Modeling Complex Diffusion Mechanisms in L 12-Structured Compounds



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Modeling Complex Diffusion Mechanisms in L12-Structured Compounds

  • Matthew O. Zacate William E. Evenson

  • Mike Lape Michael Stufflebeam


Modeling Complex Diffusion Mechanisms in L12-Structured Compounds

  • Diffusion mechanisms in intermetallic 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?

  • Conventional radiotracer sectioning methods

    • 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?



Method of simulating PAC spectra

  • Stochastic model of Winkler and Gerdau:

  • where



Method of simulating PAC spectra

  • Blume matrix



Simple vacancy diffusion in L12 compounds

  • Review of the simple vacancy model*



Simple vacancy diffusion in L12 compounds

  • Review of the simple vacancy model*



Complex Diffusion in L12 compounds



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

  • Determine unique EFGs to a cutoff distance from the probe and rates of transition

  • 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



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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