KSLStrain    

Strain tensor in the crystal coordinate system

In order to call the program determining strain with respect the reference lattice parameters, select "CCS" option and click on “Strain” command button (on main interface). This activates "Strain determination CCS" dialog box. There is a possibility to select strain components which are subject of determination. These are components of the strain tensor given in the Cartesian crystal coordinate system. One can also request fitting of pattern center and/or camera length. Both are calculated separately for each diffraction pattern. 

Strain components (and other fitted parameters) are calculated by locating a (supposedly global) minimum  of a goodness-of-fit function. Besides displayed strain componensts, one can also fit their combinations by modifying the "Transformation matrix". Bounds limiting the fitted parameters can be modified in text boxes on the "Strain determination CCS" dialog panel . The bounds are in units of strain*10000 in the case of strain, (shift of pattern center)*10000 in the case of  pattern center, and (relative camera length)*10000 in the case of  camera length.

A number of distinct goodness-of-fit functions are available by selecting “Strategy” in “Strain determination CCS”. (CCS stands for crystal coordinate system). 

The first two strategies  (referred to as "Kinematic equation of the line") are based directly on the equation of the diffraction line written in the form f(parameters)=0. The goodness-of-fit is the squared deviation of f(parameters) from zero if "Exact form" is selected. The option "Linearized" uses an approximation of  f(parameters) linear with respect to parameters.

The second group of strategies (reffered to as "Intersections of conics") uses goodness-of-fit functions based on distances between intersections of diffraction lines. 

In the case of "Intersection distances", the function is a sum of squared differences of the type (d-d’) where d represents a distance between Kossel line intersections in an experimental patterns and d’ is a distance between corresponding intersections in a (geometrically) simulated line diagram. 

In the case referred to as “Distance ratios”, the function is a sum of squared differences of the type (d - r d’) where d represents a distance between Kossel line intersections in an experimental patterns, d’ is a distance between corresponding intersections in a (geometrically) simulated Kossel line diagram, and r is a magnification factor constant for a given pattern. The magnification factor is a ratio between the average (largest) intersection distances if  “Aver” (“Max”) is selected. The domain of the intersection points (minimal and maximal intersection angles and the radius of a circle encompassing the intersections) can be modified by selecting the "Domain" command button in the "Strain determination" dialog boxes.

In some cases, it makes sense to examine "1D scans" of the objective function.

After completion of the calculation, results are displayed in the “Results” dialog box. The box allows for displaying three different groups of results.

• The first one contains values (times 10000) of strain and/or shifts of pattern centers and/or relative values of camera lengths. If the optimization bounds are reached they are considered to  be incorrect.
• The second group are estimated errors (times 10000) of strain and/or shifts of pattern centers and/or relative values of camera lengths.
• The third group contains absolute values (times 10000) of lattice parameters and/or pattern center positions and/or camera lengths.
• The fourth group contains components of the stress tensor (times 10000/C_11) and/or pattern center positions and/or camera lengths.

The “Update” in the “Results” dialog box command button will change the current settings for all patterns in terms of  orientations,  lattice parameters and/or pattern centers and/or camera lengths, whichever were subject of fitting.