Wednesday, March 21, 2012

The Science of Investment Materials

I have no backup copy of this essay, and I'm worried that the original post at warmglass.com will eventually disappear, so I'm posting the essay here as a precaution.

All of the papers listed were found in the Journal of Dental Research, and I will repost all of the URLs. For those of you unwilling or unable to follow the papers, I’ll do my best with summaries. 

Over the past year, I’ve also bought and read a few more advanced materials science papers on the subject through Science Direct. There are no URLs available for these papers (they are all restricted PDFs). I’ve also found some helpful downloads available at http://www.netzsch-thermal-analysis.com/. These are available under their Literature link, and are free. Just register to look at them. I’ve borrowed and modified a lot of the data from the restricted papers and the Netzsch site into visual graphs, which will hopefully be more helpful than all of the technical jargon. (Be forewarned, there is technical jargon involved in the following text, but I will try to explain it as we go along).

Throughout the literature, the primary material of interest is gypsum. This is as it should be. Gypsum, or calcium sulfate, or the calcium salts of sulfuric acid, chemical formula CaSO4, is the binder of first choice in traditional investments. (I prefer the term gypsum, instead of plaster, as a more general descriptive term for calcium sulfate. Plaster, in my mind, refers only to the form known as calcium sulfate hemihydrate). 

There’s any number of substitute binders available, from magnesia- and phosphate-based binders, through the colloids of silica, alumina, zirconia, etc. Substitute binders are all refractory (can take the heat), and most are relatively chemically inert at high temperatures. But not all are as readily available, as easily frangible (breakable) upon casting completion, and, most importantly, as dirt cheap as gypsum. 

Gypsum shrinks upon heating, so other components – known as fillers or extenders - are added to the investment that will counteract this shrinkage. One such extender is silica – either as powder, sand, clay, grog, etc. Silica is fairly refractory, readily available, and again, dirt cheap. 

(One popular misconception is that silica, or other extenders such as alumina, talc, etc., are added to make the investment more refractory. As you will read later, this is simply not true). 

Let’s start off with the granddaddy of the papers, first published in 1931, “Dental Casting Technic: Theory and Practice”, available at: 
http://jdr.iadrjournals.org/cgi/reprint/11/5/681.pdf.

This is a good beginning paper describing the behavior of gypsum-bonded investments, especially the thermal expansion behavior and influence of water/powder ratio. It allowed me to produce the following graph:


According to the paper, gypsum shrinks up to 2% in volume when heated. Silica expands when heated.All of the allotropic (solid exhibiting more than one crystalline state) forms of silica (tridymite, cristobalite, quartz, and fused silica) expand.

All of the forms, with the exception of fused silica (amorphous silica, e.g. glass), undergo phase transformations (changes in molecular structure). The transformation of quartz is possibly familiar to you, and is often called the quartz inversion. The quartz inversion occurs between about 500-600C (932-1112F), and results in a rapid expansion of the material. Cristobalite also undergoes a much more drastic expansion in the range 240-275C (490-527F). For silica, these transformations are reversible. Gypsum also undergoes phase transformations, but these are not reversible.

Varying the percentage of gypsum to silica can change the expansion profile of the investment material. This is a very easy way of controlling the thermal expansion of your molds. Here are some examples of the thermal expansion profile of different percentage mixes:

The next paper is “Thermal Behavior of the Gypsum Binder in Dental Casting Investments”, a must read in my opinion, and available here: http://jdr.iadrjournals.org/cgi/reprint/65/6/877.pdf.

Gypsum, or calcium sulfate, going from room to glass casting temperature and beyond, undergoes a number of phase transformations that all result in irreversible contractions. 

Dehydration of investment occurs in a double step process. Let’s start the cast investment at room temperature. The first form of gypsum is plaster – calcium sulfate dihydrate: CaSO4 + 2 H2O.

The idealized structure of pure gypsum consists of lattice planes of calcium sulfate molecules weakly bonded to alternating layers of water. The bond is an ionic one between the oxygen atoms and the hydrogen atoms in water – very easily broken. Water thus weakly bonded is often called the water of crystallization. As gypsum is heated, the water is diffused out of the matrix, and the plaster converts to calcium sulfate hemihydrate: CaSO4 + ½ H2O. (Obviously, there is not half a molecule of water, one water molecule is shared by two calcium sulfate molecules). This conversion is completed at 177C (350F). This is step 1.

Further heating of the investment will release all remaining water. This occurs at 200C (392F). This is step 2. 

In numerous DTA (Differential Thermal Analysis), and DSC (Differential Scanning Calorimetry) experiments, this double step can be seen as two endothermal (heat-releasing) peaks. In other words, as the temperature was increased, the heat capacity of the material jumped, which resulted in less heating required to increase the temperature. What this also means is that 100% dehydration did not magically occur at 200C (392F). It takes time for the water to completely disperse from the matrix. The second endothermal peak does not bottom out – indicating 100% dehydration - until about 300C (572F).

Here’s a fun little graph from Netzsch, that illustrates what I just said: 
http://www.netzsch-thermal-analysis.com/en/materials-applications/ceramics-glass/gypsum-and-quartz-sand-phase-transitions.html. The graph shows two curves. The first curve shows the TG profile of gypsum over temperature range (TG means “thermogravitic” which is just a fancy term for “as we heated it up, we weighed it"). The TG curve shows the thermal behavior of gypsum over temperature. The second curve is the DSC profile, which shows the heat capacity of the material. For an explaination of what Differential Scanning Calorimetry is and what it means, here is a URL: http://pslc.ws/macrog//dsc.htm

Yes, yes. I know its a web page about plastics. Amorphous polymers behave like glass. They have a glass transition range, and can undergo devitrification. In fact, pretty much any material, heated up and cooled correctly, can go through a glass phase - including metals. This has been well-documented since the 1960s. (And if you don't know what a glass transition is, maybe you should do a little googling, or maybe a lot). 

(A popular misconception is that steam can crack a mold if all the water is not removed. It will take some time for a solid block of investment to release all the water. While this is occurring, the varying temperatures within the block of investment will be well below or near the boiling point of water - due to escaping water drawing heat from the mold through evaporation. True, there is a point where the surface and exterior layers of the mold will start to calcine, as the remaining water cannot evaporate quickly enough to cool it. But regardless of the air temperature within the kiln, the mold will remain “cold” while water is within it. Since the water diffuses out of the matrix at about the same pressure as sea level atmosphere, it is impossible for steam pressure to crack the mold – simply because there is no steam within the mold to begin with. This is not to say you can crank the kiln temperature with a wet mold. An unnecessarily fast heating rate can and will crack a mold. As the outer layers dry out, they will undergo a different thermal expansion than the interior layers. This puts tension of the outer layers, which causes cracking. In short, an excessive heating rate will crack a mold – not steam).

Once the mold is completely dehydrated, the hemihydrate has converted to anhydrite: CaSO4 + 0 H2O. (Obviously, each form of gypsum does not convert instantaneously upon hitting a temperature benchmark. It is a continuous conversion, and each phase retains some quantity of the last phase, which slowly converts. So, the dihydrate has some small portion of unreacted hemihydrate, and the anhydrite, some portion of hemihydrate, etc). 

As noted in the above paper, Posnjak (1938) introduced the terminology of naming the three polymorphic forms of anhydrite alpha, beta, and gamma. However, confusion can occur with existing terms used in the gypsum industry for alpha and beta hemihydrate powders (produced by the wet or dry calcining methods, respectively). I therefore use the same terminology in describing anhydrite as is used in the paper, namely III-, II-, and I-CaSO4.

(A quick aside here. As noted above, the hemihydrate of gypsum, plaster, call it what you will, can come in one of two forms - alpha and beta. Alpha hemihydrate is traditionally produced by heating a sized gypsum or lump rock under elevated steam pressure in an autoclave. Beta hemihydrate is produced by heating finely ground gypsum at atmospheric pressure. Beta hemihydrate consists of rough, fractured, fragmented particles, and has the attractive properties of high plasticity, high compressive strength, and high density. Alpha hemihydrate consists of finer, denser, more well-formed and orderly crystals than the beta. Alpha has a higher set strength than the beta, and produces molds and patterns of high accuracy, high surface hardness, and low expansion during drying and curing, and is, to some extent, machinable. Most products are made up of a blend of the alpha and beta forms. Some products, such as mixtures for potter's plaster and gypsum wallboard, contain only the beta. Other products, such as Hydrocal FGR-95 or 115 Gypsum Cement, consist of only the alpha form). 

At 200C (392F) gypsum exists in the form of III-CaSO4 (and increasingly small portions of hemihydrate). III-CaSO4 is also known as soluble anhydrite, which is metastable. This means the III-CaSO4 would convert back to hemihydrate if removed from the kiln and exposed to atmospheric moisture. Paraphrased from the paper: “This is a familiar phenomenon encountered in the manufacture of (gypsum). The freshly calcined material possesses the property of rapidly absorbing moisture from the air with a marked increase in temperature, requires large amounts of water in mixing, product sets too rapidly (“fiery”), but it may set too slowly. The mixing characteristics of (gypsum) improve if the powder is allowed to mature under ambient air in storage (aging)”. In other words, you could, for what arcane reason I know not, remove your dehydrated mold from the kiln, place it in a bucket of water, and return it to a liquid slurry. Or grind it up, let it age in air, and then remix it later with water into another mold. Thus the term soluble anhydrite.

Upon continued heating, the largest shrinkage will occur in the range of 348-400C (658-752F), which is accompanied by an exothermal (heat absorbing) reaction. This marks the conversion of metastable III-CaSO4 into stable II-CaSO4, or soluble anhydrite into insoluble anhydrite. This is a phase transformation in which the “crystalline hexagonal needle shape of III-CaSO4 converts to thicker, shorter needles of orthorhombic crystals of the II-CaSO4”. Under experimental recovery (cooling and rehydration of investment), it was found to reach zero recovery for the temperature of 800C (1472F). In other words, all III-CaSO4 was completely converted to II-CaSO4 by 800C (1472F). Paraphrased from the paper: “This is also a familiar phenomenon in the manufacture of plaster. Gypsum that has been heated to a red heat becomes inert in water and is called ‘dead burnt’”. 

(In a different thread, I investigated a hypothesis that this conversion range, when III-CaSO4 converts to II-CaSO4, might require a more delicate touch in the heating schedule, and that molds were more prone to crack here than in other parts of the ramp-up. The idea being that, with the lowest point of thermal conductivity occurring here, along with the inevitable non-uniform temperature gradient between interior and exterior mold layers, would produce conflicting compressive and tensile tangential forces in the mold wall, resulting in the symptom known as a “crack”. The consequence being that you could put short cuts in the heating schedule – heat faster in other parts of the ramp-up, and just go slow in this “danger zone”. So far, the hypothesis has not been proven, and no danger zone found).

Let’s shoot past the (to me) relatively mild glass casting temperatures, to get to the II-I conversion. II-CaSO4 converts to I-CaSO4 at around 1227C (2240F). This crystal form has been reported as “cubic”, density of gypsum increases slightly, and is the result of crystals sintering together. Not much else to say about it, really, except that you can still cast glass in it if you wanted to - with a few provisos coming up.

Various temperatures have been tossed out for the thermal breakdown temperature for gypsum. By “breakdown” I mean the thermal decomposition of chemical bonds. They have varied wildly, from as low as 700C (1292F) to as high as 1500C (2732F). The reason for the discrepancy is interesting. 

Calcium sulfate breaks down according to the following reactions:

CaSO4 ==> CaO + SO3
SO3 ==> SO2 + ½ O2

The above formulas are as follows: CaSO4 is calcium sulfate (gypsum), CaO is calcium oxide (lime, quicklime, a caustic alkali, refractory up to 2572C (4661F)), SO3 is sulfur trioxide, and SO2 sulfur dioxide. 

Sulfur dioxide is a gas highly corrosive to metals, producing an insoluble sulfide on the surface of castings, making it a bugaboo in the jewelry and dental trades. But sulfur dioxide actually strengthens glass, producing a surface substance known as “bloom”. This is a white deposit that forms on glass and is easily washed off. It improves the durability of glass by removing alkalis such as sodium from the glass matrix – an effect known from the wood, oil and coal-burning days of lehrs and annealers. This "dealkalization" reaction is an ion exchange that is made possible by the removal of the sodium ion as sodium sulfate. The general chemical reaction is:

2Na (glass) + SO2 + ½ O2 + H2O ==> 2H (glass) + Na2SO4

It has been determined – under repeated and rigorous laboratory conditions – that calcium sulfate breakdown commences at about 1240C (2264F) and is practically complete at 1450C (2642F). Melting of a CaO/CaSO4 eutectic mixture occurs at around 1350C (2516F), so we will set the upper usable casting limit of gypsum at 1230C (2246F). That’s a pretty good temperature, but, of course, not really realistic. Gypsum could be used as a casting medium, but as we have seen, it drastically shrinks. If dimensional fidelity (cast piece is the same size as the wax piece – kind of important when making dental inlays) is an issue, then you either scale up the size of the wax, or include a material that expands upon heating, like silica.

The addition of silica (SiO2) produces a different chemical reaction:

CaSO4 + SiO2 ==> CaSiO3 + SO3
SO3 ==> SO2 + ½ O2

CaSiO3 is one variant of calcium silicate, which is highly refractory (up to around 1540C (2804F)), possesses high strength, and is used extensively for high temperature insulation (especially by your friends at ZIRCAR). The energy required for the gypsum/silica decomposition to occur is far less than for pure gypsum. As a result, the beginning of thermal decomposition is lowered to 990C (1814F), and is practically complete at 1260C (2300F).

The following chart graphically demonstrates the difference in decomposition via a TG curve:

(The above graph and information was obtained from the paper “Thermal and Microchemical Characterisations of CaSO4 – SiO2 Investment Materials” by G.M. Ingo et. al).

Being conservative, and using the beginning temperature for thermal decomposition as the maximum, one could soak safely at 989C (1812F) for an indefinite length of time! That’s well beyond normal glass casting temperatures. However, carbon also plays a role. Any burnout of organic materials in a mold will leave a halo of carbon residue embedded around the casting. The presence of carbon will reduce the decomposition temperature, as described in “Decomposition of Gypsum Investment in the Presence of Carbon”, available at: 
http://jdr.iadrjournals.org/cgi/reprint/38/3/541.pdf.

With carbon present in gypsum-silica investment, the following reaction will occur:

CaSO4 + 4C ==> CaS + 4CO
3 CaSO4 + CaS ==> 4CaO + 4SO2
CaO + SiO2 ==> CaSiO3

CaS is calcium sulfide, which acts as a catalyst causing a chain reaction to occur, rapidly converting calcium sulfate into calcium oxide. Carbon acts as a flux, lowering the temperature of the reaction. This reaction is well known and happily taken advantage of by chemists in the concrete manufacturing and steel industries. Coke and limestone is used to draw silicates out of iron ore, producing calcium silicate slag. The above reaction starts to take place at 700C (1292F). The decomposition is displayed in the following chart:

Is this thermal breakdown necessarily bad news for glass casters? In terms of structural integrity, the effect is almost nil. You have already ruined any structural integrity the mold possessed by dehydrating it. It is probably a good bet that calcium silicate does not react with the glass. And the mold will be just as refractory as when it was composed entirely of gypsum-silica, especially when you consider that calcium silicate is an ingredient in refractory cements and investments used in metal casting, such as Hydroperm. 

However, the thermal expansion, heat capacity, and thermal conductivity characteristics of the mold have changed because of the new compounds created. How much exactly, I’ve not been able to ascertain. But I suspect the thermal expansion of the new mold composition to be much less than the original mold composition. And if some portions of the mold remain unaffected, you are creating thermal strain that is at least different, and quite probably far worse, than a uniform block of material. If you can avoid the introduction of carbon into your mold, I would advise doing so. But it appears gypsum-silica investments are much tougher than we have been led to believe. Prepared and treated properly, it can take the heat, and for long durations.

A quick note on water/powder ratios. Ralph Carter, a chemist at Ransom & Randolph, presented a paper on the subejct which can be found here: 
http://www.ransom-randolph.com/Effect_of_Changing_Water_Powder_Ratio_on_JI.pdf

The water/powder ratio may be the most critical aspect of investment mold making - or it may not be. Varying the water/powder ratio will certainly change the the thermal conductivity of the investment, as well as the expansion profile. The W/P ratio usually varies from .28 (28 parts water to 100 parts investment) to .50 (.50 is 1 part water to 2 parts powder). 

Less water within this range, and the investment paste is too stiff to give a good impression, more water than this range, and the investment may be too weak to stand the ramp up in your firing. W/P ratio also affects the porosity of your investment. Porosity is defined as a percentage, and can be determined by weight. Weigh the investment after setting at room temperature, and again after dehydration (this is called the bulk/matrix ratio). The result will be the percent porosity of your investment. I think you will be surprised to find out that mold porosity is around 60% (give or take). Here’s a visual aid:

The needle shapes are calcium sulfate crystals, the larger conchoidal shapes are silica particles. The black stuff in between is empty space – filled with water when hydrated, air when it is not. That’s definitely porous. Porosity changes the thermal profile of the investment. More porous means less density, and less thermally conductive. On the other hand, highly porous materials reduce crack propagation. The "holes" tend to stop cracks - similar to drilling a hole at the end of a crack in a piece of glass or fatigued metal.

Perhaps the best illustration of the effects of the w/p ratio can be seen Chart 6 of Carter's paper. This chart lists the "fired" compressive strength of various mixtures. 

The terms "green-" and "fired-" strength, borrowed from ceramics, are not particularly helpful. A ceramic material will be stronger after firing. Investment is strongest once it is set - when it is "green". It can be seen that there is a sharp decline in compressive strength from a ratio of .34 (34 parts water to 100 powder, or about 1 part water to 3 parts powder) to .36 and above. This is not to say that a .34 ratio is the optimal or best ratio, merely that, within the constraints of Mr. Carter's test, that ratio showed the highest strength after mold dehydration and cooling. One could infer that the mold material would have a similar compressive strength in the high-end soak of the firing schedule, and that may not be the most dangerous assumption. But unless the assumption is tested, it remains exactly that.

One thing that struck me in reading Carter's paper was the lack of defects in the castings regardless of the w/p ratio. Carter surmised that this was due to the robust nature of the R&R premium investment. To confirm this, he then used a "non-premium brand of investment" (presumably a competitors). The molds held up "for the most part" (Carter downplaying the fact that the non-premium brand worked just as well?). The results are not entirely clear cut. It seems that w/p ratios may not be as important as suggested, and that the investment, regardless of the brand, is fairly forgiving, and can withstand "some mishandling". I would suggest that further tests be done on this metric.

Of course the use of the compressive strength metric in making investment forms doesn't provide any great insight. We are much more interested in the tensile strength of the material. Very few materials have similar compressive and tensile strength profiles, and certainly gypsum does not. But compressive strength is much more easily and consistently measured, and so, I suppose we must make do with this measure, but we should recognize the lack of utility in using it. 

For example, let's say I wish to calculate the hydrostatic pressure to determine mold failure. Actually, since this is glass, the measure would be vitreostatic pressure, but anyways... Let's say, for convenience, that the "fired" crush strength of my mold material is 50 psi. That is considered pretty weak. How much glass can I pile on top of it before it breaks? Well, hydrostatic - or vitreostatic - pressure is calculated simply by density x gravity x height. Better still, specific weight has density and gravity terms in it already, so pressure = specific weight x height. The specific weight of water is 1 gm / centimeter cubed. Most soda-lime glasses are around 2.5 times the specific weight of water, so let's use that number: 2.5 gm per centimeter cubed. Converting to pounds per cubic foot, and then to cubic inches, gives me the specific weight of glass = .09 psi. So we simply multiply that term by height in inches. A casting 8 inches in height will exert .72 psi on the mold surface. That's not much. How much glass do I have to pile up to crush my mold? Well, 50 / .09 = 555.55 inches = around 46 feet of glass! That sounds ridiculous. I'd better double check. Okay, the water pressure at the deepest part of the ocean is around 16,000 psi. That's with seven miles of water on top. 7 miles x 5280 feet x 12 inches = 443,520 inches. 16,000 / 443,520 inches gives me .036 psi for water, times 2.5 is .09 psi for glass, so yeah, the calculation is correct - but it still sounds ridiculous. The compressive strength as a useful metric for investment stength is practically useless. 

What about tensile strength? There are varying reports of tensile strength for gypsum investments, ranging from 1/6 to 1/15th the compressive strength of the material. This will vary according to the thickness of the material and the amount of flexure. Perhaps it is easier to calculate the pressure upon the sides of a form. Lets take 50 lbs of glass in the form of a cube. A cube of 50 lbs of glass is a little over 8 inches on a side, but for convenience sake, we shall use 8 inches. Vertical pressure upon the bottom of the mold is easy to calculate, but pressure on the side is a bit more complicated. Pascal's Law tells us that pressure is equivalent in all directions. Thus, at the top of the mold, the first inch of glass will press upon the side at .09 lbs /square inch, but this pressure progresses linearly until at the bottom of the mold, the glass presses upon the side at .72 lbs / square inch. This is known as a pressure prism, and we would have to integrate over the surface area of the side to get the total pressure. Fortunately, basic mechanics provides a straightforward formula for a vertical rectangle in the form of specific weight * midpoint of the side * area of the side = .09 psi * 4 inches * (8 inches) squared = 22.94 lbs of pressure. That's not much at all. If I assume (and this is just a rank and totally unsupported assumption) that tensile strength increases linearly with thickness, and say, a quarter inch of investment, possessed of 60 psi crush strength, has a tensile strength 1/15th that value (i.e. tensile strength is 4 psi), then the mold wall thickness should be about 1 and 1/2 inches to overcome side pressure at the bottom of the mold. Doesn't mean anything really, but I suspect we are all making our molds much, much thicker than they actually need to be.

The addition of other materials to create an investment composite is well known. The addition of the metal reinforcements, such as steel wire, hardware cloth, chicken wire, etc. have been used. Personally, I find they rarely add any strength to the investment. Given the relatively extreme kiln temperatures and oxidation that they undergo, metals soften and weaken very quickly. The addition of refractory materials, such as coarse ground mullite, perlite, etc., again, from a personal standpoint, add nothing to the strength of the investment. True, mullite will form long needle-like crystals similar to gypsum, but only when ground to a fine particle size, and formation occurs only above around 1000C (1832F). 

The one material which would seem to increase tensile strength is fiberglass or ceramic fiber. 

Fiberglass has been known since ancient Egyptian times, where it was used as reinforcement for ceramic vessels. The "modern" manufacture of fiberglass dates back to 1830s France. The use of fiberglass has been rediscovered again and again by many people, and has been used to reinforce plaster architectural elements since at least the late 1960s-early 70s. Fiberglass strand is, pound for pound, approximately six to ten times as strong as steel wire (depending upon the type). Given its extensive use in the construction industries, the physical properties of glass reinforced gypsum are quite well known. The flexural strength is around 3200-4000 psi, and the tensile strength is around 1200-1400 psi. However, one must be careful to use the right type of fiberglass. The most common fiberglass, E-glass, has a softening point reported around 846C (1555F). S-glass, used in aerospace/military/marine composite materials, has a softening point of around 1055C (1932F). Anyone who has reported success with a fiberglass reinforced shell investment under glass casting temperatures has - wittingly or unwittingly - been using S-glass.

Given the relatively extreme strength of this composite material, compared to traditional gypsum-based investments, very thin investment shells are theoretically possible. However, in practical use, unless the fiberglass is embedded woven and whole within the gypsum investment, no appreciable increase in tensile strength is observed. This is due to the fact that the investment bond between fiberglass strands remains weak. It appears the "old masters" using thick and unmodified gypsum-base block molds, knew what they were doing...

6 comments:

  1. Thank you for posting your most insightful paper, I am a sculptor from South Africa who owns a small bronze foundry. Lately I have been experimenting with commercial jewelry investment with great success. I however pay for such investment at a premium and so decided to start researching investment in order to mix my own. Such insightful information as yours are virtualy non-existant on the web. Danie

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  2. Hey John, first let me say thank you. I've probably read this article a dozen times over the past 2 years (rapid prototype investment casting). It's been extremely beneficial.

    I have 2 questions about gypsum thermal decomp into sulfur dioxide in the presence of carbon. First, do you know if that reaction is exothermic? Secondly, what would the carbon/sulfur dioxide look like if I dissected a flask?

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    1. Hi Eric, I don't know. Google tells me that, in the heat range of a flask prepped for metal, the SO2 and carbon will react to form CO, CO2, and elemental sulfur. That makes sense since you see the result as the black skuzz in non-ferrous metals like copper and silver. My guess is it is not exothermic. Sorry I can't be of more help.

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    2. Thanks John. I'm trying to diagnose a defect I've found in gypsum. So far I have pictures of the defect and I know that it is created during an exothermic event. I saw your gmail in your bio, so just let me know if you'd like me to forward my findings.

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