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Abstract
We investigate the thermodynamic properties of the ceramic material Si3B3N7 which has so far only been synthesized as an amorphous compound. Using Monte Carlo simulations, we investigate the stability of both solid and fluid phases of Si3B3N7, in order to gain insights into the proper synthetic conditions needed to generate the stable amorphous and crystalline phases of this compound. We study the ternary liquid–gas region of the phase diagram at temperatures above the theoretical glass transition in this system, and construct an approximate ‘metastable’ phase diagram of Si3B3N7. In addition we study the stability of the amorphous and crystalline phases in the solid state against the decomposition into the binary phases h-BN and β-Si3N4 as a function of the size of the crystallites involved, and the stability of the melt against evolution of nitrogen as a function of nitrogen pressure.
Acknowledgements
Funding was kindly provided by the DFG via SFB408.
Notes
1Current address: FIZ Karlsruhe, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen.
Notes
1. The average pair correlation function is essentially a one-time property of the system, but distinguishing between glass and liquid requires the measurement of two-time properties representing the response to some external action, such as the viscosity.
2. Since the specific form of the potential is rather complex, we refer to the literature Citation25 for further details.
3. In addition, MD simulations in the melt (at 2500 K) were performed that allowed us to tentatively calibrate the time-scale of the MC-simulations via a comparison of the mean square displacements (at least in the high-temperature region). We found that 1 MCC corresponded to approximately 0.5 fs.
4. Note that for a system that relaxes according to a Debye law, a value of the BSPs larger than 1/e would imply that the relaxation times τ exceeded the observation time t obs.
5. For high enough pressures, we are dealing with a solid phase even at very high temperatures – there is no critical point in the solid–fluid transition.
6. We would expect the free energy barriers associated with bond switches in the liquid to be much lower than those associated with the break-up of a small molecule or cluster.
7. For V ≫ V 0 and ⟨N cl⟩ t ≫ 1, ⟨S⟩ t ≈ ⟨N cl⟩ t ln(V/V 0).
8. The simulations presented took the equivalent of about 5 years on a 3.2 GHz processor.
9. Many other criteria did appear to indicate equilibrium at temperatures above 2000 K, however, such as the potential energy as a function of time.
10. The hexagonal unit cells had been transformed to the corresponding orthorhombic setting.
11. In earlier work Citation14, we have proposed a model for a-Si3B3N7 consisting of sintered crystal fragments of diameter ≈5–10 Å. The energy difference between this model and the phase segregated material, ≈0.2 eV/atom, agrees satisfactorily with a rough estimate of the interface energy of the crystal fragment model, ≈0.3 eV/atom.
12. In the super-cooled state, the cluster size could increase considerably.
13. An interesting extension to Gibbs ensemble simulations that cover solid-vapour phase equilibria has recently been proposed Citation38.