Do you know

Why do you see grain boundaries ? Framing it otherway, what is the source of contrast in OM and EM (SEM) in distinguishing grains and grain boundaries?

What is resolution? How do you achieve and what is the best resolution, how is it different for different source of radiation? Give examples

How is SE yield related to z? Is there any relation, if it does not have? why?

How is BSE related to Z? Explain interms of interaction volume?

Factors affecting intensity of x-rays? Why?

What are systematic absences? Physical meaning of them in each case

Derive c/a ratio, packing fraction, coordinates, void coordinates, (octahedral,tetrahedral) for HCP, fcc, bcc.

how to explain Depth of focus/field in terms of ray diagram and equation

how Laue equations and ewald's sphere come about? and why we call Laue as conditions and Bragg's law.

how scattering by electrons, atoms unit cell happen?

how can you stack 2-d nets to arrive at 14 Bravais lattices?

how to draw stereographic projection?

how to explain all symmetry elements? can you!!!!

how kikuchi lines form in EBSD?

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...

Do you know why hexagonal lattice and hcp structure are different?

hcp contains two atoms essentially one at the position 000 and the other at position 2/3,1/3,1/2. It is essential that we have these two points to construct the unit cell and hence one atom at 000 is the lattice point and the other at 2/3,1/3,1/2 is a basis. Hence hcp is a structure and hexagonal lattice does not have the basis point and it is simply called a hexagonal lattice..

I feel more understanding from my part is needed here to explain things still.

Please do contribute as usual..

Cheers

Do you know why hkil indices are used (MB indices ) instead of Miller in Hexagonal close packed lattice?

The answer is simple. Inorder to represent the permutation of indices of the form consistent, MB indices are used in hcp. that is... in hcp planes of the form {100} do not include the plane of the type (10-10) ie (100) does not include (1-10) which belongs to the same set of planes which are called prismatic planes.. Hence a third axis is chosen so that the planes of the form {10-10} include the following planes (10-10),(1-100),(-1100),(0-110),(01-10) etc. So choosing the four index systems has made the set of planes belong to that particular form avoiding confusion thereby making permuatation of indices and symmetry more obvious

In Choosing four index system actually one of the axes in the basal plane is redundant by making it dependent on the other two ensuring that the planes belong to a particular form. This is better explained in a book of crystal chemistry by Relva C. Buchanan, Taeun Park.

Please contribute to this article as well if you have more conclusive, concrete solid answer

Do you know why close packed planes are farther apart?

Close packed planes are the planes of low indices. If you have to take into account a fcc unit cell, the close packed planes are (111) planes. You can always calculate the distance between two planes using the formula

d= a/sqrt(h2+k2+l2)

which tells you that lower the indices, larger will be d.

This might be inadequate to explain the same question. Let us follow this way close packed planes are also farther apart because closer the packing of planes, higher will be the planar density of atoms. you might ask what if the planar density is going to be large, how does it affect the distance between the two planes... the answer is yes, in terms of geometry and interplanar spacing, close packed planes have high coordination and so the next planes should be kept larger apart in order that the interactions between the atomic positions make the atoms sit in the equilibrium positions.

Physically this could also be explained in terms of a simple diagram which is given in the second chapter of the book called X-ray diffraction by cullity where 2-d representation of planes in a lattice is drawn and it is shown that the interplanar spacings for closepacked planes are larger.

I don't really know whether it is a decent answer for this question. But I feel I need a physical basis still to explain the statement that close packed planes are farther apart. Though in terms of happening of slip one could explain that the close packed planes will have (t crss) minimum. This comes about from pieirls stress or the lattice frictional stress is minimum when w goes to maximum and b goes to minimum. The equation is t crss is proportional to exp (-w/b).

The above explanation might hold good to answer why slip gets activated in close packed planes and directions which inherently takes into account w to be larger or in other words d to be larger.

So please contribute to this question if you have anything further to be said. Let us discuss.

Measuring degree of Happiness

The object why I have started another blog is that I have chosen this domain exclusively to write up the concepts I understand while I read and discuss. I wish all who follow my blogs to contribute their valuable suggestions here in this arena. I would like to discuss more basic fundamentals in this avenue and hope I ll come up with few concepts in a day or so and then I hope I ll start posting my articles.

Thanks all

Happy weekend

Bharathi Rajeswaran