Structurally-induced elastic anomalies in a superlattice of (001) twist grain boundaries
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I. INTRODUCTION The discovery of the "supermodulus effect" in the biaxial modulus of composition-modulated structures of Au/Ni and Cu/Pd by Yang et al.' and its subsequent detection in several other metallic superlattices (see, for example, Refs. 2 and 3) has drawn considerable attention to the possibility of designing interface materials with mechanical properties not otherwise achievable in bulk materials. Whereas in some superlattices studied experimentally an elastic softening has been reported,2"4 the instances in which a hardening has been observed1'5"7 remain a motivating factor for the further investigation of strained-layer superlattices. The elastic constants of an alloy are usually intermediate between those of its constituents. In the original work on Au/Ni and Cu/Pd the biaxial modulus in the interface plane was observed to be 2-3 times larger (for modulation wavelengths A = 16-20 A) than for either of the constituents.1 Owing to the severe difficulties encountered in measuring the elastic constants of thin-film materials and in preparing well-characterized samples, these experimental findings have been met with some reservation. However, with the large number of different systems which have now been investigated, some of which have shown anomalously strong and some anomalously weak elastic behavior, a consensus is emerging that anomalous elastic behavior in metallic superlattices is the rule rather than the exception.8 However, whether or not superlattice materials show a strengthened elastic response remains controversial, as do the proposed physical explanations for the observed anomalies.8"10 In superlattice materials in which detailed x-ray studies exist the elastic anomalies were found to be accompa-
nied by changes in sample dimensions.2 4 In general, an expansion in the z direction (parallel to the interface-plane normal) is observed which is accompanied by dimensional changes in the interface (x-y) plane. In bulk crystals a lattice expansion is usually accompanied by a softened elastic response. Whereas the expansion in the z direction can thus explain9 both the observed3 softening of the shear elastic constant C44 (for shear parallel to the interface plane) and the recently observed4 softening of C33 (parallel to z), the strengthening reported in Young's and the biaxial modulus1'5 appears to be in conflict with these elastic-constant measurements. In several attempts 810 to explain both the elastic anomalies and related dimensional changes, electronic effects associated with the layered alloying were assumed to produce strains in the z direction distributed homogeneously throughout the bulk of the multilayer film, thus implying that the anomalies are a bulk effect. However, recent experimental evidence4'11 strongly suggests that the expansion in the z direction is localized at the interfaces. Also, the anomalously strong elastic behavior of nanocrystalline metals12 cannot easily be explained by electronicstructure arguments. Interface systems are intrinsically inhomogeneous. Moreover, the pr
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