## 6.2.1. LATTICE OPTION, [L]

next, previous Section / Table of Contents / Index [L] This option allows you to select the crystal lattice by defining lattice vectors and lattice basis vectors. Several commonly used lattices including all 14 primitive Bravais lattices are implemented internally and can be selected by key code rather than defining lattice and lattice basis vectors. The lattice option menu L reads ========== LATTICE OPTIONS ============================================== Lattice: title of lattice (latc) a= acon Select: [A] sc [B] fcc [L] fcc (Bravais hkl) [C] bcc [M] bcc (Bravais hkl) [D] hcp [N] hcp (lmnq) [E] diamond [O] diamond (Bravais hkl) [F] NaCl [P] NaCl (Bravais hkl) [G] CsCl [H] zincblende [Q] zincblende (Bravais hkl) [I] graphite [R] graphite (lmnq) [J] free lattice [S] free lattice (lmnq) [K] Bravais lattice [U]pdate free/Bravais lattice [V]lattice scaling [T]itle {[X]plot} [?,]esc =================================================================== 50 == where the title line gives the title, "title of lattice", of the presently selected lattice, the internal lattice code number, latc, and the global scaling constant (lattice constant), acon. This line does not show if BALSAC/LATTICE was started from scratch and no lattice had been defined so far. Further, with BALSAC started from scratch the plot option "[X]plot" of this menu is not available and will not be shown. The selection of some commonly used lattices is possible from this menu by key code input where > [A] selects a simple cubic (sc) lattice. > [B] selects a face centered cubic (fcc) lattice where Miller indices are defined with respect to the sc lattice (default for surface scientists). > [C] selects a body centered cubic (bcc) lattice where Miller indices are defined with respect to the sc lattice (default for surface scientists). > [D] selects a hexagonal close packed (hcp) lattice where Miller indices are defined with respect to the true reciprocal Bravais lattice. > [E] selects a diamond lattice built of two fcc sublattices where Miller indices are defined with respect to the sc lattice (default for surface scientists). > [F] selects a sodium chloride, NaCl, lattice built of two fcc sublattices where Miller indices are defined with respect to the sc lattice (default for surface scientists). > [G] selects a cesium chloride, CsCl, lattice built of two sc sublattices where Miller indices are defined with respect to the sc lattice (default for surface scientists). > [H] selects a cubic Zincblende, ZnS, lattice (to be used also for GaAs) built of two fcc sublattices where Miller indices are defined with respect to the sc lattice (default for surface scientists). > [I] selects a graphite lattice built of four hexagonal lattices where Miller indices are defined with respect to the true reciprocal Bravais lattice. > [L] selects a face centered cubic (fcc) lattice where Miller indices are defined with respect to the true reciprocal Bravais lattice. > [M] selects a body centered cubic (bcc) lattice where Miller indices are defined with respect to the true reciprocal Bravais lattice. > [N] selects a hexagonal close packed (hcp) lattice where Miller indices are given by the hexagonal 4-index notation. > [O] selects a diamond lattice built of two fcc sublattices where Miller indices are defined with respect to the true reciprocal Bravais lattice. > [P] selects a sodium chloride, NaCl, lattice built of two fcc sublattices where Miller indices are defined with respect to the true reciprocal Bravais lattice. > [Q] selects a cubic Zincblende, ZnS, lattice (to be used also for GaAs) built of two fcc sublattices where Miller indices are defined with respect to the true reciprocal Bravais lattice. > [R] selects a graphite lattice built of four hexagonal lattices where Miller indices are given by the hexagonal 4-index notation. The selection of the above lattice types is confirmed by title of lattice selected, code = latc where "title of lattice" gives the internal lattice name and latc is the respective lattice code number, see below. This is followed by a prompt Global lattice scaling constant a= asking for a global lattice constant a to scale all lattice and lattice basis vectors (a = 1.0 yields no scaling). This completes the lattice definition and BALSAC/LATTICE moves to the Miller index option (main option [M]) if the lattice section is built from scratch or returns to the BALSAC/LATTICE main option menu. > [J] selected from submenu L allows you to define any non-primitive lattice in the most general way where lattice plane directions are denoted by Miller indices with respect to the reciprocal Bravais lattice vectors, see Sec. 6.2.3. After a message free lattice selected, code = 10 the prompt Title of free lattice (A40, "-"=esc) : asks for a title of the lattice given by an alphanumeric string with up to 40 characters (longer names will be truncated). Then the three prompts Lattice vectors : R1 = (x1, y1, z1) : R2 = (x2, y2, z2) : R3 = (x3, y3, z3) : ask for cartesian coordinates (x,y,z) (three numbers) of each lattice vector, R1, R2, R2, and No. of lattice basis vectors (<0=rel, >0=abs, 1=primtv, 0=esc): asks for the number nc of different atoms (described by basis vectors, radii and nuclear charges) of the elementary cell of the lattice. Here nc = 1 defines a primitive lattice with one atom (hydrogen) placed at r = (0, 0, 0). > 0 assumes a non-primitive lattice with nc atoms per unit cell where the following nc prompts Input lattice basis (abs:X,Y,Z,RAD,NUC) : Atom 1 ( X, Y, Z, RAD, NUC) : ... Atom nc ( X, Y, Z, RAD, NUC) : ask, for each atom, for five numbers defining absolute cartesian coordinates (x,y,z) of the lattice basis vector, an atomic radius rad, and a nuclear charge nuc. Atomic radii do not need to be known at this point. If (at least) one of the radii is set to zero all rad values are determined as renormalized covalent radii (according to respective nuclear charges nuc, see Sec. 5.3). The renormalization is performed such that highest packing without overlapping spheres is achieved. The first atom center will serve as origin of a cartesian coordinate system which is used later on to determine any lattice structure data. < 0 assumes a non-primitive lattice with |nc| atoms per unit cell analogous to nc > 0. The following |nc| prompts Input lattice basis (rel:Q1,Q2,Q3,RAD,NUC) : Atom 1 (Q1,Q2,Q3, RAD, NUC) : ... Atom nc (Q1,Q2,Q3, RAD, NUC) : ask, for each atom, for five numbers (lattice basis vector, atomic radius rad, nuclear charge nuc) analogous to nc > 0. However, the lattice basis vectors are defined in multiples of the lattice vectors r = q1 * R1 + q2 * R2 + q3 * R3 rather than by absolute cartesian coordinates (x, y, z). = 0 leaves an existing lattice basis vector set unchanged while building a lattice from scratch repeats the above prompt enforcing lattice basis input. After the lattice basis has been defined BALSAC moves to the lattice update menu LU where the atom basis definition can be further modified, see [U] of submenu L below. > [S] selected from submenu L is identical to option [J] allowing you to define any non-primitive lattice. However, lattice plane directions are denoted by Miller indices using the hexagonal 4-index notation which is confirmed by the lattice code -10 in the message free lattice selected, code = -10 and becomes useful for non-primitive hexagonal lattices, see Sec. 6.2.3. > [K] selected from submenu L allows you to define any of the 14 primitive Bravais lattices which can be updated to include a lattice basis for the most general definition of a non-primitive lattice. Details of the Bravais lattice option are described in Sec. 6.2.1.1. > [U] selected from submenu L allows you to update or redefine a free lattice definition including Bravais lattices selected before. Details of the lattice update option are described in Sec. 6.2.1.2. > [V] selected from submenu L has no effect if the lattice is built from scratch. Otherwise, BALSAC asks Global lattice scaling constant a= for an updated lattice constant A used to rescale the present lattice definition. If A' was the previous lattice constant, all lattice and lattice basis vectors and atom radii are scaled by a factor A/A'. After this BALSAC returns to the BALSAC/LATTICE main option menu. > [T] selected from submenu L has no effect if the lattice is built from scratch. Otherwise, the prompt Title [ ... old title ... ] New (A40,"-"=esc) : shows the present title and asks for a new title (up to 40 characters, longer text will be truncated). If this prompt is answered by the one character title "-" the old title will be kept and BALSAC returns to the BALSAC/LATTICE main option menu. > [X] selected from submenu L (not shown and unavailable if the lattice is built from scratch) 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 L returns to the BALSAC/LATTICE startup menu if the lattice section is built from scratch. Otherwise BALSAC returns to the BALSAC/LATTICE main option menu, see Sec. 6.2.0. After a lattice definition is complete BALSAC/LATTICE moves to the Miller index option (main option [M]) if the lattice section is built from scratch or returns to the BALSAC/LATTICE main option menu. In interactive mode, atom sphere radii are constructed as radii of touching spheres and may be modified later, see Sec. 6.2.2. If the lattice option is used with a structure input file values of the atomic radii are always read in. If (at least) one of the atomic radii equals zero a touching spheres geometry is assumed and all radii are recomputed, see also below. For predefined lattices with diatomic bases (NaCl, CsCl, cubic ZnS) the ratios of the radii are taken from Coulson's tables of ionic radii, see Secs. 5.3, 6.2.2. In structure input files code numbers, latc, are used instead of characters to denote lattice types. These code numbers are also shown on the first line of the BALSAC/LATTICE main option menu and of the lattice option menu L. The following table connects option codes used interactively in submenu L with lattice code numbers used in structure files. option code option code option code option code [A] 1 [B] 2 [C] 3 [D] 4 [E] 5 [F] 6 [G] 7 [H] 8 [I] 9 [J] 10 [K] 10 [L] -2 [M] -3 [N] -4 [O] -5 [P] -6 [Q] -8 [R] -9 [S] -10 NOTE that in structure output files generated by BALSAC/LATTICE all structural parameters (lattice vectors, lattice basis vectors, radii) are rescaled to a global lattice scaling constant A = 1.0 and A is given separately in the first part of the file. next, previous Section / Table of Contents / Index