<p>The advanced quantum mechanical approach, <i>density functional theory</i>, has been employed to investigate the anisotropic ternary complex material <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3220_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="76" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {CePt}_4\hbox {Ge}_{12}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>CePt</mtext> <mn>4</mn> </msub> <msub> <mtext>Ge</mtext> <mn>12</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> to investigate electronic, structural, and thermoelectric properties. We achieved structural minimization, thereby enhancing the conductive nature of the material and obtaining the desired results. Next, we compare the calculations with the previously collected theoretical and experimental data. The electronic nature estimation reveals that the material <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3220_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="76" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {CePt}_4\hbox {Ge}_{12}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>CePt</mtext> <mn>4</mn> </msub> <msub> <mtext>Ge</mtext> <mn>12</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> is metallic and exhibits conductor characteristics. The material under investigation had a predominantly ionic bonding nature. The density of states (DOS) clarifies that materials have dense electronic states, which is important for possible energy applications. <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3220_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="76" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {CePt}_4\hbox {Ge}_{12}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>CePt</mtext> <mn>4</mn> </msub> <msub> <mtext>Ge</mtext> <mn>12</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> exhibits complex up-and-down behaviour in its Seebeck coefficient (S) caused by sharp changes in its electronic structure near to the Fermi level. The thermoelectric performance of the material is influenced by this phenomenon, which is observed at temperatures of 600, 800, and 1000&#xa0;K. These features increase thermopower and have an impact on the thermoelectric figure of merit (ZT), which peaks at 0.26 for 1000&#xa0;K and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3220_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu = +0.035\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>μ</mi> <mo>=</mo> <mo>+</mo> <mn>0.035</mn> </mrow> </math></EquationSource> </InlineEquation>&#xa0;eV. In the <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3220_Article_IEq7.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation> range of <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3220_Article_IEq8.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(-0.07\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>0.07</mn> </mrow> </math></EquationSource> </InlineEquation>&#xa0;eV to <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3220_Article_IEq9.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(+0.13\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>+</mo> <mn>0.13</mn> </mrow> </math></EquationSource> </InlineEquation>&#xa0;eV, the material exhibits promising thermoelectric performance, indicating the possibility of doping optimization.</p>

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First-principles study of electronic, structural, and thermoelectric nature of \(\hbox {CePt}_4\hbox {Ge}_{12}\)

  • Muhammad Amir Khan,
  • Zahid Ullah

摘要

The advanced quantum mechanical approach, density functional theory, has been employed to investigate the anisotropic ternary complex material \(\hbox {CePt}_4\hbox {Ge}_{12}\) CePt 4 Ge 12 to investigate electronic, structural, and thermoelectric properties. We achieved structural minimization, thereby enhancing the conductive nature of the material and obtaining the desired results. Next, we compare the calculations with the previously collected theoretical and experimental data. The electronic nature estimation reveals that the material \(\hbox {CePt}_4\hbox {Ge}_{12}\) CePt 4 Ge 12 is metallic and exhibits conductor characteristics. The material under investigation had a predominantly ionic bonding nature. The density of states (DOS) clarifies that materials have dense electronic states, which is important for possible energy applications. \(\hbox {CePt}_4\hbox {Ge}_{12}\) CePt 4 Ge 12 exhibits complex up-and-down behaviour in its Seebeck coefficient (S) caused by sharp changes in its electronic structure near to the Fermi level. The thermoelectric performance of the material is influenced by this phenomenon, which is observed at temperatures of 600, 800, and 1000 K. These features increase thermopower and have an impact on the thermoelectric figure of merit (ZT), which peaks at 0.26 for 1000 K and \(\mu = +0.035\) μ = + 0.035  eV. In the \(\mu\) μ range of \(-0.07\) - 0.07  eV to \(+0.13\) + 0.13  eV, the material exhibits promising thermoelectric performance, indicating the possibility of doping optimization.