10/108 = exp{-230(x)11.3}
1x10-7 = exp{-2599x}
thickness of lead foil = x = 0.0062 cm = 0.062 mm
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.
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.
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.
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°.
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
d = l / 2sinq
d = 0.6199 / 2sin1.35 = 13.16 Å
d = 0.1240 / 2sin1.35 = 2.63 Å
Range of d-spacings that can be measured are 2.63 - 13.16 Å
5.
(i) -x, y, -z
2 fold rotation axis through (0,0,0) parallel to the Y direction.
(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).
(iii) -x, -y, -z
point of inversion at (0,0,0).
(iv) -x, -y, 1/2+z
Two-one screw axis parallel to c.
(v) x, y, -z
Mirror plane perpendicular to the Z axis.
(vi) 1/2+x, -y, z
Glide plane a through (0,0,0) perpendicular to b.
(vii) 1/2+x, -y, -z
Two-one screw axis parallel to a.
(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.
(ix) -x, 1/2-y, z
2 fold rotation axis at (0, 1/4, z) parallel to the Z axis.
(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).