This document discusses the diffraction of X-rays by crystals. It begins by defining diffraction as the scattering of X-rays by crystal atoms that produces an interference pattern, giving information about the crystal structure. It then introduces X-rays as highly penetrating electromagnetic radiation with wavelengths between 10-8 to 10-11 meters. The document notes that X-ray crystallography was initiated in 1914 by W.H. Bragg and W.L. Bragg to study atomic crystal structures using X-ray diffraction. It explains that X-rays diffract into specific directions when incident on a crystal due to the crystalline atoms, allowing determination of electron density and atomic positions. Bragg's Law relating diffraction angle and interplanar spacing is then heur

1. DIFFRACTION OF X-RAYS
BY CRYSTALS
Presented By:-
ATEEQ SINDHU
Ist YEAR

2. What is Diffraction ?
A scattering of X-rays by the atoms of
a crystal that produces an interference
effect so that the diffraction pattern
gives information on the structure of
the crystal or the identity of a
crystalline substance.

3. Introduction of X-rays :
X ray, invisible, highly penetrating electromagnetic
radiation of much shorter wavelength (higher
frequency) than visible light. The wavelength range
for X rays is from about 10 - 8 m to about 10 - 11 m, or
from less than a billionth of an inch to less than a
trillionth of an inch; the corresponding frequency
range is from about 3 × 10 16 Hz to about 3 × 10 19
Hz (1 Hz = 1 cps).

4. History of X-Rays crystallography
The study of atomic structure of crystals by X-rays was initiated in 1914 by W.H. Bragg and W.L
Bragg with remarkable achievements. They found that a monochromatic beam of X-rays was
reflected from a crystal plane as if it acted like mirror. To understand this effect, a series of atomic
planes of constant interplanar spacing d parallel to a crystal face are shown by lines PP’, P1 P’1,
P2P’2 , and so on, in Fig below.

5. Diffraction of x-rays by crystals :
X-ray crystallography is a tool used for identifying
the atomic and molecular structure of a crystal, in
which the crystalline atoms cause a beam of
incident X-rays to diffract into many specific
directions. By measuring the angles and intensities
of these diffracted beams, a crystallographer can
produce a three-dimensional picture of the density
of electrons within the crystal. From this electron
density, the mean positions of the atoms in the
crystal can be determined, as well as their
chemical bonds, their disorder and various other
information.

6. Suppose that a single monochromatic wave (of any type) is incident on aligned plane of lattice points, with separation d, at angle
θ. Points A and C are on one plane, and B is on the plane below. Points ABCC’ form a quadrilateral.
(AB + BC) – (AC’)
The tow separate waves will arrive at a point with the same phase, and hence undergo constructive interference, if and only if this path
difference is equal to any integer value of the wavelength, i.e.
(AB + BC) – (AC’) = nλ ,
Where the same definition of n and λ apply as above.
Therefore,
AB = BC =
𝑑
𝑆𝑖𝑛 θ
and AC =
2𝑑
tan 𝜃
,
From which it follows that
AC’ = AC . cos θ =
2𝑑
tan 𝜃
cosθ = (
2𝑑
sin 𝜃
cos θ) cos θ =
2𝑑
sin 𝜃
cos 2 θ.
Putting everything together,
nλ =
2𝑑
sin 𝜃
(1-cos 2 θ) =
2𝑑
sin 𝜃
sin2 θ ,
Which simplify to
nλ = 2d sin θ ,
Which is Bragg’s Law.
Heuristic derivation