PRINCIPLES OF SOLUTION HARDENING. TECHNICAL REPORT NO. 12 Page: 9 of 80
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lattice disturbances caused by randomly distributed solute atoms. Theoretical
treatments-by Cottrell(21), Suzuki(22), Fisher(23), and others has shown that
solution hardening is very likely due to small groups of solute atoms concentrated
in the lattice, and not due to randomly dispersed atoms.
Cottrell has pointed out that internal stresses due to randomly dispersed
solute atoms should have almost no hardening effect. If a dislocation line is
considered as a rigid linear discontinuity, then along its length there will be .
equal numbers of positive and negative stress fields due to solute atoms, Half
of these act to move the dislocation line forward and half urge it in the
backward direction, Thus, .these randomly alternating stress fields would nearly
cancel, and, therefore, dislocations could move through the alloy crystal almost
as easily as they could move through a crystal of the .pure metal, As Mott
and Nabarro(2h)(25) have shown, however, dislocation lines are not rigid, They
may assume a smoothly curved form, but only on a scale that is large compared
with atomic dimensions. When the regions of lattice distortion are far apart,
the dislocation line may follow a path around the highly stressed areas. When
the distance between stressed regions approaches atomic dimensions, the dislocation
line can no longer curve around the stressed regions because of the high
energy required to produce sharp curves in a dislocation line.
The energy of a dislocation has been estimated by Mott and Nabarro(26) as
about Gd per unit length of a dislocation line, where G is the shear modulus
and d is the atomic spacing (Gd3 is of the order of a few electron volts). As
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Parker, E.R. & Hazlett, T.H. PRINCIPLES OF SOLUTION HARDENING. TECHNICAL REPORT NO. 12, report, October 1, 1953; United States. (https://digital.library.unt.edu/ark:/67531/metadc1024439/m1/9/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.