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
The following equation is used to calculate the Lattice Strain.
LS = (As – Al) / As
- Where LS is the lattice strain
- As is the substrate lattice constant
- Al is the layer lattice constant
To calculate the lattice strain, subtract the layer lattice constant from the substrate lattice constant, then divide by the substrate lattice constant.
What is Lattice Strain?
Lattice strain is a special type of strain that occurs in crystals because of the underlying lattice structure. The most common example of this is in single crystals, although it can also occur in polycrystals.
In single crystals, lattice strains are caused by stresses on the crystal lattice that exist as a result of other internal or external forces acting upon the material. When these forces cause the crystal to distort from its ideal shape, large deformations can occur, especially at grain boundaries where there are weak bonds between adjacent grains. As such, lattice strain is measured at grain boundaries, because this is where the largest deformations manifest themselves and can be measured with high precision.
Tolerance limits are typically set for lattice strain values so that they do not exceed a certain level. This is important because if too much lattice strain occurs in a material, it can cause failure to occur.
For example, if stress causes the crystal to bend in one direction and then back again due to residual stress while being cooled after fabrication, it might snap instead of relaxing back into its original position. This would lead to failure at high temperatures or if the stress were applied repeatedly over time.
The degree of lattice strain can be calculated by comparing the length and width of a crystal before and after it is subjected to stress. If the length and width both increased by 10%, for example, then the degree of strain would equal 1%. A 5% change in both dimensions would be 2%, while a 2% increase in one dimension and a 20% increase in the other would total 3%.
In general, metals with higher melting points undergo greater degrees of lattice strain than do metals with low melting points.
For example, lead and bismuth, two elements with relatively low melting points, undergo little lattice strain when subjected to temperatures above their melting points; silver and gold, on the other hand, have significantly higher melting points and experience much more dramatic changes in size when heated.