# Electron Diffraction Intensity and Reciprocal Lattic

• GL_Black_Hole
In summary, the conversation discusses a Low-energy electron diffraction (LEED) experiment on a deposition of argon (Ar) and xenon (Xe) on a graphite single crystal. The lattice structure formed by the atoms is triangular, with one Xe atom and three Ar atoms in the primitive basis. The lattice translation vectors are expressed in terms of cartesian unit vectors and the nearest neighbor distance. The fractional coordinates of the atoms in the basis are also determined. The structure factor for a diffracted beam and the conditions for observable diffraction peaks are discussed. The relative intensity ratio for certain peaks is determined, and the relative intensity for a lattice made entirely of Ar and with vacancies is also considered.
GL_Black_Hole

## Homework Statement

Low-energy electron diffraction (LEED) experiments are carried on to study a deposition of argon (Ar) and
xenon (Xe) on the surface of a graphite single crystal. In the regime of vapor pressure considered, 75% of Ar
and 25% of Xe are adsorbed on the (hexagonal) crystalline surface of graphite. The Ar-Ar distance and Ar-Xe distances are both ##a##. The Ar atoms and the Xe atoms organize themselves in the two-dimensional lattice structure shown below. We take the relative form factor of Xe, over that of Ar to be R.
(img at https://ibb.co/cb76ac)
a)
Identify a space lattice and a primitive basis suitable to describe the arrangements of argon and xenon
atoms in the figure above.
b) Considering the Xe atoms alone, what is the space lattice formed by the Xe atoms?
c)Express the lattice translation vectors ##a_1## and ##a_2## in terms of the cartesian unit vectors ##x## and ##y##, and the nearest neighbour distance ##a##.
d)
What are the fractional coordinates of the Ar atoms and Xe atoms in the basis.
e)
Determine the basis structure factor for a diffracted beam with the scattering vector ##q## in the
xy plane of the lattice
f) What are the conditions on the ##G=q## indices h and k for observable diffraction peaks?
g) Determine the relative intensity ratio for the (h,k,0) peaks.
h) What would be the relative intensity if the lattice were made entirely of Ar?
i) What would be the relative intensity if all of the Ar was replaced with vacancies?

## Homework Equations

##S(q) = \sum_{j=1}^{s} f_j exp(-i2\pi({x_j}h+{y_j}k)##

## The Attempt at a Solution

a) The space lattice is triangular and the primitive basis is also triangular with one Xe atom(white) and three Ar atoms(grey).
b)The Xe atoms also form a triangular space lattice.
c) The lattice translation vectors are therefore ##a_1 =a(1,0)## and ##a_2 = a(\frac{1}{2},\frac{\sqrt{3}}{2})##.
d) Choosing the Xe atom to be at (0,0), the other fractional coordinates are ##(\frac{1}{2},0), (0,\frac{1}{2})##, and ##(\frac{-1}{2},\frac{1}{2})##.
e) With these coordinates the structure factor is:
##S(q) = f_{Xe} +f_{Ar} [exp(-i\pi(h)) +exp(-i\pi(k)) +exp(-i\pi(k-h))]##
f) The structure factor cannot vanish so the conditions have to come directly from ##G=q## but I have no clue how they would.
g) Not even sure what is meant by relative intensity( i.e. relative to what baseline?)
h) Now it is possible for the structure factor to vanish, so some previously valid (h,k,0) should have zero intensity. [/B]

i) With vacancies, the structure factor should reduce to something like ##S(q)= f_{Xe} +f_{Ar}[exp(-i\pi(h)) +exp(-i\pi(k))]##.

## 1. What is electron diffraction intensity?

Electron diffraction intensity is a measurement of the intensity of electrons diffracting off a material. It is a measure of the strength of the scattered electron beam and can provide information about the atomic structure of the material.

## 2. How is electron diffraction intensity measured?

Electron diffraction intensity is measured using a detector, such as a phosphor screen or CCD camera, which captures the pattern of diffracted electrons. This pattern is then analyzed to determine the intensity of the diffraction spots, which can provide information about the structure of the material.

## 3. What is the relationship between electron diffraction intensity and reciprocal lattice?

Electron diffraction intensity is directly related to the arrangement of atoms in a material's reciprocal lattice. The diffraction pattern produced by electrons passing through a crystal is a result of the periodicity of the atoms in the crystal, which is reflected in the reciprocal lattice.

## 4. How does the crystal structure affect electron diffraction intensity?

The crystal structure of a material is a major factor in determining the electron diffraction intensity. The arrangement of atoms in a crystal lattice can cause diffraction spots to appear brighter or darker, depending on the constructive or destructive interference of the diffracted electrons.

## 5. What factors can affect the intensity of electron diffraction?

The intensity of electron diffraction can be affected by several factors, including the quality of the electron beam, the crystal structure of the material, and the orientation of the crystal relative to the electron beam. Other factors such as temperature, pressure, and defects in the crystal can also impact the intensity of the diffraction pattern.

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