ME115 - Week 3

Miller Indices

Allotropic/polymorphic

When certain materials can have more than one crystal structure, this can also change the volume of the material.

E.g. at room temperature iron has a BCC structure, but if you heat it to 912 Celsius it becomes FCC and if you heat it to 1394 Celsius it goes back to BCC. Or how carbon can be diamond or graphite (determined by the temp and pressure that the crystals form at).

Polymorphism is only for compounds (more than one element)

Examples of SC crystals

Polonium, alpha manganese

Examples of BCC crystals

Iron (ferrite; alpha-Fe), titanium (beta-Ti), tungsten (W), potassium, sodium, zirconium (beta-Zr), chromium, molybdenum, niobium, tantalum, vanadium

Examples of FCC crystals

Iron (austenite; gamma-Fe), copper, silver, lead, nickel, gold, platinum

Examples of close-packed hexagonal crystals (HCP)

Titanium (alpha-Ti), magnesium, zinc, beryllium, cobalt, zirconium (alpha-Zr), cadmium

Anisotropy

The structural property of a material or system where physical, mechanical, or optical properties vary depending on the direction of measurement.

This is the case with young’s modulus where the young’s modulus of bulk materials is the average of the young’s modulus in each direction.

How to find the miller indices for a direction

1. Determine the coordinates of 2 points

2. Subtract the coordinates of the initial point from those of the final point

3. Clear fractions and/or reduce the results to the lowest integers.

4. Enclose the numbers in square brackets []. (No commas)

5. Negatives are represented by bar above number.