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A complete representation of structure–property relationships in crystals


Whereas structure–property relationships have long guided the discovery and optimization of novel materials1,2,3, formal quantitative methods to identify such relationships in crystalline systems are beginning to emerge4,5,6,7,8. Among them is cluster expansion9,10,11,12,13, which has been successfully used to parametrize the configurational dependence of important scalar physical properties such as bandgaps14, Curie temperatures15, equation-of-state parameters16,17 and densities of states18,19,20. However, cluster expansion is currently unable to handle anisotropic properties, a key distinguishing feature of crystalline systems central to the design of modern epitaxial structures and devices. Here, I introduce a tensorial cluster expansion enabling the prediction of fundamental tensor-valued material properties such as elasticity, piezoelectricity, dielectric constants, optoelectric coupling, anisotropic diffusion coefficients, surface energy and stress. As an application, I develop predictive ab initio models of anisotropic properties relevant to the design and optimization of III–V semiconductor epitaxial optoelectronic devices21,22.

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Figure 1: Graphical representation of each term of the TCE on the cation sublattice of the wurtzite structure expressing the configurational dependence of a symmetric rank-two tensor.
Figure 2: Structure–property relationships.


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This research was supported by the US National Science Foundation through TeraGrid resources provided by NCSA and SDSC under grant DMR060011N and through the Center for the Science and Engineering of Materials at Caltech.

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van de Walle, A. A complete representation of structure–property relationships in crystals. Nature Mater 7, 455–458 (2008).

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