Due on: 14 Sep 2017.
Marks: 30 (All questions carry equal marks) / Topics: X-ray diffraction, Microscopy
1) Using a diffractometer and a radiation of wavelength (l) 1.54 Å, only one reflection from a CCP material is observed at 2θ equal to 121°. What are the indices of this reflection? What is the interplanar spacing of the corresponding plane in real space? What is the lattice parameter? Show that in the current experimental scenario, the next higher index reflection cannot occur.
2) A 'standard' powder pattern is obtained from a "BCC crystal". The lattice parameter of the crystal (a) = 2.86 Å. X-rays of wavelength equal to 1.54 Å are used in the experiment. What are the 'reflections' observed and at what Bragg angles?
3) Fig.1 shows the X-ray diffraction powder pattern from an equimolar NiCoFe ternary alloy. The Bragg peaks are observed at the following 2q values: 43.81°, 51.03°, 75.11°, 91.23°, 96.59° & 119.15°.
(i) What is the type of lattice? (ii) Determine the lattice parameter.
(iii) How many different phase(s) are there in the alloy? (iv) How can we rationalize the observation to the answer for (iii).
Data: (i) l=1.54Å. (Hint: error in d spacing decreases with q → use high angle lines for lattice parameter calculation), (ii) rNi = 1.25Å, rCo = 1.26 Å, rFe = 1.26 Å, (iii) ENNi = 1.91, ENCo = 1.88, ENFe = 1.83. Note: 'strictly speaking' atomic diameter of an element is dependent on the atomic environment in which it is present.
Fig.1.
4) The Bragg angle for the first reflection from SiC is 17.2°. In the present case SiC adopts a ZnS type structure (Zinc Blende, cF8, ). (i) Determine the Bragg angle for the second reflection. (ii) The second reflection is absent in the DC structure and is weak in the current case. Explain why this is so.
5) Copper and Nickel (both CCP) dissolve in each other in all proportions at room temperature in the solid state (form a continuous series of substitutional solid solutions as they satisfy the Hume-Rothery rules). From a sample of Cu-Ni alloy of unknown composition, a ''powder pattern'' is obtained using monochromatic radiation of wavelength 1.54 Å. The first reflection is observed at value of . aCu = 3.61 Å, aNi = 3.52 Å. Estimate the percentage of copper in the alloy, assuming a linear variation of lattice parameter with composition (Vegard's law).