Finite-temperature elasticity of fcc Al: Atomistic simulations and ultrasonic measurements

Abstract

Though not very often, in literature there are cases where discrepancies exist in temperature dependence of elastic constants of materials. A particular example of this case is the behavior of C 12 coefficient of a simple metal, aluminum. Here, we attempt to provide insight into various contributions to temperature-dependence in elastic properties by investigating the thermo-elastic properties of fcc aluminum as a function of temperature through the use of two computational techniques and experiments. First, ab initio calculations based on density functional theory (DFT) are used in combination with quasi-harmonic theory to calculate the elastic constants at finite temperatures through a strain-free energy approach. Molecular dynamics (MD) calculations using tight-binding potentials are then used to extract the elastic constants through a fluctuation-based formalism. Through this dynamic approach, the different contributions (Born, kinetic and stress fluctuations) to the elastic constants are isolated and the underlying physical basis for the observed thermally-induced softening is elucidated. The two approaches are then used to shed light on the relatively large discrepancies in the reported temperature dependence of the elastic constants of fcc aluminum. Finally, the polycrystalline elastic constants (and their temperature dependence) of fcc aluminum are determined using Resonant Ultrasound Spectroscopy (RUS) and compared to previously published data as well as the atomistic calculations performed in this work.

Atomistic Modeling‐Based Design of Novel Materials

“…Although this method is computationally more demanding, as it requires more calculations to obtain enough datapoints for the quadratic fitting, it allows to pick up also non-quadratic (i.e., beyond linear-elasticity) effects in a straightforward manner and, thus, to establish, for example, third order elastic constants, C ijk [92][93][94]96] Even more importantly, in the most recent studies this method has been used to establish also temperature dependence of the elastic constants. [97][98][99] It is also worth mentioning that, if all parameters are carefully chosen, both stress-strain and energy-strain approaches yield the same results (as they should, since both are based on the Hooke's law and linear elasticity). [91,100] Again, the SQS methodology has proved to be useful for predicting compositional trends of solid solutions, as well as to treat the magnetic disorder in paramagnetic CrN-based systems.…”

“…It is convenient to apply specially selected deformation modes, which result in simple (quadratic) functional dependences in Equation 6. [97][98][99] It is also worth mentioning that, if all parameters are carefully chosen, both stress-strain and energy-strain approaches yield the same results (as they should, since both are based on the Hooke's law and linear elasticity). [97][98][99] It is also worth mentioning that, if all parameters are carefully chosen, both stress-strain and energy-strain approaches yield the same results (as they should, since both are based on the Hooke's law and linear elasticity).…”

Comparative molecular dynamics study of fcc-Al hydrogen embrittlement

“…To enable the Al/H bulk simulations presented here, we extended the ReaxFF Al/H training set used previously to study hydrogen storages and alane chemistry [25] with DFT-data describing the hydrogen binding strength and diffusion barriers in the Al-bulk interstitial sites and the hydrogen binding energies to aluminum metal subsurface vacancy sites and neighboring sites. DFT/experiment 104 [28]; 116 [29] 55.9 [28]; 64.8 [29] 29.5 [28]; 30.9 [29] 0.45 [5]; 0.52 [18] 140; 93 [18] DFT calculations [30] for force-field training were performed with VASP software [31] using the projector-augmented-wave (PAW) potentials [32] in the spin-polarized form [33] and the generalized gradient approximation (GGA-PBE) [34]. The 32-atom 2×2×2 conventional supercell of fcc aluminum was used for bulk calculations.…”

Deformation Behavior of Thick Aluminum Wire during Ultrasonic Bonding

“…The gradients of "z F and "z E collaterally indicate the elastic modulus of the Al wire before and after applying the ultrasonic vibration, respectively. Therefore, the difference in these two gradients imply the change in the elastic modulus by heating 16) during applying the ultrasonic vibration. Although the peak temperature of the wire in the vicinity of the interface may change depending on the bonding force, unloading the bonding force one second after finishing the application of ultrasonic vibration gives the Al wire an enough time to homogenize and to converge the temperature into a similar value slightly higher than the room temperature.…”