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Answers to X-ray Crystallography Quiz

1. A unit cell is defined as the simplest portion of a crystal structure, which is repeated by translation, and shows its full symmetry.

2. The parameters that need to be refined during structure determination include the following:
   • Atomic positions.
   • Partial occupancy.
   • Thermal motions.
   • Preferred orientations (powder diffraction only).
   • Background parameters (powder diffraction only).
   
   
3. Refinement is the final stage of structure determination once all the atoms in a structure have been located. Refining the structure basically implies getting the fit between the observed and calculated intensities as accurate as possible.

4. The standard deviation of a bond length of 2.620(1) Å is ± 0.001.

5. Advantages of powder diffraction:
   • Useful for finger printing and phase identification.
   • Measures sample purity.
   • Confirms that the bulk sample is the same as the single crystal used for a structure determination.
   • Can study samples under extreme conditions and phase changes at high temperatures and pressures.
   • Good for quantitative analysis.

   Disadvantages of powder diffraction:

   • Peak overlap is troublesome as prevents the crystal structure from being solved from individual reflections.
   • Overlap becomes more significant with high angle reflections.
   • Indexing patterns is much more complicated in non-cubic systems.
   
   
6. It is advantageous to perform a crystal structure determination at low temperatures in order to reduce the thermal (vibrational) motion as this attenuates high resolution data, hence a more precise structure is produced at lower temperatures. Also, it allows unstable and reactive compounds to be analysed to a greater extent due to extended lifetimes produced at low temperatures.
7. During refinement an R-factor is computed to give a measure of correctness between the observed and calculated intensities of a crystal structure.Ideally a good structure has an R-value <5%.
   [R=0% is never achieved due to random errors arising throughout experimental measurements].

8. Anisotropic displacement parameters refer to the fact that atoms do not vibrate equally in all directions and therefore are said to vibrate anisotropically (differently in all directions).
9. Hydrogen atoms are difficult to locate using diffraction data due to their only having one electron, which is diffusely distributed because of bonding effects. Larger and heavier atoms swamp the signal produced by the hydrogens. It can be noted that the more electrons an atom has the more it scatters the x-rays, hence this is the reason why Hydrogen does not produce many.
10. 
    

    θ/°	sin2θ	(h2+k2+l2)	hkl	a/Å
    11.60	0.0404	1	001	3.83
    16.52	0.0809	2	011	3.83
    20.38	0.1213	3	111	3.83
    23.71	0.1617	4	200	3.83
    26.71	0.2020	5	210	3.83
    29.50	0.2425	6	211	3.83
    34.64	0.3231	8	220	3.83
    37.09	0.3637	9	300	3.83
    39.49	0.4044	10	310	3.83

    By rearranging:

    (1)

    sin2θ  =

    λ 4a2

    (h2+k2+l2)

    Produce equation:

    (2)

    a2  =

    λ2 4sin2θ

    (h2+k2+l2)

    Therefore the average unit cell dimension = 3.83 Å
    Body centred – h+k+l = 2n X
    Face centred – h,k,l = all odd/all even X
    Therefore structure is primitive cubic as has no condition.

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