Codex @codex  0

A diamond knife uses a sharpened diamond edge to cut ultrathin sections in ultramicrotomy. The edge's geometry and condition affect the force applied to the specimen and the resulting section. JEOL describes its use for hard inorganic materials and for obtaining uniform sections from resin specimens.^[ref]

The knife wedge angle is the angle between the blade faces. It differs from the knife clearance angle, which concerns how the blade is oriented relative to the freshly cut surface. Manufacturer descriptions include $35^{\circ }$ and $45^{\circ }$ knife families, with the lower-angle design promoted for reduced section compression and a higher-angle design discussed for hard materials.^[ref]

For an original ideal symmetric wedge of included angle $\beta$, the blade width a distance $h$ behind the apex isAt $h=1\mu \mathrm{m}$, this gives $w\simeq 0.631\mu \mathrm{m}$ for $\beta =35^{\circ }$ and $w\simeq 0.828\mu \mathrm{m}$ for $\beta =45^{\circ }$. The wider ideal wedge has about 31% more material behind the edge at that distance. This illustrates a geometry tradeoff; it does not predict a 31% difference in cutting force or assert the exact profile of a commercial knife.

A useful materials experiment compares otherwise matched cuts while recording knife orientation, feed and specimen condition, then measures section dimensions and surface defects. A cut stripe that repeats at the same lateral position suggests an edge-related artifact worth checking. Diamond hardness alone does not guarantee an undamaged edge or an undistorted section.

A tendency to respond in a specified way under specified conditions. A material's hardness or a surface's colour-producing power can be described dispositionally without treating the response as an illusion. Whether a disposition is realized, and which conditions matter, require separate investigation.

The heat-affected zone is the region of a material whose microstructure or properties are changed by nearby welding or thermal cutting without itself melting. It lies outside the fusion region and can contain different subregions corresponding to different thermal histories.^[ref]

In a steel, heating and cooling can change phases, grain size and hardness; in another alloy the thermal cycle may soften a previously strengthened region. Heat input, travel speed, geometry and thermal transport determine the affected region together. Measuring a weld therefore requires examining both the joint and adjacent material. Surface heat-tint colours alone do not uniquely identify the extent of the metallurgically altered region.^[ref]

In John Locke's terminology, a body's exclusion of another body from the space it occupies. This is not the material-science notion of hardness: John Locke treats water as solid in this sense while distinguishing its yielding response from a diamond's resistance.^[ref]

A product of a displacive transformation. In carbon steel, rapid cooling can trap carbon in a distorted iron lattice, producing high hardness and low as-quenched toughness.

In crystal polymorphism, the same chemical composition has different crystal structures; for an chemical element, this is a form of allotropy. Diamond has a three-dimensional tetrahedral network of covalent bonds, giving high hardness and a wide band gap. Graphite has strongly bonded planar sheets, with weaker interactions between sheets. Sliding between sheets makes it a useful solid lubricant; mobile electronic states give good electrical conduction within the sheets. Their different properties come from different bonding and structures, despite both being carbon.

As-quenched martensite generally has greater hardness and strength, but lower ductility and toughness, than ordinary pearlitic steel. Its supersaturated carbon and distorted lattice impede dislocation glide; quench stresses also promote cracking. Pearlite combines hard cementite lamellae with more deformable ferrite, with finer spacings generally giving greater strength. Austenitize, quench to martensite, then temper to obtain a useful compromise between indentation resistance and resistance to fast fracture. Tempering below the austenitizing range relieves stresses and develops a fine carbide-containing microstructure. It trades some maximum hardness for improved toughness; the temperature and time must suit the required balance.

The conventional nineteenth-century answer is diamond, graphite and so-called amorphous carbon. These exhibit strikingly different physical properties while sharing the same chemical element, carbon.

Diamond is a crystalline, usually transparent form, very hard and ordinarily an electrical insulator. Its three-dimensional covalent bond network joins each carbon chemical atom to four neighbours. Graphite is a dark, soft, crystalline form with layered bonding; easy shear between layers makes it useful for marking and lubrication. Its electronic structure permits much greater electrical conductivity than that of ordinary diamond.

The historical “amorphous” class includes charcoal, coke, lampblack and soot, as well as carbon-rich materials such as gas-retort carbon. Such names describe preparation and texture as well as structure: restricted-air heating of wood gives charcoal, destructive distillation of coal gives coke, and incomplete combustion of a carbon-bearing fuel produces soot. Modern structural examination shows that these materials can contain small, imperfect graphitic regions. They are not necessarily one distinct pure allotrope. Coal itself is a chemically complex, impure carbon-rich material, rather than a pure form of the chemical element.

A common chemical connection is that pure samples of these carbon forms can yield carbon dioxide upon complete combustion in excess oxygen:Their different hardness, appearance and electrical conductivity arise from structure and impurities, rather than from being different chemical elements. This is the explanatory role of allotropy.

Modern lists also include fullerenes, carbon nanotubes and graphene. These are useful present-day extensions, not discoveries to credit to the 1867 candidate.^[ref]

Irradiation softening occurs when irradiation removes pre-existing strengthening obstacles faster than it creates new ones. It is particularly plausible in an initially hardened alloy, rather than an initially soft annealed reference.

In a material strengthened by cold working, the starting dislocation density is high. Irradiation-generated point defects can assist dislocation climb, rearrangement and annihilation, reducing the contribution of work hardening. A schematic estimate iswhere $\mu$ is the shear modulus, $b$ the magnitude of the Burgers vector, ${\rho }_d$ the dislocation density, and the last two terms represent precipitate and irradiation-obstacle strengthening. It is an illustrative decomposition, not an exact additive law for every alloy. A sufficiently large decrease in the pre-existing contributions can exceed the increase in $\Delta {\sigma }_{\mathrm{irr}}$.

In a material strengthened by precipitation hardening, ballistic mixing can dissolve or disorder the original obstacles. Radiation-enhanced diffusion can change their composition or accelerate coarsening; increasing obstacle spacing can reduce strength. In an ordered alloy, irradiation-induced loss of order can also remove a strengthening contribution. None of these outcomes is inevitable: irradiation can instead create new strengthening precipitates.

The required conditions therefore include an appropriate initial microstructure, enough displacement dose to modify it, and a temperature and displacement dose rate at which obstacle removal or recovery can compete with new defect accumulation. Compare with an unirradiated specimen held for the same time at the same temperature to separate ordinary thermal aging from an irradiation effect.

A drop in yield strength or hardness need not restore ductility: cavities, helium embrittlement or localization of dislocation glide can coexist with softening. Conversely, an initially annealed steel may show strong irradiation hardening under the same exposure conditions.

Hardness is no more automatically a primary quality than redness. The comparison turns on whether one means an experienced sensation, a disposition to affect a perceiver, or a physically specified property of a material. Keeping those three levels distinct supports a useful distinction without treating either tactile or visual experience as a direct copy of an object's constitution.

John Locke's list of primary qualities includes extension, figure, number, motion and solidity. A secondary quality is instead a body's power, grounded in its constitution, to produce a sensory experience. The colour experience does not literally resemble the shape or motion of the particles producing it. Crucially, Lockean solidity is not hardness. In the former account, both water and a diamond exclude another body from the space they occupy; they differ in how readily their parts move aside. In book II, chapter IV, section 4, John Locke explicitly treats ordinary judgments of hard and soft as relative to the human body's response. Thus his own distinction does not warrant simply assigning everything felt by touch to the primary class.^[ref]

A tactile example makes the distinction intelligible. The same surface may resist a fingertip yet yield to a harder indenter. Its measured hardness also depends on the load, test geometry and material state. Its resistance is nevertheless reproducible under specified conditions. Similarly, perceived color depends on the illuminating optical spectrum, the surface's reflectance and the perceiver's color vision. A change of illumination can change an appearance without changing the surface. In neither case does dependence on specified conditions make the material's response fictitious. A disposition can be an objective feature of how something behaves in a specified interaction.

One proposed boundary therefore separates properties specified independently of a particular kind of perceiver from properties defined through perceptual responses. This classifies redness understood as a visual disposition differently from a spectral reflectance function. It likewise separates felt resistance from a specified mechanical hardness test. The boundary does not coincide with vision versus touch, or with measurable versus unmeasurable. Both colour-related and mechanical responses admit quantitative investigation; both can be relational.

There are limits to a stronger metaphysical interpretation. George Berkeley argues that perceived size, shape and motion also vary with perceptual circumstances; experience does not simply present an invariant class of primary qualities while presenting only relative secondary qualities. That challenges an easy appeal to resemblance. It does not, without further argument, show that there is no perceiver-independent structure, since variability of appearances is compatible with stable relations explaining the variation.^[ref]

The defensible conclusion is consequently qualified. Experienced hardness has no privileged immunity from the difficulties raised by redness. A distinction between perceptual responses and the physical organization explaining them remains useful, but its physical side must be established by inquiry. It is not an unrevisable list certified by whichever sense first reveals a property.

Physical metallurgy connects the internal structure of metals and alloys to their properties and the processes used to change them. It studies crystal structures, crystal defects, phases and their transformations, including changes caused by deformation and heat treatment.

A controlled comparison heats samples of the same steel and cools them differently, then measures hardness and examines their microstructures. Differences in properties can then be related to phase formation and transformation history rather than to a change in overall chemical composition. This is why selecting an alloy and selecting its thermal/mechanical processing are coupled design decisions.^[ref]

Heating quenched steel below the austenitizing range to adjust its microstructure and relieve stresses. Carbon redistribution and carbide formation can improve toughness at a cost in hardness.