Small-angle X-ray Scattering Studies on Aging Precipitation of High-strength Soft-magnetic Stainless Steels

Abstract

We investigated the effect of alloying elements Ni, Al, and Mo on the mechanical properties of precipitation-hardened soft-magnetic stainless steels, whose aging condition and chemical composition were varied. Thermodynamic calculations suggested that the aging treatments led to precipitation of a β-NiAl compound with B2 structure and Fe₂Mo-type Laves phases. Although coarse precipitates, which are less effective for precipitation hardening, were observed in bright-field images obtained by transmission electron microscopy (TEM), the B2-type precipitates were detected in TEM electron diffraction patterns. By changing the concentration of the alloying elements, the B2-type β-NiAl precipitates were mainly responsible for the precipitation hardening, and the Vickers hardness was hardly affected by the Mo content. Small-angle X-ray scattering analysis was used to determine the size and number density of the fine β-NiAl precipitates, which contributed to the hardening. The high-density β-NiAl precipitates grew to a few nanometers in radius after an adequate period of aging, suggesting that the β-NiAl precipitates were responsible for the precipitation-hardening characteristics. On the other hand, the size of the precipitates was less affected by the amounts of Ni and Al, and the number density decreased with decreasing Ni and Al content. The improvement in hardness resulting from the β-NiAl precipitates had a linear relationship with the square root of the product of the precipitate size and number density.

1. Introduction

Soft-magnetic stainless steels have been widely used as magnetic core materials of solenoid valves in fuel injectors of automobiles because of their excellent soft magnetic properties. However, since their hardness (typical Vickers hardness of 85–200 Hv) is lower than that required in automobile components (more than 300–350 Hv), surface hardening treatments, such as hard chromium plating and nitriding, are needed in the production of these solenoid valves. Thus, there has been a strong demand for improvements in the mechanical properties themselves to avoid the surface modification process. To obtain high mechanical strength, precipitation-hardened stainless steels have been produced with alloying elements such as copper, nickel, titanium, aluminum, and molybdenum.¹⁾ For example, commercial Fe–17Cr–4Ni–4Cu stainless steel is hardened by precipitating nanometer-sized Cu precipitates.²⁾ In Fe–20Ni–23Co–0.07Al–0.17Ti steel, the hardening is mainly achieved by precipitating a nanometer-sized Ni₃Ti intermetallic phase in the austenite matrix.³⁾ A martensitic precipitation-hardened stainless steel containing nickel and aluminum can be hardened by fine β-NiAl precipitates.^4,5,6,7,8) On the other hand, there have been few reports on the application of precipitation-hardened stainless steel as a soft magnetic material. Recently, a precipitation-hardened soft-magnetic stainless steel containing alloying elements Ni, Al, and Mo has been developed, and it exhibits high hardness (typical Vickers hardness of 370 Hv) with excellent soft-magnetic properties as well as corrosion resistance.⁹⁾ It is expected that uniformly-dispersed nanoscale precipitates, which are formed upon adequate aging, would contribute to strengthening. However, details of the strengthening mechanism remain unclear because several types of precipitates coexist in the matrix structure.

To further improve the performance of the newly developed precipitation-hardened soft-magnetic stainless steel, detailed microstructural features of the precipitates, such as the crystal structure, size, and number density, need to be characterized; in particular, the size and the number density of the precipitates are dominant factors that determine the mechanical properties of the material. Precipitates formed by aging treatments have generally been studied by transmission electron microscopy (TEM). However, when precipitates measuring several nanometers in size are coherent with the matrix phase, it is generally difficult to analyze their size and shape with TEM. On the other hand, small-angle X-ray scattering (SAXS), which can evaluate a much larger volume than that under TEM observation, can be used to estimate the size and number density of precipitates with high statistical precision. Therefore, SAXS can be a powerful tool for obtaining quantitative information on the growth behavior of precipitates in various metallic materials. Previous studies reported that the size and the number density of nanosized precipitates and oxides in steels were determined using SAXS and/or small-angle neutron scattering to understand the hardening mechanism.^{10,11,12,13,14)}

This study investigates intermetallic compounds comprising precipitates in a precipitation-hardened soft-magnetic stainless steel alloyed with Ni, Al, and Mo; the variations in precipitation behavior with aging condition and chemical composition were characterized by SAXS. The precipitates were also investigated by using thermodynamic calculations and TEM observation. Based on the analytical data, the strengthening mechanism for this soft-magnetic stainless steel, which is principally dependent on the growth behavior of the precipitates, were determined.

2. Experimental Procedure

A commercial precipitation-hardened soft-magnetic stainless steel (K-M57, Tohoku Steel Co., Ltd.), which will be referred to as M0 hereafter, and samples with slightly different chemical compositions (M1, M2, and M3) were prepared in a bar shape. These samples were solution treated above 1323 K. The chemical composition of each sample is shown in Table 1. According to thermodynamic calculations, which will be discussed in section 3.1, the precipitates β-NiAl and Fe₂Mo were expected to be formed in the M0 sample. Thus, the atomic fractions of Ni and Al were reduced in the M1 sample compared to those in the M0 sample, and the atomic fraction of Mo in the M2 sample was less than half of that in the M0 sample. In the M3 sample, whose atomic fraction of Mo was considerably small, the atomic fractions of Ni and Al were higher than those in the other samples. The solution-treated M0 sample was aged at different temperatures of 773, 798, 823, 848, and 873 K for 3 h to investigate the growth behavior of precipitates at each aging temperature. The hardness was measured with a Vickers microhardness tester when a load of 980.7 mN was applied for a holding period of 5 s. The hardness values were determined from an average of five different measurements. The type and the volume fraction of the intermetallic compounds formed in the M0 sample were estimated from thermodynamic calculations performed using the Thermo-Calc software.

Table 1. Chemical composition (in mass%) of the steel samples.

Sample	Fe	Cr	Ni	Mo	Ti	Al	C
M0	Bal.	14.57	2.62	1.71	0.15	1.08	0.013
M1	Bal.	12.04	1.96	1.76	0.10	0.81	0.002
M2	Bal.	12.01	2.73	0.74	0.10	1.05	0.016
M3	Bal.	11.98	2.96	0.03	0.10	1.18	0.016

The microstructure was observed by using a TEM (JEM-3010, JEOL) at an accelerating voltage of 300 kV. Thin foil samples were prepared for the TEM observation by mirror polishing and subsequent ion milling (Model 1010, E.A. Fischione Instruments, Inc.).

To evaluate a variation in the size distribution and the number density of fine precipitates when the aging temperature and the chemical composition were varied, SAXS measurements were carried out with an incident beam of Mo Kα, which was collimated to a diameter of about 0.6 mm by using a three-pin-hole optical system. The scattered X-rays were collected on a two-dimensional detector (PILATUS 100K, Dectris) in the transmission mode. The beam path from the collection mirror to the detector was vacuumed to prevent air scattering. The distance between the collection mirror and the detector was 350 mm, allowing values of the scattering vector q (q = 4π sin(2θ/2)/λ) to range from 0.3 to 10 nm⁻¹, where λ is the wavelength of the incident X-ray and 2θ is the scattering angle. Samples for the SAXS measurements were polished to a thickness of about 60 μm to obtain an X-ray transmission rate of 20% and then polished to a mirror finish using diamond paste. The exact thickness of the samples at an X-ray irradiation position, t_S, was determined from the transmission rate, T_S, using the following equation:   

$$t_{\text{S}}=ln(1/T_{\text{S}})/{\mu }_{\text{S}},$$(1)

where μ_S is the linear absorption coefficient for X-ray irradiation. A specimen of glassy carbon with thickness of 1 mm, which had been characterized at Argonne National Laboratory, was used as a standard to convert the measured scattering intensity (counts) into absolute units. Since the background scattering resulting from surface imperfections, concentration fluctuations, and crystal defects overlapped with the intrinsic X-ray scattering by the nanoscale precipitates, the SAXS profile measured with a solution-treated sample, whose precipitates almost disappeared in the metallurgical phase, was subtracted from that of the corresponding aged samples. The average size, size distribution, and number density of the precipitates were estimated by fitting the measured SAXS profile with the theoretical profile calculated from Eq. (2),   

$$I(q)=\mathrm{\Delta }{\rho }^2\int V{(r)}^2{F}^2\left(q,r\right)N\left(r\right)\hspace{0.17em}\text{d}r,$$(2)

where I(q) and ρ are the scattering intensity and the scattering length density, respectively; and V(r) and F(q,r) are the volume factor and form factor of the precipitates, respectively. The normalized number density distribution of precipitates, N(r), at a radius r was assumed to have a log-normal distribution. The square of the increment in a scattering length density, Δρ², is defined as follows:   

$$\mathrm{\Delta }{\rho }^2={\left({\rho }_{\text{precipitate}}-{\rho }_{\text{matrix}}\right)}^2.$$(3)

3. Results and Discussion

3.1. Thermodynamic Calculations

To predict the phase of intermetallic compounds that were formed as a result of the aging treatment, thermodynamic calculations were performed for the chemical composition of the M0 sample; the results are shown in Fig. 1. The calculations showed that two types of intermetallic compounds—β-NiAl with the B2 structure and Fe₂Mo with the Laves-phase structure—would be precipitated. It should be noted that the volume fraction of the β-NiAl phase was predicted to markedly decrease with increasing temperature, whereas the volume fraction of the Fe₂Mo phase was expected to slightly decrease with increasing temperature.

Fig. 1.

Volume fraction of NiAl and Fe₂Mo precipitates in the M0 sample as a function of temperature, which was estimated from thermodynamic calculation.

3.2. Mechanical Property

Figure 2 shows the Vickers hardness of the M0 sample as a function of the aging temperature. The Vickers hardness rose with temperature up to 823 K and then gradually decreased with further increases in temperature, indicating that the peak aging temperature of this alloy was 823 K. Generally, higher aging temperatures can induce coarsening of precipitates, thus causing a decrease in the number density of precipitates. Moreover, according to Fig. 1, the volume fraction of the β-NiAl phase became smaller as the aging temperature increased. Therefore, the decrease in the Vickers hardness above 823 K must have originated from decreases in the number density or volume fraction of the precipitates, or a combination of both factors. Figure 3 shows a comparison of the Vickers hardness of the solution-treated and aged samples, M0, M1, M2, and M3. The aging treatments were carried out at 823 K for 3 h. The M1 sample, which had lower amounts of Ni and Al than the M0 sample, exhibited lower hardness than the M0 sample; on the other hand, the M3 sample, which contained higher amounts of Ni and Al and a much smaller amount of Mo, exhibited higher hardness than the M0 sample. Furthermore, in the M2 sample, which had almost the same Ni and Al content and half the Mo content, no significant difference was observed in the hardness when compared with the M0 sample. These results suggest that the β-NiAl phase exerted a much more dominant effect on the Vickers hardness than the Fe₂Mo phase.

Fig. 2.

Vickers hardness as a function of aging temperature of the M0 sample that was aged for 3 h.

Fig. 3.

Vickers hardness of the M0, M1, M2, and M3 samples that were solution-treated and then aged at 823 K for 3 h.

3.3. Precipitation Observed by TEM

TEM observations were carried out to clarify the shape and phase of precipitates formed during the aging treatment. No precipitates were observed in the bright-field image in the solution-treated specimen of the M0 sample (Fig. 4(a)), and only the ferritic phase was confirmed in the corresponding electron diffraction pattern, as shown in Fig. 4(d). After the aging treatment of the M0 sample, the presence of needle-like precipitates was confirmed by a strain contrast in the image (Fig. 4(b)). However, the strain contrast was not observed in the image of the aged M3 sample (Fig. 4(c)). According to thermodynamic calculations in section 3.1, the precipitates β-NiAl and Fe₂Mo were expected to be formed in the M0 sample. Because the M3 sample was almost free of Mo, the needle-like precipitates of the M0 sample in Fig. 4(b) were probably the Fe₂Mo phase. The shape of the Fe₂Mo precipitates with the Laves-phase structure is consistent with the primarily needle- or a plate-shaped form of Fe₂Mo precipitates in steels in previous studies.^15,16,17) Since the inter-precipitate distance of Fe₂Mo was approximately a few hundred nanometers, these Fe₂Mo precipitates were less effective in enhancing the Vickers hardness.

Fig. 4.

(a–c) TEM bright-field images and (d–f) electron diffraction patterns from [0 0 1] zone axes of the α-Fe matrix: (a, d) solution-treated M0 sample; (b, e) M0 sample aged at 823 K; (c, f) M3 sample aged at 823 K.

Figures 4(e) and 4(f) show electron diffraction patterns of the aged M0 and M3 samples, respectively. Superlattice spots were observed in the [0 0 1] zone axis pattern of the α-Fe matrix, and they can be indexed as a B2 structure that was coherent with the matrix. According to thermodynamic calculations, the B2 structure can be assigned to the β-NiAl phase. Because the presence of the B2 structure was confirmed both in the aged M0 and M3 samples, these β-NiAl precipitates were expected to be effective in enhancing the Vickers hardness. It should be mentioned that precipitates of the β-NiAl phase were not observed in the bright-field images of Figs. 4(b) and 4(c), probably because the coherent precipitates of the β-NiAl phase were substantially fine. Thus, the size and the number density of the β-NiAl precipitates could not be evaluated with the TEM observations.

3.4. Evaluation of Size and Number Density of β-NiAl Precipitates

Figure 5 shows SAXS profiles of the M0 samples that were aged at 798, 823, 848 and 873 K and the M1, M2, and M3 samples that were aged at 823 K. Humps were found in the q region of 0.4–4 nm⁻¹ in the scattering profiles, indicating that precipitates with dimensions of several nanometers were generated. Figure 4(b) indicates that the size of the Fe₂Mo precipitates was about 20 nm; therefore, humps for the Fe₂Mo precipitates should appear in the region below 0.2 nm⁻¹, thus implying that the scattering profiles in Fig. 5 could be principally ascribed to β-NiAl precipitates. Moreover, the scattering intensity was scarcely affected by the Fe₂Mo precipitates because the scattering length density Δρ² (as described in Eq. (3)) of the Fe₂Mo precipitates in the matrix phase was lower than that of the β-NiAl precipitates. It should be mentioned that a variation in chemical composition of the matrix phase with the formation of nano-precipitates was negligible small. Thus, there is little change in the scattering length density of the matrix phase; therefore, the scattering length density was calculated using the chemical composition listed in Table 1. The position of the humps in Fig. 5(a) shifts towards lower q values with increasing aging temperature, which means that the size of precipitates increased at higher aging temperatures. However, the humps for the M1, M2, and M3 samples aged at 823 K appear at almost the same q-position in Fig. 5(b), indicating that the differences in the size of their precipitates were small. On the other hand, the scattering intensity of the M1 sample was lower than the intensities of the M2 and M3 samples, suggesting that the number density of precipitates in the M1 sample was much lower than the densities in the M2 and M3 samples. Oscillations can be seen in almost all of the SAXS profiles in Fig. 5, which implies that the size distribution of the precipitates was rather small.

Fig. 5.

SAXS profiles of (a) M0 samples aged at different temperatures and (b) M1, M2, and M3 samples aged at 823 K. The dotted and solid lines represent the experimental and calculated results, respectively. (Online version in color.)

The expression F²(q,r) in Eq. (2), which corresponds to the form factor of precipitates, is defined in Eq. (4) when they are assumed to be spherical shapes:   

$$F^2(q,r)={\left[\frac{3\left(sin\left(qr\right)-\left(qr\right)cos\left(qr\right)\right)}{{\left(qr\right)}^3}\right]}^2.$$(4)

The theoretical SAXS profiles, based on the assumption that the precipitates were spherical, agree well with the measured profiles shown in Fig. 5. Previous studies reported that fine β-NiAl precipitates have spherical shapes in the matrix of the ferritic phase of martensitic stainless steels.^4,5,18) Therefore, the β-NiAl precipitates should have an isotropic shape.

Figure 6 shows variations in the average radii and number density of precipitates in the M0 samples that were aged at different temperatures. The inset in Fig. 6(a) shows the size distribution of the precipitates. The average radius of the precipitates increased monotonically with increasing aging temperature. On the other hand, the number density of the precipitates was almost constant up to the peak aging temperature of 823 K and then decreased at higher aging temperatures. It should be noted that while the average radii of the precipitates in the specimens aged at 848 and 873 K differed from that of the specimen aged at 823 K by a factor of about 2 and 3, respectively, their number density decreased by a factor of about 1/9 and 1/32. More specifically, the decreasing rate of the number density was approximately proportional to the inverse cube of the increasing rate of the average radii at aging temperatures above 823 K. This relationship clearly indicates that Ostwald ripening occurred when the aging temperature was above 823 K. A transition in the major growth mechanism to Ostwald ripening would have been responsible for the decrease in Vickers hardness of the M0 samples that were aged at temperatures above 823 K. It can be calculated from the average radii and the number density of the precipitates that the volume fraction of β-NiAl precipitates in the M0 samples was 0.2, 1.3, 1.3, and 1.0% when they were aged at 798, 823, 848, and 873 K, respectively, for 3 h. These values are lower than the volume fractions of the β-NiAl precipitates in Fig. 1, which were obtained by thermodynamic calculations, possibly because the thermodynamic calculations were based on a state of thermodynamic equilibrium. It should be mentioned that while the thermodynamic calculations predicted substantial decreases in the volume fraction of the β-NiAl phase with increasing aging temperature, the volume fraction evaluated by the SAXS method was almost constant above 823 K. Therefore, the decrease in the Vickers hardness above 848 K, as shown in Fig. 2, was less affected by the volume fraction of the β-NiAl precipitates.

Fig. 6.

Variations in (a) the average size in radius and (b) the number density of NiAl precipitates in M0 samples that were aged at different temperatures. The inset in (a) shows the corresponding size distribution of NiAl precipitates in the aged M0 samples. (Online version in color.)

Figure 7 shows the average radius and number density of the β-NiAl precipitates in the M1, M2, and M3 samples that were aged at 823 K. Although the amounts of Ni and Al in the M1 sample were lower than those in the M2 and M3 samples, the average radius of the precipitates of the M1 sample was almost comparable to that of the M2 or M3 sample. In contrast, the number density of the precipitates of the M1 sample was much lower than those of precipitates of the M2 and M3 samples. Because the M1 sample contained smaller amounts of the alloying elements, nucleation of the precipitates occurred to a smaller degree in the M1 sample than in the M2 and M3 samples. It should be mentioned that the precipitation behavior of β-NiAl was not affected by the differences in Mo content among the M1, M2, and M3 samples.

Fig. 7.

(a) Average radius and (b) number density of NiAl precipitates in the M1, M2, and M3 samples aged at 823 K.

On the basis of the Orowan equation, a particular mechanical property of alloys, including dispersed hard particles, can be described by the following equation:¹⁹⁾   

$$\mathrm{\Delta }\sigma =A\sqrt{d_{\text{N}}D},$$(5)

where Δσ is an increase in the tensile strength caused by the particle dispersion; d_N and D are the number density and diameter of the dispersed particles, respectively; and A is a proportionality constant. Figure 8 is a plot of the increase in the Vickers hardness as a function of $\sqrt{d_{\text{N}}D}$ of the β-NiAl precipitates. It should be mentioned that Eq. (5) can be roughly applied to alloys with different compositions if the intermetallic compounds are identical.¹⁹⁾

Fig. 8.

Increase in Vickers hardness with aging treatment as a function of $\sqrt{d_{\text{N}}D}$.

The plots roughly follows a linear relationship. The difference between the plots and the line in Fig. 8 might originate from the error in Vickers hardness or the change in the matrix composition with the aging treatments. Thus, it can be safely said that the mechanism to control the hardness can mainly be attributed to the distribution of nanoscale β-NiAl precipitates, regardless of the aging temperature and the Ni, Al, and Mo content, while the Fe₂Mo precipitation in the alloys was a minor factor in the hardening process.

4. Conclusions

Soft-magnetic stainless steels containing Ni, Al, and Mo as alloying elements exhibit high hardness while maintaining excellent soft-magnetic properties as well as corrosion resistance. In this work, we analyzed the precipitation-hardening mechanism by characterizing the precipitation behavior, namely determining the changes in metallurgical phases, size, and number density, with changes in the aging temperature and the amounts of the alloying elements Ni, Al, and Mo. The main conclusions are as follows:

(1) Thermodynamic calculations suggested that the precipitates were the intermetallic compounds NiAl with the B2 structure and Fe₂Mo with the Laves-phase structure. TEM observation showed that the Fe₂Mo precipitates were coarse and sparse. NiAl precipitates were not directly observed in the bright-field image, but they were identified in the TEM diffraction pattern, suggesting that they were finely precipitated.

(2) SAXS analysis revealed variations in the average radius and number density of the NiAl precipitates with increasing aging temperature. While the average radius monotonically increased with increases in the aging temperature, the number density decreased above a peak aging temperature of 823 K, suggesting that Ostwald ripening occurred above this temperature.

(3) The amounts of Ni and Al in the alloys had an effect on the number density of the NiAl precipitates and little effect on the size of the precipitates.

(4) The aging-induced hardness of the soft-magnetic stainless steel was proportional to the square root of the product of the size and number density of the NiAl precipitates; the precipitation of Fe₂Mo had a smaller effect on the precipitation hardening of the present alloy system.

Acknowledgments

The authors gratefully acknowledge Eiji Aoyagi and Makoto Nagasako of Institute for Materials Research, Tohoku University, for the TEM observations. This study was financially supported by a Grant-in-Aid (No. 16K14430 and No. 267212) from the Japan Society for the Promotion of Science (JSPS) Fellows.

References

• 1)   K. H.  Lo,  C. H.  Shek and  J. K. L.  Lai: Mater. Sci. Eng. R, 65 (2009), 39.
• 2)   U. K.  Viswanathan,  S.  Banerjee and  R.  Krishnan: Mater. Sci. Eng. A, 104 (1988), 181.
• 3)   I. L.  Cheng and  T.  Thomas: Trans. Am. Soc. Met., 61 (1968), 14.
• 4)   V.  Seetharaman,  M.  Sundararaman and  R.  Krishnan: Mater. Sci. Eng., 47 (1981), 1.
• 5)   P. W.  Hochanadel,  C. V.  Robino,  G. R.  Edwards and  M. J.  Cieslak: Metall. Mater. Trans. A, 25 (1994), 789.
• 6)   H. L.  Marcus,  J. N.  Peistrup and  M. E.  Fine: Trans. Am. Soc. Met., 58 (1965), 176.
• 7)   R.  Taillard,  A.  Pineau and  B. J.  Thomas: Mater. Sci. Eng., 54 (1982), 209.
• 8)   R.  Taillard and  A.  Pineau: Mater. Sci. Eng., 56 (1982), 219.
• 9)   T.  Ebata and  T.  Takiguchi: Electr. Furn. Steel, 75 (2004), 289.
• 10)   J.  Coakley,  K. M.  Rahman,  V. A.  Vorontsov,  M.  Ohnuma and  D.  Dye: Mater. Sci. Eng. A, 655 (2016), 399.
• 11)   H.  Oka,  T.  Tanno,  S.  Ohtsuka,  Y.  Yano,  T.  Uwaba,  T.  Kaito and  M.  Ohnuma: Nucl. Mater. Energy, 9 (2016), 346.
• 12)   H.  Wang,  H.  Ren, Z. Jin and S. Xing: ISIJ Int., 48 (2008), 1451.
• 13)   A.  Deschamps,  M.  Militzer and  W. J.  Poole: ISIJ Int., 41 (2001), 196.
• 14)   Y.  Oba,  S.  Koppoju,  M.  Ohnuma,  T.  Murakami,  H.  Hatano,  K.  Sasakawa,  A.  Kitahara and  J.  Suzuki: ISIJ Int., 51 (2011), 1852.
• 15)   S.  Kobayashi,  T.  Takeda,  K.  Nakai,  J.  Hamada,  N.  Kanno and  T.  Sakamoto: ISIJ Int., 51 (2011), 657.
• 16)   T.  Koutsoukis,  A.  Redjaïmia and  G.  Fourlaris: Mater. Sci. Eng. A, 561 (2013), 477.
• 17)   K.  Miyata,  Y.  Sawaragi,  H.  Okada,  F.  Masuyana,  T.  Yokoyama and  N.  Komai: ISIJ Int., 40 (2000), 1156.
• 18)   D. H.  Ping,  M.  Ohnuma,  Y.  Hirakawa,  Y.  Kadoya and  K.  Hono: Mater. Sci. Eng. A, 394 (2005), 285.
• 19)   M.  Ohnuma,  J.  Suzuki,  S.  Ohtsuka,  S. W.  Kim,  T.  Kaito,  M.  Inoue and  H.  Kitazawa: Acta Mater., 57 (2009), 5571.