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Chapter 3: Problem 63

Explain why the properties of polycrystalline materials are most often isotropic.

Short Answer

Expert verified
Answer: The properties of polycrystalline materials are considered isotropic because the random orientation of their grains and large number of grain boundaries cause the material's anisotropic properties to average out. The directional dependence of individual grain's properties is effectively lost due to the large number of different grain orientations and their unique anisotropic characteristics being combined, resulting in overall isotropic properties.

Step by step solution

01

Understanding Polycrystalline Materials

Polycrystalline materials are composed of a large number of small crystals or grains, which are randomly oriented. Each individual grain has a highly ordered atomic structure and distinct anisotropic properties. This means that the grain's properties depend on the crystal orientation and will vary with their direction.
02

Defining Isotropic Properties

Isotropic properties are those that do not depend on the direction in which they are measured. In other words, they are independent of the orientation of the material. In an isotropic material, the physical and mechanical properties (such as elastic modulus, thermal expansion, and electrical conductivity) remain the same in all directions.
03

Random Orientation of Grains in Polycrystalline Materials

The key characteristic of polycrystalline materials is the random orientation of their grains. Each grain's lattice orientation is different from its neighbors, and no particular crystallographic direction is prevalent throughout the whole material. The grains are surrounded by grain boundaries where two grains of different orientations meet, each boundary being in between neighboring grains.
04

Averaging Effects

In polycrystalline materials, the random orientation of grains and large number of grain boundaries cause the material's anisotropic properties to average out. When a force is applied to the material in any direction, the directional dependence of individual grains' properties is essentially lost. This happens due to the large number of different grain orientations and their unique anisotropic characteristics being combined.
05

Isotropic Properties of Polycrystalline Materials

The averaging of anisotropic properties from different grains with random orientation effectively makes the overall properties of polycrystalline materials isotropic. These isotropic overall properties are beneficial in many applications as the properties stay consistent regardless of the direction of forces and stress acting on the material. This is why the properties of polycrystalline materials are most often considered isotropic.

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Most popular questions from this chapter

Convert the \([110]\) and \([00 \overline{1}]\) directions into the four-index Miller-Bravais scheme for hexagonal unit cells.

(a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius \(R\). (b) Compute and compare linear density values for these same two directions for iron \((\mathrm{Fe})\).

Indium (In) has a tetragonal unit cell for which the \(a\) and \(c\) lattice parameters are \(0.459\) and \(0.495\) \(\mathrm{nm}\), respectively. (a) If the atomic packing factor and atomic radius are \(0.693\) and \(0.1625 \mathrm{~nm}\), respectively, determine the number of atoms in each unit cell. (b) The atomic weight of In is \(114.82 \mathrm{~g} / \mathrm{mol} ;\) compute its theoretical density.

The metal niobium (Nb) has a BCC crystal structure. If the angle of diffraction for the (211) set of planes occurs at \(75.99^{\circ}\) (first-order reflection) when monochromatic x-radiation having a wavelength of \(0.1659 \mathrm{~nm}\) is used, compute the following: (a) The interplanar spacing for this set of planes (b) The atomic radius for the Nb atom

Calculate the radius of a tantalum (Ta) atom, given that Ta has a BCC crystal structure, a density of \(16.6 \mathrm{~g} / \mathrm{cm}^{3}\), and an atomic weight of \(180.9 \mathrm{~g} / \mathrm{mol}\)
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