Comprehensive Investigation of Dynamic, Thermodynamic, Piezoelectric and Elastic Properties of Ferroelectric SrHfO3 Using First-Principles Calculations

<p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">In this study, the elastic, piezoelectric, dynamic and thermodynamic properties of the ferroelectric <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">SrHfO<span class="s1" style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 7px; line-height: normal;">3</span> crystal were investigated using density functional theory (DFT). The calculations were <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">performed using the ABINIT package program within the framework of the generalized gradient <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">approximation (GGA). First, the components of the elastic stiffness tensor (<i>C</i><span class="s1" style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 7px; line-height: normal;"><i>ij</i></span>) for the ferroelectric <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">SrHfO<span class="s1" style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 7px; line-height: normal;">3</span> crystal were calculated. Many mechanical parameters such as bulk modulus, shear modulus, <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">Young modulus and Poisson's ratio were obtained using the components of the calculated elastic <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">stiffness tensor. In addition, the Pugh ratio and Cauchy pressure were evaluated, and the brittleness or <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">ductility character of the material was determined. The ferroelectric SrHfO3 crystal also exhibits <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">piezoelectric properties. The components of the piezoelectric tensor (<i>d</i><span class="s1" style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 7px; line-height: normal;"><i>ij</i></span>) were calculated for the SrHfO<span class="s1" style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 7px; line-height: normal;">3</span> <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">crystal. As a dynamic property, the phonon distribution of SrHfO<span class="s1" style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 7px; line-height: normal;">3</span> and the phonon density of states <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">(PDOS) were calculated accordingly. Finally, in thermodynamic properties, thermodynamic parameters <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">such as temperature dependent heat capacity, entropy, enthalpy and free energy were calculated. Also, <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">parameters such as thermal expansion coefficient and Debye temperature were obtained. This study <p style="text-align: justify; margin-bottom: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 11px; line-height: normal; font-family: &quot;Times New Roman&quot;;">provides a comprehensive understanding of the elastic, dynamic and thermodynamic properties of <p style="text-align: justify; margin-bottom: