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Yang Y, Cai C, Lin J, Gong L, Yang Q. Accurate determination of lattice parameters based on Niggli reduced cell theory by using digitized electron diffraction micrograph. Micron 2017; 96:9-15. [PMID: 28208085 DOI: 10.1016/j.micron.2016.12.006] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2016] [Revised: 12/19/2016] [Accepted: 12/19/2016] [Indexed: 11/29/2022]
Abstract
In this paper, we used Niggli reduced cell theory to determine lattice constants of a micro/nano crystal by using electron diffraction patterns. The Niggli reduced cell method enhanced the accuracy of lattice constant measurement obviously, because the lengths and the angles of lattice vectors of a primitive cell can be measured directly on the electron micrographs instead of a double tilt holder. With the aid of digitized algorithm and least square optimization by using three digitized micrographs, a valid reciprocal Niggli reduced cell number can be obtained. Thus a reciprocal and real Bravais lattices are acquired. The results of three examples, i.e., Mg4Zn7, an unknown phase (Precipitate phase in nickel-base superalloy) and Ba4Ti13O30 showed that the maximum errors are 1.6% for lengths and are 0.3% for angles.
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Affiliation(s)
- Yi Yang
- School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, China
| | - Canying Cai
- School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, China
| | - Jianguo Lin
- School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, China
| | - Lunjun Gong
- School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, China
| | - Qibin Yang
- School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, China.
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Abstract
The problem of identifying the coincidence site lattices produced by the disorientations of any rational lattice is investigated. A very simple new procedure for computing the CSLs is presented, based on Grimmer's reciprocity theorem and application of the reduction algorithm introduced by Buerger for finding reduced cells. The point symmetries of a lattice imply that any orientation relationship that produces a CSL can be alternatively expressed by a variety of different rotations. Two simple numerical methods (one based on integral matrix operations and one based on quaternions) are demonstrated for finding all the equivalent rotations that produce the same CSL and for obtaining a single “canonical” rotation as a representative of an equivalence class.
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Della Valle RG, Venuti E, Brillante A, Girlando A. Are crystal polymorphs predictable? The case of sexithiophene. J Phys Chem A 2008; 112:6715-22. [PMID: 18593103 DOI: 10.1021/jp801749n] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Using sexithiophene as a benchmark compound, we present a very effective strategy for searching the potential energy minima of a crystalline material, described in terms of rigid molecules with Coulombic and atom-atom interactions. The strategy involves uniform sampling of the many-body energy hypersurface, mechanical identification of all constraints deriving from the crystallographic symmetry, and a "sight-resight" method, originally introduced in wildlife ecology, for assessing the completeness of the search. Thousands of distinct potential energy minima, with a surprising variety of structural arrangements, are identified for sexithiophene. Despite the large number of competing minima, the system presents a small number of deep minima, with very different structures and not particularly congested in energy or density. The two deepest minima correspond to the structures of the two known experimental polymorphs, which are satisfactorily described.
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Affiliation(s)
- Raffaele Guido Della Valle
- Dipartimento di Chimica Fisica e Inorganica and INSTM-UdR Bologna, Universita di Bologna, Viale Risorgimento 4, I-40136 Bologna, Italy
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Kuleshova LN, Antipin MY. Cambridge Structural Database as a tool for studies of general structural features of organic molecular crystals. RUSSIAN CHEMICAL REVIEWS 2007. [DOI: 10.1070/rc1999v068n01abeh000453] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Della Valle RG, Venuti E, Brillante A, Girlando A. Inherent structures of crystalline tetracene. J Phys Chem A 2007; 110:10858-62. [PMID: 16970382 DOI: 10.1021/jp0611020] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We have systematically sampled the potential energy surface of crystalline tetracene to identify its local minima. These minima represent all possible stable configurations and constitute the "inherent structures" of the system. The crystal is described in terms of rigid molecules with Coulombic and atom-atom interactions. Hundreds of distinct minima are identified, mostly belonging to the space groups P (triclinic) and P2(1)/c (monoclinic), with a variety of structural arrangements. The deepest minimum corresponds to the high temperature-low pressure polymorph. This is the only polymorph with a completely described X-ray structure, which is satisfactorily described by the calculations. The next deep minimum is likely to correspond to the low temperature-high pressure polymorph, which has been experimentally identified but not yet fully described.
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Affiliation(s)
- Raffaele Guido Della Valle
- Dipartimento di Chimica Fisica e Inorganica and INSTM-UdR Bologna, Università di Bologna, Viale Risorgimento 4, I-40136 Bologna, Italy
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Pittelkow M, Reenberg TK, Nielsen KT, Magnussen MJ, Sølling TI, Krebs FC, Christensen JB. Synthesis, Structure, and Properties of 4,7-Dimethoxybenzo[c]tellurophene: A Molecular Pyroelectric Material. Angew Chem Int Ed Engl 2006. [DOI: 10.1002/ange.200601298] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Pittelkow M, Reenberg TK, Nielsen KT, Magnussen MJ, Sølling TI, Krebs FC, Christensen JB. Synthesis, Structure, and Properties of 4,7-Dimethoxybenzo[c]tellurophene: A Molecular Pyroelectric Material. Angew Chem Int Ed Engl 2006; 45:5666-70. [PMID: 16858711 DOI: 10.1002/anie.200601298] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Michael Pittelkow
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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Li XZ. Computer programs for unit-cell determination in electron diffraction experiments. Ultramicroscopy 2005; 102:269-77. [PMID: 15694673 DOI: 10.1016/j.ultramic.2004.10.008] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2004] [Revised: 10/11/2004] [Accepted: 10/24/2004] [Indexed: 11/22/2022]
Abstract
A set of computer programs for unit-cell determination from an electron diffraction tilt series and pattern indexing has been developed on the basis of several well-established algorithms. In this approach, a reduced direct primitive cell is first determined from experimental data, in the means time, the measurement errors of the tilt angles are checked and minimized. The derived primitive cell is then checked for possible higher lattice symmetry and transformed into a proper conventional cell. Finally a least-squares refinement procedure is adopted to generate optimum lattice parameters on the basis of the lengths of basic reflections in each diffraction pattern and the indices of these reflections. Examples are given to show the usage of the programs.
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Affiliation(s)
- X Z Li
- Center for Materials Research and Analysis, University of Nebraska, WSCE N 104, Lincoln, NE 68588-0656, USA.
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The use of (R)-(+)-α-methylbenzylamine and (S)-(−)-α-methylbenzylamine as chiral moieties to obtain monomers for second harmonic generation crystals. J Mol Struct 2003. [DOI: 10.1016/s0022-2860(02)00708-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Della Valle RG, Venuti E, Brillante A, Girlando A. Inherent structures of crystalline pentacene. J Chem Phys 2003. [DOI: 10.1063/1.1527896] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Krebs FC, Larsen PS, Larsen J, Jacobsen CS, Boutton C, Thorup N. Synthesis, Structure, and Properties of 4,8,12-Trioxa-12c-phospha-4,8,12,12c-tetrahydrodibenzo[cd,mn]pyrene, a Molecular Pyroelectric. J Am Chem Soc 1997. [DOI: 10.1021/ja962023c] [Citation(s) in RCA: 85] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Frederik C. Krebs
- Contribution from the Macromolecular Chemistry Group, Department of Solid State Physics, Risø National Laboratory, DK-4000 Roskilde, Denmark
| | - Peter S. Larsen
- Contribution from the Macromolecular Chemistry Group, Department of Solid State Physics, Risø National Laboratory, DK-4000 Roskilde, Denmark
| | - Jan Larsen
- Contribution from the Macromolecular Chemistry Group, Department of Solid State Physics, Risø National Laboratory, DK-4000 Roskilde, Denmark
| | - Claus S. Jacobsen
- Contribution from the Macromolecular Chemistry Group, Department of Solid State Physics, Risø National Laboratory, DK-4000 Roskilde, Denmark
| | - Carlo Boutton
- Contribution from the Macromolecular Chemistry Group, Department of Solid State Physics, Risø National Laboratory, DK-4000 Roskilde, Denmark
| | - Niels Thorup
- Contribution from the Macromolecular Chemistry Group, Department of Solid State Physics, Risø National Laboratory, DK-4000 Roskilde, Denmark
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Hill AM, Levason W, Preece SR, Webster M. Synthesis and spectroscopic studies of trans and cis rhodium(III) complexes of o-C6H4(PMe2)2 and o-C6H4(AsMe2)2. Crystal structures of trans-[Rh{0-C6H4(PMe2)2}2Cl2]Cl and [Rh{o-C6H4(AsMe2)2}2I2]BF4. Polyhedron 1997. [DOI: 10.1016/s0277-5387(96)00406-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Sung CM, Williams DB. Principle and applications of convergent beam electron diffraction: a bibliography (1938-1990). JOURNAL OF ELECTRON MICROSCOPY TECHNIQUE 1991; 17:95-118. [PMID: 1993941 DOI: 10.1002/jemt.1060170110] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- C M Sung
- Materials Characterization Department, GTE Laboratories Inc., Waltham, Massachusetts 02254
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