Modeling Complex Diffusion Mechanisms in L 12-Structured Compounds

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

• Step 2

• Determine unique EFGs:
• Determine reorientation rate from EFG q to EFG r:

• Step 3

• For q indexing a defect free EFG, so that

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 = 1.3·105Q× exp(-(0.4 eV)/kBT) wB = 1.3·105Q× 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