projection of quasi-crystals
note the following assumption
input data
*********************************************************
origin of the vector ej should be in a occupation
domain
*********************************************************
(0) inpm, iapprx, ireshp
inpm=0 separatel file (standard input, flnm1 and flnm2)
=1 standard input only
iapprx 0 : no approximation
1 : approximation with domain distortion by linier phason
ireshp 0 : no reshape 1 reshpe
c jsimod : order of simirality transformation for the definition
c of occupation domain (ej in (05) below)
(1) title
*******for semi-quasicrystals (isys=0)
(2_1) isys,a,b,c,cosa,cosb,cosc (for isys=0)
isys: 0 semi-quasicrystals
******* if isys>0 skip (2') and (2")
(2_2) ndm
a*,b*,c* components of a wave vector
(2_3) k
k: a*,b*,c* components of a wave vector
***** if isys != 0 skip (6')
this is necessary for getqe and getqi
********** repeat (2_3) ndm times
(2_4) isetting
isetting : 1 c axis unique, 2 b axis unique, 3 a axis unique
(2_5) v
v : matrix ((v(i,j),j=1,3),i=1,6)
6x3 U matrix, which gives the a1-a3 coefficient of
6 unit vectors in reciprocal space, is calculated from
iseging and a*,b*,c*,cosa*,cosb*,cosc* and k1,k2,k3
6x3 V matrix, which gives the a4-a6 coefficient of
6 unit vectors in reciprocal space, should be given
here
first 6x3 part of 6x6 R matrix is U while
second 6x3 part is V
in the standard setting for modulated structure
first 3x3 part of V is zero matrix while second 3x3
part is unit matrix for many cases, but may be
different for triclinic,monoclinic,hexagonal system
in idm=5
for example, k1 and k2 are in the a*-b* plane in hexagonal system,
we may take v(4,1)=a*, v(4,2)=0, v(4,3)=0
v(5,1)=-a*/2, v(5,2)=sqrt(3)a*/2, v(5,3)=0
v(6,1)=v(6,2)=v(6,3)=0
the best v(1,1)-v(3,3) are sample-dependent for which
the modulation wave should be parallel to the internal space
v(1,1)=v(1,2)=...=v(3,3)=0 gives the standard setting for
modulated structure but this is not appropriate for
semi-quasicrystals
*******for quasicrystals (isys>0 or <0)
(2_1) isys,a,(c)
1 icosahedral or its pentagonal distortion
-1 projected structure along a 5-fold axis (for icosahedral)
2 icosahedral or its cubic or orthrhombi distortion
(***icosahedral or its trigonal distortion)
-2 projected structure along a 2-fold axis (for icosahedral)
3 decagonal or its orthorhombic distortion
-3 projected structure along a 3-fold axis (for icosahedral)
4 octagonal
5 dodecagonal
(****isys < 0 cases have not been not implemented yet****)
a,c : lattice papameter
****** if(isys = 0) skip (2')
(2_2) eps1,eps2,eps3,eps4,eps5,eps6,ists (for isys>0 or <0)
eps1: pentagonal phason distortion (isys=1)
cubic phason distortion (isys=2)
eps2: orthorhombic phason distortion 1 (1,1 element) (isys=1,3..)
(***trigonal phason distortion (3,3) element (isys=2))
eps3: orthorhombic phason distortion 2 (2,2 element) (isys=1,3..)
(***trigonal phason distortion (1,1)=(2,2) element (isys=2))
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)
****trigonal phason eps2 and eps3 in isys=2 include cubic phason****
****therefore eps1 should be fixed at zero in the trigonal case****
****** the phason matrix used is
obtained by fortran program lphason.f
but this is the transpose of U in
Acta Cryst A52 509 (1996)
******************************************
ists: 0 true site symmetry operators are used
1 fictitious site symmetry operators are used for all atoms
(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 icosahedral
=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 normal
lattice into those in superlattice
c P_2c for color symmetry
'g' is for the groupoid symmetry in quasicrystal
**************************************************************
when brv='s', give x, xe,xi,ej in the fundamental cell.
they are transformed into those of the supercell in the program.
**************************************************************
(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,ne0,itype,st
n : serial number for the guide to the eye
nej0 :number of edge vectors for predefined occupation domain (<=nemax=20)
itype : 1 domain with icosahedral, degagonal or octagonal symmetry
2 domain with other symmetry
-1 domain with icosahedral, degagonal or octagonal symmetry for test
-2 domain with other symmetry for test
str : string for comments
(05) ej : edge vectors of their internal components or principal axes
ej(1)-ej(6)
repeat (02) ne times
(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 rhombus
(for isys=3,4,5)
(07) iaslct(1-(nsymo+icent*nsymo)) (60i1) 1:selected, 0:skipped **na times
******** 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 vectors
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) x : x(1)-x(6): coordinate of atom in 5D, or 6D for dihedral and ico
(03) xe1 : xe1(1)-xe1(6),u1 shift vector in ve and magnitude (5D,6D or 7D)
(04) xe2 : xe2(1)-xe2(6),u2 shift vector in ve and magnitude (5D,6D or 7D)
(05) xe3 : xe3(1)-xe3(6),u3 shift vector in ve and magnitude (5D,6D or 7D)
(06) xi :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
************************************************
(07) ej
ej: edge vectors of two triangles in the 6D coordinate system
repeat (5) ne times
***************notice****************
the internal components of consecutive ej are regarded as
the consecutive edge vectors of the polyhedron defining
the occupation domain
***************notice***************
(08) 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)
******** repeat (01) (08) na times
############################################################################
(5') itempf
If itempf=1
xe1,xe2,xe3 are used to describe anisotropic temperature factor
however if xe1 and xe2 are orthogonal then third axis orthogonal
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 system
in the external space is used instead for that atoms (or OD)
(6) nx
(7) 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 (7) nx times********
if itempfi=0 skip (7')
(7') itempfi (80i1)
itempfi : 0 for iso 1 for anisotropic temperature factor
for individual atom
(8) icont
*******if icont = 0 skip (9) **********
(9) flnm3
filename of the parameter file
(10) jaslct (80i)
atom selection: if j-th column is 1 or 0 j-th atom is selected or skipped
(11) iel (iel(1)-iel(3))
iel : kind of atom for first, second and third atoms in each atomic
scattering factor table (1<=iel(1),iel(2),iel(3)<=3)
(repeat ne times) atp
(12) job,iatom,iwxy,ldev,inum
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)
iatom= 1: plot atoms
0: plot no atoms
iwxy : give 1 to output x-y coordinate of plotted atoms
ldev : 1 B & W display or printer, 2 color display or printer
inum : 1 plot atom number 0 no atom number
*********** if |job|=1, output x, y, z coordinates and OD No.
into atomxyz.mld file (in comma-separated mld format)
into atomxyz.xyz file (in blank-separated xyz format)
(12) ihmax
ihmax: maximum lattice vector indices, -ihmax(i)<=h(i)<=ihmax(i)
(i=1,2,..,6)
default=3 for decagonal (usually ihmax(i)<=5)
for job=2 ihmax(i)=1 should be sufficient for all i
if an appropriate isim is chosen ? (isim = -1 ?)
and bond length
(13) jbc
jbc: kind of map 1 : axes are unit vectors for ext. and int. spaces
-1 : axes specified in (14) (lattice vectors)
**if jbc=-1, or jbc=-2 then give (14) else skip (14)**
(14) 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 &D // 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))
(13) iax
iax(1),iax(2),,,iax(6) : q coordinates
density in 3D space spanned by iax(1),iax(2),iax(3) axes is calculated
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)
************if job=1 or job=-1 geve (12') else skip (12')*****
(12') iel0 (iel0(1), iel0(2) iel0(3))
element number in periodic table for iel = 1, 2, 3
********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) x0
x0 : 6D coordinate of origin (-0.5<orign(i)<0.5)
(15_2) x0e
x0e: 6d coordinate its external part is added to x0
(15_3) x0i
x0i: 6d coordinate its internal part is added to x0+x0e
when brv='s', give x0,x0e,x0i in the fundamental cell
with the lattice constant a0=a/2.
origin = x0+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 domain
***** 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 occupation
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) flnm4
file name of xyz file for the output of x,y,z coordinates of plotted atoms
File translated from
TEX
by
TTH,
version 3.02.
On 16 Aug 2005, 08:57.