Rob Whittock

Assignment 2.

 

  1. What thickness of lead foil (x) (in mm) is required to attenuate a

Cu Ka x-ray beam of intensity 108 photons/s down to 10 photons/ s, and explain why the main beam stop would be much thicker than this.

10/1x10-6 = exp{(-230) 11.3 X}

1x10-6 = exp{-2599X}

x = 18.4206 / 2599

X = 0.007 cm

X = 0.07 mm.

The reason why the main beam-stop for an unfiltered non-monochromated copper x-ray source would be much thicker is because the mass absorption for Cu Kb x-ray radiation (much larger than Cu Ka ) has to be taken into account.
  1. Briefly discuss how narrow peaks might be obtained from a laboratory diffractometer configured for Bragg-Bretano geometry. Briefly explain how and why narrow peaks can be obtained with organic samples on synchrotron angle-dispersive powder diffractometers.

    2. Narrow diffraction peaks may be obtained by applying a fine powder coating of the sample, to a silicon single crystal sample holder. Unfortunately this method of sample preparation causes the peak intensities to be larger or smaller, due to preferred orientation and small volume of diffracting material, respectively.

    Angle-dispersive synchrotron experiments allow the wavelength used to be slightly above or well below the absorption edges of the elements in the sample. This results in less absorption of the x-rays and a higher resolution powder diffraction pattern. Also because synchrotron radiation is more intense than that used in the laboratory, synchrotron radiation gives a better signal to noise ratio.

  2. If the wavelength of the instrument is changes from 0.75 to 0.65 Å, what angle must the monochromator be rotated if silicon (111) planes are used?

    3. l = 2d sinq

    0.75 = 2 (3.136) sin q 1

    sin q 1 = 0.75 / 2 (3.136) = 0.11958

    q 1 = 6.87o.

    0.65= 2 (3.136) sin q 2

    sin q 2 = 0.65 / 2 (3.136) = 0.103635

    q 2 = 5.95.

    The angle the monochromator must be moved :-

    q 1 - q 2 = -0.920 (to 2dp).

  3. What range of d-spacings can be measured for a detector designed to record x-ray photons with energies in the range 20-100 keV, when the detector angle is set to 2.7o ?

    4. E = 12.398 / l

    l = 12.398 / E

    l 1 = 12.398 / 20 = 0.6199 Å.

    l 2 = 12.398 / 100 = 0.12398 Å.

    l = 2d sin q

    d = [(l )/ sin q ] / 2

    d = [0.6199/ (sin 2.7)] / 2 = 6.59 Å (to 2dp).

    d = [0.12398/(sin 2.7)] / 2 = 1.32 Å (to 2dp).

    The range of d-spacings that can be measured

    by detector = 1.32 to 6.59 Å (to 2dp).

  4. For each symmmetry operator listed below, state the corresponding symmetry element and give reasons for your answer.

(i). (–x, y, -z).

Two fold rotation (180o rotation about y axis).

(ii). (1/2+x, 1/2+y, z) – ?

(iii). (-x, -y, -z).

Inversion (inversion through origin).

(iv). (-x, -y, 1/2+z).

Two fold screw axis (180o rotation about Z axis,

followed by translation about Z axis).

(v). (x, y, -z).

Mirror plane (about Z axis).

(vi). (1/2 +x, -y, z).

Glide plane (Reflection about y axis

followed by translation about x axis).

(vii). (1/2 +x, -y, -z).

Two one screw axis (180o Rotation about X axis,

followed by translation about x axis).

(viii). (1/2-x, 1/2-y, -z). ?

(ix). (x, 1 / 2 –y, z). ?