E2 Microstructure: Grain Size

Topic

The grain size of this polycrystalline metal is the fundamental geometric parameter that describes this model, and it is the same linear intercept method, originally proposed by Heyn and already used for this same purpose by another model of this set, which measures it directly on a microscopic image of the sample. The fact that the line of known length drawn by this linear intercept method crosses more grain boundaries as it traverses that image makes the measured grain size of this metal correspondingly smaller.

That same grain size, once measured, can be expressed in two different and mutually equivalent ways: as an ASTM index, a numerical scale in which each increasing unit represents approximately half the grain size of the previous unit, or directly as a circular equivalent diameter, the diameter that a circle with the same area as the average observed grain would have. That this ASTM index is greater means that the corresponding circular equivalent diameter is, consequently, smaller, because both ways describe, in opposite directions, the same increasingly finer grain size.

That same grain size also determines the mechanical resistance of this metal, according to the Hall-Petch relationship that will describe in detail another model of this set: the grain boundaries act as obstacles to the movement of the dislocations, and the more grain boundaries there are per unit volume, the more obstacles each dislocation encounters along its path. The fact that this grain size is smaller, with more grain edges per unit of volume, means that, according to the same Hall-Petch relationship, the mechanical resistance of this metal is greater; The fact that this grain size is larger means that the mechanical resistance is lower.

That is why this model, with the grain size and the linear intercept method with which it was opened, also determines the kinetics of two different transformations that describe two other models of this set: the recrystallization of this metal, which progresses faster the smaller this initial grain size is, because there is more grain boundary available from which each new recrystallized grain can nucleate; and the sintering of this metal in powder form, which also progresses faster the smaller the grain size of the starting particles, for the same geometric reason. That this grain size, determining for both kinetics and for the mechanical resistance already established by the Hall-Petch relationship, can be measured by two independent experimental methods means that another model in this set measures it by X-ray diffraction, through the Williamson-Hall analysis, cross-confirming the same grain size that is already measured, directly on a microscopic image, by the linear interception method.

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