Phonons and low thermal expansion in sodalite zinc borate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Zn</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">B</mml:mi><mml:mn>6</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>12</mml:mn></mml:msub><mml:mi>X</mml:mi></mml:mrow><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">O</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">S</mml:mi><mml:mo>,</mml:mo><mml:mo mathvariant="normal">Se</mml:mo><mml:mo>)</mml:mo></mml:math>
Zhongsheng Wei, Xingxing Jiang, Anthony E. Phillips, Zheshuai Lin, Martin T. Dove
Abstract
We examine isotropic near-zero thermal expansion in the cubic materials ${\mathrm{Zn}}_{4}{\mathrm{B}}_{6}{\mathrm{O}}_{12}X(X=\mathrm{O},\mathrm{S},\mathrm{Se})$ using density functional theory calculations of the lattice dynamics within the Gr\"uneisen approximation. The calculated thermal expansion is in excellent agreement with experiment. The near-zero thermal expansion is shown to arise from a balance between two specific groups of vibrations that favor positive and negative thermal expansion, respectively. This gives a clear general indicator of how crystal structures can be engineered to give near-zero thermal expansion.
Topics & Concepts
Thermal expansionPhysicsPhononMaterials scienceThermodynamicsCondensed matter physicsThermal Expansion and Ionic ConductivityFerroelectric and Piezoelectric MaterialsMicrowave Dielectric Ceramics Synthesis