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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 70, 2016 - Issue 5
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Original Articles

Heat, mass, and crystal growth of GaN in the ammonothermal process: A numerical study

, &
Pages 460-491 | Received 05 Oct 2015, Accepted 10 Feb 2016, Published online: 17 Aug 2016

References

  • A. Denis, G. Goglio, and G. Demazeau, Gallium Nitride Bulk Crystal Growth Processes: A Review, Mater. Sci. Eng.: R: Rep., vol. 50, no. 6, pp. 167–194, 2006.
  • S. Porowski, High Pressure Crystallization of III-V Nitrides, Acta. Physica. Polonica, vol. 87, no. 2, pp. 295–302, 1995.
  • H. Yamane, M. Shimada, S. J. Clarke, and F. J. DiSalvo, Preparation of GaN Single Crystals Using a Na Flux, Chem. Mater., vol. 9, no. 2, pp. 413–416, 1997.
  • R. Dwilinski, GaN Synthesis by Ammonothermal Method, Acta Physica Polonica, A, vol. 88, no. 5, pp. 833–836, 1995.
  • R. Dwilinski, On GaN Crystallization by Ammonothermal Method, Acta physica Polonica, A, vol. 90, no. 4, pp. 763–766, 1996.
  • D. Ehrentraut and T. Fukuda, The Ammonothermal Crystal Growth of Gallium Nitride; A Technique on The Up Rise, Proc. IEEE, vol. 98, no. 7, pp. 1316–1323, 2010.
  • D. Ehrentraut, Y. Kagamitani, T. Fukuda, F., Orito, S. Kawabata, K. Katano, and S. Terada, Reviewing Recent Developments in the Acid Ammonothermal Crystal Growth of Gallium Nitride, J. Cryst. Growth, vol. 310, no. 17, pp. 3902–3906, 2008.
  • D. Ehrentraut, Y. Kagamitani, C. Yokoyama, and T. Fukuda, Physico-chemical Features of the Acid Ammonothermal Growth of GaN, J. Cryst. Growth, vol. 310, no. 5, pp. 891–895, 2008.
  • R. Dwilinski, R. Doradzinski, J. Garczynski, L. P. Sierzputowski, A. Puchalski, Y. Kanbara, K. Yagi, H. Minakuchi, and H. Hayashi, Excellent Crystallinity of Truly Bulk Ammonothermal GaN, J. Cryst. Growth, vol. 310, no. 17, pp. 3911–3916, 2008.
  • R. Dwilinski, R. Doradzinski, J. Garczynski, L. Sierzputowski, J. M. Baranowski, and M. Kaminska, Exciton Photo-luminescence of GaN Bulk Crystals Grown by the AMMONO Method, Mater. Sci. Eng.: B, vol. 50, no. 1–3, pp. 46–49, 1997.
  • D. R. Ketchum, and J. W. Kolis, Crystal Growth of Gallium Nitride in Supercritical Ammonia, J. Cryst. Growth, vol. 222, no. 3, pp. 431–434, 2001.
  • A. P. Purdy, R. J. Jouet, and C. F. George, Ammonothermal Recrystallization of Gallium Nitride With Acidic Mineralizers, Cryst. Growth Des., vol. 2, no. 2, pp. 141–145, 2002.
  • B. Raghothamachar, W. M. Vetter, M. Dudley, R. Dalmau, R. Schlesser, Z. Sitar, E. Michaels, and J. W. Kolis, Synchrotron White Beam Topography Characterization of Physical Vapor Transport Grown AlN and Ammonothermal GaN, J. Cryst. Growth, vol. 246, no. 3–4, pp. 271–280, 2002.
  • B. Raghothamachar, J. Bai, M. Dudley, R. Dalmau, D. Zhuang, Z. Herro, R. Schlesser, Z. Sitar, B. Wang, M. Callahan, K. Rakes, P. Konkapaka, and M. Spencer, Characterization of Bulk Grown GaN and AlN single Crystal Materials, J. Cryst. Growth, vol. 287, no. 2, pp. 349–353, 2006.
  • M. J. Callahan, B. Wang, L. O. Bouthillette, S. Q. Wang, J. W. Kolis, D. F. Bliss, and F. David, Growth of GaN Crystals Under Ammonothermal Conditions, Materials, vol. 798, pp. 1–6, 2003.
  • A. Yoshikawa, E. Ohshima, T. Fukuda, H. Tsuji, and K. Oshima, Crystal Growth of GaN by Ammonothermal Method, J. Crystal Growth, vol. 260, no. 1–2, pp. 67–72, 2004.
  • T. Hashimoto, K. Fujito, B. A. Haskell, P. T. Fini, J. S. Speck, and S. Nakamura, Growth of Gallium Nitride Via Fluid Transport In Supercritical Ammonia, J. Cryst. Growth, vol. 275, no. 1–2, pp. e525–e530, 2005.
  • T. Hashimoto, K. Fujito, M. Saito, J. S. Speck, and S. Nakamura, Ammonothermal Growth of GaN on an Over-1-inch Seed Crystal, Jpn. J. Appl. Phys., Part 2, vol. 44, no. 50–52, pp. L1570–L1572.
  • Y. Kagamitani, D. Ehrentraut, A. Yoshikawa, N. Hoshino, T. Fukuda, S. Kawabata, and K. Inaba, Ammonothermal Epitaxy of Thick GaN Film Using NH4Cl Mineralizer, Jpn. J. Appl. Phys., Part 1, vol. 45, no. 5A, pp. 4018–4020, 2006.
  • T. Hashimoto, F. Wu, J. S. Speck, and S. Nakamura, Ammonothermal Growth of Bulk GaN, J. Cryst. Growth, vol. 310, no. 17, pp. 3907–3910, 2008.
  • T. Hashimoto, F. Wu, J. S. Speck, and S. Nakamura, Growth of Bulk GaN Crystals by the Basic Ammonothermal Method, Jpn. J. Appl. Phys., vol. 46, no. 10L, p. L889, 2007.
  • B. Wang, M. J. Callahan, K. D. Rakes, L. O. Bouthillette, S. Q. Wang, D. F. Bliss, and J. W. Kolis, Ammonothermal Growth of GaN Crystals in Alkaline Solutions, J. Cryst. Growth, vol. 287, no. 2, pp. 376–380, 2006.
  • B. Wang, and M. J. Callahan, Ammonothermal Synthesis of III-Nitride Crystals, Cryst Growth Des, vol. 6, no. 6, pp. 1227–1246, 2006.
  • B. Wang, and M. J. Callahan, Transport Growth of GaN Crystals by the Ammonothermal Technique using Various Nutrients, J. Cryst. Growth, vol. 291, no. 2, pp. 455–460, 2006.
  • R. Dwilinski, R. Doradzinski, J. Garczynski, L. P. Sierzputowski, A. Puchalski, Y. Kanbara, K. Yagi, H. Minakuchi, and H. Hayashi, Bulk Ammonothermal GaN, J. Cryst. Growth, vol. 311, no. 10, pp. 3015–3018, 2009.
  • R. Dwilinski, R. Doradzinski, J. Garczynski, L. P. Sierzputowski, M. Zajac, and M. Rudzinski, Homoepitaxy on Bulk Ammonothermal GaN, J. Cryst Growth, vol. 311, no. 10, pp. 3058–3062, 2009.
  • S. Zhang, N. S. A. Alt, E. Schlücker, and R. Niewa, Novel Alkali Metal Amidogallates as Intermediates in Ammonothermal GaN Crystal Growth, J. Cryst. Growth, vol. 403, pp. 22–28, 2014.
  • S. Zhang, F. Hintze, W. Schnick, and R. Niewa Intermediates in Ammonothermal GaN Crystal Growth under Ammonoacidic Conditions (Eur. J. Inorg. Chem. 31/2013), Eur. J. Inorg. Chem., 2013, vol. 2013, no. 31, pp. n/a–n/a.
  • T. Richter, and R. Niewa, Chemistry of Ammonothermal Synthesis, Inorganics, vol. 2, no. 1, p. 29, 2014.
  • E. Letts, T. Hashimoto, S. Hoff, D. Key, K. Male, and M. Michaels, Development of GaN Wafers via the Ammonothermal Method, J. Cryst. Growth, vol. 403, pp. 3–6, 2014.
  • S. Pimputkar, S. Kawabata, J. S. Speck, and S. Nakamura, Improved Growth Rates and Purity of Basic Ammonothermal GaN, J. Cryst. Growth, vol. 403, pp. 7–17, 2014.
  • W. Jiang, D. Ehrentraut, B. C. Downey, D. S. Kamber, R. T. Pakalapati, H. D. Yoo, and M. P. D'Evelyn, Highly Transparent Ammonothermal bulk GaN Substrates, J. Cryst. Growth, vol. 403, pp. 18–21, 2014.
  • T. G. Steigerwald, N. S. A. Alt, B. Hertweck, and E. Schluecker, Feasibility of Density and Viscosity Measurements Under Ammonothermal Conditions, J. Cryst. Growth, vol. 403, pp. 59–65, 2014.
  • F. Tuomisto, T. Kuittinen, M. Zając, R. Doradziński, and D. Wasik, Vacancy–hydrogen Complexes in Ammonothermal GaN, J. Cryst. Growth, vol. 403, pp. 114–118, 2014.
  • R. Kucharski, M. Zajac, A. Puchalski, T. Sochacki, M. Bockowski, J. L. Weyher, M. Iwinska, J. Serafinczuk, R. Kudrawiec, and Z. Siemiątkowski, Ammonothermal Growth of GaN Crystals on HVPE-GaN Seeds Prepared with the use of Ammonothermal Substrates, J. Cryst. Growth, vol. 427, pp. 1–6, 2015.
  • D. Ehrentraut, R. T. Pakalapati, D. S. Kamber, Jiang, W., D. W. Pocius, B. C. Downey, M. McLaurin, and M. P. D'Evelyn, High Quality, Low Cost Ammonothermal Bulk GaN Substrates, Jpn. J. Appl. Phys., vol. 52, no. 8S, p. 08JA01, 2013.
  • D. Ehrentraut, and T. Fukuda, Ammonothermal Crystal Growth of Gallium Nitride – A Brief Discussion of Critical Issues, J. Cryst. Growth, vol. 312, no. 18, pp. 2514–2518, 2010.
  • Bockowski, M., Bulk Growth of Gallium Nitride: Challenges and Difficulties, Cryst. Res. Technol., vol. 42, no. 12, pp. 1162–1175, 2007.
  • T. Fukuda, and D. Ehrentraut, Prospects for the Ammonothermal Growth of Large GaN Crystal, J. Cryst. Growth, vol. 305, no. 2, pp. 304–310, 2007.
  • M. Yoshimura, and K. Byrappa, Hydrothermal Processing of Materials: Past, Present and Future, J. Mater. Sci., vol. 43, no. 7, pp. 2085–2103, 2008.
  • B. Roux, O. Louchart, and O. Terhmina, Hydrodynamic aspect of hydrothermal synthesis of quartz bulk flow regimes, J. De Physique IV, vol. 04, no. C2, pp. C2–3–C2–11, 1994.
  • Q.-S. Chen, V. Prasad, and A. Chatterjee, Modeling of Fluid Flow and Heat Transfer in a Hydrothermal Crystal Growth System: Use of Fluid-Superposed Porous Layer Theory, J. Heat Transfer, vol. 121, no. 4, pp. 1049–1058, 1999.
  • Q. S. Chen, V. Prasad, A. Chatterjee, and J. Larkin, A porous media-based transport model for hydrothermal growth, J. Cryst. Growth, 198–199, Part, vol. 1, no. 0, pp. 710–715, 1999.
  • Q. S. Chen, V. Prasad, and W. R. Hu, Modeling of Ammonothermal Growth of Nitrides, J. Cryst. Growth, vol. 258, no. (1–2), pp. 181–187, 2003.
  • Q. S. Chen, S. Pendurti, and V. Prasad, Effects of Baffle Design on Fluid Flow and Heat Transfer in Ammonothermal Growth of Nitrides, J. Cryst. Growth, vol. 266, no. 1–3, pp. 271–277, 2004.
  • Q. S. Chen, S. Pendurti, and V. Prasad, Modeling of Ammonothermal Growth of Gallium Nitride Single Crystals, J. Materi. Sci., vol. 41, no. 5, pp. 1409–1414, 2006.
  • H. Li, E. A. Evans, and G.-X. Wang, Flow of Solution in Hydrothermal Autoclaves with Various Aspect Ratios, J. Cryst. Growth, vol. 256, no. 1–2, pp. 146–155, 2003.
  • D. C. Wilcox Turbulence Modeling for CFD, DCW Industries, Inc., California, 1994.
  • H. Li, G.-X. Wang, and E. A. Evans, Three-dimensional Flow of Solution in an Industry-size Hydrothermal Autoclave Subjected to Non-uniform Heating—effects of a Baffle on Flow and Temperature Separation, J. Cryst. Growth, vol. 271, no. 1–2, pp. 257–267, 2004.
  • H. Li, E. A. Evans, and G. X. Wang, Single- and Multi-hole Baffles—a Heat Transfer and Fluid Flow Control for Hydrothermal Growth, J. Cryst. Growth, vol. 275, no. 3–4, pp. 561–571, 2005.
  • H. Li, and M. J. Braun, Numerical Investigation on Multi-hole Baffle Designs for Industry Hydrothermal Synthesis of Single Crystals, Modell. Simulation Mater. Sci. Eng., vol. 13, no. (8), pp. 1249–1266, 2005.
  • H. Li, M. J. Braun, E. A. Evans, G. X. Wang, G. Paudel, and J. Miller, Natural Convection Flow Structures and Heat Transfer in a Model Hydrothermal Growth Reactor, Int. J. Heat Fluid Flow, vol. 26, no. 1, pp. 45–55, 2005.
  • H. Li, C. Xing, and M. Braun, Natural Convection in a Bottom-heated top-cooled Cubic Cavity with a Baffle at the Median Height: Experiment And Model Validation, Heat Mass Transfer, vol. 43, no. 9, pp. 895–905, 2007.
  • H. Li, C. Xing, and M. Braun, Flows in a Lower Half Heated Upper Half Cooled Cylindrical Model Reactor Loaded with Porous Media, Heat Mass Transfer, vol. 43, no. 11, pp. 1201–1211, 2007.
  • H. Li, and M. Braun, Flow Structure and Transport Mechanism in Lower Half Heated Upper Half Cooled Enclosures in Laminar Flow Regime, Heat Mass Transfer, vol. 42, no. 9, pp. 823–834, 2006.
  • H. Li, and M. Braun, Flow Structure and Wall Layer Control in a Lower Half Heated Upper Half Cooled Enclosure with Superimposed Temperature Deviations, Heat Mass Transfer, vol. 42, no. 11, pp. 1049–1061, 2006.
  • H. Li, The Wall Layer Interactions in a Partially Heated Rectangular Enclosure, Int. J. Chem. Reactor Eng., 8, 2010.
  • Y. Masuda, A. Suzuki, Y. Mikawa, Y. Kagamitani, T. Ishiguro, C. Yokoyama, and T. Tsukada, Numerical Simulation of GaN Single-crystal Growth Process in Ammonothermal Autoclave – Effects of Baffle Shape, Int. J. Heat Mass Transfer, vol. 53, no. 5–6, pp. 940–943, 2010.
  • Y. Masuda, A. Suzuki, Y. Mikawa, V. Chani, C. Yokoyama, and T. Tsukada, Numerical Simulation of Hydrothermal Autoclave for Single-Crystal Growth Process, J. Therm. Sci. Technol., vol. 3, no. 3, pp. 540–551, 2008.
  • Y. Masuda, A. Suzuki, T. Ishiguro, and C. Yokoyama, Heat and Fluid Flow in Solvothermal Autoclave for Single-Crystal Growth Process, J. Ther. Sci. Technol., vol. 7, no. 2, pp. 379–386, 2012.
  • Y. Masuda, A. Suzuki, T. Ishiguro, and C. Yokoyama, Numerical Simulation of Heat, and Fluid Flow in Ammonothermal GaN Bulk Crystal Growth Process, Jpn. J. Appl. Phys., vol. 52, no. 8, pp. 08JA05–08JA05–03, 2013.
  • J. Erlekampf, J. Seebeck, P. Savva, E. Meissner, J. Friedrich, N. S. A. Alt, E. Schlücker, and L. Frey, Numerical Time-dependent 3D Simulation of Flow Pattern and Heat Distribution in An Ammonothermal System with Various Baffle Shapes, J. Cryst. Growth, vol. 403, pp. 96–104, 2014.
  • S. Pendurti, Q. Chen, S., and V. Prasad, Modeling Ammonothermal Growth of GaN Single Crystals: The Role of Transport, J. Cryst. Growth, vol. 296, no. 2, pp. 150–158, 2006.
  • V. N. Popov, Y. S. Tsivinskaya, B. T. Bekker, K. A. Kokh, and A. E. Kokh, Numerical Investigation of Heat-mass Transfer Processes in Hydrothermal Growth System, J. Cryst. Growth, vol. 289, no. 2, pp. 652–658, 2006.
  • Y.-N. Jiang, Q.-S. Chen, and V. Prasad, Numerical Simulation of Ammonothermal Growth Processes of GaN Crystals, J. Cryst. Growth, vol. 318, no. 1, pp. 411–414, 2011.
  • S. V. Patankar Numerical Heat Transfer and Fluid Flow, Taylor & Francis, 1980.
  • M. Kaviany Principles of Heat Transfer in Porous Media, Springer-Verlag, New York, 2012.
  • C. Beckermann, S. Ramadhyani, and R. Viskanta, Natural Convection Flow and Heat Transfer Between a Fluid Layer and a Porous Layer Inside a Rectangular Enclosure, J. Heat Transfer, vol. 109, no. 2, pp. 363–370, 1987.
  • C. Beckermann, R. Viskanta, and S. Ramadhyani, Natural Convection in Vertical Enclosures Containing Simultaneously Fluid and Porous Layers, J. Fluid Mech., vol. 186, pp. 257–284, 1988.
  • S. Whitaker, Advances in Theory of Fluid Motion in Porous Media, Ind. Eng. Chem., vol. 61, no. 12, pp. 14–28, 1969.
  • K. Vafai, and C. L. Tien, Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media, Int. J. Heat Mass Transfer, vol. 24, no. 2, pp. 195–203, 1981.
  • Mirzaee I. Kakhki Comprehensive computational investigation of gallium nitride ammonothermal crystal growth, Doctorate Dissertation, Universit of Massachusetts Lowell, 2015.
  • P. W. Gibson, and M. Charmchi, Modeling Convection/diffusion Processes in Porous Textiles with Inclusion of Humidity-dependent Air Permeability, Int. Commun. Heat Mass Transfer, vol. 24, no. 5, pp. 709–724, 1997.
  • I. M. Kakhki, M. Charmchi, and H. Sun, Computational Investigation of Gallium Nitride Ammonothermal Crystal Growth, Proc. ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology, American Society of Mechanical Engineers, pp. V003T009A001-V003T009A001.
  • V. Prasad, Convective Flow Interaction and Heat Transfer Between Fluid and Porous Layers, Convective Heat Mass Transfer Porous Media, vol. 196, pp. 563–615, 1991.
  • N. Epstein, On Tortuosity and the Tortuosity Factor in Flow and Diffusion Through Porous Media, Chem. Eng. Sci., vol. 44, no. 3, pp. 777–779, 1989.
  • B. P. Boudreau, The Diffusive Tortuosity of Fine-grained Unlithified Sediments, Geochimica et Cosmochimica Acta, vol. 60, no. 16, pp. 3139–3142, 1996.
  • G. H. Neale, and W. K. Nader, Prediction of Transport Processes within Porous Media: Diffusive Flow Processes within an Homogeneous Swarm of Spherical Particles, AIChE J., vol. 19, no. 1, pp. 112–119, 1973.
  • O. Levenspiel Chemical Reaction Engineering, 3rd ed., John Wiley & Sons, New York, NY, 1999.
  • R. Carbonell, and S. Whitaker Heat and Mass Transfer in Porous Media, in J. Bear and M. Y. Corapcioglu (eds.), Fundamentals of Transport Phenomena in Porous Media, Springer, Netherlands, pp. 121–198, 1984.
  • K. J. Laidler, The Development of the Arrhenius Equation, J. Chem. Educ., vol. 61, no. 6, p. 494, 1984.
  • D. L. Youngs Time-dependent Multi-Material Flow with Large Fluid Distribution, in Numerical methods for fluid dynamics, Morton and Norman, Editor, pp. 187–221, 1996.
  • W. F. Noh and P. Woodward, SLIC (Simple Line Interface Calculation), Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede, A. Vooren, and P. Zandbergen, eds., Springer Berlin Heidelberg, pp. 330–340, 1976.
  • B. D. Nichols, W. C. Hirt, and R. S. Hotchkiss SOLA-VOF: A Solution Algorithm for Transient Fluid Flow with Multiple Free Boundaries, Technical report, La-8355, Los Alamos National Lab, 1980.
  • A. J. Chorin, Curvature and Solidification, J. Comput. Phys., vol. 57, no. 3, pp. 472–490, 1985.
  • J. Y. Poo, and N. Ashgriz, A Computational Method for Determining Curvatures, J. Comput. Phys., vol. 84, no. 2, pp. 483–491, 1989.
  • J. U. Brackbill, D. B. Kothe, and C. Zemach, A Continuum Method for Modeling Surface Tension, J. Comput. Phys., vol. 100, no. 2, pp. 335–354, 1992.
  • E. Shirani, N. Ashgriz, and J. Mostaghimi, Interface Pressure Calculation Based on Conservation of Momentum for Front Capturing Methods, J. Comput. Phys., vol. 203, no. 1, pp. 154–175, 2005.
  • M. Seifollahi, E. Shirani, and N. Ashgriz, An Improved Method for Calculation of Interface Pressure Force in PLIC-VOF Methods, Eur. J. Mech.- B/Fluids, vol. 27, no. 1, pp. 1–23, 2008.
  • M. Bussmann, J. Mostaghimi, and S. Chandra, On A Three-dimensional Volume Tracking Model of Droplet Impact, Phys. Fluids, vol. 11, no. 6, pp. 1406–1417, 1999.
  • M. Pasandideh-Fard, S. Chandra, and J. Mostaghimi, A Three-dimensional Model of Droplet Impact and Solidification, Int. J. Heat Mass Transfer, vol. 45, no. 11, pp. 2229–2242, 2002.
  • M. Pasandideh-Fard, M. Bussmann, S. Chandra, and J. Mostaghimi, Simulating Droplet Impact on a Substrate of Arbitrary Shape, Atomization Sprays, vol. 11, no. 4, pp. 397–414, 2001.
  • I. Mirzaii, and M. Passandideh-Fard, Modeling Free Surface Flows in Presence of An Arbitrary Moving Object, Int. J. Multiphase Flow, vol. 39, pp. 216–226, 2012.
  • S. J. Cummins, M. M. Francois, and D. B. Kothe, Estimating Curvature from Volume Fractions, Comput. Struct., vol. 83, no. 6–7, pp. 425–434, 2005.
  • W. J. Rider, and D. B. Kothe, Reconstructing Volume Tracking, J. Comput. Phys., vol. 141, no. 2, pp. 112–152, 1998.
  • H. Esmailzadeh, and M. Passandideh-Fard, Numerical and Experimental Analysis of the Fluid-structure Interaction in Presence of a Hyperelastic Body, J. Fluids Eng., vol. 136, no. 11, p. 12, 2013.
  • I. Mirzaii, H. Sabahi, M. Passandideh-Fard, and N. Shale Simulation of Liquid Fuel Atomization in an Industrial Spray Nozzle of a Powerplant Boiler, Proc. ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels, American Society of Mechanical Engineers, pp. 1827–1833.
  • I. M. Kakhki, M. Charmchi, H. Sun, and M. Song Numerical Simulation of Air Sampling in Micro Scale Rising Bubbles, Proc. ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology, American Society of Mechanical Engineers, pp. V003T009A008-V003T009A008.
  • Mirzaee I. Kakhki, and M. Passandideh Fard The Impact of a Solid Object on to a Liquid Surface, Proc. 19th Annual Conference on Mechanical Engineering-ISME2011.
  • I. Mirzaii, and M. Passandideh-Fard Simulation of Solid-Liquid Interaction in Presence of a Free Surface, Proc. ASME-JSME-KSME 2011 Joint Fluids Engineering Conference, American Society of Mechanical Engineers, pp. 2361–2371.
  • H. Zhang, M. Charmchi, D. Veilleux, and M. Faghri, Numerical and Experimental Investigation of Melting in the Presence of a Magnetic Field: Simulation of Low-gravity Environment, J. Heat Transfer, vol. 129, no. 4, pp. 568–576, 2006.
  • D. Veilleux, E. Gonçalves, M. Faghri, Y. Asako, and M. Charmchi, Phase Change in a Three-dimensional Rectangular Cavity Under Electromagnetically Simulated Low Gravity: Top Wall Heating with an Unfixed Material, Numer. Heat Transfer; Part A: Appl., vol. 48, no. 9, pp. 849–878, 2005.
  • D. L. Veilleux, M. Faghri, Y. Asako, and M. Charmchi, Convection Enhancement in Melting by Electromagnetic Fields in a Low-gravity Environment: Side Wall Heating, Numer. Heat Transfer; Part A: Appl., vol. 51, no. 2, pp. 129–158, 2007.
  • D. L. Veilleux, E. Gonçalves, M. Faghri, Y. Asako, and M. Charmchi, Phase Change in a Three-dimensional Rectangular Cavity Under Electromagnetically Simulated Low-gravity: Side Wall Heating, Int. J. Numer. Methods Heat Fluid Flow, vol. 15, no. 7, pp. 710–739, 2005.
  • E. Gonçalves, M. Faghri, Y. Asako, and M. Charmchi, Nemrical Solution of Melting in Side-heated Rectangular Enclosure Under Electromagnetically Simulated Low Gravity, Numer. Heat Transfer, Part A: Appl., vol. 47, no. 4, pp. 315–332, 2005.
  • E. Gonçalves, M. Faghri, Y. Asako, and M. Charmchi, Numerical Sollution of Melting Processes for Unfixed Phase-Change Material in the Presence of Electromagnetically Simulated Low Gravity, Numer. Heat Transfer, Part A: Appl., vol. 46, no. 4, pp. 343–365, 2004.
  • Y. Asako, E. Gonçalves, M. Faghri, and M. Charmchi, Nemrical Solution of Melting Processes for Fixed and Unfixed Phase Change Material in the Presence of Magnetic Field-simulation of Low-gravity Environment, Numer. Heat Transfer, Part A: Appl., vol. 42, no. 6, pp. 565–583, 2002.
  • S. Alavi, M. Passandideh-Fard, and J. Mostaghimi, Simulation of Semi-molten Particle Impacts Including Heat Transfer and Phase Change, J. Therm. Spray Tech, vol. 21, no. 6, pp. 1278–1293, 2012.
  • Y. Asako, M. Faghri, M. Charmchi, and P. A. Bahrami, Numerical Solution for Melting of Unfixed Rectangular Phase-change Material Under Low-gravity Environment, Numer. Heat Transfer, Part A: Appl., vol. 25, no. 2, pp. 191–208, 1994.
  • W. D. Bennon, and F. P. Incropera, Developing Laminar Mixed Convection with Solidification in a Vertical Channel, J. Heat Transfer, vol. 110, no. 2, pp. 410–415, 1988.
  • B. Ghasemi, and M. Molki, Melting of Unfixed Solids in Square Cavities, Int. J. Heat Fluid Flow, vol. 20, no. 4, pp. 446–452, 1999.
  • Y. Cao, and A. Faghri, A Numerical Analysis of Phase-change Problems Including Natural Convection, J. Heat Transfer, vol. 112, no. 3, pp. 812–816, 1990.
  • M. Asako, and Y. Faghri, Effect of Density Chage on Melting of Unfixed Rectangular Phase-change Material Under Low-Gravity Environment, Numer. Heat Transfer, Part A: Appl., vol. 36, no. 8, pp. 825–838, 1999.
  • National Institute of Standards and Technology, http://www.nist.gov/.
  • H. Shibata, Y. Waseda, H. Ohta, K. Kiyomi, K. Shimoyama, K. Fujito, H. Nagaoka, Y. Kagamitani, R. Simura, and T. Fukuda, High Thermal Conductivity of Gallium Nitride (GaN) Crystals Grown by HVPE Process, Mater. Trans., vol. 48, no. 10, pp. 2782–2786, 2007.
  • C.-H. He, and Y.-S. Yu, New Equation for Infinite-Dilution Diffusion Coefficients in Supercritical and High-Temperature Liquid Solvents, Ind. Eng. Chem. Res., vol. 37, no. 9, pp. 3793–3798, 1998.
  • A. J. Chapman, Fundamentals of Heat Transfer, Prentice Hall, NJ, 1987.
  • T. L. Bergman, A. S. Lavine, F. P. Incropera, D. P. Dewitt, Chemical Reaction Engineering, 7th ed., John Wiley & Sons, New York, NY, 2007.
  • Q. Bao, M. Saito, K. Hazu, Y., Kagamitani, K. Kurimoto, D. Tomida, K. Qiao, T. Ishiguro, C. Yokoyama, and S. F. Chichibu, Ammonothermal growth of GaN on a self-nucleated GaN seed crystal, J. Cryst. Growth, vol. 404, pp. 168–171, 2014.

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