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 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 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 word "crystallography" is derived from the Greek words κρύσταλλος (krystallos) "clear ice, rock-crystal", with its meaning extending to all solids with some degree of transparency, and γράφειν (graphein) "to write". In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography. [1]

Contents

Before the development of X-ray diffraction crystallography (see below), the study of crystals was based on physical measurements of their geometry using a goniometer. [2] 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.

Crystallographic methods now depend 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 crystallography, neutron diffraction and electron diffraction . These three types of radiation interact with the specimen in different ways.

Because of these different forms of interaction, the three types of radiation are suitable for different crystallographic studies.

Theory

With conventional imaging techniques such as optical microscopy, obtaining an image of a small object requires collecting light with a magnifying lens. The resolution of any optical system is limited by the diffraction-limit of light, which depends on its wavelength. Thus, the overall clarity of resulting crystallographic electron density maps is highly dependent upon the resolution of the diffraction data, which can be categorized as: low, medium, high and atomic. [3] For example, visible light has a wavelength of about 4000 to 7000 ångström, which is three orders of magnitude longer than the length of typical atomic bonds and atoms themselves (about 1 to 2 Å). Therefore, a conventional optical microscope cannot resolve the spatial arrangement of atoms in a crystal. To do so, we would need radiation with much shorter wavelengths, such as X-ray or neutron beams.

Unfortunately, focusing X-rays with conventional optical lens can be a challenge. Scientists have had some success focusing X-rays with microscopic Fresnel zone plates made from gold, and by critical-angle reflection inside long tapered capillaries. [4] Diffracted X-ray or neutron beams cannot be focused to produce images, so the sample structure must be reconstructed from the diffraction pattern.

Diffraction patterns arise from the constructive interference of incident radiation (x-rays, electrons, neutrons), scattered by the periodic, repeating features of the sample. Because of their highly ordered and repetitive atomic structure (Bravais lattice), crystals diffract x-rays in a coherent manner, also referred to as Bragg's reflection.

Notation

Techniques

Some materials that have been analyzed crystallographically, such as proteins, do not occur naturally as crystals. Typically, such molecules are placed in solution and allowed to slowly crystallize through vapor diffusion. A drop of solution containing the molecule, buffer, and precipitants is sealed in a container with a reservoir containing a hygroscopic solution. Water in the drop diffuses to the reservoir, slowly increasing the concentration and allowing a crystal to form. If the concentration were to rise more quickly, the molecule would simply precipitate out of solution, resulting in disorderly granules rather than an orderly and usable crystal.

Once a crystal is obtained, data can be collected using a beam of radiation. Although many universities that engage in crystallographic research have their own X-ray producing equipment, synchrotrons are often used as X-ray sources, because of the purer and more complete patterns such sources can generate. Synchrotron sources also have a much higher intensity of X-ray beams, so data collection takes a fraction of the time normally necessary at weaker sources. Complementary neutron crystallography techniques are used to identify the positions of hydrogen atoms, since X-rays only interact very weakly with light elements such as hydrogen.

Producing an image from a diffraction pattern requires sophisticated mathematics and often an iterative process of modelling and refinement. In this process, the mathematically predicted diffraction patterns of a hypothesized or "model" structure are compared to the actual pattern generated by the crystalline sample. Ideally, researchers make several initial guesses, which through refinement all converge on the same answer. Models are refined until their predicted patterns match to as great a degree as can be achieved without radical revision of the model. This is a painstaking process, made much easier today by computers.

The mathematical methods for the analysis of diffraction data only apply to patterns, which in turn result only when waves diffract from orderly arrays. Hence crystallography applies for the most part only to crystals, or to molecules which can be coaxed to crystallize for the sake of measurement. In spite of this, a certain amount of molecular information can be deduced from patterns that are generated by fibers and powders, which while not as perfect as a solid crystal, may exhibit a degree of order. This level of order can be sufficient to deduce the structure of simple molecules, or to determine the coarse features of more complicated molecules. For example, the double-helical structure of DNA was deduced from an X-ray diffraction pattern that had been generated by a fibrous sample.

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 takes diffraction patterns of polycrystalline samples with a large number of crystals, plays 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.

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. [5] 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. In fact, 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. [6] 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 crystallography has been used to determine some protein structures, most notably membrane proteins and viral capsids.

Contribution of women to X-ray crystallography

A number of women were pioneers in X-ray crystallography at a time when they were excluded from most other branches of physical science. [7]

Kathleen Lonsdale was a research student of William Henry Bragg, who with his son Lawrence founded the science of X-ray crystallography at the beginning of the 20th century. She is known for both her experimental and theoretical work. Bragg had 11 women research students out of a total of 18. Kathleen joined his crystallography research team at the Royal Institution in London in 1923, and after getting married and having children, went back to work with Bragg as a researcher. She confirmed the structure of the benzene ring, carried out studies of diamond, was one of the first two women to be elected to the Royal Society in 1945, and in 1949 was appointed the first female tenured professor of chemistry and head of the Department of crystallography at University College London. [8] Kathleen always advocated greater participation of women in science and said in 1970: "Any country that wants to make full use of all its potential scientists and technologists could do so, but it must not expect to get the women quite so simply as it gets the men. ... It is utopian, then, to suggest that any country that really wants married women to return to a scientific career, when her children no longer need her physical presence, should make special arrangements to encourage her to do so?". [9] During this period, Kathleen began a collaboration with William T. Astbury on a set of 230 space group tables which was published in 1924 and became an essential tool for crystallographers.

Molecular model of penicillin by Dorothy Hodgkin, 1945 Molecular model of Penicillin by Dorothy Hodgkin (9663803982).jpg
Molecular model of penicillin by Dorothy Hodgkin, 1945

In 1932 Dorothy Hodgkin joined the laboratory of the physicist John Desmond Bernal, who was a former student of Bragg, in Cambridge, UK. She and Bernal took the first X-ray photographs of crystalline proteins. Hodgkin also played a role in the foundation of the International Union of Crystallography. She was awarded the Nobel Prize in Chemistry in 1964 for her work using X-ray techniques to study the structures of penicillin, insulin and vitamin B12. Her work on penicillin began in 1942 during the war and on vitamin B12 in 1948. While her group slowly grew, their predominant focus was on the X-ray analysis of natural products. She is the only British woman ever to have won a Nobel Prize in a science subject.

Photograph of DNA (photo 51), Rosalind Franklin, 1952 Fig-1-X-ray-chrystallography-of-DNA.gif
Photograph of DNA (photo 51), Rosalind Franklin, 1952

Rosalind Franklin took the X-ray photograph of a DNA fibre that proved key to James Watson and Francis Crick's discovery of the double helix, for which they both won the Nobel Prize for Physiology or Medicine in 1962. Watson revealed in his autobiographic account of the discovery of the structure of DNA, The Double Helix, [10] that he had used Rosalind's X-ray photograph without her permission. Franklin died of cancer in her 30s, before Watson received the Nobel Prize. Franklin also carried out important structural studies of carbon in coal and graphite, and of plant and animal viruses.

Isabella Karle of the United States Naval Research Laboratory developed an experimental approach to the mathematical theory of crystallography. Her work improved the speed and accuracy of chemical and biomedical analysis. Yet only her husband Jerome shared the 1985 Nobel Prize in Chemistry with Herbert Hauptman, "for outstanding achievements in the development of direct methods for the determination of crystal structures". Other prize-giving bodies have showered Isabella with awards in her own right.

Women have written many textbooks and research papers in the field of X-ray crystallography. For many years Lonsdale edited the International Tables for Crystallography, which provide information on crystal lattices, symmetry, and space groups, as well as mathematical, physical and chemical data on structures. Olga Kennard of the University of Cambridge, founded and ran the Cambridge Crystallographic Data Centre, an internationally recognized source of structural data on small molecules, from 1965 until 1997. Jenny Pickworth Glusker, a British scientist, co-authored Crystal Structure Analysis: A Primer, [11] first published in 1971 and as of 2010 in its third edition. Eleanor Dodson, an Australian-born biologist, who began as Dorothy Hodgkin's technician, was the main instigator behind CCP4, the collaborative computing project that currently shares more than 250 software tools with protein crystallographers worldwide.

Reference literature

The International Tables for Crystallography [12] 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 determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various 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 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 that repeat along the principal directions of three-dimensional space in matter.

In X-ray crystallography, wide-angle X-ray scattering (WAXS) or wide-angle X-ray diffraction (WAXD) is the analysis of Bragg peaks scattered to wide angles, which are caused by sub-nanometer-sized structures. It is an X-ray-diffraction method and commonly used to determine a range of information about crystalline materials. The term WAXS is commonly used in polymer sciences to differentiate it from SAXS but many scientists doing "WAXS" would describe the measurements as Bragg/X-ray/powder diffraction or crystallography.

<span class="mw-page-title-main">Electron diffraction</span> Bending of electron beams around atomic structures

Electron diffraction refers to the bending of electron beams around atomic structures. This behaviour, typical for waves, is applicable to electrons due to the wave–particle duality stating that electrons behave as both particles and waves. Since the diffracted beams interfere, they generate diffraction patterns widely used for analysis of the objects which caused the diffraction. Therefore, electron diffraction can also refer to derived experimental techniques used for material characterization. This technique is similar to X-ray and neutron diffraction.

<span class="mw-page-title-main">Neutron diffraction</span> Imaging technique 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 physics and chemistry, Bragg's law, 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 superposition of wave fronts scattered by lattice planes, leading to a strict relation between wavelength and scattering angle, or else to the wavevector transfer with respect to the crystal lattice. Such law had initially been formulated for X-rays upon crystals. However, It applies to all sorts of quantum beams, including neutron and electron waves at atomic distances, as well as visible light at artificial periodic microscale lattices.

<span class="mw-page-title-main">Chemical structure</span> Organized way in which molecules are ordered and sorted

A chemical structure determination includes a chemist's specifying the molecular geometry and, when feasible and necessary, the electronic structure of the target molecule or other solid. Molecular geometry refers to the spatial arrangement of atoms in a molecule and the chemical bonds that hold the atoms together, and can be represented using structural formulae and by molecular models; complete electronic structure descriptions include specifying the occupation of a molecule's molecular orbitals. Structure determination can be applied to a range of targets from very simple molecules, to very complex ones.

In physics, the phase problem is the problem of loss of information concerning the phase that can occur when making a physical measurement. The name comes from the field of X-ray crystallography, where the phase problem has to be solved for the determination of a structure from diffraction data. The phase problem is also met in the fields of imaging and signal processing. Various approaches of phase retrieval have been developed over the years.

<span class="mw-page-title-main">Electron backscatter diffraction</span>

Electron backscatter diffraction (EBSD) is a scanning electron microscope–based microstructural-crystallographic characterization technique commonly used in the study of crystalline or polycrystalline materials. The technique can provide information about the structure, crystal orientation, phase, or strain in the material.

Electron crystallography is a method to determine the arrangement of atoms in solids using a transmission electron microscope (TEM).

<span class="mw-page-title-main">Powder diffraction</span>

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>

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">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 reflexions 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">Magnetic structure</span>

The term magnetic structure of a material pertains to the ordered arrangement of magnetic spins, typically within an ordered crystallographic lattice. Its study is a branch of solid-state physics.

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>

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.

This is a timeline of crystallography.

References

  1. UN announcement "International Year of Crystallography". iycr2014.org. 12 July 2012
  2. "The Evolution of the Goniometer". Nature. 95 (2386): 564–565. 1915-07-01. Bibcode:1915Natur..95..564.. doi: 10.1038/095564a0 . ISSN   1476-4687.
  3. Wlodawer, Alexander; Minor, Wladek; Dauter, Zbigniew; Jaskolski, Mariusz (January 2008). "Protein crystallography for non-crystallographers, or how to get the best (but not more) from published macromolecular structures". The FEBS Journal. 275 (1): 1–21. doi:10.1111/j.1742-4658.2007.06178.x. ISSN   1742-464X. PMC   4465431 . PMID   18034855.
  4. Snigirev, A. (2007). "Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary". Journal of Synchrotron Radiation. 14 (Pt 4): 326–330. doi:10.1107/S0909049507025174. PMID   17587657.
  5. "Materials Science and Engineering: An Introduction, 10th Edition | Wiley". Wiley.com. Retrieved 2022-09-10.
  6. 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.
  7. Kahr, Bart (2015). "Broader Impacts of Women in Crystallography". Crystal Growth & Design. 15 (10): 4715–4730. doi:10.1021/acs.cgd.5b00457. ISSN   1528-7483.
  8. Ferry, Georgina (2014). "History: Women in crystallography". Nature. 505 (7485): 609–611. Bibcode:2014Natur.505..609F. doi: 10.1038/505609a . ISSN   1476-4687. PMID   24482834.
  9. Sanz-Aparicio, Julia (2015). "Vista de El legado de las mujeres a la cristalografía | Arbor". Arbor. 191 (772): a216. doi:10.3989/arbor.2015.772n2002. Archived from the original on 2015-09-07.
  10. Watson, James D. (2000), Discovering the double helix, Cold Spring Harbor Laboratory, ISBN   978-0-87969-622-1, OCLC   48554849
  11. Glusker, Jenny Pickworth; Trueblood, Kenneth N; International Union of Crystallography (2020). Crystal structure analysis: a primer. ISBN   978-0-19-191790-5. OCLC   1241842166.
  12. 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.