The Effect of Homogeneous Mechanical Stress on the Electrical Resistance of Crystals

Abstract

It is shown from general considerations of symmetry that the effect of homogeneous mechanical stress on the electrical resistance of a conducting crystal can be expressed in terms of a set of constants, the number of which is equal to the number of elastic moduli, and which connect the resistance with stress by equations very much like the equations connecting strain with stress, except for the difference of a factor 2 in some of the terms. The results are explicitly applied to the case of bismuth, and formulas developed for the change of resistance of a rod cut from the crystal in any direction when subjected to a longitudinal tension. The formulas are checked against the recent experimental results of Miss Allen for bismuth, and agreement found within the limits of error. It is shown that tension measurements alone do not permit an evaluation of all the constants, but if the tension measurements are supplemented by measurements of the effect of hydrostatic pressure in two independent directions, the six constants are then completely determined. Numerical values of the six constants are given for bismuth. Finally the geometrical meaning of the coefficients is briefly discussed and attention called to an effect produced by stress in crystals which is the analogue of the Hall effect produced by a magnetic field in isotropic materials.