An Effectual Way to Construct Phase Diagrams

D0I:10.13374/j.issn1001053x.1991.02.011 第13卷第2期 北京科技大学学报 Vol.13 No.2 1991年3月 Journal of University of Science and Technology Bcijing March 1991 An Effectual Way to Construct Phase Diagrams' Qiao Zhiyu'Liang Jingkui·Rao Guanghui· (乔芝郁) (梁敬魁) (饶光辉) ABSTRACT:It is described that the effectual way to construct phase dia- grams is the combination of computer calculation with some critical measure- ments.Examples of application to the CuO-RE2Os (RE:La,Y,Nd),Na2 B20,K2B20s and PrCl3-CaCl2-MgCl2 systems are given. KEY WORDS:phase diagram,computer calculation,DTA CALPHAD (Computer Calculation of Phase Diagram))technique,deve- loped very quickly over the past fifteen years,is of great significance to the phase diagram construction.But,mainly due to the lack of thermodynamic data,especially excess thermodynamic data and the difficulty for predicting new phase formation in the investigated systems,it is still difficult to calculate phase diagrams of lots of unknown systems which have potential application to high technology.Thus,from our point of view,the effectual way to construct phase diagram is the combination of computer calculation and experi- mental measurements.The limited phase diagram data obtained by DTA,X- ray diffraction and other technigues could be used to predict ihermodynamic parameters according to a given model.Then,the whole phase diagram can be caculated by computer.It is clear that this method is time and money saving. The available phase diagram should be more reliable and thermodynamically self consistent with thermody namic data.Particularly,this method is crucial 1990-07-11收稿 The Project Supported by National Natural Science Foundation of China 理化系(Department of Physical Chemistry) ..Institute of Physics,Acadcmia Sinica,Bcijing 154

第 卷第 期 年 月 北 京 科 技 大 学 学 报 一 — 一一 一 一 一 一 一 一 一 一 一 一 一一 一 一一 一一 一 一 一 一 月 一一一一 ‘ ， 乔芝郁 ‘ ” 夕 ” 梁敬魁 夕 ， ， 饶光辉 扭 扭 一 ‘ ， 一 一 丁 ， ， ， ， ， 。 〔 ‘ 〕 ， 、 ， 。 ， ， ， · ， ， · ， 七 · ， ， 一 一 收稿 洛 辛 理化 系 ， ， DOI ：10．13374／j ．issn1001—053x．1991．02．011

in the construction of ternary and higher order phase diagrams. 1 CuO-RE203 (RE:Rare Earths)Systems Since the discovery of high Tc Ba-La(Y)-Cu-O systems,the study on superconducting materials has come to a new stage.The characteristics of Ba-La(Y)-Cu oxide superconducting materials is sensitively related to the technology of the materials.It is out of question that the study on the BaO- La2O:(Y2O3)-CuO ternary phase diagram has great importance for improviag the preparation technology of the materials.As first step of coustructing ternary phase diagram,the determination of the binary phase diagrams of three subsystems is necessary.Up to now,there are few reported phase diagrams of the CuO-RE2Os in the literature.The reasons are partly due to the high meiting points of the rare earth oxides and the decomposition of CuO at about 1000C.An accurate determination of the CuO-RE2Os binary phase diagrams becomes quite difficult.Furthermore,there are quite few of thermodynamic data of the CuO-RE2Os systems for calculating phase diagrams.Thus,it is reasonable to construct the phase diagrams of the CuO-RE2Os systems by using combination of critical experimental measurements and computer calculation. Taking CuO-La2O3 for first sample example. First of all,using X-ray diffraction technique we determined that an inco- ngruent compound La2CuO exists in the CuO-La2Os system as shown in Fig.12).The peritectic temperature (1350C),the eutectic temperature(1025C) and some experimental data (solid circles)in the CuO-rich liquidus were determined by DTA technique. Then,the CuO-La2Oa phase diagram was calculaled by regular solution model with ion and equivalent fractions.Because there are no thermodynamic data of the CuO-La2O3 system in the literature,the interaction parameter of regular solution model was derived from our experimental information,especi- ally,invariant point data which are more accurate.The phase diagram was synthesized after approximate ireatment on the decomposition of Cuo at high temperature. In fact,due to the decompoisition of CuO at about 1 025C,the CuO-rich liquidus was the equilibrium between liquid and Cu2O rather than CuO.So in Fig.1,we used the calculated results of CuOo.s-La2CuO.to represent this equilibrium.The calculated phase diagram by such combination agreed with experimental results well.The deviation of liquidus was within about 10C. It meant that this approximate treatment on the decomposition of Cuo could be applied to other binary and ternary systems involving CuO. 155

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2500 2500 2100 L 2100 1.:L8203 1700 LY293 1700 1350℃ L+Cu20 1300 L1C120 L&2CuO 1300 10?5℃ -L+Y2CU2O5- 100气 a2Cu04*L*203 900 900 L82CuO4CHo Y2Cu205+ Y2Cu295+Y20 2Cu2Os La2CuO4 500 0 0 40 60 80100 500L 0 20 40 60 80100 Cuo mol% La203 Cuo mol% Y203 Fig.1 Phase diagram of Cuo-LaaO3 Fig.2 Phase diagram of Cuo-Y2O3 binary system binary system -Calculated, -Calculated, Experimental, Experimental, Decomposition of Cuo .Decomposition of Cuo Using the same method,the CuO-Y203 and CuO-Nd2O3 binary phase diagrams as shown in Fig,2(a)and Fig.3(4)have been constructed very recently.Up to now,superconductivitity has been found in most of the RE- Ba-Cu-C systems (RE=rare earths except Ce,Pr,Tb and Pm).As a syste- matic research work,we plan to construct the phase diagrams of all CuO- RE2O;(RE:rare earths)systems using this method. 2 BaB204-based Systems Many metaborates have potential nonlinear optical properties.For example, barium metaborate is an excellent ultraviolet SHG (Second Harmonic Generator) material.Obviously,the study of the phase diagrams of metaborate systems is significant for the utilization of new metaborate materials and better under- standing of their physico-chemical properties. As one of the systematical study of metaborate phase diagrams,the phase diagrams of the BaB2O.-Na2B2O-K2B2O system and its subsystems were constructed by combination of computer calculation and limited experimental measurements. 156

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1100 2000广 1000 1500 o ExperimeinL --.DoCD 900 16t0 1·2 800 5 】400 一I23 L14'u0 1200 9 700 NdaXJ2Cu L》 1100 600 (L0 800- 20 40 60 80 100 500L 0 Nd2O3 Cuo 20 1o% 60 100 Na2B204 kI320 mol Fig.3 Phase diagram of Nd203 Cuo Fig.4 Phase diagram of Na2B204-K2B204 Taking Na2B2O-K2B2O system as another sample example. 2.1 Experimental Determination of the Na2B204-K2B20,Phase Diagram The phase diagram of Na2B2O,-K2B2O,binary system was firstly deter- mined by means of DTA and X-ray diffraction methods.Just shown in Fig.4, it is a complete solid solution system with minimum melting point at Tm= 836C and Xmin=0.357mol K2B2O.In the figure4."denotes the top temperature of melting peak in DTA curve,4."denotes the extrapolated onset temperature of melting peak.The available results agreed well with those obtained by refe- rencest,).But,the miscibility gap shown in Fig.4 could not be observed using DTA and room temperature X-ray diffraction technique by both Bergman and ourself. 2.2 Computer Calculation of the Na2B20,-K2B20 Phase Diagram Liquidus can generally be determined more accurately than solidus because of the hysteresis of phase transition.Kohler and Pelton suggested a method to calculate solidus from liquidus if the enthalpy and excess entropy of liquidus phase as well as either the enthalpy or excess entropy of the solid phase were known.To apply the method to molten salt system CmXp-DnXr,it is more convenient to introduce ionic fractions Yi and equivalent fractions Zi for representing ideal mixing entropy and excess quantities,respectively. 157

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YA=mXA/(mXA+nXB),Y3=nXBl (mXA+nXB) and ZA=PXA/(pXA+rXB), ZB=rXB/(pXA+rXB) where 4 and B stand for CmXp and DnXr; XA and XB are mole fractions of 4 and B. For L+S equilibrium in binary system,according to the equilibrium condi- tion,we have: △°G:a)+mRTlaYk+△H-TBSk=mRT1nY8+AHR-TES (1) △°G:(B)+nRT1nY台+AHB-TS台=nRT1nY8+AH8-TES8 (2) where Y and y(i=A,B)are ionic fraction along the liquidus and solidus; AH and ES (i=A,B and j=L,S)are the partial molar enthalpies and excess entropies of the components in the liquid and solid phase; △°Gta)and△oGr(B)are the standard Gibbs free energies of fusion of pure 4 and B (Table 1) Table 1 Thermodynamic properties of fusion of pure components Components b d e Tm.P.(C) Na2B204 -59031.6 987.88 26.081 -136.377 -18.78 967 K2B204 -58440.4 966.728 25.958 -133.568 -19.031 947 △°Gr=a+6T+c·103T2+dTInT+e·105/T J/mol Differentiating eqs.(1)and (2)with respect to T,we have; FA=mRlnY员-S员+〔mnRT/X8(mX8+nX)+deG8/dX员)dX8/dT (3) FB=nRInY-ES+[mnRT/(mX+nX)+dEG/dxdx/dT (4) where FA and Fa in the left of the eqs.are Fa=-△°S:a)+mRlnY数-ESk+〔mnRT/X(mXk+X)+dG/d xdX/dT (5) FB=-△°St(a)+nRInY台-S路+〔mnRT/X(mX+nX)+dG/dX)dX/dT (6) and EG,EG(i=A,B)are excess partial Gibbs free energy of the components in liquid and solid phases.ASr (A)and ASt (are the molar entropies of fusion of the components. From egs.(3)and (4)and Gibbs-Duhem equation,it follows: XF+XFB=RCmXnY+nnY-S (7) It is clear that if EG,ES and the liquidus are known as function of composition,FA and Fs can be derived after eqs.(5)and (6),then the solidus can be calculated from eg.(7)by iteration.Once the solidus compo- 158

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sition has been computed,eqs.(1)and (2)can be used to calculate the mixing enthalpy of solid phase, △H8=XR△HR+X△H盘 As pointed out above the Na2B2O-K2B2O system is a complete solid solution system with minimum melting point.For such system,the assumption of S=0,G=0 is reasonable.To fulfill the condition of dT/dx=0 at minimum point:Tmn=836C,Xmin=37.5mol %K2B2O,the liquidus were fitted as: Xg=37.5-0.3922√-836-0.2496(t-836)mo1%K2B,04 for Na2B2O-rich,while for K2B20-rich: XB=37.5+2.1799√t-836+1.6579105(t-836) +3.1369103(t-836)2mol%K2B204 where t is liquidus temperature in centigrade.Since T=t+273.15,dT=dt. Thus,the solidus were calculated after eqs.(5)-(7)and shown in Fig.4. The calculated solidus was very close to onset temperature of melting peak of DTA experiment.Generally,the onset temperature of melting peak are ado- pted as solidus temperature approximately for the system with solid solubility. From the calculated solidus and measured liquidus,AHs coud be derived after eqs.(1)and (2).Considering the assumption for this system,the AFs is equal to excess Gibbs free energy of solid phase,G could be fitted by least-square method as: BGa=△H8=XaXB(38638.82-33788.59XB)J1mo1 So the molar Gibbs free energy of the solid phase was: Ga=Xx°G8+XB°G8+2 RTCXAInYA+YalnYB]+EGa (8) From this expression,it is obvious that >In the case of complete solid solution with minimum point,if >0,there often exist a miscibility gap.It was computed and shown in Fig.4. 2.3 High Temperature X-ray Diffraction As mentioned previously,the miscibility gap shown in Fig.4 could not be observed by room temperature X-ray diffraction.The reason may be due to the hydration of specimens.In order to experimentally examine the miscibi- lity gap existence,we did the high temperature X-ray diffraction of pure Na2B2O and K2B2O as well as the specimen containing 44 mol%K2B2O at 500C.The photographs of X-ray diffraction at 500C(5)show that the latter was a mixture of two phases due to the existence of the miscibility gap. Although the lattice parameters of one phase were close to those of NazB2O 159

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while the lattice parameters of the other phase were greater than those of Na2B2Os but smaller than those of K2B2O.Since the lattice parameters of Na2B2Os were a=1,1921nm,c=0.6418nm and those of K2B2Os were a=1.275nm, c=0.733nm.Our high tem perature X-ray diffraction resultss indicated that one of the two phases in mixture was rich in Na2B2O,while the other phase was rich in K2B2O4.Furthermore,the Na:B2Os-rich phase was with smaller solubility,while the KaB2O.rich phase with greater solubility.These behaviors were in agreement with the calculated miscibility gap shown in Fig.4. Although the miscibility gap of solid solution phase in the Na2B2O4- K2B2O,binary system could not be observed in DTA and room temperature X-ray diffraction experiments,it could be theoretically predicted by thermo- dynamical analysis and confirmed by high temperature X-ray diffraction.This is an excellent example to show that the combination of limited experiments and thermodynamical calculation is a powerful way to construct accurate phase diagrams. 3 Rare Earth Chloride Systems Dealing with binary phase diagrams involving rare earth chlorides,not a few papers have been published.But,there are few references related on the ternary phase diagrams of rare earth chloride systems.Obviously,for so large number of possible ternary rare earth chloride systems,it is not only time and money consuming,but also very tedious to measure their phase diagrams one by one. In order to critical assess the binary phase diagrams published in references, lots of binary phase diagrams involving rare earth chlorides have been opti- mized by combination of limited experiments and computer-assisted calcula- tiont10-12).The assessed binary phase diagrams and thermodynamic data with selfconsistency are a better basis for constructing multicomponent phase diagrams. Taking the PrCl,-CaCla-MgCl2 ternary phase diagram as an example,on the basis of critical assessement of its three subsystems,using Li-Qiao modelt1s) or Hillert model(14)as well as taking MgCla as an asymmetric component,the PrCl3-CaCl2-MgCla phase diagram has been calculated.The good agreement between the calculated results and some critical measured data,including ternary eutectic point as well as compositions and temperatures of diflecting points on liquidus in some vertical sections (see Fig.6)showed that the constructed phase diagram is reliable.By combining computer calculation and limited experiments,a series of ternary phase diagrams involving rare earth chloride are being constructed in our group and will be published. 160

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PrCl3 ·Measured data,℃ (from right to left): 622 II 593 1 586 11 546 615c)/ (645℃) 564 650 590 1. 700 人70 11 CaCl2 e1(609C) MgCl2 mol Fig.5 Phase aiagram of ternary system PrCls-CaCla-MgCl2 年 Measured deflecting point on liquidus E-Measured cutectic point (516C) E'-Calculated eutectic point (560C) -Calculated Acknowledgement The authors sincerely thank NSFC and Office of Rare Earth Metals,Mini- stry of metallurgical Industry for financial support. Reference 1 CALPHAD.The International Research Journal for Caculation of Phase Diag rams,Cambridge Massaschusetts,USA,1977-1991 2 Rao G H,Qiao Z Y,Liang J K.Kexue Tongbo,1989,(6):577 3 Rao G H,Qiao Z Y,Liang J K.Journal of the Less-Common Metals, 1988,144:215 4 Chen X L,J K,Liang Xie SS,Qiao Z Y.Journal of the Less-Common Metals,1990,159:147 5 Rao G H,Liang J K,Qiao Z Y.Huang Q Z.CALPHAD,1989,(2):169 6 Rao G H,Qiao Z Y,Liang J L.CALPHAD,1989,(2):177 7 Rao G H.Theses (Doctor of Science),Academia Sinica,1988 8 Bergman A G,et al.Zh.Neorg.Khim.,1957,(2):2641 9 Bergman A G.et al.Zh.Neorg.Khim.,1969,(2):2872 10 Qiao Z Y,Wang M S,Zhen C G,Duan S.Journal of the Chinese Rare Earth Society,1989,(7):16 11 Qiao Z Y,Wang M S,Zhen C G,Duan S.Journal of University of Science and Technology Beijing,1989,(1):597 12 Wang M S.Theses (Master of Science),USTBEIJING,1988 13 Li R Q,Qiao Z Y.Rare Metals,1990,10:18 14 Hillert M,CALPHAD,1980,(4):1 161

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