OU Crystallography Lab

Department of Chemistry & Biochemistry
Chemical Crystallography Laboratory

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Crystallographic Data Collection

The following sections include a brief discussion of the instruments and methods used to collect X-ray diffraction data. Emphasis is placed on collecting single-crystal diffraction for small-molecule samples; however, numerous notes on instrument differences for powder and protein crystallography are also included. A detailed description of the steps taken to collect data with the Bruker-AXS Apex instrument on a platform goniometer is given at the CCD page.

Outline of Major Steps

  1. Data Collection Hardware
  2. Data Collection Strategy
  3. Data Collection Steps
  4. Corrections to the Data
  5. Merging Data
  6. Placing Data on an Absolute Scale
  7. Determine the Space Group
  8. References

Data Collection Hardware

All diffraction instruments have the following components, a radiation source and optics, a sample positioning and orienting stage, a detector system, and a controlling computer system. Nearly all modern single-crystal diffraction instruments also use a low-temperature device to cool the sample. Occasionally, a high-pressure cell is available.

For the vast majority of small molecule samples, both single-crystal and polycrystalline(powder) encountered in the lab, a sealed-tube X-ray source provides an adequate and simple-to-maintain radiation source. A few small molecule labs need the extra flux of X-rays provided by a rotating-anode generator. Protein crystallography labs routinely use rotating-anode generators or the added flux available at a synchrotron. For all single-crystal studies the radiation source is set to produce a spot beam shape. X-Ray sources used with powder instruments are usually set to produce a line beam shape.

Modern instruments have either a safety enclosure installed around the goniometer, or are located in a separate room with a radiation barrier. In either case, opening the enclosure will cause the shutter mechanism on the X-ray source to close for the user's safety.

The instrument optics shape and modify the X-ray beam before it hits the sample. To reduce the extraneous Kβ radiation, a graphite crystal monochromator is inserted in the incident beam path just after the safety shutter in small molecule single-crystal experiments. Protein crystallography labs use mirrors that selectively absorb the Kβ radiation. Powder diffractometers either use a monochromator in the diffracted beam path or a detector with strong energy discrimination. Small molecule single-crystal instruments now utilize collimators lined with a single glass capillary to increase the incident beam flux of radiation. Powder diffraction instruments often use a a multi-capillary array of collimators to match the line source. Protein diffractometers typically use mirrors to provide as high a flux of X rays as possible with as small of a beam as possible.

Goniometers are devices that position or rotate the sample in a variety of orientations. These devices often include a support for the radiation source and nearly always include a support for the detector. Goniometers use either two or three circles to rotate the sample around a fixed point in space.

drawing of a 4-circle goniometer 
      showing the 2 theta, omega, phi, and chi circles
A 4-circle or Eularian goniometer.
In most single crystal instruments there is a main rotation axis called the ω axis that is typically oriented in the horizontal plane (rotating around a vertical axis). Many goniometers include a motion in the vertical plane called χ. The χ axis can be a full circle, somewhat more than a quarter circle, or a fixed arm.

At least two companies prodce a bending χ arm that is called a κ rotation. All instruments include a motion around the spindle of the goniometer head called the φ axis. In addition to the sample motions, the goniometer includes a motion for the detector. This axis is aptly called the 2θ axis when a point detector is used.

drawing of a kappa-geometry 
      goniometer showing the 2 theta, omega, phi, and kappa circles
A kappa-geometry goniometer.

When an area detector is installed this axis is simply labeled the detector swing angle. All motions of the sample and detector should occur around one fixed point in space. Either a microscope or a magnifying video camera is provided to aid in the centering of the crystal onto this center point of the instrument.

4-circle goniometer with a scintillation 
   detector on the left side

A variety of detectors are available for diffraction measurements. Point type detectors are nearly always made of a scintillator (NaI doped with thorium), photomultiplier tube, and electronics. Other point detectors include either sealed or flow-type proportional counters or solid-state detectors. Area detectors include image plates, multi-wire proportional counters, vidicons (TV cameras), charge-coupled devices (ccds), and complimentary metal oxide semiconductors (cmos). For small-molecule single crystal work, the ccd or cmos detectors have become the most popular because of their short <10 second readout time, broad counting range, and robust nature. Modern ccds are somewhat more expensive than the other types of area detectors, but the increased speed of data collection compared to the other area detectors makes these devices the clear choice. The two great benefits of area detectors over point detectors are 1) the background is greatly reduced, so that weaker spots are measured more precisely and 2) the entire diffraction pattern is collected quickly. Collecting the entire pattern is essential if the sample exhibits non-merohedral twinning. Both point and area detectors produce good estimates for the values of the strong intensities.

Routine protein crystallography is commonly performed using an image plate, a multi-wire or a ccd area detector. The phosphors used with ccd area detectors are somewhat more sensitive for Mo Kα than for Cu Kα radiation. Also the solid angle coverage of area detectors is generally greater for image plates and multi-wire detectors than for ccds. Thus image plate and multi-wire area detectors are being used in most protein crystallography labs. However, ccd detectors are preferred at synchrotrons because of their greater speed (vs image plate systems) and their greater robust nature (vs multi-wire systems). Ccd detectors can withstand the direct beam at a synchrotron, but multi-wire detectors would melt a wire from any strong beam hitting the detector.

Data Collection Strategy

All symmetry-unique data should be collected. For small-molecule studies the data are collected to sinθ / λ of at least 0.6Å-1max > 25° for Mo radiation, θmax > 67° for Cu radiation). Laue symmetry unique data are all the data that are absolutely necessary for centrosymmetric crystal structures. Friedel-related data are also needed for any sample that crystallizes in a noncentrosymmetric space group. It is always wise to collect redundant or repeated measurements for each unique (h k l). Repeated measurements greatly improve the quality of data and add little extra effort when collecting data using an area detector.

The cell parameters usually suggest the crystal system of the material. Sometimes the cell parameters suggest a higher symmetry than is shown later by the diffracted intensities. If only the minimum amount of data initially suggested by the cell parameters is collected and the Laue symmetry is shown to be lower than was originally expected, (e.g. the three cell angles are 90o within experimental error, suggesting orthorhombic symmetry, but the sample exhibits only monoclinic symmetry), then more data will have to be collected later. Thus, it is typical to collect at least one hemisphere (more is better) of data when using an area detector regardless of the symmetry of the sample. Because point detectors can only collect about 1000 reliable data per day, users with point detector instruments are often forced to collect only the minimum amount of data needed.

Data Collection Steps

The following steps describe a general procedure used to collect data with any type of single crystal instrument. The order of most of the steps after collecting the data is not crucial. Selection of an appropriate crystal and alignment of the crystal on the instrument must be carefully performed in order to get the best results from the data.

Corrections to the Data

The general process of converting electronic measurements into usable diffraction data is called data reduction. For each intensity maxima, data reduction includes an integration of the peak including corrections for the spot shape, subtraction of the relative background intensity, corrections for the geometry of the instrument, corrections for crystal decay, and averaging or merging of symmetry-equivalent data. An estimation of the standard deviation of the intensity of each peak is made during each step of reduction process.

The first step involves both an integration of the peak and a subtraction of the background. The integration step must include corrections for overly strong peaks that have been recollected with attenuators. This step sometimes includes corrections for the shape of the diffraction spot. The background, that is presumed to run beneath the peak measurement, is measured both before and after the peak in point detector measurements or is sampled in various areas around the peak in area detector measurements. Background scattering may be due to scattering from the sample mount, scattering from air, fluorescent radiation from the sample or mount, and cosmic radiation.

Data reduction produces both raw intensities and estimates of the standard deviations, often called standard uncertainties, in the intensities. The standard uncertainties calculated directly from counting statistics were found to be underestimates of the true uncertainties. Now standard uncertainties in intensities include a small instrument instability correction term.

For a small crystal completely bathed in a uniform beam of radiation, the integrated intensity, I, is given by:

I = Io (re)2 (Lp/A) (λ/Ω) (F/V)2 λ2υ

The quantity re = e2/mc2 = 2.82 × 10-13 cm is the classical radius of an electron. V is the unit cell volume; υ is the volume of the crystal. Ω is the angular velocity of the sample as the peak moves through the Ewald sphere. Correction terms include the Lorentz correction, L, the polarization correction, p, and the absorption correction, A. Usually the constants in the expression are merged together and neglected until refinement. During refinement, an overall scaling factor between the observed and calculated data is applied. Thus, the following expression is usually applied in calculating structure factor amplitudes.

Ihkl = K (Lp/A) Fhkl2

Lorentz Correction

Some peaks, such as those peaks near to the rotation axis, spend more time passing through the Ewald sphere of reflection than do others. This difference in time is corrected by a term called the Lorentz factor. For point detector systems performing either ω-2θ or ω scans, this correction is simply

L = 1/(sin 2θ)

Area detector intensities that are located in the horizontal plane of the detector would use the formula above for the Lorentz correction. Other intensity maxima located above and below the plane would use different formulas that would also depend upon whether the data are being collected using ω or φ scans.

Polarization Correction

The incident beam of X rays is considered to be circularly polarized, that is the electric components of the different photons have random directions relative to one another. When this beam hits a sample, the sample attenuates the beam depending upon the angle of scattering. Incident beams with electric components aligned parallel with the surface of the diffraction plane have little attenuation; however, incident photons with their electric vectors aligned in the diffraction plane suffer significant attenuation as shown in the figure.

Attenuation of the diffracted beam based 
   upon the direction of the electric components of the incident X-ray photons relative 
   to the diffraction plane.

When the beam hitting the sample is circularly polarized then the following formula for polarization holds.

p = (1 + cos22θ)/2

If a monochromator is inserted in the incident beam, then the X rays impinging on the sample are already partially polarized from the monochromator crystal and a different formula is used that depends upon the geometry of the monochromator.

Decay Correction

Data are usually corrected for sample decay after the geometric corrections are applied. If data were collected at low temperatures, then there is seldom any decay. Point detector data are corrected by an examination of 3 or more peaks that were remeasured periodically throughout the data collection process. Area detector data are corrected by an examination of symmetry-equivalent peaks that were measured in the beginning images and ending images.

For point detector data sets it is often found that the intensities of the monitor reflections increase slightly after the first hour or two of data collection. This small increase in the intensities of the monitor peaks is believed due to an annealing of the crystal by the X-ray beam.

Absorption Correction

The absorption of X rays follows Beer's Law:

I / Io = exp(-μ × t)

where I = transmitted intensity, Io = incident intensity, t = thickness of material, μ = linear absorption coefficient of the material. The linear absorption coefficient depends on the composition of the substance, its density, and the wavelength of the radiation. Since μ depends on the density of the absorbing material, it is usually tabulated as the related function mass absorption coefficient μm = (μ / ρ). The linear absorption coefficient is then calculated from the formula:

μ = ρ ∑ (Pn / 100) × (μ / ρ) = ρ ∑ (Pn / 100) × μm

where the summation is carried out over the n atom types in the cell, and Pn is the percent by mass of the given atom type in the cell.

Absorption of X rays by the sample is often the most difficult correction to perform. The extent of absorption depends on the size and shape of the crystal as well as the types and relative amounts of different atoms in the sample, and the wavelength of radiation used in the experiment. Also absorption from the sample mount may need to be included in the correction. Most researchers try to reduce the effects of absorption by reshaping the sample, properly mounting the sample, using a smaller crystal, or by using a higher energy radiation. There are four general classes of absorption corrections, analytical, empirical, geometrical, and Fourier.

Analytical absorption correction methods depend upon a careful indexing the faces of the crystal.1,2 Instructions to index the faces of a crystal using the Lab's diffractometer have been prepared. Analytical absorption corrections are accomplished by mathematically dividing the sample into very small pieces and calculating the transmittance for each piece of the crystal for each reflection measured. The analytical method is definitely preferred for very strongly absorbing samples. Unfortunately, this method does not correct for the absorption effects of the sample mount. Thus depending on the sample mount and instrument geometry, it may be necessary to follow an analytical absorption correction by an empirical absorption correction to correct for the absorption of the sample mount.

The empirical method requires that more than the minimum Laue unique data be collected.3,4 By comparing the intensities from the redundant measurements, an absorption surface for the sample is calculated. This method is typically chosen because it only requires the instrument to collect more data and because this correction is useful for both the sample and the mount. Area detector data sets usually have sufficient redundancy of the data to be used directly for the correction. For point detector data sets, one or more (h k l) are selected with values of χ near 90°. These peaks are then measured in a series of φ values. These types of scans are called ψ scans. This method was originally developed for protein samples at a time when protein samples were mounted in glass capillaries. However, because of its simplicity and success, it is the absorption correction method of choice for the majority of small molecule samples.

Geometrical absorption corrections depend on the sample shape being approximately the shape of some known geometrical object, usually either a sphere or a cylinder. From the dimensions of the crystal and the transmittance of the sample, these calculations apply approximate corrections to the data.

The Fourier methods for absorption corrections amount to solving the structure and refining the model with isotropic displacement parameters. At this point it is assumed that any differences in the calculated and observed data are due to absorption. As with the empirical method above, an absorption surface is calculated, and a correction based on this surface is applied to all of the data. These methods are NOT recommended because they alter the data to fit the model. Thus interesting features not yet incorporated into the model may be lost.

Placing Data on an Absolute Scale

One of the first tasks needed in processing data is to approximately put the data on an absolute scale. The most widely used method for scaling data was put forward in a note from A. J. C. Wilson in 1942. Much of the discussion in this section is taken from a paper from Robert H. Blessing and David A. Langs.

Structure factors are given in matrix form by

F(h) = Σj fj exp(-Bjs2) exp(2πihTxj)

where s = sin(θ/λ) and the summation is over the j atoms.

Thus the intensities become:

|F(h)|2 = Σj fj2 exp(-2Bjs2) + 2ΣjΣk>j fjfk exp[-(Bj + Bk)s2] × cos(2πhT(xj-xk)]

The previous two equations presume that the displacement parameters are isotropic. If it is further assumed that the individual displacement parameters Bj can be approximated by a common or average B and that the scale factor k for the relative measurements of |F(h)|2 become:

k2|F(h)|meas2 = exp(-2Bs2) {Σjfj2 + 2ΣjΣk>j fjfk × cos(2πhT(xj-xk)]}

Merging Data

Symmetry-equivalent intensity data are merged using the following relationship

F2 = ∑ ωj Fj2 / ∑ ωj

where the summations are over the set of symmetry-equivalent data. In this formula, weights can be either from statistics (ω = 1/σ(F2)) or unit values (&omgea; = 1). Sometimes outliers are either removed from the merging or are given lower weights to reduce their effects on the subsequent refinement.

One measure of how well the data merge together is given by the term Rint

Rint = ∑ [ ∑ |Fj2 - <F2>| ] / ∑ [ (∑ Fj2) ]

where the inner sums are over the symmetry-equivalent reflections and the outer sums are over the unique hkl data.

Determine the Space Group

For many of the more common space groups, the systematic absences uniquely determine the space group. However, for a large number of less common space groups, there are two or more possible space groups that will match a given set of systematic absences. In these cases, the possible space groups are usually tried beginning with the highest symmetry space group until the structure is determined. If there are no strong biases in the distribution of electron density, (e.g. a very heavy atom, or all atoms on a plane) then statistical tests for a center of symmetry will often stear one to the appropriate space group.

References

  1. P. Coppens, L. Leiserowitz, & D. Rabinovich, Acta Cryst., 1965, 18, 1035-1038.
  2. P. Coppens, J. de Meulenaer, & H. Tompa, Acta Cryst., 1967, 22, 601-602.
  3. A. C. T. North, D. C. Phillips, & F. S. Mathews, Acta Cryst., 1968, A24, 351-359.
  4. R. H. Blessing, Acta Cryst., 1995, A51, 33-38.
  5. A. J. C. Wilson, Nature, 1942, 150, 152.
  6. R. H. Blessing & D. A. Langs, Acta Cryst., 1988, A44, 729-735.
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