Lasercut Contact Goniometer for Crystallography

Just a quick one this time. Here’s a simple lasercut design for a ‘contact goniometer‘ which is used for measuring the angles between two faces of a crystal.

 

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It’s lasercut from 3mm acrylic, and to make the engraved text stand out, I rubbed green acrylic paint on the surface, then wiped it off before it dried. The paint stays in the engraved sections and highlights them nicely.

By holding the edges against the crystal face, both the direct and internal angle can be read out. I was originally only going to include one scale, then I realised various people use different conventions.

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The object I’m measuring in the photos is the excellent 3d printed quartz crystal by Pmoews here.

Files up on thingiverse for anyone that wants to make their own.

 

 

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CPK Molecular Models with Polymer Clay

I’ve been getting into molecular modelling recently, and I wanted to experiment with different ways of making my own models cheaply and easily. I liked the colour scheme and layout of the CPK modelling made by Linus Pauling and others, but their models are fairly chunky, so I decided to go with half the scale they used (1 Angstrom now being 6.25mm)

This was my first idea, a 6mm deep template to mark out the right volume of clay for each atom type: thumb_IMG_2868_1024.jpg

Once you have the right amount of clay, a heavily scientific process known as ‘smushing’ is used to turn it into a sphere:

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A perfect 1.7 Angstrom radius carbon atom. 

While that worked, it wasn’t terribly quick. After playing around a bit, I redesigned it to allow multiple atoms to be cut out at once. Also, the edges of the jig are used to support a rolling pin exactly 6mm from the surface, so the volume is nicely repeatable.

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How you split an atom. 

Also note the different coloured markings on the edges, allowing you to divide up the clay for different atom sizes. I simplified it a bit down to only four sizes, since I figured people won’t be able to tell the different between a sphere of radius 1.52A and 1.55A just by holding it in their hand.

Once the atoms are divvied up, you can even put in some rare earth magnets to make a suitably geeky fridge magnet:

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Astute readers will note that the clay making up these atoms, is actually made of atoms also, which I maintain makes this a fractal. 

You should really use a better work surface than MDF too, my clay got all grubby because I didn’t think to prepare something cleaner. A glass countertop is perfect to work on and easy to clean afterwards.

Then just bake the clay as normal in the oven:

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Being cooked. Does that make this a reactor? 

Rather than my home oven which I’ve used previously, I used a turbo oven so I could bake them at the R+D space. Turns out the turbo oven I used either isn’t perfect for polymer clay, or I need to work on getting the airflow managed better. The models I made broke apart, but were easily superglued back together. I’m not concerned, the main thing I wanted to get sorted was the cutting jig, and I’m extremely happy with how that turned out.

While mushing clay atoms together isn’t going to give the world’s most precise atomic angles, it’s certainly capable of capturing the feel of a various compound, and I’d suggest it’s a good way to aid learning.

Files up here for anyone that wants to make their own:

https://www.thingiverse.com/thing:2406785

And if you do make your own model, please let me know and I’d love to see a pic!

 

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Lego Crystallography

I’ve been reading up on crystallography recently for an upcoming project, and I was having a hard time wrapping my head around Miller indices. I kinda got it, but I wanted something tangible to work with, darn it.

I started making 3D models in CAD, and also cutting up pieces of wood to glue together, when I realised that I already had a prototyping system in my living room that would be perfect for the job.

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Lego. Is any engineer’s bookcase really complete without it? 

It’s perfect for displaying the various crystal faces.

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Lego with a Miller Index of (1,0,1)

And you can see how the ratios of unit cells in X,Y,Z lead to different angles on the face:

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Playing around with these models gives one an extremely clear demonstration of the reason behind Steno’s Law (That angles between corresponding faces on crystals are equal for all crystals of the same material). In this metaphor “same material” translates to “same size unit cell” same size lego brick.

And of course the standard 100, 010, and 001 faces. In this case they’re at right angles to each other, but that’s only because the (lego) unit cell is orthogonal. It’s perfectly possible to find crystals where 100 and 010 faces are at angles other than 90 degrees. thumb_IMG_2979_1024.jpg

So, I’m now happy I understand the basics of the Miller Indices, but much like Mary Poppins, lego can’t stay still in one place forever. I decided to make a more permanent set of faces to have on hand so I could free up my lego again.

Here’s some I made from balsa bricks:

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The unit cell here is anything but cubic, which I’m actually quite pleased with. It shows how crystals aren’t just a collection of perfect platonic solids. 

And a few years ago I did a large bulk purchase of cedar cubes and spheres (I had a rough idea of making a marble computer), and I decided to put them to good use: thumb_IMG_2984_1024.jpgthumb_IMG_2983_1024.jpg

I attempted to try and cram in the most informative faces for a fixed number of cubes by fitting in the (0,~2,1) and (0,1,1) face as well.

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Turn Binomials into Gaussians with Polymer Clay

I’ve been playing a bit further with the visual demonstrations of the binomial/ central limit theorems. I love polymer clay as a medium, it’s extremely easy to work with, colourful, and you can even make fractal patterns with it.

Here’s my first approach, it turned out a bit less intuitive than I was hoping, but it was still fun to make.

The first step was to make a series of square stacks, encoding all possible 3-bit values (000, 001, 010…… 111):

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Then slice them in quarters and make long strands from each:

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Turn each one into a long rope:

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And assemble into a Galton board style device, with each path represented by the colour ordering of the strand (e.g. 010 = Left, Right, Left)

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You can immediately see that at the final clusters at the bottom, the number of each colour bands is the same (e.g. three blues, two blues and an orange, etc).

Representing that in the Galton board left-left-right leads to the same result as right-left-left.

I was fairly happy with that, but I wanted a more detailed model, and I decided to drop the encoded-strings idea as being to difficult to implement without distorting. Here’s my results for simple strings:

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This I’m pretty happy with. You can see at a glance why the middle result is 6x more probable than the right hand result (since six paths lead there versus only one), and you also don’t have to wait for the balls to collect as with the conventional display.

After baking the models in the oven for half an hour they’re now robust and permanant, and I’ll keep them on the shelf for the next time the central limit theorem comes up.

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Braided Galton Boards – Visualizing Probabilities with String

I’ve been playing around with Galton Boards recently. They’re an awesome demonstration of the central limit theorem, and how several independent 50/50 events sum together to make a Gaussian/Bell curve.

Seeing the standard Galton board gives an intuitive feel for how random variables behave, but it takes time to run the experiment and see the results accumulate.

I wanted a more immediate visual demonstration, and after a few prototypes I settled on using a thread to represent each possible path through the system:

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I used 12.5mm dowels cut to size, and hammered into the lasercut wood.

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The 64 and 32 string versions

The strings are cut to length, then held in place with a screw clamp and threaded through one at a time:

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Stats and craft therapy all in one

It might be because I finished this late at night, but I found it very difficult to thread without making a mistake. The strategy I ended up using was to hold the previous thread in my left hand and the next thread in my right. By jiggling my left hand I saw the old thread bounce, which gave a good reminder of where I was in the sequence, and hence to put the new thread in the right spot.

 

Files here for anyone that wants to make their own:

https://www.thingiverse.com/thing:2362584

It took a bit of prototyping before I got a form factor I was happy with. Here’s two of the failed attempts, that I avoided because they either weren’t practical, or they were slightly too opaque a display of the concept:

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Lasercut Yarn Bobbins

I’m working on a project that involves lots of different coloured cords, and I wanted a way to avoid tangles while transporting & working with them.

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Files here:

https://www.thingiverse.com/thing:2360450

 

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Bayes’ Ruler – A Bayesian Slide Rule

I’m a big fan of Bayesian statistics, and also old analog computers. It occured to me one day that I hadn’t ever seen a slide rule for calculating Bayes’ theorem…

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Behold a fine posterior

Here’s how to use it. Let’s say you’re a doctor, and treating a patient with a 80% chance of having gallstones. You order a new test done, and it comes back positive. What’s the probability they have gallstones?

After looking in the medical texts, you find the test is 5:1 more likely to be positive if the person has gallstones than if they don’t.

So, we align the arrow with our ‘prior’ on the left at 80% (4:1 odds), and look for the 5:1 diagnostic odds, which gives us a result of 20:1, or 95.2% probable the patient has gallstones.

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There’s far better explanations out there than this, please check out Wikipedia for what’s almost certainly better worded than mine.

I didn’t have the heart to design something like this by hand in inkscape. Instead I used Python and the DXFwrite library  to generate the files, and then lasercut it from acrylic.

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I also made a wooden version with a clear acrylic top, which should be less fragile in a bag:

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Files are here for anyone that wants to make their own:

https://www.thingiverse.com/thing:2347920

 

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