(i). 200 reflection.

d₂₀₀ = 5.638 / Ö 2²+0²+0² = 2.819

½ (2.819) = sin q / l = 0.177Å^-1

å _{n ¦ n} cos {360 (h_x+k_y+l_z)} = 4 (8.39 cos {360 (0) }) + 4(8.39 cos {360 (1) })

=33.56+33.56 = 67.12

å _{n¦ n}sin {2p (h_x+k_y+l_z)}= 4 (8.39 {sin{2p (0)}) + 4 (8.39 {sin{2p (1)})

= 0 +3.67 = 3.67

F₂₀₀² = (67.12)² +(3.67)² = 4518 (to 0dp).

I₂₀₀ = F₂₀₀² = 4518 units.

(ii). d₁₀₀ = 5.638/Ö 1²+0²+0² = 5.638.

½ (5.638) = sin q /l = 0.0887Å^-1

å _{n¦ n}cos {360(h_x+k_y+l_z)} = 4 (9.05 cos {360(0)}) + 4(9.035 cos {360(1/2)})

=36.14 –35.14 = 0.

å _{n¦ n}sin {2p (h_x+k_y+l_z)}= 4 (9.035 {sin{2p (0)}) + 4 (9.035 {sin{2p (1/2)})

= 0 +1.9806.

F₁₀₀² = 0²+(1.9806)² = 3.923.

I₁₀₀² = F₂₀₀² = 3.923 units.

J₂₀₀ = 2.

2 sets of planes (200 and –200).

d₂₀₀ = 5.638/Ö 2²+0²+0² = 5.638/2 = 2.819Å^-1.

1.54 = 2 x 2.819 x sinq

sinq = 0.273

q = sin^-1 (0.273) = 15.843

2q = 31.69o (to 2dp).

Cos (2q ) = 0.724

1+cos²(2q ) = 1.724

P₂₀₀ = (1+cos²(2q ))/2 = 0.862.

Polarization produces a reduction in intensity of 86% in the case of the 200 reflection.

q = 15.84^o

Sin q = 0.273

Sin² q = 0.075

Cos q = 0.962

Sin^2q cosq = 0.0722

L₂₀₀ = 1/sin^2q cosq = 13.85 (200 reflection).

I₂₀₀ = j₂₀₀xP₂₀₀xL₂₀₀xF₂₀₀²

I₂₀₀ = 2 x 0.862 x 13.85 x4518

I₂₀₀ = 107, 878 c units (to 0dp).

I₁₁₁/I₂₀₀ = 52347 / 107878 = 0.485 (to 3dp).

Constant (c) = 0.485 (to 3dp).

Question 6.

Plausible factors (additional to j, p and l) which might be the cause of the disagreement between the measured and predicated I₁₁₁ / I₂₀₀ ratio:

(i). Sample preparation – if crystals within sample are not randomly orientated, then preferred orientation will give rise to a higher intensity value than the predicted value.

(ii). Texture – Presence of large crystals that are therefore not numerous enough, to provide a true powder average.

(iii). Spinning – if the spinning rate of the sample is too low, then not enough crystallites will satisfy the Bragg condition and diffraction intensities will be lower than predicted.

(iv). Transparency – If the sample is transparent, then diffraction peaks will be shifted to lower scattering angles, therefore intensities at predicted peaks will be different in the measured spectrum.

(v). Signal to noise ratio - the predicted value does not take into account the noise that appears in the measured spectrum.