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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.

 Comment: 1 digit lacks precision a bit. Also you have written 10-6, yet taken the log of 10-8 in the calculation
Minor comment: underline end tag (</U>) may be nested incorrectly? This also applies to some of the other end tags (e.g. </SUP>, </P>, </OL>) (see submitted HTML source)
2 Marks

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.

 Comment: Only one reason given
1 Mark
  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.

     Comment: Slightly too brief
    2 Marks

    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.

     Comment: See model answer for correct reasons
    0 Marks

  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.

     Minor comment: subscripts would be better than superscripts
    4 Marks

    The angle the monochromator must be moved :-

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

     1 Mark

  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.
    Minor comment: use &deg; for degree symbol

    E = 12.398 / l

    l = 12.398 / E

    l 1 = 12.398 / 20 = 0.6199 Å.

    l 2 = 12.398 / 100 = 0.12398 Å.
    2 Marks

    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).

         Comment: You need to use q and not 2q
    1 Mark

    The range of d-spacings that can be measured

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

  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).
Warning: you used an 8-bit character "–" in front of the x that doesn't display properly with X-windows for the minus sign. If you want a minus sign instead of a hyphen, simply set use the hyphen in the symbol font which will display as minus character (i.e. "-" versus "-")
1 Mark

(ii). (1/2+x, 1/2+y, z) – ?


See model answer
0 Marks

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

Inversion (inversion through origin).
1 Mark

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

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

followed by translation about Z axis).
Minor comment: say "parallel to" and not "about" when discussing translational component
1 Mark

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

Mirror plane (about Z axis).
Minor comment: say "perpendicular to" and not "about" and you should also say where it intercepts the z axis
1 Mark

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

Glide plane (Reflection about y axis

followed by translation about x axis).
Comment: you need to be more specific here - see model answer for more detail
0 Marks

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

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

followed by translation about x axis).
See earlier comment re use of words like about see model answer for solution
1 Mark

(viii). (1/2-x, 1/2-y, -z). ?
See model answer
0 Marks

(ix). (x, 1 / 2 –y, z). ?
See earlier comment re use of 8 bit characters and see model answer for solution
0 Marks

 

 
GENERAL COMMENT: The HTML produced by Word is far from ideal, though that produced by Word97 is not as proprietory as later versions. As a result of students using Word2000 for producing HTML, we are now formally forbidding use of this product since it can potential problems when the marked work is viewed with browsers running on X-windows systems (e.g. Linux). Note that the HTML produced by Word97 is still full of errors, especially incorrect nesting of start and end tags: this can produce anomalous effects with non MS-based browsers.

Beware also of long lines - manually insert linefeed/carriage returns.

If you have any questions re the model answers for Q.5, please email us.