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تسجيل مستخدم جديدAnomalous thermal expansion in $alpha$-titanium
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We provide a complete quantitative explanation for the anisotropic thermal expansion of hcp Ti at low temperature. The observed negative thermal expansion along the c-axis is reproduced theoretically by means of a parameter free theory which involves both the electron and phonon contributions to the free energy. The thermal expansion of titanium is calculated and found to be negative along the c-axis for temperatures below $sim$ 170 K, in good agreement with observations. We have identified a saddle-point Van Hove singularity near the Fermi level as the main reason for the anisotropic thermal expansion in $alpha-$titanium.
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