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. 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?
Back in the seventeenth and eighteenth centuries, coffee houses were places to go for debate, discussion or even to learn something new. The Grecian was known for science. Maths instruction (particularly for gambling) could be found with Abraham de Moivre (1667-1754) at Old Slaughter’s on St Martin’s Lane. Other coffee houses were meeting centres for literature, politics, philosophy or even espionage*. Coffee houses became known as “Penny Universities”. The Black Penny on Great Queen St is a café that wants to continue this tradition, with a downstairs “seminar pit” ready to host such discussions. Although the events page still says “coming soon”, if the events do indeed come, this is very much something that’s worth keeping an eye on.
Even without the seminars though, The Black Penny is definitely worth a visit. Entering from the street, the bar is on the left and is stocked with a good looking selection of cakes. We were shown through to the relatively large, bright and airy seating area at the back where a jar of water (infused with cucumber and mint) had been put on the table for us. I had a very good long black and a lovely apple and blackberry muffin with which to take in my surroundings. The muffin was confidently asserted to be nut-free, and so the Black Penny gets a tick in the ‘good nut knowledge’ section on the Daily Grind. The coffee beans were roasted by the Black Penny themselves and while it still says that they serve ‘Alchemy’ coffee on their website, this no longer appears to be the case.
A strange form of coat hook? The things that catch your eye in cafes
Inside, there are some very interesting architectural features to notice, the remains of a ceiling for example (now removed to reveal the roof) and the acoustics introduced by the speaker positioning. Downstairs in the seminar pit there is apparently a very old stove, though I didn’t get to see that on my visit. However, what immediately struck my eye was what appeared to be a series of coat hooks that looked very similar to a well known brand of battery. Quite what these hooks were for or why they looked like batteries I didn’t manage to ascertain, however, it did get me thinking, can you use coffee-power to light an LED?
You may have heard of a potato battery, or a lemon battery. These are often used in science outreach experiments in schools to demonstrate electricity, or the concepts of current/voltage. Made from an ordinary potato (or a lemon), a copper wire is stuck into one end of the potato and a different metal (usually zinc) is stuck into the other end of the potato. At the Black Penny, there were three things left on the table. My coffee, the mint and cucumber infused water and the tea of my accomplice in many of these reviews (I’d eaten the muffin). Which of these would perform better as a battery?
Can 6 coffee ‘cells’ with aluminium and copper electrodes light up an LED? (The answer may be in the photo)
Although people suggest using galvanised screws as the source of the zinc electrodes, I didn’t have many of those to hand and so had to manage with aluminium foil for one electrode, copper wire for the other. By putting the aluminium on one side of a shot glass, the copper wire on the other and then filling the glass with coffee, I was able to get 0.5-0.8V across the electrodes when I measured it with my digital multimeter (DMM). Fantastic you may think, almost an AA battery, but then if you were to measure the voltage across the water rather than coffee, you will find that you get a voltage of 0.6-0.7V. The result for tea was, perhaps unsurprisingly, about 0.6V.
But voltage is not the whole story. A battery does not just supply a voltage, it gives a current. The current depends on the electrical conductance of the liquid that the electrodes are in. In the case of the potato or the lemon battery, the acid (phosphoric or citric respectively) means that there are free hydrogen ions in the ‘battery’ between the electrodes which mean the electric current can flow through the circuit. Coffee consists of many acids (chlorogenic, quinic, citric etc etc.) and so it seems sensible to ask if coffee could be used to produce a battery with a current that could power an LED? LEDs require both voltage and current, (1.6V and 10mA for the LEDs used here). Hooking up a series of coffee battery-cells meant that, by 6 ‘cells’, I had 3V across the contacts. However the electric current through the coffee battery was very low (the maximum current I recorded using the low acidity Roasting House Sierra de Agalta Honduran coffee prepared in a cafetière was 155 μA). Although this was higher than the current through water (max 81 μA), it is much lower than the current through white vinegar (770 μA under the same conditions). Consequently, in order to light the LED connected to my coffee battery, I had to add salt to each coffee cell which serves as a way of massively boosting the current through the coffee (salt forms a solution of Na+ and Cl- ions that conduct electricity through the coffee). Though even then, my LED only lit dimly and intermittently.
How it should be done. The “Alessandro Volta Temple” in Como, Italy, is a fantastic place to learn about the history of electricity
Sadly then, I do not see coffee power as a future for lighting in our cafés, (unless you want to use bulletproof coffee with salted butter). However, it has started to make me wonder, could we use a single coffee-cell to monitor the acidity of our coffee? If you find a method of brewing or a particular coffee especially acidic, it should produce a higher current for the same voltage through the cell, or equivalently, the resistance of the coffee-cell should decrease as the acidity of your coffee increases. Although obviously, it would be a bad idea to drink the coffee after putting it into a cell with copper and zinc (or aluminium) electrodes, you could pour a small amount of your coffee into a shot glass to test it while you were drinking the rest of the coffee. I intend on testing this hypothesis over the next couple of weeks but in the meanwhile, if you have thoughts on this to share (or the results of your experiments), please let me know either via the comments section, email, Facebook or Twitter.
The Black Penny is at 34 Great Queen St, WC2B 5AA
* A history of coffee houses can be found in “London Coffee Houses”, Bryant Lillywhite, (1963)
I finally got around to visiting Store St Espresso two weeks ago while visiting the nearby Institute of Making’s 3rd birthday science-outreach party. Although the café was crowded, we managed to find a place to perch while we enjoyed a soya hot chocolate, caffé latte and my V60. Beans are from Square Mile while the V60 and filter coffee options featured guest roasters. Despite the narrow frontage, there is actually plenty of seating inside and people were happy to share tables with other customers when it got particularly busy. The café is well lit with sunlight streaming in through the sky lights above (indeed, the extra electric lighting indoors seemed a bit unnecessary given the amount of sunlight coming through the windows on such a good day). On the walls of the cafe were pieces of artwork, including quite a large pencil/charcoal piece right at the back of the cafe.
I was meeting a friend for coffee before going to the science event and so thought it would be good to combine a cafe-physics review with a visit to the science. It is always interesting to hear other people’s observations of the same space that you are ‘reviewing’. In this case, I was taken by the floor which showed some very interesting crack structures but what fascinated my friend (who was enjoying her caffe-latte) was the way that the sound from the stereo was reflecting from the bare walls, floor and ceiling. While cracks and fracture processes can be very interesting, perhaps it is worth following her observations as it leads, in a round about way, back to the coffee that she was drinking.
A caffe latte and a soya hot chocolate at Store St Espresso
While studying for my physics degree, a lecturer in a course on crystallography told us an anecdote. The story concerned a physicist walking past an apple orchard. As he was walking past, he noticed that at certain points he could hear the church bells from a distant church. As he walked on, the sound of the bells faded, before suddenly, he could hear them again. The physicist went on to derive the laws of X-ray diffraction, a technique that is now used routinely in order to understand the arrangement of atoms in crystals (like salt, diamond or caffeine). X-rays are part of the electromagnetic spectrum (just like visible light) but they have a very short wavelength. The orchard had been inspirational to the physicist because, just as a crystal is a regular array of atoms, so the apple orchard is a regular array of trees; as you travel past an orchard (on the train, in a car or on foot), there are certain angles at which you can see straight through the trees, they have been planted in a 2D lattice. The church bells could only be heard at certain angles because of the way that the sound was being reflected from the multiple layers of the trees. The effect occurs because the sound made by church bells has a similar wavelength to the spacing of the trees (eg. ‘Big Ben’ chimes close to the note E, which has a wavelength of approximately 1m). The distance between atomic layers in a crystal is similar to the wavelength of the X-rays (the wavelength of X-rays frequently used for crystallography = 1.54 Å, size of the repeating structure in a salt crystal: 5.4 Å, 1 Å = 1/100000 of the smallest particle in an espresso grind). The physicist realised that the orchard affected the church bells in exactly the same way that the atoms in a crystal, be it salt, diamond or caffeine, will affect the deflection of X-rays. Suddenly, it became possible to actually ‘see’ crystal structures by measuring the angles at which the X-rays were scattered from substances.
Not quite a regular 2D lattice. By controlling the size of the bubbles and the number of layers, you can simulate the crystal structure of different metals. Seems I need more practice in making bubbles of a similar size.
We can perhaps imagine an apple orchard but what do crystals look like? Crystals can come in many forms, all they need to be is a repeating structure of atoms through the solid. Some crystals are cubic, such as salt, some are hexagonal, others form different shapes. Metals, such as that making up the shiny espresso machine in the cafe are often a certain form of cubic structure and to visualise it, we can return to my friend’s caffé latte (via some soap). Two people who were instrumental in understanding X-ray diffraction were the father and son physicists, William Henry and William Lawrence Bragg. While attempting to make a model of crystal structures, William Lawrence Bragg found that the bubbles that could be formed on top of a soap solution were a very good approximation of the sort of crystal structures observed in metals (his paper can be found here). As they form, the soap bubbles (provided they are of similar size) form a regular cubic structure on the surface of the soap solution held together by capillary attraction, a very good model for the sort of bonding that occurs in metals. By controlling the size of the bubbles, the number of layers and the pressures on the layers of the bubbles, all sorts of phenomena that we usually see in crystals (grain boundaries, dislocations etc) could be made to form in “crystals” formed from soap bubbles. Why not look for such crystal structures in the foam of your cafe latte, though be careful to see how the size of the bubbles affects the arrangement of the bubbles through the foam structure.
Sadly, I have never found a reference to the story of the physicist and the apple orchard and it may even have been apocryphal. The closest reference I can find is that W. Lawrence Bragg (after whom the laws of X-ray diffraction are named) had a “moment of inspiration” for how X-rays would ‘reflect’ from multi-layers of atoms while he was walking in an area called “The Backs” in Cambridge. If any reader of this blog does know a good reference to this story I would be very much obliged if they could tell me in the comments section (below). To this day, I have been unable to pass by an orchard (or even a palm oil estate in Malaysia) without thinking about crystal structure, X-ray diffraction and church bells!
It seems that taking time to appreciate how sound is reflected (or diffracted) from objects, either in Store St Espresso or in an apple orchard, could be a very fruitful thing to do. If you have an observation of science in a cafe that you would like to share, please let me know here.
Store St Espresso can be found at 40 Store St. WC1E 7DB
The physics of X-ray diffraction and some great bubble crystal structures can be found in the Feynman Lectures on Physics, Vol II, 30-9 onwards.
Does your coffee appear to steam more next to a polluted road than in the countryside?
This is a question that has been bothering me for some time. Perhaps it seems an odd question and maybe it is, but it is all about how clouds form. Maybe as you read this you can glance out the window where you will see blue skies and fluffy white clouds. Each cloud consists of millions, billions, of water droplets. Indeed, according to the Met Office, just one cubic metre of a cloud contains 1 hundred million water droplets. We know something about the size of these droplets because the clouds appear white which is due to the way that particles, including water droplets, scatter sunlight. Clouds appear white because the water droplets scatter the sunlight in all directions. In contrast, the particles in a cloudless sky scatter blue light (from the Sun) more than they scatter red. Consequently, from our viewpoint, the scattered light from the clouds appears white while the sky appears blue. The sort of directionless light scattering that comes from the clouds happens when the scattering sites (ie. the water droplets) are of a size that is comparable to, or larger than, the wavelength of light. This means that the water droplets in a cloud have to be larger than about 700 nm in diameter (or approximately just less than a tenth of the size of the smallest particle in an espresso grind). The particles in the atmosphere on the other hand scatter blue light more than they scatter red light because they are smaller than the wavelength of the blue light. You can find out more about light scattering, blue skies and cloudy days, with a simple experiment involving a glass of milk, more details can be found here.
A glass of (diluted) milk can provide clues as to the colours of the clouds in the sky as well as the sky itself
So each of the one hundred million water droplets in a cubic metre of cloud is at least about a micron in diameter. We can then estimate how many water molecules make up one droplet by dividing the mass of a droplet of this size by the mass of one water molecule. This turns out to be more than 1000 million water molecules that are needed to make up one droplet of cloud. So, 1000 million water molecules are needed for each of the 100 million drops that make up one, just one, cubic metre of cloud. These numbers are truly huge.
But can so many molecules just spontaneously form into so many water droplets? Unlike a snowball, the water droplet in a cloud cannot start very small and accumulate more water, getting larger and larger until it forms a droplet of about a micron in size. Water droplets that are much smaller than about a micron are unstable because the water molecules in the drop evaporate out of it before they get a chance to form into a cloud (precise details depend on the exact atmospheric conditions). Water droplets need to come ‘ready formed’ to make the clouds which seems unlikely. So how is it that clouds can form?
Look carefully at the rim of the mug. Do you see the condensation?
It turns out that the water droplets form by the water condensing onto something in the atmosphere. That something could be dust, or salt or one of the many other sorts of aerosol that are floating around in our skies. Just as with a cold mug filled with hot coffee, the dust in the air gives the water molecules a cold surface onto which they can condense. This sort of water droplet can ‘snowball’ into the bigger droplets that form clouds because the water is now condensing onto something and so does not evaporate off again so easily. At the heart of each water droplet in a cloud is a bit of dust or a tiny crystal of salt. Which brings me back to my question. It is much more dusty along a polluted road than it is in the clean air of the countryside. Is this going to be enough of an effect to affect the probability of cloud formation? Does your coffee steam more as you cross the road than when you walk through the park?
It is a question that demands an experiment (and associated video). Last year, the Met Office suggested this simple experiment for observing clouds in a bottle. Unfortunately however, I have yet to make this experiment work in a way that would allow me to test whether polluted air produces thicker clouds than cleaner air. If you have any suggestions as to a good experiment (that will work on camera!) please let me know either in the comments section, by emailing me, or on Facebook. In the meanwhile, I’d be interested to know what you think, so if you think this post is about you, please let me know.
