Glossary of Solid State Chemistry Terms

Excerpted from Solid State Chemistry of Drugs, 2nd Edition

Accelerated stability tests—A series of tests using high temperatures and/or humidities over the course of several months. These data are used to estimate the expiration date of the drug product.

Activation energy (Arrhenius activation energy)—A physicochemical quantity that represents the barrier for a chemical reaction.

Adjunct—A substance added to a drug formulation to improve its pharmaceutical performance.

Amorphous form—A solid that does not give a distinctive powder X-ray diffraction pattern. Amorphous solids are usually considered noncrystalline materials (i.e., glasses).

Angle of incidence—The angle at which X-rays strike a plane in the crystal.

Anhydrate—A crystal form that contains no solvent of crystallization.

Anisotropic behavior—A term used to describe cases where a solid-state reaction proceeds through different directions of the crystal at different rates; also referring to any observed property that varies in different directions in or on a crystal.

Atomic displacement parameter—A measure of the mobility or disorder of a given atom in a crystal structure, formerly called the temperature factor.

Automated diffractometerSee Diffractometer.

Avrami–Erofe’ev equation—The equation that treats a solid-state reaction as a process controlled by random nuclei growing in three dimensions and ingesting other nuclei. The equation is:

[–ln(l – a)]n = kt

where a is the fraction reacted, n and k are constants, and t is time.

Ball mill—A relatively high-energy mill consisting of one or more balls in a chamber and used to reduce the particle size of solids. In the process, the ball mill may induce undesired solid-solid reactions or create amorphous material.

BET (Brunauer–Emmet–Teller) adsorption isotherm—A curve (usually sigmoidal) that describes the manner in which a substance absorbs a monolayer of an inert gas (usually nitrogen or krypton) at reduced temperatures.

Biaxial crystal—Crystals in which the propagation of light differs in two directions. These crystals are of the triclinic, monoclinic, and orthorhombic systems.

Bioavailability—A term used to describe the biological availability of a drug. The bioavailability depends on the absorption, distribution, metabolism, and excretion of the drug. For example, the absorption of the drug depends on the dissolution profile of the dosage form, hence, the importance of dissolution testing in assuring consistent bioavailability.

Biobatch—Manufactured batch of a drug preparation that is used to test for biological response.

Birefringence—An optical property of all anisotropic crystals (i.e., virtually all drugs) observed as light and dark areas while the sample is rotated on the microscope stage of a polarizing microscope.

Bloch-decay experiment—A solid-state NMR experiment where a single pulse on the observed nucleus is followed immediately by acquisition with high-power proton decoupling and usually magic-angle spinning. This technique accentuates highly mobile carbon nuclei.

Body-centered space group—A crystallographic space group containing a body-centered lattice, a lattice that contains a site in the center of the unit cell. A crystallographic space group containing a lattice point in the center of the unit cell symbolized by I.

Bragg equation—The equation that relates the scattering of X-rays from a crystal to the d-spacing between planes:

nl = 2d sinq

Bulk density—The mass of powder in a unit volume. Note this is not the true density of the substance, which is the mass per unit volume in a single crystal.

Capping—A failure of tablets evidenced by the loss of layers of the tablet during routine handling.

Catemer—A network extending throughout a system; a type of hydrogen bonding arrangement consisting of an infinite chain.

Chiral compound—A compound that contains at least one asymmetric atom and is optically active.

Close-packing theory—A theory of crystal packing advanced by Kitaigorodskii that states a crystal will contain the closest possible packing of molecules.

Cocrystal—A mixed crystal or crystal that contains two different molecules.

Color dimorphism—The existence of two crystalline forms of the same compound in which each exists as a different color.

Configurational polymorphism—A type of polymorphism in which one labile isomer of a compound (e.g., a keto form) is present in one polymorph and another labile isomer (e.g., an enol form) is present in the other polymorph.

Conformational polymorphism—A type of polymorphism in which the conformation of the independent molecule in each polymorph is different.

Contact time—A solid-state NMR term referring to the length of the spin-lock period in which the Larmor frequencies of the proton and carbon are matched.

Contracting area (disc, cylinder, or rectangle) equation—A kinetics equation used to fit solid-state kinetic data to a two-dimensional advancement of a phase boundary from the outer edges inward across the surface of the solid.

Contracting volume (cube or sphere) equation—A kinetics equation used to fit solid-state kinetic data to a three-dimensional advancement of a phase boundary from the surface inward through the solid.

Coulter method—A technique for determination of particle size distribution in which suspended particles pass through an orifice while changes in the resistance at the gap are recorded.

Cross polarization—A technique which provides enhancement of nuclei with a low magneticgyro ratio (g) by transferring proton magnetization to the observed nucleus via matched spin-locking (Hartmann–Hahn) conditions at both frequencies. Since the sensitivity enhancement occurs on each scan (according to the ratios of the g values) the experiment can be repeated much faster because of the faster relaxation of the higher g nuclei.

Crystal—An orderly, infinite arrangement of molecules or atoms in a solid.

Crystal form—A general term used to refer to the various types of crystalline solids of the same compound that can be obtained (i.e., polymorphs and pseudopolymorphs); synonymous with crystal modification.

Crystal habit—Crystals with the same internal structure but different external shape, thus, crystal in which different faces have developed during growth; synonymous with morphology.

Crystal lattice—The three-dimensional molecular repetition of the motif within a crystal.

Crystal packing—The arrangement of molecules in a crystal and the contacts between these molecules.

Crystal ripening—The process of reaching equilibrium after a crystallization is largely complete by continued stirring. This may bring about changes in crystal size, shape and perfection as high-energy sites are driven to equilibrium.

Crystal structure—The internal arrangement of atoms (and thus molecules) in a solid. The crystal structure is determined by X-ray crystallographic techniques and includes information about intramolecular and intermolecular contacts.

Crystal system—The space group and crystal lattice to which a crystal structure belongs.

Crystalline form—A solid form that is crystalline; a solid form that gives a diffraction pattern. This include polymorphs, solvates, hydrates, and desolvated solvates.

Crystallinity—The ratio of crystalline and amorphous components in a sample. High crystallinity connotes a low amorphous component.

Cube-root kinetics—A diminishing sphere kinetics model with regard to particles of radius r:

r(1 – a)3 = kt

where r is the particle radius, a is the fraction reacted, k is a constant, and t is time.

Cubic crystal class—A crystal class containing four three-fold rotation axis, one along each unit cell diagonal. This class contains 36 space groups and has two restrictions: 1) the lengths of all axes are equal, and 2) all angles are equal to 90°.

Cycloaddition reaction—A chemical reaction that involves the addition of two substrates to form a ring system (e.g., the solid-state photodimerization of cinnamic acids). Cycloaddition reactions are controlled by the Woodward–Hoffmann rules.

Decarboxylation reaction—A chemical reaction that involves the loss of CO2 from a solid (e.g., the decarboxylation of 4-aminosalicylic acid).

Defects—Sites of imperfection in the crystal packing of solids. The most common defects are screw dislocations, slip dislocations, and orientational defects.

Dehydration reaction—A reaction that involves loss of water from the crystal. The loss may be due to the physical loss of water from the crystal lattice or through a chemical reaction.

Dehydrogenation reaction—A reaction that involves loss of hydrogen gas.

Deliquescence—The uptake of atmospheric moisture by a solid, sometimes ending in spontaneous liquefaction of the solid.

Density rule—The rule states that if a polymorph has a lower density than another polymorph at room temperature, then it may be assumed that at absolute zero the form with the lower density is metastable.

Desolvated solvate—A crystalline solvate that has lost the solvent of crystallization but has largely retained the original crystalline lattice.

Desolvation—A reaction in which the solvent of crystallization is lost from a crystal. Desolvation can be accompanied by a polymorphic transformation, or the original crystal structure can be maintained to produce a desolvated crystal.

Differential scanning calorimetry (DSC)—An analytical technique measuring the heat flux (the quantity of heat transmitted per unit time) of the sample during a controlled heating process.

Differential thermal analysis (DTA)—An analytical technique in which the difference in temperature between the sample and an inert reference is detected during a controlled heating process.

Diffraction pattern—The recorded form of diffraction peaks and their relative intensities obtained when a material is subjected to X-ray diffraction analysis. The pattern may be in the form of a chart tracing or as bands on photographic film.

Diffractometer—A device used to accurately measure the intensities of diffracted X-rays as a function of the incident angle of the X-ray beam. This unit is usually computer-controlled and measures the intensities using a counter.

Dimerization—A chemical reaction in which two monomers combine to form a single molecule.

Dipole moment—A vector indicating the magnitude and direction of the uneven charge distribution in a covalent bond or molecule. The vector is represented by the symbol µ with units of Debyes, abbreviated D.

Direct methods—A group of statistical methods used to determine a crystal structure based on analysis of diffracted intensities.

Dissolution profile—A multi-time point description of the dissolution of a dose under standardized conditions.

Dissolution rate—The rate of dissolution of a solid, usually measured in water at physiological pH and temperature. An important physicochemical quantity used to predict the bioavailability of drugs.

Drug delivery—The field of developing formulation modifications to enhance the efficiency and timing of delivering a drug to the biologically active site. Also, the total sequence of events leading to that delivery.

DSCSee Differential scanning calorimetry.

d-Spacing—The spacing between lattice planes in a crystal. d-Spacing is measured by a diffraction experiment and is defined by Bragg’s law.

DTASee Differential thermal analysis.

Dynamic mode—A common thermogravimetric analysis technique in which the temperature is raised at a known rate, typically linear.

E RaySee Extraordinary ray.

Efflorescence—The loss of gas from a solid or liquid.

Electron-density map—A plot of electron density versus location in a unit cell. Electron-density maps are used early in a crystal structure solution to solve the structure.

Electron-spin resonance (ESR) spectroscopy—A method involving measuring the resonance of free electrons in material. This method can provide structural and dynamic information about a solid.

Electrophilic aromatic substitution reaction—A common chemical reaction that involves the attack of the p electrons of an aromatic ring on an electrophile to form a resonance-stabilized carbocation intermediate that then looses a proton to form a substituted aromatic compound.

Enantiomer—In a chiral compound, either of the two molecular species, R and S, having equal optical rotation but of opposite sign and in which the mirror image is not superimposable with the original structure.

Enantiotropy—Referring to a situation in which the rank order of stability of the various solid forms changes at different temperatures (in contrast to monotropic).

Enthalpic change—A change in the heat (∆H) of the compound. For example, a change in the crystal form or structure is an enthalpic change.

Enthalpy of fusion rule—If the higher melting form has the lower enthalpy (heat) of fusion the two modifications are enantiotropic. If the lower melting form has the lower entropy (heat) of fusion the two modifications are monotropic.

Enthalpy of transition rule—This rule states that if an endothermic transition is observed at some temperature it may be assumed that there is a transition point below it and that the two forms are related enantiotropically. If an exothermic transition is observed at some temperature it may be assumed that there is no transition point below it and that the two forms are either related monotropically or the transition temperature is higher.

εE—The refractive index of the extraordinary ray having the maximum value.

εE´—The refractive index of the extraordinary ray that is between the maximum and minimum index values.

Excimer—An excited-state complex formed by two or more molecules.

Excipient—Additives used in the preparation of the dosage form to either improve the handling and manufacturing of a product or to act as a filler (i.e., lactose, cellulose, starch, or dicalcium phosphate).

Expiration date—The date appearing on the label of a drug after which it should not be used or sold.

Extraordinary ray—The component of plane-polarized light that travels through a uniaxial crystal at a direction-dependent velocity.

Face—Any one of the outer plane surfaces of a crystal or geometric solid.

Face-centered space group—A crystallographic space group containing a pair of lattice points on opposite faces (symbolized by A, B, or C if the bc, ac, or ab faces are centered or F is all faces are centered).

Filterability—Ability to filter a solid; related to particle size and morphology of the solid.

Flowability—A measure of the freedom with which a powder flows through tubes and orifices such as those encountered in unit operations.

Formulation—Studies leading to the choice of specific processes and additives to be used in the final preparation of a drug dosage form. Also, the composition of that preparation.

Fourier transform (FT)—The mathematical treatment of data in which an ensemble of sinusoidal signals are deconvoluted into individually contributing frequencies, amplitudes, and phases.

Fraunhofer diffraction—A laser-light scattering in which particles create radially symmetrical diffraction patterns consisting of a bright center and coaxial light and dark rings. The angle of diffraction is size dependent; smaller particles diffract at larger angles compared to larger particles. Also known as static-light scattering (SLS) or low-angle forward light scattering.

Free-radical reaction—A chemical reaction that conceptually involves three sequential types of reactions: 1) initiation steps in which free radicals (e.g., R or Cl) are formed, 2) propagation steps in which the free radicals react with molecules to form products and other free radicals, and 3) termination steps in which free radicals combine to form molecules.

Gas chromatography—A chromatographic technique in which the sample is volatilized and passed through a column to separate the components of a sample. The column is packed either with a polymeric stationary phase coated on a solid support or simply a thin layer of polymer on the inner surface of a capillary.

Glass—A solid that does not have an ordered arrangement of molecules and is hard or brittle; an amorphous solid below its glass-transition temperature.

Glass transition temperature—The temperature above which a glassy amorphous solid becomes rubbery, Tg.

Glassy state—A state of an amorphous material having rather low mobility, as in window glass.

Glide plane—A symmetry element involving reflection through a plane followed by a translation.

Goniometer head—A device used to mount crystals and control their orientation at precise angles.

HabitSee Crystal habit.

Hammett equation—A linear free-energy relationship for substituent effects in reactions or ionizations (pKa) given as:


where kH is the rate constant or equilibrium constant for the parent compound, kX is the constant for the compound bearing a substituent X, r is a constant for a given reaction under a given set of conditions, and sX is a constant characteristic of the group X.

Hartman–Hann Condition—A spin-lock experiment that increases the efficiency of cross polarization; it uses two rf fields, one at the Larmor frequency of the protons and one at the Larmor frequency of the carbons.

Heat capacity rule—This rule states that at a given temperature, if the higher melting polymorph has a heat capacity greater than another modification, the system is enantiotropic. Otherwise, the system is monotropic.

Heat conduction calorimetry—A technique in which the response of the instrument is directly proportional to the rate of the heat produced in the sample cell. The advantage of this technique is that small values of heat (µW) can be detected.

Heat of fusion ruleSee Enthalpy of fusion rule

Heat of transition ruleSee Enthalpy of transition rule

Heavy-atom method—A method used to determine the crystal structure of compounds that contain atoms with atomic numbers greater than 17.

Helium pycnometry—An analytical method for determining the density of a powdered solid. An accurately weighed sample (~5 g) is placed in a sample cell and evacuated to remove ambient gases. The cell is then pressurized with helium, followed by adiabatic expansion into a chamber of known volume. The resulting pressure is recorded after thermal equilibrium. The density of the solid is calculated as follows:


where WS is the weight of the sample, VS is the volume of the sample, V1 is the volume of the sample cell, V2 is the volume of the expansion chamber, P1 is the original pressure of the sample cell, and P2 is the pressure of the system after the expansion step.

Hexagonal crystal class—A crystal class containing one six-fold rotation axis. This class contains 27 space groups and has three restrictions: 1) the lengths of the a and b axes are equal, 2) the a and b angles are equal to 90°, and 3) the g angle is equal to 120°.

High-performance liquid chromatography (HPLC)
—A chromatographic technique that involves passing a solution at high pressures through a packed column of fine particles. The components of a sample are separated on the column and noted by a detector (e.g., UV-Vis, refractive index, potentiometric, etc.) An octadecylsilyl (C-18) column is the most commonly used column and a UV detector is the most commonly used detector.

Hygroscopic solid—A solid that can adsorb atmospheric moisture. There is both a kinetic and a thermodynamic component to this process. The kinetic component determines the rate of water uptake, while the thermodynamic component determines the energy of this process.

Hygroscopicity—The hygroscopic nature of a solid.

Image analysis—An automated microscopic technique for analyzing particle properties, especially shape and size distributions.

Independent molecule—A term used to describe the unique, non-symmetry-related molecules in a unit cell.

Indicatrix—A structural representation, portrayed as an ellipsoid, of the magnitudes and directions of the O and E rays within a crystal.

Infrared spectroscopy—A method of analysis that involves the absorption of infrared energy by the sample. The molecules that absorb the infrared energy are in an excited, vibrational state and the wavelengths of the various vibrations reveal structural details of the given molecules.

Interfacial angle—The angle between faces in a crystal. This angle is dictated by the Miller indices of the faces and the crystallographic unit cell.

Intermolecular contacts—Contacts between adjacent molecules in a crystal. These contacts define the crystal packing.

Interrupted decoupling—A brief delay (20–50 µs) in the 1H–13C contact time during which the magnetization of the carbons directly attached to protons rapidly dephase, with the exception of methyl carbons. The result is an enhancement of nonprotonated carbons, methyl groups, and sometimes highly-mobile methylenes. Also known as NQS (non-quaternary suppression).

Intramolecular contacts—Non-covalent contacts between atoms in the same molecule within a crystal.

Intrinsic dissolution—A method of measuring dissolution that eliminates the effect of surface area.

Intrinsic dissolution rate (IDR)—The rate of dissolution measured in an intrinsic dissolution apparatus. The intrinsic dissolution rate is independent of surface area.

Ionic bond—A bond in which the predominant forces are ionic in nature.

Ionic crystal—A crystal composed of ions in which each ion of a given charge is equidistant from a small number of ions of opposite charge (e.g., sodium chloride).

Isomorphous replacement method—A method of determining crystal structure used for proteins. This method involves replacing heavy atoms in a crystal with different heavy atoms.

Isothermal mode—A thermogravimetric analysis technique in which the temperature of the sample is held constant.

Isotropic—Having identical properties in all directions.

Jander equation—A simplified version of the three-dimensional diffusion kinetic equation.

Larmor frequency—The frequency of precession of a nucleus in a magnetic field.

Laser light scattering—Various particle-size distribution analyses that examine the optical response of a suspended powder to illumination by a laser (cf. Fraunhofer diffraction, time-domain and image analysis).

Law of rational indices—A rule stating that the major faces on a crystal will generally be related to the principle dimensions of the unit cell and will have Miller indices with low integer values [(100), (101), (210), etc.]

LooseningSee Molecular loosening.

Magic angle—The angle (54° 44′) at which solid samples are often spun in solid-state NMR spectroscopy. This spinning removes the effect of the random orientation of the powdered solid with respect to the magnetic field.

Magic-angle spinning—A solid-state NMR technique involving spinning the sample at an angle of 54°44’ to reduce the anisotropic chemical shifts in a solid.

Melt-back—A phenomena that occurs during lyophilization (freeze drying) where the solid melts to form a crust.

Metastable form—A form other than the most stable form.

Microscopy—Examination of crystals on a microscope by various techniques.

Miller index—A set of three integers used to designate the lattice planes of the crystal. Miller indices are used to designate: a) a set of lattice planes [e.g., the (010) plane], b) a particular member of this set, or c) a face of a macroscopic crystal [e.g., the (010) face].

Mirror plane—A crystallographic plane corresponding to a reflection operation (see Table 1.1).

Molecular change—The second step of a hypothetical solid-state reaction. This step involves the actual chemical reaction that occurs. This step is similar to the corresponding reaction in solution.

Molecular loosening—The first step of a hypothetical solid-state reaction. This step allows the reacting molecules to gain enough molecular freedom to react. For solid–gas reactions, this step also involves diffusion of gases to the reaction site.

Monoclinic crystal class—A crystal class containing one two-fold rotation axis along the b axis. This class consists of 13 space groups and has no restrictions on the lengths of the axes except that one angle (b by convention) is not equal to 90°.

Monohydrate—A crystal form containing one mole of water per mole of compound.

Monotropic—Referring to a system in which various solid forms retain the rank order of their stabilities at all temperatures (in contrast to enantiotropic).

Morphology—The external shape of a crystal; synonymous with the crystal habit.

Non-bonded interaction—A through-space interaction of atoms that are typically electrostatic or van der Waals in nature.

Non-covalent attractive forceSee Non-covalent interaction.

Non-covalent attractive interactionSee Non-covalent interaction.

Non-covalent interactions—The van der Waals forces between multipoles in molecules that are responsible for many phenomena including cohesion of most solids, surface tension, friction, changes of phase, viscosity, the Joule-Thomson effect, and causing deviations in the ideal gas law.

Non-stoichiometric hydrate (or solvate)—A solvated crystal structure in which the solvent molecules are not in well-defined positions and therefore are present in variable amounts, depending on the vapor pressure of the solvent in the system, (i.e., the relative humidity in the case of crystal hydrates).

NQSSee Interrupted decoupling.

Nuclear magnetic resonance (NMR) spectroscopy—An analytical method used to study both liquid and solid samples. It involves placing the sample in a magnetic field and measuring the energy differences between spin states of the nuclei (most commonly protons and carbons).

Nucleation—The formation of stable molecular assemblies leading to crystallization. Also, the initiation of a solid-state reaction. This occurs at a defect or impurity site in the crystal. The solid-state reaction often spreads from this site throughout the crystal.

Nucleation site—The place at which nucleation occurs within a crystal.

Nuclei—Ordered arrays of solute molecules of sufficient size to persist in a given solution.

O RaySee Ordinary ray.

Optical axis—The direction in a crystal in which both components of the plane-polarized light are equal.

Optical goniometrySee Reflective goniometry.

Ordinary ray—The component of plane-polarized light that travels through a uniaxial crystal with a constant velocity.

Organic crystal—A crystal consisting of a regular arrangement of organic molecules held together by van der Waals forces.

Orientational defect—A defect at which the tenant molecule takes up an abnormal orientation.

Ortep drawing—A structural representation of a set of atoms in which the atoms are portrayed as ellipsoids that depicts the atomic displacement parameters for those atoms. These representations were originally drawn using the ORTEP program.

Orthorhombic crystal class—A crystal class containing three mutually perpendicular two-fold rotation axes. This class consists of 59 space groups and has one restriction: all of the angles are equal to 90°. There are no restrictions on the lengths of the axes.

Ostwald ripening—A spontaneous process during which ultrafine (high-energy) crystals dissolve and the corresponding material redeposits on larger crystals.

PackingSee Crystal packing.

Particle-size distribution—The size distribution of particles in a solid, typically represented graphically as a histogram or numerically as three values: 1) 10% of the sample is less than the value stated, 2) 50% of the sample is less than the value stated (the median), and 3) 90% of the sample is less than the value stated.

Phase problem—Although the amplitude F(hkl) of the diffracted beam is readily available, the phase a(hkl) necessary to compute the electron density is not known because X-rays cannot be focused. The phase is needed to determine the three-dimensional arrangement of the atoms without which the stereochemistry cannot be determined.

Phase transformation—A transformation of one crystalline form of a solid to another. This can be a solid-solid, a solid-liquid-solid, or a vapor-mediated transformation.

Photochromism—A compound exhibits photochromism if, upon exposure to light, a color change occurs. Often the color change is reversible.

Photomicrography—The technique of photographing a crystal on a microscope, sometimes at various stages in a reaction.

Physical stability—A term used to refer to the stability of a drug with respect to physical transformations, for example, to another polymorph or crystal form.

Physical transformation—A transformation of a solid in which the crystal structure or content of the crystal changes but in which no covalent bonds are made or broken. Physical transformations include polymorph transformations and desolvations.

Plane-polarized light—The result of light passing through a polarizing filter resulting in only the extraordinary ray emerging as light polarized in only one plane.

Pleochroic—Showing more than one color.

PLS (partial least-squares) treatment—A technique used to perform quantitative analyses on multicomponent mixtures with overlapping bands. PLS also allows calibration using mixtures permitting the modeling of interactions between components and the use of combinations of multiple numbers of wavelengths in the calibration.

Polarizability—The ability to be polarized.

Polarography—An analytical technique that measures the current flow at a liquid-drop electrode at a given potential. The current flow is proportional to the amount of compound present.

Polychromism—The capcity of a solid to exhibit more than one color.

Polymorph (polymorphism)—One of the different crystal structures in which a compound can crystallize. Polymorphs are best characterized by their space group and unit-cell parameters. This term is usually reserved for materials with the same elemental analysis.

Polymorphic transformation—A physical transformation in which the crystal structure of a compound is converted to a different crystal structure.

Powder bridging—The formation in a bulk powder of large cohesive regions, or “bridges,” that interfere with uniform flow of the powder in pharmaceutical operations.

Powder diffraction methodSee X-Ray powder diffraction.

Precession camera—A camera used in X-ray crystallography in which the center of a flat film is always kept aligned with the direct beam of X-rays as a crystal is oscillated.

Precession photograph—An X-ray diffraction photograph made on a precession camera. Direct measurement of all lattice parameters are possible from a series of these photographs.

Preferred orientation—The crystals in a powder are said to be in a preferred orientation when they are not randomly oriented and their diffraction intensities differ from those obtained when crystals are randomly oriented.
Primary nucleation—Nucleation in a system that does not contain crystalline matter.

Primitive space group—A space group that contains only a single lattice point or a single unit of the repeated motif in a crystal lattice; symbolized by P (or R for rhombohedral crystals).

50% Probability level—A scale factor used for Ortep representations in which the instantaneous position of the atomic center will be within the ellipsoid 50% of the time.

Prout–Tompkins kinetics—The equation that treats a solid-state reaction as a process controlled by growing nuclei that branch into chains. The equation is:


where a is the extent of reaction, k is the rate constant, and t is the time.

Pseudopolymorph—A polymorph that differs from a true polymorph by the incorporation of solvent.

Quasi-isothermal mode—A thermogravimetric analytical technique in which the sample is heated at a fixed temperature to a constant mass and the process repeated stepwise at increasingly higher temperatures.

Reaction cavity—A hypothetical volume wherein significant molecular motion, hence reaction, can take place within a solid.

Reaction order—The sum of the exponent of the reactants in the kinetics equation for a given reaction.

Rearrangement reaction—A chemical reaction in which covalent bonds are made and broken, but in which the molecular formula remains the same.

Reflected light—Used to observe gross properties of particles (cf., transmitted light).

Reflective goniometry—A technique by which the interfacial angles of a single crystal can be determined.

Refractive index—The ratios of the velocities of light in a medium and in air under the same conditions. Measured by the ratio of the sines of the angles of incidence and refraction.

Rhombohedral crystal class—A subclass of the trigonal crystal class containing a three-fold rotation axis along a diagonal of the unit cell. This class contains 7 space groups and has two restrictions: 1) the lengths of the three axes are equal, and 2) the three angles are equal, but need not equal 90°.

Rietveld method—A computational treatment of diffraction data that creates an effective separation of the overlapping data in a typical powder X-ray diffraction pattern, thereby often allowing an accurate determination of the structure without the need of single-crystal data.

Rotation axis—A symmetry element involving an n-fold rotation about an axis.

Rotatory-inversion axis—A symmetry element involving an n-fold rotation followed by an inversion. Also called a center of symmetry.

Rubber—An amorphous material somewhat above its glass transition temperature and having a rubbery consistency.

Rubbery state—The state of an amorphous material at a temperature above its glass transition temperature and below the temperature of liquefaction.

Saturation—The concentration of a solution in which a solute is at its equilibrium solubility in the respective solvent.

Scanning electron microscopy (SEM)—A microscope in which a focused beam of electrons is directed on a sample to produce several interactions of which secondary electrons and backscattered electrons are the basis of the image. Resolution is typically 100 Å and has a large depth of field.

Screw axis—A symmetry element involving an n-fold rotation followed by translation parallel to the axis of rotation. It may be visualized as a screw.

Screw dislocation—A defect in a crystal having a screw-type appearance as observed with an electron microscope or atomic force microscope.

Secondary nucleation—The occurence of crystal nuclei brought about by operations such as stirring and impact after the system has undergone primary nucleation.

Seeding—The addition of solid particles, usually of the desired phase, to a crystallization process in order to induce crystal nucleation under controlled conditions.

Semimicro hygrostat—A small chamber in which a sample is suspended over a saturated-salt solution that provides a determined relative humidity. The chamber can be disassembled with a minimum of exposure of the sample to the atmosphere while weighing to determine the increase or decrease in mass of the sample.

Sesquihydrate—A crystal form containing one and one-half moles of water per mole of compound.

Single crystal—A crystal consisting of a non-interrupted repetition of the unit cell in three dimensions. The structure of a single crystal can be determined by single-crystal X-ray diffraction.

Singlet oxygen—An oxygen atom in its singlet excited state. Singlet oxygen usually gives products resulting from cycloaddition.

Singlet-oxygen sensitizer—An organic compound (e.g., the dye rose bengal) that converts triplet oxygen to singlet oxygen by transfer of energy.

Sink condition—Conditions during a dissolution or solubility experiment where the concentration in solution is much less than the solubility.

Size distributionSee particle-size distribution.

Slip dislocation—A type of defect in which the crystal planes have slipped relative to each other. A slip dislocation can bring molecules into intermolecular interactions that are not found in the bulk crystal.

Solid form—A general term used to describe polymorphs, pseudopolymorphs, or amorphous forms; synonymous with solid modification.

Solid solution—The random distribution of one solid in another.

Solid-gas reaction—A reaction of a solid with a gas (e.g., the reaction of acid crystals with ammonia) or a reaction producing a gas and a solid as products (e.g., decarboxylation reactions).

Solid-solid reactions—Reactions between two solids without the involvement of a solvent, generally involving four steps: 1) loosening of the molecules at the reaction site, 2) molecular change, 3) solid solution formation, and 4) separation of the product phase.

Solid-state hydrolysis—A solid-state reaction in which water hydrolyzes a compound (e.g., hydrolysis of acetylsalicylic acid to form acetic acid and salicylic acid).

Solid-state oxidation reactions—A class of solid-gas reactions involving the reaction of a solid with oxygen.

Solid-state photochemical reactions—Reactions that proceed by absorption of light by the molecule and subsequent bond formation or breakage. The products of these reactions differ from those in solution.

Solid-state thermal reactions—Solid-state reactions that are heat induced. Solid-state rearrangement reactions are important members of this class.

Solubility—The amount of solute dissolved in a unit volume of a solvent at equilibrium at a given temperature and pressure. Each form of a substance has a characteristic solubility.

Solvate—A crystal form that contains either stoichiometric or nonstoichiometric amounts of solvent.

Space group—One of 230 possible three-dimensional arrangements of molecules in a crystal. A listing of all of the space groups can be found in International Tables for Crystallography, Volume 1.

Specific surface area—The characterization of a powder by determining the surface area per unit weight.

Spin locked—A technique in NMR in which the magnetization is locked along the y axis by the rf field. A means of effectively preventing chemical shift evolution by using a high-power rf field during an NMR experiment.

Stability—A term used to describe the resistance of a solid drug or solution of a drug to reaction.

Stable form—The solid form of a substance having the highest thermodynamic stability (e.g., lowest solubility) among all the forms that might be encountered under the given conditions.

Static-light scattering (SLS)See Fraunhofer diffraction.

Stereoscopic packing drawing—A three-dimensional representation of a crystalline arrangement of molecules using side-by-side views at slightly different angles. These representation may be viewed unaided or by using special viewers.

Structure factor—The intensity and phase of a diffracted X-ray by a unit cell denoted by F or F(hkl).

Sublimation—A change in state from a solid to a gas and then back to a solid. Sublimation can be used to purify a solid and also may be involved in solid-state reactions and phase transformations.

Supersaturation—A solution that contains a concentration of solute greater than the equilibrium solubility value.

Suspension—A liquid that contains undissolved solid distributed evenly throughout the mixture.

Symmetry element—The various formal spatial relationships that govern the orderly three-dimensional propagation of an object in space (i.e., in crystal growth, the molecules of the compound). (See Table 1.1).

Symmetry operation—An operation that returns the contents of the unit cell unchanged. Symmetry operations include n-fold rotations, rotary inversions, point inversions, mirror planes, glide planes, and screw axes.

Syringeability—The ability of a suspension to pass readily through a syringe and needle. For example, long needle-like crystals in suspension may have poor suspension syringeability.

Systematic absence—The absence of certain hkl reflections in the X-ray diffraction of a single crystal. Systematic absences are used to determine the space group and symmetry of a crystal.

Tableting behavior—A general term for behavior of crystals upon compression into tablets.

Temperature factor (thermal factor)See Atomic displacement parameter.

Tetragonal crystal class—A crystal class containing a four-fold rotation axis or rotatory-inversion axis along c. This class contains 68 space groups and has to restrictions: 1) the lengths of the a and b axes are identical, and 2) all angles are equal to 90°.

TgSee Glass-transition temperature.

Thermal analysis—One of a group of methods used to characterize solids, thermo­gravimetric analysis, differential thermal analysis, differential scanning calorimetry.

Thermochromism—A compound is thermochromic if, upon exposure to heat, a color change occurs. Often this color change is reversible.

Thermogravimetric analysis (TGA)—An analytical technique in which the weight change of the sample is measured during heating.

Thermomicroscopy—A technique that involves observation of crystals on a microscope during heating.

Thin-layer chromatography (TLC)—A chromatographic method of separating compounds eluted with a solvent after applying them to a thin layer of adsorbent adhered to a solid support (e.g., glass, plastic, or aluminum).

Threshold temperature—The temperature at which an arbitrarily defined 2% of the solvent of crystallization is lost from a solvate. It is conveniently measured by TGA using a 6 °C/min heating rate.

Time-domain analysis—A technique used to determine the size of a particle (0.5–3600 µm in diameter) by measuring the time required for a laser beam moving at a fixed velocity to cross a particle.

Topochemical—The term used to describe the control of solid-state reactions by selective crystal packing. A reaction is topochemical if the structure of the products can be explained by the crystal packing of the reactant crystal.

Topochemical postulate—This postulate states that, because a solid-state reaction may occur within the solid or at the surface of the solid, the outcome of the reaction is for the most part determined by the spatial relationships of the reactants.

TopotacticSee Topotaxy

Topotactic reaction—A reaction exhibiting topotaxy.

Topotaxy—A term used to describe a solid-state reaction whose products have a preferred orientation relative to a crystallographic direction of the parent crystal.

Transmitted light—Used to examine single crystals and their optical properties. (cf. reflected light).

Triclinic crystal class—A crystal class of containing either no symmetry or a rotatory-inversion axis in any direction. This class contains 2 space groups and has no restrictions on the lengths of the axes or the values of the angles.

Trigonal crystal class—A crystal class containing a three-fold rotation axis along the diagonal of the unit cell. This class is divided into two subclasses. One subclass, designated with hexagonal axes, contains 18 space groups and has three restrictions: 1) the lengths of the a and b axes are identical, 2) the a and b angles are equal to 90°, and 3) g is equal to 120°. For a description of the other subclass, see Rhombohedral crystal class.

Trituration—A process involving grinding a solid with a liquid

Twofold rotation axis—A symmetry axis in which a rotation of 180° produces no change.

Ultraviolet spectroscopy—An analytical spectroscopic technique used to study the electronic excitation of a substance. Application of this technique usually requires dissolution of the sample.

Undersaturation—The condition when solution concentration is less than the saturation value (i.e., when solute concentration is less than its solubility in the respective solvent).

Uniaxial crystal—An anisotropic crystal in which the velocities of both plane-polarized light components traveling through the crystal are equal; a crystal with only one optical axis. These crystals typically belong to the hexagonal or tetragonal crystal systems.

Unit cell—The smallest three-dimensional volume element from which the crystal can be constructed.

Unit-cell parameters—The parameters (a, b, c, a, b, g) that define the crystallographic unit cell.

van’t Hoff plot—A plot of the log of solubility values versus the reciprocal of the temperature. The plot for several forms of a substance reveals transition temperatures for the forms.

Void space—The space within a desolvated crystal that is not occupied by atoms.

Wallach’s rule—A rule stating that enantiomeric crystals tend to be more soluble (lower melting) than the corresponding racemic crystals.

Weissenberg camera—A camera consisting of a cylinder of film that, while a crystal is rotated 180°, is moved past a slit in a screen in one direction along the axis of rotation, then back again through another 180°. The result gives a pattern of intensities that is used to determine the space group and unit-cell dimensions of the crystal.

Wet etched—A technique for studying surface properties of crystals by eroding their surface with exposure to solvent.

Wg—The weight of a monolayer of water on a solid.

X-Ray diffraction pattern (X-Ray powder pattern) (XRPD)—The diffraction pattern produced by the lattice spacings in an ordered solid through exposure to X-rays. This technique can be used to identify a substance, ascertain the polymorph(s) present, and determine the crystallinity of a solid.

X-Rays—Electromagnetic radiation with a wavelength approximating that of interatomic distances, thus allowing the measurement of these distances.

Zero-order kinetics—A rate equation independent of concentration.