6.2.14.2. ANALYSIS IN GRAPHICS MODE, [Q]

next, previous Section / Table of Contents / Index [Q] The graphic analysis allows you to analyze directions, distances, angles between atoms and more based on direct information from the graphics screen/window output. It becomes available by selecting [Q] in the main graphics menu showing at the bottom of the graphics screen/window after a plot is completed, see Sec. 6.2.9. Selecting [Q] shows the graphic analysis menu Q of the BALSAC/LATTICE session at the bottom of the graphics screen/window which reads Analyze[DVRAEPMN_B_WG] build[L!_CK] draw/view[Z_IJ_FSQ+] [?,]esc and gives key codes of all available options grouped according to their use. For mouse selection of menus (Unix/X.11 version), see Sec. 3.3.8, the menu window contains all entries of the above list. Note that the graphic analysis menu is NOT available if design option [L] (atom listing), see Sec. 6.2.7, is applied. Most of the analysis options require input of one or more atom definitions to work. This is indicated by an explanatory line which shows after the option has been selected reading basically Explanation text (r1,r2,...) : where the number of ri's given in parenthesis denotes the number of atoms needed for the analysis. Alternatively, explanatory lines of the type Explanation text (x1,x2,...) : indicate that screen pixel input (independent of atom positions) is wanted. Atoms or screen pixels are selected with the graphic pointer which shows as an arrow if a mouse device is connected to your system or as a "+" at the center of the screen/window. The graphic pointer is moved inside the screen/window using cursor keys [up], [down], [left], [right] or moving the mouse up/down/left/right on the table, see Sec. 5.5. Selecting [+] or [-] increases/decreases the step size of the pointer movement by a factor 2 which can speed up the pointing process. After an analysis option requiring atom input has been chosen, any visible atom on the screen/window can be selected for analysis by placing the center of the graphic pointer, "+" or mouse "hot" spot, at the surface of the respective atom sphere and pressing [enter] or L-click. This marks the atom by a white cross "+" and shows an information line i: Xyz,R,Id ( nn )= xa ya za rad nc/el pc at the bottom of the screen/window characterizing the atom by its internal number nn, its cartesian coordinates (xa, ya, za), its atom radius rad, its nuclear charge nc, and its element name el. Further, pc gives internal number of the lattice basis vector used to construct the atom which allows you to identify the atom in the radii/charge and the restructure options, see Secs. 6.2.2, 6.2.5. Finally, number i denotes the number of atoms which have been selected for the present analysis. After n atoms required for the analysis have been selected, indicated by i = n in the above atom information line, the analysis is carried out by selecting [X] or R-click (R-click on Unix/X.11 Windows systems uses the middle of three mouse buttons!) which shows the respective analysis result at the bottom of the screen/window. After this the analysis can be repeated using different atoms. Pointing at atoms and obtaining atom information selecting [enter] or L-click can be repeated as many times as needed. If more than n atoms required for the present analysis are selected BALSAC uses those n atoms which have been selected last. Selecting [M] with any analysis option active returns to the graphic analysis menu Q allowing other analysis options. Selecting [,] or R-click returns to the main graphics menu, see Sec. 6.2.9. Note that in layer-by-layer display mode, see Sec. 6.2.7, only atoms of the layer displayed last are accessible in the graphic analysis option while all other atoms are shown but not visible to the graphic pointer. Note further that if stereo duplication of graphics was chosen, see Sec. 6.2.7, the atom selection with the graphic pointer works only on one of the two pictures (right picture by default, depending on the sign of the stereo shift, see Sec. 6.2.15). After an analysis option requiring screen pixel input has been chosen, any pixel of the screen/window can be selected by placing the center of the graphic pointer, "+" or mouse "hot" spot, appropriately and pressing [enter] or L-click. This shows an information line Select .. > X1= nx1 ny1 Define X2: nx ny or Select .. > X1= nx1 ny1 X2= nx2 ny2 Evaluate or correct: nx ny depending on whether one, or more than one pixel points have been selected so far where (nx1, ny1) and (nx2, ny2) are the coordinates of pixel points selected last while (nx, ny) gives the present pixel position on the screen/window. After enough pixel points required for the analysis have been chosen the analysis is carried out by selecting [X] or R-click (R-click on Unix/X.11 Windows systems uses the middle of three mouse buttons!) which shows the respective analysis line at the bottom of the screen/window. After this the analysis can be repeated where selecting [M] returns to the graphic analysis menu Q allowing other analysis options while selecting [,] or R-click returns to the main graphics menu, see Sec. 6.2.9. > [D] selected from submenu Q allows you to determine coordinates and distances between two visible atoms. The prompt Distance (r1,r2) : asks for two different atoms n1, n2 to be selected with the pointer after which selecting [X] or R-click shows an analysis line (X,Y,Z),LV = ( xv yv zv ) lv where vector v = (xv, yv, zv) in cartesian coordinates points from atom center n1 to n2 and lv = |v| gives the vector length. > [V] selected from submenu Q allows you to determine distances and angles defined by three visible atoms. The prompt Lengths,Angle (r0,r1,r2) : asks for three different atoms n0, n1, n2 to be selected with the pointer after which selecting [X] or R-click shows an analysis line R1,R2,Angl,Area = l1 l2 ang12 ar where l1, l2 are lengths of the vectors v1, v2 pointing from atom center n0 to n1 and n2 respectively, ang12 is the angle between vectors v1, v2, and ar gives the area of the parallelogram spanned by v1, v2. > [R] selected from submenu Q allows you to determine the distances of an atom from a plane defined by three visible atoms and the torsion angle between two atom planes. The prompt Directed plane distance / torsion angle (r0,r1,r2/r3) : asks for four different atoms n0, n1, n2 (defining the plane), and n3 (defining the single atom) to be selected with the pointer after which selecting [X] or R-click shows an analysis line Directed plane distance = dd Torsion angle = angt where the directed distance is given by dd = v3 * (v1 x v2) / |v1 x v2| with vectors v1, v2, v3 pointing from atom n0 to atoms n1, n2, n3 respectively. The absolute distance of atom n3 is always obtained by |dd|. In addition, positive dd values indicate that atom n3 lies "above" the plane through atoms n0, n1, n2 (the plane normal vector defined by v1 x v2 points towards atom n3) whereas for negative dd values atom n3 lies "below" the plane (vector v1 x v2 points away from atom 3). The torsion angle denotes the angle between the two planes defined by atoms n0, n1, n2 (plane 1) and by atoms n0, n1, n3 (plane 2). Thus, the torsion axis goes through atoms n0, n1. Note that this analysis option can also be used to determine distances between parallel planes (atoms n0, n1, n2 referring to plane 1, atom n3 to plane 2). Further, it can be used to find out whether four atoms are co-planar (dd = 0). > [A] selected from submenu Q allows you to determine the average position of a set of atoms. The prompt Average (r1...rn) : asks for n >= 1 different atoms n1, ...nn to be selected with the pointer after which selecting [X] or R-click shows an analysis line (XAV,YAV,ZAV) = ( xav yav zav ) where vav = (xav, yav, zav) gives cartesian components of the coordinate average vector of the selected n atoms defined by vav = ( r(n1) + ... + r(nn) ) / n where r(ni) are the vectors pointing to atoms ni. This information becomes useful for example if central high symmetry sites of a net plane are to be determined. > [E] selected from submenu Q allows you to determine environment shells of a visible atom. The prompt Environment shells (r1) : asks for one atom n1 to be selected with the pointer after which selecting [X] or R-click shows an analysis line NN= r1 / m1 r2 / m2 r3 / m3 r4 / m4 r5 / m6 where r1 ... r5 give the radii of the first to 5th neighbor shells with respect to the selected atom and m1 ... m5 are the number of atoms in the shells (shell multiplicity). Neighbor shells beyond the 5th shell can be obtained with the analysis option in text mode, see Sec. 6.2.14.1. 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. Further, in layer-by-layer display mode, see Sec. 6.2.7, only atoms of the layer displayed last are included in the shell counting yielding planar shell definitions. > [P] selected from submenu Q allows you to analyze neighboring (hkl) net planes of a visible atom by their distances along the net plane normal. Here (h k l) refers to the Miller direction defined for the lattice section, see Sec. 6.2.3. The prompt Neighboring (hkl) planes (r1) : asks for one atom n1 to be selected with the pointer after which selecting [X] or R-click shows an analysis line NP= d1 d2 d3 d4 d5 d6 where d1 ... d6 give the distances of up to 6 neighboring (hkl) planes relative to atom nl. Distances are shown as positive (negative) numbers for planes above (below) atom nl and the plane through atom nl will not be included. Note that this option will not work properly in layer-by-layer display mode, see Sec. 6.2.7. > [M] selected from submenu Q allows you to determine directions between two visible atoms expressed by respective Miller indices. The prompt Miller direction (r1,r2) : asks for two different atoms n1, n2 to be selected with the pointer after which selecting [X] or R-click shows an analysis line Miller (hkl)= ( hv kv lv ) where vector v pointing from atom center n1 to n2 is shown as a linear combination of the reciprocal lattice vectors v = hv * G1 + kv * G2 + lv * G3 where for (hv, kv, lv) notations of the respective lattice type are used, see Secs. 6.2.0, 6.2.3. > [N] selected from submenu Q allows you to determine directions of net planes defined by three visible atoms. The prompt Miller net plane (r0,r1,r2) : asks for three different atoms n0, n1, n2 to be selected with the pointer after which selecting [X] or R-click shows an analysis line Miller (hkl)= ( hv kv lv ) where (hv, kv, lv) are Miller indices of a lattice plane through atoms n0, n1, n2 where notations of the respective lattice type are used, see Secs. 6.2.0, 6.2.3. This allows you to examine lattice subplanes or to visually decompose surfaces into steps and terrace parts. Note that for non-primitive lattices Miller indices of any three lattice atoms may yield non-integer values. > [B] selected from submenu Q allows you to visualize periodicity vectors of the lattice and of restructured lattice layers. The prompt Basis vectors (r1) : asks for one atom n1 to be selected with the pointer. If the chosen atom is built by the original 3-dimensional lattice selecting [X] or R-click shows an analysis line 3-D basis ( x y z ) 1=(x00), 2=(xy0), 3=(xyz) where vector (x, y, z) describes the center of atom n1 in cartesian coordinates. Further, a triple of lines originating from atom center n1 is drawn and shows the three net plane adapted lattice vectors R1', R2', R3' labelled by "1", "2", "3". The text at the end of the analysis line reminds you that R1' points along the x axis of the present lattice section, R2' has a vanishing z component, while R3' may be most general. If the chosen atom belongs to a restructured layer selecting [X] or R-click shows an analysis line 2-D basis ( x y z ) rebuilt layer no. nr where vector (x, y, z) describes the center of atom n1 in cartesian coordinates. Further, two lines originating from atom center n1 are drawn showing the (modified) lattice vectors R1'', R2'' of the restructured layer labelled by "1", "2". The text at the end of the analysis line indicates that the layer is rebuilt using the restructuring scheme no. nr where nr refers to the order used in the restructure option, see Secs. 6.2.5, 6.2.14.1. > [W] selected from submenu Q allows you to visualize 2- and 3-dimensional Wigner-Seitz elementary cells inside the lattice section. The prompt Wigner-Seitz cells (r1) : asks for one atom n1 to be selected with the pointer after which selecting [X] or R-click shows an analysis line Wigner-Seitz cell at ( x y z ) where vector (x, y, z) describes the center of atom n1 in cartesian coordinates. Further, a 3-dimensional Wigner-Seitz cell about the respective atom is sketched in the plot by red (foreground) and blue (background) lines. In addition the 2-dimensional Wigner-Seitz cell of the present (h k l) lattice plane is drawn by white lines. Note that the cell sketches become more obvious if the respective atom radii are reduced in size, see Sec. 6.2.2. > [G] selected from submenu Q allows you to visualize 3-dimensional Brillouin zones (Wigner-Seitz cells of the reciprocal lattice) inside the lattice section. The prompt Brillouin zones (r1) : asks for one atom n1 to be selected with the pointer after which selecting [X] or R-click shows an analysis line Brillouin zone at ( x y z ) where vector (x, y, z) describes the center of atom n1 in cartesian coordinates. Further, a 3-dimensional Brillouin zone about the respective atom is sketched in the plot by red (foreground) and blue (background) lines. Note that the cell sketches become more obvious if the respective atom radii are reduced in size, see Sec. 6.2.2. > [L] selected from submenu Q allows you to interactively define links connecting atoms by straight lines in subsequent plots. These lines can be expanded later to sticks of finite thickness and may be given any color to visualize atom coordination or bonding relations, see below and Sec. 6.2.7.1. The prompt Links between atoms (r1,r2) : asks for two different atoms n1, n2 to be selected with the pointer after which selecting [X] or R-click shows an analysis line k-th link (Nuc1,Nuc2,Rmin,Rmax) : nuc1 nuc2 rmin rmax giving a link definition described by the nuclear charges of the two selected atoms, nuc1, nuc2, and a distance range [rmin, rmax] determined from the distance lv between the atoms by rmin = lv - eps, rmax = lv + eps with eps = 0.01. This indicates that BALSAC has added a k-th link definition (connection constraint) to the k-1 existing ones as shown in the link option, see Sec. 6.2.7.1. From now on any two atoms of the lattice section will be connected by a line if one atom is of nuclear charge nuc1, the other of charge nuc2, and if the distance between the two atoms lies inside the distance range [rmin, rmax]. The lines will be painted by the default link color defined in the initialization file, see Secs. 5.4, 6.4.10. Note that in layer-by-layer display mode only atoms of the same layer will be connected by lines or sticks while for atom-by-atom mode every two atoms of the complete section may be connected. If the maximum number of link definitions (20 at present) is exceeded with the present option any attempt to construct another connection constraint will result in a warning WARNING: maximum no. of links ( 20) exceeded : link ignored without any further action. > [!] selected from submenu Q allows you to interactively define links connecting two specific atoms by straight lines in subsequent plots. These lines can be expanded later to sticks of finite thickness and may be given any color, see below and Sec. 6.2.7.1. The prompt Link two selected atoms (r1,r2) : asks for two different atoms n1, n2 to be selected with the pointer after which selecting [X] or R-click shows an analysis line k-th link (Na1,Na2) : n1 n2 giving a link definition described by the numbers of the two atoms. This indicates that BALSAC has added a k-th link definition (connection constraint) to the k-1 existing ones as shown in the link option, see Sec. 6.2.7.1. From now on the two atoms of the lattice section will be connected by a line independent of their distance. The lines will be painted by the default link color defined in the initialization file, see Secs. 5.4, 6.4.10. Note that in layer-by-layer display mode selected links refer to atoms of the same layer and will be repeated for each layer due to the internal atom numbering scheme. This may result in unwanted visual effects. For atom-by-atom or cell mode only one pair of atoms of the section will be connected. Further, atom renumbering as a consequence of a changed lattice section size affects all selected links. > [C] selected from submenu Q allows you to interactively redefine background and atom sphere colors from the available palette. The prompt Assign colors: atoms,background (r1) : asks for one atom n1 to be selected with the pointer after which selecting [X] or R-click opens a color box on the left side of the screen/window. The left part of this box displays color blocks of all basic paint colors (palette used to paint atoms) while the right part shows blocks of the full range of color tones available for background colors. In addition, the present atom and background color definition is shown as Color = nc for layer nl, = ncb for background in layer paint mode (where nc denotes the basic color and nl the layer number of the selected atom, ncb is the present background color) or by Color = nc for element nuc/el, = ncb for background in element paint mode (where nc denotes the basic color and nuc/el the nuclear charge / element name of the selected atom, ncb is the present background color). Pointing at one of the LEFT BLOCKS of the color box and selecting [X] or L-click assigns this basic color nc to the selected atom and all atoms of the same nuclear charge or layer depending on the paint mode, see Sec. 6.2.7.2. This changes the respective color palette entry, see Secs. 5.4, 6.4.10, after which the color box is overwritten by the present background color and the selection is confirmed by updating one of the above analysis lines. Pointing at one of the RIGHT BLOCKS of the color box and selecting [X] or L-click assigns this color nc as the background color in subsequent plots. Then the color box is overwritten by the new background color and the selection is confirmed by updating one of the above analysis lines. The modified background color can also be seen in the graphics line of the main option menu, see Sec. 6.2.0, and in the graphics menu, see Sec. 6.2.7. Note that new color assignments will be effective only after the lattice section has been replotted. > [K] selected from submenu Q allows you to interactively redefine colors and thicknesses (radii) of lines/sticks connecting atoms as determined by link definitions. The prompt Assign colors/radii: links (r1,r2) : asks for two atoms n1, n2 which are connected by a visible link to be selected with the pointer. Then selecting [X] or R-click opens a box on the left side of the screen/window. The left part consists in general of two blocks separated by a white horizontal line where the color of the upper block shows the present link color. The thickness of the selected link(s) is represented by the hight H of the upper block in relative units as follows: H compared to the total box hight gives the the stick thickness compared to the smaller of the two radii of atom pairs affected by the link(s). Thus, for zero thickness the upper block becomes very small while a 50% thickness yields an upper block of half the hight of the box. The right part of this box shows blocks of the full range of colors available for painting lines/sticks. In addition, the present link color and radius definition is shown as Color = nc, radius = rad (qrad %) for link(s) i1 i2 ... where nc denotes the link color and the stick radius is given in both absolute (rad) and relative (qrad) units , see above. The list i1, i2, ... gives all links which will be affected by a reassignment. Pointing inside the LEFT BLOCKS and selecting [X] or L-click moves the white horizontal line to the pointer hight which redefines the upper block and thus modifies the stick thickness according to the above recipe. This is confirmed by updating the above analysis line. Note that relative thicknesses above 50% are usually unreasonable. Pointing at one of the RIGHT BLOCKS of the color box and selecting [X] or L-click assigns this color nc to all link definitions which apply to lines/sticks connecting the two atoms chosen before. Then the color box is overwritten by the present background color and the selection is confirmed by updating the above analysis line. Note that new color and radius assignments will be effective only after the lattice section has been replotted. > [Z] selected from submenu Q switches the line show/save flag of the analysis option between "off" (default) and "on". With this flag set to "on" (shown by a dot "." at the end of the graphic analysis menu line) every analysis involving more than one atom will result in the respective atoms being connected by white lines which enhances the visual impression. These connecting lines will show in any subsequent plot unless they are explicitly erased using option [J] below. Further, they will be adjusted if the plot view or perspective change. They will also be included as arrows connecting respective atoms in any subsequent PostScript output file as long as the line show/save flag is set to "on". Further, the PostScript output file will contain a comment line after each arrow definition which shows the analysis result as given by the analysis line. > [I] selected from submenu Q allows you to include additional lines at any location of the screen/window for labelling purposes or to aid the visual impression. The prompt Additional 2-D lines (x1,x2) : asks for two screen locations (nx1, ny1), (nx2, ny2) to be selected with the pointer (independent of any atom positions). During the selecting process the analysis line shows the present pixel position (nx, ny) of the pointer by Select line > Define X1: nx ny or Select line > X1= nx1 ny Define X2: nx ny or Select line > X1= nx1 ny X2= nx2 ny2 Evaluate or correct: nx ny depending on how many pixel points have been chosen. This allows an exact placement of lines on the screen. After two points are chosen, selecting [X] or R-click shows the analysis line Additional line (nll) : (nx1, ny1) -> (nx2, ny2) indicating that the nll-th line points from (nx1, ny1) to (nx2, ny2). Further, BALSAC draws a white or black line (depending on the tone of the background color) between the two points and labels the first point by a small circle. All additional lines will show in subsequent plots unless they are explicitly erased using option [J] below. They will keep their screen position even after plot views or perspectives have been changed. They will also be included as arrows connecting respective atoms in any subsequent PostScript output file as long as the line show/save flag is set to "on". Further, the PostScript output file will contain a comment line after each arrow definition with dummy text that can be easily converted into a text label, see Sec. 6.4.6.1. > [J] selected from submenu Q erases the last line which has been included in a plot by either analyzing with the line show/save flag set to "on", see option [Z] above, or by explicit line drawing, see option [I] above. Erasing is confirmed by overwriting black by white or white by black lines after which these lines will not show in subsequent plots. NOTE that erasing is final and does not have to be confirmed. > [F] selected from submenu Q allows you to interactively reset the view focus used in central projection. The prompt New view focus (r1) : asks for one atom n1 to be selected with the pointer after which selecting [X] or R-click resets the view focus such that it coincides with the center of atom n1. Then the lattice section is replotted with the new view focus placed at the center of the screen/window (if no additional plot shift is applied, see option [S] below) and BALSAC returns to the graphic analysis menu Q. The new focus is applied to all future plots until it is changed with option [F], [Q], or in the view menu, see Sec. 6.2.6. Refocussing can give a more natural perspective view of selected parts of a large lattice section. However, refocussing may move parts of the lattice section outside the screen/window which can be compensated by rigidly shifting the plot using option [S]. The present refocussing option is restricted to atom centers but is more direct than option [F] of the view menu, see Sec. 6.2.6. Note that refocussing requires central projection for meaningful results, see Sec. 6.2.6. > [S] selected from submenu Q allows you to shift the plot of a lattice section rigidly on the screen/window. The prompt Global 2-D plot shift (x1,x2) : asks for two screen locations (nx1, ny1), (nx2, ny2) to be selected with the pointer (independent of any atom positions). During the selecting process the analysis line shows the present pixel position (nx, ny) of the pointer by Select shift > Define X1: nx ny or Select shift > X1= nx1 ny Define X2: nx ny or Select shift > X1= nx1 ny X2= nx2 ny2 Evaluate or correct: nx ny depending on how many pixel points have been chosen. This allows an exact definition of the plot shift on the screen. After two points are chosen, selecting [X] or R-click replots the lattice section with the plot being shifted rigidly by a pixel vector s = (sx, sy) = (nx2 - nx1, ny2 - ny1) after which BALSAC returns to the graphic analysis menu Q. The shift is applied to all future plots until it is changed with option [S], [Q], or in the view menu, see Sec. 6.2.6. Shifting plots may be necessary in order to center important parts of the plot, in particular, after refocussing the view with option [F] above. The present shift option is more intuitive than option [S] of the view menu, see Sec. 6.2.6. > [Q] selected from submenu Q allows you to reset the view focus and global plot shift to default values. The prompt Confirm default focus/shift : [Q]reset [?,]esc asks you to confirm the defaults where selecting [,] or R-click returns to submenu Q while selecting [Q] resets the view focus (default focus at center of lattice section) and the global plot shift (default shift vector s = 0) after which the lattice section is replotted. Resetting to defaults may become necessary in order to undo previous (unreasonable) refocussing or shifting. > [+] selected from submenu Q replots the lattice section with present viewing and graphics parameters. This becomes useful if a plot has been analyzed and too many additional lines or circles drawn in the analysis confuse the picture. > [,] selected from submenu Q completes the graphic analysis and BALSAC returns to the main option menu in graphics mode, see Sec. 6.2.9. The most recent (up to 10) analysis lines generated by the graphics analysis will be stored internally and may be recalled in several option menus. (Option [D]ispla in radii menu, see Sec. 6.2.2, in section menu, see Sec. 6.2.4, in restructure menu, see Sec. 6.2.5, in view menu, see Sec. 6.2.6, in graphics/links menu, see Sec. 6.2.7.1.) next, previous Section / Table of Contents / Index