The Thermal Transformation Arrest Phenomenon in NiCoMnAl Heusler Alloys

Abstract

In this report, we present findings of systematic research on NiCoMnAl alloys, with the purpose of acquiring a higher thermal transformation arrest temperature (T_A). By systematic research, T_A in the NiCoMnAl alloy systems was raised up to 190 K, compared to the highest T_A of 130 K in NiCoMnIn. For a selected alloy of Ni₄₀Co₁₀Mn₃₃Al₁₇, magnetization measurements were performed under a pulsed high magnetic field, and the critical magnetic field-temperature phase diagram was determined. The magnetic phase diagram for Ni_50−xCo_xMn_50−yAl_y was also established. Moreover, from the discussion that the formerly called “kinetic arrest phenomenon” has both thermodynamic and kinetic factors, we suggest a terminology change to the “thermal transformation arrest phenomenon”.

1. Introduction

1.1. Kinetic Arrest Phenomenon and Thermal Transformation Arrest Phenomenon

It has been reported in Ni(Co)MnIn alloys that the martensitic transformation is interrupted during the cooling process, and the coexisting martensite and parent phases stay “stable” at low temperatures, even when the magnetic field is removed [1,2]. Moreover, as reported by Ito et al., when zero field heating was performed soon after field cooling, the “frozen” parent phase was “unfrozen”, and a heating-induced martensitic transformation could be observed [2]. Based on the above experimental findings, it has been thought that the “frozen” state is caused by kinetic factors that prohibit the transformation from the parent phase to the martensite phase at extremely low temperatures. Hence, this phenomenon has been termed the kinetic arrest (KA) phenomenon, and the corresponding temperature, at which the martensitic transformation is arrested, has been called the KA temperature.

Subsequently, the KA phenomenon was found in other NiMn-based alloy systems, such as Ni₃₃Co_13.4Mn_39.7Ga_13.9 [3], Ni₄₅Co₅Mn₃₁Al₁₉ [4] and Ni₃₇Co₁₁Mn_42.5Sn_9.5 [5]. For these Metamagnetic Shape Memory Alloys (MMSMAs), the ferromagnetic parent phase can be induced by applying a magnetic field from the martensite phase, as first reported in NiCoMnIn [6]. Thus, by magnetization measurements at various temperatures below the reverse martensitic transformation starting temperature (T_As), the magnetic fields of critical transition, i.e., the reverse martensitic transformation finishing magnetic field (H_Af) and the forward martensitic transformation starting magnetic field (H_Ms), can be determined. By summarizing the results of Ni₄₅Co₅Mn_36.7In_13.3 [2], Ni₃₃Co_13.4Mn_39.7Ga_13.9 [3], Ni₄₅Co₅Mn₃₁Al₁₉ [4] and Ni₃₇Co₁₁Mn_42.5Sn_9.5 [5], it can be concluded that the magnetic field hysteresis, which is defined by H_hys = H_Af − H_Ms, greatly increases at low temperatures, which strongly supports the kinetic nature of the KA phenomenon. Moreover, besides the enlargement of the H_hys at low temperatures, other experimental facts also support the kinetic nature of this unique phenomenon. For NiCoMnIn alloys, Ito et al. observed the isothermal behavior of martensitic transformation [7], and Lee et al. investigated the Time-Temperature-Transformation (TTT) diagram [8], where the time-dependent nucleation of the martensite phase has been confirmed. On the other hand, Sharma et al. [1] and Kustov et al. [9] systematically investigated the relaxation behavior during martensitic transformation, where the time-dependent growth of the martensite phase has also been confirmed. Furthermore, Nayak et al. found that the transformation hysteresis changes with the sweeping speed of the temperature and the magnetic field in the NiCoMnSb system [10]. Our group has also confirmed that for NiCoMnIn, the H_hys is greatly enlarged under a pulsed magnetic field, as compared to that under a static magnetic field [11]. Recently, in situ observation by our group has also confirmed that if the thermal activation energy related to the kinetic behavior differs, the optical microstructure also shows distinctive features [12].

Nevertheless, the derivation by Ito et al. [2] has shown that the KA phenomenon also has a thermodynamic nature. Generally, for the case of magnetic field-induced reverse martensitic transformation, the magnetic field hysteresis loop reflects the dissipation energy during the forward and reverse martensitic transformation. Therefore, the thermodynamic equilibrium condition between the two phases exists between H_Ms and H_Af, and this condition is neither related to nor affected by kinetic factors. Physically, if the magnetization differences between the two phases (ΔM)at H_Ms and H_Af are almost equal, H₀ =(H_Af +H_Ms)/2 can be assumed as the equilibrium magnetic field at which the parent phase and the martensite phase have an equal Gibbs free energy under the condition that a small amount of the martensite phase exists in the parent austenite matrix [13]. It can be concluded from [2–5] that H₀ increases with decreasing temperature and becomes almost constant below certain temperatures (KA temperatures), which is a common feature of all four alloys. The Clausius-Clapeyron equation between the magnetic field and temperature gives:

$$\frac{\text{d}{H}_0}{\text{d}T}=-\frac{\mathrm{\Delta }S}{\mathrm{\Delta }M}$$

(1)

where ΔM and ΔS are the magnetization difference and the entropy change during the transformation, respectively. Since ΔM does not change so much in a relatively small range of temperature far below the Curie temperature, ΔS should be approximately proportional to dH₀/dT for the absolute value. Thus, one can conclude that, generally, ΔS becomes zero at the KA temperature. Since the driving force, ΔG, for the thermal transformation can be estimated by ΔG ≈ ΔS · ΔT, where ΔT stands for supercooling, the transformation will stop when ΔS becomes zero. This is considered to be the thermodynamic cause of the KA phenomenon. This has also been well agreed by Cesari et al. [14]. They have suggested the term of “thermodynamic arrest” in order to reflect the thermodynamic nature of this phenomenon.

In other words, the arrested parent phase during field cooling can be considered to be a thermodynamic phenomenon, while when the magnetic field is removed, it does not transform to the martensite phase, mainly because of kinetic reasons. Therefore, the former name, “kinetic arrest phenomenon”, may mislead as to the nature of this phenomenon. In this article, we suggest and will from now on neutrally call this phenomenon the “thermal transformation arrest (TTA) phenomenon” and the corresponding temperature, at which the forward martensitic transformation stops, to be the “thermal transformation arrest temperature (T_A)”.

1.2. Considerations of the Thermal Transformation Arrest Phenomenon for Practical Applications

The TTA phenomenon is not only an interesting physical phenomenon, but it also has important implications for practical applications.

This is shown schematically in Figure 1. In the upper part of Figure 1(a), the results of the thermomagnetization (MT) measurement for a heating process of an MMSMA is shown. Under zero field heating (ZFH), where the applied magnetic field is very small, the martensite phase with weak magnetism changes to the parent phase with ferromagnetism at T_Af. While under field heating (FH), where a strong magnetic field is applied, the transformation temperature decreases to T′_Af, the MT curve being shown by the purple line. Moreover, when considering practical use, the maximum magnetic field a permanent magnet can produce is around 1.5 T, and thus, the temperature change is small, as indicated by the purple arrow. Since the process of magnetic field-induced reverse martensitic transformation is used for actuators, the consideration only focuses on the heating process, and the temperature range available for practical application is very limited, as shown by ΔT_0p. The correspondence of the MT with the critical magnetic field-temperature (H₀–T) diagram is shown in the lower part of Figure 1(a), where the definitions of H_Af and H_Ms in the H₀–T diagram are schematically shown in the inset. It can be seen that the linear part of the diagram is used and that the bending part corresponding to the TTA phenomenon is not related to this condition. Before proceeding to an explanation of the next figure, it should be pointed out that all the figures shown in Figure 1 are schematic, and this is only the case for an ideal MMSMA. For an actual MMSMA, such as NiCoMnIn, around 3–5 T of magnetic field is required for a reversible MFIT [6]. Therefore, 1.5 T is far from enough. For other systems, the required magnetic field is even larger.

For practical use, a temperature window wider than the narrow one shown in Figure 1(a) is required. As reported earlier, by simple variation of the composition, the horn-shaped H₀–T diagram can be easily shifted vertically [15]. Figure 1(b) shows the condition where the diagram is shifted downwards. As the MT curves above show, by applying a magnetic field, T_Af decreases more than the condition in Figure 1(a). Therefore, by using the flat portion of the diagram where the TTA phenomenon appears, a wider temperature window becomes available for applications, as shown by ΔT_0p.

However, to get an even wider temperature window, attempts must be made to modify the shape of the horn-shaped H₀–T diagram. As shown in Figure 1(c), if an alloy with a much higher T_A is obtained, a larger temperature range of the flat portion in the H₀–T diagram will be obtained, and thus, the upper limit of the temperature window can be greatly raised. Moreover, if the enlargement of H_hys at low temperatures can be suppressed, the lower limit of the temperature window can be further extended, as shown in the lower part of Figure 1(c). However, approaches for modification of the shape of the H₀–T diagram have not been reported to date.

1.3. The Purpose of This Study

In this report, we focus on efforts to raise the T_A in NiMn-based alloy systems. In NiCoMnIn, the tendency can be concluded from previous reports. It has been found that for Ni_50−xCo_xMn_50−yIn_y, the T_A increases from 73 K [16]to105K[17] with 2.5 at% dopant of Co and to 129 K [2] with 5 at% dopant of Co. Thus, if more Co can be added to NiMnIn, alloys with higher T_A can be expected. However, as reported by Ito et al., with a 7.5 at% addition of Co, the parent phase decomposes into two phases [18]. Therefore, we have to search for alloy systems that have larger Co solubility. As shown by Kainuma et al., though both the parent phase and martensite phase of NiMnAl alloy have very weak magnetism, by the substitution of Co for Ni, the magnetism of the parent phase drastically becomes ferromagnetic, while the martensite phase remains as weak magnetism [19]. Therefore, the magnetic relationship in NiCoMnAl between the parent and martensite phases is similar to that of the NiCoMnIn alloy system, and metamagnetic transformation has also been confirmed in NiCoMnAl [19]. In the original report [19], 10 at% of Co was added, and even larger solubility of Co, and, thus, a higher T_A, can be expected. In the present research, a systematical investigation on the NiCoMnAl alloy system was carried out, with the purpose of searching for a higher T_A.

2. Experimental Procedures

Ni_50−xCo_xMn_50−yAl_y (x = 5, 10, 15, y = 12–19, Co_xAl_y for short) samples were prepared by induction melting in an argon atmosphere. Heat treatment was conducted at 1,373 K for 24 h, followed by water quenching. Composition analysis was carried out by an Electron Probe Microanalyzer (EPMA), and the results are summarized in

Table 1. Compositions of Ni_50−xCo_xMn_50−yAl_y (Co_xAl_y for short) alloys were analyzed by Electron Probe Microanalyzer (EPMA). The composition data listed here are in atomic percentage. Data of the Curie temperature (T_C) and martensitic transformation starting temperature (T_Ms) are also listed.

Nominal	Ni at%	Co at%	Mn at%	Al at%	TC	TMs
Co5Al18.5	44.7	5.1	32.0	18.2	-	322
Co5Al20	44.4	5.1	30.5	20.0	269	129
Co5Al21	44.4	5.1	29.4	21.1	257	-
Co10Al17	39.7	10.2	33.7	16.4	428	351
Co10Al17.5	39.9	10.1	33.3	16.7	423	252
Co10Al19	39.9	10.1	30.6	19.4	394	-
Co15Al12	34.7	14.8	38.8	11.7	-	525
Co15Al14	34.5	14.8	37.0	13.7	527	450
Co15Al14.5	35.0	15.2	35.6	14.2	516	390
Co15Al14.8	35.0	15.0	35.6	14.4		360
Co15Al15	34.5	15.0	35.8	14.7	514	332
Co15Al15.5	34.5	15.1	35.4	15.0	510	-
Co15Al17	34.9	15.3	32.8	17.0	503	-

. MT measurements were performed by a Vibration Sample Magnetometer and a SQUIDmagnetometer at a sweeping speed of 2 K/min. Magnetization measurements under a pulsed magnetic field up to 55 T were measured by induction using coaxial pickup coils [20] at the Institute for Solid State Physics, the University of Tokyo.

3. Results and Discussion

3.1. Thermal Transformation Arrest Temperatures in Co-Doped Alloys

In the Co_xAl_y system, the TTA phenomenon was first realized with the compositions of Co₅Al_y [4]. As shown in Figure 2(a), the martensitic transformation is interrupted at around 40 K. The application of a magnetic field has a drastic effect on the behavior of martensitic transformation. For this alloy, with the application of a higher magnetic field, the magnetization at low temperatures continues growing, and the martensitic transformation almost stopped under a 7 T field cooling, suggesting a strong arresting.

By the arrangement of composition, the TTA phenomenon was also realized in Co₁₀Al_x in this study. Figure 2(b) shows the MT curves of Co₁₀Al_17.5 under magnetic fields of 0.05, 1, 3 and 5 T. Martensitic transformation starting temperature (T_Ms) was observed to decrease with increasing applied magnetic field. As explained in Figure 2(a), with the increase of the applied magnetic field, the magnetization in the low temperatures part also increases. This also indicates the appearance of the TTA phenomenon, and the T_A is determined to be around 160 K.

Moreover, Figure 2(c) shows the magnetization curves of Co₁₅Al₁₅ under magnetic fields of 3, 5 and 7 T, which follows Khovaylo et al. [21]. Due to the fact that both the T_C and the T_Af are high for this sample, the temperature hysteresis could not be fully measured. For this alloy, the martensitic transformation is also interrupted, and the T_A is determined to be 190 K. Thus, as shown in Figure 2, the doping of Co into NiMnAl is also found to be effective to raise the T_A, and a high T_A of about 190 K was obtained in the Co₁₅Al_x.

3.2. Magnetization Measurements in Pulsed Magnetic Field

As first reported for NiCoMnIn, the H₀–T phase diagram for the alloys with TTA behavior show horn-shaped curves [2]. The H_Ms and H_Af make up the lower and upper branches, respectively, and the H₀ becomes constant below the T_A. This behavior has been confirmed for the first time in Co₅Al₁₉ [4] in the the NiCoMnAl alloy system, and for Co₁₀Al₁₇, the investigation was conducted in this study by magnetization measurements under a pulsed magnetic field.

Figure 3(a) shows the magnetization curves for Co₁₀Al₁₇ up to 55 T at 50, 100, 200 and 300 K. Raw data of the differentiations of magnetization and magnetic field against measurement time are obtained, and the integrals yield the magnetization-magnetic field curves. Normally, calibration for obtaining the integral constants is conducted using the results of the magnetization measurements obtained by SQUID in the low magnetic field region, and the absolute values of magnetization can be also obtained. Especially for the case when a ferromagnetic-like behavior can be observed in low magnetic fields, the calibration becomes very easy. However, the calibration for the integral constants was not successful for this sample, since the magnetism in the martensite phase (which is the only state we can obtain in low magnetic fields) is paramagnetic-like. Therefore, the unit in Figure 3(a) is shown as a.u.. Nevertheless, we can clearly observe that magnetic field-induced reverse martensitic transformation for all the temperatures and an almost full parent phase were obtained, except for 50 K. Moreover, the determination of critical magnetic fields (H_Ms and H_Af) by extrapolation, as shown in Figure 3(a), is also not affected at all by the arbitrary values of magnetization. For 50 K, since the reverse martensitic transformation is not complete, H_Ms and H_Af could not be determined. Therefore, it can be generally concluded that the critical magnetic fields shift higher as the measurement temperature becomes lower.

The critical magnetic fields are summarized in Figure 3(b), and the results for Co₅Al₁₉ [4] are plotted. For Co₁₀Al₁₇, it can be seen that, below the T_A, H₀ becomes almost constant, while the H_hys begins to enlarge below this temperature. However, if the results of Co₁₀Al₁₇ and Co₅Al₁₉ are compared, one can easily find two differences between them. First, the T_A is much higher for Co₁₀Al₁₇, as already stated in Figure 2. Second, the H_hys/2 around T_A is only about 2–3 T for Co₅Al₁₉, while that of Co₁₀Al₁₇ reaches 10 T. It should be noted that both of the results of the referenced Co₅Al₁₉ or Co₁₀Al₁₇ by this study were investigated under a pulsed magnetic field. As stated in the introduction, the H_hys is enlarged under a pulsed magnetic field for the measurement of NiCoMnIn, compared to that under a static magnetic field [11]; a smaller H_hys would be expected for Co₁₀Al₁₇ if the magnetization measurement under a static magnetic field were possible. For investigations on H_hys, recent studies by our group have given some phenomenological understanding of its breakdown and temperature dependency [12,22]. Here, we plot the H_hys/2 for both Co₅Al₁₉ and Co₁₀Al₁₇ in Figure 3(c), where the H_hys for 50 K is estimated by the difference of the magnetizing and demagnetizing branches in Figure 3(a) and is shown by an open circle in Figure 3(c). As shown by the findings of Umetsu et al. [22], it is found that both the athermal term (H_μ) and the thermally activated term (H_TA) for Co₁₀Al₁₇ are much larger than those of Co₅Al₁₉. In Figure 3(c), the red solid line for fitting the H_hys/2 of Co₁₀Al₁₇ is given by [22]:

$$H_{\text{hys}}(T)/2=H_{\mu }+H_{\text{TA}}=H_{\mu }+H_{\text{TA}}(0){\left[1-{\left(\frac{m{k}_{\text{B}}T}{Q_{0\text{K}}}\right)}^{1/q}\right]}^{1/p}$$

(2)

with q =3/2, p =1/2, H_μ =8.0 T, H_TA(0) = 15.1 T and m/Q_0K =37.2 eV⁻¹, where T, being the temperature, H_TA(0), being the limit value of H_TA at 0 K, k_B, being the Boltzmann constant, m, being a dimensionless constant relating to the sweeping rate of the magnetic field, and Q_0K, being the activation energy for overcoming the kinetic barrier without thermal assist. Therefore, according to this model, the H_hys at temperatures near 0 K will be more than 46 T, and the H_Af is expected to be around 49 T. The expected tendencies of H_Ms and H_Af are illustrated by dashed lines in Figure 3(b) (note that with the definition of H_Af by extrapolation, the magnetic field over which the magnetizing and demagnetizing curves overlap, i.e., the magnetic field at which reverse martensitic transformation actually finishes, is much higher than the H_Af shown in Figure 3(b)). However, the reason for the large differences in H_hys between the two alloys is still not clear, and neither is the nature of the H_hys. Thus, further investigations are required in the future to understand the physical origins of the H_hys.

3.3. Determination of the Magnetic Phase Diagram for Ni_50−xCo_xMn_50−yAl_y

Figure 4 shows the thermomagnetization curves for Co_xAl_y, where none of the samples show martensitic transformation behaviors. For stoichiometric samples (y = 25), no martensitic transformation can be observed [23], and the samples shown in Figure 4 are nearer stoichiometry than the samples showing martensitic transformations, as illustrated in Figure 2. Only Curie temperature (T_C) is observed, and it is defined to be the temperature at which the differentiation shows a minimum (not shown). It can be observed that the T_C is greatly raised by the addition of Co content, which is consistent with the former report on Co_xAl₂₅ samples [23], and has the same tendency as compared with NiCoMnIn [18,24] and NiCoMnGa [25,26].

Similar measurements of other samples shown in Table 1 were also performed; the obtained T_Ms and T_C are listed in Table 1 and summarized in Figure 5. It can be seen that for the series of samples with the same Co content, the T_Ms decreases with increasing Al content, which is the same as NiMnAl [28]. However, the decreasing tendency enhances when below the T_C, which is similar to the case of NiCoMnIn alloys [18]. The tendencies, as well as the values of the transition temperatures are consistent with former reports [23,27–29], as shown in Figure 5. It should be also pointed out that, for solution-treated NiMnAl ternary alloys, the parent phase with a B2 structure is antiferromagnetic and the T_C does not exist [28]. With aging treatment at low temperatures, the crystal structure changes from B2 to L2₁, and this results in ferromagnetism in the parent phase near the stoichiometric composition [28,30]. Though not shown in this report, NiCoMnAl alloys in this study also showed the same tendency, i.e., the T_C increases after aging at low temperatures. The T_As obtained in Figure 2 are also indicated in Figure 5. It was found that the T_A does not seem to change in the same series of samples with the same Co composition. Furthermore, the Co addition greatly raises T_A. The TTA phenomenon has been schematically explained by Gibbs free energy curves [18] and is believed to be greatly affected by the ferromagnetic state of the parent phase. Therefore, the increase of T_A in NiCoMnAl can be easily understood, since the addition of Co strongly raises the T_C of the parent phase. Though T_A was successfully raised in NiCoMnAl alloys, which satisfies the purpose of this study, the H_hys is greatly enlarged, and this is extremely unfavorable from the viewpoint of applications. To date, the way to decreasing the H_hys is still unknown and remains to be investigated further in the future.

4. Conclusions

In this study, the magnetic properties of the Ni_50−xCo_xMn_50−yAl_y alloy system were systematically investigated with the purpose of raising the thermal transformation arrest temperature (T_A). The T_A was raised from 40 K, for the first time in this system, to about 190 K, by the substitution of Co for Ni. Furthermore, the critical magnetic field-temperature phase diagram for Ni₄₀Co₁₀Mn₃₃Al₁₇(Co₁₀Al₁₇) was determined under a pulsed high magnetic field. Magnetic field hysteresis H_hys during the magnetic field-induced reverse martensitic transformation was found to be greatly enlarged below the T_A for Co₁₀Al₁₇. The magnetic phase diagram for Ni_50−xCo_xMn_50−yAl_y was also determined in this study. Finally, a change in terminology is proposed, i.e., from “kinetic arrest phenomenon” to “thermal transformation arrest phenomenon”, which is in line with the experimental results based on phenomenological understandings.