Formula Used:
From: | To: |
Definition: The Miller Index along z-axis is a notation system in crystallography for planes in crystal (Bravais) lattices along the z-direction.
Purpose: It helps crystallographers and materials scientists describe the orientation of crystal planes.
The calculator uses the formula:
Where:
Explanation: The LCM of all Weiss indices is divided by the Weiss index along z-axis to get the Miller index along z-axis.
Details: Miller indices are crucial for describing crystal planes, which affect material properties like cleavage, electronic properties, and surface reactivity.
Tips: Enter the Weiss indices along x, y, and z axes (must be positive integers). The calculator will compute the corresponding Miller index along z-axis.
Q1: What's the difference between Weiss and Miller indices?
A: Weiss indices are the reciprocals of intercepts with crystal axes, while Miller indices are the smallest integers having the same ratio.
Q2: Why do we use LCM in this calculation?
A: LCM helps find the smallest integers that maintain the same ratio as the Weiss indices.
Q3: Can Miller indices be negative?
A: Yes, negative indices are written with a bar over the number, but this calculator only returns positive values.
Q4: What's the physical meaning of the z-axis Miller index?
A: It describes how the crystal plane intersects the z-axis of the unit cell.
Q5: How are Miller indices used in materials science?
A: They're used to describe crystal planes for diffraction studies, surface analysis, and predicting material properties.