Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density Functional Study of Cubic to Rhombohedral Transition in
  $\alpha$-AlF$_3$   Under heating, $\alpha$-AlF$_3$ undergoes a structural phase transition from
rhombohedral to cubic at temperature $T$ around 730 K. The density functional
method is used to examine the $T$=0 energy surface in the structural parameter
space, and finds the minimum in good agreement with the observed rhombohedral
structure. The energy surface and electronic wave-functions at the minimum are
then used to calculate properties including density of states, $\Gamma$-point
phonon modes, and the dielectric function. The dipole formed at each fluorine
ion in the low temperature phase is also calculated, and is used in a classical
electrostatic picture to examine possible antiferroelectric aspects of this
phase transition.

8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs