Q1.
I(l)/Io(l) = exp{-(m/r)lrx}
108/10 = exp{-(230)(11.3)x}
Error: Fraction wrong way up
107 = 1/(exp{(230)(11.3)x})
16.12 = 1/(2599x)
Error: Wrong use of log function
x = 2.387x10-5 cm
1 Mark
The main beam stop for an unfiltered, non-monochromated Cu X-ray source
would have to be thicker to stop the transmitted radiation with shorter
wavelengths.
Comment: Too brief
1 Mark
Q2.
Narrower peaks from a "transparent" sample may be obtained by using
a thinner sample (although at the cost of intensity). The use of X-ray
slits after the X-ray source to control the divergence of the incident
beam onto the sample and Soller slits to prevent divergence of the incident
X-ray beam out of the q/2q
plane of the sample may result in narrower peaks.
Comment: Too brief
2 Marks
Narrower peaks may be obtained from an angle-dispersive synchrotron
powder diffractometer by improving the resolution with the use of monochromators
and beam conditioners to obtain a better focussed monochromated beam.
Comment: Not correct answer
0 Marks
Q3.
d = 3.136 Å
l1 = 0.70 Å
sinq1 = l1/2d
q1 = 6.408O
Minor comment: Use degree symbol (HTML for °
is °)
l2 = 0.65 Å
sinq2 = l2/2d
q2 = 5.949O
Therefore the monochromator must be rotated through 0.46O
5 Marks
Q4.
q = 1.75O
E1 = 20keV
E2 = 100keV
20 = 12.398/l1
20 = 12.398/(2d1sinq)
d1 = 10.1495
100 = 12.398/l2
100 = 12.398/(2d2sinq)
d2 = 2.0299
The range of d-spacings which can be measured are therefore 2.03 - 10.15
Å
5 Marks
Q5.
i) (-x, y, -z) represents a two-fold axis parallel to the b axis
and lying at [0, y, 0]. There is no change in the y coordinate which lies
on the 2-fold axis, but x and z are rotated by 180o to
give the "negative" coordinate.
1 Mark
ii) (0.5+x, 0.5+y, 0.5+z) corresponds to a body centred point at half
the unit cell away from (x, y, z).
1 Mark
iii) (-x, -y, -z) represents a centre of symmetry lying on the origin,
(0, 0, 0). Each coordinate is shifted along a line passing through (0,
0, 0) to give the inverted coordinate.
1 Mark
iv) (-x, -y, 0.5+z) represents a two-fold screw axis parallel to the
c axis. The point x, y, z is rotated about [0, 0, 0] to give negative
x and y coordinates and then translated along half the c axis to
give 0.5+z.
Minor comment: 0,0,0 should actually
be 0,0,z
1 Mark
v) (x, y, -z) represents a mirror plane parallel to the ab plane
lying at [x, y, 0]. The point x, y, z is reflected in the mirror plane
which only changes the sign of the z coordinate.
1 Mark
vi) (0.5+x, -y, z) represents an a-glide plane lying at [x, 0, z]. The
point is reflected in the plane to give -y and then translated parallel
to the a axis by half the axial length to give 0.5+x.
1 Mark
vii) (0.5+x, -y, -z) represents a two-fold screw axis parallel to the
a axis lying at [x, 0, 0]. The point (x, y, z) is rotated about
the a axis and then translated by half the a axis.
1 Mark
viii) (0.5+x, 0.5+y, z) corresponds to C-centring where for every (x,
y, z) there is another centred on the ab plane (half way along each
of the a and b axes).
1 Mark
ix) (0.5-x, 0.5-y, z) represents a two-fold axis parallel to the c
axis and lying at [0.25, 0.25, z]. The point (x, y, z), when rotated about
this axis, is shifted by half along the a and b axes.
1 Mark
x) (x, 0.5-y, z) represents a mirror plane parallel to the ac
plane and lying at [x, 0.25, z]. The point (x, y, z) is shifted by half
along the a and b axes.
1 Mark