Q1.

I(l)/I_o(l) = exp{-(m/r)_lrx}

10⁸/10 = exp{-(230)(11.3)x}

10⁷ = 1/(exp{(230)(11.3)x})

16.12 = 1/(2599x)

x = 2.387x10^-5 cm

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.

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.

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.

Q3.

d = 3.136 Å

l₁ = 0.70 Å
sinq₁ = l₁/2d
q₁ = 6.408^O

l₂ = 0.65 Å
sinq₂ = l₂/2d
q₂ = 5.949^O

Therefore the monochromator must be rotated through 0.46^O

Q4.

q = 1.75^O
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

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 180^o to give the "negative" coordinate.

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).

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.

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.

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.

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.

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.

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).

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.

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.