Vacancy encounter model for stochastically fluctuating electric field gradients in the Cu₃Au crystal structure

ABSTRACT

A class of experimental techniques known as hyperfine methods can be used to measure electric field gradients (EFGs) through the hyperfine interaction experienced by tracer nuclei. When EFGs fluctuate at rates comparable to the inverse characteristic timescale of the hyperfine method, there is a loss of signal coherence that can be used to determine EFG fluctuation rates. This has been used to measure, for example, EFG fluctuations accompanying atomic jumps of radiotracers using perturbed angular correlation spectroscopy (PAC). Nominally, there is a one-to-one correspondence between EFG fluctuation and tracer jump, but when tracer jumps are mediated by a vacancy diffusion mechanism, a subset of multiple tracer-vacancy exchanges will not affect spectra when they occur much faster than the hyperfine timescale, leading to an underestimate of underlying tracer jump rate if this correlated random-walk effect is not taken into consideration. The present work calculates the factor by which EFG fluctuation rate differs from tracer jump rate based on a time-dependent, random-walk analysis of tracer displacement probabilities in a vacancy encounter model for the special case of self-diffusion in the L1₂ crystal structure.

KEYWORDS:

• Diffusion
• defect concentration
• encounter model
• atomic displacement probability

Acknowledgements

The authors gratefully acknowledge helpful discussions with Gary S. Collins, Randy Newhouse, and William E. Evenson.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Matthew O. Zacate http://orcid.org/0000-0001-6277-6814

Additional information

Funding

This work was supported by the National Science Foundation [Grants DMR 06-06006 and DMR 15-08189].