do you know ?

These are simple questions I thought of when I was preparing for my candidacy exam... These are more basic questions some of them you might find silly. But I would like to have them posted here... Here we go

The equation to the plane which meets the three axes ( say for instance we have 3 axes x, y and z; axes need not be orthogonal) at A, B,C respectively is given by

x/A+y/B+z/C=1

and if we define h'k'l' so that A= a/h',B=b/k' and C= c/l' and if we put them back in the previous equation where in we defined the plane, we would get

h'x/a+k'y/b+l'z/c=1

and we note that the parallel plane through the origin is

h'x/a+k'y/b+l'z/c=0 (reader is referred to the appendix1 of a book by kelly and grooves)

and when the fractions are cleared we obtain

hx/a+ky/b+lz/c=0 where (hkl) are the miller indices of the set of lattice points, to which the particular plane we are considering belongs. The whole set of lattice points is given by
hx/a+ky/b+lz/c=m

where (hkl) are the Miller indices and m takes all integral values, both positive and negative. with a reasonable choice of unit cell, small values of indices (hkl) belong to widely spaced planes containing a large areal density of lattice points ( you can see the previous post where we established the fact)

Courtesy: crystallography and crysal defects by Kelly & Grooves


Let us go to the next discussion which is lattice.

One of the definitions that I came up with while reading books was : A lattice is a set of points in space such that the surroundings of one point are identical with those of all the others.

ie, it itself intrinsically possesses a symmetry which is translational symmetry that came from the fact that a lattice is periodic.

Let me continue a little later.

Thanks for stopping by

post your comments if any...