Problem 1. Identification of a material by X-Ray Diffraction

Consider the following XRD pattern for an unknown metallic crystalline substance discovered

during a lunar exploration whose external morphology indicates that it is a cubic material. The

diffraction pattern of this material was collected using CuKa radiation of wavelength 1.54Å.

Intensity (%)

100

90

80

70

8

50

8

30

20

10

0

P

0

5

10 15 20 25 30 35 40 45 50 55

(38.43,100.0)

Diffraction

Peak #

#1

#2

# 3

(44.67,46.9)

#4

#5

1. Identify the peaks.

2. Construct a table similar to the one shown below.

Index this pattern, determine the lattice parameters, crystal structure and identify the material

Steps:

Diffraction

Angle (20)

(65.02,26.4) (78.13,27.9)

60 65 70 75

sin 0₁

(82.33,7.8)

sin² 0₁

80 85 90

sin² 0₁

sin²0₁

h²+k²+1² hkl

a (Å)/n3. Determine sin² 0₁.

4. Find the ratio of sin² 0₁ /sin² 0₁ for each peak where sin² 0₁ is the value for each

successive peak.

5. Select the result from (3) that yields h²+k+fas an integer. (hint: you may be required to

multiply all of the ratios you have calculated by a common value to do the comparison.)

6. Compare results with the sequences of h+k+values to determine the crystalline

structure of the material by comparing the ratios you have found to the characteristic lines

in Figure 1.

7. Find the lattice parameter for the material.

8. Assuming that you have a pure substance, which element do you have? (Use the table

given for lattice structures and parameters for the elements.)

(nke) →

valves

(231)

(100) (110) (111) (200) (210) (211) (220) (300) (310) (311) (222) (320) (321) (400)

Q²= K²+k²+²

I

2

SIMPLE CURIC

BODY-CENTERED-CUBIC

FACE-CENTERED-CUBIC

3

4

5

8

9

10

11

Figure 1. Observable X-Ray diffraction peaks for different cubic crystal systems.