Single-crystal X-ray Diffraction(SCXRD)

Single-crystal X-ray Diffraction is a non-destructive analytical technique which provides

detailed information about the internal lattice of crystalline substances, including unit cell
dimensions, bond-lengths, bond-angles, and details of site-ordering. Directly related is single-
crystal refinement, where the data generated from the X-ray analysis is interpreted and
refined to obtain the crystal structure.

Fundamental Principles of Single-crystal X-ray Diffraction

Max von Laue, in 1912, discovered that crystalline substances act as three-dimensional
diffraction gratings for X-ray wavelengths similar to the spacing of planes in a crystal lattice.
X-ray diffraction is now a common technique for the study of crystal structures and atomic
spacing.

X-ray diffraction is based on constructive interference of monochromatic X-rays and a

crystalline sample. These X-rays are generated by a cathode ray tube, filtered to produce
monochromatic radiation, collimated to concentrate, and directed toward the sample. The
interaction of the incident rays with the sample produces constructive interference (and a
diffracted ray) when conditions satisfy Bragg's Law (nλ=2d sinθ). This law relates the
wavelength of electromagnetic radiation to the diffraction angle and the lattice spacing in a
crystalline sample. These diffracted X-rays are then detected, processed and counted. By
changing the geometry of the incident rays, the orientation of the centered crystal and the
detector, all possible diffraction directions of the lattice should be attained.

All diffraction methods are based on generation of X-rays in an X-ray tube. These X-rays are
directed at the sample, and the diffracted rays are collected. A key component of all
diffraction is the angle between the incident and diffracted rays. Powder and single-crystal
diffraction vary in instrumentation beyond this.

Interpretation of data

Typical mineral structures contain several thousand unique reflections, whose spatial
arrangement is referred to as a diffraction pattern. Indices (hkl) may be assigned to each
reflection, indicating its position within the diffraction pattern. This pattern has a reciprocal
Fourier transform relationship to the crystalline lattice and the unit cell in real space. This
step is referred to as the solution of the crystal structure. After the structure is solved, it is
further refined using least-squares techniques. This procedure is described fully on the single-
crystal structure refinement (SREF) page.

Single-crystal X-ray Diffraction Instrumentation - How Does It Work?

X-ray diffractometers consist of three basic elements, an X-ray tube, a sample holder, and an
X-ray detector. X-rays are generated in a cathode ray tube by heating a filament to produce
electrons, accelerating the electrons toward a target by applying a voltage, and impact of the
electrons with the target material. When electrons have sufficient energy to dislodge inner
shell electrons of the target material, characteristic X-ray spectra are produced. These spectra
consist of several components, the most common being Kα and Kβ. Kα consists, in part, of
Kα1 and Kα2. Kα1 has a slightly shorter wavelength and twice the intensity as Kα2. The specific
wavelengths are characteristic of the target material. Filtering, by foils or crystal
monochrometers, is required to produce monochromatic X-rays needed for diffraction.
Kα1and Kα2 are sufficiently close in wavelength such that a weighted average of the two is
used. Molybdenum is the most common target material for single-crystal diffraction, with
MoKα radiation = 0.7107Å. These X-rays are collimated and directed onto the sample. When
the geometry of the incident X-rays impinging the sample satisfies the Bragg Equation,
constructive interference occurs. A detector records and processes this X-ray signal and
converts the signal to a count rate which is then output to a device such as a printer or
computer monitor. X-rays may also be produced using a synchotron, which emits a much
stronger beam.

Schematic of 4-circle diffractometer; the angles between the incident ray, the detector
and the sample.
Single-crystal diffractometers use either 3- or 4-circle goniometers. These circles refer to the
four angles (2θ, χ, φ, and Ω) that define the relationship between the crystal lattice, the
incident ray and detector. Samples are mounted on thin glass fibers which are attached to
brass pins and mounted onto goniometer heads. Adjustment of the X, Y and Z orthogonal
directions allows centering of the crystal within the X-ray beam.

X-rays leave the collimator and are directed at the crystal. Rays are either transmitted through
the crystal, reflected off the surface, or diffracted by the crystal lattice. A beam stop is located
directly opposite the collimator to block transmitted rays and prevent burn-out of the detector.
Reflected rays are not picked up by the detector due to the angles involved. Diffracted rays at
the correct orientation for the configuration are then collected by the detector.

Modern single-crystal diffractometers use CCD (charge-coupled device) technology to

transform the X-ray photons into an electrical signal which are then sent to a computer for
processing.

Applications
Single-crystal X-ray diffraction is most commonly used for precise determination of a unit
cell, including cell dimensions and positions of atoms within the lattice. Bond-lengths and
angles are directly related to the atomic positions. The crystal structure of a mineral is a
characteristic property that is the basis for understanding many of the properties of each
mineral. Specific applications of single-crystal diffraction include:

 New mineral identification, crystal solution and refinement

 Determination of unit cell, bond-lengths, bond-angles and site-ordering

 Characterization of cation-anion coordination

 Variations in crystal lattice with chemistry

 With specialized chambers, structures of high pressure and/or temperature phases can be
determined

 Determination of crystal-chemical vs. environmental control on mineral chemistry

 Powder patterns can also be derived from single-crystals by use of specialized cameras
(Gandolfi)
 Strengths and Limitations of Single-crystal X-ray Diffraction

Strengths

 No separate standards required

 Non-destructive

 Detailed crystal structure, including unit cell dimensions, bond-lengths, bond-

angles and site-ordering information

 Determination of crystal-chemical controls on mineral chemistry

 With specialized chambers, structures of high pressure and/or temperature phases

can be determined

 Powder patterns can also be derived from single-crystals by use of specialized

cameras (Gandolfi)

Limitations

 Must have a single, robust (stable) sample, generally between 50—250 microns in
size

 Optically clear sample

 Twinned samples can be handled with difficulty

 Data collection generally requires between 24 and 72 hours

 Sample Collection and Preparation

Data Collection
Once the crystal is centered, a preliminary rotational image is often collected to screen the
sample quality and to select parameters for later steps. An automatic collection routine can
then be used to collect a preliminary set of frames for determination of the unit cell.
Reflections from these frames are auto-indexed to select the reduced primitive cell and
calculate the orientation matrix (which relates the unit cell to the actual crystal position
within the beam). The primitive unit cell is refined using least-squares and then converted
to the appropriate crystal system and Bravias lattice. This new cell is also refined using
least-squares to determine the final orientation matrix for the sample.
After the refined cell and orientation matrix have been determined, intensity data is
collected. Generally this is done by collecting a sphere or hemisphere of data using an
incremental scan method, collecting frames in 0.1° to 0.3° increments (over certain angles
while others are held constant). For highly symmetric materials, collection can be
constrained symmetrically to reduce the collection time. Data is typically collected
between 4° and 60° 2θ for molybdenum radiation. A complete data collection may require
anywhere between 6-24 hours, depending on the specimen and the diffractometer.
Exposure times of 10-30 seconds per frame for a hemisphere of data will require total run
times of 6-13 hours. Older diffractometers with non-CCD detectors may require 4-5 days
for a complete collection run.

Corrections for Background, Absorption, etc.

After the data have been collected, corrections for instrumental factors, polarization
effects, X-ray absorption and (potentially) crystal decomposition must be applied to the
entire data set. This integration process also reduces the raw frame data to a smaller set of
individual integrated intensities. These correction and processing procedures are typically
part of the software package which controls and runs the data collection.

Phase Problem and Fourier Transformation

Once the data have been collected, the phase problem must be solved to find the unique
set of phases that can be combined with the structure factors to determine the electron
density and, therefore, the crystal structure. A number of different procedures exist for
solution of the phase problem, but the most common method currently, due to the
prevalence of high-speed computers, is using direct methods and least-squares, initially
assigning phases to strong reflections and iterating to produce a refined fit.
Structure solution

Solution of the phase problem leads to the initial electron density map. Elements can be
assigned to intensity centers, with heavier elements associated with higher intensities.
Distances and angles between intensity centers can also be used for atom assignment
based on likely coordination. If the sample is of a known material, a template may be
used for the initial solution. More information about structure solution and refinement can
be found on the single-crystal structure refinement page.
Structure Refinement

Once the initial crystal structure is solved, various steps can be done to attain the best
possible fit between the observed and calculated crystal structure. The final structure
solution will be presented with an R value, which gives the percent variation between the
calculated and observed structures. The single-crystal structure refinement page provides
further information on the processes and steps involved in refining a crystal structure.