Generation of Ultrasonic Second and Third Harmonics Due to Dislocations. I

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Abstract
By representing the effective-tension term of a dislocation (string model) as a power series in displacement gradients, and retaining the first nonlinear term, expressions for the amplitudes of the second and third harmonics of an ultrasonic wave introduced into a solid containing mobile dislocations are obtained. In the case of the second harmonic, a lattice term, a dislocation term, and a cross term contribute to the amplitude and all three terms can be of comparable magnitude. In the case of the third harmonic, in a solid containing a reasonable density of mobile dislocations, the dislocation contribution to the amplitude is dominant and usually lattice effects can be neglected. Except in special circumstances, it is difficult to separate the three terms that contribute to the amplitude of the second harmonic, and dislocation dynamics, therefore, are more easily studied through the generation of third harmonics.