CoE Varies with Temperature

Information from Bullseye shows that the Coefficient (average) of Linear Expansion changes rapidly around the annealing range.

The following is from results of a laboratory test of Bullseye clear (1101F)
Temperature range.......................COE
20C-300C (68F -­ 572F).................90.6
300C-400C (572F - ­752F).............102.9
400C-450C (752F - 842F).............107.5
570C-580C (1058F-1076F)............502.0

Bullseye glass is probably typical of soda lime glasses designed for fusing.

The change of CoE by temperature is further illustrated by Kugler (a blowing glass) who state their CoE by temperature range. Remember CoE is an average expansion over a stated range of temperatures)
CoE 93 for the range 0C-300C
CoE 96 for the range 20C - 300C
CoE 100 for the range 20C - 400C

The extension of the range by 100C beyond the brittle phase of glass has a distinct effect on the average expansion over the (larger) range. 

This shows why it is not helpful to refer to CoE without also mentioning the range of temperature.

In addition, here is an illustration of the effect. 

Image credit: Kerwin and Fenton, Pate de Verre and Kiln Casting of Glass,2000, p.32

It is understandable and common sense that as the temperature increases, so the rate of expansion increases and this applies to most solids.  Glass behaves differently as the graph above shows.  The change in expansion of Bullseye glass shows a relatively consistent average expansion until the strain point is reached.  Once out of the brittle phase, glass expansion rates change very much more rapidly.  It is not be coincidence that viscosity of glass changes at almost the same rates.  It is the viscosity that is controlling the CoE, not the other way around.   

Revised  5.1.25

Relative stress in Tack and Full Fused Glass

There is a view that there will be less stress in the glass after a full fuse than a tack fuse firing.

This view may have its origin in the difficulties in getting an adequate anneal of tack fused pieces and the uncritical use of already programmed schedules. There are more difficulties in annealing a tack fused piece than one that has all its elements fully incorporated by a flat fuse. This does not mean that by nature the tack fused piece will include more stress. Only that more care is required.

Simply put, a full fuse has all its components fully incorporated and is almost fully flat, meaning that only one thickness exists.  The annealing can be set for that thickness without difficulty or concern about the adequacy of the anneal due to unevenness, although there are some other factors that affect the annealing such as widely different viscosities, exemplified by black and white.

Tack fused annealing is much more complicated than contour or full fusing.  You need to compensate for the fact that the pieces which are not fully fused tend to react to heat changes in differently, rather than as a single unit.  Square, angled and pointed pieces can accumulate a lot of stress at the points and corners. This needs to be relieved through the lengthening of the annealing process.

The uneven levels need to be taken into consideration too.  Glass is an inefficient conductor of heat and uneven layers need longer for the temperature to be equal throughout the piece.  The overlying layers shade the heat from the lower layers, making for an uneven temperature distribution across the lower layer.

The degree of tack has a significant effect on annealing too.  The less incorporated the tacked glass is, the greater care is needed in the anneal soak and cool.  This is because the less strong the tack, the more the individual pieces react separately, although they are joined at the edges.

If you have taken all these factors into account, there will be no difference in the amount of stress in a flat fused piece and a tack fused one.  The only time you will get more stress in tack fused pieces is when the annealing is inadequate (assuming compatible glass is being used).

More information is given on these factors and how to deal with them in this post on annealing tack fused glass and in the eBook Low Temperature Kilnforming available from Bullseye and Etsy.

Revised 5.1.25

Breaks after the Piece is Cool

People sometimes fire a piece only to have it break after it is cool.  They decide to re-fire with additional decoration to conceal the break.  But it breaks again a day after it has cooled.  Their questions centre around thermal shock and annealing. They used the same CoE from different suppliers, so it must be one of these elements that caused the breakage.

Thermal Shock

This is an effect of a too rapid heat changes.  Its can occur on the way up in temperature or on the way down.  If it occurred on the way up to a fuse, the edges will be rounded.  If it occurred on the way up to a slump the edges may be sharp still, but the pieces will not fit together because the slump occurred before the slump.  It the break occurs on the way down the pieces will be sharp.  The break will be visible when you open the kiln.  More information is here.

If the break occurs after the piece is cool, it is not thermal shock.

Annealing

Another possible cause of delayed breakage is inadequate annealing.  Most guidelines on annealing assume a flat uniform thickness.  The popularity of tack fused elements, means these are inadequate guides on the annealing soak and annealing cool.  Tack fused items generally need double the temperature equalisation soak and half the annealing cool rate. This post gives information on how the annealing needs modification on tack fused items. 

The annealing break usually crosses through the applied pieces and typically has a hook at each end of the break.  If the piece has significant differences in thicknesses, the break may follow the edge of the thicker pieces for some distance before it crosses it toward an edge. This kind of break makes it difficult to tell from an incompatibility break.

Compatibility

The user indicated all the glass was of the same CoE.  

This is not necessarily helpful. 

Coefficient of Linear Expansion (CoE) is usually measured between 20°C and 300°C. The amount of expansion over this temperature range is measured and averaged. The result is expressed as a fraction of a metre per degree Celsius. CoE90 means that the glass will expand 9 one-thousandths of a millimetre for each degree Celsius.  If this were to hold true for higher temperatures, the movement at 800C would be 7.2mm in length over the starting size.  However, the CoE rises with temperature in glass and is variable in different glasses, so this does not tell us how much the expansion at the annealing point will be.  It is the annealing point expansion rate that is more important.  More information is here.

• Compatibility is much more than the rate of expansion of glass at any given temperature.  
• It involves the balance of the forces caused by viscosity and expansion rates around the annealing point.

Viscosity is probably the most important force in creating compatible glasses. There is information on viscosity here.  To make a range of compatible glass the forces of expansion and viscosity need to be balanced.  Each manufacturer will do this in subtly different ways.  Therefore, not all glass that is claimed by one manufacturer to compatible with another’s will be so. 

All is not lost.  It does not need to be left to chance.

Testing glass from different sources is required, as you can see from the above comments.  It is possible to test the compatibility of glass from different sources in your own kiln.  The test is based on the principle that glass compatible with a base sheet will be compatible with other glasses that are also compatible with that same base sheet.  There are several methods to do this testing, but this is the one I use, based on Shar Moorman’s methods.  

If you are buying by CoE you must test what you buy against what you have.

If you are investing considerable effort and expense in a piece which will use glass from different sources or manufacturers, and which is simply labelled CoE90, or CoE96, you need to use these tests before you start putting the glass together.  The more you deviate from one manufacturer’s glass in a piece, the more testing is vital. 

In the past, people found ways of combining glass that was not necessarily compatible, by different layering, various volume relationships, etc.  But the advent of manufacturers’ developing compatible lines of glass eliminated the need to do all that testing and experimenting.  While the fused glass market was small, there were only a few companies producing fusing glass.  When the market increased, the commercial environment led to others developing glass said to be compatible with one or other of the main producers of fusing compatible glass.

An incompatibility break may occur in the kiln, or it may occur days, months or years later.  Typically, the break or crack will be around the incompatible glass.  The break or crack may follow one edge of the incompatible glass before it jumps to an edge.  The greater the incompatibility, the more likely it is to break apart.  Smaller levels of incompatibility lead to fractures around the incompatible glass pieces, but not complete breaks.

If the break occurs some length of time after the piece is cool, it can be an annealing or a compatibility problem.  They are difficult to distinguish apart sometimes.  There is more information about the diagnosis of the causes of cracks and breaks here.

The discussion above shows that even with the best intentions, different manufacturers will have differences that may be small, but can be large enough to destroy your project.  This means that unless you are willing to do the testing, you should stick with one manufacturer of fusing compatible glass. 

Do not get sucked into the belief that CoE tells you much of importance about compatibility.

Revised 30.12.24

Annealing Strategies

This is a power point presentation I gave a few weeks ago to a group.  It may be of interest to others.  There is no commentary.

 

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.

Changing size in Slumping

 “I have full fused a single piece of glass with a few small pieces on top.  I thought it would shrink some as I had been told, but it maintained its size and still fit the mold for slumping.” 

I believe the enquirer is talking about a single layer circle changing size at full fuse.  Dog boning is much less evident in circles than rectangles.  The glass retreats evenly all along the edge.  This gives the appearance of retreating less than rectangles.  The absence of any big change in size may also result from thinning of the centre.  The amount of size change will be affected by the temperature of the full fuse too.  In this case there were additions which will have resisted any tendency to shrink.

Lower top temperatures, more rapid ramp rates to the top, and shorter holds will have the effect of limiting the movement of glass toward 6mm thick.

credit: Bullseye Glass Co

The viscosity of glass at full fuse is enough for it to attempt to pull up to 6mm. At casting temperatures, the viscosity is so low that 6mm of glass spreads out.  Temperature affects viscosity.

 

At slumping temperatures (620˚C - 680˚C / ca.1150˚F - 1260˚F), the viscosity high enough that the dimensions of a circle do not change. A circular piece of 3mm glass held at slumping temperatures does not change dimension.  It may, if held long enough take on a kind of satin sheen, rather than a fire polish.  But the viscosity  is low enough to allow the glass to form to the mould, given sufficient time. The resulting slumped piece will appear to be smaller than the mould. If you measure the piece around its outside curve, you will find the distance is almost the same as the diameter of the blank. 

 

Changing size on a single layer piece is dependent on the temperature and heat work applied to the piece.

Slumping contrasting colours and styles

 A question about why a tack fused 6mm/0.25” piece of combined dense white and black in a slump firing broke has been raised.  Other pieces of black and other whites also tack fused in the same firing did not break.

"Living in the Grey" Stephen Richard

Contrasting colours

Combining the most viscous and the least viscous of bullseye glasses - dense white and black - is a challenge.  The survival of other pieces in the firing with slightly less viscous white give an indication.  Their survival shows that the anneal and cooling conditions were too short and fast for the broken piece. 

It may be worth checking how much stress is in the surviving pieces.  It may not be possible directly on these fired pieces. There is a way.  Mock up the black and white in the same way as the surviving pieces.  Put this on a larger clear piece and fire in the normal way. This enables you to see stress in opalescent layups. If there is any, it is revealed on the clear by using polarising filters. 

The usual recommendation is to anneal and cool as for twice the thickness was followed in this firing.  It is important to anneal and cool more conservatively in cases of contrasting colours. Strongly contrasting colours and styles (low viscosity transparent and high viscosity white opalescent) require more time at annealing and need slower cooling.  I do that by using a schedule for one layer thicker than calculated.  In this case, as for 15mm/0.61” (two tack layers needs firing as for four tack layers, plus one extra for the high and low viscosity combination).

Viscosity

The reasons for this are viscosity:  

·        Annealing is done at a temperature that achieves a viscosity of around 10^13.4 poise. It can be done in a range from there toward the strain point of 10^14.5 poise.  Below the strain point temperature (which is determined by the viscosity), no annealing can occur.  The glass is too stiff.  The closer to the strain point that the annealing is done, the more time is required at the annealing temperature.

·        The annealing of Bullseye is already being done in the lower range of viscosities. It is possible the viscosity of the white is so high as to be difficult to anneal with the usual length of soak.

·        Although I do not know the exact viscosities of dense white and soft black at the annealing temperature, it is known white has a higher viscosity than the black.  The means to achieve less stress in the glass is to hold at the annealing temperature longer than normal.  A cooling schedule related to the length of the anneal hold is needed.  This information can be obtained from the Bullseye chart for annealing thick glass.  The rates and times apply to all soda lime glass, which is what fusing glass is. Only the temperatures need to be changed to suit the characteristics of your glass.

Slumping

The slumping of this combination of high and low viscosity glasses requires more care too.  My research has shown that the most stress-free result in slumping is achieved by firing as for one layer thicker than that used for the fuse firing.  For a tack fuse, this means firing for twice the thickness, plus one more layer for contrasting colour and style.  Then schedule the slump by adding another layer to the thickness.  This means scheduling as for 19mm/0.75"instead of as for 12mm/0.5”.  This is to account for profile, contrasting colours, and stress from slumping.  This is about three times the actual height of the piece.  

Slumping tack fused pieces of contrasting colours requires very cautious firing schedules.  These longer schedules need to have a justification.  It is not enough to add more time or slow the cooling just in case.  Excessively long anneal soaks, and slow cools can create another set of problems. 

More viscous glass needs more time at the annealing soak to an even distribution of temperature between the more and less viscous glasses.

More information about other low temperature processes can be found in my eBook Low Temperature Kilnforming.  Available from Bullseye and Etsy  

Differential Cooling of Transparent and Opalescent Glass

A statement was made on a Facebook group that transparent glass absorbs more heat than opalescent glass. And it releases more heat during cooling. The poster may have meant that the transparent heats more quickly than the opalescent, and cools more quickly.

Yes, dark transparent glass absorbs heat quicker than most opalescent (marginally), and it releases the heat more quickly (again marginally) than opalescent. The colour and degree of transparency do not absorb any more or less heat, given appropriate rates. They gain the same heat and temperature, although at slightly different rates due to differences in viscosity.

An occasional table

The rate of heating and cooling is important in maintaining an equal rate of absorption of heat. The temperature of both styles can become the same if appropriate lengths of heating, annealing, and cooling are used. The slightly different rates of heat gain can give a difference in viscosity and therefore expansion.  This slight mismatch during rapid ramp rates, might set up stresses great enough to break the glass. This can occur on the quick heat up of glass during the brittle phase (approximately up to 540ºC/1005ºF). In fact, most heat-up breaks occur below 300ºC/540ºF.

The main impact of differential heat gain/loss is during cooling. Annealing of sufficient length eliminates the problem of differential contraction through achieving and maintaining the Delta T = 5C or less (ΔT≤5C). It is during the cooling that the rates of heat loss may have an effect. The marginally quicker heat loss of many transparents over most  opalescent glass exhibits different viscosities and rates of contraction. The stresses created are temporary. But they might be great enough to cause breaks during the cooling. Slow cooling related to the thickness and nature of the glass takes care of the differential contraction rates by maintaining small temperature differentials.

Significance of Differential Heat Gain/Loss

Uneven thicknesses and the tack fusing profile both have much greater effects than the differential cooling rates of transparent and opalescent glass. It may be that strongly contrasting colours (such as purple and white) are also more important factors in heat gain and loss than transparent and opalescent combinations.  Cooling at an appropriate rate to room temperature for these factors will be sufficient to remove any risk of differential contraction between transparent and opalescent glasses.

Kilnforming with 3mm Glass

 A power point presentation I made a few months ago to the group Lunch with a Glass Artist.

It is 33 slides long.

Kilnforming with 3mm Glass.pptx

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