Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 3.1, pp. 153-154


P. F. Lindleya

aESRF, Avenue des Martyrs, BP 220, F-38043 Grenoble CEDEX, France

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Use of crystal properties for selection and preliminary study of crystals, adapted from MacGillavry & Henry (1962[link]); morphological, optical, and mechanical properties

Crystal propertyUses and commentsRelation with structure
Morphological properties
Crystal habit Setting crystal parallel to edge, or to symmetry axis, derived from goniometric measurement
Habit can be influenced by solvent, crystallization conditions, trace impurities
Well formed crystals can be accurately measured for analytical corrections for absorption
Morphological determination of crystal class may narrow down choice of space group
Best-developed faces correspond to net planes with large density of lattice or pseudo-lattice nodes (Bravais' law, extended by Donnay & Harker)
Prominent faces tend to be parallel to important bond systems
Face development correlates inversely with surface free energy
Twinning Twins may be hard to detect by morphological or diffraction methods. Investigate under the polarizing microscope: optical anomalies strongly indicate mimetic twinning, stacking faults, etc.
Mechanical twinning may occur when a single crystal is cut or ground. In such cases, the crystal should be shaped by use of a solvent
May indicate hemimorphy or pseudo-hemimorphy of the cell or supercell; see Chapter 1.3[link]
Pseudo-symmetrical stacking
Etch figures; epitaxy See IT A (2002), Section 10.2.3[link] (pp. 805–806), and chemical properties below  
Optical properties
Refractive index; birefringence (see IT A, Section 10.5.4[link] , p. 790) Checking quality of crystal: homogeneous extinction, interference figures
Extinction direction is used for setting badly formed or ground crystals
Magnitude of refractive index may be used for identification of crystal orientation
High refractive index may indicate close packing
Shape and orientation of indicatrix may be useful for finding orientation of large atomic or ionic groups with strongly anisotropic polarizability (e.g. flat or rod-shaped groups)
Optical activity Distinguishes between optical antipodes in studies of absolute configuration Difficult to measure, or even detect, in optically biaxial crystals. No obvious relation with structure
Pleochroism Identification of crystal orientation through dependence of colour on direction of light vibration Extended conjugated-bond systems have strong absorption of light vibrating parallel to system; weak absorption perpendicular to system
String-like arrangement of some atoms [e.g. iodine in poly(vinyl alcohol)] produces strong absorption parallel to string
In inorganic compounds, absorption is greatest for light vibrating along directions in which ions are distorted
Reflection of light   Opaque substances contain loosely bound electrons
Raman effect   May give information on the orientation and symmetry of scattering groups
Mechanical properties
Cleavage Useful for obtaining good surfaces for crystal setting
Useful for improving crystal shape
Correlates with bond-strength anisotropy
Hardness Anisotropy of hardness may produce ellipsoids instead of spheres when an abrasion chamber is used Hardness gives an indication of bond strength and bond density
Hardness may be very sensitive to impurities, changes in texture through ageing or heat treatment, etc.
Plasticity Single crystals: avoid cutting or grinding
Polycrystalline material: plastic deformation is often strongly anisotropic, and may then be used to produce single or double orientation
Non-directive bonding between large strongly bonded units (long-chain paraffins, layer structures)
Plastic flow may also be associated with mechanical twinning or lattice imperfections

Crystal propertyRelation with structure
Magnetic properties
In an isomorphous series of paramagnetic salts, the values of the average susceptibility and of magnetic anisotropy are dependent on the nature of the paramagnetic ion. The shape of the coordination polyhedron may be found from the crystal anisotropies
In aliphatic non-conjugated organic crystals, the numerically largest diamagnetic susceptibility is along the direction in which lie the largest molecular directions
In crystals containing aromatic compounds or molecules with coplanar conjugated bonds, the numerically largest molecular diamagnetic susceptibility is normal to the plane of the molecular orbitals, and may thus indicate the molecular orientations
Neutron diffraction by magnetic compounds may give information about the directions of the resultant spin and orbital moments. X-ray diffraction effects are usually unimportant
In magnetic materials, the interatomic distances, and, in antiferromagnetic oxides, the valency angles at the oxygen ions are related to the diameter of the electron shell
Nuclear magnetic resonance The line width in NMR spectra is related to the distances between the nuclei with magnetic moments
Electrical properties
See IT A (2002), Section 10.2.5[link] , p. 807. Ferroelectricity indicates (i) a structure of polar symmetry, and (ii) the probability of another high-symmetry structure of nearly equal energy, derivable from the ferroelectric by a displacive transition. Often there are several related structures, some ferroelectric and some antiferroelectric
Pyroelectricity indicates noncentrosymmetry. Second-harmonic generation is ordinarily a more sensitive test
Piezoelectricity Piezoelectricity gives information on symmetry; it occurs only in ten crystal classes. See IT A, Section 10.2.6[link]
Thermodynamic properties
Heat capacity
(`specific heat')
Anomalies indicate polymorphic transitions, disorder, approach to melting point, and temperature variation gives Einstein and/or Debye characteristic temperatures
Melting point Atoms in crystals with a low melting point often have large thermal movements; diffraction experiments should preferably be carried out at low temperatures
Anomalies in the variation of melting point in a series of homologues indicate a change in packing or bond type
Density For measurement, see Chapter 3.2[link] . Necessary for determination of number of formula weights per cell. May indicate liquid of crystallization, isomorphous replacement, degree of approach to close packing, first-order transitions with change of temperature or pressure
Thermal expansion Thermal expansion is usually greatest in directions normal to layers or chains. Abrupt variation with change of temperature or pressure indicates a second-order transition
Chemical properties
Chemical analysis Gives kinds of atoms in the structure and (in conjunction with the density) the number of each kind in the unit cell
Attack of surface May be used to shape crystals
Etch figures are sensitive indicators of point-group symmetry (see IT A, Section 10.2.3[link] ). Change of orientation of etch figures on a face may reveal twinning. Rows of etch pits may reveal grain or sub-grain boundaries
Oriented growth on parent crystal Epitaxy often reveals similarity of lattice parameters and even of atomic arrangement in the interface
Grain boundaries and twinning orientations may be marked by epitaxic growth, or by oriented growth of crystals or reaction products on the mother crystal (`topotaxy')