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NESC0574 MACS

MACS, Lattice Vibrations Structure Factors for Thermal Neutron Scattering in Moderators

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1. NAME OR DESIGNATION OF PROGRAM:  MACS LATTICE VIBRATION CODES
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2. COMPUTERS
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Program name Package id Status Status date
MACS NESC0574/01 Tested 01-OCT-1974

Machines used:

Package ID Orig. computer Test computer
NESC0574/01 IBM 370 series IBM 370 series
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3. DESCRIPTION OF PROBLEM OR FUNCTION

This package of seven related
codes  is  basically  aimed  at   giving  maximum  capability  for
calculating slow-neutron scattering by moderators.
   MACS-C computes crystal vibrations when the potential energy is
a  sum of  parts arising  from short-range  forces and  long-range
Coulomb  interactions.   It  also obtains  Jacobian  matrices  for
determining adjustments in force constants  and ionic charge which
can lead to  improved agreement with data.   Structure factors for
neutron inelastic scattering can also be calculated.
   MACS-J  computes   the  dynamical   matrix  for   the  harmonic
oscillations of a  crystal, its eigenvalues and  eigenvectors, the
corresponding   structure  factors   for  coherent   single-phonon
scattering of neutrons, and Jacobian matrices for use in adjusting
force constants to fit calculated to observed dispersion curves.
   REVISED-D  calculates  valance  coordinates in  terms  of  mass
adjusted  atom  displacements,  together  with  coordinates  which
define rigid group rotations.
   REVISED-MVFC  constructs force  constant  matrices  for use  in
valance force potential functions which are used in other programs
dealing with molecular and crystal vibrations.
   ADJUSTER is a force adjuster program  to obtain a least squares
fit to observed frequencies of molecules and crystals.
   DIPOLE-SUM calculates dipole sums for an arbitrary crystal.
   MODEL-PI  calculates  crystal  vibrations  when  the  potential
energy is  a sum  of short-range  and long-  or intermediate-range
terms in  the dipole  coordinate approximation.   It also  obtains
Jacobian matrices for use in adjusting input parameters.
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4. METHOD OF SOLUTION

In  MACS-C, ADJUSTER,  and REVISED-D,  matrix
manipulations  are applied  to  matrices  which describe  physical
conditions.
   In MACS-J, first-order difference equations are substituted for
partial differential equations for Jacobian elements.
   In  MVFC  the user  employs  a  set  of criteria  for  defining
different types  of interactions to prepare  by hand the  input to
the program.  For  example, if two-angle coordinates  which have a
common atom at the  end of a leg of each  angle interact, the user
must specify  the associated criteria  which include  the distance
between the two apex atoms and  between the farthest separated leg
atoms.  The REVISED-MVFC code uses  the positions in the primitive
cell and  searches for all  coordinate interactions  which satisfy
each of the  criteria stipulated in MVFC.  The user  is spared the
tedious  task  of  calculating  angles  between  bonds,  distances
between atoms, etc.
   In DIPOLE-SUM, the procedure of Kaplan and Sullivan is applied.
   In  MODEL-PI, the  eigenvalues and  eigenvectors  of a  complex
Hermitian matrix are used.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

For   all    codes
which  produce  eigenvectors,  nearly  equal  eigenvalues  can  be
encountered, in which case the basis vectors for the corresponding
vector subspace are not uniquely determined.
   In MACS-C, the largest Jacobian matrix which can be computed is
40  x  15.   The  largest force  constant  vector  applied  is  of
dimension 15.  The largest real or complex matrices are 40 x 40.
   In MACS-J, the  largest real and complex matrices are  32 x 32.
The largest force constant vector is of dimension 50.
   In REVISED-D, the  largest number of elements  in 3-dimensional
arrays is 2400.  The maximum number  of groups is 20.  The maximum
number  of atoms  per group  is  50.  The  largest force  constant
vector is of dimension 30.
   In REVISED-MVFC, the largest indices of 3-dimensional variables
are (20,8,8).  The largest matrices are  150 x 150.  The dimension
of the largest force constant vector is 60.
   In ADJUSTER, the largest matrices are 32 x 32.
   In DIPOLE-SUM,  the largest number  of alpha-beta pairs  is 15.
The largest number of k-kprime pairs is 15.
   In MODEL-PI, there cannot be more  than 4 dipoles per primitive
cell.  The  largest matrices are  32 x  32.  The dimension  of the
largest force constant vector is 50.
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6. TYPICAL RUNNING TIME

A  MACS-C  sample problem  dealing  with  6
matrices of size 16 x 6 requires less than 3 seconds with compile-
run-wait time less than 42 seconds.
   A MACS-J sample problem dealing with 6  matrices of size 16 x 6
and 7-dimensional  force constant  vectors requires  less than  50
seconds with compile-run-wait time less than 74 seconds.
   A  REVISED-D  sample   problem  dealing  with  6   atom  groups
containing (4,4,2,2,2,2) atoms  requires less than 4  seconds with
compile-run-wait time less than 26 seconds.
   A REVISED-MVFC sample  problem which defines 21  elements in h,
using 8 atoms  in each of 2  groups requires less than  10 seconds
with compile-run-wait time less than 47 seconds.
   An  ADJUSTER  sample problem  dealing  with  a  13 x  6  matrix
requires less than 7 seconds  with compile-run-wait time less than
25 seconds.
   A DIPOLE-SUM sample problem with 4 atom positions requires less
than 10 seconds with compile-run-wait time less than 27 seconds.
   A MODEL-PI  sample problem dealing with  five 32 x  12 matrices
requires less than 92 seconds with compile-run-wait time less than
140 seconds.
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7. UNUSUAL FEATURES OF THE PROGRAM

Valence     force      potential
functions  for  crystals  may  be used  as  well  as  conventional
interactions between atom pairs.
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8. RELATED AND AUXILIARY PROGRAMS

MACS-C is a revision  of at least
two  predecessor codes.   The  improvements  and reasons  for  the
changes are described in detail in reference report IN-1280.
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9. STATUS
Package ID Status date Status
NESC0574/01 01-OCT-1974 Tested at NEADB
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10. REFERENCES

- C. Noble, A. W. Solbrig, Jr., and H. L. McMurry:
  MACS M, A Program for Computing the Crystal Dynamical Matrix,
  Phonon Dispersion Relations, and Structure Factors for Neutron
  Inelastic Scattering
  IN-1125 (October 1967).
- H. Kaplan and J.J. Sullivan:
  Physical  Review, Vol. 130, p. 120 (1963).
NESC0574/01, included references:
- J.K. Boyter et al.:
  MACS C, A Computing Program for Crystal Vibrations which includes
  Long-Range Coulomb Interactions
  IN-1280 (March 1969).
- J.K. Boyter and A.W. Solbrig, Jr.:
  MACS J, A Program for Computing Crystal Phonon Dispersion
  Relations, Structure Factors for Neutron Inelastic Scattering, and
  Jacobian Matrices
  IN-1147 (January 1968).
- J.K. Boyter and H.L. McMurry:
  REVISED D, A Computer Program for Calculating Valence Coordinates
  in Terms of Mass Adjusted Atom Displacements, Together with
  Coordinates Defining Rigid Group Rotations
  ANC Note P00441 (PPCO 40*1176), (January 1969).
- J.K. Boyter and H.L. McMurry:
  REVISED MVFC, A Computer Program for Constructing Force Constant
  Matrices for Use in Valence Force Potential Functions in Molecules
  and Crystals
  ANC Note P00311 (August 1969).
- J.K. Boyter and H.L. McMurry:
  MVFC, A Computer Program for Constructing Force Constant Matrices
  Use in Valence Force Potential Functions in Molecules and Crystals
  IN-1282 (April 1969).
- J.K. Boyter and H.L. McMurry:
  ADJUSTER, A Force Constant Adjuster Program to Obtain Least Square
  Fit to Observed Frequencies of Molecules and Crystals
  IN-1148 (December 1967).
- J.K. Boyter and T.G. Worlton:
  DIPOLE SUM, A Computer Program for Calculating Dipole Sums for an
  Arbitrary Crystal
  IN-1226 (October 1968).
- W.J. Suitt and A.W. Solbrig, Jr.:
  MODEL PI
  ANC Note P01800 (July 1970).
- Dennis H. Speas:
  Matrix Read-Write Subroutine
  (August 1964).
- H. McMurry:
  Comments on Using Some of the Codes in ACC No. 574 'MACS LATTICE
  VIBRATION CODES'
  (July 31, 1975).
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11. MACHINE REQUIREMENTS

650K bytes of core are required for each of
the programs.
   In addition to standard input/output, MACS-C uses scratch units
1,  2, 3,  4, 8,  9,  and 10.   162K  of LCS  was indicated  after
compiling.
   In addition to standard input/output, MACS-J uses scratch units
1,  2, 3,  4, 8,  9,  and 10.   158K  of LCS  was indicated  after
compiling.
   144K of LCS was indicated after compiling REVISED-D.
   356K of LCS was indicated after compiling REVISED-MVFC.
   100K of LCS was indicated after compiling ADJUSTER.
   50K of LCS was indicated after compiling DIPOLE-SUM.
   In  addition to  standard input/output,  MODEL-PI uses  scratch
units 2, 3, 4, 8, 9, 11, 12, 13,  14, 15, 16, and 17.  330K of LCS
was indicated after compiling.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0574/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:   OS/360.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

   The
source programs require the FORTH450 compiler using 650K.
   MACS-J results can be affected  by cross-over errors in certain
parts of Jacobian results.  See page 10 of reference IN-1147.  The
sample problem results contained nearly  equal eigenvalues, as did
sample problems for MACS-C and MODEL-PI.
   REVISED-D results for rigid group rotations may be in error and
should be carefully examined.  See page 2, reference P00441.
   REVISED-MVFC inserts 7.7777E-07 into  the calculations when the
number of  unique interactions  for two sets  of coordinates  of a
particular interaction type exceeds twenty.
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15. NAME AND ESTABLISHMENT OF AUTHORS

                 H. L. McMurry and W. J. Suitt
                 EG&G Idaho, Inc.
                 P. O. Box 1625
                 Idaho Falls, Idaho  83401
                 T. G. Worlton
                 Solid State Science Division
                 Argonne National Laboratory
                 9700 South Cass Avenue
                 Argonne, Illinois  60439
                 R. M. Martin
                 Xerox Corporation
                 Xerox Park
                 3180 Porter Drive
                 Palo Alto, California  94304
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16. MATERIAL AVAILABLE
NESC0574/01
File name File description Records
NESC0574_01.001 MACS-C SOURCE PROGRAM (F4) 1259
NESC0574_01.002 MACS-C SAMPLE CASE DATA 190
NESC0574_01.003 MACS-C JCL 14
NESC0574_01.004 MACS-C SAMPLE CASE PRINTED OUTPUT 49
NESC0574_01.005 MACS-J SOURCE PROGRAM (F4) 1208
NESC0574_01.006 MACS-J SAMPLE CASE DATA 274
NESC0574_01.007 MACS-J JCL 14
NESC0574_01.008 MACS-J SAMPLE CASE PRINTED OUTPUT 1460
NESC0574_01.009 REVISED-D SOURCE PROGRAM (F4) 947
NESC0574_01.010 REVISED-D SAMPLE CASE DATA 56
NESC0574_01.011 REVISED-D SAMPLE CASE PRINTED OUTPUT 539
NESC0574_01.012 REVISED-MVFC SOURCE PROGRAM (F4) 1518
NESC0574_01.013 REVISED-MVFC SAMPLE CASE DATA 145
NESC0574_01.014 REVISED-MVFC SAMPLE CASE PRINTED OUTPUT 4004
NESC0574_01.015 ADJUSTER SOURCE PROGRAM (F4) 195
NESC0574_01.016 ADJUSTER SAMPLE CASE DATA 20
NESC0574_01.017 ADJUSTER SAMPLE CASE PRINTED OUTPUT 106
NESC0574_01.018 DIPOLE-SUM SOURCE PROGRAM (F4) 212
NESC0574_01.019 DIPOLE-SUM SAMPLE CASE DATA 18
NESC0574_01.020 DIPOLE-SUM SAMPLE CASE PRINTED OUTPUT 163
NESC0574_01.021 MODEL-PI SOURCE PROGRAM (F4) 1919
NESC0574_01.022 MODEL-PI SAMPLE CASE DATA 234
NESC0574_01.023 MODEL-PI JCL 30
NESC0574_01.024 MODEL-PI SAMPLE CASE PRINTED OUTPUT 6814
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17. CATEGORIES
  • W. Physics

Keywords: crystals, eigenvalues, eigenvectors, inelastic scattering, lattice vibrations, moderators.