## 4 Results and Discussion
### Attenuation Behavior of Ferrous Alloys
On the other hand, martensitic microstructures showed even lower \(\alpha\) values, which reached 3 dB/m when extrapolated  
\[\alpha\left(\text{dB/m}\right)=16.0\text{ f}+0.03\text{ f}^{4}. \tag{18b}\]3 Attenuation coefficients at 1 MHz vs. Vickers hardness of tempered steels and annealed brass. Green X: quenched F50 steel; red +: quenched F30 steel; blue circle: quenched 1020 steel; purple triangle: 360 brass in CW condition. down to 10 MHz from data at 22 MHz and higher. This trend was also observed in an earlier study [83]. This low value for martensitic 4142 disagrees with the present results. In [PERSON] [82], the martensitic samples were oil-quenched in the form of a 5 cm bar stock and machined out of the center portion. If the bar was a square bar measuring 5 cm by 5 cm, the cooling speed was much lower than needed for martensitic transformation throughout the bar, producing bainite in the mid-section of the \"martensitic\" samples. Unfortunately, no hardness data were reported. In this case, the earlier work does not contradict the present high attenuation results for martensitic microstructures. Still, further work on martensitic and bainitic samples is desirable. For practical consideration, low attenuation results for bainite are welcome, since many structural steels are most commonly utilized in applications with heavy sections, such as pressure vessels [80]. Another noteworthy observation is the contrast between two of the precipitation hardening stainless steels, A286 and 17-4 PH. In the solution-treated conditions, A286 showed the highest attenuation (see Figure 11b), while 17-4 PH showed \(\alpha\) = 9.0 dB/m at 1 MHz with the addition of the f\({}^{4}\)-scattering effect. This steel belongs to the lowest attenuation group of ferrous alloys. In the aged conditions, \(\alpha\) decreased in A286 but increased in 17-4 PH. The observed precipitation effects were opposite in these two alloy steels. No rational explanation can be given at present and repeat tests with various heat treatments are needed for clarification. Rayleigh scattering with the 4 th power frequency dependence appeared in 26 out of 101 tests, as shown in \[\alpha\left(\text{dB/m}\right)=16.0\text{ f}+0.03\text{ f}^{4}. \tag{18b}\]4 Over a half of these tests were for stainless steels and one-quarter of the tests were for annealed low-C steels. The stainless-steel group contains single-phase materials, except for the nano-scale precipitates in aged 17-4 PH (test F101). Grain boundaries are the commonly accepted source of Rayleigh scattering. The latter group of low-C steels is expected to have ferritic-pearalitic microstructures, with ferrite grain boundaries acting as scattering centers. Similar attenuation spectra were reported by [PERSON] et al. [73] (see Figure 11a), and they attributed the entire observed attenuation to Rayleigh scattering. However, the Mason-McSkimin relation can describe their spectra more rationally, with the addition of the f-dependent damping term at lower frequencies. This section presents the attenuation behavior of ferrous alloys. Most structural steels exhibited low to medium attenuation coefficients composed of the f-dependent damping term and f\({}^{4}\)-dependent term due to Rayleigh scattering or the Mason-McSkimin relation. The Rayleigh term is limited to one-quarter of the samples tested, consisting of ferritic-pearalitic low-C steels and austenitic stainless steels. CW and phase transformation resulted in vast changes in \(\alpha\) values, with two contradictory CW effects--type-p and type-n. The CW effects require further studies to fully understand the observed behavior. Precipitation hardening effects also showed contrasting behavior. Another urgent task is obtaining a quantitative explanation of the observed damping, since existing dislocation-based theories, including the proposed bow-out damping, are inadequate.