含柱状包裹体截面晶体实验数据的界面能各向异性计算方法（英文）
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摘要
给出了两种计算界面能各向异性的计算方法.这些方法是基于在定常温度场中温度梯度作用下,通过对含柱状包裹体截面的晶体数值模拟分析而提出的.文中讨论了新方法的误差分析及适用范围.同时,对选择合适的处理含柱状包裹体截面参数给出了一些建议.
Two techniques for calculation of the interfacial energy anisotropy are suggested and examined. The techniques are developed on the basis of analysis of numerical calculations of the shapes of liquid cylindrical inclusions migrating through a crystal under the action of temperature gradient in the case of the stationary thermal conditions. The errors of the suggested techniques and their limits of application are discussed in the paper. Recommendations for selecting the most appropriate cross-sectional areas of cylindrical inclusions for processing are presented.
Two techniques for calculation of the interfacial energy anisotropy are suggested and examined. The techniques are developed on the basis of analysis of numerical calculations of the shapes of liquid cylindrical inclusions migrating through a crystal under the action of temperature gradient in the case of the stationary thermal conditions. The errors of the suggested techniques and their limits of application are discussed in the paper. Recommendations for selecting the most appropriate cross-sectional areas of cylindrical inclusions for processing are presented.
引文
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[4]Gabrisch H,Kjeldgaard L,Johnson E,Dahmen U.Equilibrium shape and interface roughening of small liquid Pb inclusions in solid A1[J].Acta Materialia,2001,49:4259-4269.
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[6]Metois J J,Müller P.Absolute surface energy determination[J].Surface Science,2004,548:13-21.
[7]Müller P,Metois J J.Anisotropy of the surface thermodynamic properties of silicon[J].Thin Solid Films,2008,517:65-68.
[8]Jiang Q,Lu H M.Size dependent interface energy and its applications[J].Surface Science Reports,2008,68:427-464.
[9]Wynblatt P,Chatain D.Surface segregation anisotropy and the equilibrium shape of alloy crystals[J].Reviews on Advanced Materials Science,2009,21:44-56.
[10]Einstein T L.Equilibrium shape of crystals[M]//Nishinaga T.Handbook of Crystal Growth.2nd ed.Boston:Elsevier,2015,1:215-264.
[11]Tran R,Xu Z,Radhakrishnan B,Winston D,Sun W,Persson K A,Ong S P.Surface energies of elemental crystals[J].Scientific Data,2016,3:160080.
[12]Pfann W G.Temperature gradient zone melting[J].Trans AIME,1955,203:961-964.
[13]Pfann W G.Zone Melting[M].New York:Wiley,1958.
[14]Tiller W A.Migration of a liquid zone through a solid:Part I[J].J Appl Phys,1963,34:2757-2762.
[15]Cline H E,Anthony T R.Nonequilibrium morphology of liquid inclusions migrating in solids[J].J Appl Phys,1977,48:5096-5104.
[16]Lozovskii V N,Lunin L S,Popov V P.Temperature-Gradient Zone Recrystallization of Semiconductor Materials[M].Moscow:Metallurgiya,1987(in Russian).
[17]Morillon B,Dilhac J-M,Ganibal C,Anceau C.Study of aluminum thermomigration as a low thermal budget technique for innovative power devices[J].Microelectronics Reliability,2003,43:565-569.
[18]Eslamian M,Saghir M Z.Thermodiffusion applications in MEMS,NEMS and solar cell fabrication by thermal metal doping of semiconductors[J].Fluid Dynamics and Materials Processing,2012,8:353-380.
[19]Li X,Peng P,Liu D,Su Y,Guo J,Fu H.Dendrite coarsening in directionally solidified Sn-36 at.%Ni peritectic alloy in the presence of the migration of secondary dendrite arms[J].Materials Chemistry and Physics,2014,145:203-212.
[20]Garmashov S I,Gershanov V Yu.Velocity and cross-section shape of liquid cylindrical inclusions migrating normally to close-packed planes of a non-uniformly heated crystal under stationary thermal conditions[J].J Cryst Growth,2009,311:413-419.
[21]Gershanov V Yu,Garmashov S I.Facet effect manifestation during crystallization from small volumes of solution in melt[J].Tech Phys Lett,2011,37:640-642.
[22]Gershanov V Yu,Garmashov SI.Theory of kinetic experiment at crystal growth from solutions in melts[M]//Mancuso N A,Isaac J P.Crystal Growth:Theory,Mechanisms and Morphology.New York:Nova Science Publishers,2012:87-124.
[23]Gershanov V Yu,Garmashov S I.Inverse Gibbs-Thomson effect[J].Tech Phys,2015,60:61-65.
[24]Garmashov S I,Surnin V I.A computer model of steady-state cross-sectional shape of migrating liquid cylindrical inclusion through a crystal with account anisotropy of interfacial energyand interface kinetics[C]//Second China-Russia Conference on Numerical Algebra with Applications(CRC-NAA'13).Rostov-on-Don:Southern Federal University Publishing,2013:74-76.
[25]Garmashov S I,Prikhodko Y V.On numerical calculation of shapes of cylindrical inclusions migrating through a crystal for particular case of interfacial energy anisotropy[C]//Fourth China-Russia Conference on Numerical Algebra with Applications(CRC-NAA'15).Rostovon-Don:Southern Federal University Publishing,2015:99-103.
[2]Chernov A.Modern Crystallography III:Crystal Growth[M].Berlin/Heidelberg:SpringerVerlag,1984.
[3]Eaglesham D J,White A E,Feldman L C,Moriya N,Jacobson D C.Equilibrium shape of Si[J].Physical Review Letters,1993,70:1643-1646.
[4]Gabrisch H,Kjeldgaard L,Johnson E,Dahmen U.Equilibrium shape and interface roughening of small liquid Pb inclusions in solid A1[J].Acta Materialia,2001,49:4259-4269.
[5]Bonzel H P.3D equilibrium crystal shapes in the new light of STM and AFM[J].Physics Reports,2003,385:1-67.
[6]Metois J J,Müller P.Absolute surface energy determination[J].Surface Science,2004,548:13-21.
[7]Müller P,Metois J J.Anisotropy of the surface thermodynamic properties of silicon[J].Thin Solid Films,2008,517:65-68.
[8]Jiang Q,Lu H M.Size dependent interface energy and its applications[J].Surface Science Reports,2008,68:427-464.
[9]Wynblatt P,Chatain D.Surface segregation anisotropy and the equilibrium shape of alloy crystals[J].Reviews on Advanced Materials Science,2009,21:44-56.
[10]Einstein T L.Equilibrium shape of crystals[M]//Nishinaga T.Handbook of Crystal Growth.2nd ed.Boston:Elsevier,2015,1:215-264.
[11]Tran R,Xu Z,Radhakrishnan B,Winston D,Sun W,Persson K A,Ong S P.Surface energies of elemental crystals[J].Scientific Data,2016,3:160080.
[12]Pfann W G.Temperature gradient zone melting[J].Trans AIME,1955,203:961-964.
[13]Pfann W G.Zone Melting[M].New York:Wiley,1958.
[14]Tiller W A.Migration of a liquid zone through a solid:Part I[J].J Appl Phys,1963,34:2757-2762.
[15]Cline H E,Anthony T R.Nonequilibrium morphology of liquid inclusions migrating in solids[J].J Appl Phys,1977,48:5096-5104.
[16]Lozovskii V N,Lunin L S,Popov V P.Temperature-Gradient Zone Recrystallization of Semiconductor Materials[M].Moscow:Metallurgiya,1987(in Russian).
[17]Morillon B,Dilhac J-M,Ganibal C,Anceau C.Study of aluminum thermomigration as a low thermal budget technique for innovative power devices[J].Microelectronics Reliability,2003,43:565-569.
[18]Eslamian M,Saghir M Z.Thermodiffusion applications in MEMS,NEMS and solar cell fabrication by thermal metal doping of semiconductors[J].Fluid Dynamics and Materials Processing,2012,8:353-380.
[19]Li X,Peng P,Liu D,Su Y,Guo J,Fu H.Dendrite coarsening in directionally solidified Sn-36 at.%Ni peritectic alloy in the presence of the migration of secondary dendrite arms[J].Materials Chemistry and Physics,2014,145:203-212.
[20]Garmashov S I,Gershanov V Yu.Velocity and cross-section shape of liquid cylindrical inclusions migrating normally to close-packed planes of a non-uniformly heated crystal under stationary thermal conditions[J].J Cryst Growth,2009,311:413-419.
[21]Gershanov V Yu,Garmashov S I.Facet effect manifestation during crystallization from small volumes of solution in melt[J].Tech Phys Lett,2011,37:640-642.
[22]Gershanov V Yu,Garmashov SI.Theory of kinetic experiment at crystal growth from solutions in melts[M]//Mancuso N A,Isaac J P.Crystal Growth:Theory,Mechanisms and Morphology.New York:Nova Science Publishers,2012:87-124.
[23]Gershanov V Yu,Garmashov S I.Inverse Gibbs-Thomson effect[J].Tech Phys,2015,60:61-65.
[24]Garmashov S I,Surnin V I.A computer model of steady-state cross-sectional shape of migrating liquid cylindrical inclusion through a crystal with account anisotropy of interfacial energyand interface kinetics[C]//Second China-Russia Conference on Numerical Algebra with Applications(CRC-NAA'13).Rostov-on-Don:Southern Federal University Publishing,2013:74-76.
[25]Garmashov S I,Prikhodko Y V.On numerical calculation of shapes of cylindrical inclusions migrating through a crystal for particular case of interfacial energy anisotropy[C]//Fourth China-Russia Conference on Numerical Algebra with Applications(CRC-NAA'15).Rostovon-Don:Southern Federal University Publishing,2015:99-103.