Use of the material Zerodur in the KECK observatory telescope. The very low CTE makes ZERODUR ideal for use as part of the primary mirror. This means that over the temperature range that is possible that the telescope works in, (0-50C), the materi

Introduction

The KECK observatory lies near the summit of Mauna Kea in Hawaii. There are two telescopes close to each other on the summit, KECK I and KECK II. These combine to form one of the largest optical telescopes in the world, second only to the Gran Telescopio Canarias (GTC) in the Canary Islands. For good reason, both the KECK observatory and GTC use the same material for their primary mirrors.

The primary mirrors of the telescopes are the largest mirrors of the operation, and are designed to gather as much light as possible. The bigger the primary mirror, the more light the telescope can gather, and hence the ‘further’ into the solar system the telescope can see. With the need to see more and more of space, larger and larger telescopes are being built. However, making a mirror with a diameter of 10 metres of more out of a single sheet of a reflective substance gives a very large problem; the mirror must be very thick in order to hold its shape. When KECK I was being designed, the engineers came up with an ingenious solution, which involved splitting up the mirror into many hexagonal sections, which, when attached together, would act as a single mirror. This meant that the primary mirror would be made from smaller sections, allowing easier maintenance, installation and construction. The mirror is made of 36 hexagonal sections, and forms a slight curve, as shown in figure 1.

Fig 1. – A diagrammatical representation of the 36 segment mirror. The black hexagon in the middle represents a gap; placing a mirror here would be pointless as the light that would hit this part of the mirror is obscured by the secondary mirror, which is attached straight above this, and collects the light reflected by the other primary mirror1.

In order to work as precisely as possible, the gaps between the mirror segments must be as small as possible. During operation, the mirrors are supported by a system of active optics, which continuously adjust the mirror segments to maintain the optimal shape. The mirrors are moved by a complicated system of sensors that position the mirrors within 4nm (4 billionths of a metre) of each of the neighbouring segments2. Because such precision is required in order for the mirror to function at maximum capability, the materials that the primary mirror is made of need to stay at one size; any expansion will render the active optics useless, and will cause gaps between neighbouring mirrors.

Consequently, the mirror segments were made of a material with a near negligible coefficient of thermal expansion (thermal expansion is the amount that a material expands or contracts when it undergoes heating). This is a material called ZERODUR®, a glass-ceramic manufactured by the German company Schott. This makes up the base of each mirror segment, and is coated in a very thin layer of highly polished aluminium to give the mirror segment its reflective properties.

This picture shows a segment of the mirror before it is coated in the reflective aluminium. This photo gives an idea of the scale of the pieces of the mirror.9

Several properties of ZERODUR® make it perfect for use in telescopes;

Very low coefficient of thermal expansion (CTE)
High material homogeneity
Can be coated easily

Certain properties, such as the Young’s Modulus of the material, are not relevant to its usage in telescopes, other than to say that these are adequate for the job. For example, ZERODUR® is quite a brittle material, but ...

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This picture shows a segment of the mirror before it is coated in the reflective aluminium. This photo gives an idea of the scale of the pieces of the mirror.9

Several properties of ZERODUR® make it perfect for use in telescopes;

Very low coefficient of thermal expansion (CTE)
High material homogeneity
Can be coated easily

The very low CTE makes ZERODUR® ideal for use as part of the primary mirror. This means that over the temperature range that is possible that the telescope works in, (0-50˚C), the material won’t expand or contract much, meaning that any gaps in the mirror are due to the active optics (AO) system. However, when the two are combined; ZERODUR® and the flawless AO system, it is possible for the primary mirror to work almost perfectly. Across the temperature range of 0-50˚C, the temperature coefficient of ZERODUR® (Expansion class 0 – the best version that Schott make) is 0 ± 0.02 x 10-6m m-1 K-1.3 This means that for every increase or decrease of 1K, the material will expand or contract 0 ± 0.1 x 10-6m (or, 0 ± 0.1μm per Kelvin). When by itself, the CTE of a material carries little value; hence it is easier to compare the CTE of ZERODUR® to other known materials in order to get a feel for just how appropriate it is for the usage in telescopes.

Some known values of CTE are shown below. Because the CTE of most metals is not constant across a wide temperature range, the values below are for when the material is at 25˚C. All values use the units 10-6m m-1 K-1;

Gold - 14.2.4
Porcelain - 4.5.4
Glass - 8.5.5
Water - 69.5
Stainless steel - 17.3.5

Clearly then, with varying conditions within the building in which the telescope is housed; using other materials such as stainless steel would have caused major problems for the mirror. For example, using stainless steel;

CTE: 17.3 μm m-1 K-1

Expansion for a temperature change of 5 degrees across a mirror support 2m in diameter;

2m x 17.3 x 5K = 173μm, or 0.173mm

Obviously, this would produce a notable gap between the mirrors, and more importantly, one which the AO system couldn’t counteract.

Chemical composition and properties

There are several ‘systems’ of glass-ceramics, which in essence all differ in chemical composition. All compositions feature oxides of silicon and aluminium; however the oxides in the material differ depending on the system. For example, The MAS System uses oxides of magnesium, aluminium and silicon, whereas the LAS System contains oxides of lithium, aluminium and silicon. The LAS system is the most commonly used, and is what ZERODUR® is made of. Other uses of the LAS system include cooktops, though this is more to do with the fact that the LAS system can deal with repeated quick temperature changes, and also that it has a very low heat conduction coefficient; it is nearly transparent to light with wavelengths near and including infrared. Since it is this radiation that does that heating; hence it is beneficial if such radiation is not absorbed by the material.

In material terminology, the macrostructure of a substance is how it behaves, and properties associated with it. Examples would be things like if the material is ductile, brittle, or how hard it is.

The microstructure of a material is the molecular make up of it. This would be things like the arrangement of individual atoms or molecules, or whether the substance is amorphous or crystalline. It is important to note the difference between amorphous and crystalline as the arrangement of atoms in a molecule has a huge impact on its macroscopic properties. An amorphous substance is one in which the atoms aren’t ordered into any repeating order; they are randomly distributed throughout the volume of the material. Imagine a forest that has been planted by nature; there is no order to the placement of the trees. This is like an amorphous substance. However, imagine a forest that has been planted by humans; the trees are in rows, in a very ordered fashion. This is like a crystalline substance, where the atoms are all in a regular array. A crystal is an area of a material where all the atoms are in a regular array. The two build ups are shown in the diagram below (fig. 2).

Fig 2. – A comparison of the chemical builds of amorphous and crystalline substances.6 The black and white atoms represent two different elements, such as silicon and oxygen. The diagram on the left shows the chaotic, random arrangement in an amorphous substance, such as wax, while the diagram on the right shows the arrangement in a crystalline substance such as diamond. It is important to note that not all arrangements feature the hexagonal shape as in the diagram on the right, this is merely an example.

Both of these atomic arrangements are important because the formation of ZERODUR® contains both an amorphous phase and a crystalline phase. To start with, the mixture of chemicals is heated to form a liquid and then rapidly cooled. This is the amorphous phase, and features a random arrangement of the atoms. Amorphous solids are sometimes classed as super-cooled liquids, as, given time, the molecules within the substance will slowly slide past each other; they act as really cold liquids do. Glass is an example of such a substance. The ‘sliding past’ of its molecules can be seen in old houses and buildings, where the glass at the bottom of some windows is thicker that at the top.

However, if the hot liquid is slowly cooled, it is possible to make a crystalline substance. In contrast the amorphous phase of the material, the crystalline substance is regular in its arrangement of the atoms and molecules. The difference in structure is due to two things;

The nucleating agents that are added during cooling. Theses agents provide points around which crystals can arrange themselves and grow outwards. As there are many nucleating agents, there are many crystals that form around these; hence the final product is termed polycrystalline: It is one large structure made of several crystals that feature highly ordered atoms (see figure 3).
The slow cooling of the liquid forms fewer crystals. Ideally, over a huge period of time, it may be possible to form one, huge crystal.

Fig 3. – A false colour electron micrograph of the polycrystalline structure of electrical steel.10

Consequently, Schott use a combination of nucleating agents and cooling speed to get the right balance between quality and crystallinity. Furthermore, if perfect quality is not required, then it is easier to put in more nucleating agents or cool the liquid slower. Naturally, this version of ZERODUR® is cheaper.

Since it’s absolutely essential that the material supporting the mirror is made of a substance that won’t expand, it is better than the material is crystalline, as the substance will have increased homogeneity; the arrangement and distribution of the atoms within the substance will be near uniform throughout the atomic array. This is another key property of ZERODUR®; it has high homogeneity, meaning that any thermal expansion will be nearly uniformly distributed, so under extreme heating, the material will expand the almost same amount in every direction.

A very interesting and useful property of glass-ceramics is the changing CTE across the temperature range. The CTE is determined by the percentage of the material that is crystalline and the percentage that is amorphous. In order to achieve the 0 expansion coefficient that is required for the usage in the KECK observatories, it is necessary to balance the mix of elements, cooling rate and amount of nucleating agents in order to get the coefficients of thermal expansion of the crystalline and amorphous phases to balance across the right temperature range (in the case of ZERODUR®, the ideal range is 0-50°C). In ZERODUR® the thermal expansion coefficient is 0 in the range from 0-50°C7 because the balance of crystalline phase and amorphous phase is perfect.

As can be clearly seen from figure 4, there is a plateau where the temperature ranges between 0°C and 50°C. This signifies the 0 expansion coefficient.

Fig 4. – A graph showing the thermal expansion coefficient of ZERODUR® across a temperature range of 0 and 900K.7

Conclusion

As we have seen, ZERODUR® has a nearly flawless profile when it comes to choosing a material for usage in telescopes. It’s thermal expansion coefficient of near 0 ensures that the material is will expand or contract under heating or cooling by a negligible amount, allowing the AO system to keep the individual mirrors functioning as a single mirror to a very high level of precision. Furthermore, the high homogeneity of the material ensures that any expansion or contract of the material will be uniform, meaning it is easier for the AO system to counteract this by moving the mirrors. Finally, it can be easily coated, meaning there is little technical difficulty applying the reflective coating of aluminium.

This combination of a highly reflective coating of aluminium, ZERODUR®, and the adaptive optics system provide scientists with a near flawless system of looking further into the distances of space. This system of splitting the primary mirror into smaller section and using AO systems to keep then in the correct position is cutting edge technology, and is being used in nearly all new telescope designs, including in the James Webb Space Telescope.8

Bibliography

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Reference 10

ZERODUR® in the KECK Observatory