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".rmat" files

The collect software can read unit cell orientation matrices from ".x" files as generated from "DENZO", and alternatively from ".rmat" files specially designed for this purpose.

Here is a non-formal description of an ".rmat" file:

   # comment
   RMAT [BRAVAISTYPE]
    a*x  b*x  c*x
    a*y  b*y  c*y
    a*z  b*z  c*z
   TMAT [BRAVAISTYPE] [LAUE GROUP OR POINT GROUP]
    t11  t12  t13
    t21  t22  t23
    t31  t32  t33
   CELL a b c alpha beta gamma volume
   SIGMACELL sa sb sc salpha sbeta sgamma svolume
   QVEC f1 f2 f3 n
   QVC m1...

The only part that is obligatory is the "RMAT" line plut the three following lines defining the RMAT matrix. The "QVEC"/"QVC" part is only relevant for modulated structures, and will be ignored by the software unless the "modulated" module is installed.

The RMAT matrix part is a 3x3 matrix with the columns representing the reciprocal vectors a*, b* and c* in the laboratory coordinate system x,y,z (X pointing to the source, Z pointing to the Zenith, and Y pointing along the cross-product Z*X, pointing to the positive theta side of the KappaCCD) at the goniostat zero-position (kappa=0, omega=0, phi=0).

The TMAT matrix part is a 3x3 matrix describing the a',b',c'=(T) a,b,c transformation of the direct axes from the cell given in RMAT to the conventional cell.

Laue groups are: triclinic: "-1"; monoclinic: "2/m"; orthorhombic: "mmm"; tetragonal: "4/m" and "4/mmm"; trigonal "-3" and "-3m"; hexagonal "6/m" and "6/mmm"; cubic: "m3" and "m3m". By default, the lowest symmetry laue group will be generated for each crystal system. Collect programs also accept other point groups at this spot.

CELL and SIGMACELL are the cell parameters and their estimated standard deviations. If a "TMAT" section is present, these records represent the transformed unit cell.

Any QVEC line (you can have more than one) contains 4 numbers: 3 floating point numbers describing the Q vector in "fractional HKL", and an integer giving the maximum absolute order that needs to be considered.

In case there is more than one QVEC line, it might be useful to specify explicitly which satellites are of importance. This can be done using QVC lines. Each QVC line lists a combination of m1,m2,... that should be considered. If QVC lines are given, no other satellites will be considered than exactly those that are listed. This means that if you list "QVC 1 0" you must also add "QVC -1 0". And last but not least: ALWAYS include the "QVC 0 0" if you want to include the main lattice. Each QVC line should have exactly as many numbers as there are Q-vectors. All QVC lines should come after the last QVEC line.

If no QVC lines are given, they are automatically constructed using the maximum order given on the QVEC lines. All satellites are generated for which the sum of the m indices is smaller than the smallest limit on any of the non-zero indexed Q vectors (i.e. a "m1=1 m2=1" satellite is only generated if both m1 and m2 individually are allowed to go up to at least 2).

There are two programs that can help when you want to play with RMAT and TMAT matrices:

rmatrix: can display a unit cell as it is read from a ".rmat" file, and can optionally write a standardized ".rmat" file.
xmatrix: can extract a unit cell from a denzo ".x" file. If a destination ".rmat" file is specified on the command line, the program writes the equivalent RMAT and TMAT there.

Example

RMAT P
 -0.21749491 -0.12523507 -0.01217723
 -0.01856109  0.14177111 -0.05085664
  0.00227301 -0.10895341 -0.08341029
TMAT C 2/m
  1.00000000  1.00000000  0.00000000
 -1.00000000  1.00000000  0.00000000
  0.00000000  0.00000000  1.00000000

This corresponds to the following unit cell:

{Input cell   : a=5.3522 b=5.3522 c=10.3305 alpha=95.233 beta=95.233 gamma=119.907 P
 Reduced cell : a=5.3522 b=5.3522 c=10.3305 alpha=95.233 beta=95.233 gamma=119.907
 Conventional : a=5.3597 b=9.2659 c=10.3305 alpha=90.000 beta=100.495 gamma=90.000 C
 Volume       : 504.45; System: monoclinic; Point group: 2/m}

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