Also please try to insert more "carriage returns" so that lines wrap to reasonable length (say to around 80 characters length, and definitely less than 255): they are then easier to edit with text-based line editors

10/10⁸ = exp{-230(x)11.3}
1x10^-7 = exp{-2599x}

thickness of lead foil = x = 0.0062 cm = 0.062 mm
3 Marks

The main beam stop will be thicker than this value because the intensity of the X-rays needs to be zero, therefore, the lead foil needs to be thicker than the value of 0.062 mm, that decreases the intensity to 10 photons/s, so that the X-rays will be absorbed.
Comment: See model answer, and note that it is not practical to aim for zero counts
0 Marks

2. Sample transparency causes poor data collection. Example of transparent materials are those containing light elements, e.g., organic compounds. The X-rays are able to penetrate deeper into the samples which are diffracted and detected at smaller 2q values than if they were diffracted nearer the surface.
Bragg-Brentano geometry diffraction is when in the instrument the divergent and diffracted beams are focused at a fixed radius from the sample position. To increase the focusing of the beam and obtain narrow peaks in the diffractograms slits can be placed after the X-ray source or scattered beam. Another method would be to have a thin coating of the sample on a silicon single-crystal sample holder so the X-rays do not penetrate deep into the sample which can occur if an ordinary flat plate sample holder is used but intensities of the diffracted peaks are weaker and less reliable because preferred orientation can occur with this sample preparation.
3 Marks

In synchrotron angle-dispersive powder diffraction the l is varied so a shorter l can be chosen so penetration of the surface by the beam is reduced, therefore obtaining narrower peaks.
Comment: See model answer. Also, the use of shorter wavelengths will give increased penetration, making the problem worse not better
0 Marks

3. l changed from 0.75 to 0.65 Å
Si (111) d-spacing = 3.136 Å
l = 2dsinq

0.75 = 2(3.136)sinq	0.65 = 2(3.136)sinq
2q = 13.74°	2q = 11.9°

The monochromator would have to be rotated by 1.84° from 2q = 13.74° to 2q = 11.9°.
Comment: Note that it is necessary to rotate the monochromator only by q (although the beam will change angle by 2q after the first bounce)
4 Marks

4. E = 12.398 / l
20-100 keV, 2q = 2.7°

l = 12.398 / E
l = 12.398 / 20 = 0.6199 Å
l = 12.398 / 100 = 0.12398 Å
2 Marks

d = l / 2sinq
d = 0.6199 / 2sin1.35 = 13.16 Å
d = 0.1240 / 2sin1.35 = 2.63 Å
2 Marks

Range of d-spacings that can be measured are 2.63 - 13.16 Å
1 Mark

5.
(i) -x, y, -z
2 fold rotation axis through (0,0,0) parallel to the Y direction.
1 Mark

(ii) 1/2+x, 1/2+y, z
2 fold rotation axis through (-1/4, -1/4, z) parallel to the Z axis gives (-1/2-x, -1/2-y, z). Followed by a mirror plane perpendicular to X the axis gives (1/2+x, -1/2-y, z). Followed by a mirror plane perpendicular to the Y axis giving (1/2+x, 1/2+y, z).
Comment: See model answer - this operator corresponds to a single symmetry element
0 Marks

(iii) -x, -y, -z
point of inversion at (0,0,0).
1 Mark

(iv) -x, -y, 1/2+z
Two-one screw axis parallel to c.
Minor comment: Passing through the origin
1 Mark

(v) x, y, -z
Mirror plane perpendicular to the Z axis.
Minor comment: Passing through the origin
1 Mark

(vi) 1/2+x, -y, z
Glide plane a through (0,0,0) perpendicular to b. Minor comment: Use italics for glide plane symbol, not bold type
1 Mark

(vii) 1/2+x, -y, -z
Two-one screw axis parallel to a.
Minor comment: Passing through the origin
1 Mark

(viii) 1/2-x, 1/2-y, -z
2 fold rotation axis at (1/4, 1/4, z) parallel to the Z axis giving (1/2-x, 1/2-y, z). Followed by a mirror plane perpendicular to the Z axis. Comment: See model answer - this operator corresponds to a single symmetry element
0 Marks

(ix) -x, 1/2-y, z
2 fold rotation axis at (0, 1/4, z) parallel to the Z axis.
1 Mark

(x) x, 1/2-y, z
2 fold rotation axis at (0, 1/4, z) parallel to the z axis gives (-x, 1/2-y, z). Followed by a mirror plane perpendicular to the X axis resulting in (x, 1/2-y, z).
Comment: See model answer - this operator corresponds to a single symmetry element
0 Marks