Elastic constants calculation - WIEN 2k

We express the energy of the strained system by means of a Taylor expansion inthe distortion parameters,The linear terms vanish if the strain causes no changes in the volume of thecrystal. Otherwise, are related to the strain on the crystal and are elasticconstants and is the volume of unstrained hexagonal system and we use it toevaluate the elastic constants.There are five independent elastic constants for a hexagonal symmetry, calledC 11 , C 12 , C 13, C 33 , and C 55 [3]. Since we have five independent elastic constants,we need five different strains to determine these elastic constants. The fivedistortions used in the hex-elastic Package are described below [2,4]. The firstdistortion is written as:and it changes the size of the basal plane, while keeping the z axis constant. Thesymmetry of the strained lattice is therefore still hexagonal and the energy for thisdistortion can be obtained as:The second type of distortion is a volume conserved distortion and lead to Orthorhombicsymmetry and written as:4