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DuarteME committed Jan 13, 2025
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# Crystallography by D. M. Esteves (INESC MN/IST-ULisboa)
This is a Mathematica script to perform algebraic calculations of distances and angles between planes and directions in crystallography.

Requirements:
Mathematica >= 13.3

Quick guide:
1. To get started, you should create a list of rules ("params") with your lattice parameters. You can use your favourite units for lengths, as the results will be given in the same units. For angles, please use degrees. Example: for NaCl, a->0.56402 nm.

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- 2θ[h,k,l,λ]: gives the 2θ angle associated with the plane with Miller indices (h k l), for a radiation with wavelength λ.
- ωminus[h,k,l,m,n,o,λ]: gives the incidence angle associated with the plane with Miller indices (h k l), for a sample with surface (m n o), for a radiation with wavelength λ, in a grazing incidence geometry.
- ωplus[h,k,l,m,n,o,λ]: gives the incidence angle associated with the plane with Miller indices (h k l), for a sample with surface (m n o), for a radiation with wavelength λ, in a grazing exit geometry.
- ΔφXYZ[a,b,c,d,e,f,g,h,i]: gives the angle between the X=[P]ole/[D]irection, (a b c)/[a b c] and the Y=[P]ole/[D]irection, (d e f)/[d e f] in a sterographic projection where (g h i)/[g h i] is Z=[P]ole/[D]irection of the surface. XYZ can be PPP, PPD, PDP, DDP, DDD, depending on the situation.
- ΔφXYZ[a,b,c,d,e,f,g,h,i]: gives the angle between the X=[P]ole/[D]irection, (a b c)/[a b c] and the Y=[P]ole/[D]irection, (d e f)/[d e f] in a sterographic projection where (g h i)/[g h i] is Z=[P]ole/[D]irection of the surface. XYZ can be PPP, PPD, PDP, DDP, DDD, depending on the situation.

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