X-ray Diffraction (XRD) - Portland State University
X-ray Diffraction (XRD) 1.0 What is X-ray Diffraction 2.0 Basics of Crystallography 3.0 Production of X-rays 4.0 Applications of XRD 5.0 Instrumental Sources of Error 6.0 Conclusions
Bragg’s Lawn λ 2dsinθEnglish physicists Sir W.H. Bragg and his son Sir W.L. Braggdeveloped a relationship in 1913 to explain why the cleavagefaces of crystals appear to reflect X-ray beams at certain angles ofincidence (theta, θ). The variable d is the distance between atomiclayers in a crystal, and the variable lambda λ is the wavelength ofthe incident X-ray beam; n is an integer. This observation is anexample of X-ray wave interference(Roentgenstrahlinterferenzen), commonly known as X-raydiffraction (XRD), and was direct evidence for the periodic atomicstructure of crystals postulated for several centuries.
Bragg’s Lawn λ 2dsinθThe Braggs were awarded the Nobel Prize inphysics in 1915 for their work in determiningcrystal structures beginning with NaCl, ZnSand diamond.Although Bragg's law was used to explain the interference patternof X-rays scattered by crystals, diffraction has been developed tostudy the structure of all states of matter with any beam, e.g., ions,electrons, neutrons, and protons, with a wavelength similar to thedistance between the atomic or molecular structures of interest.
Deriving Bragg’s Law: nλ 2dsinθX-ray 1Constructive interferenceoccurs only whenn λ AB BCAB BCn λ 2ABSinθ AB/dAB dsinθn λ 2dsinθλ 2dhklsinθhklX-ray 2AB BC multiples of nλ
Constructive and DestructiveInterference of WavesConstructive InterferenceIn PhaseDestructive InterferenceOut of Phase
1.0 What is X-ray Diffraction e/index.html
Why XRD? Measure the average spacings betweenlayers or rows of atoms Determine the orientation of a singlecrystal or grain Find the crystal structure of an unknownmaterial Measure the size, shape and internalstress of small crystalline regions
X-ray Diffraction (XRD)The atomic planes of a crystal cause an incident beam of X-rays tointerfere with one another as they leave the crystal. The phenomenon iscalled X-ray diffraction.Effect of samplethickness on theabsorption of X-raysincident beamcrystaldiffracted /default.htm
Detection of Diffracted X-raysby Photographic filmsamplefilmX-rayPoint whereincident beamentersFilm2θ 0 2θ 180 Debye - Scherrer CameraA sample of some hundreds of crystals (i.e. a powdered sample) show that the diffractedbeams form continuous cones. A circle of film is used to record the diffraction pattern asshown. Each cone intersects the film giving diffraction lines. The lines are seen as arcson the film.
Bragg’s Law and Diffraction:How waves reveal the atomic structure of crystalsn λ 2dsinθn-integerDiffraction occurs only when Bragg’s Law is satisfied Condition for constructiveinterference (X-rays 1 & 2) from planes with spacing dX-ray1X-ray2lλ 3Åθ 30od 3 ÅAtomicplane2θ-diffraction ragg/
Planes in Crystals-2 dimensionλ 2dhklsinθhklDifferent planeshave differentspacingsTo satisfy Bragg’s Law, θ must change as d changese.g., θ decreases as d increases.
2.0 Basics of Crystallographysmallest building blockcd3βαa γbUnit cell(Å)Beryl crystals(cm)CsCld1Latticed2A crystal consists of a periodic arrangement of the unit cell into alattice. The unit cell can contain a single atom or atoms in a fixedarrangement.Crystals consist of planes of atoms that are spaced a distance d apart,but can be resolved into many atomic planes, each with a different dspacing.a,b and c (length) and α, β and γ angles between a,b and c are latticeconstants or parameters which can be determined by XRD.
Seven Crystal Systems - Review
Miller Indices: hkl - ReviewMiller indices-the reciprocals of thefractional intercepts which the planemakes with crystallographic axes(010)Axial lengthIntercept lengthsFractional interceptsMiller indicesa b c4Å 8Å 3Å1Å 4Å 3ż ½ 142 1hk la b c4Å 8Å 3Å 8Å 0 1 00 1 0h kl4/ 0
Several Atomic Planes and Their d-spacings ina Simple Cubic - Reviewa b c1 1 01 1 0a b c1 0 01 0 0d100(100)a b c1 1 11 1 1Cubica b c a0(110)a b c0 1½0 1 2d012(111)(012)Black numbers-fractional intercepts, Blue numbers-Miller indices
Planes and Spacings - Review
Indexing of Planes and Directions Reviewc(111)cbaa direction: [uvw] uvw : a set of equivalentdirectionsab[110]a plane: (hkl){hkl}: a set of equivalent planes
3.0 Production of X-raysCross section of sealed-off filament X-ray tubecoppercoolingwaterX-raysvacuumglasstungsten filamentelectronsto transformertargetVacuumberyllium windowX-raysmetal focusing capX-rays are produced whenever high-speed electrons collide with a metaltarget. A source of electrons – hot W filament, a high accelerating voltagebetween the cathode (W) and the anode and a metal target, Cu, Al, Mo,Mg. The anode is a water-cooled block of Cu containing desired targetmetal.
Characteristic X-ray LinesKαIntensityKα1 0.001ÅKα2Kβλ (Å)Spectrum of Mo at 35kVKβ and Kα2 will causeextra peaks in XRD pattern,and shape changes, butcan be eliminated byadding filters.----- is the massabsorption coefficient ofZr.
Specimen PreparationPowders:0.1µm particle size 40 µmPeak broadeningless diffraction occurringDouble sided tapeGlass slideBulks: smooth surface after polishing, specimens should bethermal annealed to eliminate any surface deformationinduced during polishing.
JCPDS CardQuality of data1.file number 2.three strongest lines 3.lowest-angle line 4.chemicalformula and name 5.data on diffraction method used 6.crystallographicdata 7.optical and other data 8.data on specimen 9.data on diffraction pattern.Joint Committee on Powder Diffraction Standards, JCPDS (1969)Replaced by International Centre for Diffraction Data, ICDF (1978)
A Modern Automated X-ray DiffractometerDetectorX-ray Tube2θθSample stageCost: 560K to 1.6M
Basic Features of Typical XRD Experiment1) ProductionX-ray tube2) Diffraction3) Detection4) Interpretation
Detection of Diffracted X-raysby a DiffractometerCCircle of DetectorPhoton counterBragg - Brentano Focus Geometry, Cullity
Peak Positiond-spacings and lattice parametersλ 2dhklsinθhklFix λ (Cu kα) 1.54Ådhkl 1.54Å/2sinθhkl(Most accurate d-spacings are those calculated from high-angle peaks)For a simple cubic (a b c a 0)d hkl a0h k l222a0 dhkl /(h2 k2 l2)½e.g., for NaCl, 2θ220 46o, θ220 23o,d220 1.9707Å, a0 5.5739Å
Bragg’s Law and Diffraction:How waves reveal the atomic structure of crystalsn λ 2dsinθn-integerDiffraction occurs only when Bragg’s Law is satisfied Condition for constructiveinterference (X-rays 1 & 2) from planes with spacing dX-ray1a0 dhkl /(h2 k2 l2X-ray2)½e.g., for NaCl, 2θλ 3Å220 46 , θ220 23 ,d220 1.9707Å, a0 5.5739Åoloθ 30od 3 ÅAtomicplane2θ-diffraction ragg/
XRD Pattern of NaCl Powder(Cu Kα)Miller indices: The peak is due to Xray diffraction from the {220}planes.IDiffraction angle 2θ (degrees)
Significance of Peak Shape in XRD1. Peak position2. Peak width3. Peak intensity
Peak Width-Full Width at Half MaximumFWHMPeak position 2θmodeIntensityImaxmaxImportant for: Particle orgrain size2. ResidualstrainCan also be fit with Gaussian,Lerentzian, Gaussian-Lerentzian etc.I max2BackgroundBragg angle 2θ
Effect of Lattice Strain on DiffractionPeak Position and WidthDiffractionLineNo StrainUniform Strain(d1-do)/dodod1Peak moves, no shape changesShifts to lower anglesNon-uniform Straind1 constantPeak broadensRMS StrainExceeds d0 on top, smaller than d0 on the bottom
4.0 Applications of XRD XRD is a nondestructive technique To identify crystalline phases and orientation To determine structural properties:Lattice parameters (10-4Å), strain, grain size,expitaxy, phase composition, preferred orientation(Laue) order-disorder transformation, thermalexpansion To measure thickness of thin films and multi-layers* To determine atomic arrangement Detection limits: 3% in a two phase mixture; can be 0.1% with synchrotron radiationSpatial resolution: normally none
Phase IdentificationOne of the most important uses of XRD!!! Obtain XRD pattern Measure d-spacings Obtain integrated intensities Compare data with known standards in theJCPDS file, which are for random orientations(there are more than 50,000 JCPDS cards ofinorganic materials).
Mr. HanawaltPowder diffraction files: The task of building up a collection of knownpatterns was initiated by Hanawalt, Rinn, and Fevel at the Dow ChemicalCompany (1930’s). They obtained and classified diffraction data onsome 1000 substances. After this point several societies like ASTM(1941-1969) and the JCPS began to take part (1969-1978). In 1978 it wasrenamed the Int. Center for Diffraction Data (ICDD) with 300 scientistsworldwide. In 1995 the powder diffraction file (PDF) contained nearly62,000 different diffraction patterns with 200 new being added eachyear. Elements, alloys, inorganic compounds, minerals, organiccompounds, organo-metallic compounds.Hanawalt: Hanawalt decided that since more than one substance canhave the same or nearly the same d value, each substance should becharacterized by it’s three strongest lines (d1, d2, d3). The values of d1d3 are usually sufficient to characterize the pattern of an unknown andenable the corresponding pattern in the file to be located.
Phase Identificationabc- Effect of Symmetryon XRD Patterna. Cubica b c, (a)2θb. Tetragonala b c (a and c)c. Orthorhombica b c (a, b and c) Number of reflections Peak position Peak splitting
More Applications of XRDaIntensity(004)bDiffraction patterns of threeSuperconducting thin filmsannealed for different times.a. Tl2CaBa2Cu2Ox (2122)b. Tl2CaBa2Cu2Ox (2122) Tl2Ca2Ba2Cu3Oy (2223)b a cc. Tl2Ca2Ba2Cu3Oy (2223)c(004)CuO was detected bycomparison to standards
XRD Studies Temperature Electric Field Pressure Deformation
Intensity200oCKα2Kα1250oC300oC450oC2θ(331) Peak of cold-rolled andAnnealed 70Cu-30Zn (brass)Increasing Grain size (t)As rolledHARDNESS (Rockwell B)Effect of Coherent Domain SizeAs rolled300oC450oCANNEALING TEMPERATURE ( C)0.9 λB t CosθPeak BroadeningScherrer ModelAs grain size decreases hardnessincreases and peaks becomebroader
High Temperature XRD Patterns of theDecomposition of YBa2Cu3O7-δIntensity (cps)IT2θ
In Situ X-ray Diffraction Study of an Electric FieldInduced Phase TransitionSingle Crystal FerroelectricIntensity (cps) Intensity (cps)(330)92%Pb(Zn 1/3Nb2/3)O3 -8%PbTiO3E 6kV/cm(330) peak splitting is due toPresence of 111 domainsKα1Rhombohedral phaseKα2E 10kV/cmNo (330) peak splittingKα1 Tetragonal phaseKα2
What Is A Synchrotron?A synchrotron is a particle acceleration device which,through the use of bending magnets, causes a chargedparticle beam to travel in a circular pattern.Advantages of using synchrotron radiation: Detecting the presence and quantity of trace elements Providing images that show the structure of materials Producing X-rays with 108 more brightness than those fromnormal X-ray tube (tiny area of sample) Having the right energies to interact with elements in lightatoms such as carbon and oxygen Producing X-rays with wavelengths (tunable) about the sizeof atom, molecule and chemical bonds
Synchrotron Light SourceDiameter: 2/3 length of a football fieldCost: Bi
5.0 Instrumental Sources of Error Specimen displacement Instrument misalignment Error in zero 2θ position Peak distortion due to Kα2 and Kβ wavelengths
6.0 Conclusions Non-destructive, fast, easy sample prep High-accuracy for d-spacing calculations Can be done in-situ Single crystal, poly, and amorphous materials Standards are available for thousands of materialsystems
XRF: X-Ray FluorescenceXRF is a ND technique used for chemical analysis of materials. An Xray source is used to irradiate the specimen and to cause the elementsin the specimen to emit (or fluoresce) their characteristic X-rays. Adetection system (wavelength dispersive) is used to measure thepeaks of the emitted X-rays for qual/quant measurements of theelements and their amounts. The techniques was extended in the1970’s to to analyze thin films. XRF is routinely used for thesimultaneous determination of elemental composition and filmthickness.Analyzing Crystals used: LiF (200), (220), graphite (002), W/Si, W/C,V/C, Ni/C
1) X-ray irradiates specimen2) Specimen emits characteristicX-rays or XRF3) Analyzing crystal rotates toaccurately reflect eachwavelength and satisfyBragg’s Law4) Detector measures positionand intensity of XRF peaksXRF SetupNiKαI4)2φ1)2)3)nλ 2dsinφ- Bragg’s LawXRF is diffracted by acrystal at different φ toseparate X-ray λ and toidentify elements
Preferred OrientationA condition in which the distribution of crystal orientations isnon-random, a real problem with powder samples.Random orientation ------IntensityPreferred orientation ------It is noted that due to preferred orientation several blue peaks arecompletely missing and the intensity of other blue peaks is very misleading.Preferred orientation can substantially alter the appearance of the powderpattern. It is a serious problem in experimental powder diffraction.
3. By Laue Method - 1st Method Ever UsedToday - To Determine the Orientation of Single CrystalsBack-reflection Lauecrystal[001]X-rayFilmpatternTransmission LauecrystalFilm
formula and name 5.data on diffraction method used 6.crystallographic data 7.optical and other data 8.data on specimen 9.data on diffraction pattern. Quality of data Joint Committee on Powder Diffraction Standards, JCPDS (1969) Replaced by International Centre for Diffraction Data, ICDF (1978)
X-Ray Diffraction and Crystal Structure (XRD) X-ray diffraction (XRD) is one of the most important non-destructive tools to analyse all kinds of matter - ranging from fluids, to powders and crystals. From research to production and engineering, XRD is an indispensible method for
Powder XRD is a useful application of X-ray diffraction, due to the ease of sample preparation compared to single-crystal diffraction. Powder XRD is also able to perform analysis like solid state reaction monitoring, such as the TiO 2 anata
particle size Revealed that nano Figure 1. UV-Vis and energy gap of two the metal oxides 2- X-ray diffraction analysis The nanostructure (zinc oxide and copper oxide) were explored by x-ray diffraction type (SHIMADZU XRD-6000). The XRD utilizing CuKα radiation line of 1.54 A wavelength with 2θ run (10 -80 ) .The XRD analysis for
Diffraction of Waves by Crystals crystal structure through the diffraction of photons (X-ray), nuetronsandelectrons. 18 Diffraction X-ray Neutron Electron The general princibles will be the same for each type of waves.
X-ray Powder Diffraction in Catalysis. December 18. th. 2009. This lecture is designed as a practically oriented guide to powder XRD in catalysis, not as an introduction into the theoretical basics of X-ray diffraction. Thus, the following topics are NOT covered here (refer to standard textbooks instead):
Plane transmission diffraction grating Mercury-lamp Spirit level Theory If a parallel beam of monochromatic light is incident normally on the face of a plane transmission diffraction grating, bright diffraction maxima are observed on the other side of the grating. These diffraction maxima satisfy the grating condition : a b sin n n , (1)
purging nitrogen gas flowing at 40 withdrawn from the retroml/min. X-ray diffraction X-ray scattering measurements were carried out with an X-ray diffractometer (PW 3710, Philips Ltd). A Cu Ka radiation source was used, and the scanning rate until the time of analysis.(2 h/min) was 5 C/min. X-ray diffraction (XRD) measurements were carried out on
Abrasive water jet (AWJ) machining has been known for over 40 years. It was introduced, described and presented by Hashish [1]. It is often used to cut either semi-finished products or even final products, namely from plan-parallel plates of material. Nevertheless, applications of abrasive water jets for milling [2], turning [3], grinding [4] or polishing [5] are tested more and more often .
