The Use of Ultrasound to Measure Dislocation Density

Dislocations are at the heart of the plastic behavior of materials yet they are very difficult to probe experimentally. Lack of a practical nonintrusive measuring tool for, say, dislocation density, seriously hampers modeling efforts, as there is little guidance from data in the form of quantitative measurements, as opposed to visualizations. Dislocation density can be measured using transmission electron microscopy (TEM) and x-ray diffraction (XRD). TEM can directly show the strain field around dislocations, which allows for the counting of the number of dislocations in a micrograph. This procedure is very laborious and local, since samples have to be very small and thin, and is difficult to apply when dislocation densities are high. XRD relies on the broadening of diffraction peaks induced by the loss of crystalline order induced by the dislocations. This broadening can be very small, and finding the dislocation density involves unknown parameters that have to be fitted with the data. Both methods, but especially TEM, are intrusive, in the sense that samples must be especially treated, mechanically and chemically. A nonintrusive method to measure dislocation density would be desirable. This paper reviews recent developments in the theoretical treatment of the interaction of an elastic wave with dislocations that have led to formulae that relate dislocation density to quantities that can be measured with samples of cm size. Experimental results that use resonant ultrasound spectroscopy supporting this assertion are reported, and the outlook for the development of a practical, nonintrusive, method to measure dislocation density is discussed.