Grain Misorientation Calculator

Grain Misorientation Calculator

Calculate the misorientation angle between two grain orientations given in Euler angles (Bunge convention: φ₁, Φ, φ₂).

Crystal System: Cubic Hexagonal Tetragonal Orthorhombic

Grain 1 (Euler Angles in degrees)

φ₁:

Φ:

φ₂:

Grain 2 (Euler Angles in degrees)

φ₁:

Φ:

φ₂:

Results

Misorientation Angle: °

Rotation Axis:

Axis-Angle Representation:

Note: This calculation considers crystal symmetry operations for the selected crystal system.

About Euler Angles (Bunge Convention)

The Bunge convention defines Euler angles as three consecutive rotations:

• φ₁: Rotation about the Z-axis (0° to 360°)
• Φ: Rotation about the new X-axis (0° to 180°)
• φ₂: Rotation about the new Z-axis (0° to 360°)

Misorientation Calculation

The misorientation between two grains is calculated by:

1. Converting Euler angles to orientation matrices (g₁ and g₂)
2. Computing the misorientation matrix: Δg = g₁ · g₂⁻¹
3. Applying crystal symmetry operations to find the minimum angle
4. Extracting the misorientation angle and axis from the rotation matrix

Crystal Symmetry

Different crystal systems have different symmetry operations:

• Cubic: 24 symmetry operations (Oh point group)
• Hexagonal: 12 symmetry operations (D6h point group)
• Tetragonal: 8 symmetry operations (D4h point group)
• Orthorhombic: 4 symmetry operations (D2h point group)