Correlation between effective activation energy and pre-exponential factor for diffusion in bulk metallic glasses
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Correlation between effective activation energy and pre-exponential factor for diffusion in bulk metallic glasses S.K. Sharmaa) and F. Faupelb) Technische Fakulta¨t der Universita¨t Kiel, Lehrstuhl fu¨r Materialverbunde, Kaiserstraße 2, D-24143 Kiel, Germany (Received 11 March 1999; accepted 24 May 1999)
The values of effective activation energy (Q) and pre-exponential factor (D0) reported in the literature for diffusion in the novel bulk metallic glasses, both in the glassy and the deeply supercooled liquid regions, are found to follow the same correlation as reported earlier in conventional metallic glasses, namely D0 ⳱ A exp(Q/B), where A and B are fitting parameters with values A ⳱ 4.8 × 10−19 m2 s−1 and B ⳱ 0.056 eV atom−1. A possible explanation for the observed values of A and B is given by combining an activation energy and a free volume term. The interpretation favors a cooperative mechanism for diffusion in the glassy and deeply supercooled liquid states.
Bulk metallic glasses are novel materials with high thermal stability and wide supercooled region.1,2 Unlike conventional metallic glasses these materials offer possibilities for carrying out diffusion measurements at temperatures lying much above the glass transition temperature. Several diffusion investigations3–8 have been reported in the literature in bulk metallic glasses especially, in Zr–Ti–Cu–Ni–Be (Zr 41.2 Ti 13.8 Cu 12.5 Ni10Be22.5 and Zr46.75Ti8.25Cu7.5Ni10Be27.5 known as Vitreloy V1 and V4, respectively) and Zr–Cu–Ni–Al (Zr65Cu17.5Ni10Al7.5 known as Inoue alloy). On the other hand, a substantial volume of diffusion data are available in conventional metallic glasses and these have been extensively reviewed in the literature.9–11 The diffusivity data in both conventional and bulk metallic glasses show an Arrhenius temperature dependence in the investigated temperature range, and the data in bulk metallic glasses have been split into two different Arrhenius regions lying below and above the observed kind temperature in these plots representing amorphous glassy and supercooled liquid phases.3–6 On the basis of the Arrhenius dependence, the values of activation energy (Q) and prefactor (D0) have been calculated in each case.3–8 It has to be pointed out, however, that any increase in temperature in the supercooled liquid state is accompanied by structural changes, particularly by an increase in free volume.12,13 Therefore, the activation energy determined in the supercooled region, Q ⳱ − k[⭸ln D/⭸T −1], has to be regarded as an effective quantity, which is much larger than the actual energy for overcoming activation barriers. a)
On leave from the Department of Physics, Malaviya Regional Engineering College, Jaipur 302 017, India. b) Address all correspondence to this author. e-mail: [email protected] 3200
J. Mater. Res., Vol. 14, No. 8, Aug 1999
In this communication we present an analysis of the correlation existing between the reported values of the pre-exponential factor (D0) and activation
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