Lars-Erik Briggner, Assignment 2

1. What is the thickness of lead foil required to attenuate a Cu Ka X-ray from 10⁸ to 10 photons/s?

I(l)/I₀(l) = exp{-(µ/r)_lrx}, µ/r = 230 cm²/g (lead at 1.54 Å), r = 11.3 g/cm² (lead)

i.e. 10^-7 = exp{-230*11.3*x}, thus x = 0.062 mm

The main beam-stop has to be significantly thicker in order to stop, and not just filter, all radiation. This has

to be done for all wavelenghts were different mass absorption coefficients are valid.

2. Frequently organic materials contains only light elements were the X-rays penetrate deeper. Beems reflected

from the surface and from beneath will take a slightly different path, which is seen as broadend and slightly shifted

peaks. The result can be improved by using a top loading "zero background holder" with a very thin sample layer .

The synchrotron radiation provides a highly collimated beam which is beneficial  for organic materials. By the use 

of crystals as monochromators and "multiple foils" at the detector it is possible to investigate a well defined layer

with an intense, well focused beam of the "right" wavelenght and thus avoide the "transparency problem"..

3. What range of d-spacings can be measured if E = 20 to 100 keV, detector angel (2q) 3.5°?

E = 12.398/l, thus 20 keV correspond to 0.620 Å and 100 keV to 0.124 Å

since l = 2dsinq and q is 3.5/2 = 1.75° l = 0.620 Å corresponds to d = 10 Å and 0.124 Å to d = 2

i.e. 20 to 100 keV will provide a range 2 - 10 Å of d-spacings that can be measured.

4. By what angle does a Si monochromator needs to be rotated if wavelenght should change from 0.75 to 0.65 Å?

l = 2dsinq and d = 3.136 Å, thus 0.75 Å corresponds to q = 6.87° and 0.65 Å to q = 5.95°

i.e. the monochromator has to be rotated by 0.92°

5. Write symmetry elements for the following symmetry operators:

i. -x, y, -z    a twofold axis through origin parallell to y-axis (unchanged y, "mirror" image for x and z)

ii. ½+x, ½+y, ½+z    a translation (translated one half of the repeated unit in all three directions)

iii. -x, -y, -z    inversion point at origin (all coordinates are "inverted" across origin)

iv. -x, -y, ½+z    two-one screw axis, (translation along z-axis and rotation 180° around the axis)

v. x, y, -z    mirror plane perpendicular to z-axis through origin (x and y are unchanged and z are "inverted" at origin)

vi. ½+x, -y, z    glide plane (translation along x-axis and "mirror" in y direction)

vii. ½+x, -y, -z    two-one screw axis (translation along x-axis and rotation 180° around the axis)

viii. ½+x, ½+y, z    translation (translated one half of the repeated unit in a and b direction)

ix. ½-x, ½-y, z    twofold axis (the axis goes through (1/4, 1/4, z) and parallell to z-axis)

x. x, ½-y, z    mirror plane perpendicular to y-axis (x and z are unchanged and the plane passes through y=1/4)