Crystal minimum Gibbs free energy

G is the total Gibbs free energy of the crystal. The condition for equilibrium is that the Gibbs free energy is a minimum,... 

The equilibrium shape of a crystal is that of its minimum energy. This is called the Wulff condition and indicates that the area of faces present will be such as to minimize the Gibbs free energy of the crystal. Unfortunately, the observed habit of crystals grown from solutions is often quite different from the prediction by the Wulff condition. 

Under conditions of very slow growth, the ultimate crystal shape is determined strictly by thermodynamics. Under such conditions, the faces appearing on the crystal correspond to the smallest convex polyhedron having minimum surface free energy. Gibbs... 

The axial oscillation and rotation of polymer chains in the crystal lattice yield at any temperature a minimum of Gibbs free energy at a finite long period L which in linear polyethylene (PE) for a reasonable choice of surface free energy well agrees with the experimentally observed lamella thickness. ° °... 

The above relationship also follows from the Gibbs s condition for the minimum of the surface free energy of the equilibrium crystal ... 

The surface energy theory is based on Gibbs postulate (1878). In equation (XVI) aj is the area of the ith face of a crystal bound by n faces and Qj, the surface free energy of the ith face per unit area. The total free energy of a crystal at a given temperature and pressure in equilibrium with its surroundings is minimum for a given volume. 

A crystal is surrounded at equilibrii n by flat, atomically smooth, low-index faces or, in Frank s classification, by singular faces. These faces in equilibrium forms are defined by the Gibbs definition of the equilibrium form requiring a minimum of the surface free energy of the crystal at constant volume (see Section 5.1). 

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