work has been reported by Sridharan and Sheppard [4]. Calculation showed that for Fe 80 Ni 8 P12 alloy, at 3508C, the equilibrium constitution is 52 mol% bcc with a composition of Fe–1.77at%Ni–0.02at%P and 48 mol% Fe 60 Ni 15 P25 ((Fe,Ni) 3 P). This is in agreement with the result from the very time-consuming experimental programme involving isothermal heat treatment and phase identification using X-ray diffraction. Calculations have also been extended to the more complex systems discussed in Ref. [4]. Table 1 summarises the calculation results for equilibrium phases in Fe 40 Ni 40 P14 B 6 (Metglass 2826) at 350 and 5008C. For a further alloy, Fe 32 Ni 36 Cr 14 P12 B 6 (Metglass 2826A), it was found that the equilibrium between 375 and 6008C consists of four phases. These are Cr 2 P (12 mol% at 375–4008C reducing to 11.3 mol% at Table 1 Equilibrium phase compositions (at%) in Fe 40 Ni 40 P14 B 6 alloy at 350 / 5008C: Thermo-Calc [1,2] thermodynamic calculation results Phase
Ni
Fe
P
B
Mol%
fcc Ni 3 P Fe 2 B
59.8 / 56.7 43.2 / 43.6 1.6 / 4.6
40.2 / 43.3 31.8 / 31.4 65.1 / 62.1
0.002 / 0.04 25 a 0
0 0 33.3 a
26 56 18
a
The concentrations of these are always stoichiometric in the database.
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01258-0
L18
W. Sha / Journal of Alloys and Compounds 322 (2001) L17 –L18
6008C), CrB (12 mol%), Ni 3 P (32 mol% at 375–4008C increasing to 32.6 mol% at 6008C), and fcc. In the fcc phase, the concentrations of Fe, Ni and Cr change with temperature, as shown in Fig. 1. The solubility of phosphorous in fcc increases from 0.004 at% (3758C), to 0.006 at% (4008C), and to 0.2 at% (6008C). The solubility of boron remains very small for the entire temperature range, as expected. For Ni 3 P phase, although its mole fraction remains almost constant, the iron level changes from 40.3 at% at 3758C, to 39.7 at% at 4008C, and to 33.1 at% at 6008C. In a recent study, electrodeposition was used to produce Ni–W–P alloy coating and the phase evolution upon heating was investigated using transmission electron microscopy, X-ray diffraction and microhardness measurements [5]. For the composition of the coating used in that work, Ni–31 mass%W–1 mass%B, it was found through thermodynamic calculations that the phase equilibria at 400 and 6008C are both fcc Ni, Ni 3 B and Ni 4 W. At 4008C, there are, respectively, 26 and 40 mol% of Ni 3 B and Ni 4 W in the equilibrium. The W content in fcc Ni is 11.5 at% and B content is virtually zero. At 6008C, the amount of Ni 4 W
has decreased to 34 mol%, accompanied by an increase in the W content in fcc Ni to 12.7 at%. The solubility of B in Ni is only 0.001 at%, so there is no change of the amount of Ni 3 B in equilibrium. Ni 4 W was also identified by the previous authors [5]. Jang et al. recently investigated solder reaction-assisted crystallisation of electroless Ni–P [6]. A reaction equation was proposed: 160 40 Ni 85 P15 1 ]Sn → 15Ni 3 P 1 ]Ni 3 Sn 4 3 3 Using Thermo-Calc, when an alloy composition as the left-hand side of equation was used, the equilibrium reached matches exactly the right-hand side. It is reasonable that good results are obtained by applying equilibrium calculations to what starts as a very non-equilibrium system. It is one of the tenets of thermodynamics that the equilibrium state can be reached via a number of different routes and it matters not at all that one is travelling through metastable intermediaries. Indeed using a highly distorted or highly stressed intermediary state is a common way of increasing the kinetics of sluggish reactions.
References
Fig. 1. The variation of equilibrium Ni, Fe and Cr concentrations in fcc phase in the Fe 32 Ni 36 Cr 14 P12 B 6 alloy as a function of temperature.
[1] B. Sundman, Thermo-Calc Version L Users’ Guide, Royal Institute of Technology, Stockholm, 1997. [2] B. Jansson, M. Schalin, M. Selleby, B. Sundman, in: C.W. Bale, G.A. Irons (Eds.), Computer Software in Chemical and Extractive Metallurgy, Canadian Institute of Mining, Metallurgy and Petroleum, Montreal, 1993, pp. 57–71. [3] D.W. Baudrand, in: ASM Handbook, Surface Engineering, Vol. 5, ASM International, Materials Park, OH, 1994, pp. 290–309. [4] K. Sridharan, K. Sheppard, J. Mater. Proc. Technol. 68 (1997) 109–116. [5] G. Graef, K. Anderson, J. Groza, A. Palazoglu, Mater. Sci. Eng. B 41 (1996) 253–257. [6] J.W. Jang, P.G. Kim, K.N. Tu, D.R. Frear, P. Thompson, J. Appl. Phys. 85 (1999) 8456–8462.
Journal of Alloys and Compounds 322 (2001) L17–L18
www.elsevier.com / locate / jallcom
Letter
Thermodynamic analysis of crystallisation in amorphous solids W. Sha* Metals Research Group, School of Civil Engineering, The Queen’ s University of Belfast, Belfast BT7 1 NN, UK Received 21 January 2001; accepted 6 March 2001
Abstract Thermodynamic modelling of the crystallisation products of amorphous solids has been carried out using the computer package Thermo-Calc. Systems investigated include Ni–B, Ni–P(–Sn), Fe–Ni–P, Fe–Ni(–Cr)–P–B and Ni–W–P. Excellent agreement between calculation and experimental results has been demonstrated. It is reasonable that good results are obtained by applying equilibrium calculations to what starts as a very non-equilibrium system. 2001 Elsevier Science B.V. All rights reserved. Keywords: Amorphous materials; Thermodynamic modelling
1. Introduction A significant advance in thermodynamic databases is the completion of SGTE (Scientific Group Thermodata Europe) SOLution database, SSOL [1]. In the present work, thermodynamic calculations for several amorphous systems have been carried out, and the results are compared with experimental data. The type of materials investigated is mainly amorphous coating produced using electroless or electrodeposition. The aim is to assess the viability of using thermodynamic calculation to evaluate the crystallisation products upon heating of the coating. Various authors have carried out a large amount of experimental work over the years to identify such products; it was envisaged that much of this could be replaced, or at least guided, with the much less laborious calculations. The calculations were conducted with Thermo-Calc version L [2].
2. Results and discussion The modelling starts with the most common electroless amorphous plating systems, Ni–B and Ni–P. These are well covered in literature, e.g. in the ASM Handbook [3]. In the present calculation, for Ni–B, a typical B content of 4 mass% was used. The result showed that the equilibrium *Fax: 144-28-9066-3754. E-mail address: [email protected] (W. Sha).
phases for temperatures ranging from 250 to 3758C are consistently 74 mol% Ni 3 B and almost pure Ni. This is in agreement with what was described in the ASM Handbook. In the case of Ni–P, for 6.8 mass% P, the equilibrium at 3008C consists of almost pure Ni and 48.6 mol% Ni 3 P, again in agreement with many published data. The ternary Fe–Ni–P system was investigated. Experimental work has been reported by Sridharan and Sheppard [4]. Calculation showed that for Fe 80 Ni 8 P12 alloy, at 3508C, the equilibrium constitution is 52 mol% bcc with a composition of Fe–1.77at%Ni–0.02at%P and 48 mol% Fe 60 Ni 15 P25 ((Fe,Ni) 3 P). This is in agreement with the result from the very time-consuming experimental programme involving isothermal heat treatment and phase identification using X-ray diffraction. Calculations have also been extended to the more complex systems discussed in Ref. [4]. Table 1 summarises the calculation results for equilibrium phases in Fe 40 Ni 40 P14 B 6 (Metglass 2826) at 350 and 5008C. For a further alloy, Fe 32 Ni 36 Cr 14 P12 B 6 (Metglass 2826A), it was found that the equilibrium between 375 and 6008C consists of four phases. These are Cr 2 P (12 mol% at 375–4008C reducing to 11.3 mol% at Table 1 Equilibrium phase compositions (at%) in Fe 40 Ni 40 P14 B 6 alloy at 350 / 5008C: Thermo-Calc [1,2] thermodynamic calculation results Phase
Ni
Fe
P
B
Mol%
fcc Ni 3 P Fe 2 B
59.8 / 56.7 43.2 / 43.6 1.6 / 4.6
40.2 / 43.3 31.8 / 31.4 65.1 / 62.1
0.002 / 0.04 25 a 0
0 0 33.3 a
26 56 18
a
The concentrations of these are always stoichiometric in the database.
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01258-0
L18
W. Sha / Journal of Alloys and Compounds 322 (2001) L17 –L18
6008C), CrB (12 mol%), Ni 3 P (32 mol% at 375–4008C increasing to 32.6 mol% at 6008C), and fcc. In the fcc phase, the concentrations of Fe, Ni and Cr change with temperature, as shown in Fig. 1. The solubility of phosphorous in fcc increases from 0.004 at% (3758C), to 0.006 at% (4008C), and to 0.2 at% (6008C). The solubility of boron remains very small for the entire temperature range, as expected. For Ni 3 P phase, although its mole fraction remains almost constant, the iron level changes from 40.3 at% at 3758C, to 39.7 at% at 4008C, and to 33.1 at% at 6008C. In a recent study, electrodeposition was used to produce Ni–W–P alloy coating and the phase evolution upon heating was investigated using transmission electron microscopy, X-ray diffraction and microhardness measurements [5]. For the composition of the coating used in that work, Ni–31 mass%W–1 mass%B, it was found through thermodynamic calculations that the phase equilibria at 400 and 6008C are both fcc Ni, Ni 3 B and Ni 4 W. At 4008C, there are, respectively, 26 and 40 mol% of Ni 3 B and Ni 4 W in the equilibrium. The W content in fcc Ni is 11.5 at% and B content is virtually zero. At 6008C, the amount of Ni 4 W
has decreased to 34 mol%, accompanied by an increase in the W content in fcc Ni to 12.7 at%. The solubility of B in Ni is only 0.001 at%, so there is no change of the amount of Ni 3 B in equilibrium. Ni 4 W was also identified by the previous authors [5]. Jang et al. recently investigated solder reaction-assisted crystallisation of electroless Ni–P [6]. A reaction equation was proposed: 160 40 Ni 85 P15 1 ]Sn → 15Ni 3 P 1 ]Ni 3 Sn 4 3 3 Using Thermo-Calc, when an alloy composition as the left-hand side of equation was used, the equilibrium reached matches exactly the right-hand side. It is reasonable that good results are obtained by applying equilibrium calculations to what starts as a very non-equilibrium system. It is one of the tenets of thermodynamics that the equilibrium state can be reached via a number of different routes and it matters not at all that one is travelling through metastable intermediaries. Indeed using a highly distorted or highly stressed intermediary state is a common way of increasing the kinetics of sluggish reactions.
References
Fig. 1. The variation of equilibrium Ni, Fe and Cr concentrations in fcc phase in the Fe 32 Ni 36 Cr 14 P12 B 6 alloy as a function of temperature.
[1] B. Sundman, Thermo-Calc Version L Users’ Guide, Royal Institute of Technology, Stockholm, 1997. [2] B. Jansson, M. Schalin, M. Selleby, B. Sundman, in: C.W. Bale, G.A. Irons (Eds.), Computer Software in Chemical and Extractive Metallurgy, Canadian Institute of Mining, Metallurgy and Petroleum, Montreal, 1993, pp. 57–71. [3] D.W. Baudrand, in: ASM Handbook, Surface Engineering, Vol. 5, ASM International, Materials Park, OH, 1994, pp. 290–309. [4] K. Sridharan, K. Sheppard, J. Mater. Proc. Technol. 68 (1997) 109–116. [5] G. Graef, K. Anderson, J. Groza, A. Palazoglu, Mater. Sci. Eng. B 41 (1996) 253–257. [6] J.W. Jang, P.G. Kim, K.N. Tu, D.R. Frear, P. Thompson, J. Appl. Phys. 85 (1999) 8456–8462.