0.4 0.6 0.8 1.0 1.2 1.4 1E-27 1E-23 1E-19 1E-15 1E-11 KMC Le Claire's model Experiment Y Ti Fe Diffusion Coefficient (m 2 /s) 1000/T (K -1 ) Gurpreet Kaur, P. Jegadeesan, D. Murali, B.K. Panigrahi, M.C. Valsakumar, C.S.Sundar Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu, INDIA [email protected] The strength of Nanostructured Ferritic Alloys depends on the distribution of Y-Ti-O nanoclusters in the matrix. These nanoclusters are formed during the high temperature consolidation of the ball milled (powdered) alloy. Understanding the initial phase of formation of these nanoclusters is crucial to predict their overall behavior. We have used first principles methods along with Lattice Kinetic Monte Carlo technique to study the kinetics of nanocluster formation in BCC Iron. Introduction Pairwise bonds First neighbour (eV) Second neighbour (eV) Fe-Y 0.25 0.00 Fe-Ti -0.10 0.00 Fe-O 0.35 0.17 Fe- 0.25 0.00 Y-Y 0.19 0.01 Y-Ti 0.15 0.01 Y-O 0.45 -1.05 Y- -1.40 -0.25 Ti-Ti 0.23 0.13 Ti-O -0.25 -0.55 Ti- -0.25 0.16 - 0.15 -0.21 -O -1.55 -0.75 O-O 0.60 0.40 Pairwise bond energy parameters Migration energy E m (eV) Fe- 0.65 Y- 0.10 Ti- 0.40 O 0.55 Migration Energy Barriers The bond energies are calculated from Density Functional Theory using VASP code with PAW (PBE) psuedo potential with 128 atom supercell. The migration barriers for the solute atoms in bcc iron were calculated using the Nudged Elastic Band (NEB) method Diffusion coefficients of solute atoms The diffusion coefficients of solute atoms in bcc Fe calculated using LKMC and compared with the diffusion coefficients calculated from first principles using Le Claire’s nine frequency model and also the available experimental values. 7.38906 20.08554 54.59815 2.71828 7.38906 Mean, Sigma Time ( s) Mean Sigma Size distribution of clusters References: G.R. Odette, M.J. Alinger and B.D. Wirth, Annu. Rev. Mater. Res. 38 (2008) 471. D.Murali, B.K. Panigrahi, M.C. Valsakumar, Sharat Chandra, C.S. Sundar, Baldev Raj, J. Nucl. Mater. 403 (2010) 113-116 P. Jegadeesan, D. Murali, B.K. Panigrahi, M.C. Valsakumar, C.S. Sundar, International Journal of Nanoscience 10 (2010) 1-5 . M. Ratti, D. Leuvrey, M.H. Mathon, Y.de, Carlan, J. Nucl. Mater. 386, 540-543 (2009). V.A. Borodin and P.V. Vladimirov, J. Nucl. Mater. 386, 106 (2009). 1 10 100 0 100 200 300 400 No. of Clusters Time ( s) 3 10 100 Av. Cluster Size (No. of atoms) 0 2 4 6 8 10 12 14 0 100 200 300 400 500 600 6.4 s 12.8 s 19.2 s 25.6 s 32.1 s 38.5 s 44.9 s 51.3 s 57.7 s 64.2 s Number of cluters R (in Angtrom) 3 4 5 6 7 8 9 10 11 12 13 14 0.0 0.2 0.4 0.6 0.8 1.0 Cumulative Distribution of No.of clusters R (in Angtroms) 2.0x10 -4 4.0x10 -4 6.0x10 -4 8.0x10 -4 1.0x10 -3 1.2x10 -3 1.4x10 -3 2.0x10 -7 4.0x10 -7 6.0x10 -7 8.0x10 -7 1.0x10 -6 D o Vacancy concentration Ti Fe The LKMC Model Two sublattices : 1 st sublattice: regular bcc sites with Fe, Y, Ti, vacancy ( ) 2 nd sublattice: octahedral interstitial sites with Oxygen One Monte Carlo sweep : all the Vacancy and O allowed to jump once A rigid bond model for total energy with interactions up to second neighbor (fitted to first principle calculation) Formation of Y-Ti-O clusters Randomly distributed Y, Ti, O and vacancy in Fe, evolved by vacancy jumps and interstitial O jumps, leading to the formation of clusters 88 88 88 unit cells (1.3 million sites) Y: 0.12%, O: 0.2%, Vac: 1000 ppm Temp. 1150 K Evolution of clusters with time O to Y ratio in the clusters Normal distribution is found to give the best fit for the cluster size distribution (R >4 Å) out of Lognormal, Normal and gamma distributions. [ignoring the initial decaying portion(R < 4 Å) of size distribution]. 5 1 t R k j i ij ij k n k E , ) ( ) ( 0 100 200 300 400 500 0 25 50 75 100 125 150 175 200 Without titanium Number of clusters Cluster size (No.of atoms) 0 100 200 300 400 500 0 25 50 75 100 125 150 175 200 4000 5000 With titanium (0.5at%) Number of clusters Cluster size (No.of atoms) Effect of Titanium E-sp E-init E-final Vacancy Conclusions Mechanism of growth is the coagulation of the clusters. The Cluster Size follow a normal distribution. Presence of titanium reduces the size of clusters . Time exponent shows coagulation of clusters is the growth mechanism