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Metals 2013, 3(1), 114-122; doi:10.3390/met3010114

Article
Magnetic Moment of Cu-Modified Ni2MnGa Magnetic Shape Memory Alloys
Takeshi Kanomata 1,2, Keita Endo 3, Naoto Kudo 3, Rie Y. Umetsu 4,5,*, Hironori Nishihara 6, Mitsuo Kataoka 7, Makoto Nagasako 8, Ryosuke Kainuma 8 and Kurt R.A. Ziebeck 9
1
Research Institute for Engineering and Technology, Tohoku Gakuin University, Tagajo 985-8537, Japan; E-Mail: kanomata@tjcc.tohoku-gakuin.ac.jp
2
Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
3
Faculty of Engineering, Tohoku Gakuin University, Tagajo 985-8537, Japan; E-Mails: e.keita.g@gmail.com (K.E.); nimncuga@live.jp (N.K.)
4
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
5
Japan Science and Technology Agency-Precursory Research for Embryonic Science and Technology (JST-PREST), Tokyo 102-0076, Japan
6
Faculty of Science and Technology, Ryukoku University, Otsu 520-2194, Japan; E-Mail: nishihara@rins.ryukoku.ac.jp
7
Department of Basic Sciences, Faculty of Science and Engineering, Ishinomaki Senshu University, Ishinomaki 986-8580, Japan; E-Mail: kataokam@kxe.biglobe.ne.jp
8
Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan; E-Mails: nagasako@material.tohoku.ac.jp (M.N.); kainuma@material.tohoku.ac.jp (R.K.)
9
Department of Physics, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK; E-Mail: kraz2@cam.ac.uk
*
Author to whom correspondence should be addressed; E-Mail: rieume@imr.tohoku.ac.jp; Tel.: +81-22-215-2492; Fax: +81-22-215-2381.
Received: 4 January 2013; in revised form: 24 January 2013 / Accepted: 25 January 2013 /
Published: 4 February 2013

Abstract

: The magnetization measurements at 5 K were carried out for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys. All of the magnetization curves are characteristic of ferromagnetism or ferrimagnetism. By using Arrott plot analysis the spontaneous magnetization of all samples was determined from the magnetization curves. The magnetic moment per formula unit, μs, at 5 K was estimated from the spontaneous magnetization. For Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys μs at 5 K decreases linearly with increasing x. On the other hand, the μs at 5 K for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys decreases more steeply with increasing x compared to the μs for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys. On the basis of the experimental results, the site-occupation configurations of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys are proposed.
Keywords:
magnetic shape memory alloy; Heusler alloy; Ni2MnGa; magnetic moment

1. Introduction

In recent years, Heusler alloys have become a subject of intensive experimental and theoretical investigations. Ferromagnetic shape memory alloys (FSMAs) with the Heusler-type structure (L21-type structure), which exhibit both the ferromagnetic and structural transitions, have attracted much attention due to their potential application as smart materials [1,2]. A large magnetic field-induced strain by the rearrangement of twin variants in the martensite phase was observed in the Ni-Mn-Ga FSMAs [3,4]. Moreover, a large magnetocaloric effect (MCE) accompanied by a magnetostructural transition, where both the ferromagnetic and structural transitions occur together, has been expected to be useful for devices [5,6]. Among FSMAs, the stoichiometric Heusler alloy Ni2MnGa has been the most studied. Ni2MnGa orders ferromagnetically with a Curie temperature of TC ≈ 365 K. On cooling below the martensitic transition temperature TM ≈ 200 K, a superstructure forms, and the ferromagnetic state remains below TM [7,8]. The spontaneous magnetization Ms just below TM is larger than the Ms just above TM for Ni2MnGa.

Recently, Kataoka et al. [9] and Endo et al. [10] carried out magnetization, permeability and differential scanning calorimetric (DSC) measurements on the FMSAs Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys, respectively. It was found that for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys the magnetostructural transitions between the paramagnetic austenite phase (Para-A) and the ferromagnetic martensite phase (Ferro-M) occur in the concentration range of 0.23 ≤ x ≤ 0.30 [9]. Similarly, the magnetostructural transitions between the Para-A and Ferro-M were observed in the concentration range of 0.12 ≤ y ≤ 0.14 for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys [10]. Furthermore, the characteristics of the phase diagrams of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys were found to be very similar to those of Ni2 +xMn1 − xGa (0 ≤ x ≤ 0.36) alloys [11]. Kataoka et al. explained the phase diagram of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys using the Landau-type phenomenological free energy as a function of the martensitic distortion and the magnetization [9]. Their analysis showed that the biquadratic coupling term, together with a higher order term, of the martensitic distortion and the magnetization plays an important role in the interplay between the martensite phase and the ferromagnetic phase. As the result, Kataoka et al. could obtain the satisfactory agreement between the calculated and observed phase diagrams for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys. Also the phase diagram of Ni2 − zCuzMnGa (0 ≤ z ≤ 0.8) alloys was determined from the results of the temperature dependence of the initial permeability [12]. The TC of Ni2 − zCuzMnGa (0 ≤ z ≤ 0.8) alloys increased with the Cu concentration z. While, the TM decreased abruptly with z.

In this paper, the concentration dependence of the magnetic moment for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys is examined to gain deeper insight for the magnetic properties of these FSMAs. On the basis of the experimental results, the site occupancy and the magnetic structure of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys are presented. Furthermore, the site occupancy of Ni2 − zCuzMnGa (0 ≤ z ≤ 0.4) alloys is also presented.

2. Experimental Section

The Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys were prepared by repeated arc melting of the constituent elements, namely 99.99% pure Ni, 99.99% pure Mn, 99.99% pure Cu and 99.9999% pure Ga in argon atmosphere. The heat treatments of all reaction products after the arc melting were reported in the references [9,10]. Weight loss between before and after the arc melting is within 0.5%, thus the composition of the specimens is seen to be the same with the nominal ones. By using X-ray powder diffraction measurements all samples were confirmed to be of single phase at room temperature. Magnetization measurements on prepared samples were carried out in magnetic fields up to 50 kOe using a superconducting quantum interference device (SQUID) magnetometer.

3. Results and Discussion

Figure 1, Figure 2 show the phase diagrams of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys reported by Kataoka et al. [9] and Endo et al. [10], respectively. The phase diagrams shown in Figure 1, Figure 2 have characteristics very similar to that [11] of Ni2 +xMn1 − xGa (0 ≤ x ≤ 0.36) alloys. As shown in Figure 1, the samples with x ≤ 0.20 of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys crystallize in the L21-type structure at room temperature. However, the details of the crystal structure in the martensite phase for the samples with x ≤ 0.20 are not clear. It was confirmed by the low temperature X-ray powder diffraction measurements that the sample with x = 0.23 for Ni2Mn1-xCuxGa alloy crystallizes in a 14-layered monoclinic (14M) structure (space group: C2/m) well below the martensitic transition temperature [9]. The X-ray powder diffraction pattern of the sample with x = 0.23 at room temperature shows that the cubic phase with the L21-type structure and the monoclinic phase with the 14M structure coexist. Similarly, the X-ray powder diffraction patterns at room temperature of the samples with x = 0.25 and 0.27 indicated that the L21 phase and the 14M phase coexist although the fraction of the 14M phase increases with increasing the concentration x. The sample with x = 0.35 crystallizes in a tetragonal D022-like crystal structure with no lattice modulation at room temperature. The crystal structures of the 14M and the D022-like also appear in the martensite phase of Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys depending on the Cu concentration, being similar to that of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys [10]. The magnetization curves at 5 K for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys with various concentrations x are shown in Figure 3. All of the magnetization curves are characteristic of ferromagnetism or ferrimagnetism. The magnetization M at 5 K for all samples is saturated in a field of about 20 kOe. The magnetization curves at 5 K for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys with various concentrations y are shown in Figure 4. The spontaneous magnetization at 5 K for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys was determined by the linear extrapolation to H/M = 0 of the M2 versus H/M curves (Arrott plot). The magnetic moments per formula unit, μs, at 5 K for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys were estimated from the values of the spontaneous magnetization and are plotted against concentrations x and y as shown in Figure 5. The concentration dependence of μs at 5 K for Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40) alloys is also shown in Figure 5 [12], where the values of μs for Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40) alloys were determined at 4.2 K. The μs at 5 K of the stoichiometric Ni2MnGa is estimated to be about 4 μB/f.u. by extrapolations of the μs versusx curve for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys to x = 0 and of the μsversusy curve for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys to y = 0. Recently, Ahuja et al. carried out a magnetic Compton scattering study of the near-stoichiometric Heusler alloy Ni2.03Mn0.97Ga [13]. For Ni2.03Mn0.97Ga, they found the value of μs to be 4.01 μB/f.u. at 110 K in a field of 2 T. The value of μs at 5 K for Ni2MnGa in the present study is in good agreement with the value reported by Ahuja et al. [13].

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Figure 1. Phase diagram of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.4) alloys [9]. Para and Ferro mean the paramagnetic and ferromagnetic state, respectively. A and M represent the austenite and martensite phases, respectively. Tp is the premartensitic transition temperature. TC and TM are the Curie temperature and the martensitic transition temperature, respectively.

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Figure 1. Phase diagram of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.4) alloys [9]. Para and Ferro mean the paramagnetic and ferromagnetic state, respectively. A and M represent the austenite and martensite phases, respectively. Tp is the premartensitic transition temperature. TC and TM are the Curie temperature and the martensitic transition temperature, respectively.
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Figure 2. Phase diagram of Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys [10]. Para and Ferro mean the paramagnetic state and ferromagnetic one, respectively. A and M represent the austenitic and martensitic phases, respectively. TC, TM and Tp are the Curie temperature, the martensitic transition temperature, and premartensitic transition temperature, respectively.

Click here to enlarge figure

Figure 2. Phase diagram of Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys [10]. Para and Ferro mean the paramagnetic state and ferromagnetic one, respectively. A and M represent the austenitic and martensitic phases, respectively. TC, TM and Tp are the Curie temperature, the martensitic transition temperature, and premartensitic transition temperature, respectively.
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Figure 3. Magnetization curves at 5 K for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys with various concentration x.

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Figure 3. Magnetization curves at 5 K for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys with various concentration x.
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Figure 4. Magnetization curves at 5 K for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys with various concentration y.

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Figure 4. Magnetization curves at 5 K for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys with various concentration y.
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Recently, Li et al. investigated theoretically the site preference and elastic properties of Fe-, Co- and Cu-doped Ni2MnGa alloys by using the first-principles exact muffin-tin orbital method in combination with the coherent-potential approximation [14]. According to the results of the calculation by Li et al. [14], Cu atoms for Ni2Mn0.95Cu0.05Ga occupy the vacant Mn sublattice and the magnetic moments of the Ni, Mn, Cu and Ga atoms, μNi, μMn, μCu and μGa, in Ni2Mn0.95Cu0.05Ga are 0.32 μB, 3.37 μB, −0.03 μB and −0.05 μB, respectively. The values of μNi, μMn and μGa calculated by Li et al. [14] are in good agreement with those reported earlier for the stoichiometric Heusler alloy Ni2MnGa [15,16,17,18,19,20,21,22]. In order to explain the observed concentration dependence of the magnetic moment for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys we present a simple model in which the following assumptions are made. Cu atoms for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys always occupy the vacant Mn sublattice. The magnetic moments of the Ni, Mn, Cu and Ga atoms in Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys are collinear and have Li et al.’s values independent of x. The magnetic moments of the Mn atoms are ferromagnetically coupled to the magnetic moments of the Ni atoms. Then, the total magnetic moment per formula unit, μs (cal), of Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys is given by μs(cal) = 2μNi + (1 − xMn + xμCu + μGa. The solid line in Figure 5 is the one calculated by using this equation. As seen in Figure 5, the experimental values are in good agreement with those calculated.

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Figure 5. Concentration dependence of the magnetic moment per formula unit, μs, for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40), Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) and Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40). All values of μs were determined at 5 K except for the values of μs of Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40) alloys. They were estimated at 4.2 K [12].

Click here to enlarge figure

Figure 5. Concentration dependence of the magnetic moment per formula unit, μs, for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40), Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) and Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40). All values of μs were determined at 5 K except for the values of μs of Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40) alloys. They were estimated at 4.2 K [12].
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Next, we consider the concentration dependence of μs for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys. According to the results of the calculation for the site occupation of Ni2MnGa0.95Cu0.05 by Li et al. [14], Cu atoms always occupy the sublattice of the deficient component; the configuration Ni2Mn(Ga0.95Cu0.05) is the most stable in where the components A and B in (A,B) occupy the same sublattice. In this case, the μs at 5 K for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys is almost independent of y under the assumption that Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys are collinear ferromagnets and the values of μNi and μMn are independent of x. However, as shown in Figure 5, the experimental μs at 5 K for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys decreases steeply with increasing y. We, therefore, suggest a different site-occupation configuration i.e., Ni2(Mn1 − yCuy)(Ga1 − yMny) with the Cu atoms occupying the Mn sublattice, for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys, where some of the Mn atoms move on to the Ga sublattice. Here, we assume that the magnetic moment of the Mn atoms substituted on to the Ga sites in Ni2(Mn1 − yCuy)(Ga1 − yMny) alloys is antiferomagnetically coupled to the magnetic moment of the Mn atoms on the Mn sublattice. The values of the magnetic moments of the Mn atoms on the Mn and Ga sublattices, respectively, are assumed to be 3.37 μB and −3.43 μB, which remain constant with increasing y from y = 0. The other magnetic moments μNi, μCu and μGa in the Ni2(Mn1 − yCuy)(Ga1 − yMny) alloys are the constant values 0.32 μB, −0.03 μB and −0.05 μB, respectively, as in Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys. A value of −3.43 μB was calculated by Li et al. [14] for the magnetic moment of the Mn atoms on the Ga sublattice. The antiferromagnetic coupling between nearest-neighbor Mn atoms in Ni2(Mn1 − yCuy)(Ga1 − yMny) alloys is due to the variation of the exchange interaction that becomes antiferromagnetic for small Mn-Mn interatomic distances. This antiferromagnetic coupling was already proved experimentally and theoretically in many Mn-rich Ni-Mn-Ga Heusler alloys [14,23,24,25,26,27]. Then, the μs of Ni2(Mn1 − yCuy)(Ga1 − yMny) alloys is given by μs(cal) = 2μNi + (1 − yMnI + yμCu + (1 − yGa + yμMnII, where μMnI and μMnII mean the values of the magnetic moment of the Mn atoms on the Mn sublattice and the Ga sublattice, respectively. The broken line in Figure 5 is the one calculated by using the above equation. As seen in Figure 5, the experimental values are in agreement with those calculated for low y concentrations. For samples with high y concentrations, however, the experimental values of μs deviate from the broken line in Figure 5. This may be attributed to any concentration dependence of the μMnI, μMnII and μNi values or occurrence of disorder of the constituent elements associated with the increase of y.

In the above considerations on Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys, we excluded the site-occupation configurations of (Ni2 − yCuy)(Mn1 − yNiy)(Ga1 − yMny) and (Ni2 − yMny)(Mn1 − yCuy)(Ga1 − yNiy) by taking into account the theoretical result that the formation energies of the site-occupations in Ni2Mn(Ga0.95Cu0.05) and Ni2(Mn0.95Cu0.05)(Ga0.95Mn0.05) are much smaller than those of (Ni1.95Cu0.05)(Mn0.95Ni0.05)(Ga0.95Mn0.05) and (Ni1.95Mn0.05)(Mn0.95Cu0.05)(Ga0.95Ni0.05) [14]. Unfortunately, the calculations in [14] were made for the site occupation of Cu-doped Ni2MnGa with the L21-type structure, instead of the one with the observed martensitic structure at 5 K. Nevertheless, the above satisfactory agreements between the experimental and calculated concentration dependence of the magnetic moment μs may rather confirm that the site-occupation configurations in the present analyses exist also in the martensite phase. Lastly, we consider the concentration dependence of μs for Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40) alloys. As shown in Figure 5, the experimental values of μs for Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40) alloys are almost independent of concentration z [12]. We assume that Cu atoms for Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40) alloys occupy the vacant Ni sublattice according to the results of the calculation by Li et al. [14]. Furthermore, we assume that μNi, μCu, μMn and μGa in Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40) alloys, respectively, are the constant values 0.32 μB, 0.04 μB, 3.37 μB and −0.05 μB, which are the magnetic moments calculated by Li et al. [14] for Ni1.95Cu0.05MnGa. Then, the concentration dependence of μs(cal) for FSMAs Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40) alloys is given by μs(cal) = (2 − zNi + zμCu + μMn + μGa, which is shown by the dot dash line in Figure 5. As seen in Figure 5, the experimental values are in good agreement with those calculated.

4. Summary

The magnetization measurements at 5 K of FSMAs Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) and Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys have been carried out. The μs at 5 K for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys decreases linearly with increasing concentration x. On the other hand, the μs at 5 K for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) alloys decreases steeply with increasing y compared to the μs for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40) alloys. To explain the concentration dependence of μs for the Cu-modified Ni2MnGa alloys, we suggested the site-occupation configurations, Ni2(Mn1 − xCux)Ga for Ni2Mn1 − xCuxGa (0 ≤ x ≤ 0.40), Ni2(Mn1 − yCuy)(Ga1 − yMny) for Ni2MnGa1 − yCuy (0 ≤ y ≤ 0.25) and (Ni2 − zCuz)MnGa for Ni2 − zCuzMnGa (0 ≤ z ≤ 0.40) alloys. These configurations together with some theoretical values of the magnetic moments of constituent atoms were proved to explain well the concentration dependence of μs for Cu-modified Ni2MnGa.

Acknowledgements

The authors would like to express our sincere thanks to T. Shishido and K. Obara of the Institute for Materials Research, Tohoku University for their help in the sample preparation. This work was partly supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS)/MEXT.

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