I just came across this statement on the book G.E.Dieter.Please explain me the meaning of this statement,"Note,however that the Burger's vector is the same along the entire dislocation loop.If this were not so,part of the crystal above the slipped region would have to slip by a different amount relative to another part of the crystal and this would mean that another dislocation line would run across the slipped region".
Simply stated, every point on one side (slipped side of dislocation line) of dislocation line must shear at the same direction by same amount. since a dislocation line or loop separates slipped region from unslipped region, and the whole slipped region must move as a whole; hence burgers vector must be indicated by one direction only.
Note slip is a discontinuity, so change of burgers vector in same dislocation line must mean that another dislocation must have been passed through that line/region.
Put it even more simply. suppose a 1 micron block of metal have been slipped by .1 micron. have left of the block moved .2 micron and right of the block 0.15 micron? then, how it makes sense that the block have slipped .1 micron? see the absurdity?
Now suppose , by slip, I have indicated movement of center of mass of the block by .1 micron. If other two dimensions perpendicular to slip movement are unchanged, and both of the sides of the block do not move by exactly same amount, then it means volume of the block materials, and also density of block material have been changed upon plastic deformation, that is retained even upon withdrwl of deforming agent. so, there must be a changed material density around the block, otherwise vaccum would result in near the block. Can this happen within realm of mechanical metallurgy?
Mechanical metaluurgy do not allow so.
Dear Sumit,
The meaning of the statement is within a dislocation loop there will be same amount of energy to dislocate in the same direction, if it is not so, energy required to gather the vector for dislocation will differ from the slip, i.e it will be in nonslip condition. so Twining may not occur. hence, there will be no micro blockage. Understand from HRTEM practically. You will understand well.
Hope it is helpful for you.
Ashish
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