Кристалл құрылымын және минералдарды анықтау әдісі

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. X ray crystallography has been fundamental in the development of many scientific fields. In its first decades of use, this method determined the size of atoms, the lengths and types of chemical bonds, and the atomic scale differences between various materials, especially minerals and alloys. The method has also revealed the structure and function of many biological molecules, including vitamins, drugs, proteins and nucleic acids such as DNA. X ray crystallography is still the primary method for characterizing the atomic structure of materials and in differentiating materials that appear similar in other experiments. X ray crystal structures can also help explain unusual electronic or elastic properties of a material, shed light on chemical interactions and processes, or serve as the basis for designing pharmaceuticals against diseases. Modern work involves a number of steps all of which are important. The preliminary steps include preparing good quality samples, careful recording of the diffracted intensities, and processing of the data to remove artifacts. A variety of different methods are then used to obtain an estimate of the atomic structure, generically called direct methods. With an initial estimate further computational techniques such as those involving difference maps are used to complete the structure. The final step is a numerical refinement of the atomic positions against the experimental data, sometimes assisted by ab initio calculations. In almost all cases new structures are deposited in databases available to the international community.

Crystals, though long admired for their regularity and symmetry, were not investigated scientifically until the 17th century. Johannes Kepler hypothesized in his work Strena seu de Nive Sexangula (A New Year's Gift of Hexagonal Snow) (1611) that the hexagonal symmetry of snowflake crystals was due to a regular packing of spherical water particles. The Danish scientist Nicolas Steno (1669) pioneered experimental investigations of crystal symmetry. Steno showed that the angles between the faces are the same in every exemplar of a particular type of crystal. René Just Haüy (1784) discovered that every face of a crystal can be described by simple stacking patterns of blocks of the same shape and size. Hence, William Hallowes Miller in 1839 was able to give each face a unique label of three small integers, the Miller indices which remain in use for identifying crystal faces. Haüy's study led to the idea that crystals are a regular three dimensional array (a Bravais lattice) of atoms and molecules; a single unit cell is repeated indefinitely along three principal directions. In the 19th century, a complete catalog of the possible symmetries of a crystal was worked out by Johan Hessel, Auguste Bravais, Evgraf Fedorov, Arthur Schönflies and (belatedly) William Barlow (1894). Barlow proposed several crystal structures in the 1880s that were validated later by X ray crystallography; however, the available data were too scarce in the 1880s to accept his models as conclusive. Wilhelm Röntgen discovered X rays in 1895. Physicists were uncertain of the nature of X rays, but suspected that they were waves of electromagnetic radiation. The Maxwell theory of electromagnetic radiation was well accepted, and experiments by Charles Glover Barkla showed that X rays exhibited phenomena associated with electromagnetic waves, including transverse polarization and spectral lines akin to those observed in the visible wavelengths. Barkla created the x ray notation for sharp spectral lines, noting in 1909 two separate energies, at first naming them "A" and "B" and then supposing that there may be lines prior to "A", he started an alphabet numbering beginning with "K." Single slit experiments in the laboratory of Arnold Sommerfeld suggested that X rays had a wavelength of about 1 angstrom. X rays are not only waves but also have particle properties causing Sommerfeld to coin the name Bremsstrahlung for the continuous spectra when they were formed when electrons bombarded a material. but it was not broadly accepted until 1922, when Arthur Compton confirmed it by the scattering of X rays from electrons. The particle like properties of X rays, such as their ionization of gases, had prompted William Henry Bragg to argue in 1907 that X rays were not electromagnetic radiation. Bragg's view proved unpopular and the observation of X ray diffraction by Max von Laue in 1912 confirmed that X rays are a form of electromagnetic radiation. The idea that crystals could be used as a diffraction grating for X rays arose in 1912 in a conversation between Paul Peter Ewald and Max von Laue in the English Garden in Munich. Ewald had proposed a resonator model of crystals for his thesis, but this model could not be validated using visible light, since the wavelength was much larger than the spacing between the resonators. Von Laue realized that electromagnetic radiation of a shorter wavelength was needed, and suggested that X rays might have a wavelength comparable to the unit cell spacing in crystals. Von Laue worked with two technicians, Walter Friedrich and his assistant Paul Knipping, to shine a beam of X rays through a copper sulfate crystal and record its diffraction on a photographic plate. After being developed, the plate showed a large number of well defined spots arranged in a pattern of intersecting circles around the spot produced by the central beam. The results were presented to the Bavarian Academy of Sciences and Humanities in June 1912 as "Interferenz Erscheinungen bei Röntgenstrahlen" (Interference phenomena in X rays). Von Laue developed a law that connects the scattering angles and the size and orientation of the unit cell spacings in the crystal, for which he was awarded the Nobel Prize in Physics in 1914. After Von Laue's pioneering research, the field developed rapidly, most notably by physicists William Lawrence Bragg and his father William Henry Bragg. In 1912–1913, the younger Bragg developed Bragg's law, which connects the scattering with evenly spaced planes within a crystal. The Braggs, father and son, shared the 1915 Nobel Prize in Physics for their work in crystallography. The earliest structures were generally simple; as computational and experimental methods improved over the next decades, it became feasible to deduce reliable atomic positions for more complicated arrangements of atoms. The earliest structures were simple inorganic crystals and minerals, but even these revealed fundamental laws of physics and chemistry. The first atomic resolution structure to be "solved" (i. e., determined) in 1914 was that of table salt. The distribution of electrons in the table salt structure showed that crystals are not necessarily composed of covalently bonded molecules, and proved the existence of ionic compounds. The structure of diamond was solved in the same year, proving the tetrahedral arrangement of its chemical bonds and showing that the length of C–C single bond was about 1.52 angstroms. Other early structures included copper, calcium fluoride (CaF2, also known as fluorite), calcite (CaCO3) and pyrite (FeS2) in 1914; spinel (MgAl2O4) in 1915; the rutile and anatase forms of titanium dioxide (TiO2) in 1916; pyrochroite (Mn(OH)2) and, by extension, brucite (Mg(OH)2) in 1919. Also in 1919, sodium nitrate (NaNO3) and caesium dichloroiodide (CsICl2) were determined by Ralph Walter Graystone Wyckoff, and the wurtzite (hexagonal ZnS) structure was determined in 1920. The structure of graphite was solved in 1916 by the related method of powder diffraction, which was developed by Peter Debye and Paul Scherrer and, independently, by Albert Hull in 1917. The structure of graphite was determined from single crystal diffraction in 1924 by two groups independently. Hull also used the powder method to determine the structures of various metals, such as iron and magnesium.

X ray crystallography has led to a better understanding of chemical bonds and non covalent interactions. The initial studies revealed the typical radii of atoms, and confirmed many theoretical models of chemical bonding, such as the tetrahedral bonding of carbon in the diamond structure, and the resonance observed in the planar carbonate group established the hexagonal symmetry of benzene and showed a clear difference in bond length between the aliphatic C–C bonds and aromatic C–C bonds; this finding led to the idea of resonance between chemical bonds, which had profound consequences for the development of chemistry. Her conclusions were anticipated by William Henry Bragg, who published models of naphthalene and anthracene in 1921 based on other molecules, an early form of molecular replacement. The first structure of an organic compound, hexamethylenetetramine, was solved in 1923. This was rapidly followed by several studies of different long chain fatty acids, which are an important component of biological membranes. In the 1930s, the structures of much larger molecules with two dimensional complexity began to be solved. A significant advance was the structure of phthalocyanine, a large planar molecule that is closely related to porphyrin molecules important in biology, such as heme, corrin and chlorophyll. In the 1920s, Victor Moritz Goldschmidt and later Linus Pauling developed rules for eliminating chemically unlikely structures and for determining the relative sizes of atoms. These rules led to the structure of brookite (1928) and an understanding of the relative stability of the rutile, brookite and anatase forms of titanium dioxide. The distance between two bonded atoms is a sensitive measure of the bond strength and its bond order; thus, X ray crystallographic studies have led to the discovery of even more exotic types of bonding in inorganic chemistry, such as metal metal double bonds, metal metal quadruple bonds, and three center, two electron bonds. X ray crystallography—or, strictly speaking, an inelastic Compton scattering experiment—has also provided evidence for the partly covalent character of hydrogen bonds. In the field of organometallic chemistry, the X ray structure of ferrocene initiated scientific studies of sandwich compounds, while that of Zeise's salt stimulated research into "back bonding" and metal pi complexes. Finally, X ray crystallography had a pioneering role in the development of supramolecular chemistry, particularly in clarifying the structures of the crown ethers and the principles of host–guest chemistry.

Having obtained initial phases, an initial model can be built. The atomic positions in the model and their respective Debye Waller factors (or B factors, accounting for the thermal motion of the atom) can be refined to fit the observed diffraction data, ideally yielding a better set of phases. A new model can then be fit to the new electron density map and successive rounds of refinement are carried out. This iterative process continues until the correlation between the diffraction data and the model is maximized. The agreement is measured by an R factor defined as

where F is the structure factor. A similar quality criterion is Rfree, which is calculated from a subset (~10%) of reflections that were not included in the structure refinement. Both R factors depend on the resolution of the data. As a rule of thumb, Rfree should be approximately the resolution in angstroms divided by 10; thus, a data set with 2 Å resolution should yield a final Rfree ~ 0.2. Chemical bonding features such as stereochemistry, hydrogen bonding and distribution of bond lengths and angles are complementary measures of the model quality. In iterative model building, it is common to encounter phase bias or model bias: because phase estimations come from the model, each round of calculated map tends to show density wherever the model has density, regardless of whether there truly is a density. This problem can be mitigated by maximum likelihood weighting and checking using omit maps. It may not be possible to observe every atom in the asymmetric unit. In many cases, crystallographic disorder smears the electron density map. Weakly scattering atoms such as hydrogen are routinely invisible. It is also possible for a single atom to appear multiple times in an electron density map, e. g., if a protein sidechain has multiple (<4) allowed conformations. In still other cases, the crystallographer may detect that the covalent structure deduced for the molecule was incorrect, or changed. For example, proteins may be cleaved or undergo post translational modifications that were not detected prior to the crystallization.

A common challenge in refinement of crystal structures results from crystallographic disorder. Disorder can take many forms but in general involves the coexistence of two or more species or conformations. Failure to recognize disorder results in flawed interpretation. Pitfalls from improper modeling of disorder are illustrated by the discounted hypothesis of bond stretch isomerism. Disorder is modelled with respect to the relative population of the components, often only two, and their identity. In structures of large molecules and ions, solvent and counterions are often disordered.

The use of computational methods for the powder X ray diffraction data analysis is now generalized. It typically compares the experimental data to the simulated diffractogram of a model structure, taking into account the instrumental parameters, and refines the structural or microstructural parameters of the model using least squares based minimization algorithm. Most available tools allowing phase identification and structural refinement are based on the Rietveld method, some of them being open and free software such as FullProf Suite, Jana2006, MAUD, Rietan, GSAS, etc. while others are available under commercial licenses such as Diffrac. Suite TOPAS, Match!, etc. Most of these tools also allow Le Bail refinement (also referred to as profile matching), that is, refinement of the cell parameters based on the Bragg peaks positions and peak profiles, without taking into account the crystallographic structure by itself. More recent tools allow the refinement of both structural and microstructural data, such as the FAULTS program included in the FullProf Suite, which allows the refinement of structures with planar defects (e. g. stacking faults, twinnings, intergrowths).

Once the model of a molecule's structure has been finalized, it is often deposited in a crystallographic database such as the Cambridge Structural Database (for small molecules), the Inorganic Crystal Structure Database (ICSD) (for inorganic compounds) or the Protein Data Bank (for protein and sometimes nucleic acids). Many structures obtained in private commercial ventures to crystallize medicinally relevant proteins are not deposited in public crystallographic databases.

A number of women were pioneers in X ray crystallography at a time when they were excluded from most other branches of physical science. Kathleen Lonsdale was a research student of William Henry Bragg, who had 11 women research students out of a total of 18. She is known for both her experimental and theoretical work. Lonsdale 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. Lonsdale 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?". During this period, Lonsdale 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. 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. 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, that he had used Franklin'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, 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.

Year Laureate Prize Rationale1914Max von LauePhysics"For his discovery of the diffraction of X rays by crystals"1915William Henry BraggPhysics"For their services in the analysis of crystal structure by means of X rays"William Lawrence Bragg1962Max F. PerutzChemistry"for their studies of the structures of globular proteins"John C. Kendrew1962James Dewey WatsonMedicine"For their discoveries concerning the molecular structure of nucleic acids and its significance for information transfer in living material"Francis Harry Compton CrickMaurice Hugh Frederick Wilkins1964Dorothy HodgkinChemistry"For her determinations by X ray techniques of the structures of important biochemical substances"1972Stanford MooreChemistry"For their contribution to the understanding of the connection between chemical structure and catalytic activity of the active centre of the ribonuclease molecule"William H. Stein1976William N. LipscombChemistry"For his studies on the structure of boranes illuminating problems of chemical bonding"1985Jerome KarleChemistry"For their outstanding achievements in developing direct methods for the determination of crystal structures"Herbert A. Hauptman1988Johann DeisenhoferChemistry"For their determination of the three dimensional structure of a photosynthetic reaction centre"Hartmut MichelChemistryRobert HuberChemistry1997John E. WalkerChemistry"For their elucidation of the enzymatic mechanism underlying the synthesis of adenosine triphosphate (ATP)"2003Roderick MacKinnonChemistry"For discoveries concerning channels in cell membranes [ ] for structural and mechanistic studies of ion channels"2006Roger D. KornbergChemistry"For his studies of the molecular basis of eukaryotic transcription"2009Ada E. YonathChemistry"For studies of the structure and function of the ribosome"Thomas A. SteitzVenkatraman Ramakrishnan2012Brian KobilkaChemistry"For studies of G protein coupled receptors"