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The (total) free energy per bulk unit is conveniently defined as gTiX = limn→ GTiX (n+1 ) - GTiX (n) where n is the number of bilayers in the TiX slab. Since the bulk energy does not depend on the actual surface termination, we could also replace GTiX (n+1 ) by GTiX/Ti (n+1 ) or GTiX/X (n+1 ) if we simultaneously replace GTiX (n) by GTiX/Ti (n) or GTiX/X (n), respectively.
-
The (total) free energy per bulk unit is conveniently defined as g Ti X = lim n → G Ti X (n + 1) - G Ti X (n) where n is the number of bilayers in the Ti X slab. Since the bulk energy does not depend on the actual surface termination, we could also replace G Ti X (n + 1) by G Ti X / Ti (n + 1) or G Ti X / X (n + 1) if we simultaneously replace G Ti X (n) by G Ti X / Ti (n) or G Ti X / X (n), respectively.
-
-
-
-
56
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77956705567
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We note that we could have chosen nonstoichiometric slabs as initial configurations of the surface and adsorb additional layers on one of the two equivalent sides of this slab. In this case, we need to use a modified version of the definition of Gr TiX/Ti. We emphasize, however, that the results presented here are independent of the choice of the definition of Gr TiX/Ti, that is, both definitions are equivalent.
-
We note that we could have chosen nonstoichiometric slabs as initial configurations of the surface and adsorb additional layers on one of the two equivalent sides of this slab. In this case, we need to use a modified version of the definition of G r Ti X / Ti. We emphasize, however, that the results presented here are independent of the choice of the definition of G r Ti X / Ti, that is, both definitions are equivalent.
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M. W. Chase, Jr. (American Chemical Society/American Institute of Physics for the National Institute of Standards and Technology, Washington, D.C./New York
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We are not aware of determinations of mean frequencies of Ti and X in TiX (X=C,N ) which could directly enable an estimate of the vibrational contributions similar to that given in Ref.. Because there is a large difference in masses between Ti and X one can expect a larger correction in the vibrational free energy for the lighter X. However, differences in such vibrational contributions will only shift the crossing points in the free energies of reaction and therefore not alter qualitative predictions or the value of the presented method.
-
We are not aware of determinations of mean frequencies of Ti and X in Ti X (X = C, N) which could directly enable an estimate of the vibrational contributions similar to that given in Ref.. Because there is a large difference in masses between Ti and X one can expect a larger correction in the vibrational free energy for the lighter X. However, differences in such vibrational contributions will only shift the crossing points in the free energies of reaction and therefore not alter qualitative predictions or the value of the presented method.
-
-
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59
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77956701315
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The AIT-SE formalism is essentially designed for oxides in equilibrium with an O2 -dominated environment. Here, we consider TiX in a much more complicated environment. However, the above definitions, steps, and conclusions readily carry over to growth of an oxide in an environment that is more complex than a pure or O2 -dominated environment.
-
The AIT-SE formalism is essentially designed for oxides in equilibrium with an O 2 -dominated environment. Here, we consider Ti X in a much more complicated environment. However, the above definitions, steps, and conclusions readily carry over to growth of an oxide in an environment that is more complex than a pure or O 2 -dominated environment.
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In practice, measuring the exhaust rate Rexh (as a function of the supply rate Rsup) that is required to keep the total deposition pressure constant suffices to determine the scaled deposition rate.
-
In practice, measuring the exhaust rate R exh (as a function of the supply rate R sup) that is required to keep the total deposition pressure constant suffices to determine the scaled deposition rate.
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We note that rate equations may be required even in cases where the relevant atomic chemical potential can be determined from that of gases that are supplied and for which the concentrations in the supply gas is known. Equation clearly shows that the steady-state concentrations will in general differ from the concentrations in the supply gas. Using experimental deposition parameters for TiN, we find that deviations in the steady-state pressure pi from those that are expected from the concentration in the supply gas pi0 = ci p can become as large as 20%.
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We note that rate equations may be required even in cases where the relevant atomic chemical potential can be determined from that of gases that are supplied and for which the concentrations in the supply gas is known. Equation clearly shows that the steady-state concentrations will in general differ from the concentrations in the supply gas. Using experimental deposition parameters for TiN, we find that deviations in the steady-state pressure p i from those that are expected from the concentration in the supply gas p i 0 = c i p can become as large as 20%.
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68
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72249110896
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In a previous study, we have shown how direct application of AIT-SE yields a preference for formation of nonbinding TiC/alumina interfaces, in direct contradiction with the materials use as wear-resistant coatings, 10.1088/0953-8984/22/1/015004
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In a previous study, we have shown how direct application of AIT-SE yields a preference for formation of nonbinding TiC/alumina interfaces, in direct contradiction with the materials use as wear-resistant coatings, J. Rohrer, C. Ruberto, and P. Hyldgaard, J. Phys.: Condens. Matter 22, 015004 (2010). 10.1088/0953-8984/22/1/015004
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(2010)
J. Phys.: Condens. Matter
, vol.22
, pp. 015004
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Rohrer, J.1
Ruberto, C.2
Hyldgaard, P.3
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69
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77956684254
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This ratio is, in principle, accessible by monitoring the supply and exhaust rate at a fixed pressure.
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This ratio is, in principle, accessible by monitoring the supply and exhaust rate at a fixed pressure.
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