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
3 Marks
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 Marks
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 .
2 Marks
The synchrotron radiation provides a highly collimated beam which is beneficial for organic materials. By the use
of crystals as monochromators [it is assumed that you mean "analysers" (which work by selecting a monochromatic wavelength)] 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 Marks
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
Comment: Method correct, but you need to use more
significant figures here.
3 Marks
i.e. 20 to 100 keV will provide a range 2 - 10 Å of d-spacings that can be measured.
1 Mark
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°
4 Marks
i.e. the monochromator has to be rotated by 0.92°
1 Mark
Minor comment: Slightly brief, but answer is correct
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)
1 Mark
ii. ½+x, ½+y, ½+z a translation (translated one half of the repeated unit in all three directions)
1 Mark
iii. -x, -y, -z inversion point at origin (all coordinates are "inverted" across origin)
1 Mark
iv. -x, -y, ½+z two-one screw axis, (translation along z-axis and rotation 180° around the axis)
1 Mark
v. x, y, -z mirror plane perpendicular to z-axis through origin (x and y are unchanged and z are "inverted" at origin)
1 Mark
vi. ½+x, -y, z glide plane (translation along x-axis and "mirror" in y direction)
1 Mark
vii. ½+x, -y, -z two-one screw axis (translation along x-axis and rotation 180° around the axis)
1 Mark
viii. ½+x, ½+y, z translation (translated one half of the repeated unit in a and b direction)
1 Mark
ix. ½-x, ½-y, z twofold axis (the axis goes through (1/4, 1/4, z) and parallell to z-axis)
1 Mark
x. x, ½-y, z mirror plane perpendicular to y-axis (x and z are unchanged and the plane passes through y=1/4)
1 Mark
You need to be slightly more specific for some of the answers (e.g. translation type (I, C) or glide plane type (a)), so 1 Mark total deducted for ii, vi, viii combined.