```6.2.14.1.  ANALYSIS IN TEXT MODE, [A]

[A]  This option allows you to obtain detailed information about the lattice
section including the basic lattice definition, net plane adapted basis
vectors, restructured layers, and atom geometries based on text output.
This analysis mode does not require graphics to work on your system.
Selecting [A] in the BALSAC/LATTICE main option menu shows the text mode

========== ANALYSIS OPTIONS ===========================================

[B]asic  [M]iller [R]estruct [S]ymmetry  [F]ull  [A]nalyze  [D]max( dc)
[X]plot  [?,]esc
================================================================= 31 ==

>   [B]  selected from submenu A lists the basic definition of the bulk
lattice which is used to construct the present lattice section. The

BASIC LATTICE PARAMETERS :

Title =  ..title..
a =    acon     Vol =     vol     Pack=     pack

Lattice vectors  X,Y,Z  (real)    |    Gx,Gy,Gz  (reciprocal)
x1        y1        z1   |   gx1       gy1       gz1
x2        y2        z2   |   gx2       gy2       gz2
x3        y3        z3   |   gx3       gy3       gz3

Lattice vectors are Minkowski reduced

Smallest lattice / atom distance =   demin /  dmin
Densest net plane =  ( hmin  kmin  lmin )

nc lattice basis vector(s) :
1: Xyz,R,Id=      xb   yb   zb   rad   nuc
Qrel    =      q1   q2   q3
2: Xyz,R,Id=      xb   yb   zb   rad   nuc
Qrel    =      q1   q2   q3
...

nco  of  nc  atom(s) coincide(s) within  dc

** Press [C], L-click to continue;  [,], R-click to escape **

after which pressing [C] or L-click (DOS only) returns to the text

The basic lattice output starts with the name "title" given to the
lattice and lists values of the global lattice scaling constant,
acon, of the volume of the elementary cell, vol, and of the packing
ratio of the atom spheres, pack. Next, cartesian components of the
lattice vectors of the real lattice

R1 = (x1, y1, z1)
R2 = (x2, y2, z2)
R3 = (x3, y3, z3)

and of the reciprocal lattice (given by respective vector products)

G1 = 2pi/vol * (R2 x R3) = (gx1, gy1, gz1)
G2 = 2pi/vol * (R2 x R3) = (gx2, gy2, gz2)
G3 = 2pi/vol * (R2 x R3) = (gx3, gy3, gz3)

are listed. If the real lattice is Minkowski reduced, i. e. if

|Ri*Rj| < 1/2 * min(Ri**2,Rj**2) ,  (i,j) = (1,2), (1,3), (2,3)

then the above listing includes the sentence

Lattice vectors are Minkowski reduced

Otherwise, the output

Original lattice vectors are NOT Minkowski reduced

Minkowski reduced lattice vectors | Transformation from original
xm1        ym1        zm1   |   m11    m12    m13
xm2        ym2        zm2   |   m21    m22    m23
xm3        ym3        zm3   |   m31    m32    m33

gives the Minkowski reduced lattice vectors together with the basis
transformation

Rm1 = (xm1, ym1, zm1)  =  m11*R1 + m12*R2 + m13*R3
Rm2 = (xm2, ym2, zm2)  =  m21*R1 + m22*R2 + m23*R3
Rm3 = (xm3, ym3, zm3)  =  m31*R1 + m32*R2 + m33*R3

Next, the smallest distance between translationally equivalent
atoms (lattice nearest neighbors), demin, and between any two atoms
of the lattice, dmin, is shown. Note that dmin = demin for all
primitive lattices. The Miller indices ( hmin kmin lmin) refer to a
lattice plane of highest density using the notation defined by the
lattice option, see Secs. 6.2.1, 6.2.3.

Next, cartesian components of all nc lattice basis vectors
(xb, yb, zb) and their relative components (q1, q2, q3) with
respect to the lattice vectors together with respective atom radii
rad and nuclear charges / element names are listed. For nc > 2 the
listing has to be initiated by answering the prompt

[L]ist  [?,]esc

by selecting [L] while selecting [,] skips the lattice basis vector
output. The list concludes by giving the number nco of lattice
basis vectors which are translationally equivalent within a
distance accuracy dc (defaulted to 1.D-5). For nco > 0 the lattice
basis vector listing contains nco lines of the format

i: Xyz,R,Id=      xb   yb   zb   rad   nuc  => ieq
Qrel    =      q1   q2   q3

indicating that lattice basis vectors i and ieq are translationally
equivalent.

>   [M]  selected from submenu A lists the net plane adapted lattice basis
definition and all data relevant to net planes chosen with the
Miller index option, see Sec. 6.2.3. The first of two output pages

Miller indices : ( h k l )

Net plane normal vector = ( xn     yn     zn )

Transformed lattice vectors :
R1' :  ijk=  n11  n12  n13     Xyz=   x1'   y1'   z1'
R2' :  ijk=  n21  n22  n23     Xyz=   x2'   y2'   z2'
R3' :  ijk=  n31  n32  n33     Xyz=   x3'   y3'   z3'

Inverted transformation:      Orig. lattice vectors in ...
R1o : ijko=  p11  p12  p13    Xyzp=   xp1   yp1   zp1
R2o : ijko=  p21  p22  p23    Xyzp=   xp2   yp2   zp2
R3o : ijko=  p31  p32  p33    Xyzp=   xp3   yp3   zp3

Net plane distance      =  dn,    el. cell area =  ea
Inequivalent subplanes  =  keq  (A - x),  plane locations :
A:   deq(1),    B:   deq(2), ...

nc  transformed lattice basis vector(s) :
I) Lay    Xo    Yo    Zo  :    Q1'   Q2'   Q3'  /   Rad   Nuc
1)  A     xo    yo    zo  :    q1'   q2'   q3'  /   rad   nuc
2)  ...

** Press [C], L-click to continue;  [,], R-click to escape **

after which pressing [C] or L-click (DOS only) moves to the
second page of output describing symmetry and section size as
discussed below.

The net plane adapted lattice output starts with Miller index
definitions of the net plane stacking direction (h k l) (net
plane normal vector) using the notation defined by the lattice
option, see Secs. 6.2.1, 6.2.3. Then the net plane normal vector is
also given in absolute cartesian coordinates (xn, yn, zn).

Next, the output lists net plane adapted lattice vectors R1', R2',
R3' (where R1', R2' characterize the periodicity of the (h k l) net
planes) given in absolute cartesian coordinates as well as by
linear combinations of the original lattice vectors

R1' = (x1', y1', z1')  =  n11*R1 + n12*R2 + n13*R3
R2' = (x2', y2', z2')  =  n21*R1 + n22*R2 + n23*R3
R3' = (x3', y3', z3')  =  n31*R1 + n32*R2 + n33*R3

together with the inverted vector transformation where the original
lattice vectors are given both as multiples of (R1', R2', R3')

R1o  =  p11*R1' + p12*R2' + p13*R3'
R2o  =  p21*R1' + p22*R2' + p23*R3'
R3o  =  p31*R1' + p32*R2' + p33*R3'

and in components (X, Y, Z) of the internal coordinate system, see
Sec. 5.1.

Next, the output gives the distance dn between adjacent
(translationally) equivalent lattice planes, and the area ea of the
net plane unit cell. Then all keq (<= nc) inequivalent lattice
subplanes together with their subplane indices (A, B, ...) and
relative locations (along the net plane normal axis) deq(l),
l=1,...keq are shown.

The first page of the net plane adapted lattice output concludes
with a listing of all nc transformed lattice basis vectors (nc =1
for primitive lattices). For nc > 2 the listing has to be initiated

[L]ist  [?,]esc

by selecting [L] while selecting [,] skips the lattice basis vector
output and moves to the second output page, see below. The listing
shows each vector in absolute cartesian coordinates and as a linear
combination of the net plane adapted lattice vectors

r' =  (xo, yo, zo) = q1'*R1' + q2'*R2' + q3'*R3'

names assigned to the basis vectors.

nsur  of  nstot  symmetry elements survive :
1) element nsy : labl     vsx,    vsy,    vsz
2) ...

Section size  X,Y,Z =       lx,     ly,     lz
"       N1,N2,N3 =       n1,     n2,     n3
Initial layer NINIT =    ninit

** Press [C], L-click to continue **

after which pressing [C] or L-click (DOS only) returns to the text

This second page starts with listing all nsur point symmetry
elements of the lattice (of a total of nsy symmetry elements, see
option [S] below) which survive for the selected (h k l) lattice
planes. The symmetry elements are characterized by their internal
number isy used in the original assignment, see below and Sec. 5.3,
by symmetry labels sy (given in ASCII format), and by vectors
(vx,vy,vz) defined according to the symmetry element type where a
label

"1 "   defines the identity operation with vector (vx,vy,vz)=
(0,0,0) being meaningless,

"I "   defines the inversion operation with vector (vx,vy,vz)=
(0,0,0) being meaningless,

"Cn"   defines an n-fold (n = 2, 3, 4, 6) rotational axis with
vector (vx,vy,vz) pointing along the axis,

"Mn"   defines an to n-fold (n = 2, 3, 4, 6) mirror plane with
vector (vx,vy,vz) pointing along the mirror plane normal.
Here labels M2 denotes standard mirror planes while Mn,
n = 3, 4, 6 refer to n-fold rotations combined with
inversions.

Note that with the latest BALSAC version point symmetry elements of
all lattices are determined internally and do not have to be
provided by LATUSE format file input, see Sec. 6.4.2.

The following two lines give the size of the selected lattice
section in absolute units (lx,ly,lz) and in multiples of atomic
distances (n1,n2,n3), see Sec. 6.2.4. The final line shows the
index ninit defining the number of the lattice plane used as the
starting layer in the stacking procedure when the lattice section
is built. Note that ninit is meaningful only for non-primitive
lattices where keq > 1, see above and Sec. 6.2.4, while for
primitive lattices ninit = 1.

>   [R]  selected from submenu A lists all data relevant to restructuring of
selected layers of the present lattice section, see Sec. 6.2.5. The

RESTRUCTURING:  No layer restructured

** Press [C], L-click to continue **

if no layer restructuring is defined or

RESTRUCTURING:   nrtot layer(s) restructured

Layr Basis  Relax (S1, S2, S3) | Reconstruct (M11,M12,M21,M22)
nl   nb       s1    s2    s3  |   m11    m12    m21    m22
Xyz,R,Id(  1) :    p1     p2     pz ,     rad ,   nuc
.....
.....

** Press [C], L-click to continue **

if layers of the lattice section have been restructured. Pressing
[C] or L-click (DOS only) returns to the text mode analysis menu A.

In the above listing of nrtot restructured layers each layer is
described by its layer index nl within the range [1,n3] where n3 is
the number of layers defined in the section option, see Sec. 6.2.4.
Then, the number nb of separate atoms assigned to this layer is
shown where nb = 0 denotes the original basis of the bulk lattice.
In addition, vector s = (s1, s2, s3) defines the layer shift vector
given in multiples of the (unmodified) layer periodicity vectors
R1', R2' and of a layer normal vector Rn. Vector Rn is of length dn
equal to the distance between equivalent layers of the (unmodified)
bulk and points from layer nl towards layer nl+1. Further, the 2x2
transformation matrix with components (m11, m12, m21, m22) defines
the changed layer periodicity. The following nb lines list the
redefined layer basis set where rt' = (p1, p2, pz) are layer basis
vectors given in multiples of the (modified) layer periodicity
vectors (R1'',R2'') and of the layer normal vector Rn, see above.

>   [S]  selected from submenu A analyzes the lattice symmetry and lists
all symmetry centers and point symmetry elements (inversion, mirror
planes, rotations) of the 3-dimensional bulk lattice and of the
2-dimensional net plane lattice. First, the Minkowski reduced
lattice vectors

Minkowski reduced lattice vectors :
Rm1 =    xm1        ym1        zm1
Rm2 =    xm2        ym2        zm2
Rm3 =    xm3        ym3        zm3

are given in cartesian coordinates. Then the 3-dimensional lattice
symmetry is shown as

Bravais lattice type is  lattyp
Symops= nsy: px1,pxC2,pxC3,pxC4,pxC6,pxI,pxM2,pxM3,pxM4,pxM6
1) [sy] :   vx      vy      vz   comment  | m11 m12 ...
.....
nsy) [sy] :   vx      vy      vz   comment  | m11 m12 ...

where lattyp denotes the Bravais lattice type (orthorhombic-F,
triclinic-P, trigonal-R, etc., see Sec. 5.3). Further, nsy defines
the number of point symmetry operations of the lattice together
with a listing of all operations in short form where "1" refers to
the identity, "I" to inversion, "Cn" to n-fold rotations, and "Mn"
to n-fold mirror planes (multiplicators p are used if a symmetry
operation appears more than once). This is followed by an explicit
listing of all symmetry elements. For n-fold rotational axes (sy =
"Cn", n = 2, 3, 4, 6) vector (vx,vy,vz) points along the axis. For
n-fold mirror planes (sy = "Mn", n = 2, 3, 4, 6) vector (vx,vy,vz)
points along the mirror plane normal. Note that M2 denotes standard
mirror planes while Mn, n = 3, 4, 6 (improper rotations) refer to
n-fold rotations combined with inversions. A possible comment at

"2-dim" meaning that this symmetry element survives in the
2-dimensional lattice of the present net plane
definition, see below,
or
"=>neq" which refers to an equivalent operation of the same
symmetry listed as no. neq.

The end of the line lists all elements (m11,m12,m13,m21,m22,m23,
m31,m32,m33) of the 3x3 matrix referring to the symmetry
transformation of the (Minkowski reduced) lattice vectors.

Next, the listing

Centers of highest symmetry :
1) Xyz =    xcsy    ycsy    zcsy   ( q1    q2    q3  )
Nsym= nsyc: px1,pxC2,pxC3,pxC4,pxC6,pxI,pxM2,pxM3,pxM4,pxM6
Operators:  XXXXXXXXXX.XXXXXXXXXX.XXXXXXXXXX.XXXXXXXX
2)...

shows all (or up to 16) centers which yield highest symmetry in the
full (non-primitive) lattice. The centers are given in cartesian
coordinates (xcsy,ycsy,zcsy) and as multiples (q1,q2,q3) of the
Minkowski reduced basis. Here, nsys defines the number of point
symmetry operations of the center and a listing of all operations
in short form is added as above. The following line states which of
the nsy symmetry operations of the Bravais lattice survives at the
center. Here X="T" at the n-th position means that the n-th
operation survives while X="F" indicates the respective loss of
symmetry.

The 3-dimensional analysis is followed by an analysis of the point
symmetries of the 2-dimensional lattice net planes which are
defined at present. The listing

Netplane is   ( h k l )
R1 =  x1'     y1'     z1'
R2 =  x2'     y2'     z2'
R3 =  x3'     y3'     z3'

Bravais type (2-dim.) is  lattyp
Symops=  nsy2 :  px1, pxC2, pxC3, pxC4, pxC6, pxM2
1) [sy] :   vx      vy      vz   comment  | m11 m12 ...
.....
nsy2) [sy] :   vx      vy      vz   comment  | m11 m12 ...

gives the present net plane by its Miller indices (h k l) and shows
the net plane adapted lattice vectors  R1, R2, R3. Then lattyp
denotes the Bravais lattice type (oblique, rectangular-P, etc., see
Sec. 5.3). Further, nsy2 defines the number of point symmetry
operations of the net plane lattice together with a listing of all
operations as explained above for the 3-dimensional case. For each
symmetry element the end of the line lists all elements (m11,m12,
m21,m22) of the 2x2 matrix referring to the symmetry transformation
of the lattice vectors R1, R2 defining the net plane.

NOTE that for lattices with more than 2 atoms per unit cell the
analysis may take a long time.

>   [F]  selected from submenu A combines the basic and the net plane
adapted lattice output with the restructuring output, options [B],
[M], [R] above, in one output sequence and returns to the text mode

>   [A]  selected from submenu A allows you to analyze directions,
distances, angles, and environments of selected atoms of the
lattice section. This analysis requires internal numbers of
respective atoms which are obtained from a preceding plot or
listing. Atom numbers are shown in plots with the number labeling
on (see Sec. 6.2.7.2) and in the numeric listing of all atoms
(design option [L], see Sec. 6.2.7). Atom numbers can also be
directly obtained from graphics output using the graphic analysis
option, see Sec. 6.2.14.2. The prompt

Input atom numbers for analysis (N,NA,NB: 1-nct) :

asks for three atom numbers n, na, nb within the range [1,nct].
These atoms are evaluated in their geometric properties and listed
by

Vectors for analysis :
1: Xyz,R,Id(  n )=      x      y      z      rad     nuc
2: Xyz,R,Id(  na)=      xa     ya     za     rad     nuc
3: Xyz,R,Id(  nb)=      xb     yb     zb     rad     nuc

Difference vectors :
V1(2-1):  (hkl)= (  i1   j1   k1   ), Xyz= ( x1  y1  z1 )
V2(3-1):  (hkl)= (  i2   j2   k2   ), Xyz= ( x2  y2  z2 )
|V1|=  l1,   |V2|=  l2,   Angle=  ang12,   |V1xV2|=  ar12

V1xV2 (hkl)= ( hf  kf  lf )

Neighbor shells of atom no. n :
1)  r1 ( m1 )      2)  r2 ( m2 )      3)  r3 ( m3 )
...

** Press [C], L-click to continue **

after which pressing [C] or L-click (DOS only) returns to the text

The above listing starts by coordinates and attributes of atoms n
at r = (x, y, z), na at ra = (xa, ya, za), and nb at
rrb = (xb, yb, zb) confirming the input. Then difference vectors
between the atom centers are given in absolute cartesian
coordinates and by linear combinations of the lattice vectors

v1 = ra - r = ( x1  y1  z1 ) = i1*R1 + j1*R2 + k1*R3
v2 = rb - r = ( x2  y2  z2 ) = i2*R1 + j2*R2 + k2*R3

together with their lengths l1, l2, the angle ang12 between them,
and the area ar12 of the parallelogram spanned by v1, v2. Then the
normal direction of lattice planes spanned by v1, v2 (given by the
vector product v1 x v2) is shown as a combination of reciprocal
lattice vectors defined by normalized Miller indices (hf kf lf)
where the notation defined by the lattice option is used, see
Secs. 6.2.1, 6.2.3. Note that for non-primitive lattices Miller
direction indices (hf kf lf) may assume non-integer values.

Last, neighbor shells of atom no. n (chosen as the first atom of
the above analysis input) are listed by their radii, ri, and number
of shell members, mi, where up to 30 shells are considered. Note
that only atoms inside the present lattice section are included in
the shell counting which may result in incomplete shells compared
to the extended bulk/surface.

Note that before performing the above analysis the present lattice
section has to be calculated using the execute option [X] at least
once. Otherwise, a message

WARNING:  no atoms available for analysis,
calculate section ([X])

** Press [C], L-click to continue **

shows where pressing [C] or L-click (DOS only) returns to the text
mode analysis menu A allowing you to calculate the lattice section.

If in the above analysis input atom numbers are used which lie
outside the section range [1,nct] a message

WARNING: input / n na nb / out of range [ 1,nct],  NO analysis

** Press [C], L-click to continue **

will be issued listing the incorrect numbers  n, na, nb and the
available range [1,nct] and BALSAC returns to the text mode

>   [D]  selected from submenu A allows you to reset the coincidence
distance determining the maximum distance between two lattice basis
vectors to be considered translationally equivalent, see above. The
prompt

Atom coincidence distance  ( dcold) :

shows the present value of the coincidence distance dcold (also
given in the text mode analysis menu, default = 1.D-5) and asks for
a new value dc after which BALSAC returns to the text mode analysis

>   [X]  selected from submenu A plots the lattice section (switching to
graphics mode (DOS) or opening a graphics window (Unix)) or lists
its atom coordinates depending on the plot/list mode defined in the
graphics option, see Sec. 6.2.7.

>   [,]  selected from submenu A returns to the BALSAC/LATTICE main