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Shape evolution of 3‐dimensional faceted crystals
Author(s) -
Zhang Yongchun,
Sizemore Jacob P.,
Doherty Michael F.
Publication year - 2006
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.10778
Subject(s) - crystal (programming language) , simple (philosophy) , symmetry (geometry) , set (abstract data type) , face (sociological concept) , crystallography , geometry , adipic acid , materials science , mathematics , chemistry , computer science , composite material , social science , philosophy , epistemology , sociology , programming language
A novel method for modeling the shape evolution of 3‐dimensional (3‐D) faceted crystals has been developed in which the normal distances to each face from an origin inside the crystal are represented by a system of ordinary differential equations. The model is initialized from an arbitrary initial seed shape and size but known crystallographic data (such as unit cell and symmetry). At each time step, the entire family of possible discrete shape evolution events (such as vertices bifurcating into edges or faces, etc.) are exhaustively enumerated and investigated using a new set of simple testable conditions. The evolving crystal shape is then determined from the evolving set of normal distances and the corresponding crystallographic planes. The model has been successfully applied to two organic crystal systems: adipic acid grown from water and α‐glycine grown from water. © 2006 American Institute of Chemical Engineers AIChE J, 2006