Hope you are doing well. I admit that I am in dire need of help. I am trying to figure out my Bravais lattice from a set of Miller indexes, and yet I cannot figure it out. My book is useless as well.
Overall, what I have is 111, 220, 311, 400, 331 (Cubic crystal - It is a made up problem from an exercise set). And from what I understand from my book, depending on how the number are organised, I should be able to easily find what is my lattice.
The pottential lattices are:
m Miler indexes Potential lattice
3 111 P, F, D
8 220 P, I, F, D
11 311 P, F, D
16 400 P, I, F, D
19 331 P, F, D
r/chemhelp - Miler indexes and Bravais lattices!
From the book:
Crystal Type Bravais Lattice Reflections Present for Reflections Absent for
Simple Primitive Any h. k. l h+k+l odd
Body-centered Body-centered h+k+l even h, k, and I mixed
Face-centered Face-centered h. k, and I unmixed h, k, and I mixed
Diamond cubic Face-centered As fcc, but if all h, k, and Imixed and if all evenandh + k+ Ii' 4N
even and h +k+ Ii' 4N;
I have to admit, that means nothing to me. By following the rules I get three potential Bravais lattice: P, F and D. D seems to be the less likely in my opinion, but I still do not know how to explain why. How do I pick bettwen Primitive and Face-centered? All my miller indexes seem to fit into both (or at least, I do not know how to spot the differences).
Please, let me know, already did the rest of the problem set (Calculating the lattice parameter and the d-spacing) with logical results. Also, it is also required to not use any software.
If someone could break that part down for me, that would be wonderfull.