11.6
In crystallography, crystal faces exist at specific orientations that follow simple geometric relationships.
To describe these relationships, imagine three crystallographic axes—OX, OY, and OZ —intersecting at a common origin. These axes act as reference directions in the crystal. A crystal face may cut these axes at certain distances from the origin, called intercepts.
Consider a plane PQR that intersects the axes at OP, OQ, and OR, which represent the unit intercepts a, b, and c.
Now observe another plane, KLM, intersecting the same axes. Here, the intercepts appear as simple whole-number multiples of the unit intercepts.
For example, the plane may intersect the axes at a, 2b, 3c, but not at arbitrary distances.
This pattern represents the Law of Rational Indices, which states that a crystal face intersects the crystallographic axes at distances equal to simple whole-number multiples of the unit intercepts.
This law helps relate crystal structure to measurable properties such as diffraction patterns, surface energies, and catalytic behavior.
The Law of rational indices is a fundamental principle in the field of crystallography. According to this law, the intercepts of a crystal face along the crystallographic axes (the three-dimensional axes along which a crystal is measured) can be expressed as either equivalent to the unit intercepts (a, b, c) or simple whole number multiples of them. These multiples are typically denoted as na, n'b, and n''c, where n, n', and n'' are simple whole numbers.
To illustrate, consider a crystal with three crystallographic axes labeled OX, OY, and OZ. The unit plane within this crystal is denoted as PQR. The unit intercepts in this system would be a, b, and c.
Applying the law of rational indices, the intercept of any other plane within the crystal, such as KLM, on these three axes can be expressed as simple whole number multiples of a, b, and c, respectively.
In essence, this law helps to describe the geometric arrangement of atoms within a crystal systematically and mathematically. This law is crucial in developing crystallography as a scientific discipline, enabling researchers to predict and understand the properties of crystals based on their internal atomic structures.
In crystallography, crystal faces exist at specific orientations that follow simple geometric relationships.
To describe these relationships, imagine three crystallographic axes—OX, OY, and OZ —intersecting at a common origin. These axes act as reference directions in the crystal. A crystal face may cut these axes at certain distances from the origin, called intercepts.
Consider a plane PQR that intersects the axes at OP, OQ, and OR, which represent the unit intercepts a, b, and c.
Now observe another plane, KLM, intersecting the same axes. Here, the intercepts appear as simple whole-number multiples of the unit intercepts.
For example, the plane may intersect the axes at a, 2b, 3c, but not at arbitrary distances.
This pattern represents the Law of Rational Indices, which states that a crystal face intersects the crystallographic axes at distances equal to simple whole-number multiples of the unit intercepts.
This law helps relate crystal structure to measurable properties such as diffraction patterns, surface energies, and catalytic behavior.
From Chapter 11:
Now Playing
The Solid State: Crystals and Surfaces
71 Views
The Solid State: Crystals and Surfaces
206 Views
The Solid State: Crystals and Surfaces
119 Views
The Solid State: Crystals and Surfaces
506 Views
The Solid State: Crystals and Surfaces
237 Views
The Solid State: Crystals and Surfaces
85 Views
The Solid State: Crystals and Surfaces
192 Views
The Solid State: Crystals and Surfaces
86 Views
The Solid State: Crystals and Surfaces
254 Views
The Solid State: Crystals and Surfaces
201 Views
The Solid State: Crystals and Surfaces
167 Views
The Solid State: Crystals and Surfaces
423 Views
The Solid State: Crystals and Surfaces
387 Views
The Solid State: Crystals and Surfaces
203 Views
The Solid State: Crystals and Surfaces
224 Views
See More