A Model of Superlattice Yield Stress and Hardness Enhancements
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ABSTRACT A model is presented that explains the yield stress and hardness enhancements that have been observed in superlattice thin films. The predicted strength/hardness enhancement increased with increasing superlattice period, A, before reaching a saturation value that depended on interface widths. The results indicate that superlattice strength/hardness depends strongly on interface widths and the difference in shear moduli of the two components for A values below the maximum, and on the average shear modulus for larger A.
INTRODUCTION Superlattice and multi-layer thin films generally exhibit substantial strength and hardness enhancements. 1 TiN/NbN superlattice 2 hardness H was increased to as high as 52 GPa compared with a 20 GPa rule-of-mixtures value. Starting at small superlattice period A, strength and/or hardness typically increase with increasing A, reach a maximum value, and then decrease for further increases in A. A variety of mechanisms have been used to explain the enhancements, including the effects of elastic anomalies, 3 coherency strains,2' 4 and elastic modulus differences between the superlattice layers. 5,6 It has been shown, however, that elastic anomalies are either non-existent or too small to explain the strength/hardness enhancements,7 and coherency strain effects appear to be relatively small. 8,9 On the other hand, recent results show that elastic-moduli 8 differences are a critical factor determining the enhancements. Early modulus-difference calculations provided only an upper-limit value of the strength enhancement since they were based on calculations of the stress on a dislocation near a single, abrupt interface. 5 Real superlattices are clearly more complicated; the exact shape of the composition modulation, as given by the period A, relative layer thicknesses, interface widths, and modulation amplitude, is expected to influence the properties. Models that provide more accurate predictions have been developed by including the effects of two2 ,6 or several10 abrupt interfaces. KrzanowskiII recently showed that dislocation motion across arbitrary-shaped composition modulations could be treated as a series of small step changes in modulus. However, this calculation yielded a much weaker dependence of strength on A than observed experimentally. In this paper, we describe a model of superlattice strengthening that accounts for both glide across layers and within individual layers. Dislocation glide across interfaces is calculated based on the effect of layer modulus differences, accounting for all layers and assuming broadened interfaces. Dislocation core effects are included without the need for fitting parameters. In addition, realistic results are obtained at small A values by allowing changes in the modulation shape, from trapezoidal at large A to sawtooth with a decreased modulation amplitude at small A. Dislocation flow within individual layers is calculated both for the case where the supply of dislocations is plentiful and where dislocations must be generated within the laye
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