Modelling and Measurements of Stress-Controlled Interdiffusion in Multilayered Amorphous Alloys
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F. L. YANG, W. C. SHIH AND A. L. GREER University of Cambridge, Department of Materials Science & Metallurgy, Pembroke Street, Cambridge CB2 3QZ, United Kingdom
ABSTRACT The decay of X-ray satellite intensities is used to measure interdiffusion in amorphous Ni 55 Zr 45 multilayers as a function of repeat distance, time and temperature. The data are compared to analytical expressions and a numerical simulation based on the analysis of Stephenson for stress effects. It is concluded that stress effects are very strong and that the analysis fits them quantitatively in a system such as a-Ni-Zr with marked diffusional asymmetry. 1. INTRODUCTION Stress can affect interdiffusion in multilayers through coherency between the layers [I], or with the substrate [2], substrate bending [3], and applied hydrostatic pressure [4]. Stresses can arise also as a result of the interdiffusion itself, as analysed by Stephenson [5], and their effects are the focus of the present work. When two species interdiffusing have different values of Vi.Mi (where Vi and Mi are the partial molar volume and the mobility of species i), the net transport of volume leads to stresses. As analysed in [5], the role of the stresses depends on the diffusion distance; thus multilayers with controlled repeat distances A are useful. After initial interdiffusion unaffected by stress, a quasi steady state (QSS) is established in which the increase in stress due to continuing interdiffusion is roughly balanced by the relief of stress due to viscous flow. Data on the Ni/Zr interdiffusivity D in amorphous Ni-Zr [6], analysed in [7], show that in the QSS at small A, D is: (i) limited by the rate of stress relief; (ii) orders of magnitude lower than expected from the classical Darken relation; and (iii) well fitted by the analysis in [5]. The analysis of D in a-NiZr is extended here to cover the time-dependent behaviour before the QSS is established, different temperatures and different A, and to include the pressure dependence of diffusivities. Amorphous materials are suited to the study of stress effects because microstructural effects are avoided. Amorphous Ni-Zr is chosen because many materials parameters are known: tracer diffusivities D*Ni(7) and D*Zr(T) [8-10]; the thermodynamic factor for interdiffusion ' [7,11]; partial molar volumes VNi and VZr [12]; shear viscosity 77[13]; Young's modulus E and Poisson's ratio v [14). The strong diffusional asymmetry - D*Ni is 102 to 106 x D*Zr at the same temperature - gives large stress effects, and is related to glass formability and solid state amorphization [7]. The DNi/Zr is readily measured, as in the present work, by monitoring the decay in intensity of the X-ray satellites arising from an imposed composition modulation. 2.
ANALYSIS OF STRESS EFFECTS INDUCED BY INTERDIFFUSION
From [5], for large diffusion distances (i.e., large A in multilayers), the interdiffusivity D is given by the Darken [15] relation, and is effectively dominated by the faster component: 21
Mat. Res. Soc. Symp. Proc. Vol. 356 0 1995 Material
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