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mctools / ncrystal

NCrystal : a library for thermal neutron transport in crystals and other materials
https://mctools.github.io/ncrystal/
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Wrong multiplicity factors? #67

Closed saroun closed 3 years ago

saroun commented 3 years ago

Hi Thomas, I've tested NCrystal (v2.6.1, using Python 3.6.9):

import NCrystal info = NCrystal.createInfo("Fe_sg225_Iron-gamma.ncmat") info.dump()

and see some strange values of multiplicity factors on the output, e.g.

H K L d_hkl[Aa] Multiplicity FSquared[barn] ... 1 -5 -1 0.703982 32 8.12012 ... 0 0 6 0.609667 30 6.72598 ... 1 -7 -1 0.512222 48 4.91372 ...

Actually, I think the above factors should be 24, 6, 24 instead of 32, 30, 48 ... I didn't check if it results in wrong scattering cross-sections calculated by NCrystal or it is just the problem of dump method.

tkittel commented 3 years ago

Hi Jan,

Thanks a lot for checking these details, that is very valuable! I think that what you are seeing is merely a result of the way we define hkl "families". We don't follow any sort of symmetry-based definition, rather we simply find all the planes above the d-spacing cutoff, and then put those that have the same f-squared and d-spacing into the same group ("family"). You can investigate further by asking NCrystal to show the full set of hkl points in each family using the following somewhat obscure value for the infofactory parameter (here I also increase thedcutoff to reduce the output):

$> ncrystal_inspectfile  -d 'Fe_sg225_Iron-gamma.ncmat;dcutoff=0.6;infofactory=stdncmat:expandhkl'
---------------------------------------------------------
State of matter: Solid (crystalline)
---------------------------------------------------------
Space group number      : 225
Lattice spacings   [Aa] : 3.658 3.658 3.658
Lattice angles    [deg] : 90 90 90
Unit cell volume [Aa^3] : 48.9476
Atoms / unit cell       : 4
---------------------------------------------------------
Atoms in unit cell (total 4):
     4 Fe atoms [T_Debye=333.935K, MSD=0.007094Aa^2]
---------------------------------------------------------
Atomic coordinates:
     Fe            0            0            0
     Fe            0          1/2          1/2
     Fe          1/2            0          1/2
     Fe          1/2          1/2            0
---------------------------------------------------------
Density : 7.57843 g/cm3
---------------------------------------------------------
NumberDensity : 0.0817201 atoms/Aa3
---------------------------------------------------------
Composition:
                  100% Fe
---------------------------------------------------------
Atom data:
   Fe = Fe(cohSL=9.45fm cohXS=11.2221barn incXS=0.4barn absXS=2.56barn mass=55.8472u Z=26)
---------------------------------------------------------
Temperature : 293.15 kelvin
---------------------------------------------------------
Dynamic info for Fe (100%):
   type: S(alpha,beta) [from VDOS]
   VDOS Source: 200 points
   VDOS E_max: 30.9336 meV
---------------------------------------------------------
Neutron cross-sections:
   Absorption at 2200m/s : 2.56 barn
   Free scattering       : 11.2134 barn
---------------------------------------------------------
HKL planes (d_lower = 0.6 Aa, d_upper = inf Aa):
  H   K   L  d_hkl[Aa] Multiplicity FSquared[barn] Expanded-HKL-list
  1  -1  -1    2.11195            8        13.4188 1,-1,-1 | -1,1,1 | 1,-1,1 | -1,1,-1 | 1,1,-1 | -1,-1,1 | 1,1,1 | -1,-1,-1
  0   0   2      1.829            6        13.1409 0,0,2 | 0,0,-2 | 0,2,0 | 0,-2,0 | 2,0,0 | -2,0,0
  0   2  -2     1.2933           12        12.0855 0,2,-2 | 0,-2,2 | 0,2,2 | 0,-2,-2 | 2,-2,0 | -2,2,0 | 2,0,-2 | -2,0,2 | 2,0,2 | -2,0,-2 | 2,2,0 | -2,-2,0
  1  -3  -1    1.10293           24          11.35 1,-3,-1 | -1,3,1 | 1,-3,1 | -1,3,-1 | 1,-1,-3 | -1,1,3 | 1,-1,3 | -1,1,-3 | 1,1,-3 | -1,-1,3 | 1,1,3 | -1,-1,-3 | 1,3,-1 | -1,-3,1 | 1,3,1 | -1,-3,-1 | 3,-1,-1 | -3,1,1 | 3,-1,1 | -3,1,-1 | 3,1,-1 | -3,-1,1 | 3,1,1 | -3,-1,-1
  2  -2  -2    1.05597            8         11.115 2,-2,-2 | -2,2,2 | 2,-2,2 | -2,2,-2 | 2,2,-2 | -2,-2,2 | 2,2,2 | -2,-2,-2
  0   0   4     0.9145            6        10.2223 0,0,4 | 0,0,-4 | 0,4,0 | 0,-4,0 | 4,0,0 | -4,0,0
  1  -3  -3   0.839203           24        9.60019 1,-3,-3 | -1,3,3 | 1,-3,3 | -1,3,-3 | 1,3,-3 | -1,-3,3 | 1,3,3 | -1,-3,-3 | 3,-3,-1 | -3,3,1 | 3,-3,1 | -3,3,-1 | 3,-1,-3 | -3,1,3 | 3,-1,3 | -3,1,-3 | 3,1,-3 | -3,-1,3 | 3,1,3 | -3,-1,-3 | 3,3,-1 | -3,-3,1 | 3,3,1 | -3,-3,-1
  0   2  -4   0.817954           24        9.40135 0,2,-4 | 0,-2,4 | 0,2,4 | 0,-2,-4 | 0,4,-2 | 0,-4,2 | 0,4,2 | 0,-4,-2 | 2,-4,0 | -2,4,0 | 2,0,-4 | -2,0,4 | 2,0,4 | -2,0,-4 | 2,4,0 | -2,-4,0 | 4,-2,0 | -4,2,0 | 4,0,-2 | -4,0,2 | 4,0,2 | -4,0,-2 | 4,2,0 | -4,-2,0
  2  -4  -2   0.746686           24        8.64633 2,-4,-2 | -2,4,2 | 2,-4,2 | -2,4,-2 | 2,-2,-4 | -2,2,4 | 2,-2,4 | -2,2,-4 | 2,2,-4 | -2,-2,4 | 2,2,4 | -2,-2,-4 | 2,4,-2 | -2,-4,2 | 2,4,2 | -2,-4,-2 | 4,-2,-2 | -4,2,2 | 4,-2,2 | -4,2,-2 | 4,2,-2 | -4,-2,2 | 4,2,2 | -4,-2,-2
  1  -5  -1   0.703982           32        8.12012 1,-5,-1 | -1,5,1 | 1,-5,1 | -1,5,-1 | 1,-1,-5 | -1,1,5 | 1,-1,5 | -1,1,-5 | 1,1,-5 | -1,-1,5 | 1,1,5 | -1,-1,-5 | 1,5,-1 | -1,-5,1 | 1,5,1 | -1,-5,-1 | 3,-3,-3 | -3,3,3 | 3,-3,3 | -3,3,-3 | 3,3,-3 | -3,-3,3 | 3,3,3 | -3,-3,-3 | 5,-1,-1 | -5,1,1 | 5,-1,1 | -5,1,-1 | 5,1,-1 | -5,-1,1 | 5,1,1 | -5,-1,-1
  0   4  -4   0.646649           12        7.31331 0,4,-4 | 0,-4,4 | 0,4,4 | 0,-4,-4 | 4,-4,0 | -4,4,0 | 4,0,-4 | -4,0,4 | 4,0,4 | -4,0,-4 | 4,4,0 | -4,-4,0
  1  -5  -3   0.618315           48        6.86824 1,-5,-3 | -1,5,3 | 1,-5,3 | -1,5,-3 | 1,-3,-5 | -1,3,5 | 1,-3,5 | -1,3,-5 | 1,3,-5 | -1,-3,5 | 1,3,5 | -1,-3,-5 | 1,5,-3 | -1,-5,3 | 1,5,3 | -1,-5,-3 | 3,-5,-1 | -3,5,1 | 3,-5,1 | -3,5,-1 | 3,-1,-5 | -3,1,5 | 3,-1,5 | -3,1,-5 | 3,1,-5 | -3,-1,5 | 3,1,5 | -3,-1,-5 | 3,5,-1 | -3,-5,1 | 3,5,1 | -3,-5,-1 | 5,-3,-1 | -5,3,1 | 5,-3,1 | -5,3,-1 | 5,-1,-3 | -5,1,3 | 5,-1,3 | -5,1,-3 | 5,1,-3 | -5,-1,3 | 5,1,3 | -5,-1,-3 | 5,3,-1 | -5,-3,1 | 5,3,1 | -5,-3,-1
  0   0   6   0.609667           30        6.72598 0,0,6 | 0,0,-6 | 0,6,0 | 0,-6,0 | 2,-4,-4 | -2,4,4 | 2,-4,4 | -2,4,-4 | 2,4,-4 | -2,-4,4 | 2,4,4 | -2,-4,-4 | 4,-4,-2 | -4,4,2 | 4,-4,2 | -4,4,-2 | 4,-2,-4 | -4,2,4 | 4,-2,4 | -4,2,-4 | 4,2,-4 | -4,-2,4 | 4,2,4 | -4,-2,-4 | 4,4,-2 | -4,-4,2 | 4,4,2 | -4,-4,-2 | 6,0,0 | -6,0,0
---------------------------------------------------------

As you can see, if we take the multiplicity=32 group at d=0.703982Å as an example, a code based on symmetry operators might have split this group into two groups: one of multiplicity 24 containing hkl=(1,-5,1) and one of multiplicity 8 containing hkl=(3,3,3).

As this is a cubic crystal, the fact that the two sets of familiies "coincidentally" have the same d-spacing follows from 1²+5²+1²=3²+3²+3². That the structure factors also match up would require a bit more work to prove, but apparently they do :-)

I hope that clears it up :-)

Cheers, Thomas

saroun commented 3 years ago

Hi Thomas, thank you, you are of course right, I have wrongly focused on the indexing and overlooked the missing planes in the same dhkl group. I'm sorry for reporting the false bug. I try to use NCrystal to generate input tables for SIMRES which saves me a lot of work I had to do earlier. So thanks again for this tool. Jan

tkittel commented 3 years ago

Hi Jan,

Thanks for the feedback, it is always very motivating to hear that the tool is being put to good use!

Cheers, Thomas