Matthew O. Zacate William E. Evenson Mike Lape Michael Stufflebeam
Modeling Complex Diffusion Mechanisms in L12-Structured Compounds Recent PAC findings in L12-structured compounds Stochastic models of complex mechanisms Simulations for L12 compounds
Diffusion in intermetallic compounds
Diffusion in intermetallic compounds
Diffusion in intermetallic compounds
Diffusion in intermetallic compounds How to distinguish diffusion mechanisms in alloys (elements A and B) experimentally? - Measure diffusion coefficients of each element, DA and DB and compare ratios.
- E.g. in A3B (L12)*
- 0.11 < DA/DB < 0.85 for 6-jump cycle
- 0.07 < DA/DB < 3 for divacancy
Perturbed angular correlation spectroscopy?
PAC measurements of Cd jump rates in L12 structured compounds* RIn3, RGa3, RSn3 with R=rare earth L12 structure:
PAC measurements of Cd jump rates in L12 structured compounds RIn3, RGa3, RSn3 with R=rare earth Jump rates at phase boundaries:
PAC measurements of Cd jump rates in L12 structured compounds RIn3, RGa3, RSn3 with R=rare earth Jump rates at phase boundaries indicate complex diffusion mechanism in light rare earth tri-indides No defects observed in spectra Is it possible to observe direct evidence?
Stochastic model of Winkler and Gerdau: where
Method of simulating PAC spectra
Simple vacancy diffusion in L12 compounds Review of the simple vacancy model*
Simple vacancy diffusion in L12 compounds Review of the simple vacancy model*
Simulating Simple Vacancy Diffusion in Cu3Au-Structured Compounds…
Deriving stochastic models linked to defect jump rates Developed a nearly automated 3 step process Determine all possible configurations of defects near the probe and atomic jumps among them Correct rates for transitions out of defect-free EFGs
Step 1 Step 1 - Types of defect jumps identified and assigned rates wk’
Step 2 - Determine unique EFGs:
- Determine reorientation rate from EFG q to EFG r:
Step 2 Step 2 - Determine unique EFGs:
- Determine reorientation rate from EFG q to EFG r:
Step 3
Comparison of diffusion models in L12 Defect charges chosen so that contribution of each defect to the EFG is 5.66|V0| where |V0| is the strength of the lattice EFG. All jump rates = Q All [defect] = 0.01
point charge parameters for LaIn3 point charge parameters for LaIn3 thermal vacancies with [V] = exp(1.4)× exp(-(0.36 eV)/kBT) vacancy jump rates: wA = 1.3·105Q× exp(-(0.4 eV)/kBT) wB = 1.3·105Q× exp(-(0.5 eV)/kBT)
Summary: Modeling Complex Diffusion Mechanisms… Developed a 3 step process to develop a stochastic model of fluctuating hyperfine interactions for diffusion mechanisms – applicable to any structure Demonstrated that simulations of PAC spectra for simple vacancy, divacancy, and 6-jump cycle diffusion mechanisms can look different Showed for a physically reasonable set of parameters that one can obtain a signal due to defects in the divacancy mechanism Work continues to determine conditions under which one can unambiguously identify diffusion mechanisms
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