Engr 45

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ENGIN45_Lab2.pdf

ENGIN 45 Lab #2

X-Ray Diffraction and Crystallography

Turn in the lab with all of your answers written on a separate sheet of paper.

During a lunar exploration an unknown metallic crystalline substance is discovered. The external morphology indicates that it is a cubic material. A diffraction pattern of this material, using an X-ray of length 1.54Å, provides the following data (shown here as a graph and in a table)

Diffraction Peak Bragg Diffraction angle, Ө #1 19.1 #2 22.2 #3 32.2 #4 38.8 #5 40.85

There are three options for the crystalline structure– Simple Cubic, Body Centered Cubic, and Face Centered Cubic. We will calculate the lattice parameter (a) for each angle for each crystalline structure. The correct crystalline structure will result in the same a for each diffraction angle.

Each crystalline structure has different sets of planes that produce diffraction peaks. This information is shown in the table below. Using this information, calculate (ℎ + 𝑘 + 𝑙 ) for the first five peaks for each of the crystalline structures.

Peak # 1 2 3 4 5 6 7 8 9 SC (100) (110) (111) (200) (210) (211) (220) (221) (310) BCC (110) (200) (211) (220) (310) FCC (111) (200) (220) (311) (222)

Write your calculated values in the table below

Diffraction Peak Bragg Diffraction angle, Ө

SC (ℎ + 𝑘 + 𝑙 )

BCC (ℎ + 𝑘 + 𝑙 )

FCC (ℎ + 𝑘 + 𝑙 )

#1 19.1

#2 22.2

#3 32.2

#4 38.8

#5 40.85

Write Bragg’s law in terms of (ℎ + 𝑘 + 𝑙 ) and 𝑎

Calculate 𝑎 and fill in the table below

Diffraction Peak Bragg Diffraction angle, Ө

SC 𝑎

BCC 𝑎

FCC 𝑎

#1 19.1

#2 22.2

#3 32.2

#4 38.8

#5 40.85

Using the tables of lattice structures and parameters provided as an attachment on canvas and assuming that the crystal is a pure substance, which element do you have?

Solve problems 1 and 2 involving X-Ray diffraction. Show all of your work on a separate sheet of paper that you will staple to the lab.

Problem 1

Platinum is an FCC crystal with a lattice parameter of 𝑎 = 0.392 𝑛𝑚. X-ray diffraction experiments are carried out on this Pt crystal using an X-ray beam with a wavelength of 𝜆 = 0.07110 𝑛𝑚.

What are the first four diffraction angles and what are the corresponding crystal planes (hkl)?

Problem 2

The first five peaks of the x-ray diffraction pattern for tungsten (W) are shown below, which has a BCC crystal structure; monochromatic x-radiation having a wavelength of 0.1542 nm was used.

- Write the Miller indices (i.e., give h, k, and l indices) for each of these peaks.

- Determine the interplanar spacing for each of the peaks.

- For each peak, determine the atomic radius for W.

Compare these values with the value in Table 3.1 at the front of the room

Peak Miller Indices 2Ө Interplanar spacing d (nm)

Atomic radius R(nm)

1

2

3

4

5