Phase Transitions – Series II – 3


The third stage in the second series of Phase Transitions. The lattice of the crystals is changing and this puts them under mechanical stress. As a result, they adapt their shape by twinning (a zigzagging of the crystal lattice), resulting in striped patterns. I find this image visually very fascinating.

There is an intermediate stage (see below) but here something went wrong with the scanning of the slide. There is obviously some file corruption here in the lower stripe of the image. I will have this slid rescanned and will then repost the image. Maybe one bit was flipped. If a cosmic ray or a fault on the hard disk or whatever caused this, I don’t know. However, visually, it is an interesting picture, not least because of the mistake. In this picture, the stripes of the twinning are just beginning to appear.


 Pictures: Svend Keller

Houses and Trees on a Hill


Houses and TreesA pencil sketch on paper, 13 cm x 14.2 cm, showing some houses and trees. It is unsigned but by the style, it can be ascribed to Rolf Keller. It is a typical feature of Tolf Keller’s style to draw objects, e.g. trees, with one or a few long convoluted zigzag stroke.

Other examples of his style of sketching can be found here, here and here. The more I look at these sketches, the more I like them.

There is a caption in the left lower corner but I am not sure about how to read it. It seems to say “Anlage zu 5″ (attachment to no. 5), but I am not sure if that reading is correct and if so, from which context it has been taken. It might have belonged to some letter. There are some letters of Rolf Keller that I have not evaluated yet, so it might be possible to find the context into which this belongs, but maybe that context is lost. I cannot, at this time, identify the buildings shown here, not do I know the time this was drawn (maybe the 1920s or 1930s).

Phase Transitions – Series II – 2

DSC00288The second stage in the second series of Phase Transitions. Compared with the previous stage, the crystals are growing and some more of them are showing up.

The circular dark spots on the lower left are probably bubbles of air enclosed between the surface of the heating table (a heat resistant glass coated with a thin layer of metal that can be heated electrically) and the cover slip.

Why are such structures beautiful? Let me share some thoughts from a comment I made, answering a comment to a previous post in this series.

I think there is a lot of unseen (potential) beauty in the microworld. I think structures with some mix of order and disorder have a potential of being perceived as beautiful (I have written about this in the article On Beauty before).

If you look at such stuff macroscopically, it would just be a whitish crust on the glass. It looks uniform and structureless.

Now if you zoom in, you would start seeing something like a texture, until you reach this scale where you have just a few crystals in the image, with some structure (like dendritic branching). On this scale, you have structure with order (crystals) and disorder (different sizes and orientations). If you zoom in more, you end up seeing just one crystal filling the whole picture, or a small section of it, so you have a totally ordered, boring picture again. So to a large extent, the trick might be just to find the right scale. Zoom in an out and at some point, there is a maximum of beauty or a potential of beauty because there is a mix of order and disorder.

Rocks in the Elbe Sandstone Mountains 3


Another drawing from the Elbe Sandstone Mountains; black and grey chalk on paper.

This drawing was made by Svend Keller on the same day (June 7th, 1949) as the watercolor shown in the previous post from this series. Caption: “Großes Schrammtor” (large Schramm-gate). This is part of the rock formation called “Schrammsteine”.

These particular rocks are known as the “Torsteine” (gate rocks). Nowadays, they are used by free climbers and actually the Elbe Sandstone Mountains are one of the areas where this sport originated, in the early 20th century.

Rocks in the Elbe Sandstone Mountains 2


A monochrome watercolor made by Svend Keller on June 7th, 1949. The caption reads “Schrammsteine – Wildschützensteig -“. The “Schrammsteine” is a rock formation in the Elbe Sandstone Mountains. “Wildschützensteig” is a particular way up those rocks. The name means something like “poacher’s steep track”.  You can find pictures of it on the internet. There are metal staircases in parts of the way today, but I don’t know how it looked in 1949.

There are several drawings by Svend Keller showing motives from the Elbe Sandstone Mountains. This is the second one I am showing here, the first one is here. Throughout his life, Svend Keller was fascinated by this mountain range with its rugged, steep cliffs. After moving to West Germany, he was, to his regret, unable to visit this area for several decades and only returned there after Germany’s reunification.

The picture looks almost like an abstract painting, especially if you enlarge it on your screen and look at sections of it. I like the structures and textures of it. Unlike the other watercolor paintings I have posted here before, it looks like there is no preparatory drawing in this one.

Phase Transitions 5


This is the last stage in this particular series of Phase Transitions (more are forthcoming).

The crystallites of the low temperature phase have taken over completely.

If you look at the whole series, you can see how these images are emerging from the interplay of physical laws and historical accident. Laws of nature determine the properties of these crystals, but accidents determine the exact direction and position of them. The initial melt is of a featureless symmetry, treating all places and all directions in the same way, at least on the scale visible through the microscope. When crystals form, this symmetry is broken, and domains form in which certain directions have different properties. In the images, this is reflected in the emergence of color and structure. Some of this structure is then obliterated in further phase transitions which create new symmetries and break existing ones, leading to a complex but partially ordered image that we perceive as beautiful.

The chance components of these processes are unpredictable, leading to a different outcome each time you perform this experiment, so this is an example of a system that generates new information. In a sense, this little blob of matter under the microscope is creative.