Crystallographic Databases
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A crystallographic database is a database specifically designed to store information about the structure of
molecules A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioc ...
and
crystals A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
. Crystals are
solids Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structura ...
having, in all three dimensions of space, a regularly repeating arrangement of
atoms Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas ...
,
ions An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
, or
molecules A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioc ...
. They are characterized by symmetry, morphology, and directionally dependent physical properties. A
crystal structure In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns t ...
describes the arrangement of atoms, ions, or molecules in a crystal. (Molecules need to crystallize into solids so that their regularly repeating arrangements can be taken advantage of in
X-ray X-rays (or rarely, ''X-radiation'') are a form of high-energy electromagnetic radiation. In many languages, it is referred to as Röntgen radiation, after the German scientist Wilhelm Conrad Röntgen, who discovered it in 1895 and named it ' ...
,
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...
, and
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...
diffraction based
crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wo ...
.) Crystal structures of crystalline material are typically determined from
X-ray X-rays (or rarely, ''X-radiation'') are a form of high-energy electromagnetic radiation. In many languages, it is referred to as Röntgen radiation, after the German scientist Wilhelm Conrad Röntgen, who discovered it in 1895 and named it ' ...
or
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...
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 Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is cal ...
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 Electron diffraction refers to the bending of electron beams around atomic structures. This behaviour, typical for Wave (physics), waves, is applicable to electrons due to the wave–particle duality stating that electrons behave as both particle ...
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 nanocrystals and can be identified by comparing zone axis subsets in lattice-fringe fingerprint plots with entries in a lattice-fringe fingerprinting database.
Crystallographic Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wo ...
databases 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 A relational database is a (most commonly digital) database based on the relational model of data, as proposed by E. F. Codd in 1970. A system used to maintain relational databases is a relational database management system (RDBMS). Many relatio ...
model and support the
Crystallographic Information File Crystallographic Information File (CIF) is a standard text file format for representing crystallographic information, promulgated by the International Union of Crystallography (IUCr). CIF was developed by the IUCr Working Party on Crystallograph ...
( CIF) as a universal data exchange format.


Overview

Crystallographic Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wo ...
data are primarily extracted from published scientific articles and supplementary material. Newer versions of crystallographic
databases In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spa ...
are built on the
relational database A relational database is a (most commonly digital) database based on the relational model of data, as proposed by E. F. Codd in 1970. A system used to maintain relational databases is a relational database management system (RDBMS). Many relatio ...
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 (CIF) is a standard text file format for representing crystallographic information, promulgated by the International Union of Crystallography (IUCr). CIF was developed by the IUCr Working Party on Crystallograph ...
(CIF) format. The CIF format is the standard file format for the exchange and archiving of crystallographic data. It was adopted by the
International Union of Crystallography The International Union of Crystallography (IUCr) is an organisation devoted to the international promotion and coordination of the science of crystallography. The IUCr is a member of the International Council for Science (ICSU). Objectives T ...
( IUCr), who also provides full specifications of the format. It is supported by all major crystallographic databases. The increasing automation of the
crystal structure In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns t ...
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 Open access (OA) is a set of principles and a range of practices through which research outputs are distributed online, free of access charges or other barriers. With open access strictly defined (according to the 2001 definition), or libre o ...
journals. ''
Acta Crystallographica Section E ''Acta Crystallographica'' is a series of peer-reviewed scientific journals, with articles centred on crystallography, published by the International Union of Crystallography (IUCr). Originally established in 1948 as a single journal called ''Act ...
'' 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 (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating syste ...
( 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 is data that is openly accessible, exploitable, editable and shared by anyone for any purpose. Open data is licensed under an open license. The goals of the open data movement are similar to those of other "open(-source)" movements ...
, 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

As of 2008, more than 700,000 crystal structures had been published and stored in crystal structure
databases In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spa ...
. 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 Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas ...
ic parameters, and differences in diffraction technique or experimental conditions. As of 2016, there are about 1,000,000 molecule and crystal structures known and published, approximately half of them in
open access Open access (OA) is a set of principles and a range of practices through which research outputs are distributed online, free of access charges or other barriers. With open access strictly defined (according to the 2001 definition), or libre o ...
. Crystal structures are typically categorized as
minerals In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. ( ...
,
metals A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
- alloys, inorganics, organics,
nucleic acids Nucleic acids are biopolymers, macromolecules, essential to all known forms of life. They are composed of nucleotides, which are the monomers made of three components: a 5-carbon sugar, a phosphate group and a nitrogenous base. The two main cl ...
, and biological macromolecules. Individual crystal structure databases cater for users in specific
chemical A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wit ...
, 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 An intermetallic (also called an intermetallic compound, intermetallic alloy, ordered intermetallic alloy, and a long-range-ordered alloy) is a type of metallic alloy that forms an ordered solid-state compound between two or more metallic elem ...
. Metals-alloys and inorganics can be merged into ‘non-organics’.
Organic compounds In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The ...
and biological macromolecules are separated according to molecular size. Organic salts,
organometallics ''Organometallics'' is a biweekly journal published by the American Chemical Society. Its area of focus is organometallic and organometalloid chemistry. This peer-reviewed journal has an impact factor of 3.837 as reported by the 2021 Journal Cita ...
, 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 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 Open or OPEN may refer to: Music * Open (band), Australian pop/rock band * The Open (band), English indie rock band * Open (Blues Image album), ''Open'' (Blues Image album), 1969 * Open (Gotthard album), ''Open'' (Gotthard album), 1999 * Open (C ...
. 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 is the maintenance of, and the assurance of, data accuracy and consistency over its entire life-cycle and is a critical aspect to the design, implementation, and usage of any system that stores, processes, or retrieves data. The ter ...
. In terms of user numbers and daily access rates, comprehensive and thoroughly vetted
open-access Open access (OA) is a set of principles and a range of practices through which research outputs are distributed online, free of access charges or other barriers. With open access strictly defined (according to the 2001 definition), or libre o ...
crystal structure databases naturally surpass comparable databases with more restricted access and usage rights. Independent of comprehensiveness, open-access crystal structure databases have spawned
open-source software Open-source software (OSS) is computer software that is released under a license in which the copyright holder grants users the rights to use, study, change, and distribute the software and its source code to anyone and for any purpose. Ope ...
projects, such as search-analysis tools, visualization software, and derivative databases. Scientific progress has been 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 other than th
Crystallography Open Database
(COD), and is "macromolecular open-access counterpart", th
world wide Protein Database
Apart from that, several crystal structure databases are freely available for primarily educational purposes, in particular mineralogical databases an
educational offshoots of the COD
.
Crystallographic Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wo ...
databases can specialize in crystal structures, crystal phase identification,
crystallization Crystallization is the process by which solid forms, where the atoms or molecules are highly organized into a structure known as a crystal. Some ways by which crystals form are precipitating from a solution, freezing, or more rarely de ...
, crystal morphology, or various physical properties. More integrative databases combine several categories of compounds or specializations. Structures of
incommensurate phases Two concepts or things are commensurable if they are measurable or comparable by a common standard. Commensurability most commonly refers to commensurability (mathematics). It may also refer to: * Commensurability (astronomy), whether two orbital ...
, 2D materials, nanocrystals,
thin films A thin film is a layer of material ranging from fractions of a nanometer ( monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many ...
on substrates, and predicted crystal structures are collected in tailored special structure databases.


Search

Search capacities of
crystallographic Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wo ...
databases In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spa ...
differ widely. Basic functionality comprises search by keywords, physical properties, and
chemical elements A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...
. Of particular importance is search by compound name and lattice parameters. Very useful are search options that allow the use of wildcard characters and
logical connective In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...
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 In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The ...
might be searched for on the basis of certain
molecular fragments A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
.
Inorganic compound In chemistry, an inorganic compound is typically a chemical compound that lacks carbon–hydrogen bonds, that is, a compound that is not an organic compound. The study of inorganic compounds is a subfield of chemistry known as '' inorganic chemi ...
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 Supramolecular chemistry refers to the branch of chemistry concerning chemical systems composed of a discrete number of molecules. The strength of the forces responsible for spatial organization of the system range from weak intermolecular force ...
(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 A relational database is a (most commonly digital) database based on the relational model of data, as proposed by E. F. Codd in 1970. A system used to maintain relational databases is a relational database management system (RDBMS). Many relatio ...
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 Script may refer to: Writing systems * Script, a distinctive writing system, based on a repertoire of specific elements or symbols, or that repertoire * Script (styles of handwriting) ** Script typeface, a typeface with characteristics of handw ...
elements, while desktop-based databases run locally installed and usually precompiled
search engines A search engine is a software system designed to carry out web searches. They search the World Wide Web in a systematic way for particular information specified in a textual web search query. The search results are generally presented in a l ...
.


Crystal phase identification

Crystalline A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
material may be divided into single crystals, twin crystals, polycrystals, and crystal powder. In a single crystal, the arrangement of
atoms Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas ...
,
ions An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
, or
molecules A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioc ...
is defined by a single
crystal structure In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns t ...
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 In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' ( ...
. 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.


Powder diffraction fingerprinting (1D)

Applying standard diffraction techniques to
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macr ...
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 is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is cal ...
data can be plotted as diffracted intensity (''I'') versus
reciprocal lattice In physics, the reciprocal lattice represents the Fourier transform of another lattice (group) (usually a Bravais lattice). In normal usage, the initial lattice (whose transform is represented by the reciprocal lattice) is a periodic spatial fu ...
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 In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spa ...
. 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 is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys. Metallurgy encompasses both the sci ...
,
mineralogy Mineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, and physical (including optical) properties of minerals and mineralized artifacts. Specific studies within mineralogy include the proce ...
, forensic science,
archeology Archaeology or archeology is the scientific study of human activity through the recovery and analysis of material culture. The archaeological record consists of artifacts, architecture, biofacts or ecofacts, sites, and cultural landscape ...
,
condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the s ...
, and the
biological Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...
and pharmaceutical sciences.


Lattice-fringe fingerprinting (2D)

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. An instrument dedicated to performing such powder measurements is cal ...
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 refers to the bending of electron beams around atomic structures. This behaviour, typical for Wave (physics), waves, is applicable to electrons due to the wave–particle duality stating that electrons behave as both particle ...
techniques.
High-Resolution Transmission Electron Microscopy High-resolution transmission electron microscopy is an imaging mode of specialized transmission electron microscopes that allows for direct imaging of the atomic structure of samples. It is a powerful tool to study properties of materials on the ...
( 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 In physics, the reciprocal lattice represents the Fourier transform of another lattice (group) (usually a Bravais lattice). In normal usage, the initial lattice (whose transform is represented by the reciprocal lattice) is a periodic spatial fu ...
length and is limited by the point resolution of the microscope. The vertical axis is defined as acute angle between Fourier transformed
lattice fringes Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an ornam ...
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 In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spa ...
. It is, essentially, a variant of a lattice matching algorithm. 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 A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
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 crystal In materials science, a single crystal (or single-crystal solid 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.RIWD. "R ...
of the same material are, by nature, restricted to the same value. This offers the opportunity to fingerprint
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macr ...
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 In geometry, a point group is a mathematical group of symmetry operations ( isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every ...
symmetry of the measured faces and creatively apply the rule that "
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macr ...
morphologies are often combinations of simple (i.e. low multiplicity) forms where the individual faces have the lowest possible
Miller indices Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers ''h'', ''k'', and '' ...
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 In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spa ...
: 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 In physics, the reciprocal lattice represents the Fourier transform of another lattice (group) (usually a Bravais lattice). In normal usage, the initial lattice (whose transform is represented by the reciprocal lattice) is a periodic spatial fu ...
, 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 nanocrystals in the
transmission electron microscope Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a gr ...
( 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 In physics and chemistry , Bragg's law, Georg Wulff, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a crystal lattice. It encompasses the superposit ...
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 Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
or from the
Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
of a high resolution TEM image that shows crossed lattice fringes.


Lattice matching (3D)

Lattice parameters of unknown crystal phases can be obtained from
X-ray X-rays (or rarely, ''X-radiation'') are a form of high-energy electromagnetic radiation. In many languages, it is referred to as Röntgen radiation, after the German scientist Wilhelm Conrad Röntgen, who discovered it in 1895 and named it ' ...
,
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...
, or
electron diffraction Electron diffraction refers to the bending of electron beams around atomic structures. This behaviour, typical for Wave (physics), waves, is applicable to electrons due to the wave–particle duality stating that electrons behave as both particle ...
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 cell In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessari ...
s 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 In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spa ...
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 structure In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns t ...
databases In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spa ...
integrate the visualization of
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macr ...
and molecular structures. Specialized or integrative
crystallographic Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wo ...
databases may provide morphology or
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tens ...
visualization output.


Crystal structures

The
crystal structure In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns t ...
describes the three-dimensional periodic arrangement of
atoms Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas ...
,
ions An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
, or
molecules A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioc ...
in a
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macr ...
. The
unit cell In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessari ...
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 is the communication of the Meaning (linguistic), meaning of a #Source and target languages, source-language text by means of an Dynamic and formal equivalence, equivalent #Source and target languages, target-language text. The ...
. 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 A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
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 In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it ...
of a crystal is a mathematical description of the symmetry inherent in the structure. The
motif Motif may refer to: General concepts * Motif (chess composition), an element of a move in the consideration of its purpose * Motif (folkloristics), a recurring element that creates recognizable patterns in folklore and folk-art traditions * Moti ...
of the crystal structure is given by the
asymmetric unit In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystal, crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pat ...
, 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 A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atom ...
, ionic,
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
, 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 models 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 The structural formula of a chemical compound is a graphic representation of the molecular structure (determined by structural chemistry methods), showing how the atoms are possibly arranged in the real three-dimensional space. The chemical bondi ...
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 A bed sheet is a rectangular piece of cloth used either singly or in a pair as bedding, which is larger in length and width than a mattress, and which is placed immediately above a mattress or bed, but below blankets and other bedding (such a ...
, or coils, respectively. Crystal structure visualization can be integrated into a
crystallographic Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wo ...
database In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spa ...
. 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 Client(s) or The Client may refer to: * Client (business) * Client (computing), hardware or software that accesses a remote service on another computer * Customer or client, a recipient of goods or services in return for monetary or other valuabl ...
. Currently, web-integrated crystal structure visualization is based on
Java applet Java applets were small applications written in the Java programming language, or another programming language that compiles to Java bytecode, and delivered to users in the form of Java bytecode. The user launched the Java applet from a ...
s from
open-source Open source is source code that is made freely available for possible modification and redistribution. Products include permission to use the source code, design documents, or content of the product. The open-source model is a decentralized sof ...
projects such as Jmol. Web-integrated crystal structure visualization is tailored for examining crystal structures in
web browsers A web browser is application software for accessing websites. When a user requests a web page from a particular website, the browser retrieves its files from a web server and then displays the page on the user's screen. Browsers are used on ...
, 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).


Morphology and physical properties

Mineralogists, in particular, are interested in morphological appearances of individual
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macr ...
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 Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's phys ...
physical properties of crystals. The directional dependence of a crystal's physical property is described by a 3D
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tens ...
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.


See also

* Chemical database *
Biological database Biological databases are libraries of biological sciences, collected from scientific experiments, published literature, high-throughput experiment technology, and computational analysis. They contain information from research areas including genom ...


References


External links


Crystal structures


American Mineralogist Crystal Structure Database (AMCSD)
(contents: crystal structures of minerals, access: free, size: large)
Cambridge Structural Database (CSD)
(contents: crystal structures of organics and metal-organics, access: restricted, size: very large) * Crystallography Open Database (COD) (contents: crystal structures of organics, metalorganics, minerals, inorganics, metals, alloys, and intermetallics, access: free, size: very large)
COD+
(Web Interface for COD) (contents: crystal structures of organics, metalorganics, minerals, inorganics, metals, alloys, and intermetallics, access: free, size: very large)
Database of Zeolite Structures
(contents: crystal structures of zeolites, access: free, size: small)

(contents: incommensurate structures, access: free, size: small) *
Inorganic Crystal Structure Database Inorganic Crystal Structure Database (ICSD) is a chemical database founded in 1978 by Günter Bergerhoff (University of Bonn) and I. D. Brown (University of McMaster, Canada). It is now produced by FIZ Karlsruhe in Europe and the U.S. National ...
(ICSD) (contents: crystal structures of minerals and inorganics, access: restricted, size: large)
MaterialsProject Database
(contents: crystal structures of inorganic compounds, access: free, size: large)
MaterialsWeb Database
(contents: crystal structures of inorganic 2D materials and bulk compounds, access: free, size: large)

(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)

(contents: crystal structures of metals, alloys, and intermetallics, access: restricted, size: large)

(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)

(contents: crystal structures of inorganics, minerals, salts, oxides, hydrides, metals, alloys, and intermetallics, access: restricted, size: very large)
Worldwide Protein Data Bank (PDB)
(contents: crystal and molecular structures of biological macromolecules, access: free, size: very large)
Wiki Crystallography Database (WCD)
(contents: crystal structures of organics, metalorganics, minerals, inorganics, metals, alloys, and intermetallics, access: free, size: medium)


Crystal phase identification



(method: powder diffraction fingerprinting)

(method: lattice matching)
Powder Diffraction File (PDF)
(method: powder diffraction fingerprinting)


Specialized databases


Educational Subset of the Crystallography Open Database (EDU-COD)
(specialization: crystal and molecule structures for college education, access: free, size: medium)
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: very small)
Database of Hypothetical Structures
(specialization: predicted zeolite-like crystal structures, access: free, size: large)
Database of Zeolite Structures
(specialization: crystal structures of zeolites, access: free, size: small)
Hypothetical MOFs Database
(specialization: predicted metal-organic framework crystal structures, access: free, size: large)

(specialization: incommensurate structures, access: free, size: small)
Marseille Protein Crystallization Database (MPCD)
(specialization: crystallization of biological macromolecules, access: free, size: medium)
MOFomics
(specialization: pore structures of metal-organic frameworks, 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)

(spezialization: predicted crystal structures of organics, metal-organics, metals, alloys, intermetallics, and inorganics, access: free, size: very large)
Theoretical Crystallography Open Database (TCOD)
(spezialization: crystal structures of organics, metal-organics, metals, alloys, intermetallics, and inorganics that were refined or predicted from density functional theory with some experimental input, access: free, size: small)
ZEOMICS
(specialization: pore structures of zeolites, access: free, size: small)
Materials Platform for Data Science (MPDS) or PAULING FILE
(specialization: critically evaluated crystal structures, as well as physical properties and phase diagrams, from the world scientific literature, access: partially free, size: very large) {{DEFAULTSORT:Crystallographic Database Physical chemistry