Description of Surface Energy Anisotropy for BCC Metals

Abstract:

Surface energy anisotropy (SEA) has long been a hot topic in interface science as it has an important role in the interface/surface behaviours for crystalline phases. Most studies aim to determine the numerical values of the anisotropic surface energy in some particular orientations, but few investigate the whole orientation-dependent trend, or the morphology of the polar plot. The present work propose descriptions for SEA of both body centred cubic (BCC) and face centred cubic (FCC) metals by considering the interactions between an atom and its 1^st, 2^nd and 3^rd nearest neighbouring (NN) atoms. The expression makes use of only three coefficients K₁, K₂ and K₃ which are correspondent to the contribution of 1^st, 2^nd and 3^rd NN interactions respectively. This allows estimation of surface energy for all crystallographic orientations if the values for (111), (100) and (110) orientations are provided. Matching of our model with modified analytical embedded-atom method (MAEAM) results demonstrates less than 0.5% average relative error. We also construct the polar plots of BCC metals based on our model and compare them with some other models.

• Periodical: Advanced Materials Research (Volume 922)
• Pages: 446-451
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.922.446
• Online since: May 2014
• Authors: Y.K. Luo*, Rong Shan Qin
• Keywords: Crystal Structure, Interface, Interface Anisotropy, Surface Anisotropy

References

[1] S. Curiotto, H. Chien, H. Meltzman, S. Labat, P. Wynblatt, G.S. Rohrer, W.D. Kaplan, and D. Chatain, Copper crystals on the sapphire plane: orientation relationships, triple line ridges and interface shape equilibrium, J. Mater. Sci. 48 (2013) 3013-3026.

DOI: 10.1007/s10853-012-7080-0

[2] R. V. Zucker, D. Chatain, U. Dahmen, S. Hagège, and W.C. Carter, New software tools for the calculation and display of isolated and attached interfacial-energy minimizing particle shapes, J. Mater. Sci. HTC (2012) 1-13 .

DOI: 10.1007/s10853-012-6739-x

[3] H. Meltzman, D. Chatain, D. Avizemer, T.M. Besmann, and W.D. Kaplan, The equilibrium crystal shape of nickel, Acta Mater. 59 (2011) 3473-3483.

DOI: 10.1016/j.actamat.2011.02.021

[4] J.S. Hong, W. Jo, K.J. Ko, N.M. Hwang, and D.Y. Kim, Equilibrium shape of nickel crystal, Philos. Mag. 89:32 (2009) 2989-2999.

DOI: 10.1080/14786430903164598

[5] A.S. Barnard, X.M. Lin, and L.A. Curtiss, Equilibrium morphology of face-centered cubic gold nanoparticles >3nm and the shape changes induced by temperature, J. Phys. Chem. B. 109 (2005) 24465-24472.

DOI: 10.1021/jp054279n

[6] D. Chatain, V. Ghetta, and P. Wynblatt, Equilibrium shape of copper crystals grown on sapphire, Interface Sci. 12 (2004) 7-18.

DOI: 10.1023/b:ints.0000012290.07441.a8

[7] W. Luo, W. Hu, K. Su, and F. Liu, The calculation of surface free energy based on embedded atom method for solid nickel, Appl. Surf. Sci. 265 (2013) 375-378.

DOI: 10.1016/j.apsusc.2012.11.015

[8] Y.N. Wen and J.M. Zhang, Surface energy calculation of the bcc metals by using the MAEAM, Com. Mat. Sci. 42 (2008) 281-285.

DOI: 10.1016/j.commatsci.2007.07.016

[9] B. Lee and M. Baskes, Second nearest-neighbor modified embedded-atom-method potential, Phys. Rev. B. 62 (2000) 8564-8567.

DOI: 10.1103/physrevb.62.8564

[10] R.L. Davidchack, J.R. Morris, and B.B. Laird, The anisotropic hard-sphere crystal-melt interfacial free energy from fluctuations, J. Chem. Phys. 125 (2006) 094710.

DOI: 10.1063/1.2338303

[11] F. von der Lage and H. Bethe, A method for obtaining electronic eigenfunctions and eigenvalues in solids with an application to sodium, Phys. Rev. 71 (1947) 612-622.

DOI: 10.1103/physrev.71.612

[12] V. Heinonen, A. Mijailović, C.V. Achim, T. Ala-Nissila, R.E. Rozas, J. Horbach, and H. Löwen, Bcc crystal-fluid interfacial free energy in Yukawa systems, J. Chem. Phys. 138 (2013) 044705.

DOI: 10.1063/1.4775744

[13] A. Jaatinen, C. Achim, K. Elder, and T. Ala-Nissila, Thermodynamics of bcc metals in phase-field-crystal models, Phys. Rev. E 80 (2009) 031602.

DOI: 10.1103/physreve.80.031602

[14] R.S. Qin and H.K.D.H. Bhadeshia, Phase-field model study of the effect of interface anisotropy on the crystal morphological evolution of cubic metals, Acta Mater. 57 (2009) 2210-2216.

DOI: 10.1016/j.actamat.2009.01.024

[15] R.S. Qin and H.K.D.H. Bhadeshia, Phase-field model study of the crystal morphological evolution of hcp metals, Acta Mater. 57 (2009) 3382-3390.

DOI: 10.1016/j.actamat.2009.04.001

[16] K.A. Wu and A. Karma, Phase-field crystal modelling of equilibrium bcc-liquid interfaces, Phys. Rev. B. 76 (2007) 184107.

DOI: 10.1103/physrevb.76.184107

[17] Z. Yu and A. Flodström, Orientation of (1x1)-surface free energies of crystals, Surf. Sci. 401 (1998) 236-247.

DOI: 10.1016/s0039-6028(97)01084-4