The order of a reaction is empirically observed and determined by the sum of the powers of the concentrations of the rate equation. If the rate of a reaction, R, is proportional to the concentration of one species, R = k[A], where k = constant and [A] = concentration of species A, then this is a first-order reaction. A second-order reaction may have a rate equation of R = k[A][B] for two reactants, A and B, and the powers of each sum to 1 + 1 = 2. Sometimes, the rate determining step can be deduced from knowing the reaction order of a series of reactions.

The reciprocal lattice, first constructed by P. Ewald, involves a set of points, each of which represents a set of planes in space, 1/d from the origin. The value of d is the spacing between a set of planes in a unit cell. This lattice is useful to better visualize a diffraction pattern and its geometric relationship to the unit cell of the crystal under study. The relationship is obtained from the modified Bragg equation (1/d_hkl = 2sinθ/λ), which is the condition where a possible X-ray reflection can occur. Thus, the point located at 1/d represents the cross-section of the pole of this set of planes, hkl, and corresponds to a possible X-ray reflection from the crystal. The unit cell as determined by the reciprocal lattice (referred to as the “reciprocal unit cell”), by construction, is defined in relation to the unit cell of the atomic structure (referred to as a the “direct cell” or “real cell”) of the crystal under study: a* is perpendicular to the plane containing b and c, b* is perpendicular to the plane containing a and c, and c* is perpendicular to the plane containing a and b, where the * (referred to as “star”, as in “a star”, “b star”, etc.) indicates a reciprocal lattice measurement.
Cf., crystallographic axis, Bragg’s law

a) Senso stricto. solid-state transformation(s) of crystalline material to another crystalline material. In this process, larger, more defect-free grains result than the predecessor grains. Although the bulk composition does not change, the resultant assemblage may be of the same mineralogy or different (e.g., polymorphs) mineralogy. In rocks, this is a mechanism by which plastic deformation can ultimately produce, via recrystallization, an assemblage of strain-free grains. It is unclear if recrystallization is truly “solid state” because the process may involve the formation in inter-granular fluid films. A “secondary recrystallization” also can result where there is an increase in particle size of grains by subsuming neighbors. It is unlikely that clay minerals transform in this manner; low-temperature transformations involving clays usually require the presence of water.

b) Senso lato. Conversion of pre-existing chemical and mineralogical composition (either crystalline, poorly crystalline, or amorphous) either to new crystalline material of the same mineralogy or to a new phase assemblage, commonly involving limited amounts of aqueous fluids. For clays, the crystal-surface energy to crystal volume is reduced to drive recrystallization, even at low temperatures.
See Ostwald ripening

A regular interstratification of dioctahedral mica-like layers and dioctahedral smectite-like layers in a ratio of 1:1 (Brown and Weir, 1963). The structure may be described more completely as pairs of dioctahedral 2:1 layers with alternate interlayers that are mica-like and montmorillonite-like. Mica-like layers may be paragonite-like and the smectite-like layers may be beidellitic. The non-swelling mica interlayers contain about 0.85 univalent cations per mica formula unit and the swelling interlayers about 0.35 univalent cations (e.g., Na, K, but divalent Ca is known also) per smectite formula unit (Bailey, 1982). In the older literature, the name “allevardite” has been used (Bailey, 1982), but the term rectorite has priority.

See hollandite.

See unit cell.

an albite-like mineral with B in the tetrahedral site, Na(Si3B)O8. Cf., alkali feldspar, feldspar, plagioclase feldspar

An albite-like mineral with B in the tetrahedral site, Na(Si₃B)O₈.
Cf., alkali feldspar, feldspar, plagioclase feldspar

See hydrotalcite group.

See mirror plane.