1,834 results on '"*MATHEMATICAL crystallography"'
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2. Topology of Misorientation Spaces.
- Author
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Ayzenberg, Anton A. and Gugnin, Dmitry V.
- Abstract
Let and be finite subgroups of . The double quotients of the form were introduced in materials science under the name misorientation spaces. In this paper we review several known results that allow one to study the topology of misorientation spaces. Neglecting the orbifold structure, one can say that all misorientation spaces are closed orientable topological -manifolds with finite fundamental groups. In the case when and are crystallographic groups, we compute the fundamental groups and apply the elliptization theorem to describe these spaces. Many misorientation spaces are homeomorphic to by Perelman's theorem. However, we explicitly describe the topological types of several misorientation spaces without appealing to Perelman's theorem. The classification of misorientation spaces yields new -valued group structures on the manifolds and . Finally, we outline the connection of the particular misorientation space with integrable dynamical systems and toric topology. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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3. Ideas of lattice‐basis reduction theory for error‐stable Bravais lattice determination and abinitio indexing.
- Author
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Oishi-Tomiyasu, Ryoko
- Subjects
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UNIT cell , *MATHEMATICAL crystallography , *CRYSTAL lattices , *INDEXING , *CRYSTALLOGRAPHY - Abstract
In abinitio indexing, for a given diffraction/scattering pattern, the unit‐cell parameters and the Miller indices assigned to reflections in the pattern are determined simultaneously. 'Ab initio' means a process performed without any good prior information on the crystal lattice. Newly developed abinitio indexing software is frequently reported in crystallography. However, it is not widely recognized that use of a Bravais lattice determination method, which is tolerant of experimental errors, can simplify indexing algorithms and increase their success rates. One of the goals of this article is to collect information on the lattice‐basis reduction theory and its applications. The main result is a Bravais lattice determination algorithm for 2D lattices, along with a mathematical proof that it works even for parameters containing large observational errors. It uses two lattice‐basis reduction methods that seem to be optimal for different symmetries, similarly to the algorithm for 3D lattices implemented in the CONOGRAPH software. In indexing, a method for error‐stable unit‐cell identification is also required to exclude duplicate solutions. Several methods are introduced to measure the difference in unit cells known in crystallography and mathematics. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. JGD 提拉单晶炉晶体模型的数字化.
- Author
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陈川贵, 丁雨憧, 龙 勇, 何 晔, 吴 昊, 岑 伟, and 李青蔚
- Abstract
Copyright of Piezoelectrics & Acoustooptics is the property of Piezoelectric & Acoustooptic and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2024
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5. From Friezes to Quasicrystals: A History of Symmetry Groups
- Author
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Brückler, Franka Miriam, Stilinović, Vladimir, Sriraman, Bharath, Section editor, and Sriraman, Bharath, editor
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- 2024
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6. The prime state ideal theorem in state residuated lattices.
- Author
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Woumfo, Francis, Temgoua Alomo, Etienne Romuald, and Lele, Celestin
- Subjects
LATTICE theory ,MATHEMATICAL analysis ,MATHEMATICS theorems ,MATHEMATICAL crystallography ,MATHEMATICAL functions - Abstract
The aim of this paper is to establish the prime state ideal theorem in state residuated lattices (SRLs). We study the state ideals lattice SI(L) of a state residuated lattice (L, φ) and prove that it is a complete Brouwerian lattice in which the meet and the join of any two compact elements are compact (coherent frame). We characterize the notion of prime state ideals in SRLs. In addition, we establish the condition for which the lattice SI(L) is a Boolean algebra. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
7. On saturated prefilter monads.
- Author
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Gao Zhang and Wei He
- Subjects
MONADS (Mathematics) ,MATHEMATICAL analysis ,ALGEBRA ,CONTINUOUS lattices ,MATHEMATICAL crystallography - Abstract
In this paper we show that the prime saturated prefilter monads are sup-dense and interpolating in saturated prefilter monads. It follows that CNS spaces are the lax algebras for prime saturated prefilter monads. As for the algebraic part, we prove that the Eilenberg-Moore algebras for saturated prefilter monads are exactly continuous I-lattices. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
8. Indexing of grazing-incidence X-ray diffraction patterns.
- Author
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Simbrunner, Josef, Salzmann, Ingo, and Resel, Roland
- Subjects
- *
DIFFRACTION patterns , *X-ray diffraction , *CRYSTAL symmetry , *THIN films , *CRYSTAL lattices , *AZIMUTH , *TRANSPORT planes - Abstract
Grazing Incidence X-ray Diffraction (GIXD) has been established as a powerful tool for the structural characterization of thin films. However, indexing of the experimentally observed diffraction peaks without prior knowledge of the involved crystal lattices has turned out as a challenging task. During the last years a series of works were published which introduce indexing methods for different methods of GIXD experiments. Static GIXD measurements are performed at fixed sample positions for thin films with preferred orientation of the crystallites relative to the substrate surface but without any in-plane order. Rotated GIXD measurements use rotation of the thin film sample about the substrate normal and collect for each rotation angle a single detector image. This method is used for crystals with azimuthal alignments within the thin film. A comprehensive mathematical framework is developed which provides the assignment of Laue indices to the individual diffraction peaks. The algorithms are even reduced from the three-dimensional case to two-dimensional representation of the experimental results. Despite the fact that GIXD experiments provide only a limited number of diffraction peaks, indexing became possible even for thin film crystals with low symmetry, different preferred orientations and multiple azimuthal alignments. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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9. NEW MECHANISMS FOR HETEROCLINIC CYCLES IN SYSTEMS WITH Z³2 SYMMETRY.
- Author
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MURZA, ADRIAN C.
- Subjects
HOPF bifurcations ,SYMMETRY groups ,MATHEMATICAL crystallography ,EIGENVALUES ,POLYNOMIALS ,INTEGERS - Abstract
We analyze the generating mechanisms for heteroclinic cycles in Z³
2 -equivariant ODEs, not involving Hopf bifurcations. Such cycles have been observed in different areas of physics see [1, 8, 12], as well in modelling the geomagnetic field of Earth [15], and as far as we know, there is no available theoretical data explaining these phenomena. We use singularity theory to study the equivalence in the group-symmetric context, as well as the recognition problem for the simplest bifurcation problems with this symmetry group. Singularity results highlight different mechanisms for the appearance of heteroclinic cycles, based on the transition between the bifurcating branches. [ABSTRACT FROM AUTHOR]- Published
- 2022
10. Crystal structures.
- Subjects
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CRYSTAL structure , *MATHEMATICAL crystallography , *ELECTRON density , *DIFFRACTIVE scattering , *ELECTRON scattering , *X-ray diffraction , *ATOMIC displacements - Abstract
A personal view is offered on various solved and open problems related to crystal structures: the present state of reconstructing the crystal electron density from X‐ray diffraction data; characterization of atomic and molecular motion from a combination of atomic displacement parameters and quantum chemical calculations; Bragg diffraction and diffuse scattering: twins, but different; models of real (as opposed to ideal) crystal structures from diffuse scattering; exploiting unexplored neighbourhoods of crystallography to mathematics, physics and chemistry. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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11. Correlation between two‐ and three‐dimensional crystallographic lattices for epitaxial analysis. I. Theory.
- Author
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Simbrunner, Josef, Domke, Jari, Forker, Roman, Resel, Roland, and Fritz, Torsten
- Subjects
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CRYSTAL lattices , *MOLECULAR crystals , *THIN films , *PHYSICAL vapor deposition , *UNIT cell , *EPITAXY , *RIESZ spaces - Abstract
The epitaxial growth of molecular crystals at single‐crystalline surfaces is often strongly related to the first monolayer at the substrate surface. The present work presents a theoretical approach to compare three‐dimensional lattices of epitaxially grown crystals with two‐dimensional lattices of the molecules formed within the first monolayer. Real‐space and reciprocal‐space representations are considered. Depending on the crystallographic orientation relative to the substrate surface, proper linear combinations of the lattice vectors of the three‐dimensional unit cell result in a rhomboid in the xy plane, representing a two‐dimensional projection. Mathematical expressions are derived which provide a relationship between the six lattice parameters of the three‐dimensional case and the three parameters obtained for the two‐dimensional surface unit cell. It is found that rotational symmetries of the monolayers are reflected by the epitaxial order. Positive and negative orientations of the crystallographic contact planes are correlated with the mirror symmetry of the surface unit cells, and the corresponding mathematical expressions are derived. The method is exemplarily applied to data obtained in previous grazing‐incidence X‐ray diffraction (GIXD) measurements with sample rotation on thin films of the conjugated molecules 3,4;9,10‐perylenetetracarboxylic dianhydride (PTCDA), 6,13‐pentacenequinone (P2O), 1,2;8,9‐dibenzopentacene (trans‐DBPen) and dicyanovinyl‐quaterthiophene (DCV4T‐Et2) grown by physical vapor deposition on Ag(111) and Cu(111) single crystals. This work introduces the possibility to study three‐dimensional crystal growth nucleated by an ordered monolayer by combining two different experimental techniques, GIXD and low‐energy electron diffraction, which has been implemented in the second part of this work. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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12. The twinned crystal structure of [4,4′-bipyridine]-1,1′-diium hexachloridostannate(IV), C10H10N2SnCl6.
- Author
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Reiss, Guido J. and van Megen, Martin
- Subjects
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HYDROGEN bonding , *COORDINATION polymers , *CRYSTAL structure , *MATHEMATICAL crystallography , *MOLECULAR structure , *CUCURBITURIL - Abstract
Keywords: 2144049 EN 2144049 281 284 4 03/11/22 20220401 NES 220401 A selected region of the hydrogen bonded layered title crystal structure is shown in the figure with view along [-100]. Each I bipy i H SB 2 sb cation is connected to four neighboring [SnCl SB 6 sb ] SP 2- sp anions by four weak bifurcated N-H Cl hydrogen bonds (see the figure; N1 Cl1 3.367(5) Å). The twinned crystal structure of [4,4'-bipyridine]-1,1'-diium hexachloridostannate(IV), C10H10N2SnCl6 This finding came as no surprise, as the large number of hydrogen bond acceptor atoms of the [SnCl SB 6 sb ] SP 2- sp anion only has to be related to one I bipy i H SB 2 sb dication in this AB salt compound. [Extracted from the article]
- Published
- 2022
- Full Text
- View/download PDF
13. The twinned crystal structure of [4,4′-bipyridine]-1,1′-diium hexachloridostannate(IV), C10H10N2SnCl6.
- Author
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Reiss, Guido J. and van Megen, Martin
- Subjects
HYDROGEN bonding ,COORDINATION polymers ,CRYSTAL structure ,MATHEMATICAL crystallography ,MOLECULAR structure ,CUCURBITURIL - Abstract
Keywords: 2144049 EN 2144049 281 284 4 03/11/22 20220401 NES 220401 A selected region of the hydrogen bonded layered title crystal structure is shown in the figure with view along [-100]. Each I bipy i H SB 2 sb cation is connected to four neighboring [SnCl SB 6 sb ] SP 2- sp anions by four weak bifurcated N-H Cl hydrogen bonds (see the figure; N1 Cl1 3.367(5) Å). The twinned crystal structure of [4,4'-bipyridine]-1,1'-diium hexachloridostannate(IV), C
10 H10 N2 SnCl6 This finding came as no surprise, as the large number of hydrogen bond acceptor atoms of the [SnCl SB 6 sb ] SP 2- sp anion only has to be related to one I bipy i H SB 2 sb dication in this AB salt compound. [Extracted from the article]- Published
- 2022
- Full Text
- View/download PDF
14. Dynamical Generation of Graphene
- Author
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Myronova, M., Bourret, E., Kielanowski, Piotr, editor, Odzijewicz, Anatol, editor, and Previato, Emma, editor
- Published
- 2019
- Full Text
- View/download PDF
15. Search for anisotropy in the Debye-Waller factor of HCP solid 4He.
- Author
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Barnes, Ashleigh L. and Hinde, Robert J.
- Subjects
- *
MATHEMATICAL models , *ANISOTROPY , *MATHEMATICAL crystallography , *CRYSTALLOGRAPHY , *PROPERTIES of matter - Abstract
The properties of hexagonal close packed (hcp) solid 4He are dominated by large atomic zero point motions. An accurate description of these motions is therefore necessary in order to accurately calculate the properties of the system, such as the Debye-Waller (DW) factors. A recent neutron scattering experiment reported significant anisotropy in the in-plane and out-of-plane DW factors for hcp solid 4He at low temperatures, where thermal effects are negligible and only zero-point motions are expected to contribute. By contrast, no such anisotropy was observed either in earlier experiments or in path integral Monte Carlo (PIMC) simulations of solid hcp 4He. However, the earlier experiments and the PIMC simulations were both carried out at higher temperatures where thermal effects could be substantial.We seek to understand the cause of this discrepancy through variational quantum Monte Carlo simulations utilizing an accurate pair potential and a modified trial wavefunction which allows for anisotropy. Near the melting density, we find no anisotropy in an ideal hcp 4He crystal. A theoretical equation of state is derived from the calculated energies of the ideal crystal over a range of molar volumes from 7.88 to 21.3 cm3, and is found to be in good qualitative agreement with experimental data. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
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16. Role of structural factors in formation of chiral magnetic soliton lattice in Cr1/3NbS2.
- Author
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Volkova, L. M. and Marinin, D. V.
- Subjects
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CRYSTAL lattices , *MATHEMATICAL crystallography , *TOPOTACTIC transitions , *TEMPERATURE , *CLATHRATE compounds - Abstract
The sign and strength of magnetic interactions not only between nearest neighbors, but also for longer-range neighbors in the Cr1/3NbS2 intercalation compound have been calculated on the basis of structural data. It has been found that left-handed spin helices in Cr1/3NbS2 are formed from strength-dominant at low temperatures antiferromagnetic (AFM) interactions between triangular planes of Cr3+ions through the plane of just one of two crystallographically equivalent diagonals of side faces of embedded into each other trigonal prisms building up the crystal lattice of magnetic Cr3+ions. These helices are oriented along the c axis and packed into two-dimensional triangular lattices in planes perpendicular to these helices directions and lay one upon each other with a displacement. The competition of the above AFM helices with weaker inter-helix AFM interactions could promote the emergence of a long-period helical spin structure. One can assume that in this case, the role of Dzyaloshinskii-Moriya interaction consists of final ordering and stabilization of chiral spin helices into a chiral magnetic soliton lattice. The possibility of emergence of solitons in M1/3NbX2 and M1/3TaX2 (M=Cr, V, Ti, Rh, Ni, Co, Fe, and Mn; X=S and Se) intercalate compounds has been examined. Two important factors caused by the crystal structure (predominant chiral magnetic helices and their competition with weaker inter-helix interactions not destructing the system quasi-one-dimensional character) can be used for the crystal chemistry search of solitons. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
17. Role of structural factors in formation of chiral magnetic soliton lattice in Cr1/3NbS2.
- Author
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Volkova, L. M. and Marinin, D. V.
- Subjects
CRYSTAL lattices ,MATHEMATICAL crystallography ,TOPOTACTIC transitions ,TEMPERATURE ,CLATHRATE compounds - Abstract
The sign and strength of magnetic interactions not only between nearest neighbors, but also for longer-range neighbors in the Cr
1/3 NbS2 intercalation compound have been calculated on the basis of structural data. It has been found that left-handed spin helices in Cr1/3 NbS2 are formed from strength-dominant at low temperatures antiferromagnetic (AFM) interactions between triangular planes of Cr3+ ions through the plane of just one of two crystallographically equivalent diagonals of side faces of embedded into each other trigonal prisms building up the crystal lattice of magnetic Cr3+ ions. These helices are oriented along the c axis and packed into two-dimensional triangular lattices in planes perpendicular to these helices directions and lay one upon each other with a displacement. The competition of the above AFM helices with weaker inter-helix AFM interactions could promote the emergence of a long-period helical spin structure. One can assume that in this case, the role of Dzyaloshinskii-Moriya interaction consists of final ordering and stabilization of chiral spin helices into a chiral magnetic soliton lattice. The possibility of emergence of solitons in M1/3 NbX2 and M1/3 TaX2 (M=Cr, V, Ti, Rh, Ni, Co, Fe, and Mn; X=S and Se) intercalate compounds has been examined. Two important factors caused by the crystal structure (predominant chiral magnetic helices and their competition with weaker inter-helix interactions not destructing the system quasi-one-dimensional character) can be used for the crystal chemistry search of solitons. [ABSTRACT FROM AUTHOR]- Published
- 2014
- Full Text
- View/download PDF
18. Vibrational states of a water molecule in a nano-cavity of beryl crystal lattice.
- Author
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Zhukova, Elena S., Torgashev, Victor I., Gorshunov, Boris P., Lebedev, Vladimir V., Shakurov, Giľman S., Kremer, Reinhard K., Pestrjakov, Efim V., Thomas, Victor G., Fursenko, Dimitry A., Prokhorov, Anatoly S., and Dressel, Martin
- Subjects
- *
PHYSICAL & theoretical chemistry , *POLARIZATION (Electricity) , *ENERGY levels (Quantum mechanics) , *CRYSTAL lattices , *MATHEMATICAL crystallography , *MAGNETIC dipoles , *LATTICE theory - Abstract
Low-energy excitations of a single water molecule are studied when confined within a nano-size cavity formed by the ionic crystal lattice. Optical spectra are measured of manganese doped beryl single crystal Mn:Be3Al2Si6O18, that contains water molecules individually isolated in 0.51 nm diameter voids within the crystal lattice. Two types of orientation are distinguished: water-I molecules have their dipole moments aligned perpendicular to the c axis and dipole moments of water-II molecules are parallel to the c-axis. The optical conductivity σ(v) and permittivity ε′(v) spectra are recorded in terahertz and infrared ranges, at frequencies from several wavenumbers up to v = 7000 cm-1, at temperatures 5-300 K and for two polarizations, when the electric vector E of the radiation is parallel and perpendicular to the c-axis. Comparative experiments on as-grown and on dehydrated samples allow to identify the spectra of σ(v) and ε′(v) caused exclusively by water molecules. In the infrared range, well-known internal modes v1, v2, and v3 of the H2O molecule are observed for both polarizations, indicating the presence of water-I and water-II molecules in the crystal. Spectra recorded below 1000 cm-1 reveal a rich set of highly anisotropic features in the low-energy response of H2O molecule in a crystalline nano-cavity. While for E∥c only two absorption peaks are detected, at ∼90 cm-1 and ∼160 cm-1, several absorption bands are discovered for E⊥c, each consisting of narrower resonances. The bands are assigned to librational (400-500 cm-1) and translational (150-200 cm-1) vibrations of water-I molecule that is weakly coupled to the nano-cavity "walls." A model is presented that explains the "fine structure" of the bands by a splitting of the energy levels due to quantum tunneling between the minima in a six-well potential relief felt by a molecule within the cavity. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
19. Structural and vibrational properties of phenanthrene under pressure.
- Author
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Huang, Qiao-Wei, Zhang, Jiang, Berlie, Adam, Qin, Zhen-Xing, Zhao, Xiao-Miao, Zhang, Jian-Bo, Tang, Ling-Yun, Liu, Jing, Zhang, Chao, Zhong, Guo-Hua, Lin, Hai-Qing, and Chen, Xiao-Jia
- Subjects
- *
PHYSICS research , *PHENANTHRENE , *HYDROCARBONS , *DIFFRACTIVE scattering , *X-ray diffraction , *RAMAN spectroscopy , *SPACE groups , *MATHEMATICAL crystallography - Abstract
The structural and vibrational properties of phenanthrene are measured at high pressures up to 30.2 GPa by Raman spectroscopy and synchrotron X-ray diffraction techniques. Two phase transitions are observed in the Raman spectra at pressures of 2.3 GPa and 5.4 GPa which correspond to significant changes of intermolecular and intramolecular vibrational modes. Above 10.2 GPa, all the Raman peaks are lost within the fluorescence background; however, upon further compression above 20.0 GPa, three broad peaks are observed at 1600, 2993, and 3181 cm-1, indicating that phenanthrene has transformed into amorphous phase. Using X-ray diffraction, the structures of corresponding phases observed from Raman spectra are indexed with space groups of P21 for phase I (0-2.2 GPa), P2/m for phase II (2.2-5.6 GPa), P2/m+Pmmm for phase III (5.6-11.4 GPa) which has a coexistence of structures, and above 11.4 GPa the structure is indexed with space group of Pmmm. Although phenanthrene has transformed to a hydrogenated amorphous carbon structure above 20.0 GPa, these amorphous clusters still show characteristic crystalline behavior based on our X-ray diffraction patterns. Our results suggest that the long-range periodicity and the local disorder state coexist in phenanthrene at high pressures. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
20. An efficient method for indexing grazing‐incidence X‐ray diffraction data of epitaxially grown thin films.
- Author
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Simbrunner, Josef, Schrode, Benedikt, Domke, Jari, Fritz, Torsten, Salzmann, Ingo, and Resel, Roland
- Abstract
Crystal structure identification of thin organic films entails a number of technical and methodological challenges. In particular, if molecular crystals are epitaxially grown on single‐crystalline substrates a complex scenario of multiple preferred orientations of the adsorbate, several symmetry‐related in‐plane alignments and the occurrence of unknown polymorphs is frequently observed. In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal‐space vectors. However, if the sample exhibits unit cells in various orientations and/or with different lattice parameters, it is necessary to assign all experimentally obtained reflections to their associated individual origin. In the present work, an effective algorithm is described to accomplish this task in order to determine the unit‐cell parameters of complex systems comprising different orientations and polymorphs. This method is applied to a polycrystalline thin film of the conjugated organic material 6,13‐pentacenequinone (PQ) epitaxially grown on an Ag(111) surface. All reciprocal vectors can be allocated to unit cells of the same lattice constants but grown in various orientations [sixfold rotational symmetry for the contact planes (102) and (102)]. The as‐determined unit cell is identical to that reported in a previous study determined for a fibre‐textured PQ film. Preliminary results further indicate that the algorithm is especially effective in analysing epitaxially grown crystallites not only for various orientations, but also if different polymorphs are present in the film. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
21. The explanation of barrier height inhomogeneities in Au/n-Si Schottky barrier diodes with organic thin interfacial layer.
- Author
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Taşçıoğlu, İlke, Aydemir, Umut, and Altındal, Şemsettin
- Subjects
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SCHOTTKY barrier diodes , *GAUSSIAN distribution , *ENERGY-band theory of solids , *MATHEMATICAL crystallography , *EXCITON theory - Abstract
The forward bias current-voltage (I-V) characteristics of Au/n-Si Schottky barrier diodes (SBDs) with Zn doped poly(vinyl alcohol) (PVA:Zn) interfacial layer have been investigated in the wide temperature range of 80-400 K. The conventional Richardson plot of the ln(Io/T2) versus q/kT has two linear regions: the first region (200-400 K) and the second region (80-170 K). The values of activation energy (Ea) and Richardson constant (A*) were obtained from this plot and especially the values of A* are much lower than the known theoretical value for n-type Si. Also the value of Ea is almost equal to the half of the band gap energy of Si. Therefore, the [uppercase_phi_synonym]ap versus q/2kT plot was drawn to obtain the evidence of a Gaussian distribution (GD) of barrier heights (BHs) and it shows two linear region similar to ln(Io)/T2 versus q/kT plot. The analysis of I-V data based on thermionic emission of the Au/PVA:Zn/n-Si SBDs has revealed the existence of double GD with mean BH values (
[uppercase_phi_synonym] B0) of 1.06 eV and 0.86 eV with standard deviation (σ) of 0.110 eV and 0.087 V, respectively. Thus, we modified ln(Io/T2)-(qσ)2/2(kT)2 versus q/kT plot for two temperature regions (200-400 K and 80-170 K) and it gives renewed mean BHs[uppercase_phi_synonym] B0 values as 1.06 eV and 0.85 eV with Richardson constant (A*) values 121 A/cm2 K2 and 80.4 A/cm2 K2, respectively. This obtained value of A*=121 A/cm2 K2 is very close to the known theoretical value of 120 A/cm2 K2 for n-type Si. [ABSTRACT FROM AUTHOR]- Published
- 2010
- Full Text
- View/download PDF
22. Electronic structure, phonons, and thermal properties of ScN, ZrN, and HfN: A first-principles study.
- Author
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Saha, Bivas, Acharya, Jagaran, Sands, Timothy D., and Waghmare, Umesh V.
- Subjects
- *
PHYSICS research , *PHONON spectra , *CRYSTAL lattices , *MATHEMATICAL crystallography , *LATTICE dynamics , *THERMAL conductivity - Abstract
With a motivation to understand microscopic aspects of ScN, ZrN, and HfN relevant to the thermoelectric properties of nitride metal/semiconductor superlattices, we determine their electronic structure, vibrational spectra and thermal properties using first-principles calculations based on density functional theory with a generalized gradient approximation of the exchange correlation energy. We find a large energy gap in the phonon dispersions of metallic ZrN and HfN, but a gapless phonon spectrum for ScN spanning the same energy range, this suggests that a reduced thermal conductivity, suitable for thermoelectric applications, should arise in superlattices made with ScN and ZrN or ScN and HfN. To obtain an electronic energy band gap of ScN comparable to experiment, we use a Hubbard correction with a parameter U (=3.5 eV). Anomalies in the acoustic branches of the phonon dispersion of ZrN and HfN, manifested as dips in the bands, can be understood through the nesting of Fermi surface determined from our calculations. To connect with transport properties, we have determined effective masses of ScN and determined their dependence on the U parameter. Using the relaxation time approximation in the Boltzmann transport theory, we estimate the temperature dependence of the lattice thermal conductivity and discuss the chemical trends among these nitrides. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
23. Micropipe absorption mechanism of pore growth at foreign polytype boundaries in SiC crystals.
- Author
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Gutkin, M. Yu., Sheinerman, A. G., Smirnov, M. A., Argunova, T. S., Je, J. H., Nagalyuk, S. S., and Mokhov, E. N.
- Subjects
- *
SCIENTIFIC photography , *ELECTROMAGNETIC waves , *ABSORPTION , *MATHEMATICAL models , *MATHEMATICAL crystallography , *CRYSTAL defects - Abstract
Formation of pores at foreign polytype boundaries in bulk SiC crystals is studied by means of synchrotron radiation phase-sensitive radiography, optical and scanning electron microscopies, and color photoluminescence. It is demonstrated that pores are formed through coalescence of micropipes and extend along the polytype boundaries by means of micropipe absorption. A theoretical model is suggested, which describes the micropipe absorption by an elliptic pore nucleated at the boundary of a foreign polytype inclusion. It is shown that depending on the inclusion distortion, the pore can either be a separate micropipe, or grow up to a certain length, or occupy the whole facet of the inclusion. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
24. Structural properties of tensily strained Si layers grown on SiGe(100), (110), and (111) virtual substrates.
- Author
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Destefanis, V., Rouchon, D., Hartmann, J. M., Papon, A. M., Baud, L., Crisci, A., and Mermoux, M.
- Subjects
- *
CHEMICAL vapor deposition , *SURFACE roughness measurement , *EPITAXY , *ANISOTROPY , *RELAXATION phenomena , *GERMANIUM , *TWINNING (Crystallography) , *MATHEMATICAL crystallography - Abstract
We have studied the structural properties of tensily strained Si (t-Si) layers grown by reduced pressure–chemical vapor deposition on top of SiGe(100), (110), and (111) virtual substrates (VSs). Chemical mechanical planarization has been used beforehand to eliminate the as-grown surface crosshatch on all orientations and reduce by 10 up to 100 times the surface roughness. A definite surface roughening has occurred after the epitaxy of t-Si on (110) and (111). For the lowest Ge contents investigated, top Si(100) and (110) layers are locally “defect-free” whereas numerous {111} stacking faults are present in the t-Si(111) layers. For higher Ge content SiGe VS, a degradation of the crystallographic quality of (110) and (111) t-Si layers has been evidenced, with the presence of dislocations, stacking faults, and twins. Quantification of the strain level in the t-Si layers has been carried out using visible and near-UV Raman spectroscopy. The Ge contents in the VS determined by Raman spectroscopy were very close to the ones previously obtained by secondary ion mass spectrometry or x-ray diffraction. Stress values obtained for t-Si(100) layers were whatever the Ge content similar to those expected. Stress values corresponding to pseudomorphic t-Si growths have been obtained on (110) and (111) SiGe VSs, for Ge contents up to 35% and 25%, respectively. The stress values obtained on (110) surfaces for such Ge contents were high, with a noticeable anisotropy along the [001] and [1-10] directions. Degradations of the (110) and (111) Raman profiles likely coming from twin-assisted strain relaxation have been noticed for t-Si layers on SiGe VS with Ge contents higher than 35% and 25%, respectively. UV and visible Raman mapping of the growth plane strain fluctuations has finally been carried out. Original surface arrays have been highlighted for each surface orientation. Such strain fields are related to the plastic relaxation of strain in the SiGe graded layer underneath through the emission of misfit dislocations, twins, and stacking faults. Promising results have been obtained for t-Si layers on (110) SiGe VS while the technological usefulness of the (111) ones is more questionable. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
25. Response of seven crystallographic orientations of sapphire crystals to shock stresses of 16–86 GPa.
- Author
-
Kanel, G. I., Nellis, W. J., Savinykh, A. S., Razorenov, S. V., and Rajendran, A. M.
- Subjects
- *
SAPPHIRES , *OPTICAL properties , *SHOCK wave scattering , *MATHEMATICAL crystallography , *SPALLATION (Nuclear physics) - Abstract
Shock wave profiles of sapphire (single-crystal Al2O3) with seven crystallographic orientations (c, d, r, n, s, g, and m-cut) were measured with time-resolved VISAR (velocity interferometer for a surface of any reflector) interferometry at shock stresses in the range 16–86 GPa. Shock propagation was in the direction normal to the surface of each cut. The angle between the c-axis of the hexagonal representation of the sapphire crystal structure and the direction of shock propagation varied from 0 for c-cut up to 90° for m-cut in the basal plane. Based on published shock-induced transparencies for three directions of shock propagation, shock-induced optical transparency correlates with the smoothness of the mechanical shock wave profile. The ultimate goal was to find the direction of shock propagation for which shock-compressed sapphire is most transparent as a window material. In the experiments particle velocity histories were recorded at the interface between a sapphire crystal and a LiF window. In most cases measured wave profiles are noisy as a result of heterogeneity of deformation. Measured values of Hugoniot elastic limits (HELs) depend on direction of shock compression and peak shock stress. The largest HEL values (24 GPa) were recorded for shock loading along the c-axis and perpendicular to c along the m-direction. Shock compression along the m- and s-directions is accompanied by the smallest heterogeneity of deformation and the smallest rise time of the plastic shock wave. m- and s-cut sapphires most closely approach ideal elastic-plastic flow, which suggests that m- and s-cut sapphires are probably the sapphire orientations that remain the most transparent to the highest shock pressures. Under purely elastic deformation sapphire demonstrates very high spall strength, which depends on both load duration and peak stress. Plastic deformation of sapphire causes loss of its tensile strength. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
26. Nature of the cubic to rhombohedral structural transformation in (AgSbTe2)15(GeTe)85 thermoelectric material.
- Author
-
Cook, B. A., Kramer, M. J., Wei, X., Harringa, J. L., and Levin, E. M.
- Subjects
- *
MATHEMATICAL crystallography , *THERMOELECTRIC materials , *GEOMETRICAL constructions , *CALORIMETRY , *X-ray diffraction - Abstract
The existence of a large thermoelectric figure of merit in (AgSbTe2)15(GeTe)85 has been known for many years. However, the nature of the crystallographic transformation in these materials from a high-temperature cubic to a low-temperature rhombohedral polymorph and its effect on electrical transport has not been clearly established. Transmission electron microscopy studies were performed that show extensive twinning in the low-temperature structure, resulting from lattice strain during the dilation along the (111) crystallographic direction. Analysis of differential scanning calorimetric studies indicates that the transformation is of second order, so that the high-temperature cubic phase is nonquenchable. High-temperature x-ray diffraction was performed to establish the transformation temperature, which was found to be complete upon heating at a temperature of 510 K. Results of electrical conductivity measurements as a function of temperature on as-cast samples are discussed in terms of the observed twinning. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
27. Photonic crystal all-polymer slab resonators.
- Author
-
Böttger, G., Schmidt, M., Eich, M., Boucher, R., and Hübner, U.
- Subjects
- *
PHOTONICS , *CRYSTAL lattices , *MATHEMATICAL crystallography , *CAVITY resonators , *WAVEGUIDES , *SPECTRUM analysis , *ELECTRICAL conductors - Abstract
Moderate air-hole-fraction photonic crystal square lattice structures defining small cavity resonators were created by etching air holes of 0.15 μm radius to a depth of 3 μm in an all-polymer slab waveguide. Transmission measurements with subnanometer resolution resolved the complete transmission spectra and highly resonant defect peaks with quality factors Q larger than 400. Simulations demonstrate the importance of high-aspect-ratio etching depths for maintaining vertical index-confinement and vertically quasisymmetric field distributions despite the material index asymmetry. Experimental spectra are shown to match the three-dimensional finite-integration simulations. Enhanced quality factors of up to 20 000 were found in the simulations for cavities bounded by modified radius air holes. In this manner resonators with very low out-of-cavity losses and high defect state transmission may be created in moderate index contrast polymer waveguide slabs. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
28. A solution of the effective-mass Schrödinger equation in general isotropic and nonparabolic bands for the study of two-dimensional carrier gases.
- Author
-
Gómez-Campos, F. M., Rodríguez-Bolívar, S., López-Villanueva, J. A., Jiménez-Tejada, J. A., and Carceller, J. E.
- Subjects
- *
EQUATIONS , *SEMICONDUCTORS , *QUANTUM wells , *ENERGY-band theory of solids , *MATHEMATICAL crystallography , *QUANTUM theory - Abstract
In this paper we develop a suitable method for solving the effective-mass Schrödinger equation for two-dimensional electron and hole gases in semiconductor structures such as quantum wells using a general nonparabolic band structure. We present two different ways to treat barriers, the first being the exact solution and the second a suitable option when the band structure is not determined inside the gap. As a first application, this procedure was implemented to solve the effective-mass Schrödinger equation for holes in Si and Ge using an analytical valence-band model. Analyzing the results obtained enabled us to demonstrate the importance of nonparabolicity in energy quantization in these systems and to discuss the suitability of each of these two procedures for dealing with barriers. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
29. Transmission electron microscopy study on Nd-rich phase and grain boundary structure of Nd–Fe–B sintered magnets.
- Author
-
Shinba, Y., Konno, T. J., Ishikawa, K., Hiraga, K., and Sagawa, M.
- Subjects
- *
MORPHOLOGY , *CRYSTAL grain boundaries , *DIFFRACTION patterns , *MATHEMATICAL crystallography , *GROUP theory - Abstract
The crystal structure and morphology of the Nd-rich phase in postannealed sintered Nd-Fe-B hard magnets were investigated by transmission electronmicroscopy (TEM). The Nd-rich phase at grain boundaries thinner than about 2 nm was found to be amorphous; as the boundary region broadened, it assumed a face-centered cubic (fcc) structure with α ≈ 0.54 nm; eventually, the selected area diffraction pattern exhibited systematically allowed superlattice spots, revealing that the Nd-rich phase belongs to the space group Iα&3macr; with α≈1.1 nm. The elemental analysis of the Nd-rich phase showed that it contains a considerable amount of oxygen. These findings indicate that the Nd-rich phase with α ≈ 1.1 nm is in fact isostructural to cubic Nd2O3 structure). We also found Nd-rich fcc precipitates (α ≈ 0.54 nm) of several ten to hundred nm inside the Nd2Fe14B grains. Both intergranular and intragrain Nd-rich phases possess simple orientation relationships with the matrix Nd2Fe14B phase, such as (111)Nd2Fe14B‖(111)Nd-rich [211]Nd2Fe14B‖[211]Nd-rich and (010)Nd2Fe14B‖(111)Nd-rich[001]Nd2Fe14B‖[110]Nd-rich. Our Lorentz TEM observation suggested that the intragrain Nd-rich precipitates frequently disrupt magnetic domain wall arrangements, and that the magnetic interaction across thin amorphous Nd-rich phase are dominated by a simple dipole interaction. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
30. Indexing grazing‐incidence X‐ray diffraction patterns of thin films: lattices of higher symmetry.
- Author
-
Simbrunner, Josef, Hofer, Sebastian, Schrode, Benedikt, Garmshausen, Yves, Hecht, Stefan, Resel, Roland, and Salzmann, Ingo
- Subjects
- *
GRAZING incidence , *X-ray diffraction , *THIN films , *CRYSTAL growth , *CRYSTAL texture - Abstract
Grazing‐incidence X‐ray diffraction studies on organic thin films are often performed on systems showing fibre‐textured growth. However, indexing their experimental diffraction patterns is generally challenging, especially if low‐symmetry lattices are involved. Recently, analytical mathematical expressions for indexing experimental diffraction patterns of triclinic lattices were provided. In the present work, the corresponding formalism for crystal lattices of higher symmetry is given and procedures for applying these equations for indexing experimental data are described. Two examples are presented to demonstrate the feasibility of the indexing method. For layered crystals of the prototypical organic semiconductors diindenoperylene and (ortho‐difluoro)sexiphenyl, as grown on highly oriented pyrolytic graphite, their yet unknown unit‐cell parameters are determined and their crystallographic lattices are identified as monoclinic and orthorhombic, respectively. A general indexing procedure for grazing‐incidence X‐ray diffraction patterns recorded from fibre‐textured films is introduced for lattices of monoclinic and higher‐symmetry systems. The analytical mathematical expressions are given and their use is demonstrated in detail for two cases (monoclinic and orthorhombic). [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
31. Synthesis, Crystal Structure, and Studies on Mechanism of D-π-A Ferrocene Derivative.
- Author
-
Zhang, Y. M., Gao, X., and Liu, P.
- Subjects
- *
AROMATIC aldehydes , *BENZALDEHYDE , *X-ray crystallography , *CHEMICAL reactions , *MATHEMATICAL crystallography - Abstract
Abstract: Microwave-assisted solvent-free synthesis of new (D-π-A) chromogenes, 2-ferrocenyl-1,1-dicyanobuta-1,3-diene derivatives (II), have been accomplished through the condensation of 2-(1-ferrocenylethylidene)malononitrile (I) and aromatic aldehydes with sarcosine as the catalyst and identified by 1H NMR, 13C NMR and FT-IR. Compound IId was determined by X-ray crystallography (CIF file CCDC no. 1056735). The crystal belongs to monoclinic, space group P21/c. The possible reaction mechanism has been studied. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
32. Localized epitaxial growth of CrSi2 on silicon.
- Author
-
Shiau, F. Y., Cheng, H. C., and Chen, L. J.
- Subjects
- *
EPITAXY , *SILICON , *MATHEMATICAL crystallography - Abstract
Presents a study which investigated epitaxial CrSi[sub2] grown on (001) and (011) silicon. Role of lattice match in the epitaxial growth of CRSi[sub2] on silicon; Results of crystallographic analysis; Quality of CRSi[sub2] epitaxy.
- Published
- 1986
- Full Text
- View/download PDF
33. Electronic and related properties of crystalline semiconducting iron disilicide.
- Author
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Filonov, A. B., Migas, D. B., Shaposhnikov, V. L., Dorozhkin, N. N., Petrov, G. V., Borisenko, V. E., Henrion, W., and Lange, H.
- Subjects
- *
ENERGY-band theory of solids , *MATHEMATICAL crystallography - Abstract
Deals with a study which performed band structure calculations for β-FeSi[sub2] through the linear muffin-tin orbital method. Details of the calculations; Experimental procedures; Results and discussion.
- Published
- 1996
- Full Text
- View/download PDF
34. The equilibrium properties of a 6mm polycrystal exhibiting transverse isotropy.
- Author
-
Ferrari, Mauro and Johnson, George C.
- Subjects
- *
CRYSTALS , *MATHEMATICAL crystallography - Abstract
Presents a study which determined the thermoelectromechanical properties of an aggregate of crystals exhibiting transverse isotropy by averaging the corresponding crystal properties. Discussion on the textual analysis used in evaluating effective aggregate properties; Physical properties of crystals.
- Published
- 1988
- Full Text
- View/download PDF
35. Finite Element Analysis of Stress Transfer Mechanism from Matrix to the Fiber in SWCN Reinforced Nanocomposites.
- Author
-
Günay, E.
- Subjects
- *
FINITE element method , *NANOCOMPOSITE materials , *SINGLE walled carbon nanotubes , *CRYSTAL lattices , *MATHEMATICAL crystallography - Abstract
This study defined as micromechanical finite element (FE) approach examining the stress transfer mechanism in single-walled carbon nanotube (SWCN) reinforced composites. In the modeling, 3D unit-cell method was evaluated. Carbon nanotube reinforced composites were modeled as three layers which comprises CNT, interface and matrix material. Firstly; matrix, fiber and interfacial materials all together considered as three layered cylindrical nanocomposite. Secondly, the cylindrical matrix material was assumed to be isotropic and also considered as a continuous medium. Then, fiber material was represented with zigzag type SWCNs. Finally, SWCN was combined with the elastic medium by using springs with different constants. In the FE modeling of SWCN reinforced composite model springs were modeled by using ANSYS spring damper element COMBIN14. The developed interfacial van der Waals interaction effects between the continuous matrix layer and the carbon nanotube fiber layer were simulated by applying these various spring stiffness values. In this study, the layered composite cylindrical FE model was presented as the equivalent mechanical properties of SWCN structures in terms of Young's modulus. The obtained results and literature values were presented and discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
36. General expression for effective diffusivity of foreign atoms migrating via a fast intermediate.
- Author
-
Chen, Kejia, Vaidyanathan, Ramakrishnan, Seebauer, Edmund G., and Braatz, Richard D.
- Subjects
- *
PHYSICS research , *SEMICONDUCTOR industry , *CRYSTAL lattices , *MATHEMATICAL crystallography , *LATTICE dynamics , *ATOMS , *SEMICONDUCTOR doping - Abstract
In many solids, diffusion of foreign atoms takes place primarily through highly mobile intermediate species that periodically exchange with atoms in the crystalline lattice. The governing reaction-diffusion equations include a diffusion coefficient as well as kinetic parameters describing the exchange of the intermediate species. Yet it is often convenient to model a diffusive process in terms of a single parameter, no matter what the time regime. This communication derives for a delta function initial profile an exact expression for the effective diffusivity that is valid in all time regimes. In the case of semiconductor solids, such an expression can be helpful in the interpretation of dopant diffusion measurements. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
37. First Principles Investigations of the Crystal Structure, Electron Spectra, and Chemical Bonding in the Low-Temperature Phase of Lithium Imide.
- Author
-
Kravchenko, N. G., Zhdanov, V. V., Kaizer, E. B., and Poplavnoi, A. S.
- Subjects
- *
LITHIUM-ion batteries , *SPACE groups , *MATHEMATICAL crystallography , *DENSITY functional theory , *HYDROGEN bonding - Abstract
The density functional method in the full-electron approximation is used to calculate optimized structural parameters, band spectrum, density of states, electron density maps and to study chemical bonding in the low-temperature phase of lithium imide with a crystal structure of the space group Ima2. The valence band width is 15.14 eV, and it consists of three subzones (slightly dispersed bottom subzone, medium subzone, and top subzone with a width of ~2.4 eV) due to dispersion cased by hybridization of hydrogen s states and nitrogen p states. The top of the valence band and the bottom of the conduction band are in the center of the Brillouin zone, the width of the band gap is 4.48 eV, the absorption edge is direct. The electron density maps demonstrate chains of N-H complexes bound by pairs of Li atoms. The Li-N bond is predominantly ionic, while the N-H bond is polar covalent. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
38. Crystallographic shelves: space‐group hierarchy explained.
- Author
-
Nespolo, Massimo, Aroyo, Mois Ilia, and Souvignier, Bernd
- Subjects
- *
SPACE groups , *CRYSTALLOGRAPHERS , *CRYSTAL structure , *CRYSTAL symmetry , *MATHEMATICAL crystallography - Abstract
Space groups are classified, according to different criteria, into types, classes, systems and families. Depending on the specific research topic, some of these concepts will be more relevant to the everyday crystallographer than others. Unfortunately, incorrect use of the classification terms often leads to misunderstandings. This article presents the rationale behind the different classification levels. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
39. WEAK CAYLEY TABLE GROUPS OF SOME CRYSTALLOGRAPHIC GROUPS.
- Author
-
HUMPHRIES, STEPHEN P. and PAULSEN, REBECA A.
- Subjects
CAYLEY algebras ,ISOMORPHISM (Mathematics) ,MATHEMATICAL crystallography ,GROUP theory ,SYMMETRY groups - Abstract
For a group G , a weak Cayley table isomorphism is a bijection ƒ : G → G such that ƒ(g
1 g2 ) is conjugate to ƒ(g1 ) ƒ(g2 ) for all g1 , g2 ∈ G. The set of all weak Cayley table isomorphisms forms a group (G) that is the group of symmetries of the weak Cayley table of G. We determine (G) for each of the 17 wallpaper groups G , and for some other crystallographic groups. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
40. Mechanical Stress in InP Structures Etched in an Inductively Coupled Plasma Reactor with Ar/Cl2/CH4 Plasma Chemistry.
- Author
-
Landesman, Jean-Pierre, Cassidy, Daniel T., Fouchier, Marc, Pargon, Erwine, Levallois, Christophe, Mokhtari, Merwan, Jimenez, Juan, and Torres, Alfredo
- Subjects
CRYSTAL lattices ,MATHEMATICAL crystallography ,DEFORMATIONS (Mechanics) ,INDIUM phosphide ,PLASMA etching - Abstract
We investigated the crystal lattice deformation that can occur during the etching of structures in bulk InP using SiN
x hard masks with Ar/Cl2 /CH4 chemistries in an inductively coupled plasma reactor. Two techniques were used: degree of polarization (DOP) of the photo-luminescence, which gives information on the state of mechanical stress present in the structures, and spectrally resolved cathodo-luminescence (CL) mapping. This second technique also provides elements on the mechanical stress in the samples through analysis of the spectral shift of the CL intrinsic emission lines. Preliminary DOP mapping experiments have been conducted on the SiNx hard mask patterns without etching the underlying InP. This preliminary study demonstrated the potential of DOP to map mechanical stress quantitatively in the structures. In a second step, InP patterns with various widths between 1 μm and 20 μm, and various depths between 1 μm and 6 μm, were analyzed by the 2 techniques. DOP measurements were made both on the (100) top surface of the samples and on the (110) cleaved cross section. CL measurements were made only from the (100) surface. We observed that inside the etched features, close to the vertical etched walls, there is always some compressive deformation, while it is tensile just outside the etched features. The magnitude of these effects depends on the lateral and depth dimensions of the etched structures, and on the separation between them (the tensile deformation increases between them due to some kind of proximity effect when separation decreases). [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
41. Indexing of grazing‐incidence X‐ray diffraction patterns: the case of fibre‐textured thin films.
- Author
-
Simbrunner, Josef, Simbrunner, Clemens, Schrode, Benedikt, Röthel, Christian, Bedoya-Martinez, Natalia, Salzmann, Ingo, and Resel, Roland
- Subjects
- *
CRYSTAL models , *X-ray diffraction , *THIN film crystallography - Abstract
Crystal structure solutions from thin films are often performed by grazing‐incidence X‐ray diffraction (GIXD) experiments. In particular, on isotropic substrates the thin film crystallites grow in a fibre texture showing a well defined crystallographic plane oriented parallel to the substrate surface with random in‐plane order of the microcrystallites forming the film. In the present work, analytical mathematical expressions are derived for indexing experimental diffraction patterns, a highly challenging task which hitherto mainly relied on trial‐and‐error approaches. The six lattice constants a, b, c, α, β and γ of the crystallographic unit cell are thereby determined, as well as the rotation parameters due to the unknown preferred orientation of the crystals with respect to the substrate surface. The mathematical analysis exploits a combination of GIXD data and information acquired by the specular X‐ray diffraction. The presence of a sole specular diffraction peak series reveals fibre‐textured growth with a crystallographic plane parallel to the substrate, which allows establishment of the Miller indices u, v and w as the rotation parameters. Mathematical expressions are derived which reduce the system of unknown parameters from the three‐ to the two‐dimensional space. Thus, in the first part of the indexing routine, the integers u and v as well as the Laue indices h and k of the experimentally observed diffraction peaks are assigned by systematically varying the integer variables, and by calculating the three lattice parameters a, b and γ. Because of the symmetry of the derived equations, determining the missing parameters then becomes feasible: (i) w of the surface parallel plane, (ii) the Laue indices l of the diffraction peak and (iii) analogously the lattice constants c, α and ß. In a subsequent step, the reduced unit‐cell geometry can be identified. Finally, the methodology is demonstrated by application to an example, indexing the diffraction pattern of a thin film of the organic semiconductor pentacenequinone grown on the (0001) surface of highly oriented pyrolytic graphite. The preferred orientation of the crystallites, the lattice constants of the triclinic unit cell and finally, by molecular modelling, the full crystal structure solution of the as‐yet‐unknown polymorph of pentacenequinone are determined. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
42. Lusztig data of Kashiwara–Nakashima tableaux in types B and C.
- Author
-
Kwon, Jae-Hoon
- Subjects
- *
KAZHDAN-Lusztig polynomials , *QUANTUM groups , *EMBEDDINGS (Mathematics) , *MATHEMATICAL models , *MATHEMATICAL crystallography , *MATHEMATICAL notation - Abstract
We provide an explicit combinatorial description of the embedding of the crystal of Kashiwara–Nakashima tableaux in types B and C into that of i -Lusztig data associated to a family of reduced expressions i of the longest element w 0 . The description of the embedding is simple and elementary using only the Schützenberger's jeu de taquin and RSK algorithm. A spinor model for classical crystals plays an important role as an intermediate object connecting Kashiwara–Nakashima tableaux and Lusztig data. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
43. STIELTJES FUNCTIONS OF FINITE ORDER AND HYPERBOLIC MONOTONICITY.
- Author
-
BONDESSON, LENNART and SIMON, THOMAS
- Subjects
- *
INTEGRAL representations , *ALGEBRAIC number theory , *MATHEMATICAL crystallography , *REPRESENTATIONS of groups (Algebra) , *GROUP theory - Abstract
A class of Stieltjes functions of finite type is introduced. These satisfy Widder’s conditions on the successive derivatives up to some finite order and are not necessarily smooth. We show that such functions have a unique integral representation along some generic kernel which is a truncated Laurent series approximating the standard Stieltjes kernel. We then obtain a two-to-one correspondence, via the logarithmic derivative, between these functions and a subclass of hyperbolically monotone functions of finite type. This correspondence generalizes a representation of HCM functions in terms of two Stieltjes transforms earlier obtained by the first author. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
44. Some crystallographic Haar type composite dilation wavelets for.
- Author
-
Deshpande, R. and Bhate, H.
- Subjects
- *
MATHEMATICAL crystallography , *HAAR function , *WAVELETS (Mathematics) , *GROUP theory , *DIFFERENTIAL equations - Abstract
Composite dilation wavelets generate bases or frames using two groups of dilations. One group is associated with a set where is an expanding matrix with an integer. The second group is associated with the subgroup of matrices with Here, we present crystallographic Haar type composite dilation wavelets generated by such two dilation groups associated with Further, we provide matricial filters and reconstruction formulae at various scales. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
45. Continuity and representation of valuations on star bodies.
- Author
-
Tradacete, Pedro and Villanueva, Ignacio
- Subjects
- *
CONTINUITY , *MATHEMATICAL crystallography , *ALGEBRAIC number theory , *REPRESENTATIONS of groups (Algebra) , *INTEGRAL representations - Abstract
It is shown that every continuous valuation defined on n -dimensional star bodies has an integral representation in terms of the radial function. Our argument is based on the non-trivial fact that continuous valuations are uniformly continuous on bounded sets. We also characterize continuous valuations on the n -dimensional star bodies that arise as restriction of a measure on R n . [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
46. Na3Tb(PO4)2: Synthesis, crystal structure and greenish emitting properties.
- Author
-
Zhao, Dan, Ma, Zhao, Liu, Bao-Zhong, Zhang, Rui-Juan, Wu, Zhi-Qiang, Wang, Jian, and Duan, Pei-Gao
- Subjects
- *
MATHEMATICAL crystallography , *CRYSTALLOGRAPHY , *CRYSTAL lattices , *CRYSTAL symmetry , *RADIOGRAPHY - Abstract
A anhydrous orthoborate Na 3 Tb(PO 4 ) 2 has been prepared and its crystal structure was determined by X-Ray diffraction of a non-merohedral twinned single crystal. The results show that the compound crystallizes in monoclinic space group C 2/ c and the structure features a 3D framework containing PO 4 , NaO 6 , NaO 7 , NaO 8 and TbO 8 polyhedra. Under near-UV excitation (370 nm), Na 3 Tb(PO 4 ) 2 shows intense characteristic emission bands of Tb 3+ (490 nm, 543 nm, 585 nm and 620 nm) with the CIE coordinate of (0.3062, 0.5901), corresponding to greenish color. The excitation spectrum covers a wide range from 340 nm to 390 nm, which indicates that phosphor Na 3 Tb(PO 4 ) 2 can be efficiently activated by near-UV LED ship. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
47. A note on Gamma Wick products.
- Author
-
Catrina, Florin and Stan, Aurel I.
- Subjects
- *
INTEGRAL representations , *MATHEMATICAL crystallography , *EXTREME value theory , *PROBABILITY theory , *GAMMA distributions - Abstract
An integral representation of the Wick product for Gamma distributed random variables, with mean greater than , is presented first. We use this integral representation to prove a Hölder inequality for norms of Gamma Wick products. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
48. K2[B3O3(OH)5]: A new deep-UV nonlinear optical crystal with isolated [B3O3(OH)5]2- anionic groups.
- Author
-
Wang, Qian, Lin, Chensheng, Zou, Guohong, Liu, Mengjiao, Gao, Daojiang, Bi, Jian, and Huang, Ling
- Subjects
- *
SPACE groups , *CRYSTAL optics , *ADDITION polymerization , *MATHEMATICAL crystallography , *OXYGEN atom transfer reactions - Abstract
A new noncentrosymmetric material, namely, K 2 [B 3 O 3 (OH) 5 ] has been obtained by conventional solution reaction. It crystallizes in the orthorhombic space group Ama 2 (no. 40). In the structure of K 2 [B 3 O 3 (OH) 5 ], the BO 2 (OH) triangles and BO 2 (OH) 2 tetrahedra are linked via sharing corners forming the isolated [B 3 O 3 (OH) 5 ] 2- anionic groups with no dangling bonds in oxygen atoms. And K 2 [B 3 O 3 (OH) 5 ] is the first synthetic noncentrosymmetric borates with [B 3 O 3 (OH) 5 ] 2- anionic groups. Powder second-harmonic generation (SHG) using the Kurtz−Perry technique showed that K 2 [B 3 O 3 (OH) 5 ] is type I phase-matchable, and the measured SHG coefficient is 0.32 times that of KH 2 PO 4 . The UV transmittance spectroscopy measurement indicated that the UV absorption edge was below 200 nm, suggesting that K 2 [B 3 O 3 (OH) 5 ] might be a promising deep-UV nonlinear optical material. Band structure and optical property calculations based on DFT methods were also performed. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
49. First principles investigation of the electronic properties of graphitic carbon nitride with different building block and sheet staggered arrangement.
- Author
-
Sun, S.P., Gu, S., Sun, J.H., Xia, F.F., and Chen, G.H.
- Subjects
- *
GRAPHITE , *SPACE groups , *THERMODYNAMICS , *THERMAL conductivity , *BAND gaps , *MATHEMATICAL crystallography - Abstract
The electronic properties of g-C 3 N 4 with different building block and sheet staggered arrangement are studied by using first-principles calculations. The calculated lattice constants and band gaps of bulk g-C 3 N 4 with different space group P -6m2, R 3 m , Cmcm and P 6 3 / mmc consistent well with the previous results. The hybrid functional HSE06 is performed to evaluate the electronic properties of graphitic carbon nitride, and it is suggested that the HSE06 hybrid functional could predict more reasonable band gap than the traditional functional. The band gaps of bulk g-C 3 N 4 with P -6m2, R 3 m , Cmcm and P 6 3 / mmc structure are about 2.8 eV, 2.6 eV, 2.6 eV and 2.4 eV, respectively. The electronic properties of monolayer triazine- and heptazine-based structure for g-C 3 N 4 are also studied, and the corresponding band gaps are 3.0 eV and 2.7 eV, respectively. Compared to the monolayer g-C 3 N 4 , the decreasing band gaps of bulk structures should be attributed to the band overlapping among the neighboring graphitic CN sheets. The thermodynamic properties of bulk g-C 3 N 4 are also investigated, and the results show that the heptazine-based structures have larger thermal expansion coefficient and relatively smaller thermal conductivity compared to the triazine-based structures. These calculated results are suggested that not only building block but also sheet staggered arrangement has important effect on the electronic properties of g-C 3 N 4 . Furthermore, the charge density of monolayer g-C 3 N 4 shows that C and N atoms of g-C 3 N 4 sheets with different building block are all sp 2 hybridization, which is similar to that of graphite. Our results unveil that the building block and sheet staggered arrangement are effective factors to tune the electronic structure and enhance the sunlight absorption efficiency of g-C 3 N 4 . [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
50. Synthesis, characterization and computational studies of 3-{(E)-[(2-hydroxyphenyl)imino]methyl}benzene-1,2-diol and molecular structure of its zwitterionic form.
- Author
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Ezeorah, Julius Chigozie, Ossai, Valentine, Obasi, Lawrence Nnamdi, Elzagheid, Mohamed I., Rhyman, Lydia, Lutter, Michael, Jurkschat, Klaus, Dege, Necmi, and Ramasami, Ponnadurai
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CONDENSATION , *CRYSTAL lattices , *X-rays , *MATHEMATICAL crystallography , *FUNCTIONAL analysis - Abstract
The Schiff base 3-{( E )-[(2-hydroxyphenyl)imino]methyl}benzene-1,2-diol was synthesized by the condensation of 2,3-dihydroxybenzaldehyde and 2-aminophenol in water at room temperature. The crystal was grown using two solvents (dry methanol and 60% methanol). The compound was characterized using elemental microanalysis, IR, NMR, UV spectroscopies and single-crystal X-ray diffraction crystallography. The X-ray structure reveals that the Schiff base crystallizes as a methanol solvate in dry methanol with triclinic crystal system, space group P-1 and Z = 2 in the unit cell and as a non-methanol solvate in 60% methanol with triclinic crystal system, space group P-1 and Z = 4 in the unit cell. The compound showed absorption bands at 272, 389, 473 and 602 nm in DMSO. These bands were assigned as π → π ∗ , n → π ∗ and n-σ ∗ transitions. The 473 and 602 nm bands in DMSO reveal that the compound exists in tautomeric forms. The presence of N-H, C-O and C N stretching vibrations in the IR spectrum indicates that the compound is zwitterionic in the solid state. This study was supplemented using density functional theory method. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
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