{ What is usually going to cause you trouble? Texture effects - affects peak intensity Sample displacement - affects peak 2q position { Identification processes depend on position, intensity pairs
Optics of a Diffractometer Incident Beam Slits b a O Specimen S Diffractometer Axis Line Source F Receiving Slit to counter
Diffractometer Geometry goniometer circle focusing circle R q O F rf 2 q S specimen Specimen needs to be: centered on the goniometer circle and Tangent to the focusing circle
Specimens and Sampling Types of Specimens Thick samples Good intensity…but problems defining depth (position) Thin specimens No penetration depth effect (good position)… but low intensity
Texture and Specimen Displacement Particle size Particle orientation Particle shape Particle statistics X-ray absorption Particle Size Particle Distribution
Example: Is there real gold in Goldschlager?
Preferred Orientation Results in Exaggerated Au (200) Peak
Preferred Orientation Results in Exaggerated Alpha Lactose Hydrate (040,080) Peak Heavy Orientation on 040,080 Raw Data Effexor Ventafaxine HCl PDF 02-078-5277 Lactose Hydrate PDF 00-027-1947
Tip – Examine Peak Widths Peak width (FWHM) narrower than instrumental broadening
ZAP ! Childrens Vitamin Note: 400 lightning strikes/hr during data collection
Specimens and Sampling Crystallite Statistics How many crystallites are enough? Are the crystallites randomly oriented? Particle Size Effects Particle size distributions Amorphous surface layers
Specimen Preparation Properties of a Good Specimen Representative of the sample Grain size less than 200 mesh (74 microns) Finer sizes may be required Preferably as loose grains
Specimen Preparation Instrument Geometry and Absorption Beam must see specimen unimpeded Working thickness of specimen defined by beam penetration (t0.5 = 1/ Ideal position has t0.5 on axis of rotation Thin or tiny specimens may yield sharpest diffraction peaks or lines
Tip: Narrow or spotty peaks may be a sign of orientation or poor sampling statistics (small samples) Film Courtesy Forensic Science Service Counter - Courtesy ORNL 2D Detector - Courtesy Bruker-AXS
Geometry of a Diffractometer 3 Angle is too high? Sample is high. Angle is too low? Sample is low. 1 2 Rotation Axis 1. Ideal diffracted beam position 2. Diffracted beam from low specimen 3. Diffracted beam from high specimen - Rule of displaced specimens 0.001 inch = 25m = 0.01o 2
Diffractometer Specimens Specimen Requirements Flat specimen surface Smooth specimen surface Area greater than that irradiated by beam Specimen support gives zero diffraction or zero contribution Thickness greater than 10t0.5 Random grain orientation Sufficient grains for crystallite statistics
Properties of a Sample Size of sieved particles 200 mesh 74 m 325 mesh 45 m 400 mesh 38 m 600 mesh 25 m 1000 mesh 10 m Minimum diameter passes sieve
Properties of a Sample Particle Shapes Equant equal dimensional Tabular 1 short dimension Bladed long, intermediate, short Acicular 2 short dimensions Long dimensions align parallel to the specimen surface
Before shaking After shaking Before shaking Before shaking After shaking After shaking [Tim] – demo with trail mix
Particle Size vs. Crystallite Size Particles may be aggregates of crystals Particle size greater than crystallite size
Particle Size vs. Crystallite Size Particles may be single crystals Particle size equal to crystallite size
Particle Size vs. Crystallite Size Particles may be imperfect single crystals Particle size larger than crystallite size
Particle Size vs. Crystallite Size Crystal domains Individual domains are perfect Boundaries Dislocations Twin walls Anti-phase walls Stacking faults
Particle Statistics The limiting factor in modern QXRPD is the specimen Preferred orientation Is the sample random? Particle statistics Are there enough particles?
Particle Statistics How many particles are necessary for randomness? Describe orientation analytically Represent all Bragg planes of a given set (hkl) by a perpendicular vector Toothpick & candy
Particle Statistics Randomness requires that the “weighted” distribution of these vectors be uniform over space Number of vectors per crystallite is the multiplicity
Particle Statistics If the specimen is random, vectors (toothpicks) from a given hkl set trace out a hemisphere “dome” above the sample – kush ball effect Only small portion of this dome actually sampled in q-2q scan detector X-ray source Specimen
XRD2: Definition - Diffraction Pattern in 3D Space (a) Single crystal pattern (b) Polycrystalline samples with poor grain sampling statistics (large grain size, thin film, inhomogeneous structure, micro area, small amount of sample) (c) Ideal powder diffraction pattern
Grit from man’s clothing Control grit from gasoline-powered grinder Small specimen Limited particles
X-ray source accepted range detector Specimen
Example of a highly oriented polycrystalline material: ZnO ~2000 Å across c-axis a-axis Typical grain Microstructure happens to take on symmetry of molecular structure. Not always the case! ZnO unit cell: a = 3.25, c = 5.2 Å (many orders of mag. smaller!!!) ~½ billion unit cells in typical grain (0.2 mm across, 1 mm long)
Since grains have the appearance of fibers this makes for a simplistic picture of our grain orientation model. We can place our vector parallel to the long (c-axis) of the grains and see the ‘kush ball’ effect. random oriented
Number of Particles Volume of sample in X-ray beam V= (area of beam) (2x half-depth of penetration) Assume area = 1cm x 1cm = 100mm2 t1/2 = 1/m,where m = linear absorption coefficient mSiO2 = 97.6 cm-1 ~ 100 cm-1 = 10 mm-1 V = (100) (2) (10-1) mm3 = 20 mm3 Assume crystallite size = particle size
Number of Particles # of particles in irradiated volume D = 40 mm 10 mm 1mm Particles in 20 mm3 5.97 x 105 3.82 x 107 3.82 x 1010 How many particles are sufficient to allow randomness to be achieved?
Analyzing the Particle Distribution Area of a sphere of unit radius = 4p steradians Effect of particle size 40 mm 10 mm 1 mm Area/Pole AP = 4p = 2.11 x 10-5 3.27 x 10-7 6.58 x 10-10 #
Analyzing the Particle Distribution Because the particle is small compared to the sample, the divergence is limited by the size of the X-ray target and the particle size.
Conditions for Diffraction X-ray Target Divergence Slit Sample Diffracting Particle This tends to further limit the accepted toothpicks
Summary # of Particles which may diffract area that represents the window of accepted toothpicks area of the sphere designated to an individual toothpick # = Top view of unit sphere = AD AP
Summary 40mm 10mm 1mm # diffraction particles 12 760 38000 To achieve 1% accuracy s = n/n Std. err. = 2.3 s < 1% n>52900
Summary Even 1 mm particles do not achieve goal Other factors affecting analysis % of phase in sample Decreases # of particles per phase hkl multiplicity Increases with crystal symmetry *Maybe crystallite size is smaller than particle size - will help boost statistics
TABLE I Intensity measurements on fractions of less than 325-mesh quartz powder. Tabulated values are areas in arbitrary units of the 3.33A maximum as counted with the Geiger- counter X-ray spectrometer using CuKa radiation. (Klug and Alexander, 1974) 15-50um 5-50um 5-15um Less than 5um Specimen No. Fraction Fraction Fraction Fraction 1 7,612 8,668 10,841 11,055 2 8,373 9,040 11,336 11,040 3 8,255 10,232 11,046 11,386 4 9,333 9,533 11,597 11,212 5 4,823 8,530 11,541 11,460 6 11,123 8,617 11,336 11,260 7 11,051 11,598 11,686 11,241 8 5,773 7,818 11,288 11,428 9 8,527 8,021 11,126 11,406 10 10,255 10,190 10,878 11,444 Mean area: 8,513 9,227 11,268 11,293 Mean deviation: 1,545 929 236 132 Mean % deviation: 18.2 10.1 2.1 1.2
Theoretical % Mean Deviation of Intensities High absorption magnifies intensity variation Effective Particle Dimension m) Volume m)3 = 5 20 % Mean Deviation of I 100 500 2000 1 1 0.02 0.04 0.1 0.2 0.4 2 8 0.06 0.1 0.3 0.6 1.2 5 125 0.2 0.5 1.1 2.4 4.9 10 1000 0.7 1.4 3.1 6.9 13.8 20 8000 2.0 3.9 8.7 19.5 39.0 50 125000 7.7 15.4 34.5 - - Organics Metal- SiO2 Cu, Ni, Ag, Pb Organics TiO2 After A,K,K (1948)
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