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

next, previous Section / Table of Contents / Index [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 menu A which reads ========== 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 output reads 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 mode analysis menu A. 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 reads MILLER ADAPTED LATTICE PARAMETERS : 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 by answering the prompt [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' where rad, nuc denote atom radii and nuclear charges / element names assigned to the basis vectors. The second page of the net plane adapted lattice output reads 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 mode analysis menu A. 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 output reads either 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. Finally, rad and nuc are respective atom radii and nuclear charges. > [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 each line reads either "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 ) Adapted lattice vectors : 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 analysis menu A. > [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 mode analysis menu A. 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 analysis menu A. > [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 menu A. > [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 option menu, see Sec. 6.2.0. next, previous Section / Table of Contents / Index