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Phase transitions

Structural changes during phase transitions and the critical and noncritical order parameters in the (NH$_4$)$_3$Nb(O$_2$)$_2$F$_4$ crystal

M. S. Molokeev^a, S. V. Misjul<sup>b

a</sup> L. V. Kirensky Institute of Physics, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk
^b Siberian Federal University, Krasnoyarsk

Abstract: The structures of two phases of the (NH$_4$)$_3$Nb(O$_2$)$_2$F$_4$ crystal, namely, the parent cubic phase and the most distorted low-temperature phase, have been determined from data of an X-ray diffraction experiment performed for a powder sample. The profile and structural parameters have been refined according to the procedure implemented in the DDM program. The results obtained have been discussed with invoking the group-theoretical analysis of the complete order parameter condensate, which takes into account the critical and noncritical atomic displacements and allows the interpretation of the obtained experimental data. It has been found that the most probable sequence of structural transformations occurring in the crystal can be schematically represented in the following form:
$$ Fm\bar{3}m \underset{(\eta1,\eta1,\eta)}{\overset{\Gamma_5^+(11-7)}{\longrightarrow}} C2/m \underset{(\eta1,\eta1,\eta1)(0,0,0,0,0,\xi,0,-\xi,0,0,0,0)}{\overset{\Gamma_5^+(11-7)\otimes \Sigma_2(4-2)}{\longrightarrow}} P2_1/m \underset{(\eta1,\eta1,\eta)(0,0,0,0,0,\xi,0,-\xi,0,0,0,0)(0,0,0,0,0,\varepsilon,0,\varepsilon,0,0,0,0)}{\overset{\Gamma_5^+(11-7)\otimes \Sigma_2(4-2)\otimes \Sigma_3(4-3)}{\longrightarrow}} P2_1/n. $$


Received: 31.05.2011

 English version: Physics of the Solid State, 2012, 54:1, 143–154

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