projection of quasi-crystals
note the following assumption
input data
*********************************************************
origin of the vector ej should be in a occupation
domain
*********************************************************
(0) inpm, iphas
inpm=0 separatel file (standard input, flnm1 and flnm2)
=1 standard input only
iphas=1 for periodic phason (long-wavelength phason)
0 for non-periodic phason (liniear phason)
(1) title
(2) isys,a,(c),eps1,eps2,eps3,eps4,eps5,eps6,ists
isys: 1 icosahedral or its pentagonal distortion
2 icosahedral or its cubic or orthrhombi distortion
(***icosahedral or its trigonal distortion)
3 decagonal or its orthorhombic distortion
4 octagonal
5 dodecagonal
a,c : lattice papameter
eps1: pentagonal phason distortion (isys=1)
cubic phason distortion (isys=2)
eps2: orthorhombic phason distortion 1 (1,1 element) (isys=1
(***trigonal phason distortion (3,3) element (isys=2))
eps3: orthorhombic phason distortion 2 (2,2 element) (isys=1
(***trigonal phason distortion (1,1)=(2,2) element (is
eps4: monoclinic phason distortion 3 (1,2 element) (isys=1,3
orthorhombic phason distortion (2,2) element (isys=2)
difference from cubic
eps5: monoclinic phason distortion 4 (2,1 element) (isys=1,3
orthorhombic phason distortion (3,3) element (isys=2)
difference from cubic
eps6: phonon distortion (along z-axis isys=1,3)
trigonal phonon distortion 2 (isys=2)
ists: 0 true site symmetry operators are used
1 fictitious site symmetry operators are used for all at
(3) na npod ne isim imod
na: number of atoms
npod : number of predefined occupation domsins
ne : number of elements
isim: order of similarity transformation
isim = 0 no magnification
isim > 0 deflate by tau**-isim times
isim < 0 inflate by tau**-isim times
isim=-2,-1,0,1, or 2 etc.
tau: ratio of selfsymilarity
=(1+sqrt(5))/2=1.618 for decagonal
and face-centered icosahed
=sqrt(2)=1.414 ? for octagonal
imod: 1: lattice constant a is multiplied by tau**isim
this makes inflation or deflation impossible
but isim > 0 and imod=1 may be effective for
reducing the value of ihmax in (8) and for
fast calculation
0: no multiplication for the lattice constant
******** if inpm=0 skip (4) ******
(4) flnm1
flnm1 : filename which gives the following items
******** if inpm=1 skip (01)-(07) ******
#######################################################################
(01) nsymo,icent,brv
nsymo: number of generators in symmetry operations
icent: give 1 for centrosymmetric
otherwise give 0
brv : 'p','i','f' 's' 'c' bravais lattice
s in icosahedral ==> face-centered superlattice
s in decagonal ==> Edagawa type superlattice
s translates x,ej,xi in the normal lattice into those
in superlattice
in decagonal case, s also translates sym. op in norma
lattice into those in superlattice
c P_2c for color symmetry
'g' is for the groupoid symmetry in quasicrystal
*************************************************************
when brv='s', give x0,xe,xi,ej in the fundamental cell.
they are transformed into those of the supercell in the progr
*************************************************************
(02) 'symmetry operator' header and
(03) symmetry operator in the I.T. format: x,y,z,t,u,v etc.
***** repeat (03) nsymo times
(03') if brv='g'
hull element (header)
hull operator in the IT format including x,y,z,t,u,v
and centering translations
repeat this ig times.
(03") innn: number of repeats of transformation given above
****** (isys=4,brv='s' only)******
(04) n,nej0,itype,str (*)
n : serial number for the guide to the eye
nej0 :number of edge vectors for predefined occupation domain
itype : 1 domain with icosahedral, degagonal or octagonal symm.
2 domain with other symmetry
-1 domain with icosahedral, degagonal or octagonal symm.
-2 domain with other symmetry for test
str : string for comments
(05) ej
ej: edge vectors of two triangles in the 6D coordinate syste
repeat (5) nej0 times
***************notice****************
the internal components of consecutive ej are regarded a
the consecutive edge vectors of the polyhedron defining
the occupation domain
***************notice***************
(06) nth, (mej(1),mej(2),,),... nth times
nth: number of tetrahedra
mej: a triplet of vector numbers specifying a tetrahedron
(for isys=1,2)
mej: a pair of vector numbers specifying a tetrahedron
(for isys=3,4,5)
(07) iaslct(1-(nsymo+icent*nsymo)) (60i1) 1:selected, 0:skipped **
******** repeat (01)-(07) npod times
######################################################################
******** if inpm=0 skip (5) ******
(5) flnm2
flnm2 : filename which gives the following items
******** if inpm=1 skip (01)-(08) ******
######################################################################
(01) no,symb,ien,ish,nev,be,bi,ramin,ramax,p,s1,s2 (*)
no: atom number
symb: site symbol
ien: element number (1:Al 2:Mn etc.)
if ish > 0: ish-th predefined occupation domain
else
for icosahedral case
ish=0 polyhedron
ish=-1: ellipsoid
ish=-2: sphere ( rmax: the radius of the sphere in a )
for dihedral case
ish=0 triangle
ish=-1: ellips
ish=-2: circle ( rmax: the radius of the sphere in a )
nev: number of edge vectors for ish=0 (<=nemax=50)
number of principal axes (=2 or 3) for ish=1
consequtive three vectors are regarded as the edge vector
of a tetrahedron defining the occupation domain (ish=0)
be: isotropic temperature factor in external space
bi: isotropic temperature factor in internal space
****** for decagonal case *****
be: isotropic temperature factor in the plane normal to 10
bi: isotropic temperature factor along 10
ramin : scale for unoccupied tetrahedron or rhombohedron
ramax : scale for occupied tetrahedron or rhombohedron
if ish=2 ramax=1 means shere with radius of 1.4325 (ca)
(radius of the shere equivalent to unit triacontahedron
creating the 3d penrose pattern)
p : occupation probability
s1 : percentage of first component
s2 : percentage of second component
(** one site is assumed to be occupied by two atoms**)
***** ish=-1 to use truncated triacontahedron *****
ra or rb=1 corresponds to the triacontahedron with
unit edge length
(02) x0(1)-x0(6): coordinate of atom in 5D, or 6D for dihedral an
(03) xe1(1)-xe1(6),u1 shift vector in ve and magnitude (5D,6D or
(04) xe2(1)-xe2(6),u2 shift vector in ve and magnitude (5D,6D or
(05) xe3(1)-xe3(6),u3 shift vector in ve and magnitude (5D,6D or
(06) xi(1)-xi(6),v shift vector in vi and magnitude (5D,6D or 7D
5D: octagonal, 6D: decagonal and icosahedral 7D: dodecagonal
****** for colored atom give xi(6)=1 (normal color)
or -1 (inverse color)********
****** colored atom should be black (icol=0) or white (icol=10) **
******** colored symmetry is only available for polygonal cases **
******* if(ish.gt.0) skip (07) (08)****
the following judge is used for icosahedral cases
rimax: maximum |ej|
rimin: minumum |ej| which is calculated in getnii
or in getnid
ri > rimax out of the domain
ri < rimin in the domain
rimax > ri > rimin need accurate calculation
using the domain shape
Note that this is not correct in general
Please include the origin in the domain
************************************************
######################################################################
(5') itempf
If itempf=1
xe1,xe2,xe3 are used to describe anisotropic temperature fact
however if xe1 and xe2 are orthogonal then third axis orthogo
to them are used neglecting specified xe3. in this case
zero vector xe3 can be specified if it is not necessary
as a shift vector
but if more than two of them is zero, cartesian coordinate sy
in the external space is used instead for that atoms (or OD)
(6) flnm3
filename for the data given by (60)-(61)
(60) nx
(61) z,jz,(ja1(j),ja2(j),ea(j),j=1,jz)
z : independent parameter
jz : number of terms related with z
ja1: atom number
ja2: u,v,be,be,ramin,ramax,p,s for 1-8
ea : coefficient
u,v,etc. = z*ea
*******repeat (61) nx times********
if itempfi=0 skip (7)
(7) itempfi (80i1)
itempfi : 0 for iso 1 for anisotropic temperature factor
for individual atom
(8) icont
icont=0 : does not use parameters in flnm4 file
1 : use parameters in flnm4 file
(9) flnm4
filename of the parameter file
(10) jaslct (80i)
atom selection: if j-th column is 1 or 0 j-th atom is selecte
(11) iel (iel(1)-iel(3))
iel : kind of atom for first, second and third atoms in
scattering factor table (1<=iel(1),iel(2),iel(3)<
(repeat ne times) atp
if(isys<=2) skip iarrow
(12) job,icase,ihmax,iatom,iwxy,ldev,inum
if(isys>=3)
(12) job,icase,ihmax,iatom,iwxy,ldev,inum,iarrow
job=0 plot projection of quasi-crystal along an axis
=1 generation of structural data (for prjap and iatom)
(serial No. OD No. element No. x y z p1 p2 p3)
=-1 generation of structural data
(serial No. OD No. x y z h qe qi)
icase= 1: projection along n-fold axis (n=5,8,10,12)
z: n-fold (z-) axis in dihedral quasicrystal
y: y axis in dihedral quasicrystal
2: projection along 3-fold axis
z: 3-fold axis in cubic approximant
x: 2-fold axis in cubic approximant
3: projection along 2-fold axis
z: 2-fold (y-) axis in pentagonal quasicrystal
x: 5-fold axis (z-) in pentagonal quasicrystal
4: projection along z-axis in cubic approximant
z: z-axis in cubic approximant
x: x-axis in cubic approximant
5: projection along specified direction
ihmax: maximum indices, -ihmax<=h(i)<=ihmax
default=3 for decagonal (usually ihmax<=5)
for job=2 ihmax=1 should be sufficient
if an appropriate isim is chosen ? (isim = -1 ?)
iatom= 1: plot atoms
0: plot no atoms
iwxy : give 1 to output x-y coordinate of plotted atoms
and bond length
(if |job|=1, output x, y, z coordinates)
ldev : 1 B & W display or printer, 2 color display or printer
inum : 1 plot atom number 0 no atom number
iarrow: 1 write arrow parallel to xe1 0 no arrow
*** xe1 should be the vector normal to n-fold axis (n=8,10,12)***
************if job=1 or job=-1 geve (12') else skip (12')*****
(12') iel0
element number in periodic table for iel 1,2,..ne
**************if(icase is not equal to 5, skip (13)************
(13) q3,q2 (six-dimensional vector specifying directions)
q3: z-axis (projection axis)
q2: y axis
0,1,1,0,0,0 x-axis in cubic approximant
1,0,0,0,1,0 y-axis in cubic approximant
0,0,0,-1,0,1 z-axis in cubic approximant
**************************************************************
********if iatom=0 skip (14) *******
(14) icntsm
icntsm(i) i=1,ne : center symbol coresponding to ien
0: sphere
1: sphere
2: triangle
3: square
4: pentagon
5: star
(15) amag
amag: magnification (cm/angstrom)
(15_1) x0o
x0o: 6D coordinate of origin (-0.5<orign(i)<0.5)
(15_2) x0e
x0e: 6d coordinate its external part is added to x0o
(15_3) x0i
x0i: 6d coordinate its internal part is added to x0o+x0e
when brv='s', give x0,x0e,x0i in the fundamental cell
with the lattice constant a0=a/2.
origin = x0o+x0e+x0i
****if job =2 then
(16) xmin,xmax,ymin,ymax,zmin,zmax,shiftx,shifty
xmin-xmax: view area in angstrom
ymin-ymax: view area in angstrom
zmin-zmax: view area in angstrom
shiftx: shift before plot in cm
default max(2,-xmin*amag+2)
shifty: shift before plot in cm
default max(2,-ymin*amag+2)
****if job =2 then
(16) dmin, dmax
dmin : minimum interatomic distances to be calculated
dmax : maximum interatomic distances
(17) ncp (ncp <= 20)
ncp: number of atoms with concave parts in the occupation do
***** if ncp=0 skip (18)
(18) npart atm
npart : number of concave parts (with a negative occupation
probability) of the occupation domains of
the atom specified by atm0
atm : atom number with positive occupation probabilities
followed by (npart) related atoms with negative occupa
probabilities
***** repeat (18) ncp times *****
**********if job=0 or +-1 then (19)-(23)
(19) raplt
raplt(1)-raplt(ne): radus of elements
(20) icolor : color of ne elements
lightness=0 or a means black or white
satulation=0 means gray
background color =10 white
black = 1
white =10
gray ( 1- 9)
blue =15 (11-19)
magenta=45 (41-29)
red =75 (71-39)
yellow =105 (101-109)
green =135 (131-139)
cyan =165 (161-169)
(21) nbond
different kinds of bonds (<=10)
(22) ie1, ie2, bmin, bmax, bcol, bwdt, klin
ie1,ie2: element pair to be joined by a bond
bmin: minimum length of a bond in angstrom
bmax: maximum length of a bond in angstrom
bcol: bond color
bdwt: bond width
klin: kind of lines 0: bold, 1: dashed 2: dotted
******bond length affected by isim******
repeat (22) nbond times
(23) nsl,no1,no2
nsl: number of slices upward and downward
along the projection axis
no1-th to no2-th slices are calculated (default: all
slices are calculated)
**** if job = +-1 skip (24) ****
(24) flnm5
file name of xyz file for the output of x,y,z coordinates of
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