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 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”.

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]

Is Pate de Verre Watertight?

Clear frit sintered at 690C, 670C, and 650C (left to right)

"This is fascinating. I had no idea about the water leaving the glass at different temperatures."

 This comment was made in relation to some of my tests of pate de verre at different temperatures. I sintered glass at 620°C, 650°C and 690°C (1150°F, 1200°F, and 1275°F) to test for the strength of bonds at different temperatures and thicknesses.

 Because the glass appeared porous in some cases, I tested to see if vessels would be watertight at the different sintering temperatures. I found that at 620°C/1150°F the glass leaked water slowly. At 650°C/1200°F the water “sweated” out. At 690°C/1275°F it was watertight.

 It is not that the water leaves the glass. There is no water in glass. The question is whether the sintering is watertight at different temperatures. At the lower range, the sintered glass is porous; mid-range they sweat like unglazed pottery, but at the higher temperature they are watertight.

 Pate de verre is a form of sintering glass – normally in a mould. In pate de verre, a vessel needs to be fired at a higher temperature to be watertight. If a porous wall is acceptable, it can be fired to a lower temperature to preserve the granular appearance on the inside. The outside – which is in contact with the mould – will retain the granular appearance at all these temperatures. If the object is decorative, it can be sintered at a lower temperature which will preserve the brilliance of the colours.

 

The Mechanism of Sintering

 "Do glass molecules actually migrate when they are sintered together? "

Sintering occurs at the atomic level, where the atoms at the edge of the particles attach to others in other particles. An analogy occurs to me of Scottish country dancing. In big gatherings, small groups are formed to perform the dance, say an eightsome reel. As the dance goes on the groups become more coordinated and eventually form one large group, held together by the people on the edges of each group.

A more scientific description comes from Wikipedia:

“Sintering … is the process of compacting and forming a solid mass of material by heat or pressure without melting it. … The atoms in the materials diffuse across the boundaries of the particles, fusing the particles together and creating one solid piece. Because the sintering temperature does not have to reach the melting point of the material, sintering is often chosen as the shaping process for materials with extremely high melting points such as tungsten and molybdenum.”

Applied to glass this means that you can make a solid piece of glass out of multiple touching or overlapping pieces that do not change their shape. This uses low temperatures and very long soaks.

 Schematic-diagram-for-the-sintering-and-fusion-reaction-of-the-glass-frits-on-a-substrate.
Credit: ResearchGate

The usual process is to take the glass at a moderate rate up to the lower strain point. The rate of advance is slowed to 50°C or less to a temperature between slumping and the bottom of the tack fuse range.

The slow rate of advance allows a lot of heat work to be put into the glass. This, combined with a long soak (hours), gives the atoms of the molecules time to combine with their neighbours in other particles.

Sintering occurs in the range of 610°C to 700°C (1130°F to 1275°F). The lower limit is determined by the strain point of the glass and by practicality. The length of time required at the strain point - 540°C/1005°F - is so long (days) that it is impractical.

The upper limit is determined by the onset of devitrification. This has been determined by the scientific studies of sintered glass as a structure for growing bone transplants. Devitrification reduces the strength of the bonds of the particles at the molecular level. The process of crystallisation breaks the bonds already formed between the atomic structures of the molecules. These studies showed that the onset of devitrification is at 650°C/1204°F and is visibly apparent at 700°C/1292°F regardless of the glass used.

The lowest practical temperature for sintering is 650°C/1203°F. Indications are that at least an additional two hours are needed for the sinter soak for each 10°C/18°F reduction below 650°C/1203°F. This would make for a 12-hour soak at 610°C/1131°F. For me this is not practical.

More information on the kilnforming processes and sintering experimentation is available in this eBook: Low Temperature Kiln Forming.

Fixing a Broken Piece

This conversation is reproduced by permission (with some editing out of extraneous information). It is presented as an example of how conducting a critique of your schedule can have dramatic effects on the results of your firing. 

This is the piece as it came out of the kiln.

Picture credit: Ike Garson

You may have seen the photo I posted of a large copper blue streaky piece that has cracked right across. …  I’m wondering if it would be better trying to bring the 2 pieces together instead of opening up the 2 pieces and inserting frit. I was thinking of firing it with a tack or contour schedule.

This is the crack that developed later through the frit and single layer centre.

Picture credit: Ike Garson

I have 4 questions:

A.   Even if I manage to fix it, do you think that fissure line will always be too weak and liable to break off at any point?

The strength of the joint will be dependent on the firing conditions.  To make it strong, the temperature should go to full fuse.  Tack fusing will leave the joint more visible and weaker.  To stop the joint rounding during heat up, you will need to dam the piece tightly to stop the normal expansion of the glass and ensure the glass is forced together during the higher temperatures.

B.     I have some large pieces of clear confetti. Would it benefit using them to bridge the 2 sections from below?

Anything you put on the bottom will have distinct outlines and visibility.  The temperature on the bottom can be 10C or more different from the top surface, which is why you can get crisp lines with the flip and fire technique.

C.    Would clear powder hide the crack or would it always be visible after firing?

Any additions to the top may be less visible, but adding clear powder makes the join more obvious.  You need to use powder of the same colour as the sheet glass.  Since you are using a streaky glass, you can’t use coloured power either as it is very difficult to imitate the steaks even with powders of the same colours. 

More information was given indicating the first contour fuse schedule in Celsius:

1. 260 730 00.20
2. FULL 515 00.60
3. 260 150 End

This is the contour schedule I have used many times successfully but never for a piece during this week.

My critique of the schedule. 

Segment 1.

• ·    It is too fast for the small distance to the side of the kiln. 
• ·    It is too fast for a piece of varying thicknesses. Most expansion breaks occur above 300˚C, so a soak at ca.260˚C will help ensure the glass maintains an even temperature, especially with large differences in thickness. Then you can advance more quickly. 
• ·   There is no bubble squeeze.
• ·   The top temperature seems low for a good tack, or the soak is a bit short.  Long soaks allow the glass molecules to bind at the atomic level firmly. This is the principle used in pate de verre.
• ·   It definitely needs to be on fibre paper covered with thinfire to allow air out.

Segment 2.

• ·   The soak at 515˚C is better done at 482˚C for Bullseye.
• ·   My tests have shown that contour firing a piece like this at rates and holds for 1.5 times the height of the piece is necessary for good results.

Segment 3.

• ·   Also, my tests have shown that a three-stage cooling provides the best result.  Slow cooling keeps the glass within the 5°C difference required for avoiding stress.
• ·   Annealing at the bottom end of the range combined with an appropriate length of soak and slow cooling gives a denser glass than soaking at the middle of the annealing range. 
• ·   The best cooling comes from a three-stage cooling process.  This involves a slow rate for the first 55C, a rate of 1.8 times this for the second 55C, and a rate of 3 times this for the final cool to room temperature.

These points mean that I would recommend you fire for at least 10mm thick.  This recommendation is for a new piece, not a repair. In this repair case and for the conditions, I would choose 12mm as being more cautious. My schedule would look something like:

1. 120˚C to 260˚C, 20’
2. 300˚C to top temperature, 10’
3. Full to 482˚C, 120’
4. 20˚C to 427˚C,0’
5. 36˚C to 370˚C, 0’
6. 120˚C to room temperature, off

The anneal soak is for a piece 12mm thick.  The cool rates are for 21mm thick.  This is to compensate for the nearness of the glass to the edge of the kiln.  It will help to ensure the glass does not have excess stress locked into the piece during the cooling.

D. Do you think this schedule would work [for a repair]? It's adapted from a standard tack schedule.. 

1. 222 677 00.30
2. 222 515 00.40
3. FULL 482 01.30
4. 63 371 ENDS

Critique of the schedule.

Segment 1. 

• ·   Too fast given earlier difficulties. 
• ·   Too low for good adhesion unless you use about 10 hours soak. 
• ·   Even at sintering temperature (690°C) you would need 2 hours.  But at sintering temperature you do not alter the surface 

Segment 2. 

• ·   Too slow a cool from top temperature and risks devitrification. Should be FULL.
• ·   You do not need the soak at 515˚C.  It only delays the annealing process.  It seems this idea of soaking at the upper portion of the annealing range was introduced by Spectrum over 2 decades ago. 
• ·   Any advantage that might be achieved by the higher soak is cancelled by the FULL rate to the annealing soak. 
• ·   Go straight to the anneal soak. 

Segment 3. 

• ·   You need a more controlled 3 stage cooling to get the best result.

My schedule for repair would look something like this:

1. 120˚C to 540˚C, 10’
2. 300˚C to 780˚C, 10’
3. Full to 482˚C, 210’
4. 20˚C to 427˚C,0’
5. 36˚C to 370˚C, 0’
6. 120˚C to room temperature, off

I am making the assumption that 780˚C is full fuse in your kiln.  Anything less than full fuse will certainly show the crack.

 

A Look at Causes.

• ·  The piece is far enough away from the elements.  It is not on the floor. These are not the causes.
• ·  It is very near the sides of the kiln.  These are always cooler than the centre. There is always a risk of breaking in this case.  Very slow rates are needed. 
• ·  There is a 3.5 times difference in thickness within the piece. This also requires slow rates.
• ·  If the break were to have been on the heat up these elements of uneven heating, and rapid rates are a problem.  But the break occurred after the cool down. So, the annealing soak and cool is a problem. 
• ·  I have suggested some alterations to the schedules to address these things.

 

Fixing for Yourself

• ·   Dam it tightly to avoid expansion within the glass as it heats.  This holds the join together and causes the glass to gain a little height. 
• ·   Place the piece on 1mm or thicker fibre paper topped with thinfire.  This will help avoid a bubble forming in the clear.
• ·   I have suggested a schedule which is slower to ensure no further breaks.  It is slow to the strain point and fast after that. 
• ·   It needs to be a full fuse to fully join the two pieces and ensure it is sound.
• ·   The cool to annealing should be FULL.  Eliminate the soak in the upper annealing range. The effects of the time spent there is nullified by the rapid rate to the main annealing soak. 
• ·   Anneal as for 12mm, but with slower cool rates (for 21mm) to ensure there are no stresses built into the piece by the nearness of the glass to the edge of the kiln.
• ·   These methods and schedules will make it a strong whole.  But the join will still show on the bottom. 
• ·   After fixing, if you are still not satisfied, break it up for incorporation in other projects.

Finally, and unfortunately, I do not think it can be satisfactorily repaired for a client.  The crack will show on the back. You will know it is a repair, rather than a whole. And that will reflect on your feeling about the piece, and possibly your reputation.

 

Conclusion

The commission was successfully re-made from scratch by the artist using some of my suggestions on scheduling. This is the resulting piece.

 

Picture credit: Ike Garson

 

Careful analysis of the conditions around a break are important to making a successful piece in the future. Many factors were considered, but the focus became the schedule. Analysis of each step of the schedule led to changes that resulted in a successful piece with the original vision and new materials.