# X-RAY DIFFRACTION METHODS

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### X-RAY DIFFRACTION METHODS:

X-RAY DIFFRACTION METHODS

### INTRODUCTION:

INTRODUCTION Electromagnetic radiation, short wavelength Wavelength range-0.02 to 100Ao, 0.01-7 nm (0.01x10 -9 to 7x10 -9 m) Discovered by Wilhelm Conrad Rontgen Energy of x-ray (KeV) = 1.24/(nm) wavelength of importance=0.1 to 25 A o Visible light wavelength is 0.56 m (560 nm) Spacing between atoms in metals range from 2-3 A (0.2-0.3 nm) X-ray techniques- X-ray absorption methods X-ray diffraction methods X-ray fluorescence methods

### Generation of x-rays:

Generation of x-rays

### Properties of X-rays :

Properties of X-rays An x-ray photon can interact with the electrons in the target by one of 4 ways: No interaction (the x-ray photons experience no change in energy ) Completely absorbed (photon energy is transferred to the target electrons. X-ray radiography)   

### PowerPoint Presentation:

The x-ray photon is completely absorbed and another x-ray photon of lower energy is produced (x-ray fluorescence) The x-ray photon produces an oscillating electric field in the electrons of the target object. The target object generate photons if the same wavelength at many different angles w.r.t. the incident photons. Each interaction is elastic scattering. (This is the main interaction that is important for x-ray diffraction)  1  2   1 <  2   

### Interference of Waves:

Interference of Waves Constructive interference: mutual reinforcement of the scattered x-rays Can happen if the difference in distances traveled by the various x-ray parallel beams are a multiple of wavelength. ( d = n*) Destructive interference: scattered beams are out of phase and cancel each other. ( d = n*/2) Diffraction: constructive interference of x-rays

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CONSTRUCTIVE INTERFERENCE DESTRUCTIVE INTERFERENCE

### BRAGG’S LAW:

BRAGG’S LAW Bragg’s law: the positions of the discrete x-ray spots I the diffraction pattern is caused by the x-ray reflection by equally spaced parallel planes of atoms. Bragg’s law is necessary but not sufficient n  = 2*d*sin n is the diffraction order =1,2,.. : wavelength : Bragg’s angle d : spacing between planes For cubic crystals, d (hkl) = a/ √ (h 2 +k 2 +l 2 )

### PowerPoint Presentation:

n = 2d Sin n is an integer and is the order of the reflection For Cu K  radiation ( = 1.54 Å) and d 110 = 2.22 Å n Sin   1 0.34 20.7 º First order reflection from (110) 2 0.69 43.92 º Second order reflection from (110) Also written as (220) The angle of incidence = angle of scattering. The path length difference is equal to an integer number of wavelengths-constructive interference

### PowerPoint Presentation:

Bragg’s equation is a negative law  If Bragg’s eq. is NOT satisfied  NO reflection can occur  If Bragg’s eq. is satisfied  reflection MAY occur Diffraction = Reinforced Coherent Scattering Reflection versus Scattering Reflection Diffraction Occurs from surface Occurs throughout the bulk Takes place at any angle Takes place only at Bragg angles ~100 % of the intensity may be reflected Small fraction of intensity is diffracted X-rays can be reflected at very small angles of incidence

### X-RAY DIFFRACTION:

X-RAY DIFFRACTION X –ray beam is incident upon substance. The electron of these atoms oscillate at similar frequency. They emit similar frequency as diffracted beams , forming a pattern unique to its structure.

### Reflection planes in cubic lattice :

Reflection planes in cubic lattice

### X-RAY CRYSTALLOGRAPHY:

X-RAY CRYSTALLOGRAPHY

### What is crystallography?:

What is crystallography? Originated as the study of macroscopic crystal forms “ Crystal” has been traditionally defined in terms of the structure and symmetry of these forms. Modern crystallography has been redefined by x-ray diffraction. Its primary concern is with the study of atomic arrangements in crystalline materials

### PowerPoint Presentation:

The definition of a crystal has become that of Buerger (1956): “ a region of matter within which the atoms are arranged in a three-dimensional translationally periodic pattern .” This orderly arrangement in a crystalline material is known as the crystal structure. X-ray crystallography is concerned with discovering and describing this structure (using diffraction as a tool).

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LATTICE- is a representation of crystal structure as an array of points in space. UNIT CELL- is defined as the fundamental pattern of minimum number of atoms or molecules which represent the full character of the crystal. LATTICE PLANES- parallel equidistant planes passing through the lattice points

### The Lattice:

The Lattice Lattice is “ an imaginary pattern of points (or nodes) in which every point (node) has an environment that is identical to that of any other point (node) in the pattern . A lattice has no specific origin, as it can be shifted parallel to itself.” (Klein, 2002) The lattice must be described in terms of 3-dimensional coordinates related to the translation directions . Lattice points, Miller indices, Lattice planes (and the “d-spacings” between them) are conventions that facilitate description of the lattice.

### PowerPoint Presentation:

Although it is an imaginary construct, the lattice is used to describe the structure of real materials . NaCl crystal lattice NaCl unit cell

### MILLER INDICES:

MILLER INDICES A notation system used in crystallography to designate a plane in a crystal by three numbers (h,k,l)

### Lattice plane & miller indices:

Lattice plane & miller indices Lattice plane may be regarded as aggregate of a set of parallel equidistance planes passing through the lattice point. Miller put forward a method to designate a plane in the crystal by three number (h,k,l) known as miller indices. They are the symbolic vector representation for the orientation of an atomic plane in a crystal lattice & defined as the reciprocal of the functional intercepts which the plane makes with the crystallographic axes . Miller indices are used in crystallography to characterize planes within a crystal structure. The orientation of the planes is important

### PowerPoint Presentation:

Lattice Notation Origin chosen as 000 Axis directions a , b , c and unit measurements defined by particular crystal system Axes are shown with brackets, i.e., [001] Lattice points are defined in 3-dimesions as units along the axes, without brackets (i.e., 111, 101, 012, etc.)

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STEP1:IDENTIFY THE INTERCEPTS ON THE X,Y,Z AXES Intercept on x-axis is at the point (a,0,0) Intercept on y and z-axes is at infinity Intercepts-a ,  ,  STEP II:SPECIFY THE INTERCEPTS IN FRACTIONAL COORDINATES Divide the intercepts by respective cell dimension a/a,  /a,  /a Fractional intercepts:1,  ,

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STEP 111:TAKE RECIPROCALS OF THE FRACTIONAL INTERCEPTS Reciprocals of 1 and  are 1 and 0 respectively Miller indices:(100) Therefore the surface or the plane illustrated is the (100) plane of the cubic crystal

### General principle:

General principle If a Miller Index is zero, the plane is parallel to that axis The smaller a Miller Index, the more nearly parallel the plane is to the axis The larger Miller Index, the more nearly perpendicular the plane is to the axis Multiplying or dividing a Miller Index by a constant has no effect on orientation of plane

### INSTRUMENTATION:

INSTRUMENTATION X-RAY SOURCE COLLIMATOR MONOCHROMATOR DETECTOR

### X-ray source:

X-ray source A. Coolidge tube B. Synchroton radiation C. Radioisotopes D. Secondary fluorescent sources

COOLIDGE TUBE

COLLIMATOR

### MONOCHROMATORS:

MONOCHROMATORS FILTERS Absorbs undesirable radiation Eg ; zirconium filter used for molybdenum radiation CRYSTAL MONOCHROMATOR Suitable analyzing crystal graphite, NaCl, LiF, quartz Flat crystal monochromator Curved crystal monochromator

### DETECTORS:

DETECTORS Two methods- Photographic method Counter methods Detection is based on the ability of X-rays to ionize matter

### PHOTOGRAPHIC METHOD:

PHOTOGRAPHIC METHOD Records position and intensity of x-ray beam D-density units Io-intensity of incident ray I - intensity of transmitted ray Densitometer is used to measure D D=log Io/I

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DISADVANTAGES Time consuming method Exposures of several hours are required Rarely used for quantitative measurements

### COUNTER METHODS:

COUNTER METHODS Geiger – Muller tube counter Proportional counter Scintillation counter

### GEIGER MULLER COUNTER:

GEIGER MULLER COUNTER

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Filled with argon xenon or krypton gas Each photon of x-ray interacts with an atom of argon causes lose of electron- photoelectron Has large KE. This K.E is lost to ionize several other atoms of the gas. ADVANTAGES Inexpensive Relatively trouble free DISADVANTAGES Counts low rates only Efficiency falls of at wavelength below 1Amstrong Cannot be used to measure the energy of x-ray

### SCINTILLATION DETECTOR:

SCINTILLATION DETECTOR

### PROPORTIONAL COUNTER:

PROPORTIONAL COUNTER Construction is similar to GMC Filled with xenon or crypton Output pulse is proportional to intensity of the x-rays ADVANTAGE Counts high rates DISADVANTAGE Circuit is complex and expensive

### X-RAY DIFFRACTION METHODS:

X-RAY DIFFRACTION METHODS Laue photographic method Bragg x-ray spectrometer method Rotating crystal method Powder diffraction method

### PowerPoint Presentation:

Crystal structure determination Monochromatic X-rays Panchromatic X-rays Monochromatic X-rays Many s (orientations) Powder specimen POWDER METHOD Single  LAUE TECHNIQUE  Varied by rotation ROTATING CRYSTAL METHOD

### LAUE METHOD:

LAUE METHOD ACCORDING TO LAUE,IF A BEAM OF X-RAY IS PASSED THROUGH A CRYSTAL, THE EMITTED X RAY BY THE CRYSTAL ARE OBTAINED ON PHOTOGRAPHIC PLATE IN THE FORM OF A PATTERN KNOWN AS LAUE’S PHOTOGRAPH .

### LAUE PHOTOGRAPHIC METHOD:

LAUE PHOTOGRAPHIC METHOD Transmission Laue method - The film is placed behind the crystal to record beams which are transmitted through the crystal Back-reflection method - The film is placed between the x-ray source and the crystal. The beams which are diffracted in a backward direction are recorded

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TRANSMISSION METHOD

### TRANSMISSION METHOD:

TRANSMISSION METHOD THIS METHOD IS SUITABLE FOR INVESTIGATION OF PREFERED ORIENTATION OF SHEETS OR FIBRES. THIS METHOD IS ALSO USED FOR DETERMINATION OF SYMMETRY OF SINGLE CRYSTALS .

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BACK REFLECTION METHOD

### BACK-REFLECTION METHOD:

BACK-REFLECTION METHOD IT IS THE ONLY METHOD FOR THE INVESTIGATION OF LARGE AND THICK SPECIMENS. DISADVANTAGES : A LARGE CRYSTAL IS REQUIRED.

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BRAGG’S SPECTROMETER METHOD

### BRAGG’S X-RAY SPECTROPHOTOMETERMETHOD :

BRAGG’S X-RAY SPECTROPHOTOMETERMETHOD The x-rays are allowed to fall on the crystal surface. The crystal is rotated and the x-rays are made to reflect from various lattice planes The intense reflections are measured as function of ionization. And the glancing angles for each reflections are recorded . Advantage Measurement of wavelength. Determination of crystal structure

### ROTATING CRYSTAL METHOD:

ROTATING CRYSTAL METHOD Developed by schiebold in 1919. Two methods Complete rotation method: Oscillation method :

### COMPLETE ROTATION METHOD:

COMPLETE ROTATION METHOD Series of rotation Each set of plane in the crystals diffract 4 times during the rotation. Distributed into a rectangular pattern about the central point of the photograph. One can measure the size of the unit cell.

### OSCILLATION METHOD:

OSCILLATION METHOD The crystal is oscillated through an angle of 15-20 The position of a spot on the plates indicates the orientation of the crystal at which the spot was formed.

### X-RAY POWDER DIFFRACTION:

X-RAY POWDER DIFFRACTION Rapid identification technique for phase identification of crystalline materials 1mg of the sample material is sufficient Unknown crystalline substances can be identified by comparing the diffraction data with the data of International Centre for Diffraction Data

### X-ray diffraction methods:

X-ray diffraction methods These methods are based on the scattering of x-rays by crystals. One can identify the crystal structures of various solid compounds. Very important as compared with X-ray absorption and X-ray fluorescence method.

### PowerPoint Presentation:

Beam of X- ray is incident, the electrons of the substance – small oscillators. These on oscillating with same frquency as that of incident –emit EMR in all directions. Every crystalline sub. Scatters the X-ray in its own unique diffraction pattern – fingerprint of its atomic or molecular structure . The conditions for diffraction is governed by Bragg’s law. Diffracted beams are often reffered to as reflections

### Powder Diffraction:

Powder Diffraction Powder diffractometer: An x-ray instrument used to determine angles of diffraction (2 ) for a polycrystalline specimen or a powder as a function of diffracted beam intensities. The specimen must be flat and polycrystalline .

### PowerPoint Presentation:

Each peak in the diffraction pattern correspond to a set of crystallographic planes {hkl} Diffraction pattern can be used to: Identify crystalline phases Determine unit cell size and R Structure determination by indexing Diffraction rules: SC all planes BCC h+k+l=even FCC h,k,l unmixed

POWDER METHOD

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THE POWDER METHOD Cone of diffracted rays

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BRAGG-BRENTANO DIFFRACTOMETER

### DEBYE-SCHERRER CAMERA:

DEBYE-SCHERRER CAMERA

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http://www.matter.org.uk/diffraction/x-ray/powder_method.htm Diffraction cones and the Debye-Scherrer geometry Film may be replaced with detector Different cones for different reflections

### POWDER CRYSTAL METHOD:

POWDER CRYSTAL METHOD Powder method was devised by Debye and Scherer in Germany A monochromatic x-ray beam is allowed to fall on fine powder struck on a hair by means of gum suspended vertically. This enables sharp lines to be obtained in the form of circular arc on the photographic plate. The crystal structures can be obtained from the arrangement of the traces and their relative intensities.

### INFORMATIONS FROM XRPD:

INFORMATIONS FROM XRPD Peak position crystal system space group symmetry translational symmetry unit cell dimensions qualitative phase identification Peak intensity unit cell contents point symmetry quantitative phase fractions

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Nature of sample perfect crystal Imperfect crystal Liquid or glass

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This method is most useful for cubic crystals . To determine the complex structres of metals and alloys. Useful to make distinction between allotropic modification of the same substance .

### INTERPRETATIONS:

INTERPRETATIONS A typical X-ray spectra may be as follows :

### PowerPoint Presentation:

After a scan of the sample the X-ray intensity can be plotted against the angle θ (usually reported as 2 θ ) to produce a chart. The angle 2 θ for each diffraction peak can then be converted to d-spacing, using the Bragg equation. One can then work out the crystal structure and associate each of the diffraction peaks with a different atomic plane The parameters scattered angle (2 θ ), d-spacing & % Relative Intensity will be unique for every crystalline substance

### PowerPoint Presentation:

A group known as the International Center Diffraction Data (ICDD) formerly known as the Joint Committee on Powder Diffraction Standards (JCPDS) has collected data on thousands of crystalline substances. This data can be obtained as the JCPDS Powder Diffraction File. Since every compound with the same crystal structure will produce an identical powder diffraction pattern, the pattern serves as kind of a " fingerprint " for the substance, and thus comparing an unknown mineral to those in the Powder Diffraction file enables easy identification of the unknown

### APPLICATIONS:

APPLICATIONS STRUCTURE OF CRYSTALS Non-destructive method Molecular structure and size of crystal planes POLYMER CHARACTERISATION Degree of crystallinity of the polymer Ratio of area of diffraction peaks to scattered radiation is proportional to the ratio of crystalline to non crystalline material

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STATE OF ANNEAL IN METALS Well annealed metals-sharp diffraction lines If subjected to hammering or bending-diffused diffraction pattern PARTICLE SIZE DETERMINATION a) Spot counting method >5microns b) Broadening of diffraction lines particles of the range 30-1000Ao

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APPLICATION TO COMPLEXES a) Determination of cis-trans isomerism b) Determination of linkage isomerism MISCELLANEOUS APPLICATIONS a) Soil classification based on crystallinity b) Analysis of industrial dusts c) Assessment of weathering and degradation of natural and synthetic minerals d) Study of corrosion products e) Examination of tooth enamel and dentine f) Effects of diseases on bone structure

### PowerPoint Presentation:

X-RAY POWDER DIFFRACTION FILE