CHM9012 Materials And Structural Analytical Methods Coursework

Q1 (a) Show that X-ray diffraction from a X-ray source of wavelength, modelled as reflection between two hkl planes separated by a distance dhkl gives rise to the Bragg Equation (Eqn.1)

        2𝑑!𝑘𝑙𝑠𝑖𝑛𝜃!𝑘𝑙 = 𝑛𝜆 (𝑛 = 1,2,3. . )              (Eqn 1.)

(b) Using schematic diagram(s), show how the Bragg-Brentano diffractometer, measures the diffraction angle, 2θ , during a PXRD experiment. Explain how changes in the divergence slit (at the source) and receiver slit (at the detector) might affect:

(i) peak intensity and
(ii) peak resolution in the PXRD pattern.

(c) State the possible Bravais lattices for centred cubic systems and briefly explain how General Systematic Absences in the X-ray diffraction data arise when lattice centring is present and how this can be identified when indexing a cubic system.

(d) In an experiment to prepare nanodiamonds on a niobium metal substrate with chemical vapour deposition, the diffraction pattern shown below was obtained from a sample using Cu-Kα radiation (λ = 1.542 Å).

Peak information is given in the table below

Niobium and diamond adopt centred cubic structures with a = 3.300 and 3.567 Å respectively.

(i) Index each peak in the pattern and assign them to Nb or C(diamond) phases.
(ii) Obtain unit cell dimensions for each phase and confirm your assignments from part (i)
(iii) Comment on the relative breadth of the peaks in the pattern and suggest a reason for the broadening of certain peaks.
(iv) Outline an experimental approach for quantifying the nanodiamond surface coverage using PXRD.

Q2 In a study of an archaeological artefact thought to be a mask of Coptic Egyptian origin, a fragment was inspected using powder X-ray micro-diffraction to explore the possibility of identifying pigments and/or fillers in the paintwork applied to the surface of the mask. X-Ray diffraction data were collected with a Bruker D8 Discover diffractometer with Cu-Kα radiation (λ = 1.5406 Å) operating in parallel beam geometry collimated to 2 mm. Data were collected were collected from three separate sample sites with coupled θ-2θ scans in the 2θ-range 5-80° with dwell time of 0.5 s for each 0.02° increment.

The fragment studied is shown in the Figure below. Its surface is uneven and the fabric coating appears to be composed of a blue-green upper layer above a white, grainy sub-layer. Preliminary XRF studies have identified the presence of copper, calcium and silicon

(a) Briefly explain the terms microdiffraction and why parallel beam geometry might be an advantageous choice in the analysis of the uneven surface of the sample. Illustrate your answer with a suitable diagram.

(b) ASCII ‘xy’ data files from the experiment are provided on the module Blackboard.

Provide a short report for the study comprised of the following components:
(i) A plot of intensity vs. 2θ for the data and, from this, an initial assessment of crystalline vs amorphous nature of the sample and its composition as single phase or as mixture of phases.
(ii) A short description of ca. 3-5 candidate phases that might be in the coating of the fragment (consider both the pigment and its base). Briefly discuss your choice
(iii) Plots of the data compared to the candidate phases from (ii) 
(iv) A critical evaluation of the presence of each candidate phase in the sample.
(v) A brief conclusion of the study including suggestions for further work on the sample