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Significance Statement
The wide-band gap material gallium nitride (GaN) is of great importance as it has enabled high efficiency white solid-state lighting sources along with numerous other high efficiency devices in the realm of optoelectronics and electronics. Growth of bulk single crystal GaN for future use as a substrate is of great interest, though is challenging due to near impossibility of realizing a congruent, stoichiometric melt. The ammonothermal method circumvents this challenge by dissolving GaN in a supercritical ammonia solution. Little is know about the thermodynamic properties of this solvent under typical operating conditions (T = 400—600 °C, P = 1000—3000 atm) leading to a significant deficiency in understanding the underlying chemical reactions controlling the growth of these crystals. Recent advances have now lead to the development of an equation of state (EOS) for NH3 and its NH3-N2-H2 mixture under these conditions, which in turn has permitted the determination of the equilibrium constant for the ammonia decomposition reaction. This is a foundational step for the ammonothermal process as a whole as it aids in building a platform for the growth of numerous exciting nitride materials in this environment. With this knowledge, the next layer of insight can now be obtained by investigating the solubility of species in this solvent and related on-going chemical reactions leading to improved growth of nitride crystals.
Journal Reference
The Journal of Supercritical Fluids, Volume 107, January 2016, Pages 17-30.
Siddha Pimputkar, Shuji Nakamura
Materials Department, Solid State Lighting and Energy Electronics Center, University of California, Santa Barbara, CA 93106, USA
Abstract
Ammonothermal growth of nitrides occurs at temperatures in excess of 800 K and pressures greater than 150 MPa. For this region, no experimentally verified equation of state (EOS) exists for ammonia, nor is there any accurate description available for the equilibrium constant of the ammonia decomposition reaction for pressures in excess of 100 MPa. To fill this void, experimental P-v-T data was collected for pure ammonia atT > 700 K and compared to extrapolated data from the reference EOS for ammonia. For the extrapolated region, the reference EOS provided excellent agreement to within error of the collected experimental data. A simplified EOS based on the Beattie–Bridgeman (BB) EOS was derived and fit to calculated and, for ammonia, extrapolated reference EOS data for ammonia, hydrogen, and nitrogen (T < 1000 K, P < 300 MPa). By applying mixing rules with separated contributions for polar and non-polar interactions, an EOS was derived for NH3–N2–H2 mixtures. With these expressions, an accurate description for the equilibrium constant for the ammonia decomposition reaction as a function of pressure and temperature was derived and verified against experimental data determined for total system pressures of 92, 151 and 210 MPa at T ∼810 K. Coupling of the EOSs with the equilibrium constant permitted accurate modeling of a sealed autoclave filled with pure ammonia, after incorporating corrections for the expansion of the internal free volume due to thermal expansion and elastic strain response of the autoclave walls due to internal pressure buildup. Calculated total system pressure and equilibrium ammonia density at various temperatures and initial ammonia fill densities are in very good to excellent agreement with experimental data. This paper thus provides a simple EOS for ammonia, hydrogen, nitrogen and NH3–N2–H2 mixtures accurate to within approximately 1–2% in pressure for temperatures greater than 700 K. The equilibrium constant for the ammonia decomposition reaction includes non-ideal mixing contributions from the second virial coefficient with a resulting accuracy in the equilibrium mole fraction of ammonia of approximately 2% for T < 850 K.
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