# Presentation: 334321

## Diffusion along dislocation cores in metals

- G. P. Purja Pun and Y. Mishin
- Department of Physics and Astronomy, George Mason University, Fairfax, VA

_*Support*_*:* Air Force Office of Scientific Research (AFORS), Metallic Materials Program

**How do atoms move in the dislocation core?**

## Outline

- What do we know about dislocation (“pipe”) diffusion?
- Experimental data
- Theory and modeling
- Diffusion along a 1⁄2<110> screw dislocation in Al
- Methodology
- Results
- Do we need point defects for dislocation diffusion?

## Processes controlled/affected by dislocation diffusion:

- Precipitation and phase transformations
- Dynamic strain ageing
- Solute segregation
- Creep
- Coarsening
- Mechanical alloying
- Sintering
- Many others

** ****Dislocation diffusion in materials:**
**Why is it important?**

- Nucleation, growth

- Segregation

- Coarsening

## Measurements of dislocation diffusion

- Usually require radioactive isotopes
- Based on simplified models: *a la* Fisher but with a regular arrangement of parallel dislocations (wall or network)
- Interpretation of experimental data often problematic
- Most of the direct measurements have been done in the 1960s-70s and summarized by Balluffi and Granato (1979). Few measurements in the 1980s-1990s; ***very*** few these days.
- The most recent paper on dislocation self-diffusion in metals:
- 	Y. Shima et al.Mater. Trans. 43, 173 (2002), ultra-high-purity iron
- SIMS can be used for impurity diffusion
**Indirect methods:** from kinetics of processes
- Internal friction
- Dislocation climb
- Dislocation loop shrinkage
- Void shrinkage
- Based on crude models with unknown parameters. Highly inaccurate

**Measurements of dislocation diffusion**

## Simulations of dislocation diffusion

- Mainly calculations of vacancy formation energies and jump barriers at 0 K. Low barriers - fast diffusion
- Identification of “high-diffusivity paths”
- Correlation factors are ignored. – Big mistake!
- Quasi-1D confinement may lead to strong correlation effects (Stark, late 1980s; Qin and Murch, 1993)
- MD simulations: diffusion coefficients of vacancies, not atoms
- Only vacancies were considered in almost all studies

##  What do we know about dislocation diffusion today?

- Dd >> D; Qd = (0.6-0.7)Q; both depend on the dislocation Burgers vector and character (edge/screw)
- Diffusion is *believed* to be mediated by vacancies. The actual diffusion mechanisms remain unknown
- Analogy with GB diffusion suggest a variety of possible mechanisms

**- Not much...**

##  Diffusion along a 1⁄2[110] screw dislocation in Al

- EAM potential for Al. Accurately reproduces cij,  SF, point defects, diffusion, etc.
- Cylindrical block with dynamic and fixed atoms (7344 total)
- Dissociation into Shockley partials in agreement with experiment
- Introduce a single defect (vacancy or interstitial), or no defect
- Run MD for 30 nanoseconds at 750-1000 K (Tm= 1042 K)
- MSD of atoms for 3-7 ns:
- Correction for equilibrium defect concentration

## Mean-squared displacements

- With a vacancy

**Mean-squared displacements**

- R=0.7 nm

## How to find the dislocation diffusivity

**How to find the dislocation diffusivity**

- Intrinsic

- With a vacancy

- D*I*d  A/e; rd

- Ddraw  A/e; rd

- Similar equation for interstitials

## Intrinsic dislocation diffusivity

- Ed = 0.65 eV
- Dd0 = 7.2410-8 m2/s
- rd = 0.59 nm
- E = 1.32 eV
- Ed/E = 0.49

## Comparison with experiment

## Contribution of vacancy diffusion

- Ed = 0.66 eV

**The vacancy contribution is relatively small**

## Contribution of interstitial diffusion

**The interstitial contribution is negligible**

**The intrinsic diffusion dominates!**

- Ed = 0.65 eV

## What is the intrinsic mechanism?

- The dislocation line moves around the average position due to thermal fluctuations
- The motion occurs by the nucleation and spreading of double-jogs  shuffling of atoms
- This thermal motion has a stochastic component which gives rise to diffusion
- Perfect sliding would translate entire rows  zero correlation factor
- Need to understand more details

## Dislocation with a vacancy

**Dislocation with a vacancy**

- The vacancy is wandering around the core
- The vacancy is not absorbed by the core
- Due to the thermal motion, the dislocation easily breaks away from the vacancy
- Does the vacancy induce the jog formation?

- Visualization by potential energy

## Dislocation without point defects

**Dislocation without point defects**

- Still observe jog formation and thermal motion

## Vacancy excursions: Intrinsic case

- 0 ns

- 0.2 ns

- 0 ns

- 0.2 ns

**T = 900 K**

## Ongoing and future work

- What exactly happens in the core during the extrinsic diffusion process?
- Extension to edge and mixed dislocations
- 	[preliminary result: no significant intrinsic diffusion in edge dislocations]
- Instead of Al, try a metal with a low stacking fault energy
- Extension to the Al-Li
- If the intrinsic diffusion is confirmed, we may need to reconsider the role of point defects in dislocation diffusion