Peakref glossary

Legenda: this is a vector, this is a matrix.

Axes systems
Calculated Impact
delmm
delrot
Residue
rotend
rotstart

Axes Systems

All axes systems units are in mm.

Laboratory System

The laboratory system has its origin on the crystal.

x points to the xray source
z points up (zenith)
y makes a right handed system.

Crystal system

The crystal shifts are defined in an axis system on the goniometer head, before mounting the head on the goniostat. Put the goniometerhead in front of you on a table. Then

x points to you
z points up (zenith)
y makes a right handed system.

The goniometerhead system coincides with the laboratory system when mounted on an (euler) goniostat with all angles zero.

Detector System

Points on the detector are defined in a two-dimensional axis system. The origin is at the centre of the detector. When viewed from the crystal, positive horizontal points right, positive vertical points up.
To transform a point on the dector to the laboratory system:

x = -detectordistance
y = hor
z = ver
apply detector shifts
apply detector rotations
rotate around swing axis over swing degrees.

Calculated Impact

Impact type records do not contain reflection indices, but only impact positions hor_obs, ver_obs and rot_obs. The impact positions are converted to a diffraction vector c_obs (using goniostat and detector parameters). Reflection indices h,k,l are calculated using:
h = D·c_obs where D = R^-1
The reflection indices h,k,l of the vector h are rounded to the nearest integer, and a diffraction vector c_calc is calculated using:
c_calc = R·h

Using the goniostat and detector parameters, the orientation matrix and the reflection indices h,k,l, an impact position (hor_calc, ver_calc and rot_calc) is calculated.

delhor

The distance in mm between the calculated and observed horizontal impact position.

delhor = abs(hor_obs−hor_calc)

delver

The distance in mm between the calculated and observed vertical impact position.

delver = abs(ver_obs−ver_calc)

delmm

The distance in mm between the calculated and observed impact position.

delmm = √( delhor² + delver² )

delrot

The difference in degrees between the calculated (rot_calc) and observed (rot_obs) rotation value.

HKL format
delrot = abs( rot_obs − rot_calc )
HKL2 format and IMPACT format
- rot_obs < rot_start
  delrot = abs( rot_obs − rot_start )
- rot_start ≤ rot_obs ≤ rot_end
  delrot = 0.0
- rot_obs > rot_end
  delrot = abs( rot_obs − rot_end )

(the result is a value between -π and π)

Residue

Nfree_i: number of free variables. These are the free variables which depend on the reflections of orientation matrix i. You may set this number to zero using freedom off.
Nref_i: number of allowed reflections of orientation matrix i.

reshor

The total horizontal mm residue. For all available orientation matrices a total residue is calculated.


           Nref_i      ∑(delhor)
reshor = ∑—————— × —————————————   
           Ntot    (Nref_i−Nfree_i)

resver

The total vertical mm residue. For all available orientation matrices a total residue is calculated.


           Nref_i      ∑(delver)
resver = ∑—————— × —————————————   
           Ntot    (Nref_i−Nfree_i)

resmm

The total mm residue. For all available orientation matrices a total residue is calculated.


          Nref_i      ∑(delmm)
resmm = ∑—————— × —————————————   
          Ntot    (Nref_i−Nfree_i)

resmmang
resmm is the average mm residue. resmm will increase if the experiment was done with a larger crystal-detector distance. The value of resmm gives no (absolute) information on the correctness of observed and calculated values. The difference between observed and calculated impact can also be expressed as the difference in angle between the two corresponding outrays. This average angle, resang, is independent of the actual distance, and is a better (absolute) qualifier for the refinement result.
For all available orientation matrices a total residue is calculated.
```
             Nref_i    ∑atan(delmm/dist)
resmmang = ∑—————— × ——————————————————   
             Ntot      (Nref_i−Nfree_i)
```
resrotpartial
The total rot residue for partial reflections. Partial reflections are reflections impacting at least 2 images. For all available orientation matrices a total residue is calculated.
```
           Nref_i      ∑(delrot)
resrot = ∑—————— × ——————————————   
           Ntot     (Nref_i−Nfree_i)
```
resrotinside
The total rot residue for inside reflections. Inside reflections are found within one frame only. For all available orientation matrices a total residue is calculated, similar to resrotpartial
resrotoutside
The total rot residue for outside reflections. Outside reflections are inside reflections with a calculated rotvalue outside the one frame. For all available orientation matrices a total residue is calculated, similar to resrotpartial.
resrotall
The total rot residue for all reflections. For all available orientation matrices a total residue is calculated, similar to resrotpartial

resicr

s = scale factor for image
I_i = intensity reflection i
I_mean = mean intensity of equivalent reflections


           ∑ |s*I_i-I_mean|
resicr = —————————————————   
             ∑ |I_mean|

res
The total residue is a linear combination of mm and rotation residues. The coefficients of the combination are set by resfactor. The default coefficients are 0 1 1 0 0, leading to
res = 1*resmmang + 1*resrotpartial

rotend

The rotation end value of the image.

rotstart

The rotation start value of the image.

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