Isothermal Grain Growth Studies on Nanostructured 9Cr-1Mo and 9Cr-1W Ferritic Steels Containing Nano-sized Oxide Dispers
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Variation of grain size with annealing time at different temperatures in (a) 9CM, 9CMT, and 9CMYT alloys, and in (b) 9CW 9CWY alloys. Data of nc-Fe[4] and nc-Fe-10Cr alloys,[7] from the literature are included for comparison in (b).
size (r) of 2.5 nm and a volume fraction of 0.051, is ~400 nm, and for 9CMY and 9CWY alloys, containing Y2O3 particles with an average size (r) of 10 nm and a volume fraction of 0.099, is ~130 nm. From an analysis of large amount of experimental data, Manohar et al.[18] have shown that the calculated GZener is always higher compared to the actual grain sizes. In the present study, the grain sizes after annealing for 90 minutes at 1073 K (800 C) were ~70 to 80 nm for all particle containing alloys, and this is lower (factor of ~5 in 9CMYT alloy and factor of ~2 in 9CMY and 9CWY alloys) than the calculated GZener and this is consistent with the analysis of Manohar et al.[18] The grain growth is often analyzed (when the difference between initial grain size (G0) and the G after annealing for time, t, is smaller) using the relation G ¼ ktn ; Fig. 4—Variation of grain size with different annealing temperatures at constant annealing time (5 min) in 9CM, 9CMT and 9CMYT alloys, 9CW and 9CWY alloys. Data of nc-Fe[4] from the literature are included for comparison.
Ti) leading to the formation of ultrafine carbides and nitride particles. Although the volume fraction of such particles will be very less (undetected by XRD analysis), but their influence on the grain growth behavior cannot be neglected. The pinning pressure due to the particles increases with decrease in size for a given volume fraction (f) according to the Zener equation as 3cf/2r, where c is the gb energy and r is the particle radius. The grain growth ceases when the drag force on the gb equals the driving force for the boundary migration and this is known as the Zener limiting grain size, GZener and is given as 4r/3f.[17] From the average particle size and volume fraction data obtained from microscopy, the GZener limiting grain sizes were evaluated. The calculated GZener for 9CMYT alloy containing Y-Ti-O-based NCs with an average particle 1686—VOLUME 45A, APRIL 2014
½1
where ‘‘k’’ is a rate constant (temperature dependent factor), and ‘‘n’’ is time exponent. This equation may not be suitable for the present data, because we observe a rapid increase in the grain size in the early stages of annealing (Figure 3). For this situation, we employed the relation suggested by Beck et al.[19]: 1=n
G1=n G0
¼ kt
On differentiation and taking logarithm, we get dG 1 ¼ logðkÞ þ logðnÞ þ 1 log G log dt n
½2
½3
Rate constant, k, can be expressed by Arrhenius equation Q k ¼ k0 exp ½4 RT k0 is the frequency term (numerical constant), R is the gas constant (8.314 J/mol K), Q is the activation METALLURGICAL AND MATERIALS TRANSACTIONS A
energy (kJ/mol) of grain growth, and T is the temperature in K. The kinetics of grain growth depends on two factors, namely, the time exponent (n) and activation energy (Q). The grain growth data (
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