Sealing MEMS Devices with Glass

 

Krista Grayson

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December 5, 2023

Micro-electromechanical systems (MEMS) have revolutionized various industries by integrating miniaturized mechanical and electrical components onto a single substrate, enabling the creation of highly sensitive and efficient devices. They are key elements in an array of medical, automotive, industrial, and defense applications.

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However, the success of MEMS devices often hinges on maintaining a hermetic environment to protect their delicate internal components. This is where glass frit sealing technology comes into play, providing a superior solution for achieving reliable hermetic seals in precise applications like MEMS manufacturing and packaging.²

Understanding Hermetic Sealing and its Importance

Hermetic sealing involves creating an airtight barrier around a device to prevent the entry of contaminants, moisture, and other external elements. This sealing technique is crucial for MEMS devices as even minute environmental influences can alter their performance or lead to premature failure. In applications where stability, precision, and reliability are paramount, such as in the aerospace, medical, and telecommunications industries, achieving a hermetic seal is essential.²

Glass Frit Sealing: The Ideal Solution for MEMS

Among the various methods available to achieve hermetic seals, glass frit sealing stands out as a versatile and high-yield approach, particularly suited for MEMS applications. This technique leverages the unique properties of glass to create a reliable, robust, and precise encapsulation for MEMS devices while imposing minimal stress on the bonding surface. In a three-step process, a glass paste is screen-printed on a capping wafer, which is then bonded to the subject device through thermocompression for 10 minutes. During this process, 1000 mBar of force and 440 °C are applied to the material under a vacuum. Capable of bonding both hydrophobic and hydrophilic surfaces, this technique can be applied to almost all commonly used microsystem surface materials, such as aluminum, silicon, and glass.^3,4

Tailoring Precision Using the Coefficient of Thermal Expansion (CTE)

As the name implies, glass frit sealing makes use of glass particles, known as frit, which can be precisely formulated to match the coefficient of thermal expansion (CTE) of different materials.⁴ The CTE of a material refers to how its dimensions change with temperature fluctuations. By tailoring the glass frit’s composition, its CTE can be adjusted to closely match that of the MEMS device and the encapsulating material. This compatibility ensures that, when subjected to temperature variations, the seal remains intact without compromising the structural integrity of the device.²

Mo-Sci, a pioneering glass technology company, has been at the forefront of developing and perfecting glass frit sealing solutions for various high-tech applications, including MEMS devices. Its expertise lies in creating sealing glasses with customizable thermal expansion coefficients. With a diverse range of glass-metal and glass-ceramic seals that are meticulously matched in terms of CTE and are capable of enduring temperatures as high as 1600°C, Mo-Sci is an ideal partner for MEMS manufacturers seeking reliable hermetic sealing solutions.^2,5

The Versatility of Glass Frit Sealing

The applications of glass frit sealing extend beyond MEMS devices and encompass a range of cutting-edge technologies:

1. Solar Cells

Sealing glasses find utility in encapsulating perovskite photovoltaic elements. These elements are promising alternatives to traditional silicon solar cells due to their high efficiency and lower production costs. However, perovskite cells are highly sensitive to moisture, whereby even small amounts can completely prevent function. Laser-assisted bonding of glass frit sealing guarantees a durable hermetic barrier, shielding perovskite cells from moisture exposure and locking in lead-containing chemicals.²

2. Metal Ion and Thermal Batteries

In the evolving landscape of energy storage solutions, glass frit sealing plays a pivotal role in enhancing the reliability and longevity of metal ion batteries, including lithium-ion and sodium-ion batteries. These batteries require seals that can withstand high temperatures and resist chemical corrosion. Sealing glasses provide a resilient barrier that enables the efficient operation of these advanced battery technologies.

Sealing glass is also a viable solution for molten salt batteries. These batteries are highly dependent on sodium salts, including sodium-nickel and sodium-sulfur chloride, to achieve remarkable energy and power densities. For this reason, they are an appealing option for large-scale industrial and energy storage applications.

Sealing glasses are classed as a high-energy alternative to conventional polymeric or metal seals as they exhibit excellent resilience against demanding chemical environments but also against the rigorous operating temperatures inherent to molten salt batteries, which can range from 300 °C to 350 °C.²

3. High Temperature Sensors

Glass frit sealing also finds applications in high-temperature environments, such as automotive systems and chemical processing plants. The predictable thermal expansion and corrosion-resistant nature of sealing glass ensure the longevity and stability of sensors operating in extreme conditions.²

4. Solid Oxide Fuel Cells (SOFCs)

SOFCs hold tremendous promise for clean and efficient power generation, but their high operating temperatures present engineering challenges. To create high-temperature sealant materials for SOFCs, Mo-Sci currently utilizes two methods. One relies on a traditional glass-ceramic seal, wherein the glass undergoes crystallization to establish bonds with the sealing components.

The second approach involves the development of viscous-compliant glass seals. These seals remain vitreous throughout application and can self-heal, mitigating the risks associated with thermal stresses and ensuring the long-term stability of SOFCs.This groundbreaking technology is anticipated to play a pivotal role in facilitating the commercialization of SOFCs and driving their widespread adoption.^2,6

Embracing the Future with Glass Frit Sealing

Glass frit sealing technology has emerged as a transformative solution for achieving hermetic seals in MEMS devices and a wide array of other advanced applications. By precisely engineering the properties of sealing glasses, companies like Mo-Sci enable manufacturers to create highly reliable and robust encapsulation systems.

As industries continue to push the boundaries of technological innovation, the role of glass frit sealing in safeguarding sensitive components and ensuring optimal device performance becomes increasingly vital.

References and Further Reading

1. Forbes. Why Timing Must Be Tough Enough For Our Digital World. Available at: https://www.forbes.com/sites/forbestechcouncil/2021/09/02/why-timing-must-be-tough-enough-for-our-digital-world/ (Accessed on 10 August 2023).
2. Mo-Sci. Sealing Glass Applications. Available at: https://mo-sci.com/sealing-glass-applications/ (Accessed on 10 August 2023).
3. Chang H-D, et al. (2010). High hermetic performance of glass frit for MEMS package. 2010 5th International Microsystems Packaging Assembly and Circuits Technology Conference. https://doi.org/10.1109/IMPACT.2010.5699539
4. Knechtel R. (2015). Chapter 31 – Glass Frit Bonding. Handbook of Silicon Based MEMS Materials and Technologies (Second Edition). https://doi.org/10.1016/B978-0-323-29965-7.00031-2
5. Mo-Sci. Matching Coefficient of Thermal Expansion in Glass Seals. Available at: https://mo-sci.com/matching-cte-in-glass-seals/ (Accessed 10 August 2023).
6. Mo-Sci. Sealing Glass. Available at: https://mo-sci.com/products/sealing-glass/ (Accessed on 10 August 2023).

source:https://mo-sci.com/sealing-mems-devices-with-glass/?utm_source=Mo-Sci+Newsletter&utm_campaign=b5090c88ed-EMAIL_CAMPAIGN_2023_09_28_06_45_COPY_01&utm_medium=email&utm_term=0_-cf8dcfb60f-%5BLIST_EMAIL_ID%5D&mc_cid=b5090c88ed&mc_eid=0ab94327fb

Coe and compatibility

From time to time you will see the statement:

“CoE is the determinant of compatibility”

This is Not True!  

I wish I could come up with something simple to counteract this CoE fallacy, but glass is complicated and I can’t think of a snappy phrase to help.  To understand why the statement above is false, some background on what CoE does mean and what range of temperature it applies to is important.

What CoE measures

The coefficient of expansion can be a measure of either linear or volumetric expansion.  It is most often conducted over the range of 20°C to 300°C.  The result is expressed as an average over this range.  If there are variations in rates of expansion, they are absorbed in this coefficient, ie., average.  The measure is of the part of one metre the material expands for each degree Celsius increase in temperature.  In the glass community this coefficient is expressed as two digits such as 83 which represents the expansion of glass by 0.0000083 of a metre for each degree Celsius change in the measured temperature range.

Relevant temperature range

Note the temperature range over which this is measured – up to 300°C.  This coefficient works well for crystalline solids, but not for glass.  Amorphous solids do not have linear expansion rates throughout the working range of temperatures. Room temperature to 300°C is not a critical temperature range for glass.  After all, many of us turn the kiln off around 370°C.  This means that the CoE measured up to 300°C is not really relevant to us, as we have discovered that the expansion rates for 6mm or less thick glass are not critical below 370°C.

Annealing range

The CoEs at annealing temperatures – the critical range for glass -  are in the 400 to 500 range.  It is in the annealing range – generally about 45°C above and below the annealing point of the glass – that CoE is most important.  The annealing point is above the now popular, but lower, annealing soak temperature. This is where the glass is soaked to obtain a temperature with a differential of no more that 5°C throughout the glass.  The practice has become to do this temperature equalisation at the lower portion of the annealing range.  Often this is only 10°C above the lower boundary of the annealing range. This gives a shorter cool and increases the density of the glass. Do not confuse annealing point with the annealing soak. They are not the same.

Critical temperature range for CoE

The Coefficient of Expansion is more important at the glass transition point. This is the temperature at which the molten material becomes a slightly flexible solid. The CoE and the viscosity interact in this range.  It is critical, as the opposing forces of viscosity and CoE must balance.  The CoE is adjusted by the manufacturer to create this balance.  It shows that CoE is dependent on the viscosity of the glass.  And the characteristics of each colour must also match all the other glass in the range of tested compatible fusing glass. This is not a simple thing to do.  If it were, there would be lots of companies doing it.

Experience of moving to a single CoE for fusing glass

The Bullseye experience of attempting to achieve compatibility across a range of glass in the early days of making fusing compatible glass showed that less compatibility was experienced when the colours had matching CoEs. Lani Macgreggor describes this experience well in this blog, “Eclipse of the Fun”. 

An expert’s explanation

A Bullseye article by Dan Schwoerer - possibly the major expert on making compatible glass - on achieving compatibility through compensating differences is the key to understanding the balancing of CoE with the viscosity.  It is on the Bullseye site as Tech Note #3.

There is a more impassioned description of matters relating to compatibility in five linked blogs by Lani Macgregor in the To BE or not BE blog.

Manufacturing to a range of CoE

Spectrum long ago stated that the CoE of their glass ranges up to 10 points  to achieve a compatible range of fusing glass.  This is probably true for every manufacturer of fusing compatible glass. 

Why CoE is NOT the determinant of fusing compatible glass

The things that mean CoE cannot be the determinant of compatible glass are:

• ·        The coefficient is for an inappropriate temperature range for glass.
• ·        The critical temperatures for expansion are in the annealing range, for which there are no widely published figures.
• ·        The expansion rates need to be adjusted to match the viscosity in this annealing range.
• ·        A major manufacturer has indicated their glass, known by the CoE of its fusing standard glass, has a 10-point range of CoEs within their fusing range.

It is not true that CoE is a determinant of compatibility.

CoE is an inappropriate number to indicate compatibility.  It does not guarantee compatibility.  It is a suspiciously accurate number leading people to erroneously believe any glass labelled with a given number will be compatible with any other with the same number. 

Other blog posts on CoE:

CoE does not determine critical temperatures: 

https://glasstips.blogspot.com/2017/08/coe-as-determinant-of-temperature.html

Demonstration that CoE does not determine annealing or fusing temperatures:

https://glasstips.blogspot.com/2017/08/comparisons-of-coe-and-temperatures.html

Note on the physical changes at annealing

https://glasstips.blogspot.com/2014/03/annealing-physical-changes.html

Absence of any correlation between specific gravity and CoE:

https://glasstips.blogspot.com/2018/11/specific-gravity-cole-and-colourants-of.html

Compatibility of Glasses with the Same CoE

Questions such as “How compatible are Wissmach W90 and Bullseye?” are asked from time to time.  This does show some awareness that Bullseye may not be Coe 90 and that CoE does not equal compatibility.  The same question may be asked about whether Youghiogheny Y96, Wissmach W96 and Oceanside are compatible with each other.

What is CoE

It is important to know what CoE means before the question can be answered.  It is a measure of average expansion from 20°C to 300°C.  This is suitable for crystalline materials as their low temperature expansion rates can be projected onto the behaviour of the material until near molten temperatures.  However, it is not suitable for non-crystalline materials, such as plastics or glass, as their behaviour is much more unpredictable as the temperature rises.  Measurementsof CoE have been made of glass at the glass transition temperatures which show at least seven times greater expansion near the annealing temperature than at 300°C. 

An extended essay on compatibility written by Lani Mcgregor is here, 

and here

Compatibility Tests

The degree of compatibility is uncertain between different manufacturers.  Each manufacturer will take their own way toward balancing the viscosity with the CoE.  While they can say their glass has similar characteristics to another manufacturer’s glass, they cannot guarantee compatibility.

When using glass from different manufacturers together, the best advice is to test the glasses yourself for compatibility. Do this before you commit to the project.  Bullseye notes how they do their stress tests on the education section.  I have been unable to ascertain how other manufacturers test for compatibility within their range of fusing glasses.  Another simple method of testing for stress is here.

There are reports that W90 and Bullseye work together and others that say they don’t.  There are those that say the 96 CoEs work with Oceanside, and those who say they don’t. Testing for yourself is the only way to know what works.

Scale

It seems that combining different manufacturers’ glasses may work at smaller scales, but less well at larger.  Since very few people test for compatibility before, or after, when combining different manufacturer's glasses, they don't know whether their pieces are showing signs of stress. Just because the pieces do not break immediately does not mean they are compatible or stress free. 

Size, Shape and Quantity

You should also note that the relative sizes and shapes of the combined glasses effect the survivability (rather than compatibility) of the piece.

Shape

The shape of the main piece has an effect.  Circular or broad ovals can contain the stress much more easily than a long rectangle or a wedge-shaped piece.

The same applies to the pieces added.  Pointed pieces concentrate the stress more than rectangular ones.  The stress from circular additions are easier than rectangles for the base piece to hold.

Placing

Where you place the additions is important.  Anything placed near the edge of the base is more likely to cause enough stress that it can not be contained and so the piece breaks.

Mass

How much of another manufacturers’ glass are you putting on the base?  The bigger the area or the thicker the piece(s) the less well the base will be able to hold the stress before breaking.

CoE Useage

Does anyone know what CoE means?

·         First the proper abbreviation is CoLE.

·         This means Coefficient of Linear Expansion.

·         A coefficient is an average.  This number may be exact at a given temperature, or an average over a range.

·         Linear is the length.  

·         Expansion is measured in fractions of a metre e.g., 0.0000096 metre.

·         The coefficient is given as the average amount of expansion per each degree Celsius.
     The temperature range used is 20C to 300C.  Expansion characteristics vary greatly at higher temperatures.

So CoE is the average amount (in metres) that glass expands for each degree (Celsius) increase in temperature from 20C to 300C. 

Whether you call it CoE or CoLE is immaterial, as it still does not equal compatibility.

It does not measure viscosity. Viscosity is a (possibly the major) element in making a range of compatible fusing glasses.

It does measure expansion rates, but up to 300C only.  It does not tell you how glass expands above that temperature.  Note: it does not behave in a linear pattern as crystalline materials do.

The CoE must be adjusted to match the viscosity to achieve compatible glass.  Spectrum has stated that their glass has a range of CoE of at least ten points to make compatible fusing glass.  Bullseye have stated their range to be 5 points. They also have indicated their base glass is nearer to 91 than 90.  

The only constant required in fusing glass is compatibility. 

CoE varies within each manufacturer’s range of fusing compatible glass to match the viscosity. And remember the CoE of glass at the critical annealing point is  higher than the low temperature expansion rate. See this post for details.

Viscosity varies according to the materials used in the colouration of the glass and their proportions, requiring the glass manufacturer to make adjustments in CoE to get compatible fusing glass.  More information here.

CoE does not mean compatibility.  It does not measure volume expansion at the glass transition point.  It does not measure the most important element – viscosity.  It is not even the correct term for the measure – CoLE is.

Since CoE does not mean a fusing compatible glass, its continued use can lead people (especially novices) to believe the simple number means any glass labelled with that number will be compatible with others so labelled.  This leads to unexpected incompatibilities for newcomers to the field.

My plea is: STOP USING COE TO MEAN COMPATIBILITY.

What can you use instead? It is easy – use the manufacturer’s name.  Where the manufacturer is making more than one range of fusing compatible glass use the manufacturer’s nomenclature.

Please: STOP USING COE TO MEAN COMPATIBILITY.

CoE as the Determinant of Temperature Characteristics

Many people are under the impression that CoE can tell you a wide number of things about fusing glass. 

What does CoE really mean?

The first thing to note is the meaning of CoE.  Its proper name is the coefficient of linear expansion.  It tells you nothing certain about the expansion in volume, which can be as or more important than the horizontal expansion. 

It is an average determined between 20°C and 300°C.  This is fine for materials that have a crystalline structure. Glass does not.  Glass behaves quite differently at higher temperatures. 

It may have an average expansion of 96 from 20°C-300°C – although there is no information on the variation within that range – but may have an expansion of 500 just above the annealing point. 

The critical temperatures for glass are between the annealing and strain points.  One curious aspect to the expansion of glass is that the rate of expansion decreases around the annealing point.  The amount of this change is variable from one glass composition to another.

The CoE of a manufacturer’s glass is an average of the range which is produced.  Spectrum has stated that their CoE of their fusing compatible glass is a 10 point range.  Bullseye has indicated that their CoE range is up to 5 points. These kind of ranges can be expected in every manufacturer’s compatible glass.

CoE does not tell us anything about viscosity, which has a bigger influence on compatibility than CoE alone. 

Comparison of CoE and Temperature

Among the things people assume CoE determines is the critical temperatures of the strain, annealing and softening points of various glasses.

Unfortunately, CoE does not necessarily tell you fusing or annealing temperatures. 

“CoE 83”

Most float glass is assumed to be around CoE 83.  The characteristics depend on which company is making the glass and where it is being made.

Pilkington float made in the UK has an annealing point of 540°C and a softening point (normally the slump point) of 720°C.

Typical USA float anneals at 548°C and has a softening point of 615°C.

Typical Australian float has a CoE of 84 and anneals in the range 505°C -525°C.

“CoE 90”

Uroboros FX90 has an annealing point of 525°C compared to Bullseye at 482°C, and Wissmach 90 anneal of 510°C. 

Wissmach 90 has a full fuse temperature of 777°C compared to Bullseye's 804 - 816°C.   

There is a float glass with a CoE of 90 that anneals at 540°C and fuses at 835°C.

Bullseye has a slump temperature of 630°C-677°C and Wissmach’s 90 slumps between 649°C and 677°C, slightly higher.

“CoE 93”

Kokomo with an average CoE of 93 has an annealing range of 507°C to 477°C. Kokomo slumps around 565°C

“CoE 94”

Artista with a CoE of 94 has an annealing point of 535°C and a full

fuse of 835°C, almost the same as float with a Coe of 83. 

“CoE96”

Wissmach 96 anneals at 482°C with a full fuse of 777°C and a slump temperature of 688°C.

Spectrum96 and its successor Oceanside Compatible anneals at 510°C and full fuses at 796°C.

Conclusion

In short, CoE does not tell you the temperature characteristics of the glass. These are determined by several factors of which viscosity is the most important. More information can be gained from this post or from your own testing and observation as noted in this post.

"CoE Equals Compatibility" - Kiln Forming Myths 10

CoE equals compatibility.

This is as persistent myth.  CoE is an abbreviation for Coefficient of Linear Expansion.  It is not an abbreviation for Compatibility.  

Apparently, CoE is used by manufacturers of glass that is being marketed to capitalise on the popularity of fused glass without the necessity of carrying out the testing and quality control required to ensure compatibility.  It is also used as a marketing device by wholesalers and retailers possibly to make greater sales.  It is used by individuals who have been lead into sloppy thinking about the materials they are using.

There are several facts to reinforce the assertion that CoE does not equal, nor is a shorthand for, compatibility.

·         Glass marketed as CoE90 or CoE96 has to be tested by the user.  Many users have often found that the compatibility with their other glass is suspect and inconsistent. This comes from breakages that occur with one sheet of glass but not another.

·         The System 96 range was made by two glass manufacturers who had testing and quality control to ensure their whole range is compatible.

·         Uroboros makes fusing compatible glass that many claim to be compatible with Bullseye.  In general, that is the case.  But many have found that it is important to test the compatibility of the glasses from Uroboros and Bullseye against each other before committing to a project, as the compatibility is not (and cannot) be guaranteed.

·         Not all float (window) glass is compatible between manufacturers.  Even the coloured glass is marketed with a range of 6 CoE points.  And some float glass is not compatible with the accessory glass. There is even a float glass that has a CoE of 96, but it is nowhere near compatible with System 96 glass.

·         There are physical reasons too.  Coefficient of Linear Expansion is tested as the average expansion between 20°C and 300°C.  This is the brittle range for glass.  We are much more interested in what happens at the glass transition point – the small range of temperature where the glass changes from a viscous liquid to a solid – generally between 480°C and 530°C. 

·         At the glass transition there is a surprising (to me) reduction in the CoE before a rapid rise.  This variation is influenced by the viscosity of the glass.  Also, at this temperature the CoE is much higher than at the measured region and cannot be taken as a guide to what is happening at the transition point.

·         In the early attempts to make compatible glass for fusing, it was discovered that the closer to the same CoE the glass was made, the less compatible it became.

·         Viscosity is the important element in the making of compatible glass.  The change in viscosity at the glass transition point must be balanced with the expansion characteristics of the glass.  A more viscous glass requires to be balanced by a different CoE glass than a less viscous one. Thus the CoE is being adjusted – not the viscosity – to balance the forces within the glass.

·         Finally, I believe the CoE of Bullseye’s clear glass is actually 90.6 rather than 90, so if we are rounding, Bullseye might be called CoE91. 

Whether the clear CoE90 or CoE96 of other manufacturers is the same as the Bullseye, System96, or Uroboros is not the relevant point.  The relevant point is whether it is compatible.  Whether these other companies have the quality control to ensure all their glass is compatible with the claimed fusing glass without further user testing is the essential point.  At this time, it appears that they do not have that capacity.  So, those using glass marketed as CoE90 or CoE96 will need to continue to test for compatibility with each sheet they use.

Other posts on Compatibility are here:
Is Coe Important?
What is Viscosity?
CoE varies with temperature
Defining the glass transition stage

All myths have an element of truth in them otherwise they would not persist.

They also persist because people listen to the “rules” rather than thinking about the principles and applying them.  It is when you understand the principles that you can successfully break the “rules”.

CoE and Temperatures

CoE as a Determinant of Temperature Characteristics

What CoE Really Tells Us

The wide spread and erroneous use of CoE to indicate compatibility (it does not) seems to have led to the belief that CoE tells us about other things relating to the characteristics of fusing glasses.  It is important to know what CoE means.  

First it is an average of linear expansion for each °C change between 0°C and 300°C.  This is fine for metals with regular behaviour, but not for glasseous materials where we are more interested in the 400°C to 600°C range.  Measurements there have shown very different results than at the lower temperatures at which CoLE (coefficient of linear expansion) are measured.  In kiln forming we are also interested in volume changes and CoE tells us nothing about that.

Unfortunately, CoE does not tell you fusing or annealing temperatures. 

And not even relative temperatures.  

Some examples: 

• Uroboros FX90 has an annealing point of 525C compared to Bullseye (516/482C), and to the Wissmach 90 anneal of 510C. 
• Wissmach 90 has a fuse temperature of 777C compared to Bullseye's 804C.  
• Another example is Kokomo with an average CoE of 93 which has an annealing range of 507-477C and slumps around 565C. 
• There is a float glass of a CoE of 90 that anneals at 540C and fuses at 835C.  
• Artista (which is no longer made, except in clear) had a Coe of 94 with an annealing point of 535C and fuse of 835C, almost the same as float with a Coe of 83. 

These examples show that CoE can not tell you the temperature characteristics of the glass. These are determined by a number of factors of which viscosity is the most important. More information can be gained from this post on the characteristics of some glasses, or from testing and observation as noted in this post .

CoE does not tell you much about compatibility either, since viscosity is more important in determining compatibility.  CoE needs to be adjusted and varied in the glass making process to balance the viscosity of the glass.  Viscosity is described here .

This post and its links describes why Coe is not a synonym for compatibility. 


What CoE REALLY tells us is that we look for simple answers, even when the conditions are complex.  

Mixing COE

Our use of Coe as an equivalent for compatibility can lead to difficulties. The only compatibility that can be relied on is that given by the manufacturer. No manufacturer can attest to the compatibility of another manufacturer's glass. They can only verify their own.

So, if you mix manufacturers' glass even though advertised as the same COE, it does not make them compatible. There is much more than expansion rates that goes into compatibility. You need to test different manufacturers' glass against each other before you use it.

These are notes on aspects of compatibility.

COE

Importance of COE

COE variations

Viscosity

Annealing

Is CoE Important?

CoE is more important to the manufacturer (in combination with viscosity) than to the kiln worker. It has gained a heightened profile, as it has been used as a shorthand for compatibility. So it is important to know what CoE is and what the numbers mean.

“During heat transfer, the energy that is stored in the intermolecular bonds between atoms changes. When the stored energy increases, so does the length of the molecular bond. As a result, solids typically expand in response to heating and contract on cooling; this response to temperature change is expressed as its coefficient of … expansion. 





“The ... expansion coefficient is a thermodynamic property of a substance. It relates the change in temperature to the change in a material's linear dimensions. It is the fractional change in length [metres] per degree [C] of temperature change [expressed as a two digit whole number]. 





“Most solids expand when heated. The reason for this is that this gives atoms more room to bounce about with the large amount of kinetic energy they have at high temperatures. Thermal expansion is a relatively small effect which is approximately linear in the [absolute] temperature range.”

Source

What does CoE mean?

There are at least two types of expansion with increasing temperature. One is volume expansion and the other that we are more interested in, is the linear expansion. “The Coefficient of Linear Expansion of a substance is the fraction of its original length by which a rod [or sheet] of the substance expands per degree rise in temperature.” Source 

What do the numbers mean?

The numbers attached to a CoLE -usually referred to as CoE – are an expression of the average amount that a material expands per degree over a given temperature range. The standard temperature range is 0ºC to 300ºC and the unit of length is one metre. They are expressed as a two digit number times 10 to the power of -6. That means the two digit number really has 6 decimal points in front of the whole number. So a CoLE of 85 means the same as an expansion rate of .000085 metres per degree C; or .0085mm/ºC.

However the rate of expansion is not a straight line when graphed against higher temperatures. The ranges in which kiln formers work show an erratic and much higher rate of expansion. Have a look at the CoE ranges at different temperatures to see how variable the expansion rates are at elevated temperatures.  Other examples are:

Graph showing the change in the CoLE of aluminium between 0ºC and 527ºC (Kelvin being about 273 degrees lower than Celsius)

This graph shows a material that actually contracts briefly as it warms.  Its CoLE would be between 20 and 35 - an extremely low rate of expansion.

This shows an idealised material that has a CoLE of  about 40 at 0ºC and around 60 at 300ºC, remaining thereabouts as the temperature rises toward 1200ºC

Should We use CoE?

CoLE is “a meaningless number unless defined by the temperature range in which the measurement is taken. Calling any glass or glass combination “compatible” without specifying under what conditions is no more useful than identifying a glass by its COE without specifying the relevant temperature range.” [L. MacGreggor]