Materials Chemistry 2016, Valencia, Spain Solute effect on grain boundary migration Yan Huang BCAST, Brunel University London, UK Thanks to: EPSRC UK for financial support Alcan (Rio-Tinto) Inter for supplying materials The University of Manchester for experimental support Mr I Brough and Mr S Dover for technical assistance Prof J Humphreys for technical and academic guidance.

Materials Chemistry 2016, Valencia, Spain Solute effect on GBM  Experiments and results – kinetics of grain boundary migration  “Solute drag” theory  Linear thermodynamics of GBM  “Solute trap” model  Summary

Materials Chemistry 2016, Valencia, Spain GBM-experiments  Material High purity Al (5Ns) Single-phase binary Al alloys: Al-0.05Si Al-0.13Mg, Al-0.91Mg Al-0.05Mn, Al-0.3Mn  Specimen preparation Single crystal growth-{110} CDC at RT, Spark-cut and polish   3  1mm disks. Channel die compression (CDC)Hot stage for in situ annealing SEM in-situ annealing + EBSD µ

Materials Chemistry 2016, Valencia, Spain BSI image and EBSD map Al-0.05Mn GBM-results  Deformed/recovered matrix was uniform, providing uniform driving pressure.  REX was initiated from the scratch.  Only a few grains grew extensively.  The growth was directional. Inverse pole figures showing the distribution of misorientation axes of the fast growing grains. Misorientation

Materials Chemistry 2016, Valencia, Spain Effect of misorientation angle GBM-results Effect of misorientation axis

Materials Chemistry 2016, Valencia, Spain Velocity vs pressure in HP-Al, l-0.05Si HP-AlAl-0.05Si GBM-results

Materials Chemistry 2016, Valencia, Spain Al-0.13MgAl-0.91Mg Velocity vs pressure in Al-Mg GBM-results

Materials Chemistry 2016, Valencia, Spain Al-0.05MnAl-0.3Mn GBM-results Velocity vs pressure in Al-Mn

Materials Chemistry 2016, Valencia, Spain GBM-results  Velocity V  effective driving pressure P: V = MP  Mobility M=M 0 exp(-Q/RT) is thus defined by V/P

Materials Chemistry 2016, Valencia, Spain Basic experimental observations:  Substantially reduced boundary mobility M, 2-4 orders   Increased recrystallization temperature, >200°C   Linear velocity and pressure relationship, V  P  Increased activation energy Q   M 0 ~ , much higher than D 0 ~10 -4 The kinetics is against the widely accepted “solute drag” theory! Solute controlled GBM

Materials Chemistry 2016, Valencia, Spain  A solute “atmosphere” in GB.  The atmosphere diffuses along with but lags behind the moving GB — the origin of “solute drag”. Lücke and Detert’s: Acta Met., 5 (1957)628. J. W. Cahn, Acta Met., 10(1962)789. K. Lücke and H. Stüwe, Recovery and Recrystallization of Metals, Interscience, New York, (1963) 131. — CLS theory Lücke and Detert’s model “Solute drag” theory The interaction between GB and solute explains the solute effect. E - the interaction energy between a solute atom and GB X gb, X m - the solute concentration in GB and the matrix respectively.

Materials Chemistry 2016, Valencia, Spain  Lücke and Stüwe’s model The drag force due to the interaction between solute atoms and the GB, N v –atom number per unit volume C(x) - solute concentration in GB x - distance from the centre plane of GB  Cahn’s model C 0 - the solute concentration in the matrix.  Velocity and pressure relationship where,  and  are constants. CLS assumed E(x) “Solute drag” theory

Materials Chemistry 2016, Valencia, Spain  Total derivative of E(x) with respect to x, dE(x)/dx, does not exist!!!  Chemical potential gradient determines the kinetics of diffusion.  For an ideal solution  Solute segregation occurs to eliminate the chemical potential gradient across GB  “Solute drag” does not exist!! “Solute drag” theory

Materials Chemistry 2016, Valencia, Spain  Atoms jump to either side of GB   G results in a net GB velocity, V = V 1  2 - V 2  1  When  G/kT<<1 then where Atomic free energy across GB Thermodynamics of GBM Q=  H*=  G*+T  S* V=MP

Materials Chemistry 2016, Valencia, Spain In the linear thermodynamic state  G/kT<<1; V << V 1  2 or V 2  1 The free energy difference is small compared to the system energy level or the net rate of change in one direction is small compared to the two rates in opposite directions. There is a microscopic reversibility or local equilibrium Equilibrium laws apply locally and “solute drag” is impossible. Thermodynamics of GBM

Materials Chemistry 2016, Valencia, Spain Thermal processes during annealing without external field is in the linear region Typical values of  G/kT for aluminium alloys Thermodynamics of GBM

Materials Chemistry 2016, Valencia, Spain  The interaction between solute atoms and boundary lowers the free energy of the boundary.  An extra entropy accompanies with the segregation.  A segregated GB behaves like an energy trap, requiring higher level of thermal agitation for atoms to pass through — “solute trap” “Solute trap” model — Basic idea

Materials Chemistry 2016, Valencia, Spain — Activation energy increase “Solute trap” model  Free energy decrease per atom due to solute segregation: X gb -solute concentration (mole fraction) in GB.  Entropy increase (for a binary system)  Activation energy increase.  M 0 increase

Materials Chemistry 2016, Valencia, Spain  Reduction of M and increase of T REX due to Q increase.  The linear relationship V=MP.  M dependence on solute type, concentration and boundary characters.  Increase of M 0 with solute concentration.  Linear correlation between Q and ln(M 0 ) through their links to activation entropy. “Solute trap” model — what it explains about solute effect

Materials Chemistry 2016, Valencia, Spain The correlation between M o and Q “Solute trap” model

Materials Chemistry 2016, Valencia, Spain Summary 1.Solute elements substantially reduce grain boundary mobility in Al. 2.“Solute drag” theory cannot explain linear velocity- pressure relationship and is thermodynamically incorrect. 3.Thermal activated processes during static annealing are in the range of linear thermodynamics and GB velocity and driving pressure is linearly related. 4.The proposed “solute trap” model can explain most experimental findings.

Materials Chemistry 2016, Valencia, Spain Thanks for your attention!