Phase Transitions – Series II – 4


This is the last slide in the second series of Phase Transitions. Looking at these pictures, I find it amazing how such a beautiful structure can arise by itself. We see here a mixture of the laws of physics and the accidental history of the events under the microscope.

Two substances where mixed and melted, so from two white powders, we got a liquid drop. This was the first phase transition, from solid to liquid. The old order of the crystals in the powders was forgotten. The result is an unordered jumble of molecules moving around.

When they were cooling down again, crystals started growing. This was the second phase transition, from liquid to solid. Where these crystals grow and in what direction is a matter of accidents. It might be little bits of dust, but maybe just an accidental arrangement of some molecules to form the “seed” of a crystal. This little bit of order then reproduces itself over a large section of the melt, until it hits against another crystallite. Compared with the liquid, the overall order increases. Meanwhile, symmetry decreases: while the liquid does not favor any direction, so that it has spherical symmetry with infinitely many symmetry axes, in the crystal different directions have different properties and there are only a few symmetry axes or planes of symmetry or points of symmetry left (depending on the kind of crystal).

I a further stage, these crystals changed their configuration, from one ordered lattice to another one. This third phase transition leads from one solid to another, with a different lattice structure. In this particular case, the transition leads to a change in the shape, creating mechanical tensions. As a result, patterns of stripes arise, partially regular, partially irregular.

The beginning of a further phase transitions that is going to destroy this structure can be seen in a few spots.

The result of these steps is a complex mix of order and disorder. The interference colors, depending on the thickness and orientation of the crystals, resulting from the interaction of polarized light and the “optical activity” of the crystals, add to the beauty of the result.

The last transition, however, happens in the brain and mind of the observer. This step, I have to leave to you.

Animal Studies 1 – Ruff


 A pen and pastel drawing of a ruff, undated. Caption: “Kampfläufer Philomachus pugnax Sommerkleid” (“Ruff Philomachus pugnax, summer dress”). During his apprenticeship as a graphics artist, Svend Keller had to make a couple of animal studies, using different techniques. Probably he made them from photographs. This is the first one I am posting here.

The ruff (in German “Kampfläufer” which means “fighting runner”) is a wading bird. The male birds develop a “collar” of feathers in the summer to impress the females as well as each other (during fights).

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.