Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF₃-TbF₃ System

Abstract

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’xF3 solid 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
• polymorphic transformation
• rare-earth trifluorides
• phase diagrams
• phase rule
• principle of continuity