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A systematic description of microstructure

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Abstract

A systematic treatment of microstructure is proposed. This structural level of solid matter comprehends all features which do not belong to bulk structure, or phase structure (crystals, glasses). Zero to three-dimensional discontinuities in the phase structure are defined as microstructural elements. Prototypes of two-phase microstructures are dispersion, net, cell and duplex. There may exist microstructural order, gradients, anisotropy, as well as mixtures and transformations of microstructural elements and types. Microstructural energy is given by the product of the density of a microstructural element and its specific energy. The scale of microstructure must be based on relations to properties. Fractal analysis may become useful for the description of rugged, fissured and branched microstructures.

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Abbreviations

a:

Amorphous phase

α, Β :

Crystalline phases

b :

Atomic spacing (m)

d :

Geometric dimension (integer)

d Β :

Particle diameter (m)

D :

Fractal dimension (non-integer)

ɛ :

Step or interval scale (m)

f :

Volume fraction of particles

F :

Force by obstacle on dislocation (N)

G :

Shear modulus (Pa)

γ:

Designation of any microstructure

γcell, γdispersion :

Type of microstructure

k :

Boltzmann constant (JK−1)

L :

Length of irregular curve (m)

ϱ i :

Density of microstructural elements (see Table II)

ϱ αα :

Density of grain boundaries (m−1)

ϱ αΒ :

Density of interfaces (m−1)

S Г :

Microstructural specific entropy (JK−1m−3)

S i :

Spacing of microstructural elements, grain diameter (m)

δΤ :

Increase in yield stress (Pa)

U i :

Specific energy of microstructural elements (see Table II)

δU i :

Interaction energy of microstructural elements (see Table II)

u Г :

Microstructure energy density (Jm−3)

W :

Number of configurations in a structure

x, y, z :

Cordinates in geometric space

N a :

Number of atoms per mole (mol−1)

V m :

Molar volume (m3mol−1)

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Authors and Affiliations

  1. Institut für Werkstoffe, Ruhr-Universität Bochum, Postfach 102148, 4630, Bochum 1, Federal Republic of Germany

    Erhard Hornbogen

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  1. Erhard Hornbogen
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Hornbogen, E. A systematic description of microstructure. J Mater Sci 21, 3737–3747 (1986). https://doi.org/10.1007/BF02431607

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  • DOI: https://doi.org/10.1007/BF02431607

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