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    X-Ray Diffraction

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    Merve Ayvaz Köroğlu
    The document provides an overview of x-ray diffraction (XRD), including how it works, how x-rays are produced and detected, and applications in catalysis. XRD can be used to identify crystalline phases in catalysts by analyzing lattice structures. X-rays are scattered by crystal planes based on Bragg's law, allowing calculation of lattice spacings. Common XRD techniques include using sealed x-ray tubes, rotating anodes, and synchrotrons to produce x-rays, then detecting the scattered X-rays to form diffraction patterns. Analysis of peak widths and positions allows determining properties like crystallite size using the Scherrer equation.

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    X-Ray Diffraction

    Uploaded by

    Merve Ayvaz Köroğlu
    252 views30 pages
    The document provides an overview of x-ray diffraction (XRD), including how it works, how x-rays are produced and detected, and applications in catalysis. XRD can be used to identify crystalline phases in catalysts by analyzing lattice structures. X-rays are scattered by crystal planes based on Bragg's law, allowing calculation of lattice spacings. Common XRD techniques include using sealed x-ray tubes, rotating anodes, and synchrotrons to produce x-rays, then detecting the scattered X-rays to form diffraction patterns. Analysis of peak widths and positions allows determining properties like crystallite size using the Scherrer equation.

    Original Description:

    Details of working principles and theory of x-ray diffraction

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    The document provides an overview of x-ray diffraction (XRD), including how it works, how x-rays are produced and detected, and applications in catalysis. XRD can be used to identify crystalline phases in catalysts by analyzing lattice structures. X-rays are scattered by crystal planes based on Bragg's law, allowing calculation of lattice spacings. Common XRD techniques include using sealed x-ray tubes, rotating anodes, and synchrotrons to produce x-rays, then detecting the scattered X-rays to form diffraction patterns. Analysis of peak widths and positions allows determining properties like crystallite size using the Scherrer equation.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    252 views30 pages

    X-Ray Diffraction

    Uploaded by

    Merve Ayvaz Köroğlu
    The document provides an overview of x-ray diffraction (XRD), including how it works, how x-rays are produced and detected, and applications in catalysis. XRD can be used to identify crystalline phases in catalysts by analyzing lattice structures. X-rays are scattered by crystal planes based on Bragg's law, allowing calculation of lattice spacings. Common XRD techniques include using sealed x-ray tubes, rotating anodes, and synchrotrons to produce x-rays, then detecting the scattered X-rays to form diffraction patterns. Analysis of peak widths and positions allows determining properties like crystallite size using the Scherrer equation.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 30

    1

    ChE 592

    X-ray Diffraction

    Merve Ayvaz
    Chemical Engineering Department
    Boazii University

    Introduction
    Atomic radii of atoms are smaller than 1/1000 of the wavelengths
    present in the visible light.
    A suitable wavelength to observe individual atoms is x-rays.
    For Catalysis
    It is used to identify crystalline phases inside catalysts by
    means of lattice structural parameters, kinetics of bulk
    transformation and to obtain an indication of particle size.

    Niemantsverdriet J.W.

    Introduction

    The scattered monochromic X-rays that are in phase give


    constructive interference.
    Diffraction of x-rays by crystal planes allows one to drive lattice
    spacing by using

    Bragg relation: n =2d sin


    d is charactesitic for a given compound
    n: order of reflection; : wavelength of x-rays; d: distance between two lattice planes; :
    angle between the incoming x-rays and the normal to the reflecting lattice plane

    Jenkins R.,Snyder R.L.

    Nature and Properties of X-rays


    The x-rays have wavelength from 0.1 to 100 , which are located
    between gamma radiation and ultraviolet rays.
    The wavelengths most commonly used in crystallography, range
    between 0.5 to 2.5 . If d < /2, then sin > 1, which is
    impossible. n =2d sin
    They are of the same order of magnitude as the shortest
    interatomic distances observed both organic and
    inorganic materials.

    Jenkins R.,Snyder R.L.

    Production of X-rays
    X-ray tube
    Sealed Tube
    Rotating Anode Tube

    Synchrotron

    Percharsky V.K., Zavalij P.Y.

    X-ray Tube
    Known as a laboratory or conventional x-ray source,
    Electromagnetic waves are generated from impacts of
    high-energy electrons with a metal target.
    Brightness is limited with the thermal properties of target
    material,

    Simple,
    Most commonly used,
    Must be continuously cooled,
    Low efficiency,
    Percharsky V.K., Zavalij P.Y.

    Sealed Tube
    Consist of a stationary anode coupled with
    cathode, placed in a metal/glass or
    metal/ceramic container sealed under
    vacuum
    Electrons are emitted by the cathode,
    accelerate through the anode (30 to 60 kV),
    Typical current is between 10 to 50 mA,
    The x-rays are generated by the impacts of
    high energy electrons,
    The exit the tube from Be window,

    Percharsky V.K., Zavalij P.Y.

    Synchrotron
    Advance source of x-ray radiation,
    High energy electrons are confined in a storage
    ring,
    They move in a circular orbit, electrons accelerate
    towards the center of the ring, thus emitting
    electromagnetic radiation.
    Extremely bright, (limited by the flux of electrons)
    Thermal losses are minimized,
    No target to cool,
    Percharsky V.K., Zavalij P.Y.

    Collimation and Monochromatization


    The radiation comes out from the x-ray source is
    polychromatic radiation. (K, K1, K2, K)

    Jenkins R.,Snyder R.L.

    10

    Monochromatization
    Reducing the intensity of white radiation,
    Eliminating the undesirable characteristic wavelengths
    from x-ray spectrum to K1, K2,

    Jenkins R.,Snyder R.L.

    11

    Adsorption of x-rays and B-filter


    Simplest method performed by means of filtering.
    When x-ray penetrate into a matter, they are partially
    transmitted and partially adsorbed.

    It=I0 exp(-x)
    :linear absorption coefficient of the material
    Examples of filter elements: Sc,Ti,Cr,Mn,Fe,Co,Ni,Cu

    Jenkins R.,Snyder R.L.

    12

    Angular Divergence and Collimation


    The simplest collimation can be achieved by placing a slit
    between the x-ray source and the sample.
    Angular divergence of thus collimated beam is
    established by the dimensions of the source, the size and
    the placement of the slit.

    Jenkins R.,Snyder R.L.

    13

    Detection of X-rays

    Role is to measure intensity,


    Sensitive to x-rays,
    The oldest detector of x-ray is photographic film,
    In modern detectors the signal, usually electric current,
    easily digitized and transferred to a computer for further
    processing and analysis,

    Percharsky V.K., Zavalij P.Y.

    14

    Gas Proportional Counter-Point Detector


    The x-ray photons enter to the window and is absorbed
    by the gas, it ionizes Xe atoms producing positively
    charged ions and electrons.
    The resulting electric current is measured
    The number of current pulses is proportional to the
    photons absorbed.
    The second window is usually added to enable exit of
    non-absorbed photons.

    Percharsky V.K., Zavalij P.Y.

    15

    Other types of detectors


    Scintillation detector
    Position sensitive detector
    Area detectors

    Percharsky V.K., Zavalij P.Y.

    Theory of X-Ray Diffraction

    17

    Diffraction
    X-rays scattered from different parts of the atom
    (nucleus and electrons) combine to give the effect of a
    point source.
    The radiation scattered by the atom depends on the
    number of electrons associated to atom and their
    distribution.

    Nuffield E.W.

    18

    Intensity of the Diffraction


    The intensities of the diffracted waves;
    Depend on the kind and arrangement of atoms in the
    crystal structure
    Proportional to the squares of amplitudes of the
    composite reflected waves

    Nuffield E.W.

    Derivation of Braggs Law


    AB = d sin
    n = 2 d sin

    Beams are parallel to each other


    The second beam must travel the extra distance AB + BC
    n = AB +BC
    AB = BC
    n = 2AB
    Glenn A. Richard, Mineral Physics Institute, SUNY Stony Brook

    Bragg
    Relation

    Diffraction Pattern
    A diffraction pattern records the X-ray intensity as a function of 2theta angle.

    Tube voltage
    Current
    --A starting 2-theta angle.
    --A step-size (typically 0.005 degrees).
    --A count time per step (typically 0.05-1 second).
    --An ending 2-theta angle.

    Purudue University, Geoscience Department

    Lattice Structure
    crystal can be arranged in
    sheets in a number of ways

    0A = 0B = 0C = a = the
    length of the edge of the
    unit cell
    Bragg Equation Satisfied
    for all planes

    University of Saskatchewan, Physics Department

    Miller Indices h,k,l plane


    dhkl
    h, k, l are required to describe the order of the
    diffracted waves
    Denote the orientation of the reflecting sheets
    with respect to the unit cell
    The path difference in units of wavelength
    between identical reflecting sheets
    dhkl= a/(h2 + k2 + l2)
    University of Saskatchewan, Physics Department

    Determination of the unit cell structure for


    a cubic lattice
    For a cubic lattice, primitive, fcc, bcc reflections are obsreved
    See h,k,l in the increasing order of sum h2 + k2 + l2

    10
    P 0 110 111 200 210 211 220 221 300 310 311
    11
    F 1 200 220 311 222 400 331 420 422 333 511
    11 sin2 1/ sin2 2 = (h12 + k12 + l12)/(h22 + k22 + l22)
    B 0 200 211 220 310 222 321 400 411 330 420
    P
    1:2:3:4:5:6:8
    1:1 1/3 : 2 2/3: 3 2/3: 4: 5
    F
    1/3: 6 1/3
    B
    1:2:3:4:5:6:7
    Atkins,Physical Chemistry

    All odd
    or even
    Sum is
    even

    Determination of the unit cell structure for


    a cubic lattice
    sin2 1/ sin2 2 = (h12 + k12 + l12)/(h22 + k22 + l22)
    Powder diffraction angles () are red from the pattern are:
    17.660, 25.400, 31.700, 37.350, 42.710, 47.980, 59.080
    sin2 gives
    0.0920, 0.1840, 0.2761, 0.3681, 0.4601, 0.5519, 0.7360
    These number give the ratio 1:2:3:4:5:6:8
    P

    So the cell is primitive

    F
    B

    1:2:3:4:5:6:8
    1:1 1/3 : 2 2/3: 3 2/3: 4: 5
    1/3: 6 1/3
    1:2:3:4:5:6:7

    Atkins,Physical Chemistry

    Determination of unit cell edge length for a


    cubic cell
    dhkl= a/(h2 + k2 + l2)
    = 2 d sin
    (4 sin2 )/2 = (h2 + k2 + l2)/a2

    (4 sin2 )/2 = (h2 + k2 + l2) *(1/a2)


    Augustana Collage, Chemistry and Physics Department

    26

    Principles of Determination of Crystallite Size


    Rays A, D and M all make exact Bragg angle with
    diffracting planes so A, D and M differ in phase
    by an integer number of wavelengths (M-M
    has a path length m greater than A-A)
    Consider rays coming in at angle 1 (B and L). If
    1 is selected so that the path length B-B differs
    from that of L-L by (m+1), there will be a plane
    in the middle of the crystal that scatters with path
    length difference (m+1)/2 and destructively
    interferes with x-rays on the B-B path. 1
    represent the highest angle you can go to
    before you get complete destructive
    interference.
    Consider rays coming in at angle 2 (C and N). If
    2 is selected so that the path length C-C differs
    from that of N-N by (m-1), then there will be a
    plane in the middle of the crystal that scatters
    with path length difference (m-1)/2 and
    destructively interferes with Xrays on the C-C
    path. 2 represent the lowest angle you can
    Georgia Tech., Chemistry and Biochemisrty Department
    go to before you get complete destructive

    27

    Principles of Determination of Crystallite Size


    Considering the path length differences between x-rays
    scattered from the front and back planes of the crystal
    2tsin1 = (m+1)
    2tsin2 = (m-1)
    If we subtract them
    t(sin1 sin2)=
    2tcos((1+2)/2)sin((1- 2)/2) =
    Use small angle approximation and ( 1 + 2)/2 = B
    2t[(1- 2)/2]cosB = ,
    t = /(BcosB)
    More rigorous treatment gives t = 0.9/(BcosB) for spherical
    crystals of diameter t.
    This is the Scherrer equation

    Georgia Tech., Chemistry and Biochemisrty Department

    Scherrer Equation

    K
    B 2
    t cos

    Peak width (B) is inversely proportional to crystallite thickness


    (t)
    As the crystallites in a powder get smaller the diffraction peaks in a
    powder pattern get wider
    B = (2 High) (2 Low)
    B is the difference in angles
    at half max
    The constant of proportionality, K
    (the Scherrer constant) depends on the
    shape of the crystal, and the size distribution
    the most common values for K are:
    0.94 -0.89
    K actually varies from 0.62 to 2.08

    MIT, Center for Materials Science and Engineering

    References

    Glenn A. Richard, Mineral Physics Institute, SUNY Stony Brook


    University of Saskatchewan, Physics Department
    Atkins,Physical Chemistry
    Augustana Collage, Chemistry and Physics Department
    Purudue University, Geoscience Department
    MIT, Center for Materials Science and Engineering
    Jenkins R.,Snyder R.L., Introduction to X-ray Powder Diffractometry,
    John Wiley & Sons, Inc. ,1996
    Niemantsverdriet J.W., Spectroscopy in Catalysis, Wiley-VCH,2000
    Nuffield E.W., X-ray Diffraction Methods, John Wiley & Sons, Inc.,
    1966
    Percharsky V.K., Zavalij P.Y., Fundamentals of Powder Diffraction
    and Structural Characterization of Materials, Springer, 2005

    30

    Thanks to you

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