Fourier or MEM map of quasi-crystals and semi-quasicrystals
This program generates a mem map, fourier map or patterson map
(********isys=0 does not work at present*****)
input format as follows
key=value where key is key work shown below
for character value it should be enclosed by '
as file1='filename1'
for numerical value it is like ndm=1 or f000=123.4
input data
(00) file1
file1:name for hkl-fo-fc-phase-sig file
(01) file2
file2: file name for nD density file (iplot=0)
file name for 2D density file (iplot>0)
file name for 3D density file (iplot<0) (.win file)
(1) title
(2) isys,a,c for quasicrystals (isys>0)
isys: 1:icosahedral 2:icosahedral (cubic)
3:decagonal 4:octagonal 5: dodecagonal
a: lattice parameter (in angstrom)
c: lattice parameter (in angstrom) for dihedral lattice
(3) nsymo,icent,brv
nsymo: number of generators in symmetry operations
icent: give 1 for centrosymmetryc
give 0 otherwise
brv : 'p','i' or 'f'
****** see (10) ******
(4) symmetry operator in the format of i.t.
for example x,y,z,t,u,v; x+1/2,y,z+1/2,t,u,v etc.
******** repeat (4) nsymo times
(5) f000,sg00,sg0,sg1, fmag
f000: fc at the origin
if observed structure factor includes f000, this is replaced
sg00: sigma for f000 (sg0 : sigma=sqrt(f000)*sg00 is used)
sg0: sigma=sg0 (sg0 : sigma=sqrt(fo)*sg0 is used)
sg1: sigma=sg1 for strongest (Fcal) reflections
fmag: f000,sg00,sg0,sg1,fobs,fcal are
magnifiled by this factor
(6) jbc
jbc: kind of map 1 : axes are unit vectors for ext. and int. spaces
-1 : axes specified in (7) (lattice vectors)
**if jbc=-1 or jbc=-2 then give (7) else skip (7)**
(7) s1, s2, s3, s4 : orthogonal transformation matrix for q1-q6
((s1(i,j),j=1,3),i=1,3) etc.
s1, s2 etc. should be in different lines
total 6x6 matrix is given by
s1,s3
s4,s2
for 3-fold map (isys=2 external and internal spaces // x and y)
s1= 0.5773 0.5773 0.5773 0.7071 -0.7071 0. 0.4082 0.4082 -0.8165
s2= 0.5773 0.5773 0.5773 0.7071 -0.7071 0. 0.4082 0.4082 -0.8165
s3= 0. 0. 0. 0. 0. 0. 0. 0. 0.
s4= 0. 0. 0. 0. 0. 0. 0. 0. 0.
other possiblilities
for 5-fold map (sys=1 two 5-fold axes in 6D // x and y)
s1=1. 0. 0. 0. 1. 0. 0. 0. 0.7071
s2=1. 0. 0. 0. 1. 0. 0. 0. 0.7071
s3=0. 0. 0. 0. 0. 0. 0. 0. -0.7071
s4=0. 0. 0. 0. 0. 0. 0. 0. 0.7071
for 2-fold map (sys=2 two 2-fold axes in 6D // x and y)
s1=0.8506 0. 0. 0. 1. 0. 0. 0. 1.
s2=0.8506 0. 0. 0. 1. 0. 0. 0. 1.
s3=-0.5257 0. 0. 0. 0. 0. 0. 0. 0.
s4=0.5257 0. 0. 0. 0. 0. 0. 0. 0.
for 3-fold map (sys=2 two 3-fold axes in 6D // x and y)
t1=0.8650 t2=0.5257
s1=0.4994 0.4994 0.4994 0.7071 -0.7071 0. 0.4082 0.4082 -0.8165
s2=0.4994 0.4994 0.4994 0.7071 -0.7071 0. 0.4082 0.4082 -0.8165
s3=-0.3034 -0.3034 -0.3034 0. 0. 0. 0. 0. 0.
s4= 0.3034 0.3034 0.3034 0. 0. 0. 0. 0. 0.
(see (13))
if jbc=-2 then give (7') else skip (7') (for projected structures)
(7') t1, t2, t3, t4 : orthogonal transformation matrix for q1'-q6'
which is transformed by s matrix defined by (7) (q'=sq)
for 5-fold map 24.095 = arctan(1/sqrt(5))
cost=cos(24.095) sint=sin(24.095)
t1= 1 0 0 0 1 0 0 0 cost
t2= 1 0 0 0 1 0 0 0 cost
t3= 0 0 0 0 0 0 0 0 -sint
t4= 0 0 0 0 0 0 0 0 sint
for 2-fold or 3-fold axis
cost= sint= (2-fold)
cost= sint= (3-fold)
t1= cost 0 0 0 1 0 0 0 1
t2= cost 0 0 0 1 0 0 0 1
t3= sint 0 0 0 0 0 0 0 0
t4=-sint 0 0 0 0 0 0 0 0
(8) iplot, hmax, ismtr,pkmin,rwmin (for iplot=5)
iplot =1, -1: patterson map
=2, -2: fourier map
=3, -3: difference fourier map
=4, -4: Mem map starting from flat electron density
=5, -5: MEM and LDEM starting from the result of LDEM
positive and negative iplot generate a 2D and 3D maps
if iplot < 0 .win and .rho file is generated
hmax(1-6): number of points along principal axes
ismtr : order of similarity transformations
qext => qext*tau**ismtr
qint => qint*tau**-ismtr
xext => xext*tau**-ismtr
xint => xint*tau**ismtr
pkmin : minimum peak height fraction to be printed in Fourier
or Difference Fourier map
(real minimum peak hekgit is given by pkmax*pkmin
where pkmax is the maximum peak density)
abs(peak density) > pkmax*pkmin is printed
rwmin : rw factor below which LEM method works
******(pkmin > 0)********
***** if abs(iplot)=1,2,3 skip (9)*****
(9) ex1,ex2,nex1,nex2
ex1,ex2: constants needed for smooth convergence
nex1: number of iterations in imode=1 (Yamamoto)
nex2: number of iterations in imode=2 (Sakata)
***** imode=1 mode is dangerous for accurate electron density map
***** imode=2 mode should be used for MEM
(9') icont
icont: iteration is continued from the previous result
(10) qimax, frmt
qimax: maximum q vector to be used to draw map
frmt: file format for hkl, fobs, fcal, phase, sig
(11) ldev iwhkl iprj
ldev : 1: B&W Postscript printer 2: color Postscript printer
iwhkl : 0 no output, 1: output of hkl fo fc obtained from MEM
: -1: output of hkl fc fc for all calculated points
****** fo=fc in the present version ******
iprj : 0 for a map in a cut plane, iprj=n means nD projection
****** if iprj=0 skip (11')
(11') h
h : Miller indices for projection axis
****** repeat (11') iprj times *****
for 5-fold projection in external space iprj=2
h=1 0 0 0 0 0 and h=0 1 1 1 1 1 (isys=1)
for 2-fold projection in external space iprj=2
h=0 0 0 -1 0 1 and h=0 1 -1 0 0 0 (isys=2)
(12) ng : number of graphs in a sheet (ng < 10)
****if ng=0 no map is written****
(13) iax ipers
iax(1),iax(2),,,iax(6) : q coordinates
ipers : 0 no perspective veiw 1 add psespective view
density in 3D space spanned by iax(1),iax(2),iax(3) axes is calculated
if jbc > 0 or jbc < 0
for drawing 3D density map.
for 5-fold map iax=3 6 1 2 4 5 (isys=1)
for 2-fold map iax=1 4 2 3 5 6 (isys=2)
for 3-fold map iax=1 4 2 3 5 6 (isys=2) (see (7))
for 5-fold map in external space iax=1 2 3 4 5 6 (isys=1)
for 2-fold map in external space iax=1 2 3 4 5 6 (isys=2)
(14) iaver, ismth
****** note that iaver or ismth >0 takes much time for 3D maps (iplot<0)*****
iaver : 0 noaverage 1 average 2 equivalent points in the unit cell
in the calculation of the density
ismth : 0 no smoothing
1 3 point smoothing (average)
2 5 point smoothing (average)
(11) x :coordinates of origin
(12) xe, u :coordinates of origin and displacement
(13) xi, v :coordinates of origin and displacement
(14) q :origin shift in external and internal spaces
iplot > 0
(15) xmin,xmax,ymin,ymax,hscl,xdiv,ydiv
xmin: minimum coordinate along x-axis (in a)
xmax: maximum coordinate along x-axis (in a)
ymin: minimum coordinate along y-axis (in a)
ymax: maximum coordinate along y-axis (in a)
unit vectors (ax,.. bx.. ) in the external and internal spaces
are as follows
1) for icosahedral case
ax=a*a1 ay=a*a2 az=a*a3 bx=a*a4 by=a*a5 bz=a*a6
2) for decagonal case
ax=2a*a1/sqrt(5) ay=2a*a2/sqrt(5) az=c*a5
bx=2a*a3/sqrt(5) by=2a*a4/sqrt(5)
3) for octagonal case
ax=a*a1 ay=a*a2 az=c*a5
bx=a*a3 by=a*a4
4) for dodecagonal case
ax=2a*a1/sqrt(6) ay=2a*a2/sqrt(6) az=c*a5
bx=2a*a3/sqrt(6) by=2a*a4/sqrt(6)
xmin=1 means ax A
hscl: hight scale
xdiv: length of a mesh edge in the unit of ax, etc.
ydiv: length of a mesh edge in the unit of ax, etc.
hscl: scale factor for the electron density
if iplot < 0
(15) xmin,xmax,ymin,ymax,zmin,zmax,hscl,xdiv,ydiv,zdiv
xmin,..,zmax:coordinate reanges along x,y and z axes
hscl : scale for F
xdiv, ydiv, zdiv : intervals of the scale in x and y axes
if iplot < 0 skip (16)-(18)
(16) hmin,div,lf
hmin: minimum hight (density) in the division
div : interval of hight
lf : number of contour lines
(17) amagx,amagy,shftxb,shftyb,shftxa,shftya
amagx: magnification for x
amagy: magnification for y
shftxb: shift of origin along x before plot in cm
shftyb: shift of origin along y before plot in cm
shftxa: shift of origin along x after each plot in cm
shftya: shift of origin along y after each plot in cm
**0*****repeat (9)-(18) ng times********
File translated from
TEX
by
TTH,
version 3.02.
On 10 Aug 2005, 11:48.