Multicomponent fluorides of rare earth elements (REEs-R) are phase transition-type negative thermal expansion (NTE-II) materials. NTE-II occurs in RF3-R'F3 systems formed by "mother" single-component dimorphic RF3 (R = Pm, Sm, Eu, and Gd) with a giant NTE-II. There are two structural types of RF3 polymorphic modifications: low-temperature β-YF3 (β-) and high-temperature LaF3 (t-). The change in a structural type is accompanied by a density anomaly: a volume of one formula unit (Vform) Vβ- >Vt-. The empirical signs of volumetric changes ΔV/V of NTE-II materials were considered. For the GdF3-TbF3 model system, an "operating-temperature window ΔT" and a two-phase composition of NTE-II materials follows from the thermodynamics of chemical systems: the phase rule and the principle of continuity. A necessary and sufficient sign of NTE-II is a combination of polymorphism and the density anomaly. Isomorphism in RF3-R'F3 systems modifies RF3 chemically by forming two-component t- and β- type R1-xR'xF3solid solutions (ss). Between the two monovariant curves of ss decay, a two-phase area with ΔTtrans > 0 (the "window ΔT") forms. A two-phase composite (t-ss + β-ss) is an NTE-II material. Its constituent t-ss and β-ss phases have different Vform corresponding to the selected T. According to the lever rule on a conode, Vform is calculated from the t-ss and β-ss compositions, which vary with T along two monovariant curves of ss decay. For the GdF3-TbF3 system, ΔV/V = f(T), ΔV/V = f(ΔT) and the "window ΔT" = f(x) dependencies were calculated.
Keywords: negative thermal expansion; phase diagrams; phase rule; polymorphic transformation; principle of continuity; rare-earth trifluorides.