Untersuchung der elektrischen Hyperfeinwechselwirkung in M_n+1AX_n-Phasen mittels der gestörten γ-γ-Winkelkorrelation

Determination of gradient elastic tensors: stress and strain dependencies of electric field gradients in cubic and hexagonal systems

“…Other errors which have not been factored into the estimation of the accuracy are the unknown temperature effects, the uncertainties of elastic constants, and the accuracy of the experimental values. The deviations due to temperature can be approximated to be in the order of 2-20% according to the temperature dependence of the intrinsic EFG in the hexagonal systems [32,[41][42][43][44]. Experimental elastic constants can be considered to be accurate within a few percent [45][46][47][48][49][50][51][52], the calculated values of the MAX phases are expected to be less accurate although no experimental comparison is given [53].…”

“…The used lattice parameters were obtained from an optimization of the total energy as a function of volume and, where applicable, c/a-ratio, ensuring that the system is in its ground state at zero strain. Phonon contributions to the EFG and, thus, temperature effects [38] were not treated herein; consequently, all given gradient elastic constants should be considered valid only at T = 0 K. Calculation details were adapted from previous publications in the case of the MAX phases [32] and ZnO [30]. The Perdew-Burke-Ernzerhof [39] exchange-correlation potential was used in all calculations except for metallic Cd where, according to [29], the Wu-Cohen [40] potential was used.…”

“…All calculated EFGs were axially symmetric with their V calc zz given in table 2. The experimental values V exp zz at T = 0 K [32,[41][42][43][44] were determined by extrapolation using a quadrupole moment of Q = 0.765 (15)b [29]. Since for Ti 2 AlN low temperature data was not available, the measurements were carried out separately and analyzed according to [32].…”

“…The calculation of gradient elastic constants seems to be feasible with growing computing power and progress in density functional theory (DFT) [23,24]. By using the augmented plane waves plus local orbitals method (APW+lo) implemented in the WIEN2k package [25][26][27][28], EFGs already can be reproduced ab-initio with an accuracy of more than 10% in metals [29] and semiconductors [30] but also structurally very complex systems such as MAX phases [31,32].…”