Optics Challenge

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This page provides a sample module for the Optics Challenge. Extensions, modifications, and other implementation options can be found at: Optics Extensions.

Contents

Diffractometer

Background

An X-Ray diffractometer is a device used to gain information about the internal structure of a material. Since the diffraction pattern of every substance is unique, the information gained through X-ray diffractometry can be used to identify unknown substances. In this project, students will build a working model of an X-ray diffractometer.

Diffraction

A wave spreads at it travels away from its source. If you’ve ever noticed a ripple in water traveling away from the disturbance that caused it, you have observed this phenomenon.

image:pond.jpg

Further to this is Huygen’s Principle which states that each point on a wave can itself act as a point source for a wave and will travel at the speed of the original wave. So, when a wave passes through a small gap, most of the wave will not continue past the barrier. However, the small piece of the wave that does pass through will continue to move away from the barrier and will expand, just like the ripples on the pond mentioned above.

When the barrier placed in front of the wave has two or more openings, the resulting wave fronts experience interference. This creates a series of high-intensity points, where the peaks come together and low intensity points where the troughs come together. If the incoming wave is visible light, the resulting pattern is a series of dots, where a dot would be present at each of the maximum points shown below.

The Fraunhofer equation is used to describe this type of diffraction.

How X-Ray Diffraction Works and What it can Tell Us

About 95% of solids exist in a crystalline structure. [ThermARL pdf]. This means the atoms or molecules line up in a regular, geometric pattern. For example, the atoms in the common compound sodium chloride naturally arrange in a cubic structure as shown in the diagram below.

This crystalline structure provides a barrier and slit arrangement as described in the diffraction discussion, where the atoms act as the barrier and the gaps between the atoms act as the slits. When light is passed through a crystalline material, the result is a diffraction pattern that is unique to the material.

X-ray diffraction works by exposing an unknown substance to an X-ray source. The diffraction pattern is measured and compared to a database of known substances. In this way, an unknown substance can be identified by observing its diffraction pattern.

X-rays are electromagnetic waves with a wavelength range from approximately 1 nm to 0.01 nm (10-9 through 10-11 m). This makes them useful in measuring atomic spacing since the gaps will be of this same magnitude. Recalling the Fraunhofer equation, d sinθ = m λ, d, the spacing of the gap will be of the same order of magnitude as the wavelength of the wave, therefore X-rays are the most useful for this application.

The Challenge

In this activity, you will build a model of an X-ray diffractometer using components in the Lego Mindstorms kit and a laser pointer. Instead of using X-rays, the model will use visible light from the laser pointer. For this reason, the measurements will be limited to the wavelength of the laser pointer, about 650 nm for a red laser pointer. You will be given unlabeled diffraction gratings of different spacing and asked to determine those spacings using only the NXT diffractometer you have built. You will accomplish this be running the program you have created to gather data from the swinging arm, downloading this data into a computer, loading it into a spreadsheet, and graphing intensity vs angle. The spacing between the peeks on this graph will tell you the angle of diffraction.

Materials

Each group participating in this activity will need:

  • One LEGO Mindstorms NXT kit (Item #8527)
  • LEGO Large Green base plate (Item #626)
  • Additional assorted 2x2 and 2x4 LEGO bricks
  • PC with Mindstorms NXT software and Microsoft Excel installed.
  • Laser pointer (red, 650 nM)
  • Tape or rubber band to hold the "on" button on the laser pointer
  • Electrical tape
  • Several diffraction gratings with various spacings (1 - 10 micrometer spacing works best)

Construction

The device consists of a rotating light detector, a mount for the diffraction grating and a mount for the laser pointer. Photos of the device built for this project are shown below. This device was built following guidelines provided in the paper “Modeling X-Ray Diffraction with the LEGO® NXT System” (Miller, et al). Refer to this paper for detailed assembly instructions.

Diffractometer Top View
Diffractometer Top View
Diffractometer Side View
Diffractometer Side View
Diffractometer End View (1)
Diffractometer End View (1)
Diffractometer End View (2)
Diffractometer End View (2)

Programming

The NXT program used in this project was modified from that suggested by Miller et al. The NXT program and a detailed description of its operation can be viewed here. The code itself can be downloaded here.


Documentation

Your team will be asked to submit your spreadsheet graph of the data collected by your device, as well as your calculations for determining the line spacing.

Grading

Photometer

This section of the module is not yet completed and can be expected in the 4th quarter of 2007.

Scatterometer

This section of the module is not yet completed and can be expected in the 4th quarter of 2007.

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