Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalous thermal expansion in $\alpha$-titanium   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.

31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat