Crystallography is the branch of science devoted to the study of molecular andcrystalline structure and properties.[1] The wordcrystallography is derived from theAncient Greek wordκρύσταλλος (krústallos; "clear ice, rock-crystal"), andγράφειν (gráphein; "to write").[2] In July 2012, theUnited Nations recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography.[3]
Crystallography is a broad topic, and many of its subareas, such asX-ray crystallography, are themselves important scientific topics. Crystallography ranges from the fundamentals ofcrystal structure to the mathematics ofcrystal geometry, including those that arenot periodic orquasicrystals. At the atomic scale it can involve the use ofX-ray diffraction to produce experimental data that the tools ofX-ray crystallography can convert into detailed positions of atoms, and sometimes electron density. At larger scales it includes experimental tools such asorientational imaging to examine the relative orientations at thegrain boundary in materials. Crystallography plays a key role in many areas of biology, chemistry, and physics, as well as in emerging developments in these fields.[4]
Before the 20th century, the study ofcrystals was based on physical measurements of their geometry using agoniometer.[5] This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing thesymmetry of the crystal in question. The position in 3D space of each crystal face is plotted on astereographic net such as aWulff net orLambert net. Thepole to each face is plotted on the net. Each point is labelled with itsMiller index. The final plot allows the symmetry of the crystal to be established.[6][7]
The discovery ofX-rays andelectrons 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 byMax von Laue,[8] while electron diffraction was first realized in 1927 in theDavisson–Germer experiment[9] and parallel work byGeorge Paget Thomson and Alexander Reid.[10] These developed into the two main branches of crystallography,X-ray crystallography andelectron 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 andphasing algorithms. Nowadays, crystallography is aninterdisciplinary field, supporting theoretical and experimental discoveries in various domains.[11] Modern-day scientific instruments for crystallography vary from laboratory-sized equipment, such asdiffractometers andelectron microscopes, to dedicated large facilities, such asphotoinjectors,synchrotron light sources andfree-electron lasers.
Crystallographic methods depend mainly on analysis of thediffraction patterns of a sample targeted by a beam of some type.X-rays are most commonly used; other beams used includeelectrons orneutrons. Crystallographers often explicitly state the type of beam used, as in the termsX-ray diffraction,neutron diffraction andelectron diffraction. These three types of radiation interact with the specimen in different ways.
Neutrons are scattered by the atomic nuclei through thestrong nuclear forces, but in addition themagnetic moment of neutrons is non-zero, so they are also scattered bymagnetic fields. When neutrons are scattered fromhydrogen-containing materials, they produce diffraction patterns with high noise levels, which can sometimes be resolved by substitutingdeuterium for hydrogen.[13]
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 understandingcrystallographic 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 inclay 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 crystallographictexture 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 abody-centered cubic (bcc) structure calledferrite to aface-centered cubic (fcc) structure calledaustenite when it is heated.[15] 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 togroup theory.
X-ray crystallography is the primary method for determining the molecular conformations of biologicalmacromolecules, particularlyprotein andnucleic acids such asDNA andRNA. The first crystal structure of a macromolecule was solved in 1958, a three-dimensional model of the myoglobin molecule obtained by X-ray analysis.[16]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.[17]Electron diffraction has been used to determine some protein structures, most notablymembrane proteins andviral capsids.
Macromolecular structures determined through X-ray crystallography (and other techniques) are housed in theProtein Data Bank (PDB)–a freely accessible repository for the structures of proteins and other biological macromolecules.[18] There are manymolecular graphics codes available for visualising these structures.
Coordinates insquarebrackets such as[100] denote a direction vector (in real space).
Coordinates inangle brackets orchevrons such as<100> denote afamily of directions which are related by symmetry operations. In the cubiccrystal system for example,<100> would mean [100], [010], [001] or the negative of any of those directions.
Miller indices inparentheses such as(100) denote a plane of the crystal structure, and regular repetitions of that plane with a particular spacing. In the cubic system, thenormal to the (hkl) plane is the direction [hkl], but in lower-symmetry cases, the normal to (hkl) is not parallel to [hkl].
Indices incurly brackets orbraces such as{100} denote a family of planes and their normals. In cubic materials the symmetry makes them equivalent, just as the way angle brackets denote a family of directions. In non-cubic materials, <hkl> is not necessarily perpendicular to {hkl}.
TheInternational Tables for Crystallography[19] 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.
^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.
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