Premium
Crystalline microstructures with finite surface energy
Author(s) -
Dolzmann Georg
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19980781522
Subject(s) - tetragonal crystal system , microstructure , surface energy , surface (topology) , phase transition , scale (ratio) , energy (signal processing) , elastic energy , phase (matter) , bounded function , length scale , type (biology) , materials science , geometry , measure (data warehouse) , condensed matter physics , mathematics , mathematical analysis , thermodynamics , physics , mechanics , composite material , computer science , quantum mechanics , geology , paleontology , database , statistics
Certain alloys like In‐Tl, Ni‐Ti or Cu‐Al‐Ni undergo a solid‐solid phase transition which leads to a complicated arrangement of different phases on a microscopic scale. Many of the observed geometric patterns have been successfully modelled by minimizing the elastic energy. This approach, however, does not determine the length scale of the observed microstructures. As a particular example we study a two‐dimensional model for a cubic to tetragonal phase transition. We discuss the structure of minimizers of the elastic energy and the impact of including surface energy. The mathematical analysis combines ideas from geometry and geometric measure theory. In particular we use a Liouville type theorem on sets of bounded perimeter.