Crystallographic database
Encyclopedia
A crystallographic database is a database specifically designed to store information about crystals and crystal structures. Crystals are solids having, in all three dimensions of space, a regularly repeating arrangement of atoms, ions, or molecules. They are characterized by symmetry
, morphology
, and directionally dependent physical properties. A crystal structure describes the arrangement of atoms, ions, or molecules in a crystal.
Crystal structures of crystalline material are typically determined from X-ray
or neutron
single-crystal diffraction
data and stored in crystal structure databases. They are routinely identified by comparing reflection intensities and lattice spacings from X-ray powder diffraction
data with entries in powder-diffraction fingerprinting
databases.
Crystal structures of nanometer sized crystalline samples can be determined via structure factor
amplitude information from single-crystal electron diffraction
data or structure factor amplitude and phase angle information from Fourier transforms of HRTEM images of crystallites. They are stored in crystal structure databases specializing in nanocrystal
s and can be identified by comparing zone axis subsets in lattice-fringe fingerprint plots with entries in a lattice-fringe fingerprinting database.
Crystallographic databases can be categorized as crystallographic information from supersets or subsets of inorganics
, metals/alloys, organics
, and biological macromolecules. They differ in access and usage rights and offer varying degrees of search and analysis capacity. Many provide structure visualization capabilities. They can be browser based or installed locally. Newer versions are built on the relational database
model and support the Crystallographic Information File
(CIF
) as a universal data exchange format.
model, which enables efficient cross-referencing of tables. Cross-referencing serves to derive additional data or enhance the search capacity of the database.
Data exchange among crystallographic databases, structure visualization software, and structure refinement programs has been facilitated by the emergence of the Crystallographic Information File
(CIF) format. The CIF format is the standard text file format for the exchange and archiving of crystallographic data.
It was adopted by the International Union of Crystallography
(IUCr
), who also provides full specifications of the format. It is supported by all major crystallographic databases.
The increasing automation of the crystal structure
determination process has resulted in ever higher publishing rates of new crystal structures and, consequentially, new publishing models. Minimalistic articles contain only crystal structure tables, structure images, and, possibly, abstract-like structure description. They tend to be published in author-financed or subsidized open-access journals. Acta Crystallographica Section E and Zeitschrift für Kristallographie belong in this category. More elaborate contributions may go to traditional subscriber-financed journals. Hybrid journals, on the other hand, embed individual author-financed open-access articles among subscriber-financed ones. Publishers may also make scientific articles available online, as Portable Document Format
(PDF) files.
Crystal structure data in CIF format are linked to scientific articles as supplementary material. CIFs may be accessible directly from the publisher’s website, crystallographic databases, or both. In recent years, many publishers of crystallographic journals have come to interpret CIFs as formatted versions of open data
, i.e. representing non-copyrightable facts, and therefore tend to make them freely available online, independent of the accessibility status of linked scientific articles.
As of 2008, more than 700,000 crystal structures have been published and stored in crystal structure databases. The publishing rate has reached more than 50,000 crystal structures per year. These numbers refer to published and republished crystal structures from experimental data. Crystal structures are republished owing to corrections for symmetry
errors, improvements of lattice
and atom
ic parameters, and differences in diffraction
technique or experimental conditions.
Crystal structures are typically categorized as minerals, metals-alloys, inorganics
, organics
, nucleic acids, and biological macromolecules
. Individual crystal structure databases cater for users in specific chemical, molecular-biological
, or related disciplines by covering super- or subsets of these categories. Minerals are a subset of mostly inorganic compounds. The category ‘metals-alloys’ covers metals, alloys, and intermetallics
. Metals-alloys and inorganics can be merged into ‘non-organics’. Organic compounds and biological macromolecules are separated according to molecular size. Organic salts, organometallics
, and metalloproteins tend to be attributed to organics or biological macromolecules, respectively. Nucleic acids are a subset of biological macromolecules.
Comprehensiveness can refer to the number of entries in a database. On those terms, a crystal structure database can be regarded as comprehensive, if it contains a gapless collection of all (re-)published crystal structures in the category of interest and is updated frequently. Searching for structures in such a database can replace more time-consuming scanning of the open literature. Access to crystal structure databases differs widely. It can be divided into reading and writing access. Reading access rights (search, download) affect the number and range of users. Restricted reading access is often coupled with restricted usage rights. Writing access rights (upload, edit, delete), on the other hand, determine the number and range of contributors to the database. Restricted writing access is often coupled with high data integrity
.
In terms of user numbers and daily access rates, comprehensive and thoroughly vetted open-access crystal structure databases naturally surpass comparable databases with more restricted access and usage rights. Independent of comprehensiveness, open-access crystal structure databases can spawn open-source software
projects, such as search-analysis tools, visualization software, and derivative databases. Scientific progress can be slowed down by restricting access or usage rights as well as limiting comprehensiveness or data integrity. Restricted access or usage rights are commonly associated with commercial crystal structure databases. Lack of comprehensiveness or data integrity, on the other hand, are associated with some of the open-access crystal structure databases. Apart from that, several crystal structure databases are freely available for primarily educational purposes, in particular mineralogical databases.
Crystallographic databases can specialize in crystal structures, crystal phase identification, crystallization
, crystal morphology, or various physical properties. More integrative databases combine several categories of compounds or specializations. Structures of incommensurate phases, nanocrystal
s, thin films on substrates, and predicted crystal structures are collected in tailored special structure databases.
and lattice parameters
. Very useful are search options that allow the use of wildcard characters and logical connective
s in search strings. If supported, the scope of the search can be constrained by the exclusion of certain chemical elements.
More sophisticated algorithms depend on the material type covered. Organic compounds might be searched for on the basis of certain molecular fragments. Inorganic compound
s, on the other hand, might be of interest with regard to a certain type of coordination geometry
. More advanced algorithms deal with conformation
analysis (organics), supramolecular chemistry
(organics), interpolyhedral connectivity (‘non-organics’) and higher-order molecular structures (biological macromolecules
). Search algorithms used for a more complex analysis of physical properties, e.g. phase transitions or structure-property relationships, might apply group-theoretical
concepts.
Modern versions of crystallographic databases are based on the relational database
model. Communication with the database usually happens via a dialect of the Structured Query Language (SQL
). Web-based
databases typically process the search algorithm on the server
interpreting supported scripting elements, while desktop-based
databases run locally installed and usually precompiled search engines.
, polycrystals, and crystal powder
. In a single crystal, the arrangement of atoms, ions, or molecules is defined by a single crystal structure
in one orientation. Twin crystals, on the other hand, consist of single-crystalline twin domains
, which are aligned by twin laws
and separated by domain walls
.
Polycrystals are made of a large number of small single crystals, or crystallites, held together by thin layers of amorphous solid
. Crystal powder is obtained by grinding crystals, resulting in powder particles, made up of one or more crystallites. Both polycrystals and crystal powder consist of many crystallites with varying orientation.
Crystal phases are defined as regions with the same crystal structure, irrespective of orientation or twinning
. Single and twinned crystalline specimens therefore constitute individual crystal phases. Polycrystalline or crystal powder samples may consist of more than one crystal phase. Such a phase comprises all the crystallites in the sample with the same crystal structure.
Crystal phases can be identified by successfully matching suitable crystallographic parameters with their counterparts in database entries. Prior knowledge of the chemical composition of the crystal phase can be used to reduce the number of database entries to a small selection of candidate structures and thus simplify the crystal phase identification process considerably.
techniques to crystal
powders or polycrystals is tantamount to collapsing the 3D reciprocal space, as obtained via single-crystal diffraction, onto a 1D axis. The resulting partial-to-total overlap of symmetry-independent reflections renders the structure determination process more difficult, if not impossible.
Powder diffraction
data can be plotted as diffracted intensity (I) versus reciprocal lattice
spacing (1/d). Reflection positions and intensities of known crystal phases, mostly from X-ray diffraction data, are stored, as d-I data pairs, in the Powder Diffraction File (PDF) database. The list of d-I data pairs is highly characteristic of a crystal phase and, thus, suitable for the identification, also called ‘fingerprinting’, of crystal phases.
Search-match algorithms compare selected test reflections of an unknown crystal phase with entries in the database
. Intensity-driven algorithms utilize the three most intense lines (so-called ‘Hanawalt search’), while d-spacing-driven algorithms are based on the eight to ten largest d-spacings (so-called ‘Fink search’).
X-ray powder diffraction fingerprinting has become the standard tool for the identification of single or multiple crystal phases and is widely used in such fields as metallurgy
, mineralogy
, forensic science, archeology, condensed matter physics
, and the biological and pharmaceutical sciences
.
patterns of very small single crystals, or crystallites, are subject to size-dependent peak broadening, which, below a certain size, renders powder diffraction fingerprinting useless. In this case, peak resolution is only possible in 3D reciprocal space,
i.e. by applying single-crystal electron diffraction
techniques.
High-Resolution Transmission Electron Microscopy (HRTEM) provides images and diffraction patterns of nanometer sized crystallites. Fourier transforms of HRTEM images and electron diffraction patterns both supply information about the projected reciprocal lattice geometry
for a certain crystal orientation, where the projection axis coincides with the optical axis of the microscope.
Projected lattice geometries can be represented by so-called ‘lattice-fringe fingerprint plots’ (LFFPs), also called angular covariance plots. The horizontal axis of such a plot is given in reciprocal lattice
length and is limited by the point resolution of the microscope. The vertical axis is defined as acute angle between Fourier transformed lattice fringes or electron diffraction spots. A 2D data point is defined by the length of a reciprocal lattice vector and its (acute) angle with another reciprocal lattice vector. Sets of 2D data points that obey Weiss’s zone law are subsets of the entirety of data points in an LFFP. A suitable search-match algorithm using LFFPs, therefore, tries to find matching zone axis subsets in the database
. It is, essentially, a variant of a lattice matching algorithm.
The performance of search-match procedures utilizing LFFPs, also called ‘lattice-fringe fingerprinting’, can be sped up by precalculating and storing full LFFPs of all entries, assuming either kinematic or dynamic scattering and a given point resolution of the microscope. The number of possible entries can be narrowed down on the basis of chemical compound
information.
In the case of electron diffraction patterns, structure factor amplitudes can be used, in a later step, to further discern among a selection of candidate structures (so-called 'structure factor fingerprinting'). Structure factor amplitudes from electron diffraction data are far less reliable than their counterparts from X-ray single-crystal and powder diffraction data. Existing precession electron diffraction techniques greatly improve the quality of structure factor amplitudes, increase their number and, thus, make structure factor amplitude information much more useful for the fingerprinting process.
Fourier transforms of HRTEM images, on the other hand, supply information not only about the projected reciprocal lattice geometry and structure factor amplitudes, but also structure factor phase angles. After crystallographic image processing, structure factor phase angles are far more reliable than structure factor amplitudes. Further discernment of candidate structures is then mainly based on structure factor phase angles and, to a lesser extent, structure factor amplitudes (so-called 'structure factor fingerprinting').
of the same material are, by nature, restricted to the same value. This offers the opportunity to fingerprint crystal
line materials on the basis of optical goniometry
, which is also known as crystallometry. In order to employ this technique successfully, one must consider the observed point group
symmetry
of the measured faces and creatively apply the rule that "crystal
morphologies
are often combinations of simple (i.e. low multiplicity) forms where the individual faces have the lowest possible Miller indices
for any given zone axis". This shall ensure that the correct indexing of the crystal faces is obtained for any single crystal.
It is in many cases possible to derive the ratios of the crystal axes for crystals with low symmetry from optical goniometry with high accuracy and precision and to identify a crystalline material on their basis alone employing databases such as 'Crystal Data'. Provided that the crystal faces have been correctly indexed and the interfacial angles were measured to better than a few fractions of a tenth of a degree, a crystalline material can be identified quite unambiguously on the basis of angle comparisons to two rather comprehensive databases: the 'Bestimmungstabellen für Kristalle (Определитель Кристаллов)' and the 'Barker Index of Crystals'.
Since Steno’s Law can be further generalized for a single crystal of any material to include the angles between either all identically indexed net planes (i.e. vectors of the reciprocal lattice
, also known as 'potential reflections in diffraction
experiments') or all identically indexed lattice directions (i.e. vectors of the direct lattice, also known as zone axes), opportunities exist for morphological fingerprinting of nanocrystal
s in the transmission electron microscope
(TEM
) by means of transmission electron goniometry.
The specimen goniometer
of a TEM is thereby employed analogously to the goniometer head of an optical goniometer. The optical axis of the TEM is then analogous to the reference direction of an optical goniometer. While in optical goniometry net-plane normals (reciprocal lattice vectors) need to be successively aligned parallel to the reference direction of an optical goniometer in order to derive measurements of interfacial angles, the corresponding alignment needs to be done for zone axes (direct lattice vector) in transmission electron goniometry. (Note that such alignments are by their nature quite trivial for nanocrystals in a TEM after the microscope has been aligned by standard procedures.)
Since transmission electron goniometry is based on Bragg’s Law
for the transmission (Laue) case (diffraction of electron waves), interzonal angles (i.e. angles between lattice directions) can be measured by a procedure that is analogous to the measurement of interfacial angles in an optical goniometer on the basis of Snell’s Law
, i.e. the reflection of light. The complements to interfacial angles of external crystal faces can, on the other hand, be directly measured from a zone-axis diffraction pattern or from the Fourier transform
of a high resolution TEM image that shows crossed lattice fringes.
of unknown crystal phases can be obtained from X-ray
, neutron
, or electron diffraction
data. Single-crystal diffraction experiments supply orientation matrices, from which lattice parameters can be deduced. Alternatively, lattice parameters can be obtained from powder or polycrystal diffraction data via profile fitting without structural model (so-called 'Le Bail method').
Arbitrarily defined unit cells can be transformed to a standard setting and, from there, further reduced to a primitive smallest cell. Sophisticated algorithms compare such reduced cells with corresponding database
entries. More powerful algorithms also consider derivative super- and subcells. The lattice-matching process can be further sped up by precalculating and storing reduced cells for all entries. The algorithm searches for matches within a certain range of the lattice parameters. More accurate lattice parameters allow a narrower range and, thus, a better match.
Lattice matching is useful in identifying crystal phases in the early stages of single-crystal
diffraction experiments and, thus, avoiding unnecessary full data collection and structure determination procedures for already known crystal structures. The method is particularly important for single-crystalline samples that need to be preserved. If, on the other hand, some or all of the crystalline sample material can be ground, powder diffraction fingerprinting is usually the better option for crystal phase identification, provided that the peak resolution is good enough. However, lattice matching algorithms are still better at treating derivative super- and subcells.
databases integrate the visualization of crystal
and molecular structures. Specialized or integrative crystallographic databases may provide morphology or tensor
visualization output.
describes the three-dimensional periodic arrangement of atoms, ions, or molecules in a crystal
. The unit cell represents the simplest repeating unit of the crystal structure. It is a parallelepiped containing a certain spatial arrangement of atoms, ions, molecules, or molecular fragments. From the unit cell the crystal structure can be fully reconstructed via translations
.
The visualization of a crystal structure can be reduced to the arrangement of atoms, ions, or molecules in the unit cell, with or without cell outlines. Structure elements extending beyond single unit cells, such as isolated molecular or polyhedral units as well as chain, net, or framework structures, can often be better understood by extending the structure representation into adjacent cells.
The space group
of a crystal is a mathematical description of the symmetry
inherent in the structure. The motif of the crystal structure is given by the asymmetric unit
, a minimal subset of the unit cell contents. The unit cell contents can be fully reconstructed via the symmetry operations of the space group on the asymmetric unit. Visualization interfaces
usually allow for switching between asymmetric unit and full structure representations.
Bonds
between atoms or ions can be identified by characteristic short distances between them. They can be classified as covalent
, ionic
, hydrogen
, or other bonds including hybrid forms. Bond angles can be deduced from the bond vectors in groups of atoms or ions. Bond distances and angles can be made available to the user in tabular form or interactively, by selecting pairs or groups of atoms or ions. In ball-and-stick model
s of crystal structures, balls represent atoms and sticks represent bonds.
Since organic chemists are particularly interested in molecular structures, it might be useful to be able to single out individual molecular units interactively from the drawing. Organic
molecular units need to be given both as 2D structural formulae and full 3D molecular structures. Molecules on special-symmetry positions need to be reconstructed from the asymmetric unit. Protein crystallographers are interested in molecular structures of biological macromolecules
, so that provisions need to be made to be able to represent molecular subunits as helices
, sheets
, or coils
, respectively.
Crystal structure visualization can be integrated into a crystallographic database
. Alternatively, the crystal structure data are exchanged between the database and the visualization software, preferably using the CIF
format. Web-based crystallographic databases can integrate crystal structure visualization capability. Depending on the complexity of the structure, lighting, and 3D effects, crystal structure visualization can require a significant amount of processing power, which is why the actual visualization is typically run on the client
.
Currently, web-integrated crystal structure visualization is based on Java applet
s from open-source projects such as Jmol
. Web-integrated crystal structure visualization is tailored for examining crystal structures in web browsers, often supporting wide color spectra
(up to 32 bit) and window size adaptation. However, web-generated crystal structure images are not always suitable for publishing due to issues such as resolution depth, color choice, grayscale contrast, or labeling (positioning, font type, font size).
appearances of individual crystal
s, as defined by the actually formed crystal faces (tracht) and their relative sizes (habit). More advanced visualization capabilities allow for displaying surface characteristics, imperfections inside the crystal, lighting (reflection, shadow, and translucency), and 3D effects (interactive rotatability, perspective, and stereo viewing).
Crystal physicists
, in particular, are interested in anisotropic physical properties of crystals. The directional dependence of a crystal's physical property is described by a 3D tensor
and depends on the orientation of the crystal. Tensor shapes are more palpable by adding lighting effects (reflection and shadow). 2D sections of interest are selected for display by rotating the tensor interactively around one or more axes.
Crystal morphology or physical property data can be stored in specialized databases or added to more comprehensive crystal structure databases. The Crystal Morphology Database (CMD) is an example for a web-based crystal morphology database with integrated visualization capabilities.
Symmetry
Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...
, morphology
Shape
The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...
, and directionally dependent physical properties. A crystal structure describes the arrangement of atoms, ions, or molecules in a crystal.
Crystal structures of crystalline material are typically determined from X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
or neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
single-crystal diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
data and stored in crystal structure databases. They are routinely identified by comparing reflection intensities and lattice spacings from X-ray powder diffraction
Powder diffraction
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials.-Explanation:...
data with entries in powder-diffraction fingerprinting
Powder diffraction
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials.-Explanation:...
databases.
Crystal structures of nanometer sized crystalline samples can be determined via structure factor
Structure factor
In condensed matter physics and crystallography, the static structure factor is a mathematical description of how a material scatters incident radiation...
amplitude information from single-crystal electron diffraction
Electron diffraction
Electron diffraction refers to the wave nature of electrons. However, from a technical or practical point of view, it may be regarded as a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern...
data or structure factor amplitude and phase angle information from Fourier transforms of HRTEM images of crystallites. They are stored in crystal structure databases specializing in nanocrystal
Nanocrystal
B. D. Fahlman has described a nanocrystal as any nanomaterial with at least one dimension ≤ 100nm and that is singlecrystalline.-Summary:More properly, any material with a dimension of less than 1 micrometre, i.e., 1000 nanometers, should be referred to as a nanoparticle, not a nanocrystal...
s and can be identified by comparing zone axis subsets in lattice-fringe fingerprint plots with entries in a lattice-fringe fingerprinting database.
Crystallographic databases can be categorized as crystallographic information from supersets or subsets of inorganics
Inorganic compound
Inorganic compounds have traditionally been considered to be of inanimate, non-biological origin. In contrast, organic compounds have an explicit biological origin. However, over the past century, the classification of inorganic vs organic compounds has become less important to scientists,...
, metals/alloys, organics
Organic compound
An organic compound is any member of a large class of gaseous, liquid, or solid chemical compounds whose molecules contain carbon. For historical reasons discussed below, a few types of carbon-containing compounds such as carbides, carbonates, simple oxides of carbon, and cyanides, as well as the...
, and biological macromolecules. They differ in access and usage rights and offer varying degrees of search and analysis capacity. Many provide structure visualization capabilities. They can be browser based or installed locally. Newer versions are built on the relational database
Relational database
A relational database is a database that conforms to relational model theory. The software used in a relational database is called a relational database management system . Colloquial use of the term "relational database" may refer to the RDBMS software, or the relational database itself...
model and support the Crystallographic Information File
Crystallographic Information File
Crystallographic Information File is a standard text file format for representing crystallographic information, promulgated by the International Union of Crystallography . CIF was developed by the IUCr Working Party on Crystallographic Information in an effort sponsored by the IUCr Commission on...
(CIF
Crystallographic Information File
Crystallographic Information File is a standard text file format for representing crystallographic information, promulgated by the International Union of Crystallography . CIF was developed by the IUCr Working Party on Crystallographic Information in an effort sponsored by the IUCr Commission on...
) as a universal data exchange format.
Overview
Crystallographic data are primarily extracted from published scientific articles and supplementary material. Newer versions of crystallographic databases are built on the relational databaseRelational database
A relational database is a database that conforms to relational model theory. The software used in a relational database is called a relational database management system . Colloquial use of the term "relational database" may refer to the RDBMS software, or the relational database itself...
model, which enables efficient cross-referencing of tables. Cross-referencing serves to derive additional data or enhance the search capacity of the database.
Data exchange among crystallographic databases, structure visualization software, and structure refinement programs has been facilitated by the emergence of the Crystallographic Information File
Crystallographic Information File
Crystallographic Information File is a standard text file format for representing crystallographic information, promulgated by the International Union of Crystallography . CIF was developed by the IUCr Working Party on Crystallographic Information in an effort sponsored by the IUCr Commission on...
(CIF) format. The CIF format is the standard text file format for the exchange and archiving of crystallographic data.
It was adopted by the International Union of Crystallography
International Union of Crystallography
The International Union of Crystallography is a member of the International Council for Science and exists to serve the world community of crystallographers....
(IUCr
International Union of Crystallography
The International Union of Crystallography is a member of the International Council for Science and exists to serve the world community of crystallographers....
), who also provides full specifications of the format. It is supported by all major crystallographic databases.
The increasing automation of the crystal structure
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
determination process has resulted in ever higher publishing rates of new crystal structures and, consequentially, new publishing models. Minimalistic articles contain only crystal structure tables, structure images, and, possibly, abstract-like structure description. They tend to be published in author-financed or subsidized open-access journals. Acta Crystallographica Section E and Zeitschrift für Kristallographie belong in this category. More elaborate contributions may go to traditional subscriber-financed journals. Hybrid journals, on the other hand, embed individual author-financed open-access articles among subscriber-financed ones. Publishers may also make scientific articles available online, as Portable Document Format
Portable Document Format
Portable Document Format is an open standard for document exchange. This file format, created by Adobe Systems in 1993, is used for representing documents in a manner independent of application software, hardware, and operating systems....
(PDF) files.
Crystal structure data in CIF format are linked to scientific articles as supplementary material. CIFs may be accessible directly from the publisher’s website, crystallographic databases, or both. In recent years, many publishers of crystallographic journals have come to interpret CIFs as formatted versions of open data
Open Data
Open data is the idea that certain data should be freely available to everyone to use and republish as they wish, without restrictions from copyright, patents or other mechanisms of control. The goals of the open data movement are similar to those of other "Open" movements such as open source, open...
, i.e. representing non-copyrightable facts, and therefore tend to make them freely available online, independent of the accessibility status of linked scientific articles.
Trends
Symmetry
Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...
errors, improvements of lattice
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
and atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
ic parameters, and differences in diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
technique or experimental conditions.
Crystal structures are typically categorized as minerals, metals-alloys, inorganics
Inorganic compound
Inorganic compounds have traditionally been considered to be of inanimate, non-biological origin. In contrast, organic compounds have an explicit biological origin. However, over the past century, the classification of inorganic vs organic compounds has become less important to scientists,...
, organics
Organic compound
An organic compound is any member of a large class of gaseous, liquid, or solid chemical compounds whose molecules contain carbon. For historical reasons discussed below, a few types of carbon-containing compounds such as carbides, carbonates, simple oxides of carbon, and cyanides, as well as the...
, nucleic acids, and biological macromolecules
Biomolecule
A biomolecule is any molecule that is produced by a living organism, including large polymeric molecules such as proteins, polysaccharides, lipids, and nucleic acids as well as small molecules such as primary metabolites, secondary metabolites, and natural products...
. Individual crystal structure databases cater for users in specific chemical, molecular-biological
Molecular biology
Molecular biology is the branch of biology that deals with the molecular basis of biological activity. This field overlaps with other areas of biology and chemistry, particularly genetics and biochemistry...
, or related disciplines by covering super- or subsets of these categories. Minerals are a subset of mostly inorganic compounds. The category ‘metals-alloys’ covers metals, alloys, and intermetallics
Intermetallics
Intermetallics or intermetallic compounds is a term that is used in a number of different ways. Most commonly it refers to solid-state phases involving metals. There is a "research definition" adhered to generally in scientific publications, and a wider "common use" term...
. Metals-alloys and inorganics can be merged into ‘non-organics’. Organic compounds and biological macromolecules are separated according to molecular size. Organic salts, organometallics
Organometallics
Organometallics is a journal published by the American Chemical Society. Its area of focus is organometallic, as well as organometalloid chemistry. This peer-reviewed journal received an Impact Factor of 3.888 as reported by the 2010 Journal Citation Reports by Thomson Reuters.The current...
, and metalloproteins tend to be attributed to organics or biological macromolecules, respectively. Nucleic acids are a subset of biological macromolecules.
Comprehensiveness can refer to the number of entries in a database. On those terms, a crystal structure database can be regarded as comprehensive, if it contains a gapless collection of all (re-)published crystal structures in the category of interest and is updated frequently. Searching for structures in such a database can replace more time-consuming scanning of the open literature. Access to crystal structure databases differs widely. It can be divided into reading and writing access. Reading access rights (search, download) affect the number and range of users. Restricted reading access is often coupled with restricted usage rights. Writing access rights (upload, edit, delete), on the other hand, determine the number and range of contributors to the database. Restricted writing access is often coupled with high data integrity
Data integrity
Data Integrity in its broadest meaning refers to the trustworthiness of system resources over their entire life cycle. In more analytic terms, it is "the representational faithfulness of information to the true state of the object that the information represents, where representational faithfulness...
.
In terms of user numbers and daily access rates, comprehensive and thoroughly vetted open-access crystal structure databases naturally surpass comparable databases with more restricted access and usage rights. Independent of comprehensiveness, open-access crystal structure databases can spawn open-source software
Open-source software
Open-source software is computer software that is available in source code form: the source code and certain other rights normally reserved for copyright holders are provided under a software license that permits users to study, change, improve and at times also to distribute the software.Open...
projects, such as search-analysis tools, visualization software, and derivative databases. Scientific progress can be slowed down by restricting access or usage rights as well as limiting comprehensiveness or data integrity. Restricted access or usage rights are commonly associated with commercial crystal structure databases. Lack of comprehensiveness or data integrity, on the other hand, are associated with some of the open-access crystal structure databases. Apart from that, several crystal structure databases are freely available for primarily educational purposes, in particular mineralogical databases.
Crystallographic databases can specialize in crystal structures, crystal phase identification, crystallization
Crystallization
Crystallization is the process of formation of solid crystals precipitating from a solution, melt or more rarely deposited directly from a gas. Crystallization is also a chemical solid–liquid separation technique, in which mass transfer of a solute from the liquid solution to a pure solid...
, crystal morphology, or various physical properties. More integrative databases combine several categories of compounds or specializations. Structures of incommensurate phases, nanocrystal
Nanocrystal
B. D. Fahlman has described a nanocrystal as any nanomaterial with at least one dimension ≤ 100nm and that is singlecrystalline.-Summary:More properly, any material with a dimension of less than 1 micrometre, i.e., 1000 nanometers, should be referred to as a nanoparticle, not a nanocrystal...
s, thin films on substrates, and predicted crystal structures are collected in tailored special structure databases.
Search
Search capacities of crystallographic databases differ widely. Basic functionality comprises search by keywords, physical properties, and chemical elements. Of particular importance is search by compound nameChemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...
and lattice parameters
Lattice constant
The lattice constant [or lattice parameter] refers to the constant distance between unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice constants, referred to as a, b, and c. However, in the special case of cubic crystal structures, all of the constants are...
. Very useful are search options that allow the use of wildcard characters and logical connective
Logical connective
In logic, a logical connective is a symbol or word used to connect two or more sentences in a grammatically valid way, such that the compound sentence produced has a truth value dependent on the respective truth values of the original sentences.Each logical connective can be expressed as a...
s in search strings. If supported, the scope of the search can be constrained by the exclusion of certain chemical elements.
More sophisticated algorithms depend on the material type covered. Organic compounds might be searched for on the basis of certain molecular fragments. Inorganic compound
Inorganic compound
Inorganic compounds have traditionally been considered to be of inanimate, non-biological origin. In contrast, organic compounds have an explicit biological origin. However, over the past century, the classification of inorganic vs organic compounds has become less important to scientists,...
s, on the other hand, might be of interest with regard to a certain type of coordination geometry
Coordination geometry
The term coordination geometry is used in a number of related fields of chemistry and solid state chemistry/physics.-Molecules:The coordination geometry of an atom is the geometrical pattern formed by atoms around the central atom....
. More advanced algorithms deal with conformation
Conformational isomerism
In chemistry, conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted exclusively by rotations about formally single bonds...
analysis (organics), supramolecular chemistry
Supramolecular chemistry
Supramolecular chemistry refers to the area of chemistry beyond the molecules and focuses on the chemical systems made up of a discrete number of assembled molecular subunits or components...
(organics), interpolyhedral connectivity (‘non-organics’) and higher-order molecular structures (biological macromolecules
Biomolecule
A biomolecule is any molecule that is produced by a living organism, including large polymeric molecules such as proteins, polysaccharides, lipids, and nucleic acids as well as small molecules such as primary metabolites, secondary metabolites, and natural products...
). Search algorithms used for a more complex analysis of physical properties, e.g. phase transitions or structure-property relationships, might apply group-theoretical
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
concepts.
Modern versions of crystallographic databases are based on the relational database
Relational database
A relational database is a database that conforms to relational model theory. The software used in a relational database is called a relational database management system . Colloquial use of the term "relational database" may refer to the RDBMS software, or the relational database itself...
model. Communication with the database usually happens via a dialect of the Structured Query Language (SQL
SQL
SQL is a programming language designed for managing data in relational database management systems ....
). Web-based
Web application
A web application is an application that is accessed over a network such as the Internet or an intranet. The term may also mean a computer software application that is coded in a browser-supported language and reliant on a common web browser to render the application executable.Web applications are...
databases typically process the search algorithm on the server
Server (computing)
In the context of client-server architecture, a server is a computer program running to serve the requests of other programs, the "clients". Thus, the "server" performs some computational task on behalf of "clients"...
interpreting supported scripting elements, while desktop-based
Application software
Application software, also known as an application or an "app", is computer software designed to help the user to perform specific tasks. Examples include enterprise software, accounting software, office suites, graphics software and media players. Many application programs deal principally with...
databases run locally installed and usually precompiled search engines.
Crystal phase identification
Crystalline material may be divided into single crystals, twin crystalsCrystal twinning
Crystal twinning occurs when two separate crystals share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals in a variety of specific configurations. A twin boundary or composition surface separates the two crystals....
, polycrystals, and crystal powder
Powder (substance)
A powder is a dry,thick bulk solid composed of a large number of very fine particles that may flow freely when shaken or tilted. Powders are a special sub-class of granular materials, although the terms powder and granular are sometimes used to distinguish separate classes of material...
. In a single crystal, the arrangement of atoms, ions, or molecules is defined by a single crystal structure
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
in one orientation. Twin crystals, on the other hand, consist of single-crystalline twin domains
Crystal twinning
Crystal twinning occurs when two separate crystals share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals in a variety of specific configurations. A twin boundary or composition surface separates the two crystals....
, which are aligned by twin laws
Crystal twinning
Crystal twinning occurs when two separate crystals share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals in a variety of specific configurations. A twin boundary or composition surface separates the two crystals....
and separated by domain walls
Crystal twinning
Crystal twinning occurs when two separate crystals share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals in a variety of specific configurations. A twin boundary or composition surface separates the two crystals....
.
Polycrystals are made of a large number of small single crystals, or crystallites, held together by thin layers of amorphous solid
Amorphous solid
In condensed matter physics, an amorphous or non-crystalline solid is a solid that lacks the long-range order characteristic of a crystal....
. Crystal powder is obtained by grinding crystals, resulting in powder particles, made up of one or more crystallites. Both polycrystals and crystal powder consist of many crystallites with varying orientation.
Crystal phases are defined as regions with the same crystal structure, irrespective of orientation or twinning
Crystal twinning
Crystal twinning occurs when two separate crystals share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals in a variety of specific configurations. A twin boundary or composition surface separates the two crystals....
. Single and twinned crystalline specimens therefore constitute individual crystal phases. Polycrystalline or crystal powder samples may consist of more than one crystal phase. Such a phase comprises all the crystallites in the sample with the same crystal structure.
Crystal phases can be identified by successfully matching suitable crystallographic parameters with their counterparts in database entries. Prior knowledge of the chemical composition of the crystal phase can be used to reduce the number of database entries to a small selection of candidate structures and thus simplify the crystal phase identification process considerably.
Powder diffraction fingerprinting (1D)
Applying standard diffractionDiffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
techniques to crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
powders or polycrystals is tantamount to collapsing the 3D reciprocal space, as obtained via single-crystal diffraction, onto a 1D axis. The resulting partial-to-total overlap of symmetry-independent reflections renders the structure determination process more difficult, if not impossible.
Powder diffraction
Powder diffraction
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials.-Explanation:...
data can be plotted as diffracted intensity (I) versus reciprocal lattice
Reciprocal lattice
In physics, the reciprocal lattice of a lattice is the lattice in which the Fourier transform of the spatial function of the original lattice is represented. This space is also known as momentum space or less commonly k-space, due to the relationship between the Pontryagin duals momentum and...
spacing (1/d). Reflection positions and intensities of known crystal phases, mostly from X-ray diffraction data, are stored, as d-I data pairs, in the Powder Diffraction File (PDF) database. The list of d-I data pairs is highly characteristic of a crystal phase and, thus, suitable for the identification, also called ‘fingerprinting’, of crystal phases.
Search-match algorithms compare selected test reflections of an unknown crystal phase with entries in the database
Database
A database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...
. Intensity-driven algorithms utilize the three most intense lines (so-called ‘Hanawalt search’), while d-spacing-driven algorithms are based on the eight to ten largest d-spacings (so-called ‘Fink search’).
X-ray powder diffraction fingerprinting has become the standard tool for the identification of single or multiple crystal phases and is widely used in such fields as metallurgy
Metallurgy
Metallurgy is a domain of materials science that studies the physical and chemical behavior of metallic elements, their intermetallic compounds, and their mixtures, which are called alloys. It is also the technology of metals: the way in which science is applied to their practical use...
, mineralogy
Mineralogy
Mineralogy is the study of chemistry, crystal structure, and physical properties of minerals. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, as well as their utilization.-History:Early writing...
, forensic science, archeology, condensed matter physics
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...
, and the biological and pharmaceutical sciences
Pharmaceutical sciences
The pharmaceutical sciences are a group of interdisciplinary areas of study involved with the design, action, delivery, disposition, and use of drugs...
.
Lattice-fringe fingerprinting (2D)
Powder diffractionPowder diffraction
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials.-Explanation:...
patterns of very small single crystals, or crystallites, are subject to size-dependent peak broadening, which, below a certain size, renders powder diffraction fingerprinting useless. In this case, peak resolution is only possible in 3D reciprocal space,
i.e. by applying single-crystal electron diffraction
Electron diffraction
Electron diffraction refers to the wave nature of electrons. However, from a technical or practical point of view, it may be regarded as a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern...
techniques.
High-Resolution Transmission Electron Microscopy (HRTEM) provides images and diffraction patterns of nanometer sized crystallites. Fourier transforms of HRTEM images and electron diffraction patterns both supply information about the projected reciprocal lattice geometry
for a certain crystal orientation, where the projection axis coincides with the optical axis of the microscope.
Projected lattice geometries can be represented by so-called ‘lattice-fringe fingerprint plots’ (LFFPs), also called angular covariance plots. The horizontal axis of such a plot is given in reciprocal lattice
Reciprocal lattice
In physics, the reciprocal lattice of a lattice is the lattice in which the Fourier transform of the spatial function of the original lattice is represented. This space is also known as momentum space or less commonly k-space, due to the relationship between the Pontryagin duals momentum and...
length and is limited by the point resolution of the microscope. The vertical axis is defined as acute angle between Fourier transformed lattice fringes or electron diffraction spots. A 2D data point is defined by the length of a reciprocal lattice vector and its (acute) angle with another reciprocal lattice vector. Sets of 2D data points that obey Weiss’s zone law are subsets of the entirety of data points in an LFFP. A suitable search-match algorithm using LFFPs, therefore, tries to find matching zone axis subsets in the database
Database
A database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...
. It is, essentially, a variant of a lattice matching algorithm.
The performance of search-match procedures utilizing LFFPs, also called ‘lattice-fringe fingerprinting’, can be sped up by precalculating and storing full LFFPs of all entries, assuming either kinematic or dynamic scattering and a given point resolution of the microscope. The number of possible entries can be narrowed down on the basis of chemical compound
Chemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...
information.
In the case of electron diffraction patterns, structure factor amplitudes can be used, in a later step, to further discern among a selection of candidate structures (so-called 'structure factor fingerprinting'). Structure factor amplitudes from electron diffraction data are far less reliable than their counterparts from X-ray single-crystal and powder diffraction data. Existing precession electron diffraction techniques greatly improve the quality of structure factor amplitudes, increase their number and, thus, make structure factor amplitude information much more useful for the fingerprinting process.
Fourier transforms of HRTEM images, on the other hand, supply information not only about the projected reciprocal lattice geometry and structure factor amplitudes, but also structure factor phase angles. After crystallographic image processing, structure factor phase angles are far more reliable than structure factor amplitudes. Further discernment of candidate structures is then mainly based on structure factor phase angles and, to a lesser extent, structure factor amplitudes (so-called 'structure factor fingerprinting').
Morphological fingerprinting (3D)
The Generalized Steno Law states that the interfacial angles between identical faces of any single crystalSingle crystal
A single crystal or monocrystalline solid is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries...
of the same material are, by nature, restricted to the same value. This offers the opportunity to fingerprint crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
line materials on the basis of optical goniometry
Goniometer
A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry is derived from two Greek words, gōnia, meaning angle, and metron, meaning measure....
, which is also known as crystallometry. In order to employ this technique successfully, one must consider the observed point group
Point group
In geometry, a point group is a group of geometric symmetries that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O...
symmetry
Symmetry
Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...
of the measured faces and creatively apply the rule that "crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
morphologies
Morphology
Morphology may mean:*Morphology , the study of the structure and content of word forms*Morphology , the study of the form or shape of an organism or part thereof...
are often combinations of simple (i.e. low multiplicity) forms where the individual faces have the lowest possible Miller indices
Miller index
Miller indices form a notation system in crystallography for planes and directions in crystal lattices.In particular, a family of lattice planes is determined by three integers h, k, and ℓ, the Miller indices. They are written , and each index denotes a plane orthogonal to a direction in the...
for any given zone axis". This shall ensure that the correct indexing of the crystal faces is obtained for any single crystal.
It is in many cases possible to derive the ratios of the crystal axes for crystals with low symmetry from optical goniometry with high accuracy and precision and to identify a crystalline material on their basis alone employing databases such as 'Crystal Data'. Provided that the crystal faces have been correctly indexed and the interfacial angles were measured to better than a few fractions of a tenth of a degree, a crystalline material can be identified quite unambiguously on the basis of angle comparisons to two rather comprehensive databases: the 'Bestimmungstabellen für Kristalle (Определитель Кристаллов)' and the 'Barker Index of Crystals'.
Since Steno’s Law can be further generalized for a single crystal of any material to include the angles between either all identically indexed net planes (i.e. vectors of the reciprocal lattice
Reciprocal lattice
In physics, the reciprocal lattice of a lattice is the lattice in which the Fourier transform of the spatial function of the original lattice is represented. This space is also known as momentum space or less commonly k-space, due to the relationship between the Pontryagin duals momentum and...
, also known as 'potential reflections in diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
experiments') or all identically indexed lattice directions (i.e. vectors of the direct lattice, also known as zone axes), opportunities exist for morphological fingerprinting of nanocrystal
Nanocrystal
B. D. Fahlman has described a nanocrystal as any nanomaterial with at least one dimension ≤ 100nm and that is singlecrystalline.-Summary:More properly, any material with a dimension of less than 1 micrometre, i.e., 1000 nanometers, should be referred to as a nanoparticle, not a nanocrystal...
s in the transmission electron microscope
Transmission electron microscopy
Transmission electron microscopy is a microscopy technique whereby a beam of electrons is transmitted through an ultra thin specimen, interacting with the specimen as it passes through...
(TEM
Transmission electron microscopy
Transmission electron microscopy is a microscopy technique whereby a beam of electrons is transmitted through an ultra thin specimen, interacting with the specimen as it passes through...
) by means of transmission electron goniometry.
The specimen goniometer
Goniometer
A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry is derived from two Greek words, gōnia, meaning angle, and metron, meaning measure....
of a TEM is thereby employed analogously to the goniometer head of an optical goniometer. The optical axis of the TEM is then analogous to the reference direction of an optical goniometer. While in optical goniometry net-plane normals (reciprocal lattice vectors) need to be successively aligned parallel to the reference direction of an optical goniometer in order to derive measurements of interfacial angles, the corresponding alignment needs to be done for zone axes (direct lattice vector) in transmission electron goniometry. (Note that such alignments are by their nature quite trivial for nanocrystals in a TEM after the microscope has been aligned by standard procedures.)
Since transmission electron goniometry is based on Bragg’s Law
Bragg's law
In physics, Bragg's law gives the angles for coherent and incoherent scattering from a crystal lattice. When X-rays are incident on an atom, they make the electronic cloud move as does any electromagnetic wave...
for the transmission (Laue) case (diffraction of electron waves), interzonal angles (i.e. angles between lattice directions) can be measured by a procedure that is analogous to the measurement of interfacial angles in an optical goniometer on the basis of Snell’s Law
Snell's law
In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...
, i.e. the reflection of light. The complements to interfacial angles of external crystal faces can, on the other hand, be directly measured from a zone-axis diffraction pattern or from the Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
of a high resolution TEM image that shows crossed lattice fringes.
Lattice matching (3D)
Lattice parametersLattice constant
The lattice constant [or lattice parameter] refers to the constant distance between unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice constants, referred to as a, b, and c. However, in the special case of cubic crystal structures, all of the constants are...
of unknown crystal phases can be obtained from X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
, neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
, or electron diffraction
Electron diffraction
Electron diffraction refers to the wave nature of electrons. However, from a technical or practical point of view, it may be regarded as a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern...
data. Single-crystal diffraction experiments supply orientation matrices, from which lattice parameters can be deduced. Alternatively, lattice parameters can be obtained from powder or polycrystal diffraction data via profile fitting without structural model (so-called 'Le Bail method').
Arbitrarily defined unit cells can be transformed to a standard setting and, from there, further reduced to a primitive smallest cell. Sophisticated algorithms compare such reduced cells with corresponding database
Database
A database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...
entries. More powerful algorithms also consider derivative super- and subcells. The lattice-matching process can be further sped up by precalculating and storing reduced cells for all entries. The algorithm searches for matches within a certain range of the lattice parameters. More accurate lattice parameters allow a narrower range and, thus, a better match.
Lattice matching is useful in identifying crystal phases in the early stages of single-crystal
diffraction experiments and, thus, avoiding unnecessary full data collection and structure determination procedures for already known crystal structures. The method is particularly important for single-crystalline samples that need to be preserved. If, on the other hand, some or all of the crystalline sample material can be ground, powder diffraction fingerprinting is usually the better option for crystal phase identification, provided that the peak resolution is good enough. However, lattice matching algorithms are still better at treating derivative super- and subcells.
Visualization
Newer versions of crystal structureCrystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
databases integrate the visualization of crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
and molecular structures. Specialized or integrative crystallographic databases may provide morphology or tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
visualization output.
Crystal structures
The crystal structureCrystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
describes the three-dimensional periodic arrangement of atoms, ions, or molecules in a crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
. The unit cell represents the simplest repeating unit of the crystal structure. It is a parallelepiped containing a certain spatial arrangement of atoms, ions, molecules, or molecular fragments. From the unit cell the crystal structure can be fully reconstructed via translations
Translation (geometry)
In Euclidean geometry, a translation moves every point a constant distance in a specified direction. A translation can be described as a rigid motion, other rigid motions include rotations and reflections. A translation can also be interpreted as the addition of a constant vector to every point, or...
.
The visualization of a crystal structure can be reduced to the arrangement of atoms, ions, or molecules in the unit cell, with or without cell outlines. Structure elements extending beyond single unit cells, such as isolated molecular or polyhedral units as well as chain, net, or framework structures, can often be better understood by extending the structure representation into adjacent cells.
The space group
Space group
In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains.In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered distinct...
of a crystal is a mathematical description of the symmetry
Symmetry
Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...
inherent in the structure. The motif of the crystal structure is given by the asymmetric unit
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
, a minimal subset of the unit cell contents. The unit cell contents can be fully reconstructed via the symmetry operations of the space group on the asymmetric unit. Visualization interfaces
Graphical user interface
In computing, a graphical user interface is a type of user interface that allows users to interact with electronic devices with images rather than text commands. GUIs can be used in computers, hand-held devices such as MP3 players, portable media players or gaming devices, household appliances and...
usually allow for switching between asymmetric unit and full structure representations.
Bonds
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...
between atoms or ions can be identified by characteristic short distances between them. They can be classified as covalent
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....
, ionic
Ionic bond
An ionic bond is a type of chemical bond formed through an electrostatic attraction between two oppositely charged ions. Ionic bonds are formed between a cation, which is usually a metal, and an anion, which is usually a nonmetal. Pure ionic bonding cannot exist: all ionic compounds have some...
, hydrogen
Hydrogen bond
A hydrogen bond is the attractive interaction of a hydrogen atom with an electronegative atom, such as nitrogen, oxygen or fluorine, that comes from another molecule or chemical group. The hydrogen must be covalently bonded to another electronegative atom to create the bond...
, or other bonds including hybrid forms. Bond angles can be deduced from the bond vectors in groups of atoms or ions. Bond distances and angles can be made available to the user in tabular form or interactively, by selecting pairs or groups of atoms or ions. In ball-and-stick model
Ball-and-stick model
In chemistry, the ball-and-stick model is a molecular model of a chemical substance which is to display both the three-dimensional position of the atoms and the bonds between them...
s of crystal structures, balls represent atoms and sticks represent bonds.
Since organic chemists are particularly interested in molecular structures, it might be useful to be able to single out individual molecular units interactively from the drawing. Organic
Organic compound
An organic compound is any member of a large class of gaseous, liquid, or solid chemical compounds whose molecules contain carbon. For historical reasons discussed below, a few types of carbon-containing compounds such as carbides, carbonates, simple oxides of carbon, and cyanides, as well as the...
molecular units need to be given both as 2D structural formulae and full 3D molecular structures. Molecules on special-symmetry positions need to be reconstructed from the asymmetric unit. Protein crystallographers are interested in molecular structures of biological macromolecules
Biomolecule
A biomolecule is any molecule that is produced by a living organism, including large polymeric molecules such as proteins, polysaccharides, lipids, and nucleic acids as well as small molecules such as primary metabolites, secondary metabolites, and natural products...
, so that provisions need to be made to be able to represent molecular subunits as helices
Alpha helix
A common motif in the secondary structure of proteins, the alpha helix is a right-handed coiled or spiral conformation, in which every backbone N-H group donates a hydrogen bond to the backbone C=O group of the amino acid four residues earlier...
, sheets
Beta sheet
The β sheet is the second form of regular secondary structure in proteins, only somewhat less common than the alpha helix. Beta sheets consist of beta strands connected laterally by at least two or three backbone hydrogen bonds, forming a generally twisted, pleated sheet...
, or coils
Random coil
A random coil is a polymer conformation where the monomer subunits are oriented randomly while still being bonded to adjacent units. It is not one specific shape, but a statistical distribution of shapes for all the chains in a population of macromolecules...
, respectively.
Crystal structure visualization can be integrated into a crystallographic database
Database
A database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...
. Alternatively, the crystal structure data are exchanged between the database and the visualization software, preferably using the CIF
Crystallographic Information File
Crystallographic Information File is a standard text file format for representing crystallographic information, promulgated by the International Union of Crystallography . CIF was developed by the IUCr Working Party on Crystallographic Information in an effort sponsored by the IUCr Commission on...
format. Web-based crystallographic databases can integrate crystal structure visualization capability. Depending on the complexity of the structure, lighting, and 3D effects, crystal structure visualization can require a significant amount of processing power, which is why the actual visualization is typically run on the client
Client (computing)
A client is an application or system that accesses a service made available by a server. The server is often on another computer system, in which case the client accesses the service by way of a network....
.
Currently, web-integrated crystal structure visualization is based on Java applet
Java applet
A Java applet is an applet delivered to users in the form of Java bytecode. Java applets can run in a Web browser using a Java Virtual Machine , or in Sun's AppletViewer, a stand-alone tool for testing applets...
s from open-source projects such as Jmol
Jmol
Jmol is an open-source Java viewer for chemical structures in 3D,that does not require 3D acceleration plugins.Jmol returns a 3D representation of a molecule that may be used as a teaching tool, or for research e.g...
. Web-integrated crystal structure visualization is tailored for examining crystal structures in web browsers, often supporting wide color spectra
Visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...
(up to 32 bit) and window size adaptation. However, web-generated crystal structure images are not always suitable for publishing due to issues such as resolution depth, color choice, grayscale contrast, or labeling (positioning, font type, font size).
Morphology and physical properties
Mineralogists, in particular, are interested in morphologicalShape
The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...
appearances of individual crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
s, as defined by the actually formed crystal faces (tracht) and their relative sizes (habit). More advanced visualization capabilities allow for displaying surface characteristics, imperfections inside the crystal, lighting (reflection, shadow, and translucency), and 3D effects (interactive rotatability, perspective, and stereo viewing).
Crystal physicists
Solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from...
, in particular, are interested in anisotropic physical properties of crystals. The directional dependence of a crystal's physical property is described by a 3D tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
and depends on the orientation of the crystal. Tensor shapes are more palpable by adding lighting effects (reflection and shadow). 2D sections of interest are selected for display by rotating the tensor interactively around one or more axes.
Crystal morphology or physical property data can be stored in specialized databases or added to more comprehensive crystal structure databases. The Crystal Morphology Database (CMD) is an example for a web-based crystal morphology database with integrated visualization capabilities.
Crystal structures
- American Mineralogist Crystal Structure Database (AMCSD) (contents: crystal structures of minerals, access: free, size: medium)
- Cambridge Structural Database (CSD) (contents: crystal structures of organics and metal-organics, access: restricted, size: large)
- Crystal Lattice Structures (contents: a selection of common crystal structures, access: free, size: small)
- Crystallography Open Database (COD) (contents: crystal structures of organics, metalorganics, minerals, inorganics, metals, alloys, and intermetallics, access: free, size: medium - large)
- Database of Zeolite Structures (contents: crystal structures of zeolites, access: free, size: small)
- Incommensurate Structures Database (contents: incommensurate structures, access: free, size: small)
- Inorganic Crystal Structure Database (ICSD) (contents: crystal structures of minerals and inorganics, access: restricted, size: large)
- Metals Structure Database (CRYSTMET) (contents: crystal structures of metals, alloys, and intermetallics, access: restricted, size: large)
- Mineralogy Database (contents: crystal structures of minerals, access: free, size: medium)
- MinCryst (contents: crystal structures of minerals, access: free, size: medium)
- Nano-Crystallography Database (NCD) (contents: crystal structures of nanometer sized crystallites, access: free, size: small)
- NIST Structural Database NIST Structural Database (contents: crystal structures of metals, alloys, and intermetallics, access: restricted, size: large)
- NIST Surface Structure Database (contents: surface and interface structures, access: restricted, size: small-medium)
- Nucleic Acid Database (contents: crystal and molecular structures of nucleic acids, access: free, size: medium)
- Pearson's Crystal Data (contents: crystal structures of organics, metalorganics, minerals, inorganics, metals, alloys, and intermetallics, access: restricted, size: large)
- Worldwide Protein Data Bank (PDB) (contents: crystal and molecular structures of biological macromolecules, access: free, size: medium-large)
- Wiki Crystallography Database (WCD) (contents: crystal structures of organics, metalorganics, minerals, inorganics, metals, alloys, and intermetallics, access: free, size: medium)
Crystal phase identification
- Match! (method: powder diffraction fingerprinting)
- Nano-Crystallography Database (NCD) (method: lattice-fringe fingerprinting)
- NIST Crystal Data (method: lattice matching)
- Powder Diffraction File (PDF) (method: powder diffraction fingerprinting)
- Wiki Crystallography Database (WCD) (method: lattice-fringe fingerprinting)
Specialized databases
- Biological Macromolecule Crystallization Database (BMCD) (specialization: crystallization of biological macromolecules, access: free, size: medium)
- Crystal Morphology Database (CMD) (specialization: morphology of crystals, access: free, size: small)
- Database of Zeolite Structures (specialization: crystal structures of zeolites, access: free, size: small)
- Incommensurate Structures Database (specialization: incommensurate structures, access: free, size: small)
- Marseille Protein Crystallization Database (MPCD) (specialization: crystallization of biological macromolecules, access: free, size: medium)
- Nano-Crystallography Database (NCD) (specialization: crystal structures of nanometer sized crystallites, access: free, size: small)
- NIST Surface Structure Database (specialization: surface and interface structures, access: restricted, size: small-medium)
- Linus Pauling File (LPF) (specialization: physical properties of metals, alloys, intermetallics, and inorganics, access: free, size: medium-large)
- Predicted Crystallography Open Database (PCOD) (spezialization: predicted crystal structures of organics, metal-organics, metals, alloys, intermetallics, and inorganics, access: free, size: large)