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Very recently, first-principle technique of full-potential linearizedaugmented plane-wave method, by using for exchange-correlation potential thegeneralized gradient approximation (GGA), was employed for the study of thelead chalcogenide semiconductors' alloys PbS$_{x}$Se$_{1-x}$,PbS$_{x}$Te$_{1-x}$ and PbSe$_{x}$Te$_{1-x}$. These density functionalcalculations led to the determination of structural, electronic and opticalproperties, including the values of lattice constants and bulk moduli as afunction of composition. Here, we investigate the latter properties, but byemploying a thermodynamical model which has been suggested for the formationand migration of defects in solids including several recent applications insemiconductors. The following crucial difference emerges when comparing thepresent results with those deduced by density functional calculations: Amongthe alloys studied, GGA calculations identify that PbS$_{x}$Te$_{1-x}$ exhibitsthe most evident non-linear variation of the bulk modulus versus thecomposition, while according to the thermodynamical model such an evidentnon-linear behavior -and maybe somewhat stronger- is also expected forPbSe$_{x}$Te$_{1-x}$. A tentative origin of this diversity is discussed.

Bulk moduli of PbS$_{x}$Se$_{1-x}$, PbS$_{x}$Te$_{1-x}$ and  PbSe$_{x}$Te$_{1-x}$ from a thermodynamical model compared to generalized  gradient approximation approach