“构形力”（configurational force）是经典“变形力”（deformational force）概念的拓展，另外一种常见的叫法是“材料力”（material force），有时也叫“化学力”（chemical force）、“增殖力”（accretive force）或“组分力”（compositional force）等，术语上的多变从侧面反应了“构形力学”（configurational mechanics）新兴交叉学科的特点。J. D. Eshelby在1951年的经典论文“The force on an elastic singularity”（ Phil. Trans. R. Soc. Lond. A , Vol.244, pp.87-112 ）中提出“缺陷上的力”的构想，开创了构形力学研究的先河，更早地，构形力学的思想可以追溯到1891年Burton在 Philosophical Magazine （Vol.33, pp.191-204）上的一篇论文，其中提到了“局部重构”（local structural rearrangement）的概念。晶体中位错线上的Peach-Koehler力、断裂力学中的J-积分等同构形力都有着密切的联系。构形力学中的基本物理量是Eshelby能动量张量，或简称为Eshelby张量、Eshelby应力张量。以下所列是同构形力、能动量张量、化学势、固体热力学等方面相关的一小部分文献，随着视野的深入，将不断增添新的条目...... Monographs: Maugin, G. A., Material Inhomogeneities in Elasticity , Chapman Hall, 1993 Kienzler, R., Herrmann, G., Mechanics in Material Space: with Applications to Defect and Fracture Mechanics , Springer, 2000 Gurtin, M. E., Configurational Forces as Basic Concepts of Continuum Physics , Springer-Verlag New York, Inc., 2000 Grinfeld, M., Thermodynamic Methods in the Theory of Heterogeneous Systems , Longman Scientific Technical, 1991 Epstein, M., Elzanowski, M., Material Inhomogeneities and Their Evolution: A Geometric Approach , Springer-Verlag, 2007 Wilmanski, K., Continuum Thermodynamics Part I: Foundations , World Scientific, 2008 Epstein, M., The Geometrical Language of Continuum Mechanics, Cambridge University Press, 2010 Maugin, G. A., Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics, CRC Press, 2011 Conference Proceedings: Steinmann, P., Maugin, G. A., eds., Mechanics of Material Forces , Springer, 2005 Dascalu, C., Maugin, G. A., Stolz, C., eds., Defect and Material Mechanics , Springer, 2008 Reviews: Maugin, G. A., Material forces: Concepts and applications, Appl. Mech. Rev. , Vol.48, pp.213-245, 1995 Gross, D., Kolling, S., Mueller, R., Schmidt, I., Configurational forces and their application in solid mechanics, Eur. J. Mech. A-Solids , Vol.22, pp.669-692, 2003 Steinmann, P., Scherer, M., Denzer, R., Secret and joy of configurational mechanics: From foundations in continuum mechanics to applications in computational mechanics, Z. Angew. Math. Mech. , Vol.89, pp.614-630, 2009 Research Articles: Eshelby, J. D., The force on an elastic singularity, Phil. Trans. R. Soc. Lond. A , Vol.244, pp.87-112, 1951 Eshelby, J. D., Energy relations and the energy-momentum tensor in continuum mechanics, In: Kannien, M. F., eds., Inelastic Behavior of Solids , pp.77-144, New York: McGraw-Hill, 1970 Eshelby, J. D., The elastic energy-momentum tensor, J. Elasticity , Vol.5, pp.321-335, 1975 Chadwick, P., Applications of an energy-momentum tensor in non-linear elastostatics, J. Elasticity , Vol.5, pp.249-258, 1975 Larche, F. C., Cahn, J. W., The interactions of composition and stress in crystalline solids, Acta Metall. , Vol.33, pp.331-357, 1985 Heidug, W., Lehner, F. K., Thermodynamics of coherent phase transformations in nonhydrostatically stressed solids, Pure Appl. Geophys. , Vol.123, pp.91-98, 1985 Epstein, M., Maugin, G. A., The energy-momentum tensor and material uniformity in finite elasticity, Acta Mech. , Vol.83, pp.127-133, 1990 Bartholomeusz, B. J., The chemical potential at the surface of a non-hydrostatically stressed, defect-free solid, Phil. Mag. A , Vol.71, pp.489-495, 1995 Samohyl, I., Pabst, W., The Eshelby relation in mixtures, Int. J. Non-Linear Mech. , Vol.32, pp.227-233, 1997 Norris, A. N., The energy of a growing elastic surface, Int. J. Solids Struct. , Vol.35, pp.5237-5252, 1998 Samohyl, I., Thermodynamics of reacting mixtures of any symmetry with heat conduction, diffusion and viscosity, Arch. Rat. Mech. Anal. , Vol.147, pp.1-45, 1999 Cleja-Tigoiu, S., Maugin, G. A., Eshelby's stress tensors in finite elastoplasticity, Acta Mech. , Vol.139, pp.231-249, 2000 Podio-Guidugli, P., Configurational balances via variational arguments, Interfaces and Free Boundaries , Vol.3, pp.223-232, 2001 Wu, C. H., The role of Eshelby stress in composition-generated and stress-assisted diffusion, J. Mech. Phys. Solids , Vol.49, pp.1771-1794, 2001 Wu, C. H., Chemical potential and energy momentum tensor in single phase mixtures, Mech. Res. Commun. , Vol.29, pp.493-499, 2002 Maugin, G. A., Remarks on the Eshelbian thermomechanics of materials, Mech. Res. Commun. , Vol.29, pp.537-542, 2002 Kalpakides, V. K., Dascalu, C., On the configurational force balance in thermomechanics, Proc. R. Soc. Lond. A , Vol.458, pp.3023-3039, 2002 Steinmann, P., On spatial and material settings of hyperelastodynamics, Acta Mech. , Vol.156, pp.193-218, 2002 Steinmann, P., On spatial and material settings of hyperelastostatic crystal defects, J. Mech. Phys. Solids , Vol.50, pp.1743-1766, 2002 Steinmann, P., On spatial and material settings of thermo-hyperelastodynamics, J. Elasticity , Vol.66, pp.109-157, 2002 Buratti, G., Huo, Y. Z., Muller, I., Eshelby tensor as a tensor of free enthalpy, J. Elasticity , Vol.72, pp.31-42, 2003 Guzev, M. A., Chemical potential tensor for a two-phase continuous medium model, J. Appl. Mech. Tech. Phys. , Vol.46, pp.315-323, 2005 Epstein, M., Configurational balance and entropy sinks, Int. J. Fract. , Vol.147, pp.35-43, 2007 Gupta, A., Markenscoff, X., Configurational forces as dissipative mechanisms: a revisit, C. R. Mecanique , Vol.336, pp.126-131, 2008 Runesson, K., Larsson, F., Steinmann, P., On energetic changes due to configurational motion of standard continua, Int. J. Solids Struct. , Vol.46, pp.1464-1475, 2009 Ganghoffer, J. F., Mechanical modeling of growth considering domain variation Part II: volumetric and surface growth involving Eshelby tensors, J. Mech. Phys. Solids , Vol.58, pp.1434-1459, 2010 Grabovsky, Y., Truskinovsky, L., Roughening instability of broken extremals, Arch. Rat. Mech. Anal. , Vol.200, pp.183-202, 2010
题目：化学势 时间：2010.1.22. 下午2:30 地点：16楼308（308装上新黑板了） 主讲：庞海 摘要： The definition of the fundamental quantity, the chemical potential, is badly confused in the literature: there are at least three distinct definitions in various books and papers. While they all give the same result in the thermodynamic limit, major differences between them can occur for finite systems, in anomalous cases even for finite systems as large as a cm3. We resolve the situation by arguing that the chemical potential defined as the symbol conventionally appearing in the grand canonical density operator is the uniquely correct definition valid for all finite systems, the grand canonical ensemble being the only one of the various ensembles usually discussed (microcanonical, canonical, Gibbs, grand canonical) that is appropriate for statistical thermodynamics, whenever the chemical potential is physically relevant. The zero-temperature limit of this was derived by Perdew et al. for finite systems involving electrons, generally allowing for electron-electron interactions; we extend this derivation and, for semiconductors, we also consider the zero-T limit taken after the thermodynamic limit. The enormous finite size corrections (in macroscopic samples, e.g. 1 cm3) for one rather common definition of the c.p., found recently by Shegelski within the standard effective mass model of an ideal intrinsic semiconductor, are discussed. Also, two very-small-system examples are given, including a quantum dot. 参考文献 ： T. A. Kaplan, The Chemical Potential, Journal of statistical physics, 122 (6) : 1237-1260(2006).
标签: 化学势
