Crystallography

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A crystalline solid: atomic resolution image of strontium titanate. Brighter spots are columns of strontium atoms and darker ones are titanium-oxygen columns. Stohrem.jpg
A crystalline solid: atomic resolution image of strontium titanate. Brighter spots are columns of strontium atoms and darker ones are titanium-oxygen columns.
Octahedral and tetrahedral interstitial sites in a face centered cubic structure Sites interstitiels cubique a faces centrees.svg
Octahedral and tetrahedral interstitial sites in a face centered cubic structure
Kikuchi lines in an electron backscatter diffraction pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source EBSD (001) Si.png
Kikuchi lines in an electron backscatter diffraction pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source

Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. [1] The word crystallography is derived from the Ancient Greek word κρύσταλλος (krústallos; "clear ice, rock-crystal"), and γράφειν (gráphein; "to write"). [2] In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography. [3]

Contents

Crystallography is a broad topic, and many of its subareas, such as X-ray crystallography, are themselves important scientific topics. Crystallography ranges from the fundamentals of crystal structure to the mathematics of crystal geometry, including those that are not periodic or quasicrystals. At the atomic scale it can involve the use of X-ray diffraction to produce experimental data that the tools of X-ray crystallography can convert into detailed positions of atoms, and sometimes electron density. At larger scales it includes experimental tools such as orientational imaging to examine the relative orientations at the grain boundary in materials. Crystallography plays a key role in many areas of biology, chemistry, and physics, as well new developments in these fields.

History and timeline

Before the 20th century, the study of crystals was based on physical measurements of their geometry using a goniometer. [4] This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. The position in 3D space of each crystal face is plotted on a stereographic net such as a Wulff net or Lambert net. The pole to each face is plotted on the net. Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established. [5] [6]

The discovery of X-rays and electrons in the last decade of the 19th century enabled the determination of crystal structures on the atomic scale, which brought about the modern era of crystallography. The first X-ray diffraction experiment was conducted in 1912 by Max von Laue, [7] while electron diffraction was first realized in 1927 in the Davisson–Germer experiment [8] and parallel work by George Paget Thomson and Alexander Reid. [9] These developed into the two main branches of crystallography, X-ray crystallography and electron diffraction. The quality and throughput of solving crystal structures greatly improved in the second half of the 20th century, with the developments of customized instruments and phasing algorithms. Nowadays, crystallography is an interdisciplinary field, supporting theoretical and experimental discoveries in various domains. [10] Modern-day scientific instruments for crystallography vary from laboratory-sized equipment, such as diffractometers and electron microscopes, to dedicated large facilities, such as photoinjectors, synchrotron light sources and free-electron lasers.

Methodology

Crystallographic methods depend mainly on analysis of the diffraction patterns of a sample targeted by a beam of some type. X-rays are most commonly used; other beams used include electrons or neutrons. Crystallographers often explicitly state the type of beam used, as in the terms X-ray diffraction, neutron diffraction and electron diffraction . These three types of radiation interact with the specimen in different ways.

It is hard to focus x-rays or neutrons, but since electrons are charged they can be focused and are used in electron microscope to produce magnified images. There are many ways that transmission electron microscopy and related techniques such as scanning transmission electron microscopy, high-resolution electron microscopy can be used to obtain images with in many cases atomic resolution from which crystallographic information can be obtained. There are also other methods such as low-energy electron diffraction, low-energy electron microscopy and reflection high-energy electron diffraction which can be used to obtain crystallographic information about surfaces.

Applications in various areas

Materials science

Crystallography is used by materials scientists to characterize different materials. In single crystals, the effects of the crystalline arrangement of atoms is often easy to see macroscopically because the natural shapes of crystals reflect the atomic structure. In addition, physical properties are often controlled by crystalline defects. The understanding of crystal structures is an important prerequisite for understanding crystallographic defects. Most materials do not occur as a single crystal, but are poly-crystalline in nature (they exist as an aggregate of small crystals with different orientations). As such, powder diffraction techniques, which take diffraction patterns of samples with a large number of crystals, play an important role in structural determination.

Other physical properties are also linked to crystallography. For example, the minerals in clay form small, flat, platelike structures. Clay can be easily deformed because the platelike particles can slip along each other in the plane of the plates, yet remain strongly connected in the direction perpendicular to the plates. Such mechanisms can be studied by crystallographic texture measurements. Crystallographic studies help elucidate the relationship between a material's structure and its properties, aiding in developing new materials with tailored characteristics. This understanding is crucial in various fields, including metallurgy, geology, and materials science. Advancements in crystallographic techniques, such as electron diffraction and X-ray crystallography, continue to expand our understanding of material behavior at the atomic level.

In another example, iron transforms from a body-centered cubic (bcc) structure called ferrite to a face-centered cubic (fcc) structure called austenite when it is heated. [14] The fcc structure is a close-packed structure unlike the bcc structure; thus the volume of the iron decreases when this transformation occurs.

Crystallography is useful in phase identification. When manufacturing or using a material, it is generally desirable to know what compounds and what phases are present in the material, as their composition, structure and proportions will influence the material's properties. Each phase has a characteristic arrangement of atoms. X-ray or neutron diffraction can be used to identify which structures are present in the material, and thus which compounds are present. Crystallography covers the enumeration of the symmetry patterns which can be formed by atoms in a crystal and for this reason is related to group theory.

Biology

X-ray crystallography is the primary method for determining the molecular conformations of biological macromolecules, particularly protein and nucleic acids such as DNA and RNA. The double-helical structure of DNA was deduced from crystallographic data. The first crystal structure of a macromolecule was solved in 1958, a three-dimensional model of the myoglobin molecule obtained by X-ray analysis. [15] The Protein Data Bank (PDB) is a freely accessible repository for the structures of proteins and other biological macromolecules. Computer programs such as RasMol, Pymol or VMD can be used to visualize biological molecular structures. Neutron crystallography is often used to help refine structures obtained by X-ray methods or to solve a specific bond; the methods are often viewed as complementary, as X-rays are sensitive to electron positions and scatter most strongly off heavy atoms, while neutrons are sensitive to nucleus positions and scatter strongly even off many light isotopes, including hydrogen and deuterium. Electron diffraction has been used to determine some protein structures, most notably membrane proteins and viral capsids.

Notation

Reference literature

The International Tables for Crystallography [16] is an eight-book series that outlines the standard notations for formatting, describing and testing crystals. The series contains books that covers analysis methods and the mathematical procedures for determining organic structure through x-ray crystallography, electron diffraction, and neutron diffraction. The International tables are focused on procedures, techniques and descriptions and do not list the physical properties of individual crystals themselves. Each book is about 1000 pages and the titles of the books are:

Vol A - Space Group Symmetry,
Vol A1 - Symmetry Relations Between Space Groups,
Vol B - Reciprocal Space,
Vol C - Mathematical, Physical, and Chemical Tables,
Vol D - Physical Properties of Crystals,
Vol E - Subperiodic Groups,
Vol F - Crystallography of Biological Macromolecules, and
Vol G - Definition and Exchange of Crystallographic Data.

Notable scientists

See also

Related Research Articles

<span class="mw-page-title-main">Crystal</span> Solid material with highly ordered microscopic structure

A crystal or crystalline solid is a solid material whose constituents are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification.

<span class="mw-page-title-main">X-ray crystallography</span> Technique used for determining crystal structures and identifying mineral compounds

X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract in specific directions. By measuring the angles and intensities of the X-ray diffraction, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal and the positions of the atoms, as well as their chemical bonds, crystallographic disorder, and other information.

<span class="mw-page-title-main">Crystal structure</span> Ordered arrangement of atoms, ions, or molecules in a crystalline material

In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.

<span class="mw-page-title-main">Electron diffraction</span> Bending of electron beams due to electrostatic interactions with matter

Electron diffraction is a generic term for phenomena associated with changes in the direction of electron beams due to elastic interactions with atoms. It occurs due to elastic scattering, when there is no change in the energy of the electrons. The negatively charged electrons are scattered due to Coulomb forces when they interact with both the positively charged atomic core and the negatively charged electrons around the atoms. The resulting map of the directions of the electrons far from the sample is called a diffraction pattern, see for instance Figure 1. Beyond patterns showing the directions of electrons, electron diffraction also plays a major role in the contrast of images in electron microscopes.

<span class="mw-page-title-main">Neutron diffraction</span> Technique to investigate atomic structures using neutron scattering

Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of the structure of the material. The technique is similar to X-ray diffraction but due to their different scattering properties, neutrons and X-rays provide complementary information: X-Rays are suited for superficial analysis, strong x-rays from synchrotron radiation are suited for shallow depths or thin specimens, while neutrons having high penetration depth are suited for bulk samples.

In many areas of science, Bragg's law, Wulff–Bragg's condition, or Laue–Bragg interference are a special case of Laue diffraction, giving the angles for coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength and scattering angle. This law was initially formulated for X-rays, but it also applies to all types of matter waves including neutron and electron waves if there are a large number of atoms, as well as visible light with artificial periodic microscale lattices.

<span class="mw-page-title-main">Biological small-angle scattering</span>

Biological small-angle scattering is a small-angle scattering method for structure analysis of biological materials. Small-angle scattering is used to study the structure of a variety of objects such as solutions of biological macromolecules, nanocomposites, alloys, and synthetic polymers. Small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) are the two complementary techniques known jointly as small-angle scattering (SAS). SAS is an analogous method to X-ray and neutron diffraction, wide angle X-ray scattering, as well as to static light scattering. In contrast to other X-ray and neutron scattering methods, SAS yields information on the sizes and shapes of both crystalline and non-crystalline particles. When used to study biological materials, which are very often in aqueous solution, the scattering pattern is orientation averaged.

<span class="mw-page-title-main">Miller index</span> Notation system for crystal lattice planes

Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices.

Electron crystallography is a subset of methods in electron diffraction focusing upon detailed determination of the positions of atoms in solids using a transmission electron microscope (TEM). It can involve the use of high-resolution transmission electron microscopy images, electron diffraction patterns including convergent-beam electron diffraction or combinations of these. It has been successful in determining some bulk structures, and also surface structures. Two related methods are low-energy electron diffraction which has solved the structure of many surfaces, and reflection high-energy electron diffraction which is used to monitor surfaces often during growth.

<span class="mw-page-title-main">Powder diffraction</span> Experimental method in X-ray 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 called a powder diffractometer.

<span class="mw-page-title-main">Selected area diffraction</span> Crystallographic electron diffraction technique

Selected area (electron) diffraction is a crystallographic experimental technique typically performed using a transmission electron microscope (TEM). It is a specific case of electron diffraction used primarily in material science and solid state physics as one of the most common experimental techniques. Especially with appropriate analytical software, SAD patterns (SADP) can be used to determine crystal orientation, measure lattice constants or examine its defects.

<span class="mw-page-title-main">Dynamical theory of diffraction</span>

The dynamical theory of diffraction describes the interaction of waves with a regular lattice. The wave fields traditionally described are X-rays, neutrons or electrons and the regular lattice are atomic crystal structures or nanometer-scale multi-layers or self-arranged systems. In a wider sense, similar treatment is related to the interaction of light with optical band-gap materials or related wave problems in acoustics. The sections below deal with dynamical diffraction of X-rays.

<span class="mw-page-title-main">Fiber diffraction</span> Subarea of scattering, an area in which molecular structure is determined from scattering data

Fiber diffraction is a subarea of scattering, an area in which molecular structure is determined from scattering data. In fiber diffraction, the scattering pattern does not change, as the sample is rotated about a unique axis. Such uniaxial symmetry is frequent with filaments or fibers consisting of biological or man-made macromolecules. In crystallography, fiber symmetry is an aggravation regarding the determination of crystal structure, because reflections are smeared and may overlap in the fiber diffraction pattern. Materials science considers fiber symmetry a simplification, because almost the complete obtainable structure information is in a single two-dimensional (2D) diffraction pattern exposed on photographic film or on a 2D detector. 2 instead of 3 co-ordinate directions suffice to describe fiber diffraction.

<span class="mw-page-title-main">X-ray diffraction</span> Elastic interaction of x-rays with electrons

X-ray diffraction is a generic term for phenomena associated with changes in the direction of X-ray beams due to interactions with the electrons around atoms. It occurs due to elastic scattering, when there is no change in the energy of the waves. The resulting map of the directions of the X-rays far from the sample is called a diffraction pattern. It is different from X-ray crystallography which exploits X-ray diffraction to determine the arrangement of atoms in materials, and also has other components such as ways to map from experimental diffraction measurements to the positions of atoms.

A crystallographic database is a database specifically designed to store information about the structure of molecules and crystals. 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..

In solid state physics, a superstructure is some additional structure that is superimposed on a higher symmetry crystalline structure. A typical and important example is ferromagnetic ordering.

<span class="mw-page-title-main">Crystallographic image processing</span>

Crystallographic image processing (CIP) is traditionally understood as being a set of key steps in the determination of the atomic structure of crystalline matter from high-resolution electron microscopy (HREM) images obtained in a transmission electron microscope (TEM) that is run in the parallel illumination mode. The term was created in the research group of Sven Hovmöller at Stockholm University during the early 1980s and became rapidly a label for the "3D crystal structure from 2D transmission/projection images" approach. Since the late 1990s, analogous and complementary image processing techniques that are directed towards the achieving of goals with are either complementary or entirely beyond the scope of the original inception of CIP have been developed independently by members of the computational symmetry/geometry, scanning transmission electron microscopy, scanning probe microscopy communities, and applied crystallography communities.

<span class="mw-page-title-main">Zone axis</span> High symmetry orientation of a crystal

Zone axis, a term sometimes used to refer to "high-symmetry" orientations in a crystal, most generally refers to any direction referenced to the direct lattice of a crystal in three dimensions. It is therefore indexed with direct lattice indices, instead of with Miller indices.

Structural chemistry is a part of chemistry and deals with spatial structures of molecules and solids. For structure elucidation a range of different methods is used. One has to distinguish between methods that elucidate solely the connectivity between atoms (constitution) and such that provide precise three dimensional information such as atom coordinates, bond lengths and angles and torsional angles.

This is a timeline of crystallography.

References

  1. ↑ Chapuis, Gervais (ed.). "Online Dictionary of Crystallography". Online dictionary of crystallography. International Union of Crystallography . Retrieved 2024-05-22.
  2. ↑ "Online Dictionary of Crystallography". International Union of Crystallography. 2021-10-21. Retrieved 2024-03-11.
  3. ↑ UN announcement "International Year of Crystallography". iycr2014.org. 12 July 2012
  4. ↑ "The Evolution of the Goniometer". Nature. 95 (2386): 564–565. 1915-07-01. Bibcode:1915Natur..95..564.. doi: 10.1038/095564a0 . ISSN   1476-4687.
  5. ↑ Molčanov, Krešimir; Stilinović, Vladimir (2014-01-13). "Chemical Crystallography before X-ray Diffraction". Angewandte Chemie International Edition. 53 (3): 638–652. doi:10.1002/anie.201301319. ISSN   1433-7851. PMID   24065378.
  6. ↑ Mascarenhas, Yvonne Primerano (2020-03-02). "Crystallography before the Discovery of X-Ray Diffraction". Revista Brasileira de Ensino de Física. 42: e20190336. doi: 10.1590/1806-9126-RBEF-2019-0336 . ISSN   1806-1117.
  7. ↑ Friedrich W, Knipping P, von Laue M (1912). "Interferenz-Erscheinungen bei Röntgenstrahlen" (PDF). Sitzungsberichte der Mathematisch-Physikalischen Classe der Königlich-Bayerischen Akademie der Wissenschaften zu München[Interference phenomena in X-rays]. 1912: 303.
  8. ↑ Davisson, C.; Germer, L. H. (1927). "The Scattering of Electrons by a Single Crystal of Nickel". Nature. 119 (2998): 558–560. Bibcode:1927Natur.119..558D. doi:10.1038/119558a0. ISSN   1476-4687.
  9. ↑ Thomson, G. P.; Reid, A. (1927). "Diffraction of Cathode Rays by a Thin Film". Nature. 119 (3007): 890. Bibcode:1927Natur.119Q.890T. doi:10.1038/119890a0. ISSN   1476-4687.
  10. ↑ Brooks-Bartlett, Jonathan C.; Garman, Elspeth F. (2015-07-03). "The Nobel Science: One Hundred Years of Crystallography". Interdisciplinary Science Reviews. 40 (3): 244–264. Bibcode:2015ISRv...40..244B. doi:10.1179/0308018815Z.000000000116. ISSN   0308-0188.
  11. ↑ Cullity, B. D.; Stock, Stuart R. (2001). Elements of X-ray diffraction (3rd ed.). Upper Saddle River, NJ: Prentice Hall. ISBN   978-0-201-61091-8.
  12. ↑ "ISIS Neutron Diffraction with Isotopic Substitution". www.isis.stfc.ac.uk. Retrieved 2024-07-02.
  13. ↑ Cowley, John Maxwell (1995). Diffraction physics. North-Holland personal library (3rd ed.). Amsterdam; New York: Elsevier Science B.V. ISBN   978-0-444-82218-5.
  14. ↑ "Materials Science and Engineering: An Introduction, 10th Edition | Wiley". Wiley.com. Retrieved 2022-09-10.
  15. ↑ Kendrew, J. C.; Bodo, G.; Dintzis, H. M.; Parrish, R. G.; Wyckoff, H.; Phillips, D. C. (1958). "A Three-Dimensional Model of the Myoglobin Molecule Obtained by X-Ray Analysis". Nature. 181 (4610): 662–6. Bibcode:1958Natur.181..662K. doi:10.1038/181662a0. PMID   13517261. S2CID   4162786.
  16. ↑ Prince, E. (2006). International Tables for Crystallography Vol. C: Mathematical, Physical and Chemical Tables. Wiley. ISBN   978-1-4020-4969-9. OCLC   166325528. OL   9332669M. Archived from the original on 6 May 2022.
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