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...
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MDPI AG
2023-10-01
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| Series: | International Journal of Molecular Sciences |
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| Online Access: | https://www.mdpi.com/1422-0067/24/19/14944 |
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| author | Elena A. Sulyanova Boris P. Sobolev |
| author_facet | Elena A. Sulyanova Boris P. Sobolev |
| author_sort | Elena A. Sulyanova |
| collection | DOAJ |
| description | 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. |
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| spelling | doaj.art-d893d430d98d42028acddca24c39e9cf2023-11-19T14:32:56ZengMDPI AGInternational Journal of Molecular Sciences1661-65961422-00672023-10-0124191494410.3390/ijms241914944Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF<sub>3</sub>-TbF<sub>3</sub> SystemElena A. Sulyanova0Boris P. Sobolev1Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics”, Russian Academy of Sciences, Leninskiy Prospekt 59, 119333 Moscow, RussiaShubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics”, Russian Academy of Sciences, Leninskiy Prospekt 59, 119333 Moscow, RussiaMulticomponent 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.https://www.mdpi.com/1422-0067/24/19/14944negative thermal expansionpolymorphic transformationrare-earth trifluoridesphase diagramsphase ruleprinciple of continuity |
| spellingShingle | Elena A. Sulyanova Boris P. Sobolev Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF<sub>3</sub>-TbF<sub>3</sub> System International Journal of Molecular Sciences negative thermal expansion polymorphic transformation rare-earth trifluorides phase diagrams phase rule principle of continuity |
| title | Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF<sub>3</sub>-TbF<sub>3</sub> System |
| title_full | Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF<sub>3</sub>-TbF<sub>3</sub> System |
| title_fullStr | Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF<sub>3</sub>-TbF<sub>3</sub> System |
| title_full_unstemmed | Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF<sub>3</sub>-TbF<sub>3</sub> System |
| title_short | Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF<sub>3</sub>-TbF<sub>3</sub> System |
| title_sort | thermodynamic origin of negative thermal expansion based on a phase transition type mechanism in the gdf sub 3 sub tbf sub 3 sub system |
| topic | negative thermal expansion polymorphic transformation rare-earth trifluorides phase diagrams phase rule principle of continuity |
| url | https://www.mdpi.com/1422-0067/24/19/14944 |
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