## 6.2.5. LAYER RESTRUCTURE OPTION, [C]

next, previous Section / Table of Contents / Index [C] This option allows you to restructure any set of layers of the lattice section. It can thus be used to model layer reconstruction or relaxation of any level of complexity. In addition, adsorbate or intercalation layers may be included in the structure with this option. Each layer of the unmodified lattice section is characterized by its origin vector o, two periodicity vectors (lattice vectors) R1', R2', and n layer basis vector(s) rt pointing to inequivalent atoms of the layer with appropriate nuclear charges and atom radii. With the present option, a given layer p can be restructured as follows a) origin shift o --> o + s this shifts layer p rigidly with respect to its original position where the shift vector s is 3-dimensional. b) periodicity transformation R1' --> R1'' = m11 * R1' + m12 * R2' R2' --> R2'' = m21 * R1' + m22 * R2' this changes the periodicity of layer p. The original periodicity vectors R1', R2' are transformed linearly using a 2x2 transformation matrix M. For simple cases, M is readily available. As an example we mention a p(a x b)Rx adsorbate layer ( = primitive a x b structure rotated by x degrees) where M is given by a product of two matrices ( a 0 ) ( cos(x)-A12*sin(x) A11*sin(x) ) M = T * R = ( ) * ( ) ( 0 b ) ( -A22*sin(x) cos(x)+A12*sin(x) ) with Aij = Ri'*Rj' / |R1'xR2'| For further details consult respective surface science textbooks as e.g. the one by M. A. Van Hove, W. H. Weinberg and C. M. Chan cited below. c) rebuild layer basis rt, i=1,k --> rt', i=1,k' this redefines all layer basis vectors (and atoms with radii and nuclear charges) of layer p by replacing the k original layer basis vectors (and atom parameters) by k' new ones. The new layer basis vectors are defined as 3-dimensional vectors by rt' = p1 * R1'' + p2 * R2'' + pz * rz where R1'', R2'' form the (transformed) layer periodicity basis and rz is a layer normal vector of length D (D = distance between symmetry equivalent lattice planes) pointing towards layer p+1. Note that with this definition a restructured layer basis does not need to be planar (as opposed to the strict definition of lattice planes). The following table gives examples for any combination of the three schemes. ------------------------------------------------------------------- Scheme(s) Application ------------------------------------------------------------------- a layer relaxation at surfaces. b simple planar layer reconstructions, e.g. missing row. c layer buckling, commensurate 1x1 adsorbate layers. a + b combined layer reconstruction and relaxation in simple cases. a + c may be described by c only. b + c general relaxation/reconstruction case, incommensurate structures (buckling, warping, etc.), adsorbate layers. a + b + c may be described by b + c. ------------------------------------------------------------------- Note that for non-primitive lattices with more than one inequivalent atoms in a layer BALSAC will apply restructure schemes a and b to each inequivalent atom separately starting from atom positions of the unrestructured layer. This may require to rebuild layer bases (scheme c) for non-primitive lattices even in simple restructure cases. Selecting [C] from the main option menu of BALSAC/LATTICE shows in the most general case the restructure entry menu C' which reads ========== RESTRUCTURE OPTION =================================== 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 ..... ..... Select [C]hange layer [U]ndo restructuring [?,]esc =========================================================== 87 == giving the present definition of all nrtot restructured layers and asks for the index n of a layer which is to be restructured from scratch or whose restructure parameters are to be changed, see option [L] of the restructure menu below. 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 (see building scheme c) above) where nb = 0 denotes the original basis of the bulk lattice. In addition, vector s = (s1, s2, s3) defines the layer shift vector (see building scheme a) above) given in multiples of the (unmodified) layer periodicity vectors R1', R2' and of a layer normal vector Rn, see below. Further, the 2x2 transformation matrix with components (m11, m12, m21, m22) defines the changed layer periodicity (see building scheme b) above). 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 below. Further, rad and nuc are respective atom radii and nuclear charges. > [C] selected from submenu C' allows you to set the index of a layer which is to be restructured from scratch or whose restructure parameters are to be changed. The prompt Select restructure layer N (1 - n3, 0=esc) : asks for the index nl of a layer to be restructured where nl must lie inside the range [1,n3] with n3 being the number of layers defined in the section option, see Sec. 6.2.4. Here nl = 1 will define the bottom and nl = n3 the top layer of the section (or vice versa depending on the view angles THETA, ROT, see Sec. 6.2.6.). If a layer number n within the range [1,n3] is given this layer will be added to the list of restructured layers (if needed) and BALSAC moves to the restructure menu C where the layer can be further modified, see below. Dummy input n=0 returns immediately to the BALSAC/LATTICE main option menu keeping all restructuring information. > [U] selected from submenu C' allows you to undo (cancel) restructuring of all or selected layers of the lattice section. The undo menu CU reads ============================================================= nrtot layers restructured: nl1 nl2 ... Undo [S]elected [A]ll [?,]esc ======================================================= 54 == where the indices nl1 ... of all nrtot restructured layers are listed. > > [S] selected from submenu CU allows you to delete restructuring of one layer of the listing shown in the above menu. The prompt Select layer no. (0=esc) : asks you to choose a layer number nd from the list after which the restructuring definition of this layer will be deleted and the layer will be described by its original (bulk) definition. Then BALSAC returns to submenu C' if any restructured layer(s) remain or to the BALSAC/LATTICE main option menu. Dummy input nd = 0 in the prompt will keep all layer definitions unchanged. > > [A] selected from submenu CU allows you to delete restructuring of all layers in one step resulting in the original lattice section without restructuring. This has to be confirmed in the prompt Confirm undo [A]ll [?,]esc where selecting [A] deletes all restructuring and returns to the BALSAC/LATTICE main option menu while selecting [,] keeps all layer definitions unchanged returning to submenu C'. > > [,] selected from submenu CU returns immediately to the restructure menu C'. > [,] selected from submenu C' returns immediately to the BALSAC/LATTICE main option menu. After a layer has been selected for restructuring BALSAC moves to the restructure menu C which reads ========== RESTRUCTURE OPTION ===================================== 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 ..... ..... Layer n: [L]ayrdef [R]ebuild [B]asis [U]ndo [F]rmlayr [S]hftlayr [X]plot [D]ispla [I]nfo [?,]esc ============================================================= 52 == giving the above listing of all restructured layers and the prompt line starting with "Layer n: [L]ayrdef ..." indicates that layer no. n has been chosen for input of reconstruction definitions. > [L] selected from submenu C allows you to reset the index of a layer which is to be restructured from scratch or whose restructure parameters are to be changed. This option is identical to option [C] of the restructure entry menu C' discussed above and allows you to move between layers and thus to restructure more than one layer inside the restructure option. > [R] selected from submenu C allows you to redefine the origin and 2-dimensional periodicity of layer nl. The rebuild menu CR reads ================================================================= Layer nl abs. shift(XS,YS,ZS)= xs ys zs rel. shift(S1,S2,S3)= s1 s2 s3 Mat(M11,M12,M21,M22)= m11 m12 m21 m22 Select [A]ll [S]hift(abs) s[H]ift(rel) [M]atrix [R]otate [?,]esc =========================================================== 70 == where the layer shift vector s is shown by absolute cartesian coordinates s = (xs, ys, zs) (x-axis along the (unmodified) layer periodicity vector R1', z-axis along layer normal vector) as well as in relative units s = (s1, s2, s3) with s = s1 * R1' + s2 * R2' + s3 * Rn where R1', R2' are the (unmodified) layer periodicity vectors and Rn points along the layer normal vector En and is of length D equal to the distance between equivalent layers of the (unmodified) bulk pointing towards layer nl+1. Further, the 2x2 matrix M = (m11, m12, m21, m22) which transforms the layer periodicity basis of the original layer (R1', R2') into the restructured basis (R1'', R2''), see above, by R1'' = m11 * R1' + m12 * R2' R2'' = m21 * R1' + m22 * R2' is shown with its components. > > [A] selected from submenu CR allows you to redefine both the layer shift and 2-dimensional periodicity of layer nl in one step. The prompt Input rel. shift + (2x2) matrix S1,S2,S3, M11,M12,M21,M22 ("/"=esc) : asks for three numbers, s1, s2, s3, defining the layer shift vector (in relative units) and four numbers, m11, m12, m21, m22, defining the periodicity transformation matrix. Dummy input "/" leaves the present parameter values unchanged. After complete input BALSAC returns to submenu C. > > [S] selected from submenu CR allows you to redefine the layer shift of layer nl by giving absolute cartesian coordinates, see above. The prompt Input abs. shift XS,YS,ZS ("/"=esc) : asks for three numbers, xs, ys, zs, defining the cartesian components of the layer shift vector (x-axis along the (unmodified) layer periodicity vector R1', z-axis along layer normal vector). Dummy input "/" leaves the present shift vector unchanged. After complete input BALSAC returns to submenu CR. > > [H] selected from submenu CR allows you to redefine the layer shift of layer nl in relative units, see above. The prompt Input rel. shift S1,S2,S3 ("/"=esc) : asks for three numbers, s1, s2, s3, defining the shift components with respect to vectors R1', R2', Rn, see above. Dummy input "/" leaves the present shift vector unchanged. After complete input BALSAC returns to submenu CR. > > [M] selected from submenu CR allows you to redefine the periodicity transformation matrix of layer nl, see above. The prompt Input (2x2) matrix M11,M12,M21,M22 ("/"=esc) : asks for four numbers, m11, m12, m21, m22, defining all matrix components. Dummy input "/" leaves the present matrix components unchanged. After complete input BALSAC returns to submenu CR. > > [R] selected from submenu CR allows you to rotate the restructured layer no. nl about its layer plane normal by applying an additional rotation transformation on the present periodicity transformation matrix. The prompt Input matrix rotation angle : asks for an angle (in degrees) defining the rotation after which BALSAC returns to submenu CR. > > [,] selected from submenu CR returns immediately to the restructure menu C. > [B] selected from submenu C allows you to redefine the atom basis assigned to layer nl. The basis menu CB reads ============================================================ Layer nl : rebuilt basis ( nb atom(s)) Xyz,R,Id( 1) : p1 p2 pz , rad , nuc ... Xyz,R,Id( nb) : p1 p2 pz , rad , nuc Basis: [N]ew [M]od [A]dd [D]el [?,]esc ====================================================== 69 == if a separate atom basis was defined before. Here layer basis vectors rt' = (p1, p2, pz) are given for each of the nb atoms assigned to the layer where rt' are described by multiples of the periodicity vectors R1'', R2'' of the restructured layer, and a layer normal vector Rn, see above, as rt' = p1 * R1'' + p2 * R2'' + pz * Rn Further, rad and nuc are respective atom radii and nuclear charges. If layer nl has no separate atoms assigned to it so far (indicated by nb = 0 in the layer listing of the restructure menu C, see above) the listing in the basis menu starts with Layer nl : original basis Xyz,R,Id( 1) : p1 p2 pz , rad , nuc ... giving the atom definition of the original layer without restructuring. > > [N] selected from submenu CB allows you to redefine the layer basis from scratch deleting the previous definition. The prompt New basis size NBSR (0 - 50) : asks for the size nb of the layer basis set to be used for layer nl. (At present, up to 50 layers can be restructured.) Choosing nb = 0 sets the layer basis identical to that of the unrestructured layer and returns to submenu C. For nb > 0, the prompts Input atom(s) 1 - nb : 1) P1,P2,PZ,RAD,NUC : ... nb) P1,P2,PZ,RAD,NUC : ask for nb sets of 5 numbers defining the components of each layer basis vector rt' = (p1 ,p2 ,pz ) together with the respective atom radius rad and nuclear charge nuc. Here vectors rt' are described by multiples of the periodicity vectors R1'', R2'' of the restructured layer, and a layer normal vector Rn, see above. After complete input BALSAC returns to submenu C. Note that layer basis vectors depend on the transformation matrix M. As an example we mention a c(2x2) CO adsorbate layer on top of an fcc(001) surface which may be described by a transformation matrix ( 2.0 0.0 ) M = ( ) ( 0.0 2.0 ) and a separate layer basis set (nb = 4) C: (p1, p2, pz), rad, nuc = (0.0, 0.0, 2.0), 0.5, 6 O: (p1, p2, pz), rad, nuc = (0.0, 0.0, 4.0), 0.7, 8 C: (p1, p2, pz), rad, nuc = (0.5, 0.5, 2.0), 0.5, 6 O: (p1, p2, pz), rad, nuc = (0.5, 0.5, 4.0), 0.7, 8 while an alternative description would use a transformation matrix ( 1.0 1.0 ) M = ( ) (-1.0 1.0 ) and a separate layer basis set (nb = 2) C: (p1, p2, pz), rad, nuc = (0.0, 0.0, 2.0), 0.5, 6 O: (p1, p2, pz), rad, nuc = (0.0, 0.0, 4.0), 0.7, 8 > > [M] selected from submenu CB allows you to modify a selected atom definition of the basis of layer nl. If for this layer no separate basis was defined so far (nb = 0) a message WARNING: layer basis not rebuilt ** Press [C], L-click to continue ** reminds you that you can modify basis atoms only after they have been defined (option [N] above) and BALSAC returns to submenu C. For nb > 0 the prompt Modify atom no. (1 - nb) : asks you to choose an atom na of the basis set where na lies inside the range [1,nb] after which the prompt New definition P1,P2,PZ,RAD,NUC : asks for 5 numbers defining the new components of the layer basis vector rt' = (p1 ,p2 ,pz ) together with a new atom radius rad and nuclear charge nuc assigned to atom no. na. Here rt' is described by multiples of the periodicity vectors R1'', R2'' of the restructured layer, and a layer normal vector Rn, see above. After complete input BALSAC returns to submenu CB. > > [A] selected from submenu CB allows you to add another atom to the basis of layer nl. If for this layer no separate basis was defined so far (nb = 0) a message WARNING: layer basis not rebuilt ** Press [C], L-click to continue ** reminds you that you can add basis atoms only after a separate basis has been defined (option [N] above) and BALSAC returns to submenu C. For nb > 0 the prompt Add atom no. nb+1 : P1,P2,PZ,RAD,NUC : asks for 5 numbers defining components of a layer basis vector rt' = (p1 ,p2 ,pz ) together with an atom radius rad and nuclear charge nuc assigned to atom no. nb+1 increasing the basis size by 1. Here rt' is described by multiples of the periodicity vectors R1'', R2'' of the restructured layer, and a layer normal vector Rn, see above. After complete input BALSAC returns to submenu CB. > > [D] selected from submenu CB allows you to delete an atom of the basis of layer nl. If for this layer no separate basis was defined so far (nb = 0) a message WARNING: layer basis not rebuilt ** Press [C], L-click to continue ** reminds you that you can remove basis atoms only after a separate basis has been defined (option [N] above) and BALSAC returns to submenu C. For nb > 0 the prompt Delete atom no. (0, 1 - nb) : asks you to choose an atom na of the basis set where na lies inside the range [1,nb] after which atom no. na is removed from the layer basis set and BALSAC returns to submenu C. > > [,] selected from submenu CB returns immediately to the restructure menu C. > [U] selected from submenu C allows you to undo (cancel) restructuring of all or selected layers of the lattice section. This option is identical to option [U] of the restructure entry menu C' discussed above. > [F] selected from submenu C allows you to copy the complete restructuring definition of a different layer to the present layer nl replacing its previous definition. This makes the construction of layers with identical restructuring very efficient. The prompt Get restructure info from layer N (1 - n3) : asks you to choose a layer number nf from which the restructuring definition will be taken and applied to the present layer no. nl after which BALSAC returns to submenu C. If layer no. nf was not restructured a warning WARNING: layer no. nf not restructured no action will be issued and layer no. nf will keep its present restructuring definition. > [S] selected from submenu C allows you to shift the layer indices of all restructuring definitions by a fixed amount. This shifts the complete restructuring scheme of a lattice section up or down by one or more layers. It becomes particularly useful if the number of layers of a given lattice section is changed and restructuring is to be kept fixed at the bottom or top of the section. The prompt nrtot layers restructured: nl1 nl2 ... Shift indices by dN ( ns1 - ns2 ) : shows the indices nl1 ... of all nrtot restructured layers and asks for a number n within the range [ns1,ns2] used to transfer restructuring information for all layers k to layers k + n after which BALSAC returns to submenu C. > [X] selected from submenu C 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. > [D] selected from submenu C shows up to 10 lines of the most recent output generated by the graphic analysis option, see Sec. 6.2.14.2, by ============ Latest Graphics Output ================== 1: Xyz,R,Id( n1)= x y z rad nuc ... ====================================================== This allows you to look up and use numerical output from the analysis for input within submenu C. After the listing BALSAC returns to submenu C. > [I] selected from submenu C lists all relevant data of the present lattice definition identical to the Miller adapted basis listing, option [M] of the analysis menu, see Sec. 6.2.14. Selecting [C] (or L-click (DOS)) returns to submenu R. > [,] selected from submenu C returns to the BALSAC/LATTICE main option menu, see Sec. 6.2.0. next, previous Section / Table of Contents / Index