Factors Controlling the Formation and Structure of Phases

Faculty of Science, University of Waterloo Waterloo, Ontario, Canada 

The problems which confront anyone who wishes to study the factors that control the formation and structure of phases or compounds—what combinations of what elements will form stable phases under what conditions and with what crystal structures—can best be expressed by quoting from the proceedings of a conference on phase stability in metals and alloys held in 1966/ The remarks, somewhat rearranged in order, are by W. M. Lomer.  

Evaluate self-consistent fields for the component-free atoms. 

Superpose these potentials to get band structure, and use the resulting wave function to get self-consistent solution for solid. 

I first review several methods of predicting the existence of simple phases and structures and then examine the structural constraints that arise from chemical bonding, whether ionic, saturated covalent, or metallic, and from atomic size. Next, I examine in detail several of the more important factors that control the stability of phases and structures, mainly of metals, and finally I discuss several of the more important atomic interactions that cause distortions of crystal structures. 

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Factors Controlling the Formation and Structure of Phases The Madelung constant can be defined as... 

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