The material issue to be adopted for the construction of a telescope mirror is quite fascinating.
If you are starting with a hypothetical original question (We know a priori the solution) that is: If you must build a mirror for a telescope, what material is cheaper to do it?
The obvious answer and obvious who is to say now is: "glass", because obviously they get almost all so, But if we do not have it and it was the first time that you try to build one, How do you make an objective choice shrinking it a few possible candidates ?
Well, Initially we analyze and decide the essential requirements of the project, type: minimize the mass of the component at constant deformation ... etc, After that you will refine further the choice by applying more stringent requirements for the project.
As far a telescope mirror, You can start to narrow the choice this way:
In the image above are given two equations, the first expressing the deflection of a homogeneous disk subject to your weight (at the top left) and the second that expresses the mass of the disk as a function of its volume by the density (at the top right). Going to combine the two equations and esplicandole as a function of the total mass, you get the equation at the bottom left.
If we look at the terms on this equation we see that they are all geometrical terms dictated by the form chosen for the disk except the two terms in parentheses, Depending on the type of material that you choose for the mirror. Since the equation expresses the mass of glass disk, to minimize it, It must be the minimum that relationship in parentheses (³/ρ and), shown at the bottom right as M.
Obviously minimize ³/ρ and is the same thing I say maximize its inverse, i.e. E/ρ ³.
At this point we have gotten an index that will help us to compare different types of materials, and par do this, you rely on the maps created by Michael F. Ashby, and named precisely “Ashby maps”, linking between their two different physical properties of various materials.
Then for the case analyzed, among the numerous existing charters, You should refer to that which relates And it is (modulus of elasticity) with ρ (density).
To properly compare the various materials, Depending on the specific case you are parsing, you have to move on the chart using the right angle between the guidelines in the circle in blue. In the present case the entity to maximize the ratio E/ρ ³ equivalent course And it is1/3/ρ. Then using the straight line with slope indicated, You can compare the materials with the same specific report, and then figure out which of them have maximum performance.
To have a basis for comparison, I placed a line passing by the window class (circulate Red). At this point it is easy to appreciate what materials are better or worse than glass. It is important to remember anyway, that here we are investigating only the map that will provide us with what materials that minimize the mass at constant deflection of the disc, but nothing tells us about other aspects, as thermal stability, workability etc, that will be features that can refine the choice of material, After this first screening.
Either way it shows how silicon carbide, beryllium, CFRP (carbon fibre reinforced polymer) and some polymer foams have better performance than glass, While it's also obvious why aren't built metal mirrors (steel, aluminum, Titanium ...) that would be far heavier than those in glass.
Obviously some choices you can exclude without having to investigate further, Type i diamonds (for obvious reasons of price, dimensions, workability ...), or the Driftwood, which have high performance is dimensionally very unstable atmospheric conditions change (temperature, damp etc).
As mentioned before, in this first choice you have to add a second screening which takes into account other limiting factors affecting astronomical mirror, thermal expansion type. This can be done again using a different map of Ashby, like the one below, that relates the coefficient of thermal expansion with thermal conductivity.
Also know the thermal conductivity of a material and not only its thermal expansion (than in a first approach seems to be the only important parameter) need because on equal thermal expansion coefficient that presenting a greater conductivity better manages to make the temperature uniform on the whole mass of the mirror.
To give an example, a material with low thermal conductivity, means that, If you have a temperature gradient inside mirror, This gradient hardly would tend to disappear by standardising the temperature over the entire surface, causing internal stresses and differential contractions in the mirror then same.
In the map were highlighted the 5 types of materials that were deemed the best previous screening. Through this map, you can see that for example the polymer foams represent a low ratio between thermal expansion and thermal conductivity, not that very high absolute values of the coefficient of thermal expansion, by excluding them from candidates for building a mirror astronomical.
Silicon carbide and beryllium instead, have roughly the same relationship between thermal expansion and thermal conductivity even though the silicon carbide has a much lower thermal expansion coefficient.
The class of glass stretches on a wide range of values as for linear expansion, Although glasses for astronomical use can reach very low or close to zero, making them among the best possible materials in this sense.
The CFRP instead have a coefficient of thermal expansion between the SiC and beryllium and much worse than glass while being with their comparable thermal conductivity.
Looking closely at this map, you notice how the invar is absolutely the best material from this point of view, combining high thermal conductivity at very low thermal expansion values. These properties combined with excellent mechanical properties make it an excellent structural material for space telescopes, which often employ into their components. The high density but limits its use to a minimum.
Ultimately, But why not less important is the question of costs. Looking at the map below, You can get a rough idea of the costs involved for each material:
the last table shows once more, because the glass is still the undisputed masters of the scene when it comes to telescope mirrors, given their extremely low cost compared to competing materials, not forgetting, however, that possess good or excellent in all aspects analysed. Glasses as the thermal expansion coefficients or other glass ceramics ULE have next to zero and a good relationship between E/ρ ³ which makes them particularly suitable for both terrestrial and space telescopes. Examples include all major terrestrial telescopes, the Hubble space telescope, HiRise and a multitude of other instruments.
The silicon carbide is one of the absolute best materials for astronomical mirror from a mechanical point of view, Although values of thermal expansion not to the levels of the best glasses. The density slightly higher than that of glasses does not limit anyway the use having this material a high expansion ratio and thermal conductivity, which makes it very suitable for space telescopes, which suffer very much the different thermal expansion of different materials in contact with each other, whose differential expansion causes harmful stresses in the structure and in the mirrors. SiC being often used as a structural material for load-bearing plates of space telescopes it would mate perfectly with mirrors and their supports, that they may be made of the same material, greatly simplifying system design. Glass mirrors are often the norm even in telescopes, but their different thermal expansion than their media, get other materials, involves having to predict the appropriate systems to compensate for the strains not to induce additional tensions in the mirrors, which would be forfeited under performance. For example the largest spacecraft in orbit, the Herschel Space Observatory that has a mirror of 3.5 m f/0.5 (operating in the far-infrared wavelengths) is done in SiC, as well as all mirrors of the probe Plank and those of many other probes still.
Their high ratio of E/ρ ³ makes them good candidates from a structural point of view for a mirror astronomical, Indeed, several attempts have been made in the past and studies to verify its feasibility in construction , Although to date mirrors so get did not find widespread use in the optical wavelengths.
Against them all the thermal expansion coefficient that limits its dimensional stability with temperature, aspect of prime importance for optical applications, Although the continuous progress in this type of materials, has already led to the development of solutions with extremely low CTE, opening doors maybe, to a future (maybe even too far) Revolution.
Their extremely high mechanical performance, views on the first map of Ashby, would make them the materials that would limit the total mass of the mirror, and this explains why they are widely used in the construction of radio telescopes. An example of this are the antennae from 12 mete’ ALMA (radio waves), But even the primary mirror of 1.5 m of the Planck space observatory (infrared and submillimetre) It is a famous example.
does finally peeped into the list, also a member of the category of metallic materials. Unfortunately the beryllium material is considered a human carcinogen and its workability need for rules and specific controls. As we saw in the first paper of Ashby, It is by far one of the materials that minimizes the total mass of the mirror, Although its high coefficient of thermal expansion combined with high production costs and disadvantages due to its toxicity have limited considerably the spread. Things change drastically when we speak of cryogenic applications, or for those devices that must work at temperatures close to absolute zero.
At temperatures below to 80 K the thermal expansion coefficient of beryllium in fact boils down to almost zero, and mechanical properties remain respectable causing him to pounce on the first place for its Thermo-mechanical quality for astronomical mirrors. Clearly the cost and danger of the material limits however the spread, but it is no coincidence that the greatest, expensive and complex telescope that has (now) ready to launch into space has chosen the beryllium as a material for construction of the mirror. Obviously you are talking about the James Webb Space Telescope.
Another famous example of telescope, operating in the infrared, with its ritchey chretien by 85 cm beryllium optics, is the Spitzer Space Telescope.
And it is’ keep in mind, however, that screening made in the article is very preliminary, definitely gives some good general guidelines, but it does not take into account many other factors of which in reality you have to take into account, type workability, polishing degree that you can achieve in particular material, production process necessary etc.
Despite this though, Interestingly, with just two simple tables it was possible to determine critical judgment the best candidate materials for the construction of a telescope mirror, and how these results then, accurately reflect the solutions actually adopted, the result of these decades of studies and experiments.
a particular note needs to be done for ceramic materials and composites, These types of materials are having very rapid developments in recent years, with the continued production of solutions from amazing properties, It should not surprise, If in the near future, These types of materials will assert more and more for both telescopes that earthlings.