SOLID ELECTROLYTE _2

Lets continue discussing solid electrolyte......

Figure 1 shows some other Bravais Lattices:

Figure 1. Bravais Lattice

In figure 2 (a) and 2 (b) you may watch the animation of bcc (body centered cubic) and fcc (face centre cubic) crystal structure.

Figure 2(a) an animation of body centered cubic structure ( note: there are 1/8 x 8 edge atoms + 1 atom in the centre)

Figure 2(b) an animation of face centre cubic (fcc) (note: there are 1/8 x 8 edge's atoms + 1/2 x 4 face's atoms in this structure)

Meanwhile, Figure 3 and 4 describes the miller indices of crystal planes:

Figure 3. Some of the Miller indices of planes in a cubic crystal

Figure 4. some of miller indices

ATOMIC RADII

Eventhough quantum mechanics stated that atoms and ions do not have preciselt defined radii, however the ionic crystal structure is developed by ions pack together in an extremely regular fashion in crystals, therefore their atomic positions and their interatomic distances can be measured accurately. Figure 5 describes the geometrical calculation of atomic radii.

Figure 5. geometrical calculation of atomic radii

 DETERMINATION OF CRYSTAL STRUCTURE

Crystal structure can be determined through analysis based on the Bragg's Law. This Law was developed by W.H. and W.L. Bragg ( father and son) who started experiments on using X-ray crystal diffraction as a means of structure determination. Bragg noted that X-ray diffraction behaves like 'reflection' from the planes of atoms within the crystal and that only at specific orientations of the crystal with respect to the source and detector are X-rays 'reflected' from the planes. In X-ray diffraction the reflection only occurs when the conditions for constructive interference are fulfilled. Figure 6 illustrates the reflection of X-rays by a crystal.

Figure 6. Bragg condition for the reflection of X-rays by a crystal

From figure 6, it follows that 

xy=yz= d sin (thetha), so that the difference in path length is 

2d sin(thetha)

This must be equal to an integral number, n, of wavelength. If the wavelenght of the X-ray is lambda, then,

n.lambda= 2dsin (thetha), this is known as Bragg's equation. 

POWDER DIFFRACTION

a finely ground crystalline powder contains  a very large number of small crystals, known as crystallite, which are oriented randomly to one another. The difficulty in powder diffraction is in describing which planes are responsible for each reflection, this is known as ' indexing the reflections', i.e assigning the correct hkl index to each reflection. 

Powder diffraction is difficult to use as a method of determination crystal structures for anything other than simple high-symmtry crystals because of  the structures bocemo more complex and the number of lines increases so that overlap becomes a serious problem and it is difficult to index and measure the intensities of the reflections. Accordingly, it is mostly used as a finger print method for detecting the presence of a known compound or phase in a product by comparing the pattern to a powder diffraction pattern which can be founded in data base file, such as JCPDS (Joint Committe for Powder Diffraction Standards).

The Le Bail or Rietveld method can be used to solve a structure from the powder diffraction data. The method works best if a good trial structure is already known or if the unknown structure is a slight modification of a known structure.