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"Crystallography Textbooks."
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Basic concepts of crystallography : an outcome from crystal symmetry
This textbook is based on the author's lectures.
Book
Intermolecular interactions in crystals : fundamentals of crystal engineering
This new book brings together the latest information on intermolecular bonding within molecular crystals, providing a very useful introductory text for graduates.
eBook
The Fermi energy as common parameter to describe charge compensation mechanisms: A path to Fermi level engineering of oxide electroceramics
Chemical substitution, which can be iso- or heterovalent, is the primary strategy to tailor material properties. There are various ways how a material can react to substitution. Isovalent substitution changes the density of states while heterovalent substitution, i.e. doping, can induce electronic compensation, ionic compensation, valence changes of cations or anions, or result in the segregation or neutralization of the dopant. While all these can, in principle, occur simultaneously, it is often desirable to select a certain mechanism in order to determine material properties. Being able to predict and control the individual compensation mechanism should therefore be a key target of materials science. This contribution outlines the perspective that this could be achieved by taking the Fermi energy as a common descriptor for the different compensation mechanisms. This generalization becomes possible since the formation enthalpies of the defects involved in the various compensation mechanisms do all depend on the Fermi energy. In order to control material properties, it is then necessary to adjust the formation enthalpies and charge transition levels of the involved defects. Understanding how these depend on material composition will open up a new path for the design of materials by Fermi level engineering.
Journal Article
A crystallographic approach to symmetry-breaking in fluid layers
Symmetry-breaking bifurcations, where a flow state with a certain symmetry undergoes a transition to a state with a different symmetry, are ubiquitous in fluid mechanics. Much can be understood about the nature of these transitions from symmetry alone, using the theory of groups and their representations. Here, we show how the extensive databases on groups in crystallography can be exploited to yield insights into fluid dynamical problems. In particular, we demonstrate the application of the crystallographic layer groups to problems in fluid layers, using thermal convection as an example. Crystallographic notation provides a concise and unambiguous description of the symmetries involved, and we advocate its broader use by the fluid dynamics community.
Journal Article
Mathematical Geometry and Groups for Low-Symmetry Metal Complex Systems
Since chemistry, materials science, and crystallography deal with three-dimensional structures, they use mathematics such as geometry and symmetry. In recent years, the application of topology and mathematics to material design has yielded remarkable results. It can also be seen that differential geometry has been applied to various fields of chemistry for a relatively long time. There is also the possibility of using new mathematics, such as the crystal structure database, which represents big data, for computational chemistry (Hirshfeld surface analysis). On the other hand, group theory (space group and point group) is useful for crystal structures, including determining their electronic properties and the symmetries of molecules with relatively high symmetry. However, these strengths are not exhibited in the low-symmetry molecules that are actually handled. A new use of mathematics for chemical research is required that is suitable for the age when computational chemistry and artificial intelligence can be used.
Journal Article
Kurt Mislow centennial—he changed the way people think about stereochemistry
Kurt Mislow (1923–2017) and his family were refugees from Nazi Germany. He studied at Tulane University and at Caltech and spent most of his career at Princeton University as Hugh Stott Taylor Professor of Chemistry (from 1988, Emeritus). He excelled in his research and his pedagogy of stereochemistry, introduced the term “chirality” into the chemical textbook literature, and delineated some of the theoretical underpinning of modern stereochemistry. He showed that shape, form, and symmetry play a central role in organic chemistry. He authored an introductory text on stereochemistry that has served generations. His pupils and those who learned from him through his publications carry on his legacy.
Journal Article
On Symmetries of Geometric Algebra Cl(3, 1) for Space-Time
From viewpoints of crystallography and of elementary particles, we explore symmetries of multivectors in the geometric algebra
Cl
(3, 1) that can be used to describe space-time.
Journal Article
Clarifications of concepts concerning interplanar spacing in crystals with reference to recent publications
Large number of papers are published each year on most areas of science, the majority being dependent on previously derived theories. It sometimes seems obvious that the authors have accepted the conventionally accepted theories that are the basis for their work without fully understanding all the details. We have reviewed several recent papers in the field of crystallography and found that several fundamental concepts have been applied in a manner that needs to be clarified. There are important principles imbedded in the conventional definition of Miller indices. Failure in understanding the advantages inherent within this definition has led in some recent publications to an improper redefinition of Miller indices and confusion between the concepts of lattice node and Wyckoff site and between symmetry equivalence and environment equivalence of points in lattice. Related problems involve the misleading claims that the node density among parallel lattice planes with the same Miller indices can be different, and also that lattice interplanar spacing can be different between adjacent parallel lattice planes. In this work, these problems have been clarified. A new method to calculate the relative lattice node density between planes with different Miller indices in a lattice has been developed. It illustrates that in a lattice, the node density of all the other planes with different Miller indices has already been determined if the node density of a particular plane with specified Miller indices is known. Related experimental results have also been discussed. The work shows that it is sometimes problematic for researchers to interpret experimental data via well-known theories without a full understanding of the basic science involved.
Journal Article
Experimental Charge Density Analysis and Electrostatic Properties of Crystalline 1,3-Bis(Dimethylamino)Squaraine and Its Dihydrate from Low Temperature (T = 18 and 20 K) XRD Data
Multipolar refinements of structural models fitting extensive sets of X-ray diffraction (XRD) data from single crystals of 1,3-bis(dimethylamino)squaraine [SQ, C8H12N2O2] and its dihydrate [SQDH, C8H12N2O2·2H2O], collected at very low T (18 ± 1 K for SQ, 20 ± 1 K for SQDH), led to an accurate description of their crystal electron density distributions. Atomic volumes and charges have been estimated from the experimental charge densities using the Quantum Theory of Atoms in Molecules (QTAIM) formalism. Our analysis confirms the common representation (in the literature and textbooks) of the squaraine central, four-membered squarylium ring as carrying two positive charges, a representation that has been recently questioned by some theoretical calculations: the integrated total charge on the C4 fragment is estimated as ca. +2.4e in SQ and +2.2e in SQDH. The topology of the experimental electron density for the SQ squaraine molecule is modified in the dihydrated crystal by interactions between the methyl groups and the H2O molecules in the crystal. Maps of the molecular electrostatic potential in the main molecular planes in both crystals clearly reveal the quadrupolar charge distribution of the squaraine molecules. Molecular quadrupole tensors, as calculated with the PAMoC package using both Stewart and QTAIM distributed multipole analysis (DMA), are the same within experimental error.
Journal Article
ILLUSTRATING THE IDEAL
In the stores of museums and university departments of mineralogy and crystallography, there are collections of sets of models of crystal shapes. Representing the external form of natural specimens, their use was for identification and demonstration purposes, by scientists, teachers and students from the late eighteenth century onwards. Whilst studying crystal model collections at the National Museums Scotland in Edinburgh, I came across the illustration work of Miss Delvalle Lowry. Her name, along with that of her father Wilson, appeared on plates illustrating an 1820 textbook by Nathaniel Larkin, a London teacher of solid geometry. Miss Lowry married the painter John Varley in 1825 and wrote a number of mineralogical texts that were reprinted through the first half of the nineteenth century. Delvalle Lowry was able to enjoy this career not least as a result of her ability to draw. The role of the Society of Arts in encouraging both drawing and the study of crystallography may well have been a feature of her success.
Journal Article