Lattice Strain Calculator

Enter the lattice constant of the substrate and the lattice constant of the layer into the calculator to determine the lattice strain.

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Lattice Strain Formula

Lattice strain compares the lattice constant of a substrate to the lattice constant of the layer grown or deposited on it. For this calculator, the strain is defined as:

LS = \frac{A_s - A_l}{A_s}

If you want the answer as a percentage instead of a decimal, convert it with:

LS_{\%} = LS \times 100

Variable Definitions

Because the formula divides one length by another, lattice strain has no physical unit. The only requirement is that both lattice constants are entered in the same unit.

Rearranged Equations

If you know any two variables, you can solve for the third. The calculator does this automatically, but the algebra is:

A_l = A_s(1 - LS)

A_s = \frac{A_l}{1 - LS}

How to Use the Calculator

1. Enter the substrate lattice constant.
2. Enter the layer lattice constant.
3. Click calculate to find the lattice strain.
4. If needed, multiply the decimal result by 100 to express strain as a percent.

If you are solving for a missing lattice constant instead, enter the known strain value as a decimal unless your interface explicitly expects percent.

How to Interpret the Result

• LS = 0: the substrate and layer have the same lattice constant in this calculation.
• LS > 0: the layer lattice constant is smaller than the substrate lattice constant.
• LS < 0: the layer lattice constant is larger than the substrate lattice constant.

This sign convention is useful, but not universal. Some textbooks and papers define lattice mismatch with the opposite sign. When comparing published values, always verify which formula was used.

Example

If the substrate lattice constant is 5.65 Å and the layer lattice constant is 5.60 Å, then:

LS = \frac{5.65 - 5.60}{5.65} = 0.00885

The lattice strain is 0.00885, which is:

0.00885 \times 100 = 0.885\%

Why Lattice Strain Matters

Lattice strain is an important concept in crystallography, semiconductor fabrication, thin-film growth, and materials engineering. A mismatch between the substrate and the deposited layer can affect:

• epitaxial fit between materials,
• internal stress in the film,
• defect and dislocation formation,
• electronic and optical behavior,
• mechanical stability and long-term reliability.

Even a small strain value can matter when the application requires high crystal quality or tightly controlled material properties.

Practical Notes

• Use identical units for both lattice constants. Mixing Å and nm without conversion will give an incorrect result.
• A decimal strain of 0.01 is the same as 1% strain.
• If you only care about the magnitude of mismatch, use the absolute value of the result.
• The calculated value is a geometric comparison of lattice constants; real materials may also be influenced by temperature, composition, relaxation, and defects.

Common Mistakes

• Entering one lattice constant in Å and the other in nm.
• Confusing decimal strain with percent strain.
• Comparing values from different sources without checking the sign convention.
• Assuming the calculated mismatch is identical to the fully measured strain state of a real film.

Common Questions

Is lattice strain the same as lattice mismatch?
They are closely related and are often used interchangeably in quick calculations. This calculator uses the relative difference shown in the formula above.

Do larger numbers always mean worse compatibility?
In general, a larger strain magnitude means the layer and substrate are less closely matched geometrically, which can increase the likelihood of stress-related issues.

Why is the answer unitless?
Strain is a ratio of two lengths, so the units cancel out.