crystal structure

Biscuit Crystals

biscuits gone wrong, crystals in the oven

Expanding biscuits are a 2D example of a close packed crystal lattice.

Blaise Pascal once wrote of the benefits of contemplating the vast, “infinite sphere”, of Nature before considering the opposite infinity, that of the minute¹. And although the subject of today’s Daily Grind involves neither infinitesimally small nor infinitely large, a consideration of biscuits and coffee can, I think lead to what Pascal described as “wonder” at the science of the very small and the fairly large.

The problem was that my biscuits went wrong. Fiddling about with the recipe had resulted in the biscuit dough expanding along the tray as the biscuits cooked. Each dough ball collapsed into a squashed mass of biscuit, each expanding until it was stopped by the tray-wall or the other biscuits in the tray. When the biscuits came out of the oven they were no longer biscuits in the plural but one big biscuit stretched across the tray. However looking at them more closely, it was clear that each biscuit had retained some of its identity and the super-biscuit was not really just one big biscuit but instead a 2D crystal of biscuits. The biscuits had formed a hexagonal lattice. For roughly circular elements (such as biscuits), this is the most efficient way to fill a space, as you may notice if you try to efficiently cut pie-circles out of pastry.

salt crystals

Salt crystals. Note the shape and the edges seem cuboid.

Of course, what we see in 2D has analogues in 3D (how do oranges stack in a box?) and what happens on the length scale of biscuits and oranges happens on smaller length scales too from coffee beans to atoms. Each atom stacking up like oranges in a box (or indeed coffee beans), to form regular, repeating structures known as crystal structures. To be described as a crystal, there has to be an atomic arrangement that repeats in a regular pattern. For oranges in a box, this could be what is known as “body centred cubic”, where the repeating unit is made up of 8 oranges that occupy the corners of a cube with one in the centre. Other repeating units could be hexagonal or tetragonal. It turns out that, in 3D, there are 14 possible such repeating units. Each of the crystals that you find in nature, from salt to sugar to chocolate and diamond can be described by one of these 14 basic crystal types. The type of crystal then determines the shape of the macroscopic object. Salt flakes that we sprinkle on our lunch for example are often cubic because of the underlying cubic structure on the atomic scale. Snowflakes have 6-fold symmetry because of the underlying hexagonal structure of ice.

It is possible to grow your own salt and sugar crystals. My initial experiments have not yet worked out well, but, if and when they do, expect a video (sped up of course!). In the meantime, perhaps we could take Pascal’s advice and wonder at the very (though not infinitesimally) small and biscuits. And if you’re wondering about where coffee comes into this? How better to contemplate your biscuit crystals than with a steaming mug of freshly brewed coffee?

¹Blaise Pascal, Pensées, XV 199

Diamonds are forever at Violet, Hackney

the outside of Violet

Violet in Hackney

Violet is not quite where I expected it to be. I had expected it to be in a row of shops on a main street, instead it is tucked away, a little cafe in a back street in Hackney. Despite the relative anonymity, Violet has won awards for the quality of its cakes. Award winning cakes are hard to resist and so, a few weeks ago I went along to Violet to try the coffee. With a couple of seats outside and a large room upstairs with seating, it is very easy to enjoy a good coffee and a cake while taking in the surroundings. The cakes certainly do not disappoint and, importantly for Bean Thinking, they know exactly what goes in them, meaning that if you are allergic to nuts or have other food allergies or intolerances, they are incredibly helpful. They definitely get a tick in the “cafe with good nut knowledge” category.

As it had been raining when we tried Violet, we decided to take a seat upstairs. Stacked in one corner of the room were a set of wooden chairs, reminiscent of those chairs that we had to stack at school. Each chair fitted almost exactly onto the previous one. At the top of the stack of chairs however, the uppermost chair did not fit exactly onto the previous chair, it was as if there was a defect in the stack.

stack of chairs, Violet

The chair stack in Violet.

The diagonal legs of the chairs resembled the multiple strata in a layered substance such as graphite. Each layer of graphite features a hexagonal arrangement of carbon atoms forming a structure very much like the chair legs in the chair stack. Graphene, a material of which there is currently a lot of hype, is a single layer of graphite. The carbon equivalent of one chair leg on its own. Carbon is a fascinating element. If, rather than being arranged in layers, it is arranged into a more 3D crystal structure, then you get diamond, a colourless, extremely hard crystal structure, very different from graphite. It is in diamond that defects in the stacking structure (such as with the uppermost chair) can cause spectacular effects.

If the carbon atoms are arranged into a perfect crystal structure, (the equivalent to the chairs being perfectly stacked), then diamond is colourless. If on the other hand, something happens to disrupt the structure, perhaps there is one carbon atom missing in the structure or maybe another, impurity element, such as nitrogen, has got in, the way that the electrons in the diamond react to light changes. This means that it can take on a colour. The introduction of nitrogen for example, in concentrations of only 0.1% will make the diamonds more yellow or orange. Red diamonds are a consequence not of impurities but simply defects in the crystal arrangement. The equivalent to that one last chair in the chair stack changing the properties of the stack completely. Knowing that the colour of a diamond is a result of a defect in the arrangement of carbon atoms in the structure offers us two possible viewpoints. Either people who buy red diamonds are paying a premium for defective goods, or, beauty takes many forms and what is beautiful is not necessarily what is regular and perfect. I know which view of the world I prefer to take.

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Violet is at 47 Wilton Way, E8 3ED