EMGBOdm

Program: EMGBOdm

This program generates a text file that contains a pairwise distance matrix for a set of octonions (pairs of quaternions) provided by the user. There are three different metrics available for the distance computation: octonion, Olmsted, and Riemannian; the first and third are geodesic distances (arc lengths) whereas the Olmsted metric is an approximation to the Riemannian metric. The underlying theory can be found in the following papers:

• T. Francis, I. Chesser, S. Singh, E.A. Holm and M. De Graef. "A New Octonion Metric for Grain Boundary Interpolations". Acta Materialia, 166:135-147 (2019) DOI;
• D. Olmsted, "A new class of metrics for the macroscopic crystallographic space of grain boundaries". Acta Materialia, 57:2793-2799 (2009) DOI.

The program uses a template file in the usual way:

EMGBOdm -t

and its content is as follows:

&GBOdmlist
! point group number
!   #1:    '1', #2:    '-1', #3:      '2', #4:    'm', #5:  '2/m', #6:   '222', #7:    'mm2', #8:   'mmm'
!   #9:    '4', #10:   '-4', #11:   '4/m', #12: '422', #13: '4mm', #14: '-42m', #15: '4/mmm', #16:    '3'
!   #17:  '-3', #18:   '32', #19:    '3m', #20: '-3m', #21:   '6', #22:   '-6', #23:   '6/m', #24:  '622'
!   #25: '6mm', #26: '-6m2', #27: '6/mmm', #28:  '23', #29:  'm3', #30:  '432', #31:  '-43m', #32: 'm-3m'
 pgnum = 32,
! number of threads for parallel computation (0 to use the maximum available)
 nthreads = 0,
! metric to be used:  'octonion', 'Olmsted', 'Riemannian'
 metric = 'octonion',
! are we computing a new matrix 'newmatrix' or adding column(s) to an existing one 'addcolumns' ?
 workmode = 'newmatrix',
!=======================
! if workmode = 'newmatrix'  [comment the inname and outname parameters in the next section]
!   input octonion file name (EMsoft relative pathname)
!     this file must have the number of octonions on the first line, then one octonion per line
 inname = 'undefined'
!   output file name; simple text file (EMsoft relative pathname)
!     this file will have the number of input octonions and the number of unique distances (upper diagonal)
 outname = 'undefined'
!=======================
! if workmode = 'addcolumns'  [comment the inname and outname parameters above]
!   input octonion file name (EMsoft relative pathname)
!     the first line should contain the number of NEW octonions that are added to the END of the file
! inname = 'undefined'
!   output file name; simple text file (EMsoft relative pathname)
!     the old output file will be renamed with the .save extension and a new one will be generated with the same name
! outname = 'undefined'
!=======================
! this last line must be present!
/

Most of the parameters are self-explanatory. The workmode parameter allows the user to add one or more columns/rows to the distance matrix; the appropriate rows in the name list file must then be (un)commented.

The output text file contains the pairwise distances using the selected metric; they are organized in a single column that represents the upper diagonal of the distance matrix (diagonal entries, which must be zero, are included in the list). The user can then easily reconstruct the complete matrix by filling the rows starting at the diagonal entries and then copying the upper diagonal into the lower diagonal. This program was used to obtain the starting point for the analysis presented in the following paper:

• I. Chesser, T. Francis, M. De Graef, and E.A. Holm, "Learning the grain boundary manifold: tools for visualizing and fitting grain boundary properties in 5-space," submitted to Acta Materialia (2019).