publication . Preprint . 2017

Phase field modelling of precipitate morphologies in systems with tetragonal interfacial free energy anisotropy

Roy, Arijit; Gururajan, M P;
Open Access English
  • Published: 05 Aug 2017
A wide variety of morphologies arise due to the tetragonal anisotropy in interfacial free energy. In this paper, we report on a family of Extended Cahn-Hilliard (ECH) models for incorporating tetragonal anisotropy in interfacial free energy. We list the non-zero and independent parameters that are introduced in our model and list the constraints on them. For appropriate choice of these parameters, our model can produce a many of the morphologies seen in tetragonal systems such as di-pyramids, rods, plates and their truncated variants. We analyse these morphologies and show that they indeed are equilibrium morphologies consistent with the Wulff construction.
free text keywords: Condensed Matter - Materials Science
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25 references, page 1 of 2

[1] G. Liu, J.C. Yu, G.Q.M. Lu, and H.M. Cheng, Crystal facet engineering of semiconductor photocatalysts: motivations, advances and unique properties., Chem. Commun. 47 (2011), pp. 6763{83.

[2] M. Egashira, T. Matsumoto, Y. Shimizu, and H. Iwanaga, Gas-sensing characteristics of tin oxide whiskers with di erent morphologies, Sensor. Actuator. 14 (1988), pp. 205{213.

[3] V. Lanteri, T.E. Mitchell, and A.H. Heuer, Morphology of Tetragonal Precipitates in Partially Stabilized ZrO2, J. Am. Ceram. Soc. 69 (1986), pp. 564{569.

[4] P.J. Othen, M.L. Jenkins, and G.D.W. Smith, High-resolution electron microscopy studies of the structure of Cu precipitates in -Fe, Philos. Mag. A 70 (1994), pp. 1{24.

[5] R. Monzen, K. Takada, and C. Watanabe, Coarsening of Spherical Cu Particles in an alpha-Fe matrix, ISIJ Int. 44 (2004), pp. 442{444.

[6] R. Ravelo and M. Baskes, Equilibrium and Thermodynamic Properties of Grey, White, and Liquid Tin, Phys. Rev. Lett. 79 (1997), pp. 2482{2485.

[7] W.J. Boettinger, C.E. Johnson, L.A. Bendersky, K.W. Moon, M.E. Williams, and G.R. Sta ord, Whisker and Hillock formation on Sn, Sn-Cu and Sn-Pb electrodeposits, Acta Mater. 53 (2005), pp. 5033{5050. [OpenAIRE]

[8] M. Sobiech, U. Welzel, E.J. Mittemeijer, W. Hugel, and A. Seekamp, Driving force for Sn whisker growth in the system Cu-Sn, Appl. Phys. Lett. 93 (2008), pp. 21{24.

[9] M. Chen and L.D. Schmidt, Morphology and composition of PtPd alloy crystallites on SiO2 in reactive atmospheres, J. Catal. 56 (1979), pp. 198{218.

[10] Y. Deng, J.L. Wang, K.R. Zhu, M.S. Zhang, J.M. Hong, Q.R. Gu, and Z. Yin, Synthesis and characterization of single-crystal PbTiO3 nanorods, Mater. Lett. 59 (2005), pp. 3272{ 3275.

[11] A.R. Wang and H. Xiao, Controllable preparation of SnO2 nanoplates and nanoparticles via hydrothermal oxidation of SnS2 nanoplates, Mater. Lett. 63 (2009), pp. 1221{1223.

[12] H. Uchiyama, H. Ohgi, and H. Imai, Selective preparation of SnO2 and SnO crystals with controlled morphologies in an aqueous solution system, Cryst. Growth Des. 6 (2006), pp. 2186{2190.

[13] G. Saito, S. Hosokai, M. Tsubota, and T. Akiyama, In uence of solution temperature and surfactants on morphologies of tin oxide produced using a solution plasma technique, Cryst. Growth Des. 12 (2012), pp. 2455{2459.

[14] K.N. Tu and J.C.M. Li, Spontaneous whisker growth on lead-free solder nishes, Mat. Sci. Eng. A 409 (2005), pp. 131{139.

[15] J.C. Heyraud and J.J. Metois, Surface free energy anisotropy measurement of indium, Surf. Sci. 177 (1986), pp. 213 { 220.

25 references, page 1 of 2
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