Standard ionic crystal structures

Gehman, William G.

doi:10.1021/ed040p54

Cited by 13 publications

(7 citation statements)

References 3 publications

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“…Triangular nets may be used for the description of crystal structures based oll close packings of large atoms, with different degrees of filling of the interstices (Smirnova, 1956;lida, 1957;Wells, 1954Wells, , 1958Morris & Loeb, 1960;Gehman, 1963;Loeb, 1964;Limade-Faria, 1965;Beck, 1967Beck, , 1968Lima-de-Faria & Figueiredo, 1969). They are applied either to the closest-packed layers or to the layers of interstitial atoms, octahedral and tetrahedral, when considering separately the upper and lower tetrahedral voids.…”

Section: Application To a Certain Set Of Filling Proportionsmentioning

confidence: 99%

Tessellations and plane symmetry groups as applied to the derivation of close-packed binary layers

Figueiredo¹

1973

Acta Cryst Sect A

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A method is described for the derivation of binary closest-packed layers of a given composition with the condition that the atoms of the minor component should be crystallographically equivalent. The method is based on the theory of derivatives of space groups developed by Buerger, which is here applied to those multiple cells that may be regarded as tessellations drawn over a basic triangular net. "Ihe results are presented for a set of compositions, in order to illustrate the method of derivation. IntroductionIn preceeding work concerning the systematic derivation of close-packed structure types (Lima-de-Faria & Figueiredo, 1969), a method was developed in which the rules for derivation followed directly from the conditions for structural stability already discussed (Limade-Faria, 1965). Appropriate layers were so deduced for the generation of ordered binary close-packed structures, under the previous statement of crystallographic equivalency for the atoms of the minor component.The fact that this method applied to the majority of known structures in the area investigated proved its efficacy in deriving the most probable patterns. However, it was not established that all the appropriate layers had been derived. On the other hand, a small proportion were found to have no corresponding appropriate layer; if proved, and not merely a consequence of the simplifications involved in that derivation technique, this circumstance has interesting structural implications. The aim of the present work is to verify these results by applying an exhaustive method to the derivation of these binary close-packed layers. M. O. FIGUEIREDO 235 Statement of the problemThe essential problem is to find all the two-dimensional patterns built up with symmetrically equivalent points as a result of partially filling the nodes of a triangular net.The two designations, triangular net and hexagonal lattice, will be used below to refer to the regular tessellation we are dealing with, whose Schl/~fli symbol is {3,6}; the geometrical aspect is implied with the first designation while the second applies to the crystallographic point of view.The proportion of the triangular net filled will be given by the ratio of the number of occupied nodes in a multiple cell considered over the fundamental net to the total number of nodes covered by this cell. The occupied nodes must be symmetrically equivalent, as stated above, and thus they will belong to a single set of equivalent positions, either general or special, of the plane symmetry group or groups, compatible with the two-dimensional cell used. The groups analysed are restricted to those involving symmetry elements consistent with those already found in the original lattice, and consequently the groups containing fourfold rotation points are excluded. Also, when considering the distribution of one sole component, as is the case here, the general position in pl corresponds to a monoclinic primitive lattice (Burzlaff, Fischer & Hellner, 1968). Therefore, only 13 of the 17 two-dimensional space groups ...

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Section: Application To a Certain Set Of Filling Proportionsmentioning

confidence: 99%

Tessellations and plane symmetry groups as applied to the derivation of close-packed binary layers

Figueiredo¹

1973

Acta Cryst Sect A

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“…These cycles 3,26–28 are currently employed to estimate the enthalpy values regarding the heats of formation for these lanthanide type crystals. For these purposes, several experimental data are required, such as the dissociation energies (D), the sublimation energies (S), electroafinity values (EA) and ionization potential (IP).…”

Section: Introductionmentioning

confidence: 99%

A Calculation Model of the General Theory of Interaction Potentials for Stoichiometric Lanthanide Type Crystals: Applications to the Cs2KLnCl6 System

Trescastro-López

Shanavas

Acevedo

2019

Sci Rep

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This article aims to develop a generalized model calculation model to be applicable to the general theory of interaction potentials with reference to the stoichiometric elpasolite type crystals. In this study, we have chosen to report both a theoretical model and a calculation strategy to undertake semi empirical calculations of thermodynamic properties, such as reticular energies and heats of formation for the series of systems such as: Cs2KLnCl6. We have also carried out quite a number of calculations for a variety of systems such as: Cs2NaLnF6, Cs2NaLnCl6, Cs2NaLnBr6, Rb2NaLnF6 and Cs2KLnF6 in the Fm3m space group since we aim to check the strengths and weaknesses of our model calculations. We have analyzed a substantial number of approximate theoretical models and have carried a formidable amount of computing simulations to estimate the reticular energies and the corresponding heat of formation for these type of crystal using a semi empirical model. We made use of the thermodynamic cycles of Born-Haber so as to get a broad view with reference to the accuracy of our semi empirical theoretical models. The problem itself is quite challenging since we have focused our attention upon trivalent lanthanide ions in the first inner transition series of the chemical elements: (Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu). There are a significant amount of outstanding research works published in the literature with reference to structural analysis, one photon spectroscopy, vibrionic intensity model calculations and generalized models to deal with these kind of complex crystals. The calculated energy values associated with these observables seems to be most reasonable, and these follow the expected trends, as may be expected on both theoretical and experimental grounds. Both, the advantages and disadvantages of the current model calculations, have been tested against other previous calculations performed for this type of complex systems. It is of a paramount importance, the results obtained and reported in this article with regards to convergence tests as well as some master equations derived to account for the various contributions to the total energy. The Born-Mayer-Buckingham potential is carefully examined with reference to these lanthanide type crystals Cs2KLnCl6. Finally but not at last, the most likely sources for improvement are carefully discussed in this work. We strongly believe that there is enough room for improvement and have therefore initiated a new research program of activities tackling systems of well-known optical and structural properties.

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“…It was later developed into eutectic packing of atoms (O'Keeffe, 1977) to permit larger atoms to occupy interstitial sites, and such structures are widely adopted by intermetallic and ionic compounds (Gehman, 1963). Monatomic elements are expected to crystallize in h.c.p, and c.c.p, structures.…”

Section: Introductionmentioning

confidence: 99%

A generalized description of ideal crystal structures for monatomic solids

Ng¹

1990

Acta Crystallogr Sect B

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'sillimanite'-like structure, respectively) is, however, not practicable. The dark regions within this image are assumed to be due to small domains possessing the average mullite composition. The average size of these domains is about 3-5 nm 2. They are separated by the above-mentioned, linearly arranged (parallel to [102]) white dots. An antiphase relationship between these domains cannot be confirmed for the mullite crystals investigated (x = 0.25 and x = 0.4).The results discussed above show that the intensities of the white dots on the experimental HREM images of the ac plane are influenced by all components which modulate the structure of mullite. A proportionality between the intensity of these white dots and of only the concentration of vacancies on certain sites, as assumed by several authors (Nakajima et al., 1975; Y1/i-J/i/iski & Nissen, 1983), cannot be verified.The assumption of Schryvers et al. (1988) that the oxygen vacancies are randomly distributed in mullite crystals obtained by sintering of 3A1203 + 2ZrSiO4 can be best verified by inspecting the b'c* and the a'c* diffraction pattern. In this case a continuous diffuse background rather than satellite reflexions must be obtained. Moreover, the computer simulations of Schryvers et al. (1988) along the c axis were unfortunately performed using an average structure model. According to our contrast calculations the intensity differences between the four contrast maxima within the unit cell must vanish owing to an equal vacancy distribution as shown in Fig. 7(/). The one-to-one correspondence between the HREM image contrast and the projected crystal structure of mullite, and the correspondence between the vacancy arrangement and the intensity of the simulated contrast features, can, according to the image simulations shown in Fig. 7, best be obtained on the (001) (1985). Ultramicroscopy, 16, 19-32. TANAKA, N. & COWLEY, J. M. (1987). Acta Cryst. A43, 337-346. TAYLOR, W. H. (1928). Z. Kristallogr. 68, 503-521. YL~,-J~,~,SKI, J. & NlSSEN, H.-U. (1983). Phys. Chem. Miner. 10,[47][48][49][50][51][52][53][54] Acta Cryst. (1990

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Standard ionic crystal structures

Cited by 13 publications

References 3 publications

Tessellations and plane symmetry groups as applied to the derivation of close-packed binary layers

Tessellations and plane symmetry groups as applied to the derivation of close-packed binary layers

A Calculation Model of the General Theory of Interaction Potentials for Stoichiometric Lanthanide Type Crystals: Applications to the Cs2KLnCl6 System

A generalized description of ideal crystal structures for monatomic solids

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