There is increasing evidence that vibrational entropy may significantly contribute to the entropy difference between the ordered and the disordered states of a compound. Through first-principles calculations, we investigate the magnitude of this vibrational entropy difference in Ni 3 Al, a compound where this effect is believed to be especially large. We find the vibrational entropy difference to be essentially zero and temperature independent. [S0031-9007(98)06236-X] PACS numbers: 64.70. Kb, 65.50. + m First-principles theory of order-disorder phase equilibria is a well-established field [1,2]. Typically, only configurational entropy is accounted for, and the effect of lattice vibrations on the free energy difference between the ordered and the disordered states is neglected, although no formal justification of this assumption has ever been presented. On the contrary, recent experimental data [3][4][5][6] seem to indicate that, in many systems, the vibrational entropy difference between the ordered and the disordered states is comparable to the configurational entropy difference. An especially striking example is the Ni 3 Al compound, for which the vibrational entropy difference was estimated from experimental observations to be 0.2k B [4], whereas the configurational entropy difference is at most 0.57k B . If this estimate is correct, it may explain why most first-principles calculations including only configurational entropy consistently overestimate phase transition temperatures. Based on the experimental data of Fultz and co-workers [4], Garbulsky [7] predicted that vibrational effects would shift down the calculated order-disorder transition temperature of Ni 3 Al by 18% from what it would be with a configurational-only entropy model.In order to unambiguously confirm that lattice vibrations indeed play an important role, this experimental evidence needs to be backed by a suitable theoretical investigation. Unfortunately, highly accurate first-principles calculations of the vibrational entropy are very computationally intensive tasks. In this context, several investigators turned to simplified models to estimate the vibrational entropy. In some studies [8,9], the complexity of the first-principles approach was tackled by using a simplified model for the vibrational entropy based on the Debye-Gruneisen approximation. All of these results seem to indicate that vibrational effects can be non-negligible.Calculations of the vibrational entropy difference between disordered and ordered Ni 3 Al (hereafter denoted DS o!d vib ) has so far been performed using only the semiempirical embedded atom method (EAM) [10][11][12]. Although the specific result seems to depend somewhat on the EAM potential used, all authors found values between 0.1k B and 0.3k B , which corresponds to the range of values found experimentally.Although the value of DS o!d vib calculated through EAM agrees with experimental results, there is no consensus on the origin of this difference. The EAM results indicate that disordering causes a nearl...