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Topic: Miler indexes, Bravais lattice  (Read 313 times)

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Offline KiraTiss

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Miler indexes, Bravais lattice
« on: December 20, 2021, 04:49:38 AM »
Hi everyone!

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;
                                                then absent   

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.

Offline Orcio_87

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Re: Miler indexes, Bravais lattice
« Reply #1 on: December 20, 2021, 08:09:20 AM »
I have to admit, that means nothing to me.

Some reflections are allowed when all indexes (h, k, l) are odd or even, some - when their sum is even. Diamond cubic is a special case of face centered cell (h + k + l = 4n).

How to pick between primitive and face centered cell ---> you need to check do indexes are all odd or even or mixed.

Why did you rejected diamond face centered cell ?
« Last Edit: December 20, 2021, 08:19:35 AM by Orcio_Dojek »

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