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

International Tables for Crystallography (2006). Vol. C, ch. 3.1, pp. 151-155

Section 3.1.2. Selection of single crystals

P. F. Lindleya

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

3.1.2. Selection of single crystals

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3.1.2.1. Introduction

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The final results of a structure analysis cannot be better than the imperfections of the crystal allow, and effort invested in producing crystals giving a clearly defined, high-resolution diffraction pattern is rarely wasted. The selection of twinned crystals, aggregates, or those with highly irregular shapes can lead to poor diffraction data and may prohibit a structure solution. There are many properties of crystals that can be examined prior, or in addition, to an X-ray or neutron diffraction study. These are summarized in Table 3.1.2.1[link]. Many of these properties can yield useful information about the crystal packing and the overall molecular shape. For example, the shape and orientation of the optical indicatrix may be used to find the orientation of large atomic groups that possess shapes such as flat discs or rods and therefore also have strong anisotropic polarizability. A morphological examination can reveal information not only about the crystal quality but also in many cases about the crystal system, whilst identification of extinction directions can assist in crystal mounting. It is regrettable that many modern practitioners of the science of crystallography give little more than a cursory optical examination to their specimens before commencing data collection and a structure analysis.

Table 3.1.2.1| top | pdf |
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
Paramagnetism;
diamagnetism
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
Ferromagnetism;
antiferromagnetism;
ferrimagnetism
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
Ferroelectricity;
pyroelectricity
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')

3.1.2.2. Size, shape, and quality

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A frequently occurring question involves the size and shape of single crystals required for successful diffraction studies. Among other factors, the intensity of diffraction is dependent on the volume of the crystal specimen bathed by the X-ray or neutron beam and is inversely proportional to the square of the unit-cell volume (see Chapter 6.4[link] ). Hence, small crystals with large unit cells will tend to give rise to weak diffraction patterns. This can be compensated for by increasing the incident intensity, e.g. using a synchrotron-radiation source in the case of X-rays. How large should a crystal be, and what is the smallest crystal size that can be accommodated? X-ray collimators, or slit systems, with diameters in the range 0.1 to 0.8 mm are commonly employed for single-crystal diffraction studies. For many diffractometers, the primary beam is arranged to have a plateau of uniform intensity with dimensions 0.5 × 0.5 mm. For most small inorganic and organic compounds, crystals with dimensions slightly smaller than this will suffice, depending on the strength of diffraction, although successful structure determinations have been reported on very small crystals (0.1 mm and less) with both conventional and synchrotron X-ray sources (Helliwell et al., 1993[link]). Microfocus beam lines at the third generation of synchrotron sources such as ESRF are designed to examine crystals routinely in the 10 µm range (Riekel, 1993[link]). In the case of a biological macromolecule of molecular weight 50 kDa and using a conventional X-ray source (a rotating-anode generator), a crystal of 0.1 mm in all dimensions will probably give diffraction patterns from which the basic crystal system and unit-cell parameters can be deduced, but a crystal of 0.3 mm in each dimension, i.e. roughly 30 times the volume, would be required for the collection of high-resolution data (Blundell & Johnson, 1976[link]). The higher intensity and smaller beam divergence inherent in a synchrotron X-ray source mean that high-resolution data of good quality could be obtained with the smaller crystal. Indeed, useful intensity data have been obtained with crystals with a maximum dimension of 50 µm (Subsection 3.4.1.5[link] ). At cryogenic temperatures, radiation damage is greatly reduced, and increased exposure times can be utilized (at the expense of increased background) to compensate for a small crystal volume. In the case of neutrons, the sample size is generally larger than for X-rays, owing to lower neutron flux and higher beam divergence. For a steady-state high-flux reactor such as that at the Institut Laue–Langevin (France), a crystal volume of 6 mm3 or larger is recommended for biological samples. Unfortunately, crystals of this size are not readily obtainable in most cases.

The shape or habit of a single crystal is normally determined by the internal crystal structure and the growth conditions. For diffractometry purposes, it is customary to bathe the crystal in the X-ray beam, so that elongated crystals may require cutting with a razor blade in order to trim them to an appropriate size. Large crystals of hard materials can be ground into spheres or cylinders (Jeffery, 1977[link]), so that corrections can be readily made to the observed intensities for systematic errors in absorption (see Chapter 6.3[link] ). Crystals that have elongated prismatic or needle shapes are often useful if data are collected using oscillation geometry, since the crystal can be translated in the X-ray beam at intervals during data collection to minimize radiation damage (Subsection 3.4.1.5[link] ). In general, all shapes can be accommodated, but those that are grossly asymmetric (e.g. very thin plates) may give elongated or distorted reflections, leading to poor data quality in certain regions of the diffraction pattern.

The ultimate test of the quality of a crystal and its suitability for a structure analysis is the quality of the diffraction pattern. Ideally, the reflections should appear in the case of monochromatic radiation as single spots without satellites, tails, or streaks between the spots. The diffraction pattern should be indexable in terms of a single lattice.

3.1.2.3. Optical examination [see IT A (2002), Section 10.2.4[link] ]

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Optical examination of a crystal under a polarizing microscope should be a prerequisite before mounting the specimen for a diffraction experiment. The presence of satellite crystals, inclusions, and other crystal imperfections will degrade the data quality, indicating the selection of a better specimen. The external morphology can often give a strong indication regarding the nature of the crystal system. A preliminary examination under crossed polars will often show whether the crystal is isotropic, uniaxial or biaxial (see, for example, Hartshorne & Stuart, 1960[link]; Bunn, 1961[link]; Ladd & Palmer, 1985[link]). Crystals that comprise two or more fragments will often be revealed by displaying both dark and light regions simultaneously. For uniaxial crystals, a birefringent orientation is always presented to the incident light beam if the unique axis is perpendicular to the microscope axis, and extinction will occur whenever the unique axis is parallel to the crosswires (assuming that the crosswires are parallel to the planes of polarization of the polarizer and analyser). If the unique axis is parallel to the microscope axis, a uniaxial crystal presents an isotropic cross section and will remain extinguished for all rotations of the crystal. Biaxial crystals have three principal refractive indices associated with light vibrating parallel to the three mutually perpendicular directions in the crystal. The two optic axes and their correspondingly isotropic cross sections that derive from this property are not directly related to the crystallographic axes. In the orthorhombic system, the three vibration directions are parallel to the crystallographic axes, often enabling identification of this crystal system. A monoclinic crystal lying with its unique axis parallel to the crosswires will always show straight extinction. If the crystal is oriented so that the unique axis lies along the microscope axis then, in general, the extinction directions will be oblique. In the triclinic case, the three mutually perpendicular vibration directions are arbitrarily related to the crystal axes. Even if it is not possible to discover the nature of the crystal system unequivocally, the extinction directions should at least enable the principal symmetry directions to be identified and therefore suggest how the crystals should be mounted for optimum data collection (see Chapter 3.4[link] ).

3.1.2.4. Twinning (see Chapter 1.3[link] )

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If at all possible, twinned crystals should not be used for structure analysis studies, but the recognition of twinning is critical, since unnoticed or misinterpreted twinning can prevent structure determination or lead to errors in the final structure solution. A distinction should be made between multiple crystal growth, whereby single crystals grow on or from the faces of a given single crystal, or from a common nucleation point, in non-specific orientations, and crystallographic twinning (see, for example, Phillips, 1971[link]; Bishop, 1972[link]). In the latter case, the relationship between the lattices of twinned crystals is normally that of rotation of 180° about a central lattice line, or reflection across a lattice plane. If the lattice is not geometrically symmetrical about the line or plane, two lattices with differing orientations will be produced, and the corresponding reciprocal lattices will be visible in the diffraction patterns. In ideal circumstances, the two patterns can be deconvoluted. If the lattice is geometrically symmetrical about the twin axis or plane, then the two reciprocal lattices will coincide and there may be no obvious signs of twinning in the diffraction pattern (merohedry). If the twins are present in almost equal amounts, the result will be an apparent mirror plane and perpendicular twofold axis in the Laue symmetry. It is therefore very important to examine carefully the Laue symmetry, preferably from a number of different crystals, if twinning is suspected. In some of these crystals, one twin component may be predominant, causing a breakdown in the pseudosymmetry.

Morphological evidence (a concave shape indicating an intersection between the two twin components) and optical examination under a polarizing microscope should also be employed to test for twinning. For lattices that are twinned in a geometrically nonsymmetrical manner, the different twin components will show extinction at different orientations. However, perfect optical extinction is not positive evidence of lack of twinning, since the geometrical symmetry plane (or axis) on which twinning takes place may be parallel to a symmetry plane (or axis) in the optical properties of the crystal.

Intensity statistics can also be used to detect twinning, particularly in the case of crystals twinned by merohedry (e.g. Britton, 1972[link]; Fisher & Sweet, 1980[link]). If crystallization conditions cannot be found that eliminate twinning, it is still possible, although difficult, to undertake structure analysis. Recent examples include Sr3CuPtO6 (Hodeau et al., 1992[link]), RbLiCrO4 (Makarova, Verin & Aleksandrov, 1993[link]), a serine protease from rat mast cells (Reynolds et al., 1985[link]) and plastocyanin from the green alga Chlamydomonas reinhardtii (Redinbo & Yeates, 1993[link]).

References

Bishop, A. C. (1972). An outline of crystal morphology, 3rd ed., Chap. 11, pp. 254–282. London: Hutchinson Scientific and Technical.
Blundell, T. L. & Johnson, L. N. (1976). Protein crystallography, Chap. 3, pp. 59–82. New York: Academic Press.
Britton, D. (1972). Estimation of twinning parameter for twins with exactly superposed reciprocal lattices. Acta Cryst. A28, 296–297.
Bunn, C. W. (1961). Chemical crystallography: an introduction to optical and X-ray methods, 2nd ed., Chaps. 2, 3, 4, pp. 11–106. Oxford University Press.
Fisher, R. G. & Sweet, R. M. (1980). Treatment of diffraction data from protein crystals twinned by merohedry. Acta Cryst. A36, 755–760.
Hartshorne, N. H. & Stuart, A. (1960). Crystals and the polarising microscope, 3rd ed. London: Arnold.
Helliwell, M., Kaucic, V., Cheetham, G. M. T., Harding, M. M., Kariuki, B. M. & Rizkallah, P. J. (1993). Structure determination from small crystals of two aluminophosphates, CrAPO-14 and SAPO-43. Acta Cryst. B49, 413–420.
Hodeau, J. L., Tu, H. Y., Bordet, P., Fournier, T., Strobel, P., Marezio, M. & Chandrashekar, G. V. (1992). Structure and twinning of Sr3CuPtO6. Acta Cryst. B48, 1–11.
Jeffery, J. W. (1977). Methods in X-ray crystallography, pp. 441–443. London/New York: Academic Press.
Ladd, M. F. C. & Palmer, R. A. (1985). Structure determination by X-ray crystallography, 2nd ed., Chap. 3, pp. 101–112. New York/London: Plenum.
MacGillavry, C. H. & Henry, N. F. M. (1962). Preliminary investigation and selection of crystals for X-ray study. International tables for X-ray crystallography, Vol. III, pp. 5–13. Birmingham: Kynoch Press.
Makarova, I. P., Verin, I. A. & Aleksandrov, K. S. (1993). Structure and twinning of RbLiCrO4 crystals. Acta Cryst. B49, 19–28.
Phillips, F. C. (1971). An introduction to crystallography, 4th ed., Chap. 7, pp. 171–193. Edinburgh: Oliver & Boyd.
Redinbo, M. R. & Yeates, T. O. (1993). Structure determination of plastocyanin from a specimen with a hemihedral twinning fraction of one-half. Acta Cryst. D49, 375–380.
Reynolds, R. A., Remington, S. J., Weaver, L. H., Fisher, R. G., Anderson, W. F., Ammon, H. L. & Matthews, B. W. (1985). Structure of a serine protease from rat mast cells determined from twinned crystals by isomorphous and molecular replacement. Acta Cryst. B41, 139–147.
Riekel, C. (1993). Beamline 1: microfocus beamline. In Annual Report of the European Synchrotron Radiation Facility, Grenoble, France.








































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