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Schematic of 4-circle diffractometer; theangles between the incident ray, the detector and the sample. Details

Details

Geoc hemical Instrumentat ion and AnalysisIntegr ating Research and Educatio n > Geochemical Instrumentation and Analysis > Browse Collection > Single-c ryst al X-ray Diffraction

Single-crystal X-ray DiffractionChristine M . Clark, Eastern M ichigan UniversityBarbara L. Dut row, Louisiana State University

What is Single-crystal X-ray Diffraction

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 s ite-ordering. Directly related is s ingle-crys tal refinement, where t he data generated fromthe X-ray analysis is interpreted and refined to obtain the crystal structure.

Fundamental Principles of Si ngle-crystal X-ray Diffraction

Max von Laue, in 1912, discovered that cryst alline subst ances act as three-dimensional diffraction gratings for X-ray wavelengths similar to the spacing of planes in a cryst al latt ice. X-ray diffraction is now a common technique for the study of cryst al structures and atomic spacing.

X-ray diffraction is based on c onst ructive 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 const ructive interference (and a diffracted ray) when conditions satisfy Bragg's Law (n=2 d sin). This law relates the wavelength of electromagneticradiation to the diffraction angle and the latt ice spacing in a cr ystalline sample. These diffracted X-rays are then detected, processed and counted. By changingthe 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 keycomponent of all diffraction is the angle between the incident and diffracted rays. Powder and single-crystal diffraction vary in instrumentation beyond this.

Interpretati on of data:Typical mineral structures contain several thousand unique reflections, whose spatial arrangement is referred to as a diffraction pattern. Indices ( hkl ) may beassigned to each reflection, indicating its position within the diffraction pattern. This pattern has a reciprocal Fourier transform relationship to the crystallinelattice 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-cryst al structure refinement (SREF) page.

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

X-ray diffractometers consist of three basic elements , an X-ra y tube, a samp le holder, and an X-ray detector. X-rays are generated in a cathode ray tube byheating a filament t o p roduce electrons, accelerating the electrons toward a target by app lying a voltage, and impact of the electrons with t he target material.When electrons have sufficient energy to dislodge inner shell electrons of the t arget material, characteristic X-ray spectra are produced. These spectra consis t of several components, t he most common being K and K . K consists, in part, of K 1 and K 2. K 1 has a slightly shorter wavelength and twice the intensity asK 2. The specific wavelengths are characteristic of t he target material. Filtering, by foils or crystal monochrometers, is required to produce monochromatic X-rays needed for diffraction. K 1and K 2 are sufficiently close in wavelength such that a weighted average of the two is used. Moly bdenum is the most commontarget material for single-crystal diffraction, with MoK radiation = 0.7107 . 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 andconverts 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.

Single-cryst al diffractometers use either 3- or 4-circle goniometers. These circles refer to t he four angles (2 , ,, and ) that define the relationship between the crystal lattice, the incident ray and detector. Samples aremounted on thin glass fibers which are attached to brass pins and mounted onto goniometer heads. Adjustmentof 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 islocated directly opposite the collimator to block transmittedrays 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 configurationare then collected by the detector.

Modern single-cryst al diffractometers use CCD (charge-coupled device) technology to transform t he X-ray photons into an electrical signal which are then sent t o a computer for processing.

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Goniometer head.

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 thelattice. 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 p roperties of each mineral. Specific app lications of single-crys tal diffraction include:

New mineral identification, crys tal solution and refinementDetermination of unit cell, bond-lengths , bond-angles and site-orderingCharacterizat ion of cation-anion coordinationVariations in crystal lattice with chemistry

With specialized chambers, structures of high pressure and/or temperature phases can be determinedDetermination of cryst al-chemical vs. environmental control on mineral chemistryPowder 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-dest ructiveDetailed cryst al structure, including unit cell dimensions, bond-lengths , bond-angles and s ite-ordering informationDetermination of cry stal-chemical controls on mineral chemistryWith specialized chambers, structures of high pressure and/or temperature phases can be determinedPowder patterns can also be derived from single-crystals by use of specialized cameras (Gandolfi)

Limitations

Must have a single, robust (stable) sample, generally between 50250 microns in sizeOptically clear sampleTwinned samples can be handled with difficultyData collection generally requires between 24 and 72 hours

User's Guide - Sample Collection and Preparation

Sample S ele ction and PreparationSamples for s ingle-crys tal diffraction should be selected from unfractured, op tically clear crystals. This can be determined by viewing the samples under crossed

polars on a petrographic microscope. Crystals can be broken off a larger sample and the best fragment selected. Samples should be between 30 and 300 microns,

with ideal crys tals averaging 150-250 microns in s ize. To minimize absorp tion affects, equant cryst als are preferred. Spherical cryst als can be created using asmall, air-powered crys tal t umbler, however easily cleaved minerals can break during this process. Therefore, minerals lacking cleavage are the best choice for this step. If the sample is inequant, this must be corrected for during absorption corrections to the data. Sample Mounting

Samples are mounted on t he tip of a thin glass fiber using an epoxy or cement. Care should betaken to use just enough epoxy to secure the sample without embedding it in the mountingcompound. The fiber may be ground to a point to minimize absorption by the glass. This fiber isattached to a brass mounting pin, usually by the use of modeling clay, and the pin is then insertedinto t he goniometer head.

Sample Centering

The goniometer head and sample are then affixed to t he diffractometer. Samples can be centered byviewing the sample under an at tached microscope or video camera and adjust ing the X,Y and Zdirections until the sample is centered under the cross-hairs for all crystal orientations.

Data Collection, Results and Presentation

Data Collection Once the crystal is centered, a preliminary rot ational image is often collected to screen the samplequality 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 theunit cell. Reflections from these frames are auto-indexed to select t he reduced primitive cell and calculate t he orientation matrix (which relates t he unit cell to theactual crystal position within the beam). The primitive unit cell is refined using least-squares and then converted to the appropriate crystal system and Braviaslattice. This new cell is also refined using least -squares to determine the final orientation matrix for the sample.

After t he refined cell and orientat ion matrix have been determined, intensity data is collected. Generally t his is done by collecting a sphere or hemisphere of dat ausing an incremental scan method, collecting frames in 0.1 to 0.3 increments (over certain angles while others are held constant). For highly symmetricmaterials, collection can be const rained symmetrically to reduce the collection t ime. Data is ty pically collected between 4 and 60 2 for molybdenum

radiation. A complete data collection may require anywhere between 6-24 hours, depending on the specimen and the diffractometer. Exposure times of 10-30seconds 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 acomplete 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 beapplied 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

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processing procedures are typ ically p art of the soft ware package which controls and runs the data collection.

Phase Problem and Fourier Transformation Once the dat a have been collected, the phase problem must be solved to find the unique set of phases that can be combined with the structure factors todetermine the electron density and, therefore, the crystal structure. A number of different procedures exist for solution of the phase problem, but the mostcommon method currently, due to the prevalence of high-speed computers, is using direct methods and least-squares, initially assigning phases to strongreflections and it erating 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 withhigher 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 t he initial solution. More information about st ructure solution and refinement can be found on the single-crystal structurerefinement 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. Thefinal structure solution will be presented with an R value, which gives the p ercent variation between the calculated and observed structures. The single-crystalstructure refinement page provides further information on the processes and steps involved in refining a crystal structure.

Literature

The following literature can be used t o further explore Single-crystal X-ray Diffraction

Campana, C.F., Bruker Analytical Application NotePutnis, A. (1992). Introduction to Mineral Sciences . Cambridge, UK: Cambridge University Press. Chapter 3 (pp. 41-80).

Related Links

For more information about Single-crystal X-ray Diffraction follow the links below.

An Introduction to the Scope, Pot ential and App lications of X-ray Analysis , from the International Union of CrystallographyAmerican Mineralogist Crystal Structure DatabaseInternational Centre for Diffraction DataX-ray Powder Diffraction (more info ) --USGS PublicationX-ray Inst ruments --University of California, Santa BarbaraCrystallography Clearinghouse (more info ) --IUCR Reciprocal Net --part of the National Science Digital Library (more info ) . Use the "Learn About" link to find animations of the structures of commonmolecules (including minerals), crys tallography learning resources (tu torials, databases and software), resources on crystallization, and t utorials onsymmetry and point groups.Crystallography Tutorials -- Sean Parkin, University of Kentucky

Teaching Activities and Resources

Teaching activities, labs, and resources p ertaining to Single-crys tal X-ray Diffraction.

Cambridge University X-ray TutorialInternational Union of Crystallography (IUCr) Teaching PamphletsIntroduction to X-ray Diffraction (more info ) --University of California, Santa BarbaraIntroduction to Cryst allography --from LLNLX-ray Crystallography Lecture Notes (more info ) --from Steve Nelson, Tulane University

Neil E. Johnson, 2001, X-Ray Diffraction Simulation using Laser Pointers and Printers , Journal of Geoscience Education, vol 49 #4, p . 346

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