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A line defect in a crystal structure. Its Burgers vector measures the closure failure of a circuit around the line. Motion can produce permanent plasticity without simultaneously breaking every bond across a whole plane.

Edgar Bain was an American materials scientist who studied transformations in steel. His 1924 paper The Nature of Martensite by Edgar Bain examined how the structure of martensite relates to its parent austenite, connecting the mechanical behaviour of hardened steel with changes in crystal structure.^[ref]

The Bain path expresses a geometric connection between face-centered cubic and body-centred cubic structures through a tetragonal deformation. It helps make a structural transformation concrete: changing the relative lengths along different axes can map one lattice geometry to another. Such a geometric path by itself does not specify the complete chemical kinetics or every observed feature of a transformation in real steel; those also depend on chemical composition and microstructural constraints.

Elies Molins investigated the crystal structure of an iron complex with two hydropentalenyl ligands. The structural study provides a concrete example of multihapto coordination, in which several contiguous ligand atoms interact with the same metal centre.^[ref]

E. R. Vance coauthored research on the crystal chemistry and phase control of Synroc. The scientific problem is to distribute waste elements among stable ceramic phases with suitable crystal sites.

Changing the overall composition can change which phases form and which ions each phase incorporates. This links phase equilibrium and crystal structure to the chemical durability of a waste form.^[ref]

Feldspar is a group of framework silicate minerals important in planetary crust. Common ideal endmembers include albite, $\mathrm{NaAlS}{\mathrm{i}}_3{\mathrm{O}}_8$, and calcium- and potassium-bearing compositions. Coupled substitutions preserve electrical charge while changing elemental proportions, so a natural feldspar need not have one composition shared by every specimen.

Plagioclase denotes the sodium-calcium solid-solution series. Composition and crystal structure influence a rock's physical properties and the interpretation of mineral observations. In chemical equilibrium calculations, an endmember formula is a useful component definition; it should not automatically be substituted for the full composition of a natural mixed crystal.

An $A{B}_2$ crystal structure with A on a face-centered cubic lattice and B occupying all eight tetrahedral sites of its conventional cubic unit cell. The coordination numbers are eight for A and four for B. The cubic cell contains four $A{B}_2$ formula units.

A fractional crystallographic coordinate is one of the dimensionless coefficients expressing a position in the basis of specified unit cell vectors:The three coefficients are also called fractional crystal coordinates. Reporting them requires specifying the cell vectors and origin. The core CIF coordinate items store these fractions rather than Cartesian lengths.^[ref]

For an original orthorhombic example, let the mutually perpendicular cell edges have lengths4,6 and8 angstroms. The fractional position $(1/4,1/2,1/8)$ has Cartesian coordinates $(1,3,1)$ angstroms. Adding an integer to one fractional coordinate selects the corresponding translated position in another cell; it does not change the motif's location relative to the repeating cell.

For an oblique cell, multiplying the fractions by edge lengths is insufficient to obtain Cartesian components. In a two-dimensional example, take $\mathbf{a}=(2,0)$ and $\mathbf{b}=(1,\sqrt{3})$ angstroms. The fractional position $(1/2,1/2)$ isThe crystallographic metric matrix $G_{ij}={\mathbf{a}}_i\cdot {\mathbf{a}}_j$ records the necessary lengths and angles. A displacement with fractional column vector $\mathbf{u}$ has squared length ${\mathbf{u}}^{T}G\mathbf{u}$. Applying the ordinary Cartesian distance formula directly to the fractions would discard the geometry of the crystal structure.

Fractional crystal coordinates are the dimensionless coefficients in $r=u{a}_1+v{a}_2+w{a}_3$ for specified unit cell vectors. They are not Cartesian lengths unless the vectors themselves are included. With primitive vectors, replacing $u,v,w$ by values differing by integers selects an equivalent position in another unit cell.

In the two-dimensional example under crystal structure, B has position $(0.65,0.55)$ in ordinary length coordinates, but fractional crystal coordinates $(0.65/2,0.55/1.5)=(13/40,11/30)$. Multiplying these coefficients by the two translation vectors recovers the drawn position. Reporting the axes is therefore part of reporting a structure.

Gadolinium antimonide is the binary compound $\mathrm{GdSb}$, with a rock-salt-related crystal structure. Its low-temperature antiferromagnetism and electronic transport make it useful for studying the relation between magnetic order and electronic bands.

Epitaxial thin films allow strain and thickness to be varied while measuring transport or photoemission. This separates changes caused by the host composition from those produced by its crystalline environment.^[ref]

A heavy-atom derivative is a modified crystal containing ordered heavy-atom sites that can provide a reference scattering contribution for X-ray crystallography. The crystal before modification is called native. For single isomorphous replacement or multiple isomorphous replacement, the desired crystal isomorphism means that the parent crystal structure is sufficiently preserved for its contribution to be shared between data sets. Merely detecting the added chemical element does not establish that model.

The early myoglobin work provides an experimental example. Several crystals with mercury or gold at single sites on the protein were compared with unsubstituted crystals to infer phases. These are chemically modified reference specimens, not computational substitute structures.^[ref]

Crystallographic site occupancy describes the fraction present at a modeled site. The IUCr heavy-atom dictionary defines an occupancy separately for each site and derivative.^[ref] In a simplified single-site model with fixed position and displacement behavior, let $A_H$ be the full-occupancy complex amplitude and let $q$ be occupancy. ThenFor an original illustrative reflection, choose $F_P=4+3i$ and $A_H=6$. With $q=1/2$, the derivative amplitude is $7+3i$ and its squared magnitude is58. At full occupancy it is $10+3i$ and its squared magnitude is109. The native squared magnitude is25. Thus doubling occupancy doubles this modeled heavy-atom amplitude, but does not generally double the measured intensity change: interference with the parent contribution matters.

Useful derivative assessment therefore concerns ordered scattering and comparability as well as chemical uptake. If modification changes the parent structure substantially, the assumed decomposition into unchanged parent plus added reference is inadequate. Heavy-atom labeling describes the motivation for introducing the reference; a heavy-atom derivative is the resulting experimental specimen.

Homoepitaxy is epitaxy in which the deposited crystalline material is the same material as its crystalline substrate. Growing silicon on a silicon wafer is a standard example. The substrate supplies an orientation template, allowing the new layer to continue the crystal's ordering.

Using the same material does not require identical impurity concentrations or electrical properties. Controlled semiconductor doping can create a layer with a different carrier concentration while retaining the same host crystal structure. Surface preparation, contamination and growth conditions still control defects and interfaces. Homoepitaxy is therefore useful for separating control of crystalline orientation from control of a device layer's composition and electronic behaviour.

Ice is solid water. Ordinary terrestrial ice has an open hydrogen-bonded crystal structure and a lower density than liquid water near the melting point.

Different pressure-temperature conditions stabilize different ice structures. Consequently, the word ice identifies a chemical substance and phase family without uniquely specifying its crystal structure.

An interstitial defect is an atom occupying a position between the regular atomic positions in a crystal structure. Small solute atoms or an extra host atom can occupy such positions. Different interstitial orientations can induce anisotropic local strain; an applied stress changes their relative energies. Thermally activated hopping among those positions can then produce delayed elastic strain and the Snoek effect.

An isotropic atomic displacement parameter describes the same mean-square positional displacement along every Cartesian direction in a crystal structure. Its Cartesian displacement covariance matrix isThus $U_{\mathrm{iso}}$ is a one-component variance, in squared angstroms, rather than a displacement length. The alternate conventional parameter is $B=8{\pi }^2{U}_{\mathrm{iso}}$.^[ref]

For an original example, $U_{\mathrm{iso}}=0.020{\mathring{\mathrm{A}}}^2$ givesThe radial root-mean-square displacement is instead $\sqrt{3U_{\mathrm{iso}}}\simeq 0.245\mathring{\mathrm{A}}$ because it includes three components.

For a centered isotropic normal distribution, the structure factor amplitude attenuation at reciprocal-vector magnitude $s$, measured in cycles per angstrom, isAt $s=1{\mathring{\mathrm{A}}}^{-1}$, the stated example gives $T\simeq 0.674$ and squared-amplitude attenuation $T^2\simeq 0.454$. Amplitude and intensity attenuation are therefore distinct, even in this simple Gaussian model.

An equivalent isotropic atomic displacement parameter can also summarize an anisotropic atomic displacement parameter by its Cartesian trace divided by3. Such an average can appear in the same CIF field as a genuinely isotropic parameter, but does not assert equal directional spread.^[ref]

J. A. Huntington is the first author of a 2000 structural study explaining how an inhibitory serpin can trap and deform a protease. The team determined a crystal structure of the joined serpin–protease complex, connecting a large conformational change to loss of catalytic function.^[ref]

Attack on the reactive-center loop was associated with movement of the tethered region about $71\mathring{\mathrm{A}}$ across the serpin. The attached protease was distorted, including disruption of its active site.^[ref]

This gives a physical explanation for inhibition beyond simple obstruction of an active site. The protein scaffold changes shape after attack and carries the reacting partner into an unfavourable arrangement. The structural result identifies the trapped arrangement; the detailed time course of the moving complex remains a separate experimental question.

John C. Dewan coauthored research on crystal structure.^[ref]

A crystal structure specifies the chemical species and spatial arrangement of the chemical atoms or ions in a crystal. For an ideal periodic structure, separate two ingredients: a Bravais lattice specifies the translations that repeat the arrangement, and an atomic basis of a crystal specifies the chemical motif repeated at every lattice point. The outward shape, or crystal habit, is a different description: the internal arrangement is what this article describes.

John C. Huffman coauthored research on crystal structure.^[ref]

A crystal structure specifies the chemical species and spatial arrangement of the chemical atoms or ions in a crystal. For an ideal periodic structure, separate two ingredients: a Bravais lattice specifies the translations that repeat the arrangement, and an atomic basis of a crystal specifies the chemical motif repeated at every lattice point. The outward shape, or crystal habit, is a different description: the internal arrangement is what this article describes.

John G. Kester coauthored research on crystal structure.^[ref]

A crystal structure specifies the chemical species and spatial arrangement of the chemical atoms or ions in a crystal. For an ideal periodic structure, separate two ingredients: a Bravais lattice specifies the translations that repeat the arrangement, and an atomic basis of a crystal specifies the chemical motif repeated at every lattice point. The outward shape, or crystal habit, is a different description: the internal arrangement is what this article describes.

John L. Little coauthored research on crystal structure.^[ref]

A crystal structure specifies the chemical species and spatial arrangement of the chemical atoms or ions in a crystal. For an ideal periodic structure, separate two ingredients: a Bravais lattice specifies the translations that repeat the arrangement, and an atomic basis of a crystal specifies the chemical motif repeated at every lattice point. The outward shape, or crystal habit, is a different description: the internal arrangement is what this article describes.

Josephine Paw Blaha coauthored research on crystal structure.^[ref]

A crystal structure specifies the chemical species and spatial arrangement of the chemical atoms or ions in a crystal. For an ideal periodic structure, separate two ingredients: a Bravais lattice specifies the translations that repeat the arrangement, and an atomic basis of a crystal specifies the chemical motif repeated at every lattice point. The outward shape, or crystal habit, is a different description: the internal arrangement is what this article describes.

Karolin Luger coauthored research on crystal structure.^[ref]

A crystal structure specifies the chemical species and spatial arrangement of the chemical atoms or ions in a crystal. For an ideal periodic structure, separate two ingredients: a Bravais lattice specifies the translations that repeat the arrangement, and an atomic basis of a crystal specifies the chemical motif repeated at every lattice point. The outward shape, or crystal habit, is a different description: the internal arrangement is what this article describes.