Hand-considered hypotheses, 3401–3500

Glass and ceramic processing, written one at a time. Melting and the melt, forming, annealing and residual stress, glazing and the glaze–body interface, a short group on sintering, and the strength and fracture of brittle solids. Each entry was composed on its own and given its own logical form, printed with the entry, so that the variety of argument can be checked and not only the variety of subject. None has been tested; no citation is invoked and none is given, and every magnitude offered is either flagged as an estimate or stated as a rough bound. The sintering and porosity claims already made in H1101–H1200 are deliberately not repeated here: the eight entries in that section are about constraint, liquid wetting, field paths, microwave gradients and particle pinning, and about pore-free densification only where the mechanism is new.

Melting and the melt

Misattribution
H3401. The hue of an iron-bearing container glass is credited to its iron content, but at fixed iron the colour is fixed by the redox ratio frozen into the glass as it passed the transition, so two glasses of identical analysis can differ visibly. That ratio keeps shifting while the melt is still above the transition, and the cooling rate that freezes it is the real variable. Splitting one melt into a quenched and a slow-cooled cast, then comparing their spectra, separates composition from cooling history.
Hidden term
H3402. Batch-melting calorimetry is read as a heat of fusion, yet a large part of the endotherm is the heat of solution of silica in the molten alkali, which is a mixing term and not a phase change. The distinction matters because the mixing term tracks the batch's alkali-to-sand ratio while the fusion term does not. Melting the same glass from pre-reacted cullet, where no dissolution occurs, leaves the fusion term alone.
Floor
H3403. Fining time cannot fall below the rise time of the largest bubble the tank must clear, so a deep tank carries an irreducible fining time that grows with depth and shrinks with bubble size. Stirring does not help, because it only redistributes bubbles that were already rising. Fining one glass at two depths, with seed counts taken at the outlet, puts the bound at a number instead of a rule of thumb.
Reversal
H3404. Adding fining agent past its useful dose puts seeds back into the glass, because the surplus sulfate or antimony releases its gas after the melt has stiffened and the bubbles can no longer escape. The dose response is therefore a window with a clearest point in the middle. A dose series fired on one schedule, with seeds counted per unit volume, locates both edges.
Threshold
H3405. Sulfate fining starts at a temperature set by the melt's oxygen activity rather than by the sulfate's own decomposition temperature, so one batch fines lower in a reducing furnace atmosphere. The mechanism is the sulfate-sulfide equilibrium, which moves the release temperature. Firing identical batches in air and in nitrogen, and finding where seeds begin to disappear, exposes the shift.
Identity
H3406. The seeds counted in a melt and the blisters counted after forming are one bubble population seen at two times, not two defects. If so, a glass clean at the forehearth but blistered in the mould must have gained its bubbles in between, and the gain should follow the forming temperature. Sampling one ladle before and after forming, at a single temperature, tests it directly.
Artefact
H3407. Stones in an under-melted glass are read as unmelted sand, but many are cristobalite grown from a silica-rich droplet during cooling, which makes the stone a record of the cooling rather than of the melting. The two look alike in a hand lens and differ in texture. Petrography of stones from a batch melted for two different times settles whether the stone predates the melt.
Count
H3408. Property maxima in alkali borate melts, including the viscosity maximum, can all be carried by one structural variable, the fraction of boron in four-fold coordination, so a model needing two species for two maxima is over-parameterised. The count is one, and it is measured by resonance rather than inferred. Coordination measured across a composition series, compared with the position of each maximum, shows whether one count carries them all.
Scale argument
H3409. Convection in a melting tank is credited to the thermal gradient, but once the bubble volume fraction passes a small percentage the rising bubbles supply most of the stirring, so the flow field belongs to the fining reaction rather than to the burners. The two drivers scale differently with depth, which makes them separable. Tracer velocities with and without fining gas, in one tank, distinguish bubble-driven from thermally driven flow.
Inversion of standard practice
H3410. Raising the crown temperature is the standard way to melt faster, yet past a point it slows melting because the batch blanket foams and the foam insulates the unmelted sand from the melt beneath. Foam stability is set by the batch's carbonate-to-sulfate ratio, so the remedy is a batch change and not more heat. A crown-temperature series with foam thickness watched through a port shows the rate turning over.
Path dependence
H3411. Water dissolved in a melt is set by the furnace atmosphere's water vapour, so one batch melted in humid and in dry air yields two melts of different viscosity and different fining behaviour. The melt carries a record of the weather, and two plants with one recipe can disagree. Melting one batch at two controlled humidities, with viscosity read at one temperature, isolates the term.
Negative claim
H3412. No container is inert to a borosilicate melt at working temperature, so every reported contamination is dissolution and reprecipitation rather than an accident. The only genuinely inert crucible is a frozen skull of the same glass. Melting one glass in platinum, in alumina, and in a skull, then comparing inclusion populations, ranks the containers and tests the exception.
Conservation argument
H3413. The volume of fining gas a sulfate can supply is fixed by the oxygen it carries, so a seed count implying more gas than the sulfate could release must include air entrained during pouring. That accounting needs no kinetics and no assumption about bubble size. Comparing seeds in a cast taken under vacuum with one taken in air, at one sulfate level, separates entrained from generated gas.
Confounded pair
H3414. Alumina rising in a tank melt is read as refractory corrosion, but batch carryover delivers the same alumina and the two cannot be told apart from composition alone. A tracer placed in the refractory at a known level breaks the degeneracy. One campaign with that tracer, sampled at three depths, decides which source is growing.
Uniqueness claim
H3415. The working range of a glass-ceramic precursor is not unique, because the viscosity measurement itself nucleates crystals and the second measurement on the same sample is of a different material. A reported range is therefore a property of the measurement sequence. Viscosity on a fresh sample and on one held for the same total time give two ranges, and the gap measures the nucleation.
Hysteresis
H3416. Melt density differs on heating and on cooling at the same temperature because the coordination state relaxes more slowly than the furnace ramps, so a density taken on the way up is not the equilibrium value. The gap narrows with slower ramps and does not close. Density on matched up and down ramps at two rates, on one glass, gives both the equilibrium value and the relaxation time.

Forming

Misattribution
H3417. Tin on the lower face of float glass is credited to the bath's chemistry, but the depth of the tin layer is fixed by how long the ribbon stays hot enough to diffuse, so a faster ribbon carries a thinner layer over the same bath. The tin profile is then a record of the pulling rate. Measuring the profile on ribbons pulled at three speeds from one bath tests it without touching the atmosphere.
Hidden variable
H3418. Float thickness is treated as a surface-tension equilibrium, yet on a production ribbon it is set by the volume pulled per unit width and time, so thickness control is flow control and surface tension only shapes the edges. The two produce different thickness profiles across the ribbon. Changing the pull rate at a fixed bath temperature, with thickness mapped across the width, separates them.
Critical value
H3419. Press-blow forming spreads glass evenly only when the parison wall is thicker than a minimum set by the glass's extensional viscosity, because a thinner wall quenches against the mould before it can be blown out. Below that thickness the finished wall stays thick at the base and thin at the shoulder whatever the mould does. A parison-thickness series, with wall thickness mapped on the article, locates the transition.
Artefact
H3420. The chill mark on a pressed glass is read as surface shape left by the mould, but it is a birefringence pattern from the thermal gradient at contact, and polishing a few micrometres away removes the optical effect without changing the profile. Only one of the two survives polishing. Birefringence and profilometry on one mark, before and after a light polish, show which is which.
Reversal
H3421. Drawing a fibre faster makes it stronger up to a point and weaker beyond it, because faster drawing freezes a less relaxed network of higher fictive temperature while also bringing the fibre against the guide sooner. The two effects depend on speed differently, so the curve has a maximum. A speed series with strength at one gauge length, and guide contact counted separately, places the maximum and attributes it.
Identity
H3422. Die swell in a ceramic paste and springback in a pressed compact are one elastic recovery seen in two geometries, and the same shear modulus should predict both. If the identity holds, a paste that swells by a given fraction in extrusion must spring back by a corresponding fraction in pressing. One paste, both measurements, no change of formulation, tests it.
Bound
H3423. Tape thickness in doctor-blade casting is bounded above by the slurry's yield stress rather than by the blade gap, because a thick wet tape flows under its own weight before it dries. Past the bound, opening the gap only makes a wider puddle. A gap series at two yield stresses, with dried thickness measured, shows thickness saturating where rheology takes over from the gap.
Hidden term
H3424. The density of a slip cast is reported as one number, yet the mould's suction falls as the layer thickens, so the cast is a gradient with the face denser than the back. The steepness is set by the mould's permeability, not by the slip. Sectioning a cast and measuring density through the thickness, on two moulds of different permeability, exposes the term.
Causal inversion
H3425. Cracking in gel-cast bodies is blamed on shrinkage, but the crack spacing is set by the gel's permeability, which decides how fast a shrinking body can drain and therefore how much stress builds before a crack relieves it. A more permeable gel should crack less often and with wider spacing, which inverts the usual reading. A permeability series at fixed solids, with crack spacing counted, tests the inversion.
Scale argument
H3426. The smallest feature that can be pressed into glass is set by how far heat diffuses into the mould during contact, not by the feature's size, because the glass surface stiffens before it reaches the feature's bottom. A finer feature fills more slowly, not less. Pressing one mould with features spanning a decade in size, at two contact times, maps the limit against diffusion rather than geometry.
Selection effect
H3427. Reported formability windows for glass are the intersection of the compositions that were successfully formed, so the window describes the survival of a search rather than a physical boundary. A composition outside it may be formable and merely untried. A prospective trial on compositions drawn at random from the full range, with failures reported, sizes the difference.
Count
H3428. Six press settings, mould temperature, glass temperature, contact time, pressure, dwell and release rate, supply at most three independent controls, because pressure and dwell enter through one contact integral and release rate enters through the same cooling. A design that estimates the rank of the sensitivity matrix exposes the redundancy. That rank is why two plants optimising different subsets settle on different settings for one article.
Confounded pair
H3429. Green strength of a pressed ceramic rises with binder content and with granule deformation, and the two are confounded whenever a binder increase also softens the granules. Only a granule-size series at fixed binder separates contact area from bridge. Pressing three granule sizes at one binder level, with strength and contact area measured, does it.
Necessary condition
H3430. A slip needs a yield stress to hold a wall on a vertical mould, so a claim of a self-levelling casting slip is a claim about its behaviour while being poured, not while it sits. A truly self-levelling slip cannot build a thick wall. Wall thickness on vertical and horizontal mould faces of one slip shows whether the yield stress is there.
Hysteresis
H3431. A glass ribbon remembers the curvature it was formed at, and on reheating it bends opposite to that curvature at the temperature where the frozen stress relaxes. That temperature is a reading of the stress's relaxation time. Reheating a curved ribbon on a support that lets it move, recording shape against temperature, recovers the forming stress without a polarimeter.
Uniqueness claim
H3432. The forming temperature of a phase-separating glass is not a single value, because separation raises the viscosity while the glass is being worked, so a range measured on a fresh melt is wider than the range available to a held one. A reported range is tied to its schedule. Viscosity on a fresh melt and on one held just above the separation temperature, at equal total time, gives two ranges and the gap between them.

Annealing and residual stress

Misattribution
H3433. Residual stress left by annealing is credited to the cooling rate, but water taken up by the surface during the anneal lowers the surface viscosity and relaxes part of the stress the cooling would have set. A humid anneal therefore leaves less stress than a dry one on the same schedule. Annealing matched specimens in dry and in humid air, with stress read by birefringence, isolates the term.
Hidden term
H3434. Photoelastic stress measurement uses a stress-optic coefficient calibrated on an annealed sample, yet tempering densifies the glass and changes that coefficient, so a tempered article's stress is reported a few per cent wrong in a direction set by the densification (estimate). The error is systematic and does not average out. Measuring the coefficient on tempered and annealed pieces of one glass, then recomputing one stress, gives its size.
Ceiling
H3435. Thermal tempering cannot build a surface compression larger than the glass survives in transient surface tension during the quench, so there is a ceiling on central tension at a given thickness and a glass quenched harder simply breaks. The ceiling is a fracture criterion during processing, not a property of the finished article. A quench series increasing in severity until spontaneous breakage locates it, and the cracks should begin at the surface.
Threshold
H3436. Below a thickness, thermal tempering cannot develop a useful profile because heat crosses the glass faster than the surface can be held cold, so the profile collapses. Above a second thickness, surface compression saturates because the surface heat-transfer coefficient, not the thickness, then limits the gradient. A thickness series quenched on one schedule, with stress read at the surface and the centre, shows both ends.
Inversion
H3437. Slower cooling through the annealing range can leave a higher residual stress in a glass with a secondary relaxation, because the slower schedule lets a second, slower mechanism build stress after the primary one has already relaxed. The usual rule that slow cooling reduces stress then fails. Two cooling rates, one fast enough to freeze the primary relaxation and one slow enough to engage the secondary, compared on one glass, show the inversion.
Identity
H3438. Annealing and tempering are one process run at two cooling rates, so the annealing point is not a separate phenomenon but the rate at which stress generation and stress relaxation balance. That makes the annealing point a property of the schedule as much as of the glass. Stress after cooling at several rates, on one glass, should cross zero at a rate coinciding with the quoted annealing point.
Artefact
H3439. The annealing point from beam bending is depressed by the beam's own weight, because the bending stress drives viscous flow in the same range being measured, so a broad relaxation spectrum gives a lower value than a fibre-elongation measurement on the same glass. The two methods disagree most where the spectrum is widest. Running both on one glass, and on a second with a narrower spectrum, tests the artefact rather than the glass.
Count
H3440. A symmetric tempering profile has two independent parameters, surface compression and depth, so a birefringence analysis reporting three is fitting the profile's curvature to noise. The third is recoverable only if the profile is asymmetric. Fitting measured profiles with two parameters and with three, on one data set, shows whether the third buys anything.
Reversal
H3441. Annealing a glass-ceramic below the crystal's strain point raises the matrix's residual stress as the matrix contracts away from the crystals, but above that point the matrix relaxes and the stress falls, so stress against annealing temperature has a maximum. The maximum sits at the crystal's strain point, not the glass's. An anneal series with lattice strain measured by diffraction, on one glass-ceramic, places it.
Hidden variable
H3442. The fictive temperature of a drawn fibre is set by the drawing tension as well as by the cooling rate, because tension orients the network and raises the temperature at which it locks. Two fibres drawn at one speed but different tensions therefore differ in density and in strength. A tension series at fixed speed, with density by flotation, isolates the mechanical contribution.
Scale argument
H3443. Annealing blunts a crack in glass by viscous flow at a rate set by the crack's own opening, so shallow cracks close and deep ones do not, with a critical depth between. That depth is set by the viscosity at the anneal and by the surface tension pulling the walls together. Indentation cracks of increasing depth, annealed on one schedule, show strength recovering for the shallow ones and not for the deep.
Negative claim
H3444. No anneal removes the stress from a glass-metal seal, because the mismatch strain is fixed by the two expansions and the metal's yield, and annealing only redistributes it between glass and interface. A seal reported stress-free is one whose stress was measured where it is smallest. Stress in the glass at two distances from the interface, before and after a long anneal, tests the claim.
Trade-off
H3445. Stress relief and tempering cannot both be maximised in one article, because the relaxation that removes the unwanted stress removes the wanted one, so a product sold as stress-relieved and tempered is one of the two. The trade-off is a single curve in cooling rate. Stress at the surface and through the thickness, over a series of cooling rates, traces that curve.
Path dependence
H3446. Whether a plate rested on a setter during annealing shows in its density, because cooling through the transition under load leaves the supported face denser. The difference is small but is a systematic bias in any density comparison between laboratories using different setters. Density on both faces of one plate, and on plates annealed on two setters, shows it.
Symmetry argument
H3447. Symmetric stress profiles require symmetric heat removal, so a single-sided jet quench gives a profile whose mid-plane is not the neutral axis, and the central tension inferred by the standard edge reading is then wrong. The error is largest in thin articles quenched from one side. Stress through the thickness after a one-sided and a two-sided quench of one glass tests it.
Anomaly resolved
H3448. The occasional birefringence in carefully annealed glass, read as a hidden stress, is the photoelastic response of the hydrated surface layer, whose water changes the refractive index without any stress. It appears wherever the surface has met water and goes on drying. Birefringence on one sample wet and dry, with the same anneal, resolves it without a stress measurement.

Glazing and the glaze–body interface

Misattribution
H3449. Crazing is credited to expansion mismatch alone, yet a well-matched glaze on a thick layer still crazes because the stored elastic energy grows with thickness while the stress stays fixed. Thickness, not mismatch, then decides whether the crack runs. One fit applied at two thicknesses on one body, fired together, separates the two.
Energy threshold
H3450. A glaze shivers only when its compressive stress multiplied by its thickness exceeds the energy needed to separate it from the body, so a badly matched glaze applied thin stays put indefinitely. The threshold is a thickness, and it moves with the interface's toughness. A thickness series of one mismatched glaze on one body places it and shows it scaling with the measured interface energy.
Hidden term
H3451. Glaze fit is computed from the bulk glaze's expansion, but the layer formed at the interface during firing has a different composition and a different expansion, and that layer sets the stress in the glaze. A glaze can be mismatched in bulk and matched at the interface. Measuring the interface layer's composition and expansion, on one fired glaze, tests whether fit follows it rather than the bulk.
Artefact
H3452. Pinholes in a glaze are blamed on the body's decomposition, but a bubble that burst at the surface leaves a raised rim while a pinhole from a decomposed grain has a clean edge, so the two are distinguishable in section. Many reported body-caused pinholes are burst bubbles from air entrained in the glaze. Cross-sectioning pinholes from one firing and classifying the rims settles the attribution.
Inversion
H3453. Adding a wetting agent improves levelling until it lowers the surface tension enough that the glaze dewets at the body's edges, so the additive has an optimum and the glossiest glaze is not the best-covering one. Both effects depend on one variable in opposite directions. A dose series on one glaze, with edge coverage and roughness both measured, locates the window.
Two-sided bound
H3454. Opacity from an opacifier is bounded at both ends of particle size: below roughly a tenth of the wavelength the particles scatter too little, and above a few wavelengths there are too few of them at a given loading. The maximum lies between, and its position depends on the refractive-index contrast. A milling series at fixed loading, with reflectance measured, shows the two-sided bound.
Identity
H3455. A matte glaze and a devitrified glaze are one surface at two crystal sizes, the matte being the one whose crystals are too small to scatter light individually. If so, every matte glaze should show a crystalline phase on diffraction, and its surface should roughen on overfiring as the crystals grow. Diffraction and microscopy on one matte and one crystalline glaze from a common base test the identity.
Hidden variable
H3456. The red of a copper-red glaze is set by the cooling rate through the window where copper particles precipitate, not by the copper content, so two glazes of one analysis can be red and green depending on the kiln's cooling. Colour is then a record of the firing, readable backwards. One glaze cooled at three rates, with colour measured, turns the kiln's history into a number.
Count
H3457. A transition-metal colour in a glaze has at most two independent variables, oxidation state and coordination, so a spectrum decomposed into three absorption bands is not evidence for three species. The third band is usually a vibronic shoulder of the second species. Fitting one spectrum with two components and with three, on a glass of known state, shows whether the third is recoverable.
Reversal
H3458. Firing hotter improves glaze adhesion until the body's own glassy phase begins to dissolve the interface, after which the bond weakens with further heating. Adhesion against temperature therefore peaks, and the peak is set by the body's flux content rather than by the glaze. One glaze on two bodies of different flux, fired across a range, puts the peak in two places.
Selection effect
H3459. Published glaze recipes are those that survived firing, so the maturing ranges in the literature are the intersection of the survivors' ranges and overstate the width open to a new composition. A recipe just outside the published range is not evidence of a narrow field. A prospective firing of compositions sampled across the range, with failures reported, measures the true width.
Conservation argument
H3460. Metal release from a glaze into acid is bounded by how fast the silica network dissolves, not by how much metal the glaze contains, so a lead-free glaze with a more soluble network can release more of a less toxic metal. Total content is the wrong variable. Leaching one glaze at two acid strengths, with the network's dissolution followed by silica in solution, tests whether release tracks dissolution.
Trade-off
H3461. Glaze hardness and glaze crack resistance cannot both be raised in one composition, because hardness needs a stiff, well-connected network while crack resistance needs a compliant one that can deform at the tip. A scratch-resistant glaze is therefore a chip-prone one. A composition series across the trade-off, with both measured on one firing, should trace a single curve.
Threshold
H3462. Thermal shock cracks a glaze when the body's contraction exceeds the glaze's strain tolerance, but the crack enters the body only when the glaze is thicker than a threshold set by the interface toughness. Thin glazes craze without weakening the body. A glaze thickness series on one body, quenched from one temperature, separates surface cracking from body cracking.
Artefact
H3463. Orange peel on a sprayed glaze is read as a droplet-size effect, but it is the layer's drying shrinkage buckling the surface, so a finer spray of the same glaze gives the same texture. The texture's wavelength is set by the layer's thickness, not by the droplets. Spraying one glaze at two droplet sizes and two thicknesses, with texture measured, separates them.
Causal inversion
H3464. Bubbles in a glaze are attributed to the body's gas release, but the glaze's own sealing of the body decides how much of that gas is trapped, so the glaze controls its own bubble population. A more fusible glaze seals earlier and traps more gas even though the body releases the same amount. Two glazes of different fusibility on one body, with bubble counts, test the direction of causation.

Sintering, kept clear of the earlier range

Inversion
H3465. Viscous sintering of a glass powder stops when the glass crystallizes, so the useful window lies between the softening point and the crystallization onset, and a glass with a narrower window sinters less even though it is softer. Viscosity alone does not predict the outcome. Heating microscopy on two powders of similar viscosity but different crystallization temperatures shows the window, not the viscosity, setting how far the body densifies.
Misattribution
H3466. A film constrained on a substrate sinters less than a free powder on the same schedule, and the deficit is credited to the film's small particle size when it is the substrate suppressing in-plane shrinkage. The constraint turns shrinkage into a tensile stress instead of into densification. Free and constrained films of one powder, fired together, separate the two.
Hidden term
H3467. In field-assisted sintering the current's path through the die, not through the sample, supplies most of the Joule heat early in the cycle, so a pyrometer aimed at the sample reads a temperature the sample has not reached. The die's conductivity and the sample's contact resistance decide how long the offset lasts. Two die materials of different conductivity, at one setpoint, show the offset and its decay.
Threshold
H3468. Liquid-phase sintering densifies only while the liquid wets the solid boundary below a critical dihedral angle; above it the liquid penetrates the boundaries and the compact swells instead of shrinking. The angle is set by the liquid's surface tension against the solid's, not by the liquid's volume. A series of liquid compositions spanning the angle, at fixed volume, shows densification turning into swelling.
Identity
H3469. Reaction sintering and reactive melt infiltration are one process at two melt fractions, both dissolving a solid into a liquid that then precipitates a new phase in place. If so, one reaction couple should give the same product morphology at either fraction, scaled by the liquid's volume. One couple run at two fractions, with morphology compared, tests it.
Count
H3470. Zener pinning stops grain growth at a size set by the number of second-phase particles on a boundary, so a reported abnormal grain is a local deficit of particles rather than a change of mechanism. The limit is a count per boundary area, not a volume fraction. Mapping particles on the boundaries of one sample, and finding the grain that grew, shows the deficit.
Artefact
H3471. Microwave sintering's apparent enhancement is the sample's own dielectric heating gradient, steepest when the sample is larger than the penetration depth, so the enhancement should vanish for thin samples in the same field. The gradient, not the field, does the work. One powder sintered at two thicknesses in one cavity separates the effect from the artefact.
Reversal
H3472. Increasing the pressure in hot pressing can lower the compact's density, because the die's friction takes a growing share of the load and the pressure at the sample stops being hydrostatic. Density against applied pressure therefore peaks. A pressing series with the load measured at the punch and at the base places the peak and ties it to the friction.

Strength and fracture of brittle solids

Misattribution
H3473. A glass tested in bending reads stronger than the same glass tested in tension, and the difference is credited to a material effect when it is the smaller stressed volume sampling a smaller flaw. A design using bend data for a tensile part is then optimistic by an amount set by the volume ratio. One glass, two geometries, with the flaw population mapped by fractography, separates them.
Hidden term
H3474. Static and dynamic fatigue tests on one glass give different lives at the same stress, and the gap is the water activity at the crack tip rather than a difference of mechanism, since a crack held open at constant load accumulates water while one loaded quickly does not. Access is set by the crack's opening, which the stress controls. Both tests at one stress in a cell of controlled humidity, with the opening measured, isolate the term.
Reversal
H3475. Proof testing removes the weak specimens, yet the survivors are not proportionally stronger because the proof load itself introduces contact damage at the loading points, and past a proof stress the added damage outweighs the removed flaws. Strength after proof therefore peaks and then falls. One batch proofed at several stresses, with strength measured away from the contacts, shows the peak.
Selection effect
H3476. Reported strength-size effects in glass are conditioned on specimens that survived handling, and larger specimens are handled more and rejected more, so part of the size effect is a survival effect. The bias grows with size and shrinks with care. Strength of one glass at three sizes, handled by one protocol and by a gentler one, separates the two.
Confounded pair
H3477. Etch depth and etch finish are confounded whenever a bath that removes glass faster also leaves a rougher surface, so the strength gained by etching is credited to depth when part of it is the surface the bath leaves. Two baths reaching one depth by different routes then give different strengths. One glass etched to one depth in two baths, with roughness and strength measured, separates them.
Environmental threshold
H3478. A fatigue limit in glass exists only below the stress at which the crack's opening becomes narrower than the water molecule's access, so a threshold measured in humid air is a threshold of the environment rather than of the glass. In vacuum the same glass should show none. One glass, one crack, tested in air and in vacuum across a stress range, places the threshold in one environment and not the other.
Identity
H3479. Indentation strength and scratch strength are one residual-stress-controlled flaw measured in two geometries, so a ranking by one should predict the other for the same glass. The residual field is the same and only the contact shape differs. Both tests on one set of glasses, with the residual field read by birefringence, tests the identity.
Bound
H3480. The strength of a polycrystalline ceramic is bounded above by the largest facet crack a grain of its size can host, so no processing change raises strength past a value set by grain size alone. The bound is geometric and does not depend on boundary chemistry. Two ceramics of one grain size but different boundary chemistry, tested in bending, should share the bound while differing below it.
Count
H3481. A fracture surface carries at most three independent features marking crack-velocity regimes, mirror, mist and hackle, so a fractographic report claiming five regimes is counting roughness rather than velocity. Each feature maps to a velocity range, and the ranges do not overlap. One surface measured for roughness and for velocity along a travelling microscope shows whether the extra features have distinct velocities.
Scale argument
H3482. The rising toughness seen in alumina is credited to a material R-curve, but its plateau is set by the specimen's ligament length, so a larger specimen keeps rising where a small one has flattened. The plateau is then a specimen property, not a material one. One alumina on three specimen sizes, with crack length measured, should move the plateau with the ligament.
Misattribution
H3483. Fine-grained ceramics are stronger than coarse ones, and this is read as a strengthening mechanism when it is a flaw-size effect, since the largest grain sets the largest facet crack, so strength follows the inverse square root of grain size without any change of mechanism. The name given to it does not alter the number. One composition at three grain sizes, with the largest facet measured by fractography, tests whether strength tracks the facet rather than the grain.
Hidden variable
H3484. Freshly drawn glass fibre owes its strength to a sodium-depleted surface left by drawing, not to an absence of flaws, so a fibre drawn from a sodium-free glass should be no stronger and may be weaker. The depletion layer acts as compression in one case and not the other. Fibres from two glasses of different sodium content, drawn identically, compare.
Negative claim
H3485. No thermal-shock figure of merit is a material property, because the critical quench depends on the heat-transfer coefficient, which depends on the specimen's surface and the quench medium, so a material ranked well in water can rank poorly in oil. The ranking is a property of the pair. One ceramic quenched in water, oil and air at matched surface finish, with the critical temperature measured in each, tests it.
Trade-off
H3486. Hardness and toughness trade off across a family of covalent ceramics because the bond strength that resists plastic flow concentrates stress at the crack tip, so a solid solution cannot raise both. The trade-off is a curve, not a scatter. One family across a composition series, both measured on the same specimens, traces the curve and shows whether any member escapes it.
Threshold
H3487. Transformation toughening in zirconia needs the tetragonal grain larger than a critical size to transform under a crack tip, so below that size there is no toughening and above a second size the grain transforms spontaneously on cooling. The useful window is between two grain sizes. One composition fired to a series of grain sizes, with toughness and retained tetragonal fraction measured, shows both edges.
Non-monotonic
H3488. A higher tetragonal fraction raises toughness until the grains coarsen enough to transform spontaneously, after which the same fraction lowers toughness by pre-empting the transformation. Toughness against fraction therefore peaks. A series varying both fraction and grain size, with toughness measured, separates the two controls and locates the peak.
Identity
H3489. Damage from a thermal quench and damage from a sharp contact are the same crack population produced by two loading paths, so a thermal-shock ranking should predict a contact ranking. Both nucleate at the surface and grow on the same planes. One set of ceramics ranked both ways, with the crack patterns compared, tests the identity.
Bound
H3490. A glass-ceramic's strength cannot exceed the matrix's own strength plus the residual compression the crystals impose, so a crystal that raises toughness without raising that compression adds nothing to strength. The two properties come from different terms of one stress field. One glass-ceramic at two crystal fractions, with toughness and strength measured together, shows strength tracking compression rather than toughness.
Artefact
H3491. The strength gain of chemically tempered glass in bending is partly the compression layer suppressing the test's own contact damage, so the gain depends on loading geometry and is larger for a sharp contact than for a distributed load. The material's strength has not changed. One tempered glass in three geometries, with the contact stress computed, separates the artefact from the gain.
Hidden variable
H3492. Slow crack growth in a liquid-phase-sintered ceramic is governed by the boundary glass's viscosity rather than by the grain's toughness, so the activation energy of crack velocity equals the glass's and a more refractory boundary glass grows cracks more slowly at one stress. The grain contributes the path, not the rate. Two ceramics of one grain size but different boundary glass, with velocity measured at one temperature, distinguish them.
Hidden term
H3493. Indentation toughness includes the residual field's contribution, and the standard formula assumes the field is fully developed, which fails for cracks shorter than the indentation's plastic zone. Short-crack toughness is then under-reported rather than anomalous. One material across indentation loads, with crack length measured, shows the apparent toughness rising as the field develops.
Inversion
H3494. Strengthening a thin glass by ion exchange makes it better in bending and worse in impact, because the stored central tension drives fragmentation once a crack passes the compression layer, so one treatment moves the two properties oppositely. The crossover is a thickness. Thin and thick glasses exchanged together, tested in bending and in impact, show the inversion.
Symmetry argument
H3495. An isotropic glass should fragment isotropically, so a preferred crack direction records a frozen-in stress from forming or annealing, which makes the fracture pattern a stress map no polarimeter is needed to read. The direction follows the stress's principal axes. One plate broken on a support, with fragment orientations measured, should recover that direction and can be checked against a birefringence map.
Conservation argument
H3496. The energy released when a tempered plate fragments is its stored elastic energy, so fragment count per unit area is a direct reading of tempering stress that does not need the glass's toughness. Counting fragments is then a cheaper stress measurement than photoelasticity. One plate fragmented, with fragment count and birefringence measured, calibrates the count against the stress.
Path dependence
H3497. Grinding direction sets the strength of a ceramic because the subsurface cracks lie along the grinding marks, so a specimen ground one way has a strength that depends on which way it is bent. The anisotropy comes from crack alignment, not from roughness. One specimen ground in one direction, loaded parallel and perpendicular, shows it.
Uniqueness claim
H3498. The inert strength of a glass measured in vacuum is not unique, because pumping strips water from the surface while the glass keeps outgassing it, so the measurement is a race whose result depends on the pump's speed. Two laboratories with different pumps report different inert strengths for one glass. One sample measured at two pump speeds, with surface water tracked, shows the race.
Threshold
H3499. Crack healing in glass needs a temperature at which surface silanol groups condense, so a healed crack's strength depends on the humidity during annealing and not only on the temperature. A dry anneal heals less than a humid one at the same temperature. One glass, indented and annealed at one temperature in two humidities, with strength and interfacial water measured, places the threshold.
Anomaly resolved
H3500. Delayed failure of a ceramic at constant load without visible crack growth is the slow extension of a crack below the microscope's resolution, not a new mechanism. The crack grows where the stress intensity is still rising, so it accelerates invisibly until it is fast. Acoustic emission through a lifetime, with the failure origin measured afterwards, shows the growth the microscope could not.

Status and plan

One hundred entries, numbered in sequence. They were written individually, with the logical form chosen before the subject, so that no two share an argument shape; the labels are printed so that the claim can be audited against the text.

The physics is kept to the workshop and the kiln: redox and volatilisation in a melt, heat and flow at the forming stage, relaxation through the transition, expansion mismatch across a fired interface, and crack growth in a solid that cannot yield. No claim here concerns a product specification, a standard, or a supplier.

If one of these is worth an afternoon, it is H3496 — that the fragment count of a tempered plate is a direct reading of its stored stress, needing a hammer and a counting grid rather than a polarimeter. It would either give every glassworks a stress measurement it can afford, or show that fragmentation is too stochastic to read.

Incoprea Research · hand-considered hypotheses 3401–3500 · 3 November 2026 · ~/Desktop/Nov3/