Des dangers d'utiliser sans précaution des tables de sous-groupes maximum; retour au théorème d'Hermann

Billiet, Y.

doi:10.1107/s0567739481001484

Cited by 6 publications

(4 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a recent paper, 10 devoted to KFeF

_{3}

, a

2 \times 2 \times 2

supercell (indicated as S222) of the cubic aristotype one has been built, and all possible configurations obtained populating the 8 Fe

d

shells (the unique

β

d

electron on

d_{x y}

, or

d_{x z}

, or

d_{y z}

) have been optimized. It turns out that the most stable OO pattern corresponds to a tetragonal cell (SG140–I4/mcm–see the second model in Reference 11). However many other configurations are relatively close in energy: the lowest ten are within 200

μ

_{h}

(or 5 meV, or 63 K), so that in principle many of them are expected to be populated at room and low temperature.…”

Section: Introductionmentioning

confidence: 99%

t2gd orbital ordering patterns in KBF3 (B = Sc, Ti, Fe, Co) perovskites

Pascale,

D'Arco,

Mustapha

et al. 2024

J Comput Chem

View full text Add to dashboard Cite

The orbital ordering (OO) resulting from the partial occupancy of the subshell of the transition metals in KBF (B = Sc, Ti, Ffe, Co) perovskites, and the many possible patterns arising from the coupling between the B sites, have been investigated at the quantum mechanical level ( Gaussian type basis set, B3LYP hybrid functional) in a 40 atoms supercell. The numerous patterns are distributed into 162 classes of equivalent configurations. For each fluoroperovskite, one representative per class has been calculated. The four compounds behave similarly: an identical dependence of the energy and volume (or cell parameters) on the OO pattern; the spanned energy interval is small (1 to 2 mE per formula unit), suggesting that most of the configurations are occupied at room and even at low temperature. A linear model, taking into account the relative orbital order in contiguous sites, reproduces the energy order in the full set for each compound, suggesting that it could be used for studying OO in larger supercells.

show abstract

“…In a recent paper, 10 devoted to KFeF

_{3}

, a

2 \times 2 \times 2

supercell (indicated as S222) of the cubic aristotype one has been built, and all possible configurations obtained populating the 8 Fe

d

shells (the unique

β

d

electron on

d_{x y}

, or

d_{x z}

, or

d_{y z}

μ

_{h}

(or 5 meV, or 63 K), so that in principle many of them are expected to be populated at room and low temperature.…”

Section: Introductionmentioning

confidence: 99%

t2gd orbital ordering patterns in KBF3 (B = Sc, Ti, Fe, Co) perovskites

Pascale,

D'Arco,

Mustapha

et al. 2024

J Comput Chem

View full text Add to dashboard Cite

show abstract

“…Subgroups that are Euclideanequivalent but not conjugate, however, have to be regarded separately because each class of conjugate subgroups corresponds to another type of deformation. This has recently been discussed by Billiet ( 1981 ) for the example of tetragonally distorted perovskite structures with symmetry 14/mcm [cf. also example (ii)].…”

Section: Classification Of Subgroups Of Space Groupsmentioning

confidence: 99%

“…Therefore, C222 has 11 classes of Euclidean-equivalent subgroups of index 2. In this example there do not exist pairs of conjugate subgroups because all subgroups of index 2 are nor- Billiet, 1981).…”

Section: Classification Of Subgroups Of Space Groupsmentioning

confidence: 99%

The implications of normalizers on group–subgroup relations between space groups

Koch¹

1984

Acta Cryst Sect A

View full text Add to dashboard Cite

show abstract

“…For type IIb and IIc subgroups, one entry there may correspond to more than one subgroup. One entry may correspond to subgroups whose differences can be expressed as different conventional origins of S with respect to G or with cell enlargements in different directions (see IIc maximal subgroups of G beyond that of the lowest also Billiet, 1981).…”

Section: Maximal Subgroupsmentioning

confidence: 99%