Incubation time of occurrence of magnetic field-induced martensitic transformation has been investigated in an Fe–24.8Ni–3.7Mn (at%) alloy. Under a static magnetic field of 9 T, the alloy shows an isothermal martensitic transformation with a nose at 140 K in the time-temperature-transformation phase diagram. Under a pulsed magnetic field at 77 K, however, it exhibits an athermal martensitic transformation (a burst-type one). When the maximum field of 26.8 T is applied, the martensitic transformation starts in the field applying process at 16.54 T, but when the maximum field of 14.10 T is applied, the martensitic transformation starts in the field removing process. The time delay from the maximum field is in the order of several tens of microsecond and is probably related to the requirement of time to prepare for the nucleation of martensitic transformation.

Martensitic transformations have been classified into two groups, athermal and isothermal ones, with respect to kinetics.^1–4) The former transformation has a definite transformation start temperature, M_s, and occurs instantaneously at M_s,^5–8) while the latter one does not have a definite M_s but occurs after some finite incubation time during isothermal holding.^9–17) Recently, however, we found that an isothermal martensitic transformation in an Fe–24.9Ni–3.9Mn (at%) changes to an athermal one by the application of magnetic field¹⁸⁾ (magnetic field-induced-martensitic transformation occurs within 20 µs) and an athermal martensitic transformation in an Fe–32.3Ni (at%) changes to an isothermal one under hydrostatic pressure.¹⁰⁾ This means that these two transformation processes are closely related to each other and their difference is not intrinsic but may be explained by one basic rule. Based on this finding, we constructed a statistical thermodynamic model, which gives a unified explanation for these two transformation processes.¹⁹⁾ The central idea of this model is that martensitic transformation is assumed to occur by a thermally activated process for a potential barrier known in a first-order phase transition. Therefore, time dependent nature of martensitic transformation is naturally introduced through the transition probability of atoms and electrons over the potential barrier (martensitic transformation occurs with a short incubation time when the transition probability of atoms and electrons over the potential barrier is high). In other words, a martensitic transformation is intrinsically an isothermal one, but appears to be an athermal one in many cases because the incubation time is very short and this time dependent nature is considered to be strongly related to the nucleation of martensitic transformation.

According to this model,¹⁹⁾ we previously predicted that in materials exhibiting an athermal martensitic transformation, transformation occurs isothermally by holding at a temperature between M_s and an equilibrium temperature, T₀, where there exists the potential barrier (the potential barrier is assumed to be dependent on temperature and is zero at M_s temperature in our model¹⁹⁾). In fact, we confirmed that this prediction is certainly realized in Fe–Ni alloys exhibiting an athermal martensitic transformation.¹⁰⁾ The incubation time obtained, for example, is about 10² s in an Fe–32.3Ni (at%) alloy during isothermal holding at the temperature of 6 K higher than M_s.

Based on the result described above, we can speculate the existence of the incubation time shorter than second when the potential barrier is nearly zero. However, there have not been reported on this speculation except one our work.²⁰⁾ In order to detect such a short incubation time, we will investigate a magnetic field-induced martensitic transformation in an Fe–Ni–Mn alloy because its magnetic field-induced transformation was reported to be an athermal one,¹⁸⁾ as in the Fe–Ni alloys,¹⁰⁾ where we use a pulsed magnetic field with its pulse width of millisecond or microsecond. Thus, the purpose of the present study is to confirm the above speculation related to the nucleation of martensitic transformation. In fact, we detect such a short incubation time of order of several tens of microsecond in the present study.

For the present purpose, we select the Fe–24.9Ni–3.9Mn (at%) alloy previously studied¹⁸⁾ because this alloy was reported to induce an athermal martensitic transformation under high magnetic field at low temperatures, as mentioned above.

The Fe–Ni–Mn alloy ingot was prepared by arc melting method. The plate shaped ingot with 50 g in weight was hot-forged, homogenized at 1373 K and then hot-rolled at around 1273 K to the thickness of ∼1 mm. From the rolled sheet, specimens with dimensions of 5.0 mm × 2.0 mm × 0.3 mm were cut out. Then the specimens were heat-treated at 1323 K for 1.8 ks in an evacuated quartz tube followed by quenching into ice water. The surface of the specimens was polished by emery papers to remove the surface layer where the Mn content is depleted during the heat-treatment. Then the surface was finished chemically by immersing into a mixture of hydrogen fluoride solution (5%) and hydrogen peroxide solution (95%). The composition of the specimens was determined to be the Fe–24.8Ni–3.7Mn (at%) by the inductively coupled plasma analysis although we tried to make the Fe–24.9Ni–3.9Mn (at%) alloy.¹⁸⁾ The differences in compositions of Ni and Mn are small, but not the influence on the characteristic features of martensitic transformation. Then, we also examined these features such as a time-temperature-transformation diagram. Magnetization of the specimens under static magnetic field was measured by PPMS system of Quantum Design (VSM option) with the sampling rate of 1 s. Magnetization measurements under pulsed magnetic fields were made at Center of Advanced High Magnetic Science of Osaka University. The pulse widths were 15 ms and 1.5 ms with the sampling rate of 1 µs.

Figure 1 shows temperature dependence of magnetization of the Fe–24.8Ni–3.7Mn (at%) alloy measured in the cooling process and the subsequent heating process at a fixed rate of 2 K/min under a weak magnetic field of 0.01 T. As known from the figure, the magnetization in the heating process is observed to be slightly larger than that in the cooling process. The increase in magnetization is due to the formation of a small amount of martensite phase by the thermal cycle. Such a change in magnetization is seen in an Fe–24.9Ni–3.9Mn (at%) alloy which was previously studied to show an isothermal martensitic transformation.¹⁸⁾ Then, in order to confirm the existence of an isothermal transformation in the present alloy, holding experiments under the magnetic field of 9 T have conducted because magnetic field accelerates the isothermal transformation, as previously reported.¹⁰⁾ The experiment has been made in the following sequence. First, the specimen is cooled from 300 K to a holding temperature with a cooling rate of 10 K/min. Second, magnetic field of 9 T is applied with a rate of 0.015 T/s. Third, the magnetization is measured under the fixed field of 9 T and the temperature for up to 24 h.

Fig. 1

Temperature dependence of magnetization measured in one thermal cycle under 0.01 T magnetic field.

From the magnetization measurement, we have calculated amount of martensite, Δf, by following process; the magnetization of the austenite phase under 9 T is obtained to be 0.53 μ_B/atom. On the other hand, the spontaneous magnetization in martensite phase in the present Fe–24.8Ni–3.7Mn (at%) alloy is obtained by the Slater-Pauling curve.^21,22) The spontaneous magnetization at zero Kelvin is estimated to be 2.04 μ_B/atom and this value is assumed to be essentially the same in temperatures examined in the present study because its Curie temperature is high above 800 K.

The value of Δf thus obtained (Δf = ΔM/1.51, where ΔM (μ_B/atom) is the increase in magnetization due to the occurrence of martensite phase during the holding process.) is plotted as a function of holding time in Fig. 2. In the figure, the results at 180 K, 140 K, 130 K, and 77 K are shown, where the small jumps in Fig. 2 at every 600 s is due to calibration of the VSM system and is not the result of the increase in the martensite phase.

Fig. 2

Time dependence of the fraction of the martensite phase while holding under 9 T at 77 K, 130 K, 140 K and 180 K. The inset is an enlargement at the time less than 5 × 10² s.

From the result, the evaluation of the holding time for the formation of 0.1% of martensite phase was performed and the result is shown in Fig. 3 as a time-temperature-transformation (TTT) diagram. The TTT diagram shows a clear C-curve with a nose temperature at about 140 K. The nose temperature is consistent with other Fe–Ni–Mn alloys exhibiting isothermal transformations,^1,2) although the incubation is different between the present and previous alloys.

Fig. 3

Time-temperature-transformation (TTT) diagram corresponding to the formation of 0.1% of the martensite phase in the Fe–24.8Ni–3.7Mn (at%) alloy under 9 T. Marks indicate values obtained based on experimental data as shown in Fig. 2.

Incidentally, the TTT diagram shown in Fig. 3 is constructed using the average of 5 times experiments using 5 different specimens with the same composition of the present alloys.

Prior to showing the results in the present study, we describe how to find the existence of the incubation time shorter than second through a magnetic field-induced martensitic transformation, as below. Using the present Fe–24.8Ni–3.7Mn (at%) alloy, we will measure a magnetization by applying a pulsed magnetic field with its pulse width of millisecond or microsecond and obtain the magnetization as a function of magnetic field and the magnetization as a function of its application time of millisecond or microsecond. In this measurement, we can observe the change in magnetization when a magnetic field-induced martensitic transformation occurs (the magnetization in a martensite phase is larger than that in an austenite phase in the Fe–Ni–Mn alloy used in the present study). Usually such a change in magnetization can be observed under a field-increasing process, but it can also be observed under field-removing process if the incubation time in order of several tens of microsecond exists. So, we will find this peculiar magnetization curve due to a magnetic field-martensitic transformation in the present alloy.

The specimen is cooled down to 77 K and we confirm the martensitic transformation is not induced by this process by a magnetization measurement with a low magnetic field of 0.01 T at 77 K. Then, we apply the high magnetic field to the specimen and measure its magnetization. Figure 4(a) shows a typical magnetization curve measured at 77 K with a maximum magnetic field of 26.8 T and pulse width of 15 ms, and (b) shows the time dependences of magnetic field and magnetization. As known in (a), a sharp increase in magnetization is observed at the field strength of 16.54 T as indicated by an arrow, due to the occurrence of a burst-type martensitic transformation (an athermal martensitic transformation). This field strength is termed as the critical field (H_c) for the formation of martensite phase. The similar experiments have been repeated 5 times, and the average of critical field is obtained to be 16.92 T. It is noted from an enlargement of the time dependences of magnetization at near H_c shown in (b) that a burst-type martensitic transformation occurs within about 10 µs. This time span is considered as the time span of the nucleation and growth of many martensite plates. The fraction of the martensite phase induced by magnetic field is calculated by using the magnetization described above (3.1). Such amount at the critical field is 5.5% and increases gradually until the maximum field is reached because the magnetization increases gradually. The fraction of the martensite phase at the maximum field is estimated to be 28.10%. Incidentally, the increasing in magnetization in the field removing process has not been observed although it is quite natural in general.

Fig. 4

A typical magnetization curve measured at 77 K with a maximum magnetic field of 26.8 T (a), and the time dependence of magnetic field and magnetization and an enlargement of the time dependences of magnetization at near 16.54 T are plotted in (b).

In order to confirm the existence of the incubation time with the order of microseconds, the maximum value of pulsed magnetic field increases successively from 11.79 T. The blue curve in Fig. 5(a) is the magnetization curve of the specimen at 77 K with the maximum magnetic field of 13.47 T. There is no hysteresis between field applying and removing processes. This implies that martensitic transformation does not occur when the maximum field is 13.47 T. The black curve in Fig. 5(a) is the magnetization curve with the maximum magnetic field of 14.25 T. the magnetization increases suddenly near the maximum field strength, and a hysteresis appears between the field applying and removing processes. This increase is due to martensitic transformation and this field is termed as H_C1 (14.25 T). Figure 5(b) is the corresponding time dependence of magnetic field and magnetization in the vicinity of maximum magnetic field of 14.25 T. It should be noted in the figure that the magnetization increases sharply at the time about 25 µs after the time where the magnetic field shows the maximum value. This time delay behavior is exactly the one we speculate, as mentioned before. That is, this time delay corresponds to the incubation time required to occur the martensitic transformation. The same behavior is observed by using shorter pulsed magnetic field with a pulse width of 1.5 ms, where the delay time is 10 µs in this case. Incidentally, the magnetization in Fig. 5(b) increases in two steps. The increase of magnetization in the first step is 0.065 μ_B/atom and that in the second step was 0.01 μ_B/atom. They correspond to the formation of 4.2% and 0.6% of the martensite phase, respectively. The time required for the increase in magnetization is approximately 10 µs, being the same as that in Fig. 4. The two-step burst-type martensitic transformation is probably caused by the existence of two nucleation sites that require differ incubation time possibly due to different height of potential barrier between the parent and the martensite phase. We speculate that this situation comes from inhomogeneous composition and or some defects in the present alloy. That is, we speculate that first nucleation-site may be a Nickel poor area or somewhere of the edges or surfaces of the rectangular specimen where the height of potential barrier is relatively low in the specimen. After the first nucleation-site changes to the martensite, the plastic deformation by the growth of martensite induces a strain-field and this field changes the height of potential barrier in the residual parent phase. Therefore, it needs more higher magnetic field to nucleate a second nucleus of martensite after the first nucleation. Incidentally, we could not find the microstructural difference between the magnetic field-induced martensite and the isothermally induced martensite by an optical microscope observation.

Fig. 5

The magnetic curves with maximum value of 13.47 T (blue line), 14.25 T (black line) of pulsed magnetic field applied in one sample are plotted (a). The pulsed magnetic field with maximum magnetic field of 14.25 T is plotted in detail to illustrate the delay of martensitic transformation (b).

From the above results, we confirm the incubation time of occurrence of martensitic transformation, meaning that martensitic transformation certainly occurs by a thermal activation process and needs the time of order of several tens of microsecond at least for occurrence of martensitic transformation. On the other hand, when the maximum field of 26.8 T is applied, martensitic transformation does not occur at 14.25 T (H_C1), but occurs at 16.54 T (H_c, critical magnetic field) and this critical field is nearly the same irrespective of the maximum fields higher than H_C1. Presumably, the holding time at H_C1 for occurrence of martensitic transformation is insufficient when the maximum magnetic field higher than H_C1 is applied in the present study. The value of this holding time has not been known yet, but it may be in the order of several hundreds of microsecond, as speculated from Fig. 4(b). In addition, considering an instant occurrence of martensitic transformation at a critical magnetic field, we can say that the potential barrier is quite small at a critical magnetic field, and therefore, the incubation time at a critical field is quite small. In order to estimate the quantitative value of the potential barrier described above, we calculate its value by a statistical thermodynamic model proposed by our group as below.^10,19) According to the theory, the nucleation of martensitic transformation can occur by a thermal activation process and the potential barrier was introduced to be expressed with δ − ΔG(T) in the previous model, where the value of δ (constant value) is the chemical driving force for the occurrence of martensitic transformation and is 1574 J/mol used in the present analysis by referring to previous report,¹⁸⁾ because the value was obtained in an Fe–24.9Ni–3.9Mn (at%) whose composition is nearly the same as that in the present Fe–24.8Ni–3.7Mn (at%) alloy and ΔG(T) the difference in Gibbs free energy at T between the austenite and martensite phases. Using these quantities, the potential barrier under magnetic field is expressed as,   

In Summary, the incubation time of the occurrence of magnetic field-induced martensitic transformation has been investigated in an Fe–24.8Ni–3.7Mn (at%) alloy by using a pulsed magnetic field with its pulse width of millisecond or microsecond. The main results are the followings.

The present work was supported by The Institute for Solid State Physics, the University of Tokyo as a joint research. The authors appreciate experimental supports by Masaya Tanaka and Koutaro Hatamoto, who were graduate students of Osaka University. It is noted that Dr. Takashi Fukuda passed away on 27 April 2020.

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