X-rays diffraction and X-rays flourisence, Slides of Optimization Techniques in Engineering

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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

English physicists Sir W.H. Bragg and his son Sir W.L. Bragg

developed a relationship in 1913 to explain why the cleavage

faces of crystals appear to reflect X-ray beams at certain angles of

incidence (theta, θ). The variable d is the distance between atomic

layers in a crystal, and the variable lambda λ is the wavelength of

the incident X-ray beam; n is an integer. This observation is an

example of X-ray wave interference

(Roentgenstrahlinterferenzen), commonly known as X-ray

diffraction (XRD), and was direct evidence for the periodic atomic

structure of crystals postulated for several centuries.

n λ =2dsin θ

Bragg’s Law

Deriving Bragg’s Law: n λ = 2dsin θ

X-ray 1

Constructive interference X-ray 2

occurs only when

n λ = AB + BC

AB=BC

n λ = 2AB

Sin θ =AB/d

AB=dsin θ

n λ =2dsin θ

λ = 2dhklsin θ hkl

AB+BC = multiples of n λ

Constructive and Destructive

Interference of Waves

Constructive Interference

In Phase

Destructive Interference

Out of Phase

Why XRD?

• Measure the average spacings between

layers or rows of atoms

• Determine the orientation of a single

crystal or grain

• Find the crystal structure of an unknown

material

• Measure the size, shape and internal

stress of small crystalline regions

X-ray Diffraction (XRD)

The atomic planes of a crystal cause an incident beam of X-rays to interfere with one another as they leave the crystal. The phenomenon is called X-ray diffraction.

incident beam

diffracted beam film

crystal

Effect of sample

thickness on the

absorption of X-rays

http://www.matter.org.uk/diffraction/x-ray/default.htm

Bragg’s Law and Diffraction:

How waves reveal the atomic structure of crystals

n λ = 2dsin θ

Atomic plane d=3 Å

λ =3Å θ =30o

n-integer

X-ray

X-ray

l

2 θ -diffraction angle

Diffraction occurs only when Bragg’s Law is satisfied Condition for constructive interference (X-rays 1 & 2) from planes with spacing d

http://www.eserc.stonybrook.edu/ProjectJava/Bragg/

Planes in Crystals-2 dimension

To satisfy Bragg’s Law, θ must change as d changes e.g., θ decreases as d increases.

λ = 2dhklsin θ hkl

Different planes

have different

spacings

Seven Crystal Systems - Review

Miller Indices: hkl - Review

Miller indices-the reciprocals of the fractional intercepts which the plane makes with crystallographic axes

Axial length 4Å 8Å 3Å Intercept lengths 1Å 4Å 3Å Fractional intercepts ¼ ½ 1 Miller indices 4 2 1 h k l

4Å 8Å 3Å

∞ 8Å ∞

h k l 4/ ∞ =

a b c a b c

Planes and Spacings - Review

Indexing of Planes and Directions -

Review

a

b

c

a

b

c

[110]

a direction: [uvw]

: a set of equivalent

directions

a plane: (hkl) {hkl}: a set of equi- valent planes

Characteristic X-ray Lines

Spectrum of Mo at 35kV

K α 1

K α

K β

λ (Å)

<0.001Å

K α 2

K β and K α 2 will cause

extra peaks in XRD pattern,

and shape changes, but

can be eliminated by

adding filters.

----- is the mass

absorption coefficient of

Zr.

Intensity

Specimen Preparation

Double sided tape

Glass slide

Powders: 0.1 μ m < particle size <40 μ m

Peak broadening less diffraction occurring

Bulks: smooth surface after polishing, specimens should be

thermal annealed to eliminate any surface deformation

induced during polishing.