中国物理B ›› 2006, Vol. 15 ›› Issue (4): 692-696.doi: 10.1088/1009-1963/15/4/007

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Study of surface cell Madelung constant and surface free energy of nanosized crystal grain

张维佳, 王天民, 戎霭伦, 催敏   

  1. School of Science, Beijing University of Aeronautics and Astronautics,Beijing 100083, China
  • 收稿日期:2005-03-15 修回日期:2006-02-04 出版日期:2006-04-20 发布日期:2006-04-20
  • 基金资助:
    Project supported by the National Defence Pre-Research Foundation of China (Grant No 413100202).

Study of surface cell Madelung constant and surface free energy of nanosized crystal grain

Zhang Wei-Jia (张维佳), Wang Tian-Min (王天民), Rong Ai-Lun (戎霭伦), Cui Min (催敏)   

  1. School of Science, Beijing University of Aeronautics and Astronautics,Beijing 100083, China
  • Received:2005-03-15 Revised:2006-02-04 Online:2006-04-20 Published:2006-04-20
  • Supported by:
    Project supported by the National Defence Pre-Research Foundation of China (Grant No 413100202).

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摘要： Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be greatly beneficial to the analysis of surface states and the study of the dynamics of crystal nucleation and growth. A new approximative expression of the surface energy and relevant thermodynamic data are used in this calculation. New formula and computing method for calculating the Madelung constant α of any complex crystals are proposed, and the surface free energies and surface electrostatic energies of nanosized crystal grains and the Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized-crystal-grain TiO2 and the surface electrostatic energy(absolute value) of nanosized-crystal-grain α -Al2O3 are found to be the biggest among all the crystal grains including those of other species.

关键词: Madelung constant, surface free energy, nanosized crystal grain

Abstract: Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be greatly beneficial to the analysis of surface states and the study of the dynamics of crystal nucleation and growth. A new approximative expression of the surface energy and relevant thermodynamic data are used in this calculation. New formula and computing method for calculating the Madelung constant $\alpha$ of any complex crystals are proposed, and the surface free energies and surface electrostatic energies of nanosized crystal grains and the Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized-crystal-grain TiO2 and the surface electrostatic energy(absolute value) of nanosized-crystal-grain $\alpha$-Al2O3 are found to be the biggest among all the crystal grains including those of other species.

Key words: Madelung constant, surface free energy, nanosized crystal grain

中图分类号:  (Crystal binding; cohesive energy)

  • 61.50.Lt
61.46.Hk (Nanocrystals) 68.35.Md (Surface thermodynamics, surface energies) 68.65.-k (Low-dimensional, mesoscopic, nanoscale and other related systems: structure and nonelectronic properties)