Thermodynamic Modeling of Atomic Bonding in Covalent C x (BN) 1-x ALLOYS
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worthwhile to point out high hardness, optical transparency, and insulating properties of the cubic modifications, excellent thermal conductivities of the materials, and protective properties in aggressive chemical environments at high temperatures. These facts have encouraged the interest in alloys based on the two materials. The alloy processing may be divided in two different techniques. The first technique is connected with high temperatures and high pressures', the second technique is performed at the lower temperatures and pressures of the CVD and PECVD methods2 . No comprehensive models of the possible alloy structures exist. This paper analyzes possible bonding in C,(BN)I-, alloys based on the free energy model (FEM) which has been proven to be able to predict important features of the bonding in different amorphous alloys. It is important to emphasize that the main interest of this study is connected with low temperature processes which mostly lead to amorphous structures of the alloys. FREE ENERGY MODEL The standard approach to the possible compounds in a ternary system like C-B-N includes consideration of thermodynamic equilibrium of different phases which may co-exist in the system. In Fig. I a schematic ternary phase diagram is shown with some of the most common known or predicted compounds, such as BN, B4C, and C3N4. The list of possible compounds is not complete
217 Mat. Res. Soc. Symp. Proc. Vol. 410 01996 Materials Research Society
and illustrate the complex nature of the system: all possible compounds must be taken into account to determine the minimum of the Gibbs free energy of the system. The thermodynamic predictions obviously fail when any new phase with unknown properties, or new alloy of the compounds, is formed. The C-B-N system presents an example of this situation. Even the incomplete list contains compounds which are still poorly characterized in terms of the necessary thermodynamic information for the analysis of equilibrium. For instance, C 3N 4 has been rather demonstrated to 3 exist and is considered to be metastable, in a mixture of other compounds , so no reliable information about the thermodynamic properties of the material is available. One of the ways which may help to perform the thermodynamic modeling is to apply the free energy model (FEM) to predict the bonding in the alloy.
C (x=I)
.......... . 3N4 B4C
B
... C x(BN)I"•..•-x
"
..
BN (x=O)
N
Fig. 1 Schematic ternary diagram for C-B-N system.
The FEM has been developed and applied for several different amorphous covalent systems, such as SixNyHz, SixCyHz, Si.CyGez, CxHy, etc. 4-9 The basic approach of FEM as
developed is the minimization of the Gibbs free energy of mixing for the alloy. The enthalpy of mixing is given by Hm=Eos,-Eb ,, where Ebo. are the energies of covalent bonds between nearest neighbors in the network, and Eatoms are the energies of formation of atoms. The entropy is determined by counting the number of possible distinctive bond configurations.4 In the ternary C-B-N system the total number of
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