Calculate dislocation density, total dislocation line length, or volume from any two inputs with m, cm, in, ft, and per-area unit options.
- All Physics Calculators
- Hall-Petch Equation Calculator
- Lattice Spacing Calculator
- Lattice Strain Calculator
- Scherrer Formula Calculator
- Planar Density Calculator
Dislocation Density Formula
The dislocation density calculation is based on the total dislocation line length divided by the material volume.
Rearranged forms used to calculate a missing value are:
- DLD = dislocation density, usually expressed in m-2 or per m2
- S = total dislocation line length
- V = volume of the material sample
Select the quantity to solve for and enter the other two values. A material sample must have positive volume. If you enter volume and total dislocation line length, it calculates dislocation density. If you enter dislocation density and volume, it calculates total dislocation line length. If you enter dislocation density and line length, it calculates the required volume.
Internally, the calculation is performed in SI base units: cubic meters for volume, meters for line length, and per square meter for dislocation density. The result is then converted to the selected result unit.
Common Dislocation Density Ranges
Dislocation density varies widely depending on material type, processing history, deformation, and heat treatment.
As metal examples, Northwestern’s materials text, section 4.7, gives well-annealed metals at 1010–1012 m-2 and plastically deformed metals as high as 5 × 1015 m-2. These are broad examples, not universal classification boundaries; density alone does not establish deformation history or material quality.
| Metal example | Density illustration (m-2) |
|---|---|
| Well-annealed metal | 1010–1012 |
| Plastically deformed metal | Can reach 5 × 1015 |
Unit Relationships for Dislocation Density
| Unit selected | Equivalent in m-2 |
|---|---|
| 1 per m2 | 1 m-2 |
| 1 per cm2 | 10,000 m-2 |
| 1 per in2 | 1,550.0031 m-2 |
| 1 per ft2 | 10.7639 m-2 |
Example Problems
Example 1: Calculate dislocation density
You have a sample volume of 0.002 m3 and a total dislocation line length of 500 m.
The dislocation density is 2.5 × 105 per m2.
Example 2: Calculate total dislocation line length
A material has a dislocation density of 4.0 × 1012 m-2 and a sample volume of 1.5 × 10-6 m3.
The total dislocation line length is 6.0 × 106 m.
FAQ
Why does dislocation density have units of per square meter?
Dislocation density is total line length divided by volume. In SI units, that is meters divided by cubic meters:
That is why the result is written as m-2 or per m2.
Can dislocation density be zero?
In the formula, dislocation density can be zero if the total dislocation line length is zero. Some carefully grown semiconductor single crystals can be dislocation-free. Zero line length gives zero density for any positive sample volume, so the inverse cannot determine volume from two zero values.
Why does the calculator ask for two inputs?
Choose the required result using the mode selector, then supply the other two quantities. The calculator checks zero-denominator cases and requires a positive sample volume; some zero-input combinations cannot determine a unique valid result.
