Theoretical Study on the Binary Phase Diagrams of the Zr-X (X=Li, Na, K, Sc, Hf) Systems†

doi:10.7503/cjcu20150345

Abstract

Abstract:

The Zr-X(X=Li, Na, K, Sc, Hf) systems were studied with the calculation of phase diagrams(CALPHAD) approach. A set of the thermodynamic parameters of the liquid, (αZr), (βZr), (Li), (Na), (K), (αSc), (βSc), (αHf) and (βHf) phases was obtained based on the critical review of the available experimental data. The gas phase for the three binary systems, i.e. Zr-Li, Zr-Na and Zr-K, was treated with the ideal gas model. Comparisons between the calculated and measured phase diagrams show that the experimental phase equilibria information is satisfactorily accounted for by the present thermodynamic description.

Key words: Zr-X(X=Li, Na, K, Sc, Hf) system, Binary phase diagram, Thermodynamic modeling, Calculation of phase diagrams approach

CLC Number:

O642
O614.4

TrendMD:

HU Biao, ZHOU Peng, PAN Chengling, DU Yong, LIU Shuhong, LI Yiwei, HAN Jiangjun. Theoretical Study on the Binary Phase Diagrams of the Zr-X (X=Li, Na, K, Sc, Hf) Systems^†[J]. Chem. J. Chinese Universities, 2015, 36(10): 1939.

Figures/Tables 7

Table 1 Summary of the thermodynamic parameters in the Zr-X(X=Li, Na, K, Sc, Hf) systems

System	Phase	Model	Thermodynamic parameter/(J·mol^-1)
Zr-Li	Liquid	(Li, Zr)₁	⁰ $L Li, Zr Liquid$ =92517
	(Li, βZr)	(Li, Zr)₁Va₃	⁰ $L Li, Zr : Va (Li, βZr)$ =108305
	(αZr)	(Li, Zr)₁Va_0.5	⁰ $L Li, Zr : Va (αZr)$ =89754
	Gas	(Li, Li₂, Zr, Zr₂)₁	⁰ $G Li Gas$ =RTln(P)+GASLI(T)
			⁰ $G L i 2 Gas$ =RTln(P)+GASLI2(T)
			⁰ $G Zr Gas$ =RTln(P)+GASZR(T)
			⁰ $G Z r 2 Gas$ =RTln(P)+GASZR2(T)
Zr-Na	Liquid	(Na, Zr)₁	⁰ $L Na, Zr Liquid$ =59106.339
	(Na,βZr)	(Na, Zr)₁Va₃	⁰ $L Na, Zr : Va (Na, βZr)$ =74883.736
	(αZr)	(Na, Zr)₁Va_0.5	⁰ $L Na, Zr : Na (αZr)$ =181544.538
	Gas	(Na, Na₂, Zr, Zr₂)₂	⁰ $G Na Gas$ =RTln(P)+GASNA(T)
			⁰ $G N a 2 Gas$ =RTln(P)+GASNA2(T)
			⁰ $G Zr Gas$ =RTln(P)+GASZR(T)
			⁰ $G Z r 2 Gas$ =RTln(P)+GASZR2(T)
Zr-K	Liquid	(K, Zr)₁	⁰ $L K, Zr Liquid$ =52775.945
	(K,βZr)	(K, Zr)₁Va₃	⁰ $L K, Zr : Va (K, βZr)$ =65916.68
	(αZr)	(K, Zr)₁Va_0.5	⁰ $L K, Zr : Na (αZr)$ =125195.31
	Gas	(K, K₂, Zr, Zr₂)₁	⁰ $G K Gas$ =RTln(P)+GASK(T)
			⁰ $G K 2 Gas$ =RTln(P)+GASK2(T)
			⁰ $G Zr Gas$ =RTln(P)+GASZR(T)
			⁰ $G Z r 2 Gas$ =RTln(P)+GASZR2(T)
Zr-Sc	(βZr, βSc)	(Sc,Zr)₁Va₃	⁰ $L Sc, Zr : Va (βZr, βSc)$ =-6048.834+4.4931T
	(αZr, αSc)	(Sc,Zr)₁Va_0.5	⁰ $L Sc, Zr : Na (αZr, αSc)$ =-10689.553+5.8839T
Zr-Hf	Liquid	(Hf,Zr)₁	⁰ $L Hf, Zr Liquid$ =-1467.872
			¹ $L Hf, Zr Liquid$ =-558.748
	(αZr, αHf)	(Hf,Zr)₁Va_0.5	⁰ $L Hf, Zr : Na (αZr, αHf)$ =832.587
			¹ $L Hf, Zr : Na (αZr, αHf)$ =104.255

Table 1 Summary of the thermodynamic parameters in the Zr-X(X=Li, Na, K, Sc, Hf) systems

System	Phase	Model	Thermodynamic parameter/(J·mol^-1)
Zr-Li	Liquid	(Li, Zr)₁	⁰ $L Li, Zr Liquid$ =92517
	(Li, βZr)	(Li, Zr)₁Va₃	⁰ $L Li, Zr : Va (Li, βZr)$ =108305
	(αZr)	(Li, Zr)₁Va_0.5	⁰ $L Li, Zr : Va (αZr)$ =89754
	Gas	(Li, Li₂, Zr, Zr₂)₁	⁰ $G Li Gas$ =RTln(P)+GASLI(T)
			⁰ $G L i 2 Gas$ =RTln(P)+GASLI2(T)
			⁰ $G Zr Gas$ =RTln(P)+GASZR(T)
			⁰ $G Z r 2 Gas$ =RTln(P)+GASZR2(T)
Zr-Na	Liquid	(Na, Zr)₁	⁰ $L Na, Zr Liquid$ =59106.339
	(Na,βZr)	(Na, Zr)₁Va₃	⁰ $L Na, Zr : Va (Na, βZr)$ =74883.736
	(αZr)	(Na, Zr)₁Va_0.5	⁰ $L Na, Zr : Na (αZr)$ =181544.538
	Gas	(Na, Na₂, Zr, Zr₂)₂	⁰ $G Na Gas$ =RTln(P)+GASNA(T)
			⁰ $G N a 2 Gas$ =RTln(P)+GASNA2(T)
			⁰ $G Zr Gas$ =RTln(P)+GASZR(T)
			⁰ $G Z r 2 Gas$ =RTln(P)+GASZR2(T)
Zr-K	Liquid	(K, Zr)₁	⁰ $L K, Zr Liquid$ =52775.945
	(K,βZr)	(K, Zr)₁Va₃	⁰ $L K, Zr : Va (K, βZr)$ =65916.68
	(αZr)	(K, Zr)₁Va_0.5	⁰ $L K, Zr : Na (αZr)$ =125195.31
	Gas	(K, K₂, Zr, Zr₂)₁	⁰ $G K Gas$ =RTln(P)+GASK(T)
			⁰ $G K 2 Gas$ =RTln(P)+GASK2(T)
			⁰ $G Zr Gas$ =RTln(P)+GASZR(T)
			⁰ $G Z r 2 Gas$ =RTln(P)+GASZR2(T)
Zr-Sc	(βZr, βSc)	(Sc,Zr)₁Va₃	⁰ $L Sc, Zr : Va (βZr, βSc)$ =-6048.834+4.4931T
	(αZr, αSc)	(Sc,Zr)₁Va_0.5	⁰ $L Sc, Zr : Na (αZr, αSc)$ =-10689.553+5.8839T
Zr-Hf	Liquid	(Hf,Zr)₁	⁰ $L Hf, Zr Liquid$ =-1467.872
			¹ $L Hf, Zr Liquid$ =-558.748
	(αZr, αHf)	(Hf,Zr)₁Va_0.5	⁰ $L Hf, Zr : Na (αZr, αHf)$ =832.587
			¹ $L Hf, Zr : Na (αZr, αHf)$ =104.255

Table 2 Calculated invariant equilibria in the Zr-X(X=Li, Na, K, Sc) systems compared with literature data

System	Invariant reaction	Temperature/℃	System	Invariant reaction	Temperature/℃
Zr-Li	Gas+Liquid#2=(βZr)	1854.1(1855^[4])	Zr-Na	Liquid#1+(αZr)=(Na)	97.7(98^[5])
	Gas+(βZr)=Liquid#1	1338.3(1342^[4])	Zr-K	Gas+Liquid#2=(βZr)	1853.8(1855^[6])
	Liquid#1+(βZr)=(αZr)	865.9(863^[4])		Gas+(βZr)=(αZr)	865.2(863^[6])
	Liquid#1+(αZr)=(Li)	180.6(180^[4])		Gas+(αZr)=Liquid#1	761.2(779^[6])
Zr-Na	Gas+Liquid#2=(βZr)	1854(1855^[5])		Liquid#1+(αZr)=(K)	63.7(64^[6])
	Gas+(βZr)=Liquid#1	885.4(882^[5])	Zr-Sc	(αZr, αSc)=(βZr, βSc)	1407.4(1410^[7])
	Liquid#1+(βZr)=(αZr)	865.3(863^[5] )

Fig.1 Calculated phase diagram of Zr-Li

Fig.2 Calculated phase diagram of Zr-Na

Fig.3 Calculated phase diagram of Zr-K

Fig.4 Calculated phase diagram of Zr-Sc and the experimental data

Fig.5 Calculated phase diagram of Zr-Hf and the experimental data

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