548 C. II. Mathewson — Metallographic Description 



the cast material containing 92 per cent copper at 850° (fig. 

 4, curve c) or in a 60-minute anneal of the same material at 

 775° (fig. 4, curve b). On the other hand, if we assume that 

 the annealing period is neither extremely brief nor excessively 

 prolonged, e. g., occupies from 15 to 60 minutes, the grain size 

 is fairly independent of the time, and will serve to indicate 

 the approximate temperature of anneal. In the present case, 

 the values for 700° range from 24 to 20, those for 775°, from 

 15 to 12, and those for 850°, from 10 to 7%. It would thus 

 be possible, by measuring the grain size, to estimate whether 

 a cold worked cast bronze containing 92 per cent copper had 

 been annealed at dull red (700°), cherry (900°), or at an 

 intermediate temperature, provided no other complications 

 affecting the growth of grain were present. Similarly, the 

 data plotted in figs. 2 and 3 may be used to interpret the 

 annealing treatment of bronzes containing 96 and 94 per cent 

 copper, respectively. 



Tammann (16), in discussing the relationship between tem- 

 perature and grain size, defines an end condition for each 

 temperature in terms of equilibrium between the tension at the 

 inner surfaces (inter-granular boundaries and intra-granular 

 surfaces of slip, see Theories of Deformation, p. 559) and the 

 rigidity of grain. Thus, the temperature — grain size curves 

 for increasing annealing periods at constant temperature (or 

 for decreasing rates of heating towards a convergent tempera- 

 ture) will lie superposed, the uppermost position (maximum 

 grain size) corresponding to the final condition at which the 

 above equilibrium obtains. Curves of this character, plotted 

 from the data obtained in this investigation, are shown in 

 fig. 5. Annealing periods of 5, 10, 30, and 60 ■ minutes, 

 respectively were used. Since the rate of adjustment between 

 the opposing forces increases with the temperature, the highest 

 value on the uppermost curve more nearly represents a true 

 equilibrium condition for the corresponding temperature than 

 the lower values on this curve. The position of the true 

 equilibrium curve with respect to that of the uppermost curve 

 is accordingly similar to that indicated by the adjacent dotted 

 curve. 



The grains counted at 775° and 850° C, even after very brief 

 periods of anneal, in all probability represent completely 

 recrystallized metal in which none of the internal changes due 

 to the original deformation persist. At 625°, however, after 

 a comparatively long anneal (30 m.) there is evidence that 



