Chapter 8 Annealing
2.
(a) Using the 273 K data, given in Sec. 8.5 for the Drouard, Washburn, and
Parker zinc single crystal (The activation Q for recovery of the yield point in zinc
is 83,140 J/mol. If a strained zinc crystal recovers one-fourth of its original yield
point in 5 min at 273 K), determine the value of A in the rate equation, Eq. 8.2
( 1 /   A  exp( Q / RT ) ). (b) Next determine the temperature at which the crystal
should recover one-fourth of its yield point in 5 seconds and b = 3.0 nm.
5.
One of the phenomena during the latter stages of recovery is the coalescence of
tilt boundaries into a single tilt boundary with a larger title angle. This is
accompanied by a loss of surface energy. Compute the fractional loss of surface
energy when two tilt boundaries with tilt angles of 0.5 combine to form a 1 tilt
boundary. (Use the parameters of Prob. 8.4) (   2.554  (0.5  ln  ) J / m2 , the
unit of  is in radians.)
7.
With the aid of the equation developed in Prob. 8.6 (A = 9.161015 hr-1, Q =
74,830 J/mol), determine the time to recover 50% of the yield stress of the
deformed zinc crystal at 213 K and 300 K.
9.
(a) The surface energy of a film of soap and water is about 310-2 J/m2. Compute
the increase in the pressure on the inside of a soap bubble with a diameter of 6
cm. (b) In some studies designed to investigate the effect of very rapid cooling
on the freezing point of metals, droplets of a liquid metal have been rapidly
cooled. The diameter of these droplets were of the order of 50 m. Consider the
case of liquid gold droplets of this diameter with a surface energy of 13.210-2
J/m2 and compute the increase in the internal pressure for this case.
11. If a silver specimen is annealed for a long time under conditions favoring the
development of grooves along the lines where internal grain boundaries intersect
the outer surface of the sample, a groove angle of 139.5 occurs. If the grain
boundary energy for silver is 0.790 J/m2, what is the energy of the solid-vapor
surface?
12. Determine, to a first approximation, the limiting grain size in a 2 cm-thick plate
of a metal containing a 1 percent volume fraction of a stable precipitate whose
average diameter is 600 nm.