合金元素在Mo中的活度和溶解度
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摘要
基于Miedema模型及其相关物性参数研究合金元素在Mo中的活度和溶解度,并将预测结果与第一性原理计算及其他经验方法的结果进行比较。结果表明:合金元素在Mo中的活度随着温度及合金元素浓度的增加而增大;在相同浓度条件下,主族元素Ge、Al和Si在Mo中的活度较小,过渡族元素Ti、Hf、Nb、Zr和Re等活度较大,后者往往成为钼基合金的主要合金化元素。溶解度研究表明,合金元素在Mo中的溶解度受到原子尺寸因素、电子密度因素和电负性因素的影响,而合金元素在Mo中的溶解热则是后两个因素的综合反映。以溶解热和原子尺寸参数为横纵坐标建立Miedema-Alonso图发现,其与Mo原子尺寸差异小于15%,且在Mo中溶解热在-20～20 kJ/mol之间的合金元素有望在Mo中获得较大的溶解度。
The activity and solubility of alloying elements in Mo were investigated by using Miedema's model and its related physical parameters, and these results were compared with the results predicted by the first-principle calculations and other's empirical approach. These results show that the activity of alloying elements in Mo increases with the increasing temperature and alloying concentration. Under the same concentrations, the activities of main group elements Ge, Al and Si in Mo are small, and the activities of transition elements Ti, Hf, Nb, Zr, and Re are relatively large, which the latter should be chosen as the main alloying elements of Mo-based alloys. The solubility results also point out that the solubility of alloying element in Mo is influenced by atomic size factor, electron density factor, and electronegativity factor. And the solution heat of alloying elements in Mo is a comprehensive reflection of the last two factors.Furthermore, Miedema-Alonso plot was established by using the solution heat of alloying elements in Mo and atomic size parameters as the horizontal and vertical coordinates, respectively. It is found that the alloying element, which its atomic difference from Mo is smaller than 15% and its solution heat in Mo lies in the rang from-20 to 20 kJ/mol always has large respectively solubility limit in Mo.
The activity and solubility of alloying elements in Mo were investigated by using Miedema's model and its related physical parameters, and these results were compared with the results predicted by the first-principle calculations and other's empirical approach. These results show that the activity of alloying elements in Mo increases with the increasing temperature and alloying concentration. Under the same concentrations, the activities of main group elements Ge, Al and Si in Mo are small, and the activities of transition elements Ti, Hf, Nb, Zr, and Re are relatively large, which the latter should be chosen as the main alloying elements of Mo-based alloys. The solubility results also point out that the solubility of alloying element in Mo is influenced by atomic size factor, electron density factor, and electronegativity factor. And the solution heat of alloying elements in Mo is a comprehensive reflection of the last two factors.Furthermore, Miedema-Alonso plot was established by using the solution heat of alloying elements in Mo and atomic size parameters as the horizontal and vertical coordinates, respectively. It is found that the alloying element, which its atomic difference from Mo is smaller than 15% and its solution heat in Mo lies in the rang from-20 to 20 kJ/mol always has large respectively solubility limit in Mo.
引文
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[14]卜晓兵,李落星,张立强,朱必武,徐戎,王水平.Al-2%Cu二元合金微观组织模拟中液相扩散系数的计算[J].中国有色金属学报,2013,23(5):1189-1194.BU Xiao-bing,LI Luo-xing,ZHANG Li-qiang,ZHU Bi-wu,XURong,WANG Shui-ping.Calculation of liquid phase diffusion coefficient in microstructure simulation of Al-2%Cu binary alloy[J].The Chinese Journal of Nonferrous Metals,2013,23(5):1189-1194.
[15]CHEN Song,GUO Shu-qiang,JIANG Lan,XU Yu-ling,DINGWei-zhong.Thermodynamic of selective reduction oflaterite ore by reducing gases[J].Transactions of Nonferrous Metals Society of China,2015,25(9):3133-3138.
[16]COTTURA M,CLOUET E.Solubility in Zr-Nb alloys from first-principles[J].Acta Materialia,2018,144:21-30.
[17]WANG Y,GAO H,HAN Y,DAI Y,WANG J,SUN B.First-principles study on the solubility of iron in dilute Cu-Fe-Xalloys[J].Journal of Alloys and Compounds,2017,691:992-996.
[18]HUME-ROTHERY W,MABBOT G W,CHANNEL-EVANS KM.The freezing points,melting points,and solid solubility limits of the alloys of silver and copper with the elements of the BSub-Groups[J].Philosophical Transactions of the Royal Society of London A,1934,233:1-97.
[19]CALVO-DAHLBORG M,BROWN S G R.Hume-Rothery for HEA classification and self-organizing map for phases and properties prediction[J].Journal of Alloys and Compounds,2017,724:353-364.
[20]MIZUTANI U,SATO H,INUKAI M,ZIJLSTRA E S.Theoretical foundation for the Hume-Rothery electron concentration rule for structurally complex alloys[J].Acta Physica Polonica A,2014,126(2):531-534.
[21]MIZUTANI U,SATO H,INUKAI M,NISHINO Y,ZIJLSTRAE S.Electrons per atom ratio determination and Hume-Rothery electron concentration rule for p-based polar compounds studied by FLAPW-fourier calculations[J].Inorganic Chemistry,2015,54(3):930-946.
[22]DARKEN L S,GURRY R W.Physical chemistry of metals[M].New York:McGraw-Hill,1953.
[23]MAE Y.What the Darken-Gurry plot means about the solubility of elements in metals[J].Metallurgical and Materials Transactions A,2016,47(12):6498-6506.
[24]CHELIKOWSKY J R.Solid solubilities in divalent alloys[J].Physical Review B,1979,19(2):686-701.
[25]ALONSO J A,SIMOZAR S.Prediction of solid solubility in alloys[J].Physical Review B,1980,22(12):5583-5589.
[26]DE BOER F R,BOOM R,MATTENS W C M,MIEDEMA A R,NIESSEN A K.Cohesion in metals[M].Amsterdam:NorthHolland,1988.
[27]KRESSE G,FURTHMULLER J.Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J].Physical Review B,1996,54(16):11169-11186.
[28]PERDEW J P,BURKE K M,EMZERHOF M.Generalized gradient approximation made simple[J].Physical Review Letters,1996,77(18):3865-3868.
[29]KRESSE G,JOUBERT J.From ultrasoft pseudopotentials to the projector augmented-wave method[J].Physical Review B,1999,59(3):1758-1775.
[30]MONKHORST H J,PACK J D.Special points for Brillouin-zone integrations[J].Physical Review B,1976,13(12):5188-5192.
[31]OKAMOTO H.Desk handbook:Phase diagram for binary alloys[M].2nd ed.Russell,OH:ASM International,2010.
[32]FANG S S,LIN G W,ZHANG J L,ZHOU Z Q.The maximum solid solubility of the transition metals in palladium[J].International Journal of Hydrogen Energy,2002,27(3):329-332.
[2]YANG L,ZHANG Q,HE Z,LI X.Influences of HfC particles on microstructure,mechanical properties and ablation resistance at elevated temperature of Mo-15W-HfC alloys[J].International Journal of Refractory Metals and Hard Materials,2017,67:56-67.
[3]DANISMAN C B,YAVAS B,YUCEL O,SAHIN F,GOLLERG.Processing and characterization of spark plasma sintered TZM alloy[J].Journal of Alloys and Compounds,2016,685:860-868.
[4]LENCHUK O,ROHRER J,ALBE K.Solubility of zirconium and silicon in molybdenum studied by first-principles calculations[J].Scripta Materialia,2015,97:1-4.
[5]LI W,ZHANG G,WANG S,LI B,SUN J.Ductility of Mo-12Si-8.5B alloys doped with lanthanum oxide by the liquid-liquid doping method[J].Journal of Alloys and Compounds,2015,642:34-39.
[6]成会朝,范景莲,卢明园,李鹏飞,田家敏.高强韧Mo-0.1Zr合金的制备、性能及组织[J].中国有色金属学报,2012,22(1):114-120.CHENG Hui-chao,FAN Jing-lian,LU Ming-yuan,LI Peng-fei,TIAN Jia-min.Preparation,performance and structure of high tenacious Mo-0.1Zr alloy[J].The Chinese Journal of Nonferrous Metals,2012,22(1):114-120.
[7]蓝国强,江勇,江亮.微合金化元素Zr对热障涂层关键界面的强化效应及机理[J].中国有色金属学报,2016,26(9):1967-1975.LAN Guo-qiang,JIANG Yong,JIANG Liang.Strengthening effects and mechanisms of micro-alloying Zr on key interface in thermal barrier coating systems[J].The Chinese Journal of Nonferrous Metals,2016,26(9):1967-1975.
[8]LUO Kang,ZANG Bing,FU Shang,JIANG Yong,YI Dan-qing.Stress/strain aging mechanisms in Al alloys from first principles[J].Transactions of Nonferrous Metals Society of China,2014,24(7):2130-2137.
[9]JIANG Y,SMITH J R,EVANS A G.Temperature dependence of the activity of Al in dilute Ni(Al)solid solutions[J].Physical Review B 2006,74(22):224110.
[10]MIEDEMA A R,DE CH?TEL P F,DE BOER F R.Cohesion in alloys-fundamentals of a semi-empirical model[J].Physica B,1980,100(1):1-28.
[11]SUN S P,YI D Q,LIU H Q,ZANG B,JIANG Y.Calculation of glass forming ranges in Al-Ni-RE(Ce,La,Y)ternary alloys and their sub-binaries based on Miedema’s model[J].Journal of Alloys and Compounds,2010,506(1):377-387.
[12]孙顺平,易丹青,臧冰.基于Miedema模型和Toop模型的Al-Si-Er合金热力学参数计算[J].稀有金属材料与工程,2010,39(11):1974-1978.SUN Shun-ping,YI Dan-qing,ZANG Bing.Calculation of thermodynamic parameters of Al-Si-Er alloy based on Miedema’s model and Toop model[J].Rare Metal Materials and Engineering,2010,39(11):1974-1978.
[13]孙顺平,李小平,卢雅琳,李勇,黄道远,易丹青.基于Miedema模型Al3X金属间化合物点缺陷形成焓的计算[J].稀有金属材料与工程,2013,42(7):1478-1482.SUN Shun-ping,LI Xiao-ping,LU Ya-lin,LI Yong,HUANGDao-yuan,YI Dan-qing.Calculation of formation enthalpies of point defects for Al3X(Sc,Er,Zr,Li)intermetallics based on Miedema’s model[J].Rare Metal Materials and Engineering,2013,42(7):1478-1482.
[14]卜晓兵,李落星,张立强,朱必武,徐戎,王水平.Al-2%Cu二元合金微观组织模拟中液相扩散系数的计算[J].中国有色金属学报,2013,23(5):1189-1194.BU Xiao-bing,LI Luo-xing,ZHANG Li-qiang,ZHU Bi-wu,XURong,WANG Shui-ping.Calculation of liquid phase diffusion coefficient in microstructure simulation of Al-2%Cu binary alloy[J].The Chinese Journal of Nonferrous Metals,2013,23(5):1189-1194.
[15]CHEN Song,GUO Shu-qiang,JIANG Lan,XU Yu-ling,DINGWei-zhong.Thermodynamic of selective reduction oflaterite ore by reducing gases[J].Transactions of Nonferrous Metals Society of China,2015,25(9):3133-3138.
[16]COTTURA M,CLOUET E.Solubility in Zr-Nb alloys from first-principles[J].Acta Materialia,2018,144:21-30.
[17]WANG Y,GAO H,HAN Y,DAI Y,WANG J,SUN B.First-principles study on the solubility of iron in dilute Cu-Fe-Xalloys[J].Journal of Alloys and Compounds,2017,691:992-996.
[18]HUME-ROTHERY W,MABBOT G W,CHANNEL-EVANS KM.The freezing points,melting points,and solid solubility limits of the alloys of silver and copper with the elements of the BSub-Groups[J].Philosophical Transactions of the Royal Society of London A,1934,233:1-97.
[19]CALVO-DAHLBORG M,BROWN S G R.Hume-Rothery for HEA classification and self-organizing map for phases and properties prediction[J].Journal of Alloys and Compounds,2017,724:353-364.
[20]MIZUTANI U,SATO H,INUKAI M,ZIJLSTRA E S.Theoretical foundation for the Hume-Rothery electron concentration rule for structurally complex alloys[J].Acta Physica Polonica A,2014,126(2):531-534.
[21]MIZUTANI U,SATO H,INUKAI M,NISHINO Y,ZIJLSTRAE S.Electrons per atom ratio determination and Hume-Rothery electron concentration rule for p-based polar compounds studied by FLAPW-fourier calculations[J].Inorganic Chemistry,2015,54(3):930-946.
[22]DARKEN L S,GURRY R W.Physical chemistry of metals[M].New York:McGraw-Hill,1953.
[23]MAE Y.What the Darken-Gurry plot means about the solubility of elements in metals[J].Metallurgical and Materials Transactions A,2016,47(12):6498-6506.
[24]CHELIKOWSKY J R.Solid solubilities in divalent alloys[J].Physical Review B,1979,19(2):686-701.
[25]ALONSO J A,SIMOZAR S.Prediction of solid solubility in alloys[J].Physical Review B,1980,22(12):5583-5589.
[26]DE BOER F R,BOOM R,MATTENS W C M,MIEDEMA A R,NIESSEN A K.Cohesion in metals[M].Amsterdam:NorthHolland,1988.
[27]KRESSE G,FURTHMULLER J.Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J].Physical Review B,1996,54(16):11169-11186.
[28]PERDEW J P,BURKE K M,EMZERHOF M.Generalized gradient approximation made simple[J].Physical Review Letters,1996,77(18):3865-3868.
[29]KRESSE G,JOUBERT J.From ultrasoft pseudopotentials to the projector augmented-wave method[J].Physical Review B,1999,59(3):1758-1775.
[30]MONKHORST H J,PACK J D.Special points for Brillouin-zone integrations[J].Physical Review B,1976,13(12):5188-5192.
[31]OKAMOTO H.Desk handbook:Phase diagram for binary alloys[M].2nd ed.Russell,OH:ASM International,2010.
[32]FANG S S,LIN G W,ZHANG J L,ZHOU Z Q.The maximum solid solubility of the transition metals in palladium[J].International Journal of Hydrogen Energy,2002,27(3):329-332.