1983
DOI: 10.1103/physrevb.27.4261
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Group-subgroup phase transitions, Hermann's space-group decomposition theorem, and chain subduction criterion in crystals

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1983
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Cited by 15 publications
(4 citation statements)
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“…The knowledge of group-to-subgroup relations between space groups is of great interest for understanding the mechanism of structural phase transitions in crystalline solids, using the framework of Landau formalism. In this respect, numerous theoretical works were developed recently (see for instance [l, 21 and references cited in [ 2 ] ) . These works, generally based on the theory of representations, are of a rather difficult access for experimentalists.…”
Section: Introductionmentioning
confidence: 99%
“…The knowledge of group-to-subgroup relations between space groups is of great interest for understanding the mechanism of structural phase transitions in crystalline solids, using the framework of Landau formalism. In this respect, numerous theoretical works were developed recently (see for instance [l, 21 and references cited in [ 2 ] ) . These works, generally based on the theory of representations, are of a rather difficult access for experimentalists.…”
Section: Introductionmentioning
confidence: 99%
“…Consequently, the space groups above and below the transitions have to be connected by a group-subgroup relation according to Hermann's theorem. 18,19 Therefore, we can rule out a rhombohedral distortion at 30 K by group theory: If the structure is orthorhombic below 18 K and cubic at room temperature, no rhombohedral structure is possible between these two polymorphs because no group-subgroup relation exists between the rhombohedral space group R3m and the orthorhombic space group Imm2. 20 Subsequent Rietveld refinements ͑Fig.…”
mentioning
confidence: 99%
“…Clear discontinuous changes in both lattice parameters ( a and c ) and the unit cell volume ( V ) are observed. Considering that 4 (SG #123) is not a translationengleiche subgroup of Pm (SG #200), which is actually a translationengleiche subgroup of Pm n (SG #223), we expect that the structural transition under pressure to be first order according to Hermann’s theory ( 14 , 15 ). The pressure–volume, curve in zone I was analyzed using a second-order Birch-Murnaghan equation of state (BM EOS) as shown in Fig.…”
Section: Resultsmentioning
confidence: 99%