Does mathematical crystallography still have a role in the XXI century?

Nespolo, M.

doi:10.1107/s0108767307044625

Cited by 22 publications

(8 citation statements)

References 89 publications

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“…[35] structure solution program using Charge Flipping and refined with the ShelXL-2012[36] refinement package using Least Squares minimisation. Crystal data for Th(IV) complex [(Th(NTAamide(C4))(NO 3 ) 4 )]: C 30 H 60 N 8 O 15 Th, M = 1004.90, monoclinic, space group P2 1 /c (No.14), a = 11.7963(2) Å, b = 15.8161(3) Å, c = 22.4960(4) Å, a = 90°, b = 96.0065(16)°, c = 90°, V = 4174.07(13) Å 3 , Z = 4, T = 143.00(10) K, l(Mo Ka) = 3.644 mm À1 , D calc = 1.599 g/mm 3 , 16,963 reflections measured (6.04 6 2H 6 52.74), 8533 unique (R int = 0.0342) which were used in all calculations.…”

mentioning

confidence: 99%

High selective extraction for thorium(IV) with NTAamide in nitric acid solution: Synthesis, solvent extraction and structure studies

Huang

Ding

et al. 2014

Separation and Purification Technology

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confidence: 99%

High selective extraction for thorium(IV) with NTAamide in nitric acid solution: Synthesis, solvent extraction and structure studies

Huang

Ding

et al. 2014

Separation and Purification Technology

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“…These two definitions dissolve the inconsistency with the accepted definition of "crystallographic symmetry" and at the same time conform with the well-established terminology for partial symmetries [5,7,8].…”

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confidence: 72%

“…when the operation F : S i ! S i brings a component to coincide with itself, the partial operation is of special type and is called local [8]. Also in this case, the operation F does not need to act on any component different from S i and it may be crystallographic or noncrystallographic.…”

mentioning

confidence: 98%

About the concept and definition of “noncrystallographic symmetry”

Nespolo¹,

Souvignier

Литвин³

2008

Zeitschrift Für Kristallographie

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The definition of "noncrystallographic symmetry" given in Volume B of the International Tables for Crystallography actually corresponds to the concept of "local symmetry". A new definition of "noncrystallographic symmetry" is proposed, which fully complies with that of "crystallographic symmetry" in Volume A of the International Tables for Crystallography.The concept of "noncrystallographic symmetry" is, quite obviously, directly related to that of "crystallographic symmetry" so that once a definition of the latter is given, that of the former is obtained spontaneously. This is probably the reason why no explicit definition of "noncrystallographic symmetry" is given in Volume A of the International Tables for Crystallography. Even the concept of noncrystallographic point groups, presented in section 10.1.4, is introduced without an explicit definition but only as the groups differing from the crystallographic point groups presented in Sections 10.1.2 and 10.1.3.As a matter of fact, one should not even need an explicit definition of "noncrystallographic symmetry" once that of "crystallographic symmetry" is given. Unfortunately, in the literature, and especially in the structural biology literature, the term "noncrystallographic symmetry" is used in a manner in striking contrast with what is directly implied by the definition of "crystallographic symmetry". This contradiction is so fundamental that it causes serious misunderstandings and misinterpretations. We will show that the use of "noncrystallographic symmetry" in structural biology is inconsistent with the accepted definition of "crystallographic symmetry" and suggest that an alternative terminology should be used.To understand the problem let us start with the definition of "crystallographic symmetry operations" given in [1] Section 8.1.5:A motion is called a crystallographic symmetry operation if a crystal pattern exists for which it is a symmetry operation.A motion is an isometry, a transformation keeping angles and distances unchanged, i.e. a transformation without deformation. A crystal pattern is the extension of a crystal structure to a periodic arrangement of whatever object, concrete or abstract, constitutes the structure. The atoms forming a crystal structure represent a special case of a crystal pattern. This definition applies to the n-dimensional Euclidean space E n and can be expressed in a quantitative way with the aid of group theory. With respect to a basis of E n , the symmetry operations of the space group of the crystal pattern are represented by (n þ 1) Â (n þ 1) augmented matrices where the top-left n Â n block represents the linear part of the operation (the part that leaves the origin fixed) and the additional column represents the vector part of the operation (the part which gives the translation component of the symmetry operation). The above definition of a crystallographic symmetry operation implies that with respect to a suitable basis of E n (namely a primitive basis of the periodic pattern) the linear part of the matrix represen...

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“…The paths to Cmcm are shown in Figures 10 to 11 by the corresponding modified Bärnighausen trees (Bärnighau-sen, 1980; for a recent review, see Nespolo, 2008). Each node of a Bärnighausen tree consists of a rectangle containing the label of the atom occupying the atomic position (one taken as representative if the site is statistically occupied by more than one), the Wyckoff letter, the sitesymmetry group and the fractional coordinates; the branches are arrows relating the atomic positions.…”

Section: Cmcm Aristotypementioning

confidence: 99%

Structural relations and pseudosymmetries in the andorite homologous series

Nespolo

Ozawa

Kawasaki

et al. 2012

Journal of Mineralogical and Petrological Sciences

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The structure of quatrandorite is reported for the first time from an untwinned sample from Oura mine, San Jose, Bolivia. The mineral crystallizes in P2 1 /c, a = 19.1686 (19) Å, b = 17.160 (3) Å, c = 13.042 (2) Å, β = 90.008 (12)°, V = 4289.9 (11) Å 3 , Z = 4. Refinement to R obs = 5.66% was obtained with Jana2006. Quatrandorite belongs to the andorite series, whose members share two cell parameters while the third can be expressed as n × 4.3 Å, with n = 2, 4 and 6 for ramdohrite (uchucchacuaite, fizelyite), quatrandorite and senandorite, respectively. Both quatrandorite and senandorite are strongly pseudosymmetric up to Cmcm with one parameter corresponding to n = 1 (~ 4.3 Å). The hypothetical structure corresponding to Cmcm is also the aristotype common to both minerals. The strong structural similarity of quatrandorite and senandorite may explain their co -existence in some samples, which has in the past led to hypothesize the existence of a further member of the series, nakaséite, which was however later shown to consist of a random stacking of the two minerals. The Cmcm aristotype is not common to the n = 2 minerals (uchucchacuaite, ramdohrite, fizelyite), which are thus structurally less closely related to the two other members. A common aristotype to all three minerals can nevertheless be obtained via a different path, which leads to Cmme with the same cell parameters as Cmcm; the degree of pseudo -symmetry in this supergroup is however lower and there remain a difference in one sulfur position in this aristotype. It nevertheless confirms previous reports in the literature stating that the bulk of the structure of the minerals of this series can be reduced to a common principle, essentially a distorted galena; the departures from it are however crucial for the realization of the individual structures.

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Does mathematical crystallography still have a role in the XXI century?

Cited by 22 publications

References 89 publications

High selective extraction for thorium(IV) with NTAamide in nitric acid solution: Synthesis, solvent extraction and structure studies

High selective extraction for thorium(IV) with NTAamide in nitric acid solution: Synthesis, solvent extraction and structure studies

About the concept and definition of “noncrystallographic symmetry”

Structural relations and pseudosymmetries in the andorite homologous series

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