January_AMP_Digital

A D V A N C E D M A T E R I A L S & P R O C E S S E S | J A N U A R Y 2 0 2 0 3 2 (b) (a) SINGLE-CRYSTAL X-RAY DIFFRACTION This excerpt from ASM Handbook, Volume 10: Materials Characterization describes the technique used to determine crystal structure and the arrangement of atoms in a unit cell. Vladislav V. Gurzhiy, St. Petersburg State University, Russia T he main application of single- crystal x-ray diffraction (XRD) is characterizing crystal structures, including determining symmetry, unit cell parameters, atomic coordinates and thermal displacement parameters, bond lengths and angles between the atoms, and structural motive (or topol- ogy). During the structure description process it is possible to refine such crys- tallographic characteristics as order or disorder of cations (anions), site occu- pancy factors, and possible sub- or su- perstructures. The results of crystal structure analysis can become the ba- sis for broader conclusions. Thus, de- termination of crystal structure is quite essential to understanding the forma- tion conditions of crystalline substanc- es. For instance, compounds of the same chemical composition can exist in various polymorph modifications, which directly correlates with the ther- modynamic parameters of their gene- sis. Another example is nondestructive determination of the crystal phase us- ing the values of the unit cell parame- ters, which is very useful for the jewelry industry. Modern x-ray analysis has be- come a powerful tool for studying the structure of substances, revealing many interesting facts and allowing a new look at a number of natural phenomena. The total number of sol- ved structures to date exceeds 1.1 mil- lion (more than 900,000 structures are deposited in the Cambridge Structur- al Database, a repository for small- molecule organic and metal-organic crystal structures; and about 200,000 structures are deposited in the In- organic Crystal Structure Database), and annually more than 60,000 novel natural and synthetic compounds are structurally characterized. Due to im- proved techniques, automated equip- ment, and computing facilities, it is possible to determine the structures of very complex crystals, such as proteins, which contain hundreds or even thousands of atoms. Pressures exceeding millions of times greater than atmospheric are attained within special x-ray chambers, which makes it possible to model and study the state of matter in the deep shells of the Earth. Structural analysis makes proba- bly the most significant contribution to the mineralogy and materials sciences, where XRD methods play a key role in studying the composition and structure of substances, expanding scientific concepts of the taxonomy, forms, and concentration of chemical elements in the geosphere as well as isomorphism, polymorphism, and many other crystal chemical phenomena in natural and synthetic compounds. CRYSTAL SYMMETRY The crystalline state of a sub- stance is characterized by the three- dimensional periodicity of atomic and molecular arrangement. This feature underlies the diffraction of x-rays passed through the crystal and hence is the basis of the XRD structural analysis of crystals. The periodic repeatability of identical atomic groups (in other words, the translational symmetry in their arrangement) is an obligatory property of any crystal. But atoms in a crystal can be connected not only by translations but also by other symmetry operations, whose presence also affects the diffraction pattern and therefore must be taken into account during crystal structure determination. Within symmetry theory, a lattice is a group of translations, where nodes Fig. 1 — (a) General case of a unit cell selection within the system of crystallographic axes. (b) Indexation of the nodal rows (blue arrows) and nets (green double lines). The graph shows reflections for the [010], [120], and [110] directions.