Results of first-principles (FP) total energy calculations for 32 different configurations of the μ. phase in the binary system Nb-Ni are used in the compound energy formalism (CEF) to model finite-temperature thermodynamic properties. A comparison with Cluster Expansion Hamiltonian-Cluster Variation Method (CEH-CVM) calculations indicates that the CEF describes temperature-dependent site occupancies as well as the CEH-CVM within the temperature range of interest for applications. This suggests that the Bragg-Williams-Gorsky approximation (BWGA) used in the CEF is sufficient to describe site occupancies and thermodynamics of the μ phase. A phase diagram is calculated using the μ phase description derived in the present work together with a previous Calphad description for the other phases of this system. The FP-CEF approach significantly improves the description of the thermodynamic properties as a function of composition compared to the Calphad procedure generally used up to now.