INTRODUCTION: X-rays are high energy electromagnetic waves (about 10 nm to 0.01 nm). Examples of familiar use of x-rays are diagnostic tool by physicians and dentists. X-rays are hazardous radiation and should be used with care. It is the reason why you will replace x-rays with microwaves. A model of an array of steel balls about 1.0 cm in diameter and regularly placed about 3.75 cm apart, is substituted for actual structure of atoms (as in a crustal). The steel balls are held in a regular cubic structure by ethafoam, a substance widely used as a disposable packing material. The steel balls strongly interact with microwaves while ethafoam is transparent to the microwaves. Diffraction pattern of microwaves is observed much like the x-ray diffraction by a crystal.

CAUTION: The microwave intensity in use in the lab is quite below the standard allowed. It is still advisable not to place your eye in the direction of the beam.

THEORY : The theory describing the x-ray and microwave diffraction is the same. So, study the appropriate section of your text for x-ray diffraction theory to prepare for the lab. The working formula is,

2d sin q = nl where,

q = Diffraction angle as defined with respect to Bragg plane

d = distance between the two adjacent Bragg planes

l = Wavelength of x-ray under consideration

n = Order of diffraction

EQUIPMENT: Transmitter, Receiver, 9V Power adapter, Goniometer, Rotating table, Cubic lattice and a meter ruler

EXPERIMENTAL PROCEDURE:

Arrange the equipment as shown. Adjust the transmitter and the receiver directly facing each other on opposite sides. Align the cubic lattice so that the edge of the cube will be perpendicular to the incident microwaves. Place the edge of the horn of the transmitter and receiver, at 7 inches from the closest edge of the cube. Place the cube at the center on top of the rotary mount. Turn the receiver on and set the range switch on 10 scale. Power the transmitter by plugging the adapter to 110V outlet. Adjust the range switch on the reeceiver to obtain about 1/3 full scale deflection. The orientation of the set up and the positions of the instrument, should not be changed during the course of the experiment. The diffraction angle q is the symmetric grazing angle, made by each arm with respect to Bragg planes. The cube and the receiver (movable arm) must be adjusted accordingly, to measure the intensity of microwaves. Record the initial reading for zero degree diffraction angle. Adjust the movable receiver arm by two degrees and, the cubic lattice by one degree in the same direction. Record each angle of diffraction and corresponding meter reading of intensity in a table. Continue rotating the movable arm by two degrees for every one degree rotation of the crystal, for all possible angles in step of one degree increment.

Repeat all measurements for 45o orientation of the cube.

Plot the intensity of microwaves as a function of diffraction angle for both orientations. Join the data points with a smooth continuous curve. Ignore smaller peaks at various angles of diffraction. Use only peak values to find the lattice spacing d. The known value of wavelength of the microwave radiation is 2.85 cm. Compare your results with theory. The known value of spacing type (1,0,0) is 3.75 cm.

Using the technique of Bragg diffraction of x-rays, crystallographers can determine the interatomic space inside the crystal if the wavelength of the x-rays is known. It is then possible to determine the detailed structure of the crystal by various geometric techniques.

PROBLEM #1 Suppose these microwaves you just used in your experiment, are incident on an unknown crystal model producing strong intensity maxima at 17.2, 36.2 and 62.8 degrees for n=1,2,3. What is the distance between adjacent atoms of the model ?

PROBLEM #2 To determine the x-ray wavelength, an experiment such as you have studied today must be done with actual x-rays. A prior knowledge of interatomic space is also essential. It is not easy to measure the interatomic space directly inside the crystal. Consider a crystal of potassium chloride. It consists of closely packed array of tiny cubes each of which is made up of one potassium and one chlorine atom. The density of potassium chloride is 1980 kg/m3. The atomic weights of potassium and chlorine are 39.1 and 35.5, respectively. Estimate the interatomic space in this crystal. Calculate the wavelength of the x-rays if the intensity maxima are obtained at diffraction angles of 22.5^o for n=1 and 49.3^o for n=2.

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Updated 1/24/00