Electron diffraction from polycrystalline materials showing stress induced preferred orientation

The Gibbs free energy as generalized by J. F. Nye [Physical Properties of Crystals (Clarendon Press, Oxford, 1957), p. 179] is minimized in thermodynamic systems held at constant temperature and constant stress. This function is orientation dependent in all crystal systems in stress fields which are not purely hydrostatic. There are situations in which preferred orientation arises as a result of the synthesis of materials under impressed stress conditions such as thin film growth under ion bombardment and the pressing of powders into solids. Here, we derive the orientational constraints for cubic crystals which result from growth under a general biaxial stress field. The sign of the expression delta=s(11)-s(12)-1/2s(44) determines the behavior of a cubic crystal. Electron diffraction patterns of face-centered-cubic specimens with both positive and negative values of delta are calculated using a program in MATLAB and displayed in a form suitable for direct comparison with experiment. The use of a biaxial stress with unequal principal components for producing highly oriented polycrystalline material is discussed. In the case of delta positive, as occurs in silicon, the preferred orientation is simply an alignment of the < 100 > directions along the principal stresses. For delta negative, as occurs in titanium nitride, the preferred orientation depends on the ratio of the principal stresses and low index directions are aligned with the principal stresses only when the principal stresses are either equal or one of them is zero. In the general case, arc-like diffraction patterns are produced. The results of a calculation of a diffraction pattern from a cross-sectional TiN film are compared with diffraction patterns reported by L. Hultman et al. [J. Appl. Phys. 78, 5395 (1995)] and show good agreement. (C) 1999 American Institute of Physics. [S0021-8979(99)08213-4].