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            <title xml:lang="en">EQUILIBRIUM CRYSTAL SHAPES AND SURFACE PHASE DIAGRAMS AT SURFACES IN CERAMICS</title>
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                <title xml:lang="en">EQUILIBRIUM CRYSTAL SHAPES AND SURFACE PHASE DIAGRAMS AT SURFACES IN CERAMICS</title>
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                <title level="j">Journal de Physique Colloques</title>
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              <p>The equilibrium shape of a crystal is the shape which minimizes the total surface free energy of the crystal and may contain any or all of the following : facets, sharp edges, smoothly curved surfaces, and corners. The relationship between the surface free energy per unit area, γ, and the equilibrium crystal shape is seen straightforwardly from the Wulff plot, the polar plot of γ as a function of orientation of the normal vectors, [MATH]. Cabrera, Cahn, and Rottman and Wortis have described the boundaries between surfaces on the equilibrium crystal (for example, between adjacent facet planes) as surface phase transitions. If γ([MATH]) changes with temperature, pressure, or chemical potentials of the components, the equilibrium shape of the crystal may change. This change in equilibrium shape can be represented by a surface phase diagram with axes of surface orientation, in terms of angle from an arbitrary orientation, and temperature, pressure, or chemical composition. The surface phase transitions of MgO have been determined as a function of NiO solute concentration and surface phase diagrams have been constructed.</p>
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