Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermal Expansion of Germanium Isotopes at Low Temperature   The focus of this paper is the vanishing of the thermal expansion in certain
diamond-like semiconductors. In silicon becomes zero at T = 122. K. In
germanium the situation is less clear. Previous investigations show that in
natural germanium a zero in is reported at 15.5 K and that a second zero for T
> 30 K is not observed. This paper reports on data taken on four monoisotopic
Ge crystals. All plots of lattice parameter vs temperature shows a minimum
between 40 and 50 K. The minimum is very deep for 70Ge, which also shows
anomalous behaviour for the thermal expansion alpha. The data are discussed
with ab initio theoretical results obtained by Debernardi and Cardona. Some
data do not support the Virtual Crystal Approximation.

13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: econ
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn