Contributions to the first-, second- and third-order elastic shear constants of hexagonal metals for arbitrary axial ratio

The three second-order shear constants of hexagonal materials are joined by five third-order ones when volume-conserving deformations are considered. Further, when the total energy of the material is decomposed there is a first-order shear constant for each component. These nine shear constants, denoted by g i , are listed. Electrostatic contributions are calculated at nine values of c/a: g 4 , g 5 and g 9 show considerable variation. Repulsive ion-ion contributions are calculated for three neighbourhoods, the coefficients involved being given as polynomials in c/a: g 2 , g 5 and g 6 are the most sensitive to c/a . The minimum in the electrostatic energy occurs at c/a = 1·6360±0·0002 and not at the ideal ratio.