FIGURE 25 Young’s modulus and torsion modulus versus wavelength of compositional modulations having approximately equal layers of vapor-deposited copper and nickel with {111} texture. From Baral, Ketterson, and Hilliard.43 Reprinted with permission.

As yet, we have no generally satisfactory theory for this unexpected enhancement in stiffness. One suggestion attributes the effect to coherency strains of approximately a few percent owing to lattice matching between the alternating layers,41 but thus far the supermodulus behavior has been observed only with alloy systems in which one of the components is a transition metal. For example, the modulus effect is not seen with compositionally layered copper-gold alloys.42 Another explanation is electronic in nature, namely, that the periodicity of the modulated structure introduces a Brillouin zone which happens to contact a flat portion of the Fermi surface when the layered wavelength is optimal.40 This circumstance is thought to produce a stable energy configuration, which then contributes a large measure of resistance to imposed elastic deformation.

However, more recently, separate elastic moduli (Young’s, flexural, and torsion) have been measured on multilayered Cu-Ni specimens having the same average composition and the same wavelength range as for the biaxial modulus measurements in Figure 24. It is surprising to find that the newer results in Figure 25 show two distinct peaks—at 12 and 28 angstroms—as a function of modulation wavelength.43 The elasticity interrelationships are such that the double peaks in Figure 25 are consistent with the single-peak biaxial measurements in Figure 24, but now a proper theory of the supermodulus effect must account for sharp enhancements in elastic constants at two optimal wavelengths. Obviously, a bizarre aspect of metal science has emerged here, with fertile opportunities for interactive experimental and theoretical research toward a deeper insight into the basic nature of the metallic state.



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