Moiré and Carbon Atoms

Here is one example of an optical phenomena coming from a common kitchen object, when briefly examined, I am surprised at the remarkable resemblance with something I've come across while attending microscopy lectures not too long ago. 

Figure 1

Anyway, this is a demonstration of Moiré pattern using a metallic teapot filter. If we pay attention to our surrounding, Moiré patterns are actually quite common! It is an intereference pattern caused by two grids overlaid at different grid size or orientation angle. This effect is the easiest to find when we cross two thin fabric over a bright light source. Try doing it! 

What I have, as mentioned, is a metallic filter that comes in cheap teapots. It has an arranged structure (like wire gauze or weaving of a thin linen) forming a mesh of individual holes with diameter not more than 0.5 mm. I used a white L.E.D as light source, trying to illuminate this object from various angle and capture the result Moiré pattern with my digital camera. 

Figure 2

The pattern itself is obvious even without specific lighting. But when we started to manipulate the light source, we can see how the contrast changes which are essentially reciprocal to each other. i.e. white change to black, vice-versa. 

Comparing figure 1 and 2, the patterns are reciprocal, albeit at a slightly different superperiod (superperiod is defined as the distance from one end of a repeating Moiré unit to another). Apparently the superperiod are affected by the camera's focal ratio and the distance of the teapot filter to the camera. I haven't yet explore this variable but I believe I would come back to that some day when I have a flat Moiré pattern generating object (like two pieces of transparency film with parallel lines) instead of a cylindrical (more accurately, a circular conical section) holey filter I'm using now. 

Anyway, you can say this Moiré pattern was generated by two superimposed mesh of pinholes. The pinholes are uniform in size so it is the tilt angle that creates this pattern.

Hence, from the superperiod, D, of the imposed pattern, we can estimate the angle of tilt, Z, following a few quantities such as the diameter of the pinhole, d, by this expression:

D = d / [2 sin(Z/2)]

From figure 1, we note that the superperiod is about 7 times the diameter of the pinholes. i.e. D ≈ 7d. So putting this into the equation above, should give us Z ≈ 8 degrees. Now, how do we verify this? 

Because the Moiré pattern was formed by superimposing symmetrical pinholes around a conic section,  which means the pattern is formed by overlaying the front and back part of a "cylinder", the angle of the cone can represent the angle of tilt of the pinhole mesh. 

Figure 3

Figure 3 shows the image of my teapot filter. By measuring the diameter of the bottom and the top of the conical section and the height of the filter, we are able to use simple geometry to calculate the angle of the cone, which roughly correspond to the angle of orientation tilt of the pinholes.

What I got, was 6.1 ± 0.9 degrees, taking account into the uncertainty of measuring all the parameters. So, comparing this result to the estimated tilt angle, well, it doesn't coincide perfectly but we see comparable results under forgivable error. After all, the superperiod was based on estimation of pinhole diameter without actual physical measurement. 

Anyway, what was important, is because this Moiré pattern was formed by circular pinholes, any physical phenomena that is caused by superimposing two grids of circles with identical diameter should yield the same Moiré pattern.

And that is precisely what I found in an article from the Cambridge Nanoscience Centre. According to the article, graphite (the thing that made pencil write on papers) which are made of stacks of one-atom-thick sheets of carbon (graphene) weakly "stick" to each other, can dislocate and slide from one another fairly easily. Because atoms are spherical (simply speaking), so when we see these superimposing sheets of atoms under special microscope (Scanning Tunneling Microscope) it will show interesting Moiré pattern, formed by the carbon atoms themselves! 

Figure 4

I mean, look at figure 4! When I photograph the demonstration, I used a L.E.D to cast a shadow of my teapot filter on the wall and the Moiré pattern emerged (left) matches so well with the Moiré pattern coming from overlaying two sheets of graphene that was seen using specialized microscopes (right). 

Now I'll never see my my teapot filter the same again - if at all, after I have broke the glass teapot itself which render its filter useless other than the purpose of novel photography.