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 ɛ(l₁l₂l₃) of the direction l₁l₂l₃, normal to the plane HKL, can be uniquely expressed for all crystal systems as follows: ɛ(l₁l₂l₃)={αβ(l₁l₂l₃)+(1-α)[1/(3K_V)]}σ _p+α(-(t/3)(1-3 cos² ψ){(1/2)[3/E(l₁l₂l₃) -β(l₁l₂l₃)]})+(1-α){-(t/3)(1-3 cos ² ψ)[1/(2G_V) ]}, where β(l₁l₂l₃) and E(l₁l₂l₃) denote the linear compressibility and the Young modulus, respectively. Bulk modulus K_V and shear modulus G_V are values for isostrain model. Variable ψ 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 σ_p. The second and third term, strains caused by the differential stress t, correspond to the isostress and the isostrain model, respectively. The parameter α takes a value between 0 (isostrain) and 1 (isostress). A method to determine the hydrostatic stress component σ_p, differential stress t, and the parameter α from powder x-ray-diffraction is discussed.