Ma Zhaohui;Yan Guoqing;Yan Xiao;Wu Gang;Chen Weidong;Wang Lijun;

• 1:GRINM Resources and Environment Tech.Co.
• 2: Ltd.
• 3:Zhongyuan Critical Metals Laboratory

Abstract：

As an efficient and environmentally friendly pyrometallurgical separation technology for zirconium and hafnium,molten salt distillation boasts significant advantages over the traditional hydrometallurgical solvent extraction process,such as a shorter process flow,lower cost,and less pollution.It achieves the separation of ZrCl_4 and HfCl_4 by leveraging the difference in vapor pressure between zirconium and hafnium chlorides in molten salt.Potassium chloroaluminate(KAlCl_4) is currently the most widely used distillation molten salt system,characterized by a low melting point,good fluidity,low vapor pressure,and high solubility for zirconium and hafnium chlorides.Thermodynamic parameters of zirconium and hafnium chlorides(ZrCl_4,HfCl_4) in this molten salt system,including vapor pressure and activity coefficient,are crucial basic data for conducting research on distillation mechanisms and processes.In this study,experimental data on the vapor pressure of ZrCl_4 and HfCl_4 in KAlCl_4(with mole fractions ranging from 0.165 to 0.300 and temperatures from 463 to 621 K) retrieved from literature were used to analyze and evaluate the thermodynamic properties of zirconium and hafnium chlorides in KAICl_4 molten salt under distillation conditions(623～773 K).The calculation results showed that the relationships between the vapor pressure of zirconium and hafnium chlorides in KAlCl_4 molten salt and temperature conformed to the Antonie equation with C=0.The correlation coefficients(R~2) of the Antonie fitting equations under different mole fractions were all greater than 0.9883,and this equation could be used to accurately predict the vapor pressure of ZrCl_4 and HfCl_4 at the same mole fractions within the temperature range of 623～773 K.Linear fitting was performed on the logarithms of mole fractions and vapor pressures of ZrCl_4 and HfCl_4 in the temperature range of 46.3～773 K.The results indicated that within 513～613 K,the correlation coefficients of the fitting equations for ZrCl_4 and HfCl_4 were greater than 0.95,showing a high degree of fitting,and the molten salt behaved as an ideal solution.Once the temperature deviated from this range,the correlation coefficient decreased significantly,and the solution no longer met the criteria of an ideal solution.For the non-ideal KAlCl_4-Zr(Hf)Cl_4 solution,the activity coefficients of ZrCl_4 and HfCl_4 in KAlCl_4 molten salt(with mole fractions of 0.165～0.300 and temperatures of 623～773 K) were calculated using Raoult's Law,based on the vapor pressure of pure ZrCl_4 and HfCl_4 and combined with the fitting results of the Antonie equation.On the whole,the activity coefficient increased with the increase of mole fraction;however,at the same mole fraction,it decreased as the temperature rose.Thermodynamic models including the Regular Solution model,Symmetric/Asymmetric Margules model,Van Laar model,and Redlich-Kister model were respectively used to fit and analyze the activity coefficients(f) and mole fractions(x) of zirconium and hafnium chlorides in KAlCl_4 molten salt.The results showed that the correlation coefficients of the fitting equations for the Regular Solution model and the Symmetric Margules model ranged from 0.8235 to 0.8353 and 0.7486 to 0.8114,respectively;the correlation coefficients of the Asymmetric Margules model were 0.6615～0.6834 and 0.5649～0.6392,respectively;and the fitting results of the Van Laar model failed to converge.None of the above models could well describe the relationship between mole fraction and activity coefficient.The Redlich-Kister(R-K) model was used for second-order and third-order expansions respectively to fit the mole fractions and activity coefficients of ZrCl_4 and HfCl_4.The results showed that the correlation coefficients for the degree of fitting of the second-order expansion are 0.8641～0.8752 and 0.8093～0.8506,while those of the third-order fitting equations decreased to 0.7778～0.8139 and 0.7463～0.7901.Generally,the correlation coefficient increased with the increase of the expansion order,but the inverted fitting results of the second and third orders in this study indicated the occurrence of the "overfitting-underfitting trade-off" problem.In this study,a method of "selective introduction of high-order terms" was adopted to modify the third-order expansion model:instead of setting an independent coefficient for the third-order term(B_2),B_2 was set equal to a multiple of the second-order term coefficient(B_1).When fitting the activity coefficient of ZrCl_4,setting the high-order term B_2=0.55B_1;and when fitting the activity coefficient of HfCl_4,setting B_2=0.65B_1 could maximize the correlation coefficients,which reach 0.8887～0.9067 for ZrCl_4 and 0.8731～0.8945 for HfCl_4,respectively.Residual analysis was used to analyze the errors of the fitting results of the R-K third-order expansion model with "selective introduction of high-order terms".The results showed that the residual sum of squares(RSS)of the fitting equation for the activity coefficient of ZrCl_4 ranged from 0.1166 to 0.2324,with a relative error(σ) of 10.15%～11.12%;the RSS of the fitting equation for the activity coefficient of HfCl_4 ranged from 0.1489 to 0.4443,with a σ value of 10.88%～12.31%.The linear fitting equation of activity and vapor pressure calculated using the R-K model achieved a correlation coefficient of 0.9395～0.9598,compared to the range of 0.5426～0.7202 obtained from the mole fraction fitting.With an average relative error of 6.99%～8.29%,the accuracy of the predicted data was significantly improved.Based on the findings of this study,the prediction and calculation of the vapor pressure of zirconium and hafnium chlorides in KAlCl_4 molten salt under different distillation conditions had been realized from a theoretical perspective.This provided important basic data support and theoretical reference for the optimization and design of the molten salt distillation separation process for zirconium and hafnium,the researc

Key Words： zirconium-hafnium separation;molten salt rectification;thermodynamics;vapor pressure;activity coefficient

Abstract:

Keywords:

Foundation: 国家重点研发计划项目（2023YFC2908103）;; 中原关键金属实验室开放基金项目（GJJSKFZD202406）资助

Authors: Ma Zhaohui;Yan Guoqing;Yan Xiao;Wu Gang;Chen Weidong;Wang Lijun;

DOI: 10.13373/j.cnki.cjrm.XY25080017

References：

• [1]Xu L,Xiao Y,Sandwijk A V,Xu Q,Yang Y.Production of nuclear grade zirconium:a review[J].Journal of Nuclear Material,2022,466:21.
• [2]Xiong B K.Application of hafnium[J].Rare Metals Letter,2005,24(9):46.（熊炳昆.金属铪的应用[J].中国材料进展，2005,24(9):46.）
• [3]Wang F,Wang K S,Ma L S,Zhang B,Kong L,Lin ZX.Research status and development prospects of nucleargrade zirconium and zirconium alloys[J].Ordnance Material Science and Engineering,2012,35(1):107.（王峰，王快社，马林生，张兵，孔亮，林兆霞.核级锆及锆合金研究状况及发展前景[J].兵器材料科学与工程，2012,35(1):107.）
• [4]Ma Z H,Zhou Y H,Yan G Q,Zhang J D,Wu YK,Zhang S L,Wang L J.Solid state deoxidation of zirconium-oxygen solid solution using a combination of metallic Ca and Y in CaCl2 flux[J].Journal of Alloys and Compounds,2022,919:165809.
• [5]Ma Z H,Liu H,Yan G Q,Zhang J D,Zhang S L,Wang L J.Solid state deoxidation of metal Ti and Zr using external gettering[J].Chinese Journal of Rare Metals,2022,46(9):1215.（马朝辉，刘海，闫国庆，张建东，张顺利，王力军.外部吸收法脱除金属钛，锆中的氧[J].稀有金属，2022,46(9):1215.）
• [6]Zhen S H,Zhao Z,Chai Y Q.Research progress on pyrometallurgical separation technology of zirconium and hafnium[J].Rare Metals and Cemented Carbides,2017,45(2):6.（郑仕鸿，赵卓，柴延全.火法分离锆铪技术的研究进展[J].稀有金属与硬质合金，2017,45(2):6.）
• [7]Liu H,Ma Z H,Huang J C,Zhang J D,Yan GQ,Wang L J.Preparation of Al-Hf master alloy by aluminothermic reduction of HfO2[J].Rare Metals,2021,(40):3645.
• [8]Bai W,Wang W K,Yan G Q,Zhang J D,Wang L J.Phase structure and residual stress of zirconium hydride with different hydrogen contents[J].Chinese Journal of Rare Metals,2024,48(1):138.（白伟，王文科，王智辉，闫国庆，张建东，王力军.氢含量对氢化锆相结构和残余应力的影响[J].稀有金属，2024,48 (1):138.）
• [9]Qi S,Ma Z H,Yan G Q,Wang Z H,Wang L J.Hydrogen permeation rate of coating zirconium hydride moderator-a prediction model[J].International Journal of Energy Research,2021,45(10):14710.
• [10]Ikeda K,Moriwaki H,Ohkubo Y,Iwasaki T,Konashi K.Application of hafnium hydride control rod to large sodium cooled fast breeder reactor[J].Nuclear Engineering and Design,2014,278:97.
• [11]Wu M,Wu J Y,Zhou D D,Qu J,He Z Y,Zhang Z Y,Chi R A,Wang L J,Xu Z G.Advances in basic research on solution chemistry for Zr-Hf extraction and separation system[J].Chinese Journal of Rare Metals,2025,49(6):949.（吴明，吴净昀，周多多，瞿军，何正艳，张臻悦，池汝安，王力军，徐志高.锆铪萃取分离体系溶液化学基础研究进展[J].稀有金属，2025,49(6):949.）
• [12]Akcaglar S.Separation of zirconium and hafnium tetrachloride from the nuclear power reactors using a distillation column with NaCl-KCl salt mixtures[J].Chemistry Research Journal,2019,4(1):106.
• [13]Wang L,Xu Y,Sun H F,Liu M,Chen X F,Zhang X,Yu L.Determination of Zr and Hf in zirconium sand by inductively coupled plasma atomic emission spectroscopy[J].Chinese Journal of Analysis Laboratory,2025,44(5):757.（王立，徐悦，孙海峰，刘美，陈雄飞，张晓，于磊.电感耦合等离子体发射光谱法测定锆英砂中锆和铪含量[J].分析试验室，2025,44 (5):757.）
• [14]Xu Z G,Wu Y K,Zhang J D,Wang X,Zhang L,Wang L J.Research progress in separation technique of zirconium and hafnium[J].Chinese Journal of Rare Metals,2010,34(3):444.（徐志高，吴延科，张建东，王鑫，张力，王力军.锆铪分离技术的研究进展[J].稀有金属，2010,34(3):444.）
• [15]Jung Y M,Kim G M,Lee M.Measurement of bubble point pressures of zirconium and hafnium tetrachloride mixture for zirconium tetrachloride purification process[J].International Journal of Chemical Engineering and Applications,2012,3(6):427.
• [16]Niselson L A,Egorov E A,Chuvilina E L,Arzhatkina OA,Fedorov V D.Solid-liquid and liquid-vapor equilibria in the Zr(Hf)Cl4-KAl Cl4 systems:a basis for the extractive distillation separation of zirconium and hafnium tetrachlorides[J].Journal of Chemical&Engineering Data,2009,54(3):726.
• [17]Minh L Q,Long N V D,Duong P L T,Jung Y,Bahadori A,Lee M.Design of an extractive distillation column for the environmentally benign separation of zirconium and hafnium tetrachloride for nuclear power reactor applications[J].Energies,2015,8(9):10354.
• [18]Kim J D,Spink D R.Vapor pressure in systems sodium chloride-potassium chloride (8:29 molar)-zirconium tetrachloride and sodium chloride-potassium chloride (8:29 molar)-hafnium tetrachloride[J].Journal of Chemical and Engineering Data,1974,19:36.
• [19]Eaton R B.Process for separating hafnium tetrachloride from zirconium tetrachloride[P].US:2744060,1956.
• [20]Scheller W.Process for the fractional distillation of inorganic halides[P].US:2928722,1960.
• [21]Me Laughlin D F,Stoltz R A.Zirconium and hafnium tetrachloride separation by extractive distillation with molten zinc chloride lead chloride solvent[P].US:4737244,1988.
• [22]Tangri R P,Bose D K,Gupta C K.Vapor pressure of ZrCl4 and HfCl4 over melt systems KCl+AlCl3 (1:1.04 mol)+ZrCl4 and KCl+AlCl3 (1:1.04 mol)+HfCl4[J].Journal of Chemical and Engineering Data,1995,40:823.
• [23]Antoine M C.Nouvelle relation entre les tensions et les temperatures[J].Comptes rendus hebdomadaires des séances de l??Académie des sciences,1888,107:681.
• [24]Minh L Q,Long N V D,Duong P L T,Jung Y,Bahadori A,Lee M.Design of an extractive distillation column for the environmentally benign separation of zirconium and hafnium tetrachloride for nuclear power reactor applications[J].Energies,2015,8:10354.
• [25]Ma Z H,Chen W D,Yan X,Wang L J,Yan G Q,Wu G,Zhang J D,Zhang S L.Process design of molten salt distillation separation of ZrCl4 and HfCl4 for nuclear purposes[J].Separation and Purification Technology,2025,364:132620.
• [26]Mallikarjunan R,Sehra J C.Pyrometallurgical processes for the separation of hafnium from zirconium[J].Bulletin of Materials Science,1989,12:407.
• [27]Ma Z H,Zhang J D,Yan G Q,Liu H,Huang J C,Wang L J.Thermodynamic properties of zirconium-oxygen solid solution and its deoxidation in calcium chloride molten salt[J].Journal of Alloys and Compounds,2019,810:151964.
• [28]Asvestas D A,Pint P,Flengas S N.Some thermodynamic properties of the solutions of ZrCl4 and HfCl4 in CsCl melts[J].Canadian Journal of Chemistry,1977,55:1154.
• [29]Hildebrand J H.A critique of the theory of solubility of nonelectrolytes[J].Chemical Reviews,1949,44(1):37.
• [30]Sundman B，??gren J.A regular solution model for phases with several components and sublattices,suitable for computer applications[J].Journal of Physics and Chemistry of Solids,1981,42(4):297.
• [31]Tomiska J,Neckel A.The Margules concept:the basis of modern algebraic representations of thermodynamic excess properties[J].Journal of Phase Equilibria,1996,17:11.
• [32]Luberti M,Mennitto R,Brandani S,Santori G,Sarkisov L.Activity coefficient models for accurate prediction of adsorption azeotropes[J].Adsorption,2021,27(8):1191.
• [33]Prausnitz J M.Thermodynamics and the other chemical engineering sciences:old models for new chemical products and processes[J].Fluid phase equilibria,1999,158:95.
• [34]Redlich O,Kister A T.Algebraic representation of thermodynamic properties and the classification of solutions[J].Industrial&Engineering Chemistry,1948,40(2):345.