The unit cell tranformation is given in every text books on X-ray crystallography and solid state physics and also International Tables of crystallography. You must first read these. A good excercise for learning this topic is the transformation of the pseudocubic cell of the perovskite structure to the orthorhombic or rhombohedral cell. Since most of the crystallographic programs use hexagonal cell for rhombohedral structure one has to know the rhombohedral to hexagonal tranformation. the method is very simple. You have to write down the vectorial equations relating different structure in terms of the unit vectors (cell parameters). Then you can get matrix relationship between the original and the tranformed cell. The same matrix transform the miller indices of the cells as well.

The unit cell tranformation is given in every text books on X-ray crystallography and solid state physics and also International Tables of crystallography. You must first read these. A good excercise for learning this topic is the transformation of the pseudocubic cell of the perovskite structure to the orthorhombic or rhombohedral cell. Since most of the crystallographic programs use hexagonal cell for rhombohedral structure one has to know the rhombohedral to hexagonal tranformation. the method is very simple. You have to write down the vectorial equations relating different structure in terms of the unit vectors (cell parameters). Then you can get matrix relationship between the original and the tranformed cell. The same matrix transform the miller indices of the cells as well.

I am just wondering whether young researchers in condensed matter physics get some training in basic crystallographic methods or not before they start their Ph.D. work.

Tapan's idea is simple, but wise - to read the basic literature before you start the work.

@Supratim: Homework for you:

Try to get the following books and read the suggested chapters. If you do not understand then come back to me:

Unit cell transformation is best described in the book

Crystal Structure: A working approach, H.D. Megaw, W.B. Saunders Company, Philadelphia (1973) Chapter 10, p. 186.

However this book is not available easily.

The next choices would be:

X-ray Diffraction, B.E. Warren, Addison-Wesley (1969) Chapter 2, p. 15

Elements of X-ray Diffraction, B.D. Cullity, Addison-Wesley (1978) Chapter 2, p. 32

Dear Dr Chatterji,

thank you for these suggested books, definitely I'll collect these books and try to understand and if not understood come back to you again.

Dear Dr Chatterji,

I've gone through the books of Warren (p22 onwards), Cullity (Ch2+Appendix 2), and found useful information. May I say that its a learning how to convert 14 Bravais lattice to cubic symmetry.

However, I feel I should re-frame my questions: actually I'm working on ferroelectric materials which has too many structural transition as temperature changes and finaly reaches cubic-paraelectric phase. Now, in many literature, authors simply said orthorhombic/rhombohedral/tetragonal phase is indexed with pseudocubic cell parameters. There, they also used pseudocubic cell volume simply dividing the cell volume by the numbers formula unit (which is OK to me). They also mentioned the lattice parameters in terms of pseudocubic cell such as, A = root2 Ap = C; B = 2 Ap etc. there are few more examples are in Glazer (Acta Cryst. A31 (1975) 756, etc (not understood).

My question, how these two scheme are related ??

For ferroelectric materials the book Crystal Structure: A working approach, H.D. Megaw, W.B. Saunders Company, Philadelphia (1973) Chapter 10, p. 186. would have been more useful. But you may not be able to get this rare book. What you must learn is to express the transformed cell parameters in terms of the original one in vectorial form (Warren's book tells you that). From these equations you get the transformation matrix. If you know the matrix then you can transform the cell easily. You must learn the general method of cell transformation and not particular examples.

One useful tranformation from the pseudo-cubic to the orthorhombic cell is a'=a*sqrt(2) b'=b*sqrt(2) c'=2c. In perovskites this tranformation almost always needed. You see that here you take the two diagonals of the pseudocubic cells as a' and b' and twice the pseudocubic cell length as c'. This phase is the Pbnm orthorhombic phase of the cubic perovskite cell. Another phase is the rhombohedral phase which is uually represented by the hexagonal cell.

Dear Dr. Chatterji,

I would like to thank you for all earlier discussions,while following your suggestion, I found a book of HD Megaw (Ferroelctricity in Crystals), which is extremely useful for my query and other queries too.

Thanks for showing right path for all young searchers including me.

Pseudo cubic representation is just a different view of the same atoms (as only atoms do exist, coordinate systems are "human creations"). In this particular case the pseudo cubic unit cell fits better, compared to the hexagonal representation of the rhombohedral unit cell of the distorted perovskite. Pseudo here refers to the the symmetry, as even with a metrically cubic cell (alpha = 90 deg) atoms in the pseudo cubic cell (the "content of the unit cell") cell will not have cubic symmetry.