Consider a tilt boundary of misorientation of 2^{o} in an aluminium grain. The lattice parameter of aluminium is 0.143 nm. The spacing between the dislocations that form the tilt boundary is ______ nm (round off to 2 decimal places).

# GATE MT 2022 Q34.

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I took the formula from the book by Reed-Hill (Pg. 159). They have given a simple relationship between the dislocation spacing, tilt angle and lattice parameter. sin (theta/2) = b/ 2d where theta is the misorientation angle, b is the burgers vector and d is dislocation spacing. b = lattice parameterRead more

I took the formula from the book by Reed-Hill (Pg. 159). They have given a simple relationship between the dislocation spacing, tilt angle and lattice parameter.

sin (theta/2) = b/ 2d

where theta is the misorientation angle, b is the burgers vector and d is dislocation spacing.

b = lattice parameter value.

So, sin (2 degree/2) = 0.143/2d

d = 4.097 nm = 4.10 nm

#I am not sure if this is the correct method. Let me know if there is another way to solve it.

See lessSorry I made a mistake with the value of Burgers vector Considering <110> slip direction, burger vector |b| = a/ 2^0.5 using the above equation, d = 2.90 nm

Sorry I made a mistake with the value of Burgers vector

Considering <110> slip direction, burger vector |

b| = a/ 2^0.5using the above equation, d = 2.90 nm

See lessI took the formula from the book by Reed-Hill (Pg. 159). They have given a simple relationship between the dislocation spacing, tilt angle and lattice parameter. sin (theta/2) = b/ 2d where theta is the misorientation angle, b is the burgers vector and d is dislocation spacing. b = a/ 2^0.5 for FCCRead more

I took the formula from the book by Reed-Hill (Pg. 159). They have given a simple relationship between the dislocation spacing, tilt angle and lattice parameter.

sin (theta/2) = b/ 2d

where theta is the misorientation angle, b is the burgers vector and d is dislocation spacing.

b = a/ 2^0.5 for FCC

d = 2.89 nm

#I am not sure if this is the correct method. Let me know if there is another way to solve it.

See lessI took the formula from the book by Reed-Hill (Pg. 159). They have given a simple relationship between the dislocation spacing, tilt angle and lattice parameter. sin (theta/2) = b/ 2d where theta is the misorientation angle, b is the burgers vector and d is dislocation spacing. b = a/ 2^0.5 for FCCRead more

I took the formula from the book by Reed-Hill (Pg. 159). They have given a simple relationship between the dislocation spacing, tilt angle and lattice parameter.

sin (theta/2) = b/ 2d

where theta is the misorientation angle, b is the burgers vector and d is dislocation spacing.

b = a/ 2^0.5 for FCC

d = 2.89 nm

#I am not sure if this is the correct method. Let me know if there is another way to solve it.

See less