<p>Thermodynamic properties of Ce<sub>3</sub>In were determined using low-temperature thermal relaxation calorimetry, high-temperature differential scanning calorimetry, high-temperature gallium melt drop solution calorimetry, and density functional theory (DFT) calculations. At low temperatures, the electronic and phononic terms to the specific heat are: γ = 53(1) mJ·mol<sup>−1</sup>·K<sup>2</sup>, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1728_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\({\Theta }_{D1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Θ</mi> <mrow> <mi>D</mi> <mn>1</mn> </mrow> </msub> </math></EquationSource> </InlineEquation> = 174(2) K, <InlineEquation ID="IEq100"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1728_Article_IEq100.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\({\Theta }_{D2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Θ</mi> <mrow> <mi>D</mi> <mn>2</mn> </mrow> </msub> </math></EquationSource> </InlineEquation> = 68(3) K. The standard entropy (<InlineEquation ID="IEq101"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1728_Article_IEq101.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(S^\circ\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>S</mi> <mo>∘</mo> </msup> </math></EquationSource> </InlineEquation>) and the standard entropy of formation from the elements (Δ<i>S</i><sub><i>f,298.15&#xa0;K</i></sub>) are 55.8 ± 1.5&#xa0;J·mol<sup>−1</sup>·atom<sup>−1</sup>·K<sup>−1</sup> and − 10.8 ± 1.7&#xa0;J·mol<sup>−1</sup> ·atom<sup>−1</sup>·K<sup>−1</sup>, respectively. The standard enthalpy of formation from the elements (Δ<i>H</i><sub><i>f,298.15&#xa0;K</i></sub>) is − 35.44 ± 8.95&#xa0;kJ·mol<sup>−1</sup>·atom<sup>−1</sup> from calorimetric measurements, as compared with&#xa0;Δ<i>H</i><sub><i>f,0&#xa0;K, Dudarev</i></sub> = − 30.735&#xa0;kJ·mol<sup>−1</sup>·atom<sup>−1</sup> and Δ<i>H</i><sub><i>f,0&#xa0;K, Liechtenstein</i></sub> = − 31.474&#xa0;kJ·mol<sup>−1</sup>·atom<sup>−1</sup> based on DFT + <i>U</i>. Using these parameters, the Gibbs energy of formation (Δ<i>G</i><sub><i>f,298.15&#xa0;K</i></sub>) is derived to be − 32.2 ± 8.9&#xa0;kJ·mol<sup>−1</sup>·atom<sup>−1</sup>. These thermodynamic values of Ce<sub>3</sub>In can serve as input parameters in modeling its phase stability relations with other Ce–M–In compounds.</p> Graphical abstract <p></p>

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Thermodynamic properties of Ce3In: A combined experimental and computational study

  • Andrew C. Strzelecki,
  • W. Adam Phelan,
  • Najeb M. Abdul-Jabbar,
  • S. Scott Parker,
  • Sajib K. Barman,
  • Alexander R. Muñoz,
  • Sven P. Rudin,
  • Shane C. Mann,
  • David C. Arellano,
  • Cody B. Cockreham,
  • Mark R. Wartenbe,
  • Margaret E. Reece,
  • Paul H. Tobash,
  • Hakim Boukhalfa,
  • Nathan A. Conroy,
  • Sarah C. Hernandez,
  • Eric D. Bauer,
  • Jeremy N. Mitchell,
  • Hongwu Xu

摘要

Thermodynamic properties of Ce3In were determined using low-temperature thermal relaxation calorimetry, high-temperature differential scanning calorimetry, high-temperature gallium melt drop solution calorimetry, and density functional theory (DFT) calculations. At low temperatures, the electronic and phononic terms to the specific heat are: γ = 53(1) mJ·mol−1·K2, \({\Theta }_{D1}\) Θ D 1  = 174(2) K, \({\Theta }_{D2}\) Θ D 2  = 68(3) K. The standard entropy ( \(S^\circ\) S ) and the standard entropy of formation from the elements (ΔSf,298.15 K) are 55.8 ± 1.5 J·mol−1·atom−1·K−1 and − 10.8 ± 1.7 J·mol−1 ·atom−1·K−1, respectively. The standard enthalpy of formation from the elements (ΔHf,298.15 K) is − 35.44 ± 8.95 kJ·mol−1·atom−1 from calorimetric measurements, as compared with ΔHf,0 K, Dudarev = − 30.735 kJ·mol−1·atom−1 and ΔHf,0 K, Liechtenstein = − 31.474 kJ·mol−1·atom−1 based on DFT + U. Using these parameters, the Gibbs energy of formation (ΔGf,298.15 K) is derived to be − 32.2 ± 8.9 kJ·mol−1·atom−1. These thermodynamic values of Ce3In can serve as input parameters in modeling its phase stability relations with other Ce–M–In compounds.

Graphical abstract