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cosines, 

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Lattice vectors ( a$_{GLYPH<6>}$ ) which are not along the direction of strain will undergo an additional rotation, ’$_{GLYPH<6>}$ . In the most general case of arbitrary changes in length ( GLYPH<15>$_{i}$ ) and arbitrary rotations ( ’$_{i}$ ), this becomes: 

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where i = 0 ; GLYPH<6> , and the distortion in the angular orientation of the moir´e is given by 

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In order to approximate the values of GLYPH<15>$_{i}$ for a uniform uniaxial stress, we make use of Poisson’s ratio GLYPH<23> and the strain matrix " by, GLYPH<15>$_{x}$ = "; GLYPH<15>$_{y}$ = GLYPH<0> GLYPH<23>" . 29 The strain matrix is: 

where the axes have been chosen to diagonalize the strain ma- trix. For strain in the arm chair direction, we do not need to rotate the lattice vectors a$_{i}$ with respect to " . In this case the lattice is stressed along a$_{0}$ . We can relate the strain matrix to the values GLYPH<15>$_{i}$ by applying the original definintion, 

Thus, under a small strain approximation ( " GLYPH<28> 1) we obtain 

We use the values from equations (10) and (11), along with GLYPH<23> = 0 : 5 to plot the overall distortion in the wavelength of the interference pattern. If we put these values into (6), we can compare the length distortion ( D$_{+}$ = D$_{GLYPH<0>}$ ) of the resulting moir´e pattern. Figure 4 clearly shows the expected behavior. As the rotation angle GLYPH<18> between the lattices increases, the e GLYPH<11> ect of the distortion is quickly diminished; however, for a large moir´e pattern the rotation angle is small, leaving the pattern easily distorted by the relative strain. The reason is that small angular di GLYPH<11> erences become comparable to the rotation angle ( ’ GLYPH<25> GLYPH<18> ), and lattice distortions cannot be neglected. Addi- tionally, in this regime small changes in the lattice constant a contribute greatly to the moir´e rotation angle. The shape of the moir´e hexagon su GLYPH<11> ers additional skewing in GLYPH<30>$_{i}$ due to the angular distortion of the reciprocal lattice vectors. 

Obtaining an exact measure of the strain is di GLYPH<14> cult because it can be hard to determine the direction of the applied stress. 

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