Solving a 3-dimensional quasicrystal structure in 6-dimensional space using the direct method

1993 ◽  
Vol 206 (1-2) ◽  
Author(s):  
Fu Zheng-qing ◽  
Li Fang-hua ◽  
Fan Hai-fu
Keyword(s):  
Direct Method ◽  
Dimensional Space ◽  
3 Dimensional ◽  
Quasicrystal Structure

Solving a 3-dimensional quasicrystal structure in 6-dimensional space using the direct method

1993 ◽  
Vol 206 (1) ◽  
Author(s):  
Fu Zheng-qing ◽  
Li Fang-hua ◽  
Fan Hai-fu
Keyword(s):  
Diffraction Data ◽  
Direct Method ◽  
Dimensional Space ◽  
Dimensional Structure ◽  
Test Results ◽  
Phase Problem ◽  
3 Dimensional ◽  
Structure Factors ◽  
A Direct Method ◽  
Quasicrystal Structure

AbstractA direct method was tested in solving the structure of a 3-dimensional quasicrystal in 6-dimensional space. Theoretical 3-dimensional diffraction data were used which contain Gaussian distribution errors with a mean error of about 20% for intensities. The diffraction data were firstly converted to a set of 6-dimensional structure factors. The window fuhction used for the conversion was measured from the Patterson origin peak in pseudo space. A direct method was then applied to solve the phase problem in 6-dimensional space. Test results showed that the procedure is very efficient.

scholarly journals Structure determinations for random-tiling quasicrystals

2000 ◽  
Vol 215 (10) ◽  
Author(s):  
C.L. Henley ◽  
V. Elser ◽  
M. Mihalkovic
Keyword(s):  
Structural Information ◽  
Direct Method ◽  
Dimensional Space ◽  
Waller Factor ◽  
Data Set ◽  
3 Dimensional ◽  
Random Tiling ◽  
Debye Waller Factor ◽  
Higher Dimensional ◽  
Structure Determinations

How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a higher dimensional space which yields the averaged scattering density in 3-dimensional space by the usual construction of an incommensurate cut. A novel direct method for this is summarized and applied to an i(AlPdMn) data set. This averaged density falls short of a true structure determination (which would reveal the typical unaveraged atomic patterns.) We discuss the problematic validity of inferring an ideal structure by simply factoring out a "perp-space" Debye-Waller factor, and we test this using simulations of rhombohedral tilings. A second, "unified" path is to relate the measured and modeled intensities directliy, by adjusting parameters in a simulation to optimize the fit. This approach is well suited for unifying structural information from diffraction and from minimizing total energies derived ultimately from ab-initio calculations. Finally, we discuss the special pitfalls of fitting random-tiling decagonal phases.

Crystal structure of KBSi3O8 isostructural with danburite

1993 ◽  
Vol 57 (386) ◽  
pp. 157-164 ◽  
Author(s):  
Mitsuyoshi Kimata
Keyword(s):  
Crystal Structure ◽  
Direct Method ◽  
Crystal Chemical ◽  
Chemical Formula ◽  
Crystal Chemical Formula ◽  
3 Dimensional ◽  
Tetrahedral Sites ◽  
Structural Types ◽  
Coupled Substitution ◽  
Insight Into

AbstractThe crystal structure of KBSi3O8 (orthorhombic, Pnam, with a = 8.683(1), b = 9.253(1), c = 8.272(1) Å,, V = 664.4(1) Å3, Z = 4) has been determined by the direct method applied to 3- dimensional rcflection data. The structure of a microcrystal with the dimensions 20 × 29 × 37 μm was refined to an unweightcd residual of R = 0.031 using 386 non-zero structure amplitudes. KBSi3O8 adopts a structure essentially different from recdmergneritc NaBSi3O8, with the low albite (NaAlSi3O8) structure, and isotypic with danburite CaB2Si2Os which has the same topology as paracelsian BaAl2Si2O8. The chenfical relationship between this sample and danburitc gives insight into a new coupled substitution; K+ + Si4+ = Ca2+ + B3+ in the extraframework and tetrahedral sites. The present occupancy refinement revealed partial disordering of B and Si atoms which jointly reside in two kinds of general equivalent points, T(1) and T(2) sites. Thus the expanded crystal-chemical formula can be written in the form K(B0.44Si0.56)2(B0.06Si0.94)2O8The systematic trend among crystalline compounds with the M+T3+T4+3O8 formula suggests that they exist in one of four structural types; the feldspar structures with T3+/T4+ ordered and/or disordered forms, and the paracelsian and the hollandite structures.

Triharmonic Riemannian submersions from 3-dimensional space forms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomoya Miura ◽  
Shun Maeta
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Dimensional Space ◽  
Riemannian Submersion ◽  
Partial Answer ◽  
Riemannian Submersions ◽  
Space Forms ◽  
3 Dimensional

Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.

The early attentional pancake: Lack of selection in depth for rapid exogenous cueing

2021 ◽  
Author(s):  
Ryan Edward O'Donnell ◽  
Kyrie Murawski ◽  
Ella Herrmann ◽  
Jesse Wisch ◽  
Garrett D. Sullivan ◽  
...  
Keyword(s):  
Reaction Time ◽  
Binocular Disparity ◽  
Dimensional Space ◽  
Exogenous Attention ◽  
3 Dimensional ◽  
Exogenous Cueing ◽  
Different Depths ◽  
Depth Cueing ◽  
The Difference ◽  
Attentional Selectivity

There have been conflicting findings on the degree to which exogenous/reflexive visual attention is selective for depth, and this issue has important implications for attention models. Previous findings have attempted to find depth-based cueing effects on such attention using reaction time measures for stimuli presented in stereo goggles with a display screen. Results stemming from such approaches have been mixed, depending on whether target/distractor discrimination was required. To help clarify the existence of such depth effects, we have developed a paradigm that measures accuracy rather than reaction time in an immersive virtual-reality environment, providing a more appropriate context of depth. Four modified Posner Cueing paradigms were run to test for depth-specific attentional selectivity. Participants fixated a cross while attempting to identify a rapidly masked letter that was preceded by a cue that could be valid in depth and side, depth only, or side only. In Experiment 1, a potent cueing effect was found for side validity and a weak effect was found for depth. Experiment 2 controlled for differences in cue and target sizes when presented at different depths, which caused the depth validity effect to disappear entirely even though participants were explicitly asked to report depth and the difference in virtual depth was extreme (20 vs 300 meters). Experiments 3a and 3b brought the front depth plane even closer (1 m) to maximize effects of binocular disparity, but no reliable depth cueing validity was observed. Thus, it seems that rapid/exogenous attention pancakes 3-dimensional space into a 2-dimensional reference frame.

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