Finite-Temperature Behavior of PdH x Elastic Constants Computed by Direct Molecular Dynamics
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Finite-Temperature Behavior of PdHx Elastic Constants Computed by Direct Molecular Dynamics X. W. Zhou1, T. W. Heo2, B. C. Wood2, V. Stavila1, S. Kang2, and M. D. Allendorf1 1 Sandia National Laboratories, 7011 East Avenue, Livermore, CA 94550, U.S.A 2 Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, U.S.A. ABSTRACT Robust time-averaged molecular dynamics has been developed to calculate finite-temperature elastic constants of a single crystal. We find that when the averaging time exceeds a certain threshold, the statistical errors in the calculated elastic constants become very small. We applied this method to compare the elastic constants of Pd and PdH0.6 at representative low (10 K) and high (500 K) temperatures. The values predicted for Pd match reasonably well with ultrasonic experimental data at both temperatures. In contrast, the predicted elastic constants for PdH0.6 only match well with ultrasonic data at 10 K; whereas, at 500 K, the predicted values are significantly lower. We hypothesize that at 500 K, the facile hydrogen diffusion in PdH0.6 alters the speed of sound, resulting in significantly reduced values of predicted elastic constants as compared to the ultrasonic experimental data. Literature mechanical testing experiments seem to support this hypothesis. INTRODUCTION PdHx has been widely studied as an archetype solid-state hydrogen storage material operated by a diffusional phase transformation mechanism. In this material, the mismatch strain energy between the (larger lattice constant) and the (smaller lattice constant) phases exerts an effective resistance to the transformation, and thereby plays a critical role in determining the overall (de)hydrogenation kinetics. The mismatch strain energy in turn depends on the elastic constants, which evolve with composition and can depend on the reaction temperature. Predictive models of PdHx reaction kinetics therefore require finite-temperature elastic constants that can account for the full dynamical complexity of the material under reaction conditions. Typically, elastic constants of PdHx have been measured using ultrasonic methods [1,2,3]. Extensive experiments, however, indicate that ultrasonic elastic constants can be significantly higher than the mechanical testing elastic constants (by as much as one order of magnitude for mineral materials) [4,5]. To illustrate this, the reported mechanical tensile testing curves of Pd and PdH0.6 [6] are summarized respectively in Figs. 1(a) and 1(b), where red (Pd) and blue (PdH0.6 ) lines highlight the elastic deformation regime. Fig. 1(c) focusses on the elastic response of the two materials with a significantly magnified scale (40×) in the strain- axis. Note that the literature work [6] was intended to study fracture and used a coarse strain scale (i.e., the elastic strain range sampled is negligible compared to the overall strain measured). This causes significant error in the reading of the elastic strain range, which in turn causes errors of the elastic constant measurement
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