Sir, As i have been only going through basics of xrd aren't hexogonal structures supposed to have h,k,i,l namely four paprameters? Why are we getting only 3 parameters in xrd of same sample? Kindly help me to undersand it Thank you
although for hexagonal crystals we use (hkil) indices. i= -(h+k), hence naming i is redundant.
Therefore, we normally write hkl even for hexagonal crystals. Thats why for graphite or any hexagonal crystals in XRD we normally get hkl naming for faces. (i could be just calculated from h and k)
Dear Aravindhan,
first of all I agree with Abhishek's answer. Nevertheless, I'd like to add some words about the geometry of the trigonal-hexagonal crystallographical systems.
The presence of a symmetry axis, like A3 or A6 in these systems, conventionally coincident with the z axis (c parameter), induces the appearance of three equivalent axes ( x, y, w) in a plane perpendicular to the z axis itself. The three axes are mutually rotated by 120°. But it is well known that , given the x and y axes (vectors) in a plane, a third axis (like w) is linearly dependent on the first two axes. In other words, the vectorial operation reads: x+y = - w. Consequently, the same relation holds for the lattice indices: h+h = - i , being referred to the corresponding axes. This implies that the sum of the indices in the plane perpedicular to the z axis, must be: (h+k+i) =0. As an example, for a pyramidal face, one must write: 21-34); for a prismatic face : (31-40)) and so on. Finally, the writing the third index (i) is not necessary to indicate the position of a face (or a lattice plane) in the trigonal or hexagonal systems.
But one should be cautious: The correct ways, respecting the crystallographic conventions, are only two: either hkil or hk.l, since the symbol hkl ( without the point in place of the third index) is valid only for the other crystallograhic systems: triclinic, monoclinic, orthorhombic, tetragonal and cubic. Hence the symbol (121) has nothing to do with the symbol (12.1) = ( 12 -31).
Thanks for your attention and, ... all the best !
Dino
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Carbon Materials
- Graphite