Lattice strains in crystals under uniaxial stress field

An expression for the lattice strains in a polycrystalline specimen under uniaxial stress field has been extended for all crystal systems. Apparent Miller indices (HKL) are introduced from Miller indices (hkl) and lattice parameters. The lattice strain epsilon(l(1)l(2)l(3)) of the direction l(1)l(2)l(3), normal to the plane HKL, can be uniquely expressed for all crystal systems as follows: epsilon(l(1)l(2)l(3))={alpha beta(l(1)l(2)l(3))+(1 - alpha)[1/(3K(V))]}sigma(p)+alpha(-(t/3)(1-3 cos(2) psi){(1/2)[3/E(l(1)l(2)l(3)) -beta(l(1)l(2)l(3))]})+(1 - alpha)(-(t/3) (1 - 3 cos(2) psi)[1/(2G(V))]}, where beta(l(1)l(2)l(3)) and E(l(1)l(2)l(3)) denote the linear compressibility and the Young modulus, respectively. Bulk modulus K-V and shear modulus G(V) are values for isostrain model. Variable psi is the angle between loading axis and the normal of the plane HKL. The first term is the strain caused by the hydrostatic stress component sigma(p). The second and third term, strains caused by the differential stress t, correspond to the isostress and the isostrain model, respectively. The parameter alpha takes a value between 0 (isostrain) and 1 (isostress). A method to determine the hydrostatic stress component sigma(p) differential stress t, and the parameter alpha from powder x-ray-diffraction is discussed. (C) 1996 American Institute of Physics.