Parameter definitions for "laue"
It's probably useful to look first at the special features page. You may also want to look at one of the general help files, Sliders, or
Graphs.
Inputs
- SLIDERS
- lattice constant: the lattice constant, in angstroms, of the periodic structure. For the liquid material it is the mean spacing between atoms. The two possible atom spacings for the quasicrystal are the lattice constant (a) and the spacing ratio times . (Restricted to positive values.)
- size of atom A: rms width, in angstroms, of the electron distribution for atoms of type A. (Restricted to positive values.)
- size of atom B: the same as for atoms of type A.
- atomic nr ZB/ZA: ratio of the atomic numbers of atoms of types A and B.
- atom separation: for the diatomic crystal: position in the cell of atom B relative to atom A, in units of the lattice constant (a); for two atoms: separation between the two atoms, in units of the lattice constant (a) of a fictitious lattice. For clean nulls of the diffraction patterns, the atom separation should be chosen equal to (n/m) in units of the lattice constant (a), with n odd and m even (a discrete transform effect).
- order parameter: order parameter (p) of the disordered diatomic crystal. (Restricted to the range -1 to 1.)
- wave vector: wave vector, in units of (pi/a), of the periodic (phonon) modulation of the monatomic crystal. Choosing q = (2n/N)(pi/a) is required to give proper satellite intensities (a discrete transform effect).
- wave amplitude: amplitude, in units of the lattice constant (a), of the periodic (phonon) modulation of the monatomic crystal. (Restricted to positive values.)
- sigma thermal: rms amplitude, in units of the lattice constant (a), of the random displacements of the atoms from the perfect lattice positions. (Restricted to positive values. If you wish to use 0, switch the modulation to none.)
- sigma liquid: rms amplitude, in units of the mean spacing (=lattice constant) (a), of the random random deviations of the nearest neighbor distances from their mean value (a). (Restricted to positive values.)
- spacing ratio: The ratio of the two spacings between atoms in the displacement modulated quasicrystal. (Restricted to positive values.)
- MENUS
- material: offers the choice of several arrangements of atoms.
- monatomic crystal: a single atom per cell of length the lattice constant (a).
- diatomic crystal: two atoms per cell, of types A and B, with independently specified size of atom, and variable ratio of atomic nr ZB/ZA.
- single atom: allows the calculation of the diffraction from a single atom instead of a linear array.
- pair of atoms: gives the diffracted intensity from a pair of atoms of types A and B.
- liquid: builds the chain by adding new atoms with mean spacing between atoms lattice constant but with deviations from the mean of rms value sigma liquid
- quasicrystal: gives one of two forms, type-modulation or displacement-modulation, of a one-dimensional quasicrystal.
- modulation: allows choices of a variety of deviations from perfect periodicity of the atom arrangement.
- none: leaves a perfect crystal
- phonon: gives a periodic modulation, of specified wave vector and amplitude, of the atom positions for the monatomic crystal,
- random: gives a random modulation, of rms amplitude sigma thermal, of the atom positions for the monatomic crystal.
- order-disorder allows arranging A and B atoms in a disordered fashion, consistent with an order parameter (p), for the diatomic crystal.
- displacement quasicrystal constructed by quasiperiodic arrangement of identical atoms.
- type quasicrystal constructed by quasiperiodic ordering of A- and B-type atoms on a regular lattice.
- atom shape: four alternative choices for the shape of the atomic electron distribution.
- gaussian: ~exp{-x^2/2*(size of atom)^2}
- exponential: ~exp{-|x|/(size of atom)}
- triangular: ~{2*size of atom - |x|} or 0
- pseudo atom: ~ sum of two gaussians (see the guides)
- BUTTONS
- calculate: takes the parameters from the panel and calculates the corresponding electron density and diffraction intensity. Key equivalent: =spacebar.
- copy crystal: see Graphs in the General help.
- copy diffraction: see Graphs in the General help.
- presets: Takes you to a tear-off menu with which you may select the presets. For more details, see the preset item in the miscellaneous help file.
- configure: there are three options in the configure menu.
- number of cells: determines the number of cells in the crystal. The more cells, the finer the resolution in k-space, but the longer the calculation. (The number of cells must be a power of two. The product (points sampled per atom)*(number of cells) is restricted to 2^15 or less; use only 2^13 or less for Windows 95 and Windows 3.1x.)
- points sampled per atom: defines the number of points in a cell at which the electron density is sampled. For the diatomic cell, the number of points per cell is twice this value. Larger numbers give better resolution in real space, but lengthen the calculation. (Entry must be a power of two. The product (points sampled per atom)*(number of cells) is restricted to 2^15 or less; use only 2^13 or less for Windows 95 and Windows 3.1x.)
- cutoff: for a sampling point at a distance from the center of an atom greater than (cutoff) times (points sampled per atom), the contribution from that atom to the electron density is set to zero. (Restricted to positive values.)
- {revert: updates the listed configure parameters to the current values (which may have been changed by a preset command).}
- {close: closes the configure window.}
- help: opens the help system which you have already found!
- quit: terminates "laue".
- KEY EQUIVALENTS
Outputs
- DISPLAYS
- left side: electron density as a function of position in the one-dimensional material.
- right side: diffracted intensity as a function of scattering vector, |(k-final) - (k-incident)|. The intensities are normalized to give the central peak unit intensity for the case of a single atom in the unit cell. For the diatomic crystal the central peak will have intensity (1 + ZB/ZA)^2.