Coherent Potential Approximation (CPA) Calculations

• CPA Condition: zero scattering on the average

  \[ x \frac{\epsilon_A - \Sigma}{1 - (\epsilon_A - \Sigma)\bar{G}} + (1-x)\frac{\epsilon_A - \Sigma}{1 - (\epsilon_A - \Sigma)\bar{G}} = 0 \] Using:
  • averaged Green's function: \[ \bar{G}(z) = \Omega^{-1} \int d^3k (z-H(k))^{-1} \]
  • Tight-binding Hamiltonian: \[H(k) = H_{TB}(k) - \Sigma\]

• Density of states:

  \[N(E) = -\frac{1}{\pi} \operatorname{Im} Tr \bar{G}(z)\]

The above formalism represents a tight-binding form of the CPA treating only diagonal disorder. The underlying tigh-binding Hamiltonian is based on 3-center integrals. We present three directories:

• cpabin (fcc and bcc) - which treat substitutional disorder, and
• cpahyd - which treat substochiometric hydrides in the NaCl structure.
• cpanacl - which treat substochiometric carbides and nitrides in the NaCl structure.