First-principles phonon calculations of thermal expansion in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Ti</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>SiC</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Ti</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>AlC</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Ti</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>GeC</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>

2010544 citationsJournal Articlegreen Open Access

Authors

Atsushi Togo · Office National d'Études et de Recherches Aérospatiales

Laurent Chaput · Institut de Sciences des Matériaux de Mulhouse

Isao Tanaka · Japan Fine Ceramics Center

Gilles Hug · Laboratoire d'Étude des Microstructures

Abstract

Thermal properties of ternary carbides with composition ${\text{Ti}}_{3}{\text{SiC}}_{2}$, ${\text{Ti}}_{3}{\text{AlC}}_{2}$, and ${\text{Ti}}_{3}{\text{GeC}}_{2}$ were studied using the first-principles phonon calculations. The thermal expansions, the heat capacities at constant pressure, and the isothermal bulk moduli at finite temperatures were obtained under the quasiharmonic approximation. Comparisons were made with the available experimental data and excellent agreements were obtained. Phonon band structures and partial density of states were investigated. These compounds present unusual localized phonon states at low frequencies, which are due to atomiclike vibrations parallel to the basal plane of the Si, Al, or Ge elements.

Topics & Keywords

MXene and MAX Phase Materials Boron and Carbon Nanomaterials Research Thermal Expansion and Ionic Conductivity

Publication Details

Published in: Physical Review B

Volume 81, Issue 17

DOI: 10.1103/physrevb.81.174301

Field-Weighted Citation Impact: 4.11

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Publication Details