Electrostatic lattice energy in ionic crystals: optimization of the convergence of Ewald series

1978 ◽  
Vol 34 (6) ◽  
pp. 974-979 ◽  
Author(s):  
M. Catti
Keyword(s):  
Lattice Energy ◽  
Rates Of Convergence ◽  
Unit Cell ◽  
Group Symmetry ◽  
Cube Root ◽  
Cell Dimensions ◽  
Madelung Energy ◽  
Direct Lattice ◽  
Unit Cell Dimensions ◽  
Theoretical Results

Ewald's method is reconsidered to express the dependence of Madelung energy on the ionic charges explicitly, also taking into account the space-group symmetry of the structure. Upper bounds for the residues of the two partial series have been calculated by integral approximation; that relative to the direct-lattice series is shown to depend on the cube root of the unit-cell volume. The optimum value of the parameter A, which equalizes the rates of convergence of the two sums and minimizes the total number of terms, has been determined numerically for a given termination error and for a range of unit-cell dimensions. Theoretical results are tested by calculations on some specific crystal structures.

‘Clinobarylite’–barylite: order-disorder relationships and nomenclature

2015 ◽  
Vol 79 (1) ◽  
pp. 145-155 ◽  
Author(s):  
Stefano Merlino ◽  
Cristian Biagioni ◽  
Elena Bonaccorsi ◽  
Nikita V. Chukanov ◽  
Igor V. Pekov ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Unit Cell ◽  
Group Symmetry ◽  
Orthorhombic Symmetry ◽  
Space Group ◽  
International Mineralogical Association ◽  
Cell Parameters ◽  
Holotype Specimen ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

Abstract'Clinobarylite', BaBe2Si2O7, was defined as a monoclinic dimorph of orthorhombic barylite. Subsequently, its crystal structure was also proved to be orthorhombic, differing from barylite in terms of the space group symmetry, Pmn21 instead of Pmnb, and in unit-cell dimensions. Through the order-disorder (OD) theory, the polytypic relationships between 'clinobarylite' and barylite are described. 'Clinobarylite' corresponds to the MDO1 polytype, with unit-cell parameters a = 11.650, b = 4.922, c = 4.674 Å, space group Pmn21; barylite corresponds to the MDO2 polytype, with a = 11.67, b = 9.82, c = 4.69 Å, space group Pmnb. The re-examination of the holotype specimen of 'clinobarylite' confirmed its orthorhombic symmetry. Its crystal structure has been refined starting from the atomic coordinates calculated for the MDO1 polytype and the refinement converged to R1 = 0.0144 for 929 observed reflections [Fo > 4σFo]. Owing to their polytypic relationships, 'clinobarylite' and barylite should be conveniently indicated as barylite-1O and barylite-2O, respectively; the name 'clinobarylite' should be discontinued. This new nomenclature of the barylite polytypes has been approved by the Commission on New Minerals, Nomenclature and Classification of the International Mineralogical Association (IMA 13-E).

The External Shape of Human γ GI Immunoglobulin from Crystal Sections

1971 ◽  
Vol 29 ◽  
pp. 428-429
Author(s):  
L. W. Labaw
Keyword(s):  
Molecular Weight ◽  
Sodium Phosphate ◽  
Osmium Tetroxide ◽  
Unit Cell ◽  
Monoclinic Space Group ◽  
X Ray ◽  
Large Molecular Weight ◽  
Cell Dimensions ◽  
Unit Cell Dimensions ◽  
Crystallographic Axes

Crystals of a human γGl immunoglobulin have the external morphology of diamond shaped prisms. X-ray studies have shown them to be monoclinic, space group C2, with 2 molecules per unit cell. The unit cell dimensions are a = 194.1, b = 91.7, c = 51.6Å, 8 = 102°. The relatively large molecular weight of 151,000 and these unit cell dimensions made this a promising crystal to study in the EM.Crystals similar to those used in the x-ray studies were fixed at 5°C for three weeks in a solution of mother liquor containing 5 x 10-5M sodium phosphate, pH 7.0, and 0.03% glutaraldehyde. They were postfixed with 1% osmium tetroxide for 15 min. and embedded in Maraglas the usual way. Sections were cut perpendicular to the three crystallographic axes. Such a section cut with its plane perpendicular to the z direction is shown in Fig. 1.This projection of the crystal in the z direction shows periodicities in at least four different directions but these are only seen clearly by sighting obliquely along the micrograph.

The influence of pH on the synthesis of mixed Fe-Mn oxide minerals

Clay Minerals ◽  
1990 ◽  
Vol 25 (4) ◽  
pp. 507-518 ◽  
Author(s):  
M. H. Ebinger ◽  
D. G. Schulze
Keyword(s):  
Iron Oxides ◽  
Mole Fraction ◽  
Unit Cell ◽  
Mn Oxide ◽  
Cell Dimensions ◽  
The Mean ◽  
Mn Substitution ◽  
Oxide Minerals ◽  
Unit Cell Dimensions ◽  
Influence Of Ph

AbstractMn-substituted iron oxides were synthesized at pH 4, 6, 8, and 10 from Fe-Mn systems with Mn mole fractions (Mn/(Mn + Fe)) of 0, 0·2, 0·4, 0·6, 0·8, and 1·0, and kept at 50°C for 40 days. The Mn mole fraction in goethite was <0·07 at pH 4 but increased to ∼0.47 at pH 6. Goethite and/or hematite formed in Fe and Fe + Mn syntheses at pH 4 and pH 6 at Mn mole fractions ≤0·8, and at Mn mole fractions ≤0·2 at pH 8 and pH 10. Hausmannite and jacobsite formed at pH 8 and pH 10 at Mn mole fractions ≥0·4. In the pure Mn syntheses, manganite (γ-MnOOH) formed at pH 4 and pH 6, whereas hausmannite (Mn3O4) formed at pH 8 and pH 10. As the Mn substitution increased, the unit-cell dimensions of goethite shifted toward those of groutite, and the mean crystallite dimensions of goethite decreased.

Structural studies on crystals found in the intestine of Nematodirus battus

1980 ◽  
Vol 208 (1173) ◽  
pp. 409-414
Keyword(s):  
Electron Microscopy ◽  
Unit Cell ◽  
Structural Studies ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

Crystals found in the lumen of the intestine of Nematodirus battus have been studied by electron microscopy. Two of the unit cell dimensions are 16 nm x 23 nm. The possibility of an immunological significance for these crystals is considered.

Molecular packing in crystals of the aromatic hydrocarbons

1965 ◽  
Vol 286 (1404) ◽  
pp. 98-116 ◽  
Keyword(s):  
Van Der Waals ◽  
Equilibrium Structure ◽  
Group Symmetry ◽  
Structural Variations ◽  
Angular Variation ◽  
Coupling Energy ◽  
Quadrupole Interactions ◽  
Quadrupole Coupling ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

The van der Waals energy, quadrupole-quadrupole coupling energy, and hydrogen-hydrogen repulsions have been calculated for the equilibrium structure of crystalline naphthalene and for several displaced structures. The displacements are small rotations of the molecules about their symmetry axes, phased so that the space-group symmetry and unit-cell dimensions are preserved. For structural variations of this type the hydrogen-hydrogen repulsions have a strong minimum within a few degrees angular variation from equilibrium, indicating that these repulsions are dominant and determine the crystal structure for this class of displacement. The attractive van der Waals and quadrupole interactions on the other hand are not minimized at the equilibrium structure; they vary slowly (by a few wavenumbers per degree rotation) and approximately linearly.

Crystallization of Helix pomatia agglutinin (HPA), a protein from the edible snail

1999 ◽  
Vol 55 (11) ◽  
pp. 1903-1905 ◽  
Author(s):  
John N. Lisgarten ◽  
James E. Pitts ◽  
Rex A. Palmer ◽  
Colin D. Reynolds ◽  
Minh Hoa Dao-Thi ◽  
...  
Keyword(s):  
Polyethylene Glycol ◽  
Diffraction Pattern ◽  
Helix Pomatia ◽  
Unit Cell ◽  
Hanging Drop ◽  
Helix Pomatia Agglutinin ◽  
Cell Dimensions ◽  
Protein Molecules ◽  
Unit Cell Dimensions ◽  
Drop Technique

Crystals of Helix pomatia agglutinin (HPA) have been grown by the hanging-drop technique using polyethylene glycol as the precipitant at 293 K. Over a period of one to two weeks the crystals grew to maximum dimensions of 0.10 × 0.05 × 0.02 mm. The crystals belong to space group P6322, with unit-cell dimensions a = b = 63.3, c = 105.2 Å and Z = 12 identical monomers of Mr = 13 kDa, aggregating into two 78 kDa hexameric protein molecules per unit cell, each with symmetry 32 (D 3). The diffraction pattern extends to 3.6 Å at 293 K.

scholarly journals Unit cell dimensions of some synthetic olivine group solid solutions

1968 ◽  
Vol 2 (1) ◽  
pp. 51-59 ◽  
Author(s):  
Yoshito Matsui ◽  
Yasuhiko Syono
Keyword(s):  
Solid Solutions ◽  
Unit Cell ◽  
Cell Dimensions ◽  
Unit Cell Dimensions
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