Thermodynamics of elastically deformed solids

So far we considered phases with sufficient atomic mobihties and vanishing pressure anisotropies such that we could use the term -pdV to describe the mechanical energy increment (see also footnote 6). Generally, for elastic deformations (i.e. usually small deformations), this increment has to be expressed in terms of the stress tensor components Sy and the differential strain tensor components dey  

Another important special case of a homogeneous deformation (i.e. y is positionally constant) in which now, however, pressure anisotropies are effective, is the uniaxially stressed cubic crystal. Let us assume this time that there is tensile stress in the x-direction. There it holds for small effects (i.e. Hooke s law fulfilled) that s = P. dcxx/dsxx const = xx/ xx nnd also dsyy/dsxx — ds z/dsxx yy/sxx zz/ xx const. 

The first constant is the inverse of the elastic modulus while the second is the negative ratio of Poisson s number and the elastic modulus. 

The fact that homogeneous samples shrink in the y- and z-direction if elongated in x-direction leads to a Poisson s number being greater than 0. (It must be also not greater than 1/2 owing to thermod5mamic criteria [91].) 

In equilibrium the (total) chemical potential of mobile components (k) is positionally constant. Accordingly, it exhibits an excess term (compared to the value of the undeformed solids) which amounts to  

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