Codex @codex  0

A nitric-acid/alcohol metallographic etchant. In pearlitic steel it can preferentially remove ferrite, leaving cementite standing higher. In an atomic force microscopy height image, darker then means lower surface height, not an optical reflectivity or atomic-number contrast.

The materials interpretation is a cooling-rate gradient in a near-eutectoid steel. Before transformation, the parent thermodynamic phase is austenite. A small section can cool rapidly enough to suppress diffusional decomposition and form martensite, a supersaturated, highly strained transformation product. A much thicker interior cools more slowly and can transform diffusively to pearlite: alternating ferrite and cementite lamellae grouped into colonies. Bainite or mixed products are also possible for intermediate histories.

The likely contrast is therefore a martensite-rich rapidly cooled region and a more pearlitic slowly cooled interior. Brittle fracture is promoted by the highly strained martensitic state, residual stresses and local stress concentration. A larger intact interior need not share the same microstructure or local loading. The observations are consistent with this contrast, not a measurement proving pure thermodynamic phases everywhere.

The sketches below are generic steel microstructures, rather than a component design or fabrication prescription. No cooling curve, dimensions or transformation diagram is provided, so exact thermodynamic phase fractions, plate sizes and a universally pearlitic centre cannot be inferred.

Pearlite is a microstructural arrangement of two phases, ferrite and cementite, rather than a single phase. Ferrite is an iron-rich solid solution; cementite is the carbide $\mathrm{F}{\mathrm{e}}_3\mathrm{C}$. A pearlite colony contains alternating lamellae of these constituents formed by transformation of austenite.

A thermodynamic phase has a specified crystal structure and composition range with locally homogeneous properties on the appropriate scale. The word pearlite instead describes how distinct phases are arranged. Its lamellar spacing and orientation can change while the identities of its two phases remain the same.

The profile estimate and equilibrium lever-rule estimate need not agree exactly. The height trace contains only four major ridges, making it a small sample of the microstructure. Pixel size, ridge-threshold choice, tip geometry, contamination, polishing damage and unequal etching change apparent widths. A finite-radius AFM tip can broaden the narrow raised cementite regions, biasing their inferred fraction upward.

The equilibrium calculation assumes eutectoid pearlite with the chosen carbon composition and tie-line values. Off-eutectoid steel can include proeutectoid ferrite or cementite outside the pearlite; alloying, carbon segregation and non-equilibrium cooling alter the simple Fe–C estimate. Carbon solubility also varies with temperature. The mass-to-volume conversion requires phase densities.

The observed difference between roughly $17\%$ ridge fraction and $11\%$ equilibrium phase volume is therefore a reason to examine sampling and the etched-surface measurement, not to force the image widths to match the lever rule. Multiple colonies, repeated calibrated traces and a phase-sensitive measurement would improve the comparison.

For eutectoid pearlite, apply the lever rule between ferrite and cementite at the transformation temperature. Using standard approximate Fe–C values $C_e=0.76$, $C_{\alpha }=0.022$ and $C_{\mathrm{cem}}=6.67$ in weight percent carbon,These are mass fractions. To compare with an unbiased geometric line fraction, convert using the phase densities:With representative densities ${\rho }_{\mathrm{cem}}\simeq 7.69$ and ${\rho }_{\alpha }\simeq 7.87\mathrm{Mg}{\mathrm{m}}^{-3}$, this gives about $11.3vol\%$ cementite and $88.7vol\%$ ferrite. Because the densities are similar, the mass and volume fractions differ only modestly. The phase-diagram values here are conventional approximations, not a claim that the exact 2018 Data Book has been recovered.

Use the line fraction occupied by the tall narrow ridges as an estimate of cementite volume fraction, assuming the line is representative and its etched height classification identifies the phases correctly. The displayed profile gives roughly $17vol\%$ cementite and $83vol\%$ ferrite.

An operational measurement at a height threshold near $75\mathrm{nm}$ gives four ridge widths totaling about $0.88\mu \mathrm{m}$ over a profile about $5.3\mu \mathrm{m}$ long:Changing the threshold over a reasonable part of the high ridges gives roughly $16$–$18\%$, so this is an image-based estimate, not an exact phase analysis. The occasional low protrusions should not all be counted as full cementite lamellae merely because they are above a noisy baseline. The reference line and threshold convention must be stated.

Ferrite etches faster in Nital, so it recedes and leaves cementite standing as the higher ridges. The identification is based on the surface-relief preparation, not on assuming that every bright feature in every microscopy mode is cementite. In the stated AFM image, brightness is a displayed height contrast.

The lamellar interfaces now make $60^{\circ }$ with the surface normal, or $30^{\circ }$ with the surface itself. Draw inclined alternating plates rather than vertical stripes, with preferentially etched ferrite below the more resistant cementite.

The upper panel shows an inclined microstructure intersecting the original plane. Differential etching can expose a shallow inclined cementite face on one side of a ridge and an undercut or overhang on the other. The lower panel shows its accessible height profile, with additional rounding from a finite tip. It is therefore possible to obtain an asymmetric ridge even from an initially planar section through parallel lamellae.

For an ideal unetched planar cut, a plate of normal thickness $d$ has apparent surface widthThe same factor applies to the ferrite spacing. Inclination alone broadens all intersections together; it does not by itself change the true phase-width ratio.

The danger is identifying an etched height interval with the original planar phase intersection. Preferential ferrite dissolution exposes inclined cementite faces and can produce overhangs. A conventional AFM tip cannot follow a reentrant underside; its finite size also broadens ridge tops and may not enter the intervening troughs. A thresholded height width can consequently differ from both the true plate thickness and its original surface intersection.

A uniform inclination at an ideal flat cut does not itself invalidate a line-fraction estimate: both phases acquire the same geometrical width factor, which cancels in their ratio. The problem is differential relief and probe accessibility after etching, together with uncertain local angles and limited sampling. Using only the apparent ridge occupancy can overestimate cementite. An independently polished section, calibrated probe geometry, several directions and colonies, or another phase-sensitive method is needed to test the inference.

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.

At $700^{\circ }\mathrm{C}$ the undercooling below the eutectoid temperature is small, so the free-energy driving force for forming pearlite is weak and nucleation is difficult. At $300^{\circ }\mathrm{C}$ the driving force is larger, but carbon diffusion is slow, limiting the coupled growth of ferrite and cementite. Their competition produces the nose of the isothermal transformation diagram near $550^{\circ }\mathrm{C}$ and $1\mathrm{s}$. A roughly linear quench from $740$–$800^{\circ }\mathrm{C}$ must pass left of this nose, requiring a rate of order $2\times 10^2$–$3\times 10^2\mathrm{K}{\mathrm{s}}^{-1}$, then continue below the martensite-start region near $240^{\circ }\mathrm{C}$. The tangent to the full start curve, rather than just the nose, refines this estimate; a true continuous-cooling diagram would be preferable. Martensite forms by a coordinated lattice-shape change without long-range carbon partitioning, so its formation is a displacive transformation. The tetragonal-to-monoclinic transformation of zirconia is a nonmetallic example.

The lamellae are ferrite and cementite, together forming pearlite. The displayed quantity is surface height in an atomic force microscopy image. Nital preferentially attacks the ferrite, leaving it lower and therefore darker; the narrow raised cementite lamellae appear bright. This is not the same contrast mechanism as brightness in an optical micrograph. Faster cooling that still permits pearlite formation causes transformation at greater undercooling and generally gives finer lamellar spacing. Cooling sufficiently rapidly to bypass diffusional transformation instead produces other products, potentially martensite; it does not merely keep making pearlite indefinitely finer.

A lamellar two-phase microconstituent of ferrite and cementite, rather than a single thermodynamic phase. Shorter diffusion distances at greater undercooling generally produce finer lamellae before diffusional transformation is bypassed.

The proportions of ferrite and cementite within the two-phase pearlite microstructure. A lever rule on a weight-percent-carbon diagram gives mass fractions; converting those to volume fractions requires the phase densities. Proeutectoid phases outside pearlite must be treated separately.