Misorientation Distribution Function

Computing a misorientation distribution function from EBSD data

Lets import some EBSD data and reconstruct the grains.

mtexdata forsterite
grains = calcGrains(ebsd)

 
grains = grain2d  
 
 Phase  Grains  Pixels     Mineral  Symmetry  Crystal reference frame
     0   16334   58485  notIndexed                                   
     1    4092  152345  Forsterite       mmm                         
     2    1864   26058   Enstatite       mmm                         
     3    1991    9064    Diopside     12/m1       X||a*, Y||b*, Z||c
 
 boundary segments: 147957
 triple points: 11456
 
 Properties: GOS, meanRotation
 

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The boundary misorientation distribution function

The boundary misorientation distribution function for the phase transition from Forsterite to Enstatite can be computed by

mdf_boundary = calcODF(grains.boundary('Fo','En').misorientation,'halfwidth',10*degree)

 
mdf_boundary = MDF  
  crystal symmetry : Forsterite (mmm)
  crystal symmetry : Enstatite (mmm)
 
  Harmonic portion:
    degree: 25
    weight: 1
 

The misorientation distribution function can be processed as any other ODF. E.g. we can compute the prefered misorientation via

[v,mori] = max(mdf_boundary)

v =
   38.8766
 
mori = misorientation  
  size: 1 x 1
  crystal symmetry : Forsterite (mmm)
  crystal symmetry : Enstatite (mmm)
 
  Bunge Euler angles in degree
     phi1     Phi    phi2    Inv.
  82.4065 1.06577 187.671       0
 

or plot the pole figure corresponding to the crystal axis (1,0,0)

plotPDF(mdf_boundary,Miller(1,0,0,ebsd('Fo').CS))

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The uncorrelated misorientation distribution function

Alternatively the uncorrelated misorientation distribution function can be computed by providing the option uncorrelated

mori = calcMisorientation(ebsd('En'),ebsd('Fo'))
mdf_uncor = calcODF(mori)

 
mori = misorientation  
  size: 98541 x 1
  crystal symmetry : Forsterite (mmm)
  crystal symmetry : Enstatite (mmm)
 
 
mdf_uncor = MDF  
  crystal symmetry : Forsterite (mmm)
  crystal symmetry : Enstatite (mmm)
 
  Harmonic portion:
    degree: 25
    weight: 1
 

Obviously it is different from the boundary misorientation distribution function.

plotPDF(mdf_uncor,Miller(1,0,0,ebsd('Fo').CS))

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Computing the uncorrelated misorientation function from two ODFs

Let given two odfs

odf_fo = calcODF(ebsd('fo').orientations,'halfwidth',10*degree)
odf_en = calcODF(ebsd('en').orientations,'halfwidth',10*degree)

 
odf_fo = ODF  
  crystal symmetry : Forsterite (mmm)
  specimen symmetry: 1
 
  Harmonic portion:
    degree: 25
    weight: 1
 
 
odf_en = ODF  
  crystal symmetry : Enstatite (mmm)
  specimen symmetry: 1
 
  Harmonic portion:
    degree: 25
    weight: 1
 

Then the uncorrelated misorientation function between these two ODFs can be computed by

mdf = calcMDF(odf_en,odf_fo)

 
mdf = MDF  
  crystal symmetry : Forsterite (mmm)
  crystal symmetry : Enstatite (mmm)
 
  Harmonic portion:
    degree: 19
    weight: 1
 

This misorientation distribution function should be similar to the uncorrelated misorientation function computed directly from the ebsd data

plotPDF(mdf,Miller(1,0,0,ebsd('Fo').CS))

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Analyzing misorientation functions

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Angle distribution

Let us first compare the actual angle distribution of the boundary misorientations with the theoretical angle distribution of the uncorrelated MDF.

close all
plotAngleDistribution(grains.boundary('fo','en').misorientation)

hold on

plotAngleDistribution(mdf)

hold off

For computing the exact values see the commands calcAngleDistribution(mdf) and calcAngleDistribution(grains).

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Axis distribution

The same we can do with the axis distribution. First the actual angle distribution of the boundary misorientations

plotAxisDistribution(grains.boundary('fo','en').misorientation,'smooth')

Now the theoretical axis distribution of the uncorrelated MDF.

plotAxisDistribution(mdf)

For computing the exact values see the commands calcAxisDistribution(mdf) and calcAxisDistribution(grains).

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