2.1.3 Contrast Theory

A small dislocation loop contained in a thin specimen will produce some "black-whit" contrast if imaged under dynamical two-beam conditions.
Whatever that means. Let's look at an every-day live example:

Bottom of swimming pool containing a rectangular whiter grid

Look at the bottom of a swimming pool when the sun is shining. It looks like that above. The structure at the bottom (here a white line grid) is distorted and you have strong "black-white" contrast. What you see is caused by the wavy structure of the water surface; it will also change all the time.

If you are a good theoretician you might be able to calculated what kind of water surface produces a picture as shown. If you have a feeling that it won't be all that easy, you are right.

In a general way, the image of small dislocation loops under some conditions follow the same principle. If we want to obtain properties of the dislocations loop from those "black-white" images, we need to consider the basics first. The parameters to take into account are:

The normal vector of the loop (giving the orientation of the loop plane in the specimen)
The Burgers vector of the loop (look it up)
The diffraction vector used for imaging.
The size of the (generally small) loop
The depth position in the specimen
The thickness of the specimen

The last three points are not so important, they just modulate the principal result somewhat. It's the three vectors that lead to lengthy equations.

I could show that replacing the first two vectors by a "mean" vector, sort of the average of the two, creates almost the same kind of contrast but with considerably shorter and easier equations. In the age of powerful computers that is not a big achievement but back in he time of slide rule calculations it was helpful.

Here is the relevant publication once more

WILKENS, M, .FÖLL, H.: The black-white vector I of small dislocation loops on TEM images. Phys. Stat. Sol. (a) 49 (1978) 555
Since this is a theoretical paper, there are no TEM pictures involved.