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Gitter im Real- und reziproken Raum, Röntgenbeugung


1) What does the Applet show?

The applet shows a custom crystal structure in 2 dimensions and its reciprocal counterpart, the reciprocal lattice. The structure itself is shown in the left hand side of the applet and consists of a Bravais-lattice combined with a basis of certain atoms. The reciprocal lattice is shown on the right.
In X-Ray diffraction, the diffraction pattern only has spots on points of the reciprocal lattice, and their intensity shows a certain variation due to the basis of the lattice. These intensities can be shown as well.

2) How to use the Applet?

The view on the crystal structure and the reciprocal lattice can be zoomed by scrolling your mouse-wheel, and refocused with a double click on the view.

In general terms, the adjustments in the applet are grouped into 3 sections lined up in the upper part of the applet:
- Bravais lattice
- Basis
- Additional Options

Concerning the Bravais lattice, you are able to adjust the lattice vectors a1 and a2 in Cartesian coordinates, where
a1 = (a1x, a1y), a2 = (a2x, a2y),
and in polar coordinates, where
a1 = r1 * (cos(phi1), sin(phi1)), a2 = r2 * (cos(phi2), sin(phi2))
Each of the possibilities has its advantages or disadvantages, so choose the possibility that fits your lattice best.
When adjusting the values of each variable, you can either use the given slider, or type in the desired value directly into the text field. Remember to confirm your change by pressing "Enter" when typing your value. Note that the structure may change slightly upon changing from Cartesian to polar coordinates. This reflects that the variables are fixed to the displayed values, the angle phi for instance only takes integer values here.

The basis of the lattice can be customized in the upper mid box. The box shows a current view of your basis, i.e. all atoms with their current radius.
By selecting one of them, you get additional information on the specific atom. The information panel shows:
1) The internal number of the atom inside the basis
2) The diffraction intensity which approximately corresponds to the number of electrons
When having selected an atom, you can change:
1) The diffraction intensity, using the slider or the text field (as described for the lattice vectors)
2) The radius, using your mouse-wheel and holding "Shift"
3) The position inside the basis by just dragging the atom wherever you want. Note, that there are certain positions where the atom "clicks in", these positions can be shown by double-clicking the atom or the panel
4) Remove the atom by clicking "Remove"
You are also able to zoom the current view onto the basis by using your mouse-wheel and holding "Alt"
Furthermore you can add a new atom to the basis at any time when not having selected any other atom by pressing "Add Atom". Deselecting an atom means clicking on free space.

"Additional Options" is a collection of options, that don't directly belong to "Bravais-lattice" or "Basis".
1) The first box lets you select default lattices, which are directly loaded and displayed
2) "Bravais lattice" / "Reciprocal lattice" turns on/off the visualisation of lattice points, lattice vectors, and cells.
3) "Intensity & Structure factor" turns on/off the visualisation of the reciprocal lattice intensities using the structure factor
4) "Atomic Structure factor" visualiszes the effect of the fact that atoms are no points but have a finite size. The calculation is based on a simple Gaussian shape.
5) "Logarithmic scale" enables/disables the use of a logarithmic scale to display the diffraction intensity
6) "Primitive Cell" / "Conventional Cell" / "Wigner-Seitz Cell" turns on/off the visualisation of the stated cells of the lattice
7) "1st / 2nd Brillouin Zone" turns on/off the visualisation of the 1st/2nd Brillouin zone in the reciprocal lattice
8) "Debye-Waller-factor" enables/disables the fluctuation of the atoms at a given temperature T, adjustable below, changing the diffraction intensities of the reciprocal lattice dots