Group-subgroup phase transitions, Hermann's space-group decomposition theorem, and chain subduction criterion in crystals

Deonarine, S.; Birman, Joseph L.

doi:10.1103/physrevb.27.4261

Cited by 15 publications

(4 citation statements)

References 14 publications

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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%

Group-to-Subgroup Relations in Space Groups. Application to the Structural Phase Transitions in the Perovskite-Type Layer Compounds RbAlF4 and RbVF4

Loyzance

Couzi

1984

Phys. Stat. Sol. (a)

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A simple method for the determination of all kinds of group‐subgroup relations in space‐groups is presented. This method, based on the utilization of factor‐groups, is applied to a theoretical study of the structural phase transitions in the perovskite type layer compounds RbAIF4 and RbVF4. The group‐subgroup relations that lead to the “family tree” of these compounds are derived and the phase transitions previously reported are discussed in the framework of Landau's theory.

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Section: Introductionmentioning

confidence: 99%

Group-to-Subgroup Relations in Space Groups. Application to the Structural Phase Transitions in the Perovskite-Type Layer Compounds RbAlF4 and RbVF4

Loyzance

Couzi

1984

Phys. Stat. Sol. (a)

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“…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%

Structural and magnetic phase transitions of theV4-cluster compoundGeV4S8

et al. 2008

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The phase transitions of the strongly correlated tetrahedral V 4 -cluster compound GeV 4 S 8 have been studied by low-temperature powder x-ray diffraction, magnetic susceptibility, and specific heat measurements. The crystal structure is cubic at room temperature ͑space group F43m͒ and transforms to orthorhombic ͑space group Imm2͒ at T S = 30 K. A Jahn-Teller distortion reduces the symmetry of the V 4 -cluster from 43m to mm2. The second transition at 18 K is the onset of antiferromagnetic ordering without symmetry change but with a certain increase in the distortion. The latter reflects a strong magnetoelastic coupling at T N . Specific heat anomalies at 30 and 18 K confirm the two phase transitions.

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“…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%

Strong enhancement of magnetic ordering temperature and structural/valence transitions in EuPd ₃ S ₄ under high pressure

Huyan,

Ryan,

Slade

et al. 2023

Proc. Natl. Acad. Sci. U.S.A.

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We present a comprehensive study of the inhomogeneous mixed-valence compound, EuPd 3 S 4 , by electrical transport, X-ray diffraction, time-domain 151 Eu synchrotron Mössbauer spectroscopy, and X-ray absorption spectroscopy measurements under high pressure. Electrical transport measurements show that the antiferromagnetic ordering temperature, T N , increases rapidly from 2.8 K at ambient pressure to 23.5 K at ~19 GPa and plateaus between ~19 and ~29 GPa after which no anomaly associated with T N is detected. A pressure-induced first-order structural transition from cubic to tetragonal is observed, with a rather broad coexistence region (~20 GPa to ~30 GPa) that corresponds to the T N plateau. Mössbauer spectroscopy measurements show a clear valence transition from approximately 50:50 Eu 2+ :Eu 3+ to fully Eu 3+ at ~28 GPa, consistent with the vanishing of the magnetic order at the same pressure. X-ray absorption data show a transition to a fully trivalent state at a similar pressure. Our results show that pressure first greatly enhances T N , most likely via enhanced hybridization between the Eu 4 f states and the conduction band, and then, second, causes a structural phase transition that coincides with the conversion of the europium to a fully trivalent state.

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Group-subgroup phase transitions, Hermann's space-group decomposition theorem, and chain subduction criterion in crystals

Cited by 15 publications

References 14 publications

Group-to-Subgroup Relations in Space Groups. Application to the Structural Phase Transitions in the Perovskite-Type Layer Compounds RbAlF4 and RbVF4

Group-to-Subgroup Relations in Space Groups. Application to the Structural Phase Transitions in the Perovskite-Type Layer Compounds RbAlF4 and RbVF4

Structural and magnetic phase transitions of theV4-cluster compoundGeV4S8

Strong enhancement of magnetic ordering temperature and structural/valence transitions in EuPd ₃ S ₄ under high pressure

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Group-subgroup phase transitions, Hermann's space-group decomposition theorem, and chain subduction criterion in crystals

Cited by 15 publications

References 14 publications

Group-to-Subgroup Relations in Space Groups. Application to the Structural Phase Transitions in the Perovskite-Type Layer Compounds RbAlF4 and RbVF4

Group-to-Subgroup Relations in Space Groups. Application to the Structural Phase Transitions in the Perovskite-Type Layer Compounds RbAlF4 and RbVF4

Structural and magnetic phase transitions of theV4-cluster compoundGeV4S8

Strong enhancement of magnetic ordering temperature and structural/valence transitions in EuPd 3 S 4 under high pressure

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Strong enhancement of magnetic ordering temperature and structural/valence transitions in EuPd ₃ S ₄ under high pressure