X-Ray Diffraction of Salts Preview Close Preview

Atomic Structure and Why it Matters (1/11)
Points: ___/5.0

Why are diamonds harder than glass? Why do we use graphite in our pencils instead of copper? Why does water freeze at 32 degrees? Why does iron get harder when you hit it? You can answer these questions by taking a look at how the atoms that make up these materials are arranged. The arrangement of atoms, or a material's atomic structure, will determine how a material acts.

Atoms are impossible to see with the eye, or even with a microscope, so scientists have had to figure out other ways to learn about how materials are put together. One way is through X-Ray Crystallography. Watch the video below to learn a little about this technique and then answer the questions below (Note: do not worry too much about the names of the scientists!):

Name three items whose atomic structures were determined by X-Ray Crystallography.

What is the foremost technique for working out the atomic structures of materials?

The Properties of Solids (2/11)
Points: ___/12.0

What are the properties of a solid?

Some basic facts about solids: A substance in a solid phase is relatively rigid, has a definite volume and shape. The atoms or molecules that comprise a solid are packed close together and are not compressible.* Because all solids have some thermal energy, its atoms do vibrate. However, this movement is very small and very rapid, and cannot be observed under ordinary conditions.

To learn more about the properties of solids, watch the following video and answer the questions below:

Give an example of a crystalline solid.

Define the term 'Crystal Lattice'.

What is a unit cell?

Explain the positions of atoms in a simple cubic structure.

Explain the positions of atoms in a body-centered cubic structure.

Explain the positions of atoms in a face-centered cubic structure.

Crystalline solids consist of a pattern of repeating unit cells. What physical property results from this uniformity? Why?

What trait defines an amorphous solid?

Name two examples of amorphous solids.

In an amorphous solid, the intermolecular forces are unevenly distributed throughout the structure. What physical property results from this lack of uniformity?

What happens when you apply heat to an amorphous solid?

The Basics of Crystallography (3/11)
Points: ___/5.0

Now that you understand a bit about the importance of atomic structure, it is important to learn a little bit more about how that structure is determined.

What are two challenges of X-ray diffraction?

What is actually scattering the X-rays?

Planes in a crystal lattice and the Miller Index (4/11)
Points: ___/6.0

We have seen that x-ray radiation can scatter off of atoms according to Bragg's law, where recall that d is the spacing between planes of atoms. The question is, what plane? If you imagine a fixed unit cell, like simple cubic, you can see planes of atoms if you look from the top down, the bottom up, or from side to side.

Which of these planes will scatter x-ray light? In powder x-ray diffraction, where all orientations of crystals are possible, light is scatted from each and every plane.

Is there a way to characterize the planes in a unit cell? Enter the Miller index.

What is the Miller index (h k l) for a plane with intercepts x = 1, y = inf, z = 1?

In a FCC unit cell, do the planes (1 0 0), (0 1 0), and (0 0 1) belong to the same family?

Do you think planes in the same family would give an x-ray diffraction signal at the same scattering angle (2 theta)? Why or why not?

Overview of the X-Ray Diffraction iLab (5/11)
Points: ___/6.0

What is this lab about?In this lab, you can investigate the use of powder X-ray diffraction technique to calculate the unit cell parameter (the edge length) of a cubic unit cell and to calculate the density of a crystalline salt.

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How does the lab equipment work? X-ray diffractometers consist of three basic elements: an X-ray tube, a sample holder, and an X-ray detector. X-rays are generated in a cathode ray tube by heating a filament to produce electrons, accelerating the electrons toward a target* by applying a voltage, and bombarding the target material with electrons. When electrons have sufficient energy to dislodge inner shell electrons of the target material, characteristic X-ray spectra are produced. These X-rays are collimated and directed onto the sample. As the sample and detector are rotated, the intensity of the reflected X-rays is recorded. When the geometry of the incident X-rays impinging the sample satisfies the Bragg Equation, constructive interference occurs and a peak in intensity occurs. A detector records and processes this X-ray signal and converts the signal to a count rate which is then output to a device such as a printer or computer monitor. This equipment is located at the Jerome B. Cohen X-ray Diffraction Facility at Northwestern University Materials Research Science and Engineering Center (NU-MRSEC).

The target material for the X-ray diffractometer that we will use is copper. Specifically, it uses the Cu K-alpha radiation with a wavelength of 0.15418 nm.

What can I do in this lab?You can investigate how to characterize the sample crystalline structure and determine the unit cell dimensions. From the diffraction pattern, you can index the peaks to come up with the unit cell edge length and therefore the density of the unit cell.

What two unit cell parameters are we going to determine using PXRD?

Convert the wavelength of X-ray emission into units of eV.

What inner core-electron transition is responsible for Cu K-alpha X-ray radiation? Hint: find an online resource.

Background Information for the Lab (6/11)
Points: ___/10.0

Click below to read important background information involved in this lab.

What is diffraction and Bragg's law?

What is crystallography?

How does the instrument work

Bragg's law states that a peak arises due to constructive interference. That is, there are only certain values of (h k l) that give a peak for simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC). The (h k l) for each of these units cells is different! That is great for us, as it means we can identify unit cells based on how many peaks we see and where we see them.

For a cubic system, Bragg's law can be simplified into: sin^2(theta) = A (h^2 + k^2 + l^2), where A = lambda^2 / 4a^2.

For SC, all integral values of (h k l) are allowed.

For BCC, (h k l) must add up to an even number. That is, h + k + l = even

For FCC, (h k l) must ALL be even or ALL be odd.

What is the equation for the "A constant" that we derived in the lab?

In the above, what is "a" ?

What values of h^2 + k^2 + l^2 are allowed for SC?

What values of h^2 + k^2 + l^2 are allowed for BCC?

What values of h^2 + k^2 + l^2 are allowed for FCC?

Research Question (7/11)
Points: ___/6.0

What are you trying to find out in this lab? What question are you trying to answer? This question is called your research question, which guides your experimental design in the next step.

You will be collecting two PXRD spectra:

(1) NaCl

(2) CsCl or CaO (the choice is up to you)

Write your research question below.

What is your research question for this investigation?

What is your choice for sample number 2?

Experimental Design for NaCl (8/11)
Points: ___/5.0

Design your experiment by choosing values for the variables on the left. To learn more about each variable, click on the question mark icon next to the variable.

When you click "Run", the experiment will run on the instrument located at Northwestern University in Evanston, Illinois.

Note that experiments are run one at a time, so you are being placed in a line or queue to run yours. Different samples are run at different times. If you don't want to wait, you can log out and come back later. Everything you have done up to now will be saved.

You will be collecting two PXRD spectra. The first will be NaCl. Choose NaCl from the drop down sample menu.

Intensity over Angle
Sample
Initial Angle (deg.)
Final Angle (deg.)
Width of step (deg.)
Sampling time (s)
Why did you choose these angles, step width and time to be spent in each step?

Analyze your NaCl iLabs Results (9/11)
Points: ___/10.0

Let's take a closer look at the results from your experiment.

By clicking on the tabs below, you can see the variables you chose for your experimental design, your data in table form, and a graph of your data.

Take a close look at the graph of your data in order to determine where the intensity peaks. You can select known sample overlays to compare your results to different standards.

What is your experimental unit cell parameter for NaCl (in nm) ?