12.3.3 Crystal Structure

Question 1

Crystal Structure

Answer 1

• A unit cell is a repeat unit that will recreate a crystal lattice when translated in three dimensions.
• X-ray diffraction is a technique used to determine how particles in a crystal lattice are arranged.
• The Bragg equation is a method for determining the distance between rows of particles in a crystal lattice.

Question 2

note

Answer 2

• A unit cell is a repeat unit that will recreate a crystal lattice when translated in three dimensions.
• A primitive unit cell (or primitive crystal system) is the
  simplest unit cell that can be used to create a crystal lattice. There are seven primitive unit cells in three dimensions: cubic, tetragonal, orthorhombic, trigonal, monoclinic, triclinic, and hexagonal.
• The seven primitive unit cells differ in edge length and angles.
• X-ray diffraction is a technique used to determine how particles in a crystal lattice are arranged.
• X-ray diffraction involves passing a beam of x rays through a crystal and observing the destructive and
  constructive interference patterns.
• Destructive interference occurs when two waves add out of phase. Destructive interference results in a blank spot on the photographic plate.
• Constructive interference occurs when two waves add in phase. Constructive interference results in a spot on the photographic plate.
• The second wave (represented by the arrow on the bottom in the figure) travels a little farther than the first wave before and after it is reflected. This additional distance is highlighted.
• For the second wave to be exactly in phase with the first wave after the deflection, the distance from where the second wave crosses the first thin grey line to where it crosses the second thin grey line has to be an integer multiple (n) of the wavelength ( ) of the waves. This relationship can be used to represent the distance between the planes.
• This equation is the Bragg equation. This equation can be used to determine the distance between rows of particles in a crystal lattice.

Question 3

X-rays of wavelength 154 pm are used to determine the interatomic spacing in an aluminum crystal. A first order Bragg spot was observed at 19.3°. Determine the distance between the planes of atoms in this crystal that produced this spot.

Answer 3

233 pm

Question 4

X-ray diffraction is used to determine the spacing between planes of atoms or other particles in a crystal. How is this possible?

Answer 4

X-rays have to travel further to reach the lower planes, which causes the reflected X-rays to interfere with each other.

Question 5

In the Bragg equation, 2d sin theta = n wavelength, what doe sthe factor d represent

Answer 5

The spacing between crystals

Question 6

In the Bragg equation, why is the path length difference set equal to nλ and what does the n represent?

Answer 6

The symbol n represents the number of whole wavelengths difference. The path length difference must be equal to some number of whole wavelengths in order for constructive interference to occur

Question 7

Most of the information we have about crystals and their structure comes from what?

Answer 7

X-ray diffraction

Question 8

Which of the following substances most likely has a periodic lattice structure?

Answer 8

Crystalline solids

Question 9

Which of the following best describes a unit cell?

Answer 9

The smallest volume that contains at least one of each of the discrete particles making up the crystal

Question 10

There are seven primitive unit cells of crystal lattice structures. Which of the following is not one of the seven primitive unit cells?

Answer 10

Biclinic

Question 11

What is the difference between a crystal lattice and a unit cell?

Answer 11

A unit cell is the smallest portion of the crystal lattice that reveals the three-dimensional pattern of the lattice. A crystal lattice is the entire array.

Question 12

Suppose you were given a sample of a substance and were told to determine if it was a crystal. What is the most direct method of making that determination?

Answer 12

Pass a beam of X-rays through the sample and see if it shows a diffraction pattern.