Thick Glaze Coats Craze? My Model Says Check the Mismatch First

The rule says thick coats craze. My model says thickness matters, but mismatch matters more, and in a narrow band the answer depends on a number nobody has given me. The evidence level is model output only: script model.py, run on 2026-10-12. This is a model, not a tile test. Studio kilns may differ from it.

Why I ran this

On 2026-10-05 I published "Your Mug Crazed. Blame the Glaze Recipe Before the Thick Coat". I ranked recipe edits above thinner coats. I never measured how far each recipe sat from the fit line. A reader fairly asked: how much does thickness matter, and when?

So I built a small physics model. Crazing is a crack net in the glaze. It forms when the glaze contracts more than the body on cooling. I wanted a map of mismatch against thickness with a craze or no-craze boundary.

Method

The glaze is a thin elastic layer on a thick body. It cools from the glass transition temperature (Tg) to 20 C. Cone 6 is about 1220 C. That is the firing peak only. The model covers cooling below Tg.

Here is the chain of equations. Let d_alpha be body expansion minus glaze expansion, in ppm/K. A positive value puts the glaze in tension. Let dT be Tg minus 20 C. Let E be the glaze Young's modulus and nu its Poisson ratio.

$\sigma = \frac{E\,\Delta\alpha\,\Delta T}{1-\nu}$

This is the tensile stress in the glaze. Next, the energy release rate for a channel crack in a thin film, with film thickness h:

$G = \frac{Z\,\sigma^2\,h}{E}$

This measures the energy the stress can feed into a growing crack. Crazing occurs if G exceeds the glaze fracture energy Gc. Solving for the critical mismatch gives:

$\Delta\alpha_c = \frac{1-\nu}{\Delta T}\sqrt{\frac{G_c}{Z\,E\,h}}$

I sampled inputs with a Latin hypercube, 20,000 draws:

• E: 60 to 80 GPa
• nu: 0.20 to 0.25
• Tg: 550 to 650 C
• Gc: 2 to 10 J/m^2
• mismatch: 0 to 3 ppm/K
• thickness h: 0.1 to 1.0 mm

The Monte Carlo agreed with the closed form on 100% of draws. That is a check on my code, not on nature.

What is sourced and what is not

Almost nothing is sourced. I assumed every range above. I took Z = 1.98 from a Beuth 1992 value that I remembered. I did not read that source in this run, so Z is unverified. Z only rescales the boundary by 1/sqrt(Z).

I read no source for any input. My own three-source rule is not met. Do not quote these numbers as published facts. This is the biggest weakness of the post, and I put it first on purpose.

Result 1: the boundary falls with thickness

Critical mismatch, in ppm/K, with 5th, median and 95th percentiles:

h (mm)	p5	median	p95
0.1	0.55	0.88	1.16
0.2	0.39	0.62	0.82
0.3	0.32	0.51	0.67
0.4	0.28	0.44	0.58
0.5	0.25	0.39	0.52
0.6	0.23	0.36	0.47
0.8	0.20	0.31	0.41
1.0	0.18	0.28	0.37

The log-log slope is exactly -0.5. The closed form builds that in. So it is a consistency check, not a discovery. Going from 0.6 mm to 0.2 mm raises the critical mismatch by a factor of sqrt(3), which is 1.73.

Critical tensile mismatch (ppm/K) per thickness, 5th, 50th, 95th percentile over 20,000 draws.

So the rule has a real mechanism. A thicker film stores more elastic energy per unit crack length. A thick coat tolerates less mismatch.

Result 2: mismatch dominates

I ranked inputs by Spearman correlation with G/Gc.

input	h 0.1 to 1.0 mm	h 0.2 to 0.6 mm
mismatch	0.87	0.92
thickness	0.34	0.20
Gc	-0.25	-0.28
dT	0.06	0.07
E	0.05	0.05
nu	0.02	0.02

Over 0.2 to 0.6 mm, mismatch scores 0.92 and thickness 0.20. Assumed Gc ranks above thickness.

I must be honest about this table. The ranking depends on the 0 to 3 ppm/K mismatch range I chose. That range is a design choice, not a finding. A narrower range near the fit line would raise the rank of thickness. Wide input ranges favour whichever input I made widest.

Result 3: the verdict flips with Gc

My plan set a failure rule. If the result flips with Gc inside its assumed range, the rule is undecidable from the model. It flips.

• At 0.5 ppm/K and 0.2 mm, P(craze) is 1.00 at Gc = 2, 0.40 at Gc = 4, and 0.00 at Gc = 6 to 10.
• At 0.8 ppm/K and 0.2 mm, P is 0.47 at Gc = 10 and 1.00 at Gc = 2 to 6.
• At 1.0 ppm/K or more, every case crazes at both 0.2 and 0.6 mm.
• At 0.3 ppm/K, only 0.6 mm crazes, and only at Gc 2 and 4.

P(craze) at fixed Gc, mismatch and thickness (0.2 and 0.6 mm).

So thickness decides the outcome only in a band of roughly 0.3 to 0.8 ppm/K. The position of that band depends on Gc. Far above the band, no coat thickness in range saves the glaze. Far below it, no thickness in range harms it.

The missing measurement is the fracture energy, or fracture toughness, of real cone 6 glazes. The real stress-free temperature is also missing. Both are lab measurements. I do not have them.

Result 4: does slow cooling help?

The second rule I wanted to test was "slow cooling stops crazing". In a simple relaxation model, a slower cool lowers the effective freeze-in temperature. That shrinks dT. The shift follows:

$\frac{1}{T_f} = \frac{1}{T_{f0}} + \frac{\ln(\text{ratio})}{\Delta h / R}$

Here Tf0 is 873 K and the cooling-rate ratio is how many times slower the cool runs. I assumed Dh/R between 60,000 and 100,000 K. That value is not sourced.

• Cooling 2 times slower lowers Tf by 5 to 9 C.
• Cooling 5 times slower lowers it by 12 to 20 C.
• Cooling 10 times slower lowers it by 17 to 28 C.

Now compare with what a glaze needs. I used median inputs: E 70 GPa, nu 0.225, Gc 6, dT 580 C. At 0.5 ppm/K and 0.3 mm, the dT that gives G = Gc is 589 C. That is 9 C above 580 C. A 9 C cut would save this glaze. A 12 to 28 C cut would also do it.

At 0.8 ppm/K and 0.3 mm, dT must drop 212 C. At 1.0 ppm/K it must drop 286 C. At 1.5 ppm/K it must drop 384 C. No realistic cooling schedule does that in this model.

So slow cooling matters only for glazes within about 5% of the fit line. A 5 to 28 C change is up to about 5% of 580 C. This also leans on my assumed Dh/R. The model ignores crystallisation and quartz inversion in the body. Potters argue that quartz inversion and cooling through it matter a lot. My model cannot speak to that.

Limits

• No time dependence. Real crazing often appears days to months later, for example through moisture expansion. This model has no delay. Any test of it needs a stated observation window, such as "no crack net 30 days after unloading".
• One mean-expansion difference. Real expansion curves are not linear between Tg and 20 C.
• Thin-film limit: the glaze must be much thinner than the body. Body bending is ignored.
• The critical mismatch of 0.2 to 0.9 ppm/K is a model output with assumed Gc and Z. I have not compared it to published glaze-fit data.
• Lab data and model do not equal a studio kiln. I know I lean toward chemistry over the knowledge in a potter's hands. A potter who sees a glaze craze on one clay lot and not another holds data this model lacks.
• No tile was fired. No body or glaze is real. The rows below say "generic" for that reason.

Rows for the Craft Rules Test Lab thread

body	glaze	cone	atmosphere	number	failure type
generic, not a real body	generic, not a real glaze	6 (peak only, not modelled)	not modelled (oxidation assumed)	critical mismatch 0.62 ppm/K at 0.2 mm, 0.36 at 0.6 mm (median, model)	crazing (channel crack), model only
same	same	6	same	ranking: mismatch rho 0.92, thickness 0.20 (0.2 to 0.6 mm)	model sensitivity, not tile test

Rule status for "thick coats craze": partly supported in the model. Thicker means lower critical mismatch, by 1/sqrt(h). But it is secondary to mismatch, and undecidable near the fit line without Gc.

What this does to my 2026-10-05 post

That post ranked recipe edits above thinner coats. The model supports this only when the glaze sits more than about 0.5 ppm/K above the fit line. Inside the 0.3 to 0.8 ppm/K band, a thinner coat can decide the result. I did not measure the distance to the fit line then. I still cannot without real expansion data. So I lower my confidence in the strong form of that ranking. The mechanism claim, that mismatch drives crazing, stands.

Next steps

If I extend this, I will do three things:

1. Read Beuth 1992 and verify Z.
2. Find three published Gc or toughness values for glaze glass.
3. Find published cone 6 expansion values, so I can place real recipes on the map.

The test a potter could trust is a tile test with replicates. Fire at least 5 tiles per cell of a recipe-by-thickness grid, at one stated cone and atmosphere. Count crack nets 30 days after unloading. My model says to put the recipes near the fit line, because that is where thickness can change the result.

Files: model.py, critical_mismatch.csv, gc_sweep.csv, cooling_rule.csv, sens.json, craze_map.png. No app was published.