Electron microscopy
 
Strain/Stress in Materials and Diffraction
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Strain is defined as a relative change in shape or size of an object due to externally-applied forces, given by,

           Strain/Stress in Materials and Diffraction --------------------------------------------- [1302]

where,
          ΔL - The change in shape or size,
          L - The shape or size.

Figure 1302 shows the effect of strain on the shift and shape of diffraction peak. For uniform strain, the diffraction peak moves, but its shape does not change. For instance, the diffraction peak shifts to lower angles when the lattice spacing is larger as shown in Figure 1302 (b). Figure 1302 (d) shows that the crystallographic plane has a distribution of d-spacings rather than a single d-spacing. In this case, a broader diffraction peak is observed. Such lattice distortions can be introduced by:
          i) Mechanical force,
          ii) Surface and interface tension,
          iii) Morphology of crystal shape,
          iv) Interstitial impurities.

Strain/Stress in Materials and Diffraction

Figure 1302. (a) No strain at the original lattice spacing, (b) Peak shifts to lower angles when the lattice spacing is larger (d0 < d1), (c) Peak shifts to larger angles when the lattice spacing is smaller (d2 < d0), and (d) Peak is broadened because the peak gradually shifts from lower angles (top of the crystal: d3) to larger angles (bottom of the crystal: d4) (d4 < d0 < d3).

Table 1302 lists the most typical correlations between diffraction peak aberrations, including broadening, shifts or asymmetries, and the different elements of microstructures.

Table 1302. Most typical correlations between diffraction peak aberrations
Sources of strain Peak shift Peak broadening Peak asymmetry Anisotropic peak broadening Peak shape
Dislocations   + + + +
Stacking faults + + + + +
Twinning + + + + +
Micro-stresses   +      
Internal long-range stresses +   +    
Grain boundaries + +      
Sub-boundaries + +      
Internal stresses +        
Coherency strains + + +    
Chemical heterogeneities + + +    
Point defects         +
Precipitates and inclusions     +   +
Crystallite smallness   +   + +

 

 

 

 

 

 

 

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