Strain mapping in TEM using precession electron diffraction
A sample material is scanned with a transmission electron microscope (TEM) over multiple steps having a predetermined size at a predetermined angle. Each scan at a predetermined step and angle is compared to a template, wherein the template is generated from parameters of the material and the scanning. The data is then analyzed using local mis-orientation mapping and/or Nye's tensor analysis to provide information about local strain states.
1. A method for strain mapping a material comprising the steps of:
scanning a sample of a material with a transmission electron microscope (TEM), wherein the scanning of the material occurs over multiple steps having a step size and at a beam precession angle;
comparing each scan at each step and beam precession angle to a template to produce data, wherein the template is generated from parameters of the material and information from the scanning step;
analyzing the data using local mis-orientation mapping analysis or Nye tensor analysis; and
producing a local strain map of the sample.
2. The method of 1 , wherein the step of analyzing is performed using Nye tensor analysis, and a least squares contortion value is calculated for each of the multiple steps.
3. The method of claim 2 , wherein the Nye tensor analysis further comprises estimating a lower bound GND density.
4. The method of claim 2 , wherein the Nye tensor analysis further comprises calculating a Nye tensor.
5. The method of claim 1 , wherein the step of analyzing is performed using local mis-orientation mapping analysis and further wherein a number n is selected for determining a number of nearest neighbors for each of the multiple steps.
6. The method of claim 5 , wherein the number n is selected from the range of 1-10.
7. The method of claim 5 , wherein the average mis-orientation between each nearest neighbor for each of the multiple steps is calculated.
8. The method of claim 1 , further comprising determining reliability, wherein reliability is a comparison of a best index value with a next best index value.
9. The method of claim 1 , wherein the step of analyzing is performed using Nye tensor analysis, wherein each scan at a predetermined step was considered as a center of a kernel with a radius of one and tensor components relating eight nearest neighbors in the kernel were determined.
10. The method of claim 9 , wherein a radius of the kernel is from 1-10.
11. The method of claim 1 , wherein the predetermined beam precession angle is less than 1.5°.
12. The method of claim 1 , wherein the predetermined beam precession angle is from 0.5°-1.0°.
13. The method of claim 1 , wherein a step size less than 20 nm by 20 nm.
14. The method of claim 1 , wherein the step size is less than 10 nm by 10 nm.
15. The method of claim 1 , wherein the material is a polycrystalline material.
16. A method for strain mapping a material comprising the steps of:
scanning a sample of a material with a transmission electron microscope, wherein the scanning of the material occurs over multiple steps having a step size and an angle;
comparing each scan at each step and angle to a template, wherein the template is generated from parameters of the material and information from the scanning,
analyzing the data using Nye tensor analysis, wherein a best fit of a Nye tensor for each predetermined step is calculated; and
producing a local strain map of the sample.
17. The method of claim 16 , wherein the material is a polycrystalline material.
18. The method of claim 17 , wherein the step size is less than 10 nm by 10 nm.
19. The method of claim 17 , wherein the predetermined beam precession angle is less than 1.5°.
20. The method of claim 16 , wherein the Nye tensor analysis further comprises a step of estimating a lower bound GND density.