Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical X-ray Scattering Studies of Jahn-Teller Phase Transitions in
  TbV$_{1-x}$As$_{x}$O$_{4}$   The critical behaviour associated with cooperative Jahn-Teller phase
transitions in TbV$_{1-x}$As$_{x}$O$_{4}$ (where \textit{x} = 0, 0.17, 1)
single crystals have been studied using high resolution x-ray scattering. These
materials undergo continuous tetragonal $\to$ orthorhombic structural phase
transitions driven by Jahn-Teller physics at T$_C$ = 33.26(2) K, 30.32(2) K and
27.30(2) K for \textit{x} = 0, 0.17 and 1 respectively. The orthorhombic strain
was measured close to the phase transition and is shown to display mean field
behavior in all three samples. Pronounced fluctuation effects are manifest in
the longitudinal width of the Bragg scattering, which diverges as a power law,
with an exponent given by $x=0.45 \pm 0.04$, on approaching the transition from
either above or below. All samples exhibited twinning; however the disordered x
= 0.17 sample showed a broad distribution of twins which were stable to
relatively low temperatures, well below T$_C$. This indicates that while the
orthorhombic strain continues to develop in a conventional mean field manner in
the presence of disorder, twin domains are easily pinned by the quenched
impurities and their associated random strains.

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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org