ALPHABETA TEM tilting suite

ALPHABETA is a piece of software written in Python that calculates alpha and beta tilt angles of a double tilt stage in a TEM (transmission electron microscope). The tool comes with an intuitive user interface and can be modified to be used on any TEM to uses a double-tilt holder. Operators that deal with highly deformed materials, small grained materials, or beam-sensitive materials may find this piece of software useful. Once the microscope is calibrated (which can be done in a few minutes) the tool allows the operator to quickly tilt to many different zone axes or 2-beam / Weak beam conditions. The tool also includes a way to plot

ALPHABETA was made by Niels Cautaerts, initially only for Niels Cautaerts. My motivation for making this was the extremely frustrating experience of trying to set up correct diffraction conditions on a sample of highly deformed steel (FCC), with a dense dislocation network and high density of deformation twins. While conventional wisdom dictates that an operator needs to only follow kikuchi lines to arrive at a zone axes, this process was very complex and time consuming on my samples. Often, after having spent time to go to a new zone, I could discover it was outside of the tilt range. Therefore, I decided to build a tool that could simply calculate the required tilts, so I could tilt to the right defraction conditions in image mode.

Very recently I've managed to bundle ALPHABETA into an excecutable, which you should be able to download. Instructions for running it can be found in the releases. You should be able to put this on a USB stick and take it with you to the microscope.

The details for those interested, and those that may want to work directly with the scripts and not the GUI:

The engine behind the program are some classes and methods in the temCalcs.py file. The main classes:

1. TEM: stores detector and stage objects (even though a TEM usually has only one stage, the option is left open to have multiple). To access a particular Detector (see later), Stage and Crystal objects must pass through the TEM.

2. Stage: stages contain Crystal objects (see later). It keeps track of its tilt range and current alpha and beta setting. It can calculate which alpha and beta it should tilt to given a vector expressed in Stage coordinates.

3. Detector: a detector mainly stores various calibration dictionaries: meaning in which direction do the alpha and beta tilt axes lie at different magnifications or camera lenghts. Imaging, Diffraction, and STEM are supported. I may generalize this so that a user can add any mode he or she pleases. Size calibration (real size/pixel) can be stored as well but this is not accessible in the GUI.

4. Structure: a structure is the prototype of a crystal. The 7 crystal classes are supported, but no distinction is made between space groups - sorry, I work on FCC materials and it seemed too much of a hastle. A structure does not have an orientation and can exist without the TEM. It stores crystallographic data and can be used to perform basic crystallographic calculations - length of a lattice vector (real or recyprocal), angle between lattice vectors, conversion to cartesian coordinates in a cartesian coordinate system stuck to the structure, converting a real lattice vector to the recyprocal lattice vector pointing in the same direction, etc.

5. Crystal: a Crystal is basically a piece of material with a particular structure stuck to a stage. A crystal can perform all the functions of its derivative structure, but it also stores an orientation matrix. This matrix determines how the cartesian coordinate system stuck to the crystal is rotated with respect to the coordinate system stuck to the stage. The way to calculate this orientation matrix is very easy:

a) Tilt your piece of material to any zone axis and index it correctly

b) Change the alpha and beta of the stage object so that it reflects reality

c) Call the calcOrient function on the crystal object, check in the code for the arguments to be provided. From thereon out your crystal is correctly anchored to the stage.

Note that it is important that the detectors are accurately calibrated for this to work. Look at the jupyter notebook for more details

The crystal is the workhorse class. With it you can calculate what alpha and beta you need to tilt to another zone or to a two-beam (implemented but not properly tested) or weak beam condition (not implemented yet). It does this by making reference to functions from its higher ups: the stage, the TEM and the detector.

There are some additional methods just in the file. Rotation matrixes can be defined according to a rotation around X, Y or Z or simply any rotation matrix defined by an arbitrary axis and angle.

There are some functions in there to try and get an integer representation of a vector (example (0.4, 0.6, 0.2) -> (2, 3, 1))

Also there are some functions in there to make a stereographic projection figure.

Hope with the things I have provided you can at least already get some use out of this.

temCalcs is dependent on the following packages:

numpy, math, matplotlib, re, fractions, scipy, pyQT5

Since version 2, a user interface is available that will be sufficient for most purposes. It is not meant to be idiot proof, so I'm sure there are tons of buggs to be found. The user interface is implemented using pyQT5 in the GUI.py file. The program can be run by calling "python GUI.py" in the command line. The user interface is rather self explanatory and an upcomming paper will go more into detail on the program.