## 3 Results
### Microstructures
At the higher tempering temperatures of 300 \({}^{\circ}\)C and 400 \({}^{\circ}\)C there is a higher contrast between the dark martensite matrix and the white carbides (Figure 4b,c), presumably cementite (\(\theta\)-carbide), which have replaced the small transition carbides found at the lower tempering temperatures [12]. The various lath, block, packet, and grain boundaries are seen to act as sites for cementite nucleation [25]. The precipitates are clearly coarser after tempering at 400 \({}^{\circ}\)C than at 300 \({}^{\circ}\)C. Therefore, the microstructure of the 400 \({}^{\circ}\)C tempered sample was assumed closer to conventional tempered ferrite and cementite than that of martensite [12; 13]. Based on the FESEM imaging, the evolution of the martensitic steel from the as-quenched state to the 400 \({}^{\circ}\)C tempered microstructure appeared as to have decreased homogeneity. The water quenched sample had far less precipitates and they were clearly smaller than those of the tempered steels. Then, the carbon migration slowly altered the structure into a clearer two-component structure with the dark matrix and the white carbides when the tempering temperature exceeded 300 \({}^{\circ}\)C. The water quenched variant and the 150 \({}^{\circ}\)C tempered samples had the most uniform structure, and also showed mechanical properties very close to each other, which will be discussed further in the next section. The prior austenite grain size (PAGS) was measured for the 300 \({}^{\circ}\)C tempered sample using a calculation tool recently developed by [PERSON] et al. [26]. The calculation is based on the mean linear intercept method of [PERSON] [27]. The calculated mean prior austenite grain size was 12.3 \(\upmu\)m with a standard deviation of 0.6 \(\upmu\)m. Therefore, the somewhat high austenitization temperature of 980 \({}^{\circ}\)C had not caused excessive grain growth as seen in both the optical image (Figure 5a) and in the grain size distribution calculations (Figure 5b). Only a few large grains were detected (24-30 \(\upmu\)m) and no abnormal grain growth was present. For comparison, some examples of PAGS for austenitization temperatures below 1000 \({}^{\circ}\)C of similar grade steels have been reported by [PERSON] et al. [28]. For AISI 4340, austenitization at 870 \({}^{\circ}\)C for 1 h resulted in a grain size ranging from 24 to 32 \(\upmu\)m. Austenite grain growth for the 300M ultrahigh-strength steel (a modified version of 4340 with higher silicon content) has also been studied in the temperature range of 850 to 1150 \({}^{\circ}\)C with different holding times. [PERSON] et al. [29] discovered that the grain growth rate increased rapidly when soaking 300M above 900 \({}^{\circ}\)C. Heat treatment at 950 \({}^{\circ}\)C resulted in an average grain size of 31 \(\upmu\)m, while a heating temperature  
Figure 4: FESEM images of (**a**) water quenched, (**b**) tempered at 200 \({}^{\circ}\)C for 2 h and (**c**) tempered at 400 \({}^{\circ}\)C for 2 h.  
of 1000 \({}^{\circ}\)C increased the grain size to 46 \(\upmu\)m. [PERSON] et al. [30] have found in their work that the average grain size for 300M was greater than 50 \(\upmu\)m in when austenized at 900 \({}^{\circ}\)C or above for 40 min. [PERSON] et al. [31] measured PAGS of 20 \(\upmu\)m for 4340 and 300M steels with an 870 \({}^{\circ}\)C austenitization temperature. Therefore, the mean prior austenite grain size (12.3 \(\upmu\)m) can be considered to be small for austenitization temperatures of 950 to 1000 \({}^{\circ}\)C. This is probably attributable to the presence of the microalloying elements Ti and Nb, which have inhibited the grain growth through the formation of small finely dispersed carbides or carbonitrides [32]. Also, the relatively large amount of molybdenum (0.7 wt.%) can hinder the austenite grain growth by producing strong solute drag effect by segregating at the austenite grain boundaries and thus pinning the grain boundary movement [33].