The thermodynamic properties of crystalline phases are generally represented well in terms of the compound energy formalism and the model has been implemented in all the major software packages used to calculated phase equilibria. The formalism is particularly successful in modelling defects in crystals, both the formation of holes or vacancies on lattice sites, and the dissolution of atoms on interstitial sublattices. In the former case the formalism may require the definition of data for pure vacancy itself. In this assessment we investigate the possible values for the Gibbs energy of vacancy to be used in the compound energy formalism and show that a value of zero or negative will always lead to unwanted catastrophic stability of the phase.
SundmanB and AgrenJ: ‘A regular solution model for phases with several components and sublattices, suitable for computer applications’, J. Phys. Chem. Solids, 1981, 42, 297–301.
2.
HillertM, JanssonB and SundmanB: ‘Application of the compound-energy model to oxide systems’, Z. Metallkd., 1988, 79, 81.
3.
BarryTI, DinsdaleAT, GisbyJA, HallstedtB, HillertM, JanssonB, JonssonS, SundmanB and TaylorJR: ‘The compound energy model for ionic solutions with applications to solid oxides’, J. Phase Equilib., 1992, 13, 459–475.
4.
ChenS.-L, DanielS, ZhangF, ChangYA, YanX.-Y, XieF.-Y, Schmid-FetzerR and OatesWA: ‘The PANDAT software package and its applications’, CALPHAD, 2002, 26, 175–188.
5.
BaleCW, ChartrandP, DegterovSA, ErikssonG, HackK, Ben MahfoudR, MelançonJ, PeltonAD and PetersenS: ‘FactSage thermochemical software and databases’, CALPHAD, 2002, 26, 189–228.
6.
DaviesRH, DinsdaleAT, GisbyJA, RobinsonJAJ and MartinSM: ‘MTDATA - thermodynamic and phase equilibrium software from the National Physical Laboratory’, CALPHAD, 2002, 26, 229–271.
7.
AnderssonJ.-O, HelanderT, HöglundL, ShiP and SundmanB: ‘Thermo-Calc & DICTRA, computational tools for materials science’, CALPHAD, 2002, 26, 273–312.
8.
DupinN, AnsaraI and SundmanB: ‘Thermodynamic re-assessment of the ternary system Al–Cr–Ni’, CALPHAD, 2001, 25, 279–298.
9.
MassalskiTB: ‘Structure and stability of alloys’in ‘Physical metallurgy’, (ed. CahnR W and HaasenP), 4th revised and enhanced edn, Vol. 1, 135–204; 1996, Amsterdam, North Holland.
10.
HillertM: ‘Phase equilibria phase diagrams and phase transformations: their thermodynamic basis’, 1988, Cambridge, Cambridge University Press.
11.
PecanhaRM, FerreiraF, CoelhoGC, NunesCA and SundmanB: ‘Thermodynamic modelling of the Nb–B system’, Intermetallics, 2007, 15, 999–1005.
12.
LuX, CuiY and JinZ: ‘Experimental and thermodynamic investigation of the Ni–Al–Mo system’, Metall. Mater. Trans. A;1999, 30A, 1785–1795.
13.
YinF, TedenacJ.-C and GascoinF: ‘Thermodynamic modelling of the Ti-Sn system and calculation of the Co–Ti–Sn system’, CALPHAD, 2007, 31, 370–379.
14.
CacciamaniG, FerroR, AnsaraI and DupinN: ‘Thermodynamic modelling of the Co-Ti system’, Intermetallics, 2000, 8, 213–222.
15.
OatesWA, ChenS.-L, CaoW, ZhangF, ChangYA, BenczeL, DoernbergE and Schmid-FetzerR: ‘Vacancy thermodynamics for intermediate phases using the compound energy formalism’, Acta Materialia, 2008, 56, 5255–5262.
16.
SmedskaerLC, FlussMJ, LegniniDG, ChasonMK and SiegelRW: ‘The vacancy formation enthalpy in Ni determined by positron annihilation’, J. Phys. F: Met. Phys., 1981, 11, 2221–30.
17.
GillanMJ: ‘Calculation of the vacancy formation energy in aluminium’, J. Phys.: Condens. Matter, 1989, 1, 689–711.
18.
TerblansJJ: ‘Calculating the bulk vacancy formation energy (Ev) for a Schottky defect in a perfect Cu(111), Cu(100) and a Cu(110) single crystal’, Surf. Interf. Anal., 2002, 33, 767–770.
19.
MattssonTR and MattssonAE: ‘Calculating the vacancy formation energy in metals: Pt, Pd, and Mo’, Phys. Rev. B, 2002, 66B, 214110.
