Hand-considered hypotheses, 2101–2200
Metallurgy and phase transformations: solidification, precipitation, martensite, recrystallisation, diffusion, alloy design
Written one at a time, not composed. The logical form is printed with each entry because the forms are what differ: several claim a quantity is misattributed, several assert a bound, several invert a standard practice, one asserts that a correction cannot be made at all. The distribution is uneven and was not fixed in advance. None has been tested. Any number followed by “(estimate)” is an order-of-magnitude expectation, not a measurement; nothing here is a datum, and no citation is implied.
Solidification and casting
Misattribution
H2101. Equiaxed grain refinement by an inoculant is usually credited to the particles acting as heterogeneous nuclei, but for additions that dissolve partially the operative mechanism is growth restriction, since each dissolving particle enriches the liquid ahead of the front and that constitutional undercooling activates other nuclei. Comparing a soluble and an insoluble addition at equal particle size and equal added volume fraction separates them: only the soluble one can move the columnar-to-equiaxed transition at a fixed thermal gradient.
Hidden term
H2102. A cooling curve recorded in a casting carries the thermocouple's own response time, which for a half-millimetre bead in a metal sheath is of order a second (estimate), so any recalescence undercooling read from the curve is a lower bound. Deconvolving the bead's step response, measured in the same bath, recovers the true arrest, and the correction grows with cooling rate rather than staying constant.
Threshold
H2103. Sidebranching on a dendrite tip begins only above a tip velocity at which the tip radius exceeds the capillary length by roughly a factor of ten (estimate), because below that ratio the Mullins–Sekerka instability has no wavelength to amplify. Directional solidification at a series of velocities at one gradient, with branch spacing counted on quenched fronts, is the discriminating experiment, since the gradient alone does not set the amplification.
Artefact mimics effect
H2104. Grain counts that show refinement after a melt treatment can be an artefact of the section plane cutting columnar grains obliquely, which multiplies the apparent boundaries per unit area. Serial sectioning or X-ray tomography of the same region gives the true aspect ratio, and the refinement vanishes there if the polish was the cause.
Reversal
H2105. Adding inoculant beyond a few tenths of a per cent by weight (estimate) coarsens rather than refines the structure, because the excess particles agglomerate at the front and a few large clusters then act as a few large substrates instead of many small ones. An addition series in one alloy, held at constant superheat and pouring temperature, shows whether the curve has a minimum rather than a plateau.
Count
H2106. The permeability of a mushy zone at fixed solid fraction depends on at most two geometric descriptors, the specific surface of the solid and its tortuosity, so a Darcy model fitted with more parameters is absorbing the sample's own channeling. Permeability measured on directionally solidified samples with equal fraction but different dendrite morphology, compared against a two-parameter fit, exposes the redundant terms.
Scale argument
H2107. Back-diffusion during solidification is governed by the ratio of the secondary arm spacing squared to the diffusion length, so two castings cooled at the same rate but with different arm spacing end with different solute profiles. Holding the cooling rate fixed while changing the spacing through a modifier addition tests this directly, because the profile then has to follow the spacing and not the rate.
Unit trap
H2108. Cooling rates are quoted at the surface, and the rate at the solidification front differs from them by a factor of order the Biot number, so a critical cooling rate for a glass or for a phase skip belongs to the apparatus rather than to the alloy. Measuring front velocity directly by radiography in the same mould, alongside the thermocouple record, supplies the conversion factor that the quoted number hides.
Reversal
H2109. Hot-tearing susceptibility falls with rising superheat above a threshold, because the extra liquid at the coherency point lets the intergranular film heal while strain accumulates, which is the opposite of the usual expectation that more superheat means more shrinkage and worse tearing. Casting one alloy at a series of superheats with the mould temperature fixed isolates healing from shrinkage.
Identity
H2110. Shrinkage porosity and gas porosity are one phenomenon seen at two internal pressures, since both are the growth of a void that becomes stable when the local pressure falls below the sum of the gas's partial pressure and the surface-tension term. Solidifying one charge under two external pressures at constant gas content moves a single pore population along one curve rather than switching it between families.
Selection effect
H2111. Published maps of the columnar-to-equiaxed transition are compiled from experiments in which the transition could be located, which excludes the slow-gradient regime where it is diffuse and spreads over centimetres. Re-measuring a single alloy across the whole range with tomographic volume sampling will move the map's boundary wherever the detection criterion changes.
Derived quantity
H2112. Secondary dendrite arm spacing is used as a cooling-rate thermometer, but it keeps coarsening in the solid state after the front has passed, so the spacing records the integral of coarsening down to the last temperature where diffusion matters rather than the rate at the front. Quenching from different temperatures within the solid state after one solidification run changes the spacing if that coarsening term is real.
No-go claim
H2113. No inoculant can refine an alloy whose growth-restriction factor lies below a threshold, because the constitutionally undercooled zone ahead of the front never grows wide enough to activate a particle before the front arrives. A fixed addition across an alloy series spanning the restriction factor will show a sharp onset rather than a gradual improvement.
Memory claim
H2114. Melt superheat leaves a residue as oxide and nitride clusters that survive remelting, so the grain size of a casting can depend on the furnace's previous charges rather than on the current composition. Casting one charge from a clean crucible and from one that previously held a reactive alloy, with both analysed by spark spectrometry, tests whether the clusters carry the history.
Interface budget
H2115. Eutectic spacing is selected by minimum undercooling, yet in a confined channel the spacing cannot reach its optimum because the interface area available for solute rejection is fixed by the channel width, so the structure adopts a spacing set by geometry. Directional solidification in capillaries of decreasing diameter distinguishes the two, since the spacing stays pinned at a constant value instead of following the velocity scaling.
Coupling claim
H2116. Convection and dendrite arm spacing are not independent variables in a casting, since stirring thins the solute boundary layer at the tip while coarsening the arms, so correlations that treat flow and spacing as separate causes attribute both to one. Solidifying under a magnetic field that damps flow at fixed thermal gradient separates what the flow does from what the solute field does.
Precipitation and metastability
Misattribution
H2117. The incubation before solid-state precipitation is usually charged to the interfacial energy of the critical nucleus, but in quenched alloys much of it is the decay of the vacancy supersaturation, which sets how fast solute can cluster. Two samples quenched at different rates and aged at one temperature will show incubation times that differ although their equilibrium driving force is identical.
Hidden term
H2118. Coarsening rates extracted with the Lifshitz–Slyozov–Wagner form contain a finite-volume term that grows with precipitate fraction and is usually dropped, and keeping it shifts the inferred interfacial energy by tens of per cent (estimate). Ageing a series with the same precipitate at different volume fractions, at one temperature, produces rates that collapse onto one corrected curve and not onto the dilute limit.
Threshold
H2119. Below a critical supersaturation a metastable precipitate cannot convert into the stable one even after long times, because the stable phase must nucleate on the metastable particle's interface and the interfacial energy there exceeds the bulk gain. Ageing a composition series at one temperature reveals the conversion switching off at a composition rather than slowing smoothly.
Reversal
H2120. Raising the ageing temperature can lower the peak hardness while raising the hardness at short times, so two alloys ranked at one ageing time can be ranked in the opposite order at another. The crossover sits at a fixed fraction of the peak time when the reaction is isokinetic, which hardness against log time at three temperatures can confirm by showing a single crossing point.
Identity
H2121. Precipitate-free zones at grain boundaries and the depleted matrix beside them are one solute budget seen from two sides, since the zone is what the boundary precipitate took and its width is set by the boundary's diffusion field rather than by a separate vacancy mechanism. Integrating the solute profile across a boundary and comparing it with the boundary precipitate volume must close the balance.
Count
H2122. Three parameters predict the yield strength of a given precipitate microstructure: mean size, volume fraction and the fraction of particles that remain coherent, so a strengthening model with more terms is folding measurement scatter into physics. Fitting published datasets with three parameters and then adding a fourth leaves the residual unchanged.
Scale argument
H2123. The change from particle shearing to Orowan bypassing occurs where the cutting stress equals the bypass stress, and that size scales with the antiphase-boundary energy divided by the line tension, so a critical size is not transferable between alloys. Strength against particle size for two alloys with different ordered precipitates places the transitions at sizes in the ratio of their boundary energies.
Artefact mimics effect
H2124. An endothermic event on reheating a precipitation-hardened sample in a differential calorimeter can be the pan's oxidation rather than precipitate dissolution, and it appears at the same temperature in a run with an empty pan of the same metal. Running the sample in an inert crucible and in an aluminium pan under an identical programme shows which event belongs to the alloy.
Inversion of standard practice
H2125. Two-step ageing normally starts low to nucleate and finishes high to grow, but for a system with a wide metastable gap the reversed order, high first and low second, gives a finer dispersion, because the high step fixes a large number density and the low step grows it without further nucleation. Ageing one alloy both ways to the same total time and comparing size distributions tests the inversion.
Derived quantity
H2126. Precipitate volume fractions inferred from electrical resistivity use a rule of mixtures that fails for coherent particles, whose strain field scatters electrons independently of the particle's own resistance, so the derived fraction overestimates and the excess grows with misfit. Comparing resistivity-derived fractions with atom-probe measurements across a misfit series supplies the correction.
Null claim
H2127. Small-angle scattering with contrast variation cannot resolve a core–shell precipitate when the shell is thinner than the interface roughness, because the two contrasts average inside one resolution element and the fit returns a homogeneous sphere of intermediate radius. A series with increasing shell thickness at fixed core size discriminates: the fitted radius moves only after the shell exceeds the roughness.
Memory claim
H2128. Variant selection of precipitates remembers the strain path even after recrystallisation, because the recrystallised texture inherits a bias from the deformed grain and the precipitate then selects variants from that bias. Two samples with the same final texture produced by different strain paths differ in variant fraction if the memory is real.
Crossover claim
H2129. Nucleation on dislocations becomes faster than nucleation on grain boundaries only above a dislocation density, because the elastic interaction that makes a dislocation a good site is screened when the lines are sparse. Deforming a series to different strains at one ageing temperature, and locating where the dominant nucleation site changes, tests the crossing.
Bound
H2130. There is a particle size below which a precipitate cannot be cut at any applied stress, because the Orowan bypass stress falls faster with size than the cutting stress does, so the alloy yields by bypass whatever the particle's structure. Yield strength against particle size over two decades puts the slope change at the predicted size rather than at an arbitrary one.
Martensite and displacive transformations
Misattribution
H2131. The burst of transformation at martensite nucleation is usually explained by autocatalytic nucleation of neighbouring variants, but in bulk samples part of the burst is adiabatic heating, which raises the local temperature and arrests it. Reducing the sample's thickness so heat escapes within the burst duration changes the burst size while leaving the nucleation rate untouched.
Hidden term
H2132. Martensite-start temperatures measured by dilatometry include the sample's thermal lag, which appears as an extra undercooling of a few kelvin (estimate) and differs between furnace designs. Measuring one steel in two dilatometers with different thermocouple placements, and correcting by the recorded lag, removes most of the inter-laboratory scatter.
Identity
H2133. Thermal stabilisation of austenite on interruption and the depression of the start temperature by prior transformation are one phenomenon, since both are relaxation of transformation-induced defects that harden the austenite against the shape strain. Interrupting at different fractions and measuring the start temperature on resume, against a continuously cooled reference, collapses the effects onto one curve.
Bound
H2134. The maximum martensite fraction at a given undercooling is bounded by the austenite's yield strength rather than by the driving force, because the transformation stops when the shape strain can no longer be accommodated elastically. Strengthening the austenite by a different mechanism at the same start temperature lowers the plateau fraction, and the two correlate across alloys.
Reversal
H2135. Raising carbon lowers the start temperature and raises tetragonality, and above a carbon content the accommodation cost of that tetragonality can dominate, so the transformation is suppressed by mechanics rather than by thermodynamics. Measuring the start temperature against carbon across the range where tetragonality saturates exposes a change of slope tracking the mechanical term.
Count
H2136. Under a uniaxial stress only two martensite variant groups dominate, whatever the twenty-four crystallographically equivalent variants, because selection maximises the resolved shape strain and the remainder have zero or negative interaction energy. Variant mapping by electron backscatter on a sample deformed under a known stress recovers exactly two dominant groups.
Scale argument
H2137. Martensite plate thickness scales with the austenite grain size to a power below one, near the square root (estimate), because the plate's elastic energy grows with thickness while its interfacial energy grows with area. Plate thickness across a grain-size series at constant composition gives a slope near one half on logarithmic axes.
Unit trap
H2138. Martensite fractions measured magnetically are volume fractions weighted by the saturation moment, and the tetragonal phase's moment per atom differs from the cubic phase's, so the reported fraction carries a systematic offset of a few per cent (estimate). Calibrating against Rietveld refinement on the same samples gives a coefficient that stays constant across alloys.
Artefact mimics effect
H2139. Two calorimetric peaks in a steel said to transform in two stages can be one transformation spread by a thermal gradient across the sample, and the second peak should disappear when the mass is reduced. Running the same steel at three masses and one heating rate shows whether the split is intrinsic.
No-go claim
H2140. No thermoelastic martensite can show perfect superelasticity above the stress at which the austenite yields by slip, because slip destroys the lattice correspondence the transformation needs and the reverse path is then lost. Testing a series of orientations in one alloy, so that the resolved shear for slip varies while the transformation stress does not, shows superelasticity failing at a predictable stress.
Threshold
H2141. There is a grain size below which martensite cannot form in a given alloy, because a grain smaller than the self-accommodating variant group cannot absorb the shape strain without exceeding the matrix's elastic limit. A grain-size series at fixed composition drives the transformed fraction to zero at a size comparable to the plate thickness.
Hidden variable
H2142. The austenitising atmosphere fixes a carbon profile near the surface, so a surface-sensitive start temperature is a weighted average over a gradient whose weighting changes with the probe's depth. Measuring by dilatometry, by resistivity and by X-ray diffraction on the same steel, with different penetration depths, gives three values that converge when the layer is removed.
Inversion of standard practice
H2143. Faster cooling through the transformation range can leave less martensite in a steel that transforms only partially, because the thermal stress built by the gradient arrests the transformation mechanically while the driving force is still rising. Cooling one steel at two rates in a quench dilatometer after identical austenitising reveals the faster-cooled sample with more retained austenite.
Identity
H2144. Tempering of martensite and ageing of a supersaturated ferrite are one process at two carbon levels, and the sequence of carbide precipitation is continuous across the boundary that separates them in nomenclature. Comparing a low-carbon martensite tempered at 200 °C with a ferrite of the same carbon content aged at the same temperature gives the same carbide type and kinetics.
Recovery, recrystallisation and grain growth
Misattribution
H2145. The incubation before recrystallisation is usually attributed to nucleation of new grains, but much of it is the time needed for the deformed substructure to reach a critical misorientation across a boundary that can migrate. Pre-annealing at a low temperature to build the substructure without recrystallising shortens the subsequent incubation at the higher temperature.
Hidden term
H2146. Recrystallised grain size is predicted from stored energy, which the flow stress measures only in part, because the remainder sits in the latent hardening of the texture and is released only as the new grains consume the deformed matrix. Two samples with identical flow stress but different strain paths recrystallise to different grain sizes if that hidden term matters.
Threshold
H2147. A critical strain exists below which recrystallisation does not occur at any temperature, and it is not a constant, since it scales with the initial grain size because the stored energy per unit boundary area needed for nucleation falls as the grain grows. Measuring the critical strain across a grain-size series at one temperature gives a line rather than a point.
Reversal
H2148. Raising the annealing temperature through a solvus can coarsen the grain instead of refining it, because the pinning particles dissolve and the boundaries they held become free at the moment the driving force is largest. Annealing a particle-containing alloy at a series of temperatures across its solvus, after identical strain, drives the grain size through a minimum.
Count
H2149. A recrystallisation texture produced by a single strain path contains at most three independent components, because the orientation space reachable by the active slip systems is bounded, so a decomposition into more components is fitting the measurement's noise. Fitting published orientation distributions with three and then four components leaves the residual unchanged.
Scale argument
H2150. The change from discontinuous to continuous recrystallisation occurs where the subgrain size becomes a fixed fraction of the grain size, roughly one fifth (estimate), not at a fixed subgrain size, so the transition is a geometric ratio rather than a material property. Annealing samples of different initial grain size at one temperature places the transition at a constant ratio.
Artefact mimics effect
H2151. An exothermic event between rolling passes that is read as static recrystallisation can be the sample's re-equilibration with the dilatometer's push rods, which have their own heat capacity and their own time constant. Running the same thermal programme with a non-transforming dummy of identical dimensions shows whether the event belongs to the steel.
Selection effect
H2152. Published recrystallisation kinetics are measured at strains where the transformation is detectable, so the low-strain regime is missing and the fitted activation energy is biased high, because the incubation there lies below the instrument's resolution. Re-measuring one alloy down to its critical strain with a more sensitive probe lowers the apparent activation energy.
Inversion of standard practice
H2153. Cold rolling in one direction is the usual way to raise stored energy before annealing, but for a strongly textured sheet a change of rolling direction at constant total reduction gives a finer recrystallised grain, because the new slip systems multiply nucleation sites without adding strain. Rolling one alloy unidirectionally and cross-rolled to the same reduction, then annealing identically, tests it.
Derived quantity
H2154. The Avrami exponent is derived from transformed fraction, but for grain-boundary nucleation the exponent is time-dependent when the grain size is comparable to the growing nuclei, so a single exponent fitted over the whole range is an artefact of the fit window. Fitting the same data over early, middle and late windows gives three exponents that converge only at large grain size.
Memory claim
H2155. The temperature at which a cold-worked alloy recrystallises depends on its prior ageing through the solute atmosphere on dislocations, so two samples with identical deformation but different thermal histories before deformation recrystallise at different temperatures. Pre-ageing one batch and not the other, then deforming both identically, isolates the atmosphere's contribution.
Bound
H2156. Grain growth in a thin sheet stops when the grain size reaches roughly the sheet thickness, because the boundary area available to drive growth is bounded by the two free surfaces and the grains become columnar. Annealing foils of decreasing thickness at one temperature leaves the final grain size tracking thickness rather than time.
Identity
H2157. Abnormal grain growth and secondary recrystallisation are one phenomenon at two driving forces, since both are the unpinning of a few grains from a constraint, and the distinction lies in what pins the rest rather than in the mechanism. A single alloy in which the pinning is removed by two different routes shows the same abnormal-growth signature.
Step change claim
H2158. Particle pinning fails abruptly below a critical volume fraction rather than gradually, because the boundary's curvature cannot be maintained once the particle spacing exceeds a value set by the grain size, so the Zener limit is a cliff and not a slope. Annealing alloys of decreasing volume fraction at one temperature produces a step in final grain size rather than a smooth rise.
Diffusion and interfaces
Misattribution
H2159. Fast diffusion in fine-grained metals is usually assigned to grain boundaries, but where triple junctions are dense a large part of the flux passes along the lines where three boundaries meet, which carry a wider disorder zone. Comparing a bicrystal with a tricrystal of the same boundary type at the same temperature separates the two paths.
Hidden term
H2160. Interdiffusion coefficients from a diffusion couple contain the Kirkendall shift, so using them to predict precipitate growth overestimates the growth rate by a factor that includes the vacancy wind. Measuring marker motion in the same couple, and repeating the growth experiment on a sample with the same composition but a different marker density, tests the correction.
Threshold
H2161. A dislocation cannot climb past a particle below a critical stress, because the osmotic force from the vacancy supersaturation at the particle's interface opposes the mechanical force, and the threshold scales with the particle's misfit. Creep testing alloys of different misfit at one stress and temperature exposes a sharp transition in creep rate.
Curvature claim
H2162. An Arrhenius plot of diffusivity bends across a magnetic transition rather than staying straight, because spin disorder adds an entropy term to the activation barrier, so an activation energy fitted below the Curie point overestimates the high-temperature value. Measuring one solute's diffusion coefficient through the transition in a ferromagnetic matrix recovers the curvature at the known temperature.
Identity
H2163. Uphill diffusion inside a spinodal and solute clustering in a supersaturated solid solution are one process at two wavelengths, since both amplify a pre-existing composition fluctuation and differ only in whether the fluctuation is thermal or nucleated. Quenching two alloys to one temperature, one inside and one outside the spinodal, gives amplification rates that fall on one curve against wavelength.
Unit trap
H2164. Diffusion coefficients in square centimetres per second are not comparable when one is a tracer coefficient, one a chemical coefficient and one a self-diffusion coefficient, because the correlation factor and the vacancy wind differ, and ratios of several can appear (estimate). Converting all three for one system with measured correlation factors and plotting them together shows the spread that the units conceal.
Scale argument
H2165. When the diffusion distance is shorter than a few interatomic spacings Fick's law is the wrong description, and a coefficient fitted to a nanometre interdiffusion profile is really an interface transfer coefficient. Measuring the same interface at two temperatures and two times shows the fitted coefficient depending on time once the interface term dominates.
Degeneracy claim
H2166. A ternary diffusion matrix has two independent eigenvalues, so a report of three independent cross-diffusion regimes is a fit with a degenerate basis and the third eigenvalue is a combination of the other two. Recomputing a published matrix's eigenvalues and checking whether the smallest lies inside the measurement's noise settles the question.
Artefact mimics effect
H2167. Apparent uphill diffusion beside a Kirkendall void is the void's effect on marker positions and on the composition measurement, not a thermodynamic driving force, because the void displaces material and the probe averages across it. Measuring the same couple by two methods with different spatial averaging, one of which resolves the voids, separates the artefact from the profile.
Bound
H2168. The maximum thickness of a diffusion-bonded joint is bounded by the dissolution rate of the surface oxide rather than by applied pressure or hold time, because the oxide must be removed before metal-to-metal contact can carry diffusion. Bonding an oxide-free surface and an air-exposed one under identical conditions gives strengths differing by more than the process variables do.
Memory claim
H2169. A diffusivity measured at low temperature on a quenched sample is a vacancy-assisted value rather than an equilibrium one, because the quenched-in vacancies need hours to annihilate at the measurement temperature. Annealing the same sample at that temperature for different times before the diffusion run shows the apparent diffusivity falling towards the equilibrium value.
Inversion of standard practice
H2170. Homogenisation is normally done as hot as possible below the solidus, but for a system with a steep solvus a two-step schedule, low then high, removes coring faster because the first step avoids the low-melting eutectic while building the vacancy flux the second step needs. Comparing one-step and two-step schedules at equal total time on the same cast structure tests the claim.
Kinetic bound
H2171. Lamellar growth stops below a critical spacing, because the diffusion fields of adjacent lamellae overlap and the interface can no longer advance, so the bound is kinetic and independent of undercooling. Directional solidification of a eutectic at a series of velocities, with spacing measured where growth ceases, locates it.
Derived quantity
H2172. An activation energy fitted to diffusivity over a narrow temperature range is not the migration enthalpy alone, since the vacancy formation term and the temperature dependence of the correlation factor both contribute, and the fitted value exceeds the migration enthalpy by roughly the formation enthalpy. Fitting the same data over a wide range with a two-term model and comparing the results tests the decomposition.
Alloy design and property trade-offs
Misattribution
H2173. Solid-solution strengthening in concentrated alloys is usually assigned to atomic size misfit, but modulus misfit contributes through the dislocation line energy and can dominate where the size misfit is small. Two alloys with equal size misfit and different modulus misfit, tested in compression at one temperature, differ in yield stress if the modulus term is real.
Hidden term
H2174. The configurational entropy invoked to stabilise single-phase concentrated alloys is evaluated at a temperature where the phase is not in equilibrium, so the entropy-stabilisation argument is a kinetic claim wearing a thermodynamic label. Annealing one alloy at a series of temperatures for times long enough to approach equilibrium shows the single-phase field shrinking as the times lengthen.
Identity
H2175. Sluggish diffusion in concentrated alloys and the late onset of precipitation are one effect seen at two length scales, since the same chemical complexity that slows the jump also delays nucleation. An alloy designed for sluggish diffusion shows a longer incubation at fixed supersaturation, and the two measurements scale together across a composition series.
Bound
H2176. The strength of a precipitation-hardened alloy is bounded by the Orowan stress, and beyond a certain volume fraction the interparticle spacing cannot fall further without coarsening, so the bound is geometric rather than chemical. Adding solute past the point where the spacing stops falling raises the volume fraction without raising the strength.
Reversal
H2177. Refining the grain size of a twinning-induced plasticity steel can lower its ductility, because the twinning that supplies work hardening needs a grain large enough for a twin to form and thicken, and below that size the alloy deforms by slip and hardens less. A grain-size series at one composition, tested in tension, shows a ductility maximum at an intermediate size.
Count
H2178. Independent strengthening contributions in a multi-principal-element alloy number at most the distinct obstacle types present, so a model with more terms is counting the same obstacles twice under different names. Fitting a set of alloys with one term per obstacle type and then adding a further term leaves the residual unchanged.
Threshold
H2179. The face-centred to body-centred transition in concentrated substitutional alloys is set by the valence-electron concentration at which the Fermi surface touches the zone boundary rather than by the atomic size ratio, so alloys with equal size ratio and different electron count should sit on opposite sides. A composition series holding the size ratio constant while varying the electron count decides between them.
Artefact mimics effect
H2180. A second phase appearing in an in-situ diffraction pattern during heating can be the sample's own oxide, whose lattice happens to match the claimed phase, and it grows with the residual oxygen in the instrument. Repeating the run in a reducing atmosphere, or with a getter, removes the phase without changing the alloy.
Inversion of standard practice
H2181. Alloying for strength usually lowers electrical conductivity, but in a thermoelectric alloy the same solute can raise the Seebeck coefficient more than it lowers mobility, so the power factor peaks at an intermediate content. A solute series measured for conductivity and Seebeck coefficient at one temperature shows a maximum rather than a monotone decline.
Scale argument
H2182. Critical casting thickness and the critical cooling rate measured by calorimetry are not interchangeable, because thickness scales with the square root of the ratio of thermal diffusivity to the product of nucleation rate and growth velocity, so two alloys with equal calorimetric rates can differ in castable thickness by the ratio of their growth velocities. Casting one alloy at two thicknesses and comparing the result with its measured critical rate tests the scaling.
Memory claim
H2183. The glass-forming ability of an alloy depends on its melt's history through the size and number of oxide inclusions, which act as heterogeneous nucleation sites, so two melts of identical composition can have different critical casting thicknesses. Remelting one charge under a cleaner atmosphere and re-measuring that thickness shows the inclusions' effect rather than the composition's.
Identity
H2184. Quenched-in vacancies in a crystalline alloy and excess free volume in a metallic glass are one defect population at different packing fractions, and their annihilation should follow the same function of temperature. Measuring dilatation against annealing time in both, at the same homologous temperature, gives curves that superimpose.
No-go claim
H2185. No steel can combine a martensite-start temperature above roughly 700 K with resistance to softening above 800 K (estimate), because the carbide formers that give secondary hardening also strengthen the austenite and depress the start temperature. Plotting start temperature against secondary-hardening peak temperature across published steels gives a band rather than a scatter.
Unit trap
H2186. Strength converted from hardness is not comparable across crystal structures, because the conversion tables were built on a particular class of steels, and a factor of two error is possible when an fcc alloy is compared with a bcc one. Measuring both hardness and uniaxial yield on the same samples across a structural series supplies the correction instead of assuming it.
Selection effect
H2187. Alloy-design datasets over-represent compositions that were easy to cast and homogenise, so a model trained on them under-predicts alloys that are difficult to process and were therefore never measured. Testing the model on a composition made by a route that avoids the processing difficulty shows whether the gap is processing or physics.
Characterisation, processing and measurement
Artefact mimics effect
H2188. Grain growth seen in a hot-stage electron microscope can be the foil's own thinning under the beam, which changes the local chemistry and lets boundaries move, rather than a thermal effect. Comparing an irradiated region with a neighbouring blank region held at the same temperature separates the beam from the heat.
Hidden term
H2189. Grain sizes measured by electron backscatter diffraction include the step size's rounding, so maps with a step comparable to the grain size under-report the fine fraction and over-report the mean. Re-mapping the same region at half the step changes the reported distribution if that term is significant.
Misattribution
H2190. Texture memory in a thermomechanical process is usually credited to the prior texture, but the inherited feature is the grain-boundary character distribution, which decides which boundaries can migrate in the next cycle. Two samples with the same texture but different boundary character, produced by different annealing routes, behave differently in the next deformation step.
Threshold
H2191. There is a heating rate above which austenitisation cannot complete before the next process step, because the transformation's rate is limited by diffusion of the substitutional elements while the available time falls faster than the rate rises. Intercritical annealing at a series of heating rates with a fixed hold shows the austenite fraction at the start of the hold depending on the rate.
Reversal
H2192. Quenching a thick section faster through the martensite range can leave more retained austenite, because the thermal stress built by the gradient mechanically stabilises the austenite before the transformation can finish. Quenching thin and thick sections of one steel, then measuring retained austenite at centre and surface, separates the mechanical term from the thermal one.
Count
H2193. Independent process variables in a thermomechanical treatment are bounded by the state variables the final microstructure depends on, namely temperature, strain, strain rate and time, so a design claiming more than four knobs is confounding them. Varying each knob in a designed experiment and computing the rank of the response matrix gives the true count.
Derived quantity
H2194. The Zener–Hollomon parameter absorbs temperature and strain rate into one variable, but the compensation holds only while the mechanism is unchanged, so a plot that is linear in it over a wide range indicates two mechanisms rather than one. Looking for a slope change where the mechanism should change, instead of fitting a single line, tests the assumption.
Scale argument
H2195. The size effect in micropillar compression below a few micrometres is the ratio of sample diameter to dislocation source spacing, so a pillar's strength depends on its initial dislocation density as much as on its diameter. Pillars of one diameter cut from material with two dislocation densities differ as much as pillars of two diameters at one density.
Identity
H2196. Shear band formation in a metallic glass and adiabatic shear band formation in a crystalline alloy share one instability criterion, in which thermal softening overtakes strain hardening, and differ only in the state variable that carries the softening. Measuring band width against thermal diffusivity in both classes gives one scaling.
Hidden variable
H2197. The annealing atmosphere fixes the surface's nitrogen or carbon content, so the case depth attributed to a steel's hardenability is partly the atmosphere's doing. Annealing one steel in two atmospheres of different potential, then measuring case depth by hardness traverse, separates the two contributions.
Threshold
H2198. There is a critical section size above which a steel cannot through-harden whatever its ideal diameter, because the surface heat-transfer coefficient rather than the steel's hardenability limits cooling at the centre. Quenching geometrically similar bars of increasing diameter and measuring centre hardness shows a plateau that the ideal-diameter calculation does not predict.
Inversion of standard practice
H2199. Tempering immediately after quenching is standard practice against cracking, but for a steel with a strong secondary-hardening peak a delayed temper lets the retained austenite stabilise, so the standard practice gives a worse final toughness. Comparing immediate and delayed tempering with identical final tempering settles it.
Bound
H2200. The minimum grain size reachable by severe plastic deformation is a dynamic equilibrium between refinement and recovery, so a high stacking-fault-energy material saturates at a larger size than a low-energy one. Deforming two alloys to the same very high strain at one temperature gives saturation sizes ordered by their recovery rates.
Status
One hundred entries, 2101 to 2200, contiguous. The forms were allowed to fall where the subject put them, and the tally is reported rather than balanced.
Three that a laboratory with a quench dilatometer, a directional solidification rig and a hardness tester could begin on: H2110, that shrinkage and gas porosity are one pressure-stability curve; H2133, that thermal stabilisation and the depression of the start temperature on resume are the same relaxation; and H2168, that the thickness of a diffusion-bonded joint is bounded by oxide dissolution rather than by pressure or time.
If one of these is worth an afternoon, it is H2133 — interrupt a transformation at several fractions, resume each, and compare the start temperature on resume with that of a continuously cooled sample. It needs one steel and one dilatometer.
Incoprea Research · hand-considered hypotheses 2101–2200 · metallurgy and phase transformations · 3 November 2026 · ~/Desktop/Nov3/