Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF<sub>3</sub>-TbF<sub>3</sub> System
Multicomponent fluorides of <i>rare earth elements</i> (<b>REE</b>s—<b><i>R</i></b>) are <i>phase transition-type negative thermal expansion</i> (<b>NTE-II</b>) materials. NTE-II occurs in <i>R</i>F<sub>3</s...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-10-01
|
| Series: | International Journal of Molecular Sciences |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1422-0067/24/19/14944 |
| Summary: | Multicomponent fluorides of <i>rare earth elements</i> (<b>REE</b>s—<b><i>R</i></b>) are <i>phase transition-type negative thermal expansion</i> (<b>NTE-II</b>) materials. NTE-II occurs in <i>R</i>F<sub>3</sub>-<i>R′</i>F<sub>3</sub> systems formed by “mother” single-component dimorphic <i>R</i>F<sub>3</sub> (<i>R</i> = Pm, Sm, Eu, and Gd) with a giant NTE-II. There are two structural types of <i>R</i>F<sub>3</sub> polymorphic modifications: low-temperature β-YF<sub>3</sub> (<b><i>β</i></b>−) and high-temperature LaF<sub>3</sub> (<b><i>t</i></b>−). The change in a structural type is accompanied by a density anomaly: a <i>volume of one formula unit</i> (<b>V<sub>form</sub></b>) V<b><i><sub>β</sub></i></b><sub>−</sub> >V<b><i><sub>t</sub></i></b><sub>−</sub>. The empirical signs of volumetric changes ΔV/V of NTE-II materials were considered. For the GdF<sub>3</sub>-TbF<sub>3</sub> model system, an “operating-temperature window Δ<b><i>T</i></b>” 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 <i>R</i>F<sub>3</sub>-<i>R′</i>F<sub>3</sub> systems modifies <i>R</i>F<sub>3</sub> chemically by forming two-component <b><i>t</i></b>− and <b><i>β</i></b>− type <i>R</i><sub>1−x</sub><i>R’</i><sub>x</sub>F<sub>3</sub> <i>solid solutions</i> (<b><i>ss</i></b>). Between the two monovariant curves of <i>ss</i> decay, a two-phase area with Δ<b><i>T</i></b><sub>trans</sub> > 0 (the “window Δ<b><i>T</i></b>”) forms. A two-phase composite (<b><i>t</i></b>−<i>ss</i> + <b><i>β</i></b>−<i>ss</i>) is an NTE-II material. Its constituent <b><i>t</i></b>−<i>ss</i> and <b><i>β</i></b>−<i>ss</i> phases have different V<sub>form</sub> corresponding to the selected <b><i>T</i></b>. According to the lever rule on a conode, V<sub>form</sub> is calculated from the <b><i>t</i></b>−<i>ss</i> and <b><i>β</i></b>−<i>ss</i> compositions, which vary with <b><i>T</i></b> along two monovariant curves of <i>ss</i> decay. For the GdF<sub>3</sub>-TbF<sub>3</sub> system, ΔV/V = <b><i>f</i></b>(<b><i>T</i></b>), ΔV/V = <b><i>f</i></b>(Δ<b><i>T</i></b>) and the “window Δ<b><i>T</i></b>” = <b><i>f</i></b>(<i>x</i>) dependencies were calculated. |
|---|---|
| ISSN: | 1661-6596 1422-0067 |