The Importance of Viscosity in Slumping

 What is viscosity?

The official definition is that it is a measure of the resistance to flow, e.g., honey vs water, or hard vs soft glass.  Honey and hard glass have greater resistance to flow. 

Importance of viscosity

In slumping, large differences in viscosity of the combined glasses will have different rates of deformation across the piece.  There is the possibility of uneven slumps as a result.  The stresses between the different viscosities may cause breaks or splits with rapid temperature rises.  Combining large differences in viscosity requires more caution in ramp rates and in annealing and cooling.  Of course, unusual results can be obtained by manipulating time and temperature.

Effect of temperature

Viscosity is affected more directly by temperature than heat and time.

Credit: Bullseye Glass Company

There are frequent statements about viscosity such as dark glass is less viscous than light, or transparent is less viscous than opalescent.  Also, Bob Leatherbarrow ran some slumping testes showing thick glass slumped less at a given temperature than thin.  Further, Ted Sawyer mentioned to me that some opalescent is less viscous than some transparent glass.   My experience is different, so I wanted to test my assumptions against theirs.

Experiment setup

25mm/1" wide strips were suspended with a span of 20cm/8".  Weights were placed on ends to avoid any slipping.  

Does comparative viscosity vary with temperature?

I fired samples at three temperatures and times

• 600C for 30 minutes
• 650C for 1 minute
• 690 for 1 minute

All at 150C/hr to top temperature.  The short soak time for the higher temperatures were because the glass deformed so quickly.

Results

Bullseye glass. Span of 20cm. Fired at 150C/hr to 600C for 30 minutes

            Code - name - deformation from horizontal

0126 Light Cyan              16mm

0243 Translucent White    20mm

0013 Opaque white         21mm

1101 Clear Tekta             21mm

0100 Black                     24mm

0141 Dark Forrest Green 24mm

1122 Red                       24mm

0161 Robbins egg blue    26mm

0137 French vanilla        27mm

1427 Light amber           27mm

1428 Light violet            29mm

0303 Dusky lilac            32mm

1125 Orange                 32mm

0147 Deep cobalt blue   33mm

0113 White  (.0038)      34mm

0126 Orange                 35mm

1246 Copper blue          37mm

1320 Marigold yellow     40mm

1341 Ruby pink sapphire 40mm  

(special production)

Most opals in this test were more viscous than the transparent glasses.  There are some exceptions such as Dusky lilac, Cobalt blue, Orange.  There were some exceptions too in the transparents: black, red, light amber.

Bullseye glass. Span of 20cm. Fired at 150C/hr to 650C for 1 minute

            Code - name - deformation from horizontal

0100 Black                    26mm

0013 Opaque white        30mm

1122 Red                      30mm

1428 Light violet           30mm

0243 Translucent white  31mm

0141 Dark forest green 31mm

0161 Robins egg blue    31mm

0147 Deep cobalt blue   32mm

0126 Orange opal          32mm

1101 Clear tekta           33mm

1125 Orange                34mm

0137 French vanilla       35mm

0216 Light Cyan            38mm

0303 Dusty lilac            38mm

1341 Ruby pink sapphire 39mm

1437 Light amber          41mm

1320 Marigold yellow     41mm

1246 Copper blue          43mm

0113 White  (.0038)      45mm

Some odd results appeared in this firing.  Black deformed least and white most. But in general, the opal was again more viscous than the transparent.  Exceptions were the red, and light violet in the transparents; and among the opalescents were the light cyan, dusty lilac and white.

Also of note is that the amount of deformation was very similar for the test at 600C for 30 minutes and the one at 650C for only 1 minute.  This re-inforces the concept that time and temperature are often interchangeable, so longer at a low temperature can equal the heat work effects of a shorter soak at a higher temperature.

Bullseye glass. Span of 20cm. Fired at 150C/hr to 690C for 1 minute

            Code - name - deformation from horizontal

0013 Opaque white        35mm

0141 Dark forest green   41mm

0137 French vanilla        44mm

1101 Clear                    49mm

1428 Light violet            52mm

0126 Orange                 53mm

0303 Dusty Lilac            54mm

1437 Light amber          54mm

0113 White   (.0038)     54mm

0243 Translucent white  55mm

1125 Orange                 56mm

1341 Ruby pink sapphire 59mm

1122 Red                      59mm

0161 Robins egg blue     60mm

0147 Deep Cobalt blue   62mm

1320 Marigold yellow     67mm

1246 Copper blue          90mm

The results of the higher temperature in this test showed variations in comparative viscosity.  Some opals (e.g., dark cobalt blue, robins egg blue) were less viscous than most transparents, but some transparents (e.g., light violet and light amber) were more viscous than most opals.

The test shows wide variability in the viscosity of transparent colours at a higher temperature.  It appears that hot and deep colours are the least viscous of the transparent colours in this test.  There are also significant differences in the viscosity of opalescent and transparent glasses of the same colour.  It is apparent that not all glasses have the same rate of viscosity change with the same rate of temperature change.

Summary

This test showed that in general, the opals in the test are stiffer than the transparent from 600C to 690C with some exceptions.  It appears transparent hot colours are less viscous than the light transparent colours.  This is not the same for opalescent colours which seem to have a wider range of viscosity at these temperatures.

The similar deformation of the test glasses at 600C for 30 minutes and at 650C for one minute, shows the possibility of using lower temperatures and longer times to achieve the same effects in slumping as at higher temperatures with shorter soaks.

Viscosity and expansion rate are roughly related at lower temperatures, but both change rapidly above the softening point.  This experiment demonstrates that expansion rates vary within a single fusing compatible range of glass.  Also, glass with significantly different viscosities can be compatible, since this was all Bullseye fusing compatible glass.

It is apparent from this unscientific experiment that when preparing for slumping an important piece that combines different colours and styles, testing for relative viscosity is a good idea to determine if there are widely different viscosities.  This knowledge will enable an accommodation to be made in scheduling.

Tom Sawyer comments on the subject of viscosity:

“Viscosity is not always lower for transparent glasses than for opalescent glasses.  Opalescent glasses will begin to move more at temperatures of 538ºC/1000ºF than will transparent glasses, and even at 677ºC/1250ºF, there are still some opalescent glasses that move more than many transparent glasses.  It is only when we get to fusing temperatures that we begin to see the majority of transparent glasses moving more than the majority of opalescent glasses.  In general, it is correct that darker glasses will move more than lighter glasses – both because of their chemistries and because of their greater propensity to absorb infrared energy.”

More information on the effects of viscosity in kilnforming can be found in the ebook Low Temperature Kilnforming.

Sample Tiles

credit: Tia Murphy

There are advocates for making tiles as references for future work.  

• They show the profiles achieved at different temperatures.  
• They can be stored for easy visual reference when planning a firing.  
• It is a useful practice for any kiln new to the user.  

These tiles are assembled in identical ways to enable comparisons.  They should include black and white, iridised pieces- up and down, transparent and opal, and optionally stringers, confetti, millefiori, frit and enamels.  

The tiles are fired at different top temperatures with the same heat up schedule with the top temperature of each at about 10C or 20F intervals.  These show what effect different temperatures give.  Start the temperature intervals at about 720C or 1330F.

This is a good practice, even if time consuming.  It gets you familiar with your kiln and its operation.  It gives a reference for the profiles that are achieved with different temperatures at the rates used.

Ramp rate and time

But, as with many things in kilnforming, it is a little more complicated.  The effect you achieve is affected by rate and time used as well as the temperature.

The firing rate is almost as important as the temperature.  

• A slow rate to the same top temperature will give a different result than a fast rate.  
• The amount of heat work put into the glass will affect the temperature required.  
• Slow rates increase the time available for the glass to absorb the heat.  
• Glass absorbs heat slowly, so the longer the time used by slower rates, the rounder the profile will be.

Since time is a significant factor in achieving a given profile, any soaks/holds in the schedule will affect the profile at a set temperature.  A schedule without a bubble squeeze will give a different result than one with a bubble squeeze at the same temperature.

To help achieve knowledge of the rate/time effect, make some further test tiles.  Use different rates and soaks for the test tiles of the same nature as the first temperature tests. But vary only one of those factors at a time. Consider the results of these tests when writing the schedule for more complex or thicker layups. 

Mass

Also be aware that more mass takes longer to achieve the same profile.  Slower rates and longer times will help to achieve the desired profile at a lower temperature.  It is probably not practical to make a whole series of test tiles for thicker items.  But, a sample or two of different thicknesses and mass will be helpful to give a guide to the amount of adjustment required to achieve the desired outcome.

The results of sample tiles are due to more than just temperature.  They are a combination of rate, time, and temperature (and sometimes mass).  These factors need to be considered when devising or evaluating a schedule, because without considering those factors, it is not possible to accurately evaluate the relevance of a suggested top temperature.

See also: Low Temperature Kilnforming, available from Bullseye and Etsy

Longer Soak or Higher Temperature?

 ‘Is it better to extend the soak or add more firing time when the firing program isn’t quite enough? What are the meanings of “soak,” “hold,” “ramp,” “working temperature” and “top temperature”?’  

Let’s start with some of the terms.

“Soak” and “hold” have the same meaning in scheduling.  Schedules are made up of a series of linked segments.  Each segment contains a rate, temperature, and time.  The time is often called a “hold” in the schedules.  That time can have several effects.  It can allow enough time for a process, such as slumping, to be accomplished.

Although “soak” is entered into the schedules in the same way as a hold, it has a different concept behind it.  The hold when used as a soak allows the set temperature to permeate the whole thickness of the glass.  An example is in annealing. An annealing hold/soak is set.  This is to allow the glass to become the same temperature throughout. 

The ramp is the rate at which the controller is set to increase/decrease the temperature.  This is normally the first element in the segment.

“Top” and “Working” temperature are the same thing.  It is the temperature at which the desired effect is achieved.  They have slightly different nuances.  Top temperature is normally considered as a point where the desired profile will be achieved in a few minutes.  The working temperature is also that, but includes the idea that it will take time for the effect to be achieved.

Which should you alter first – soak time or temperature?

Most important is that you alter only one at a time.  If you alter the two elements at the same time, you do not know which was the cause of the result.

In general, you lengthen the soak if the effect is not achieved at the temperature and in the time set.  There are two reasons for this.  Glass has fewer problems at lower temperatures.  Secondly, the controllers are set up in such a way that it is easy to extend the time. Check your manual for the key sequence to extend the time.  It is more difficult to alter the temperature during a firing. 

To determine if you need more time, you peek into the kiln as the kiln approaches the top temperature.  If the profile has not been achieved by the time set at your working temperature, you enter the combination of keys to keep the kiln at the top temperature until you see the effect you want.  Then enter the combination of keys to skip to the next segment.

Whether you alter time or temperature, depends on what you are doing.  Soak plus temperature equal heat work.  With heat work you can accomplish the same effect at lower temperatures.  It may be that taking more time (usually slower ramp rates) to get to the same or lower temperature, will give the results desired.

For slumping, draping and other low temperature processes extending the hold/soak is appropriate. It reduces the amount of marking that is created by the mould or surface supporting the glass.

When tack, contour, or full fusing, you should be aiming to finish the work in about 10 minutes. Soaking/holding significantly longer increases the risk of devitrification.

For high temperature processes such as pot and screen melts and some flows, increasing the temperature is probably the right thing to do, to avoid the devitrification possibilities of long holds of open face high temperature work.

These can only be guidelines.  Your instincts and experience will help you determine which is the right thing to do in the circumstances.

 

Placing of Pieces in the Kiln

 Distance from Sides of Kiln

 

"Is there a rule of thumb for interior size of kilns and piece size? (i.e., “allow for X inches between the piece and kiln walls on all sides”).  I’m thinking about how to determine piece size limitations when shopping for a kiln."

I don’t know of a formula, or rule of thumb, to determine the amount of space required between the glass and the kiln walls.

I have only been able to determine the spacing required after I have purchased the kiln.  Each kiln has different characteristics. 

The most obvious is whether the kiln is fired from the side or from the top.  More space is required with side fired kilns.  The radiant heat from the elements tends to heat the edges of the glass before the centre becomes equally hot. This requires more space or baffles between the elements and the glass.

Top fired,  with enough distance to get even distribution of heat

Side fired. Red arrows indicate the important infrared heating.
Blue arrows indicate the less effective ambient heat.

There is less concern about uneven heating with top fired kilns.  But as each kiln is different, you must test the heat distribution around the kiln.  Bullseye Tech Note #1 has a good method.  This will show where the temperature is less than the rest of the shelf.

In general, rectangular kilns are cooler in the corners.  Round kilns do not have the same characteristic, but may still have uneven temperatures, due to the configuration of the elements.  Smaller kilns seem to have more even temperatures than large kilns, which tend to be cooler along the sides.  Kilns with a ring element below the shelf seem to have the most even distribution of temperature.

I had a large kiln 2 metres by 1 metre which had a requirement of 50mm/2” from the edge to even the temperature.  A recently purchased 50cm square kiln has almost perfectly even temperatures across the whole shelf.

[The illustration is taken from the ebook Low Temperature Kilnforming, available from Bullseye and Etsy.]

The required glass distance from the side will depend on side or top elements and size but no formula is available.  Testing for heat distribution is necessary once you have the kiln.

Scheduling with the Bullseye Annealing Chart

This post is about adapting the Bullseye chart Annealing Thick Slabs to write a schedule for any soda lime glass as used in kilnforming.

I frequently recommend that people should use the Bullseye chart for Annealing Thick Slabs in Celsius  and Fahrenheit.  This chart applies to glass from 6mm to 200mm (0.25” to 8”).

“Why should the Bullseye annealing chart be used instead of some other source?  I don’t use Bullseye.”

My answer is that the information in the chart is the most thoroughly researched set of tables for fusing compatible glass that is currently available.  This means that the soak times and rates for the thicknesses can be relied upon.

“How can it be used for glass other than Bullseye?”  

The rates and times given in the chart work for any soda lime glass, even float. It is only some of the temperatures that need to be changed.

"How do I do that?"  

My usual response is: substitute the annealing temperature for your glass into the one given in the Bullseye table.

 "It’s only half a schedule."

That is so.  The heating of glass is so dependent on layup, size, style, process, and purpose of the piece.  This makes it exceedingly difficult to suggest a generally applicable firing schedule.  People find this out after using already set schedules for a while. What works for one layup does not for another.

Devising a Schedule for the Heat Up

There is no recommendation from the chart on heat up.  You have to write your own schedule for the first ramps.  I can give some general advice on some of the things you need to be aware of while composing your schedule.

The essential element to note is that the Bullseye chart is based on evenly thick pieces of glass.  Tack fusing different thicknesses of glass across the piece, requires more caution. The practical process is to fire as for thicker pieces.  The amount of additional thickness is determined by the profile being used.  The calculation for addition depends on the final profile.  The calculation for thickness is as follows:

• Contour fusing - multiply the thickest part by 1.5. 
• Tack fusing - multiply the thickest part by 2. 
• Sharp tack or sinter - multiply the thickest part by 2.5.

The end cooling rate for the appropriate thickness is a guide for the first ramp rate of your schedule.  For example, the final rate for an evenly thick piece 19mm/0.75” is 150ºC/270ºF.  This could be used as the rate for the first ramp. 

Bob Leatherbarrow has noted that most breaks occur below 260ºC/500ºF.  If there are multiple concerns, more caution can be used for the starting ramp rate.  My testing shows that using a rate of two thirds the final rate of cooling with a 20 minute soak is cautious.  In this example of a 19mm piece it would be 100ºC/180ºF per hour.

Even though for thinner pieces the rates given are much faster, be careful.  It is not advisable to raise the temperature faster than 330ºC/600ºF per hour to care for both the glass and the kiln shelf.

Once the soak at 260ºC//500ºF is finished, the ramp to the bubble squeeze should maintain the previous rate.  It should not be speeded up.  The glass is still in the brittle phase.

After the bubble squeeze you can use a ramp rate to the top temperature of up to 330C/600F.   AFAP rates to top temperature are not advisable.  It is difficult to maintain control of the overshoots in temperature that are created by rapid rates.  

The top temperature should be such as to achieve the result in 10 minutes to avoid problems that can occur with extended soaks at top temperature.

In the example of an evenly thick 19mm/0.75” piece a heat up full fuse schedule like this could be used:

• 150ºC/270ºF to 566ºC/1052ºF for 0 minutes
• 50C/90F to 643C/1191F for 30 minutes
• 333ºC/600ºF to 804ºC/1479ºF for 10 minutes

 

If a more cautious approach to the heat up is desired, this might be the kind of schedule used:

 

• 100ºC/180ºF to 260ºC/500ºF for 20 minutes
• 100ºC/180ºF to 566ºC/1052ºF for 0 minutes
• 50C/90F to 643ºC/1191ºF for 30 minutes
• 333ºC/600ºF to 804ºC/1479ºF for 10 minutes

This approach is applicable to all fusing glasses.

 

Adapting the Bullseye Annealing Chart

After writing the first part of the schedule, you can continue to apply the annealing information from the Bullseye chart.  The first part of the anneal cooling starts with dropping the temperature as fast as possible to the annealing temperature.

The method for making the chart applicable to the annealing is a matter of substitution of the temperature.  All the other temperatures and rates apply to all fusing glasses.

Use the annealing temperature from your source as the target annealing  temperature in place of the Bullseye one.  The annealing soak times are important to equalise the temperature within the glass to an acceptable level (ΔT=5ºC).  The annealing soak time is related to the calculated thickness of the piece.  This measurement is done in the same way as devising the appropriate rate for heat up. 

Applying the Cooing Rates

Then apply the rates and temperatures as given in the chart.  The three stage cooling is important.  The gradually increasing rates keep the temperature differentials within acceptable bounds with the most rapid and safe rates.

The temperatures and rates remain the same for all soda lime glasses – the range of glass currently used in fusing, including float glass.  The soak time for the calculated thickness of your glass piece will be the same as in the Bullseye chart.  

This means that the first cooling stage will be to 427ºC/800ºF.  The second stage will be from 427ºC/800ºF to 371ºC/700˚F.  And the final stage will be from 371ºC/700˚F to room temperature.

I will repeat, because it is so important, that the thickness to be used for the anneal soak and cooling rates for your schedule relates to the profile you desire.  A fuse with even thickness across the whole piece can use the times, temperatures, and rates as given in the chart as adapted for your glass.  The thicknesses to use are for:

Contour fusing - multiply the thickest part by 1.5. 

Tack fusing - multiply the thickest part by 2. 

Sharp tack or sinter - multiply the thickest part by 2.5.

An annealing cool schedule for 19mm/0.75" Oceanside glass is like this:

• AFAP to 510˚C/ 951˚F for 3:00 hours
• 25˚C/45˚F to 427˚C/800˚F for 0 time
• 45˚C/81˚F to 371˚C/700˚F for 0 time
• 150˚C/270˚F to room temperature, off.

Many will wish to turn off the kiln as early as possible.  This is not part of best kilnforming practice.  If you still wish to do this, the turn off temperature must be related to the thickness and nature of the piece.  To turn off safely, you need to know the cooling characteristics of your kiln.  This can be determined by observing the temperature against time and then calculating the kiln’s natural cooling rate. And then applying that information to cooling the kiln.

 

The best source for devising schedules is the Bullseye chart for Annealing Thick Slabs.  It is well researched and is applicable with little work to develop appropriate schedules for all the fusing glasses currently in use.

 

 

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 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.  

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]