Geology Reference
In-Depth Information
On the basis of interpretation of experimental observations and of a few cal-
culations, it is generally accepted that the value of b varies from the order of 10 -4
or less for close-packed metals (for example, copper and basal slip in zinc) to a
maximum of the order of 10 -2 for covalent crystals such as germanium and silicon
(Haasen 1978 , p. 256; Hirth and Lothe 1982 , p. 241). The best calculated values
for b for NaCl, KCl, and MgO are in the range (1-3) 9 10 -3 (Hirth and Lothe
1982 , p. 232), corresponding to a Peierls stress of around 50 MPa for the alkali
halides and 150 MPa or more for MgO. The value of the Peierls stress for dry
quartz deduced by Blacic and Christie ( 1984 ) from extrapolation of experimental
observations, namely, about 3,000 MPa, corresponds to a value of b of about
6 9 10 -2 and to a value of E p somewhat less than 1 eV per length b. Thus, it is
seen that the fluctuating component of the dislocation energy is always a small
fraction of the total.
Simple theoretical models indicate that the Peierls stress depends sensitively
(for example, exponentially) on the width of the dislocation, as defined by the zone
within which atoms are displaced by more than a certain fraction of the Burgers
vector from an ideal structural site. In close-packed metals the width of the dis-
locations is many times the Burgers vector, that is, their cores are very smeared
out, and the Peierls stress is small, while in covalent crystals the dislocation cores
tend to be very narrow and the Peierls stress relatively high. Theoretical models
also predict that, in general, the Peierls stress will tend to decrease as the inter-
planar spacing increases, promoting the occurrence of slip on low-index planes,
and that the Peierls stress for edge dislocations will tend to be less than that for
screw dislocations (Hirth and Lothe 1982 , p. 240). A high value of the Peierls
potential is manifested microscopically in a tendency for dislocation lines to be
straight and crystallographically well defined.
Two remarks are appropriate at this point. First, it is implicit in relating the
Peierls stress to dislocation motion that the additional potential energy acquired by
the dislocation at the Peierls ridge is mainly dissipated during movement into the
next valley and so is not available to assist in surmounting the following ridge.
Second, the Peierls considerations so far refer primarily to the situation at absolute
zero temperature and to the properties of straight segments of dislocation lines.
Relaxing either of the latter constraints leads to easier dislocation movement and
introduces some more complex considerations. Thus, if the dislocation line has a
step or kink in it, whereby one segment is in advance of an adjacent segment by
one lattice spacing, the kink can behave as a sort of second-order dislocation in the
linear structure of the parent dislocation, which can move along the dislocation in
displacement increments equal to the lattice spacing in that direction. This motion
can be expected to occur at a lower applied stress than the uniform motion of the
whole dislocation line. However, in its motion along the dislocation, the kink has
to surmount potential barriers analogous to the Peierls barrier for motion of a
straight dislocation line through a crystal and so the resistance to kink motion can
be expressed as an analog of the Peierls stress. Hence, the terms ''secondary
Peierls potential'' and ''secondary Peierls stress'' are sometimes used for this
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