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Structural and magnetic phase transitions in shape memory alloys Ni2 + XMn1 −XGa
~ Journal el ELSEVIER
Journal of Magnetism and Magnetic Materials 196-197 (1999) 837-839
amnatneUsm magnetic J~i materials
Structural and magnetic phase transitions in shape memory alloys Ni2 + xMnl-xGa A. Vasil'ev a, A. Bozhko a, V. Khovailo a, I. Dikshtein b, V. Shavrov b'*, S. Seletskii b, V. Buchelnikov c aMoscow State University, Moscow 119899, Russia blnstitute of Radioengineering and Electronics of RAS, ul. Mokhovaya, 11, Moscow 103907, Russia CChelyabinsk State University, Chelyabinsk 454021, Russia
Abstract
The Heusler-type alloys Ni2 +xMna- xGa exhibit well-defined shape memory properties in a ferromagnetic state. The change of composition X moves martensitic transition temperature TM and the Curie point Tc towards each other. To study this behavior, the measurements of AC magnetic susceptibility and DC resistivity were performed. The correspondence of the experimental data with calculated T - X phase diagram is discussed. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Ferromagnetism; Shape memory alloy; Martensitic phase transition
Heusler-type alloy N i : M n G a experiences martensitic transformation in a ferromagnetic state (Refs. I-1-4]). The temperature of ferromagnetic (Tc = 376 K) and structural (TM = 202 K) transitions differ significantly for the stoichiometric composition. In the present work, we undertook the partial substitution of Mn with Ni which resulted in the increase of TM and the decrease of Tc, till their coincidence. The theoretical analysis of the possible structural and magnetic-phase transitions in the cubic ferromagnet was given and the obtained results were compared with existing experimental data. The composition of the samples was characterized by Ni excess X in the range X = 0-0.20. In order to measure electrical resistivity, specific heat, and magnetic properties, samples of various shapes were spark-cut from the homogenized ingots. Direct current resistivity measurements provide a simple and effective tool to detect both structural and magnetic transitions. As shown in Fig. 1, at TM resistivity
* Corresponding author. Fax: + 7-095-2038414;e-mail: [email protected].
exhibits mainly a pronounced jump-like behavior, while at T c a change in the slope takes place. The steepening of slopes in the ferromagnetic phase can be attributed to the disappearance of electrons scattering on magnetic fluctuations. As Ni content increases, TM gradually increases and Tc gradually decreases till these temperatures merge in the samples with X ~> 0.18. In these samples the jump of resistivity is directly followed by a steepening of the slope. The temperature dependencies of the low-field AC magnetic susceptibility X, as shown in Fig. 2, exhibit very sharp changes at martensitic and magnetic transitions. The martensitic phase transition from the cubic to the tetragonal structure is indicated by the drastic drop of X. X also sharply decreases at the Curie temperature when the ferromagnetic phase is destroyed. While TM and Tc are still separated in Ni2.16Mn0.a4Ga and two anomalies occur, in Ni2n9Mn0.81Ga only one anomaly of AC magnetic susceptibility at the mixed-phase transition is observed. The results above can be described within a phenomenological model based on Landau's expansion of free energy of a ferromagnet. The thermodynamic potential
0304-8853/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 9 6 4 - 0
838
A. Vasil'er et al. /Journal q/'Magnetism and Magnetic MateriaLs' 196-197 (1999) 837-839
16f'xMnxGa
14
1 - X=0 00
1.2
2 - x=o.o~ ~-x=010 4 - X = 0 13
/
/
I
I
_
/
-"
t./.-2
i
3
i
0.6
04
i
i
200
250
•
p
i
k
300
350
400
TIK)
Fig. 1. Resistance vs. temperature dependencies of Ni,+x Mnl xGa, X = 0-0.2.
__J
10
es = e~.:, e~, - e.,, a, b and c are the linear combinations of the second-, third- and fourth-order elastic moduli, m = M / M , is the dimensionless magnetization, Ms is the saturation magnetization, ~ and 5 are the exchange constants, B~ and K are the magnetoelastic and cubic anisotropy constants. The minimization of the thermodynamic potential (1) with respect to the rest of the variables ei and mi makes it possible to determine all feasible structural and magnetic phases. As a result the following states of the ferromagnet and their stability conditions are found. (1) Cubic paramagnetic phase (M = 0, e2 - e.~ - 0). (2) Tetragonal paramagnetic phase ( M - O, e2 = O, e3:#0). (3) Cubic ferromagnetic phase ( M J p [ l l l ] . e2 = e3 = 0). (4) Tetragonal angular ferromagnetic phase (M changes its direction fi'om [1 11] to [ 0 0 I], e2 = 0, e3 :# 0). (5) Tetragonal collinear ferromagnetic phase (MIll0 0 1], e2 = 0, e~ ¢ 0). in order to compare the results of calculations with experimental data, the or-a-phase diagram can be represented on T - X coordinates. For this purpose we assume simple linear dependencies:
08 1
T~I = TMo -- 2b2/19cao) - B2/Iqao) + icX,
3
06
T c = Too - 7X,
where TMo and Tco are the temperatures of martensitic and ferromagnetic phase transitions for the stoichiometric composition (X = 01. The lines of the main phase transitions on T - X coordinates are
04
02 L
O0
150
1 - X=0.00
2 - X=005
3 X=010 5 - X=016
4 - X=O 13 6 - X=0.19
200
250
300
350
400
( 1)<=>I2):T = TMo -- Be/{qao) + ,',:X:
T IK)
Fig. 2, Low-field AC magnetic susceptibility Mnl xGa, X = 0-0.2.
of Ni_~.x
~c4.4(e 4 1 2 + e52 + eg)' 1
+ lbe3(e2 - 3e2) + ¼c(e2 + e2) 2 + ~ B l e l
\/'3
F + B2/~-~ez(m7 - m22) + ~ e 3 ( 3 m 2 kv/2 x/6 1
,
me
l
--
D/2}
J
+ B3(e~.mlm2 + e s m 2 m 3 + e6m3nq)
+~6(m~
mE
m~):
2
+ K(m~m~ + m~_m3+ m~m~).
I1)
Here ei are the linear combinations of the deformation tensor e2
components
( e : , , . - ey~,)/x/-' e3
eik:
( 1)¢:>(3):T = Too -- "/X: {3)<:>(4):T = TMo + tcX.
for a cubic crystal of space group Oh experiencing at cooling ferromagnetic and structural phase transitions is given by F = ½(q i + 2Cl2)e~ + 2aIe~l~ + e~) +
(21
e~ = (exx + e~,~.+ e=)/v/3, (2e-: -- e,-~ -- e>,), e4
e,-,.,
The analytic equations for the remaining phase transitions lines is too complicated to be presented here [5]. The phase diagram on T (temperature) and X (composition) coordinates is shown in Fig. 3. In general, the results of these experimental studies correspond to each other and establish the general tendency of martenstitic temperature TM to increase and Curie temperature Tc to decrease with Ni excess in Ni2MnGa. It appears that the characteristic temperatures in Ni2+xMn~ xGa merge at X = 0.18-0.20. In the samples of this composition range the profiles of the observed singularities changed qualitatively. It can be shown that the experimentally obtained T - X phase diagram is in a qualitative agreement with the calculated one (Fig. 3). The detailed comparison of theory with experiment can be made on the basis of low-field magnetic susceptibility measurements. It can be seen that different sequences of phase transitions can be realized in Ni2 +xMn~ - x G a of different compositions. According to Figs. 2 and 3 the temperature of magnetic-phase
A. Vasil'ev et al. / Journal of Magnetism and Magnetic Materials 196-197 (1999) 837-839
839
low-field magnetic susceptibility at T ~ 260K for stoichiometric composition (Fig. 2) can be ascribed to the transition from the cubic ferromagnetic phase 3 to the tetragonal angular phase 4. The sharp drop of Z at T ~ 202 K is due to orientational transition from phases 4to5.
400-
1
300-
This work was supported by the Russian Foundation for Basic Research Grant-in-Aid 96-02-19755.
5
~0 K F
I
0.1
0.2
x Fig. 3. Calculated T - X phase diagram of Ni2+xMnl_xGa. transition from the cubic paramagnetic phase 1 to the cubic ferromagnetic phase 3 linearly decreases with concentration X. The temperature of the phase transition from the cubic ferromagnetic phase 3 to the tetragonal ferromagnetic phases 4 and 5 increases with concentration X. The appearance of an additional anomaly of
References [1] P.J. Webster, K.R.A. Ziebeck, S.L. Town, M.S. Peak, Philos. Mag. 49 (1984) 295. [2] T. Kanomata, K. Shirakawa, T. Kaneko, J. Magn. Magn. Mater. 65 (1987) 76. [3] A. Zheludev, S.M. Shapiro, P. Wochner et al., Phys. Rev. b 51 (1995) 11310. [4] J. Worgull, E. Petti, J. Trivisonno, Phys. Rev. B 54 0996) 15695. [5] A. Vasil'ev, A. Bozhko, V. Khovailo et al., JETP, 1998, submitted.
Journal of Magnetism and Magnetic Materials 196-197 (1999) 837-839
amnatneUsm magnetic J~i materials
Structural and magnetic phase transitions in shape memory alloys Ni2 + xMnl-xGa A. Vasil'ev a, A. Bozhko a, V. Khovailo a, I. Dikshtein b, V. Shavrov b'*, S. Seletskii b, V. Buchelnikov c aMoscow State University, Moscow 119899, Russia blnstitute of Radioengineering and Electronics of RAS, ul. Mokhovaya, 11, Moscow 103907, Russia CChelyabinsk State University, Chelyabinsk 454021, Russia
Abstract
The Heusler-type alloys Ni2 +xMna- xGa exhibit well-defined shape memory properties in a ferromagnetic state. The change of composition X moves martensitic transition temperature TM and the Curie point Tc towards each other. To study this behavior, the measurements of AC magnetic susceptibility and DC resistivity were performed. The correspondence of the experimental data with calculated T - X phase diagram is discussed. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Ferromagnetism; Shape memory alloy; Martensitic phase transition
Heusler-type alloy N i : M n G a experiences martensitic transformation in a ferromagnetic state (Refs. I-1-4]). The temperature of ferromagnetic (Tc = 376 K) and structural (TM = 202 K) transitions differ significantly for the stoichiometric composition. In the present work, we undertook the partial substitution of Mn with Ni which resulted in the increase of TM and the decrease of Tc, till their coincidence. The theoretical analysis of the possible structural and magnetic-phase transitions in the cubic ferromagnet was given and the obtained results were compared with existing experimental data. The composition of the samples was characterized by Ni excess X in the range X = 0-0.20. In order to measure electrical resistivity, specific heat, and magnetic properties, samples of various shapes were spark-cut from the homogenized ingots. Direct current resistivity measurements provide a simple and effective tool to detect both structural and magnetic transitions. As shown in Fig. 1, at TM resistivity
* Corresponding author. Fax: + 7-095-2038414;e-mail: [email protected].
exhibits mainly a pronounced jump-like behavior, while at T c a change in the slope takes place. The steepening of slopes in the ferromagnetic phase can be attributed to the disappearance of electrons scattering on magnetic fluctuations. As Ni content increases, TM gradually increases and Tc gradually decreases till these temperatures merge in the samples with X ~> 0.18. In these samples the jump of resistivity is directly followed by a steepening of the slope. The temperature dependencies of the low-field AC magnetic susceptibility X, as shown in Fig. 2, exhibit very sharp changes at martensitic and magnetic transitions. The martensitic phase transition from the cubic to the tetragonal structure is indicated by the drastic drop of X. X also sharply decreases at the Curie temperature when the ferromagnetic phase is destroyed. While TM and Tc are still separated in Ni2.16Mn0.a4Ga and two anomalies occur, in Ni2n9Mn0.81Ga only one anomaly of AC magnetic susceptibility at the mixed-phase transition is observed. The results above can be described within a phenomenological model based on Landau's expansion of free energy of a ferromagnet. The thermodynamic potential
0304-8853/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 9 6 4 - 0
838
A. Vasil'er et al. /Journal q/'Magnetism and Magnetic MateriaLs' 196-197 (1999) 837-839
16f'xMnxGa
14
1 - X=0 00
1.2
2 - x=o.o~ ~-x=010 4 - X = 0 13
/
/
I
I
_
/
-"
t./.-2
i
3
i
0.6
04
i
i
200
250
•
p
i
k
300
350
400
TIK)
Fig. 1. Resistance vs. temperature dependencies of Ni,+x Mnl xGa, X = 0-0.2.
__J
10
es = e~.:, e~, - e.,, a, b and c are the linear combinations of the second-, third- and fourth-order elastic moduli, m = M / M , is the dimensionless magnetization, Ms is the saturation magnetization, ~ and 5 are the exchange constants, B~ and K are the magnetoelastic and cubic anisotropy constants. The minimization of the thermodynamic potential (1) with respect to the rest of the variables ei and mi makes it possible to determine all feasible structural and magnetic phases. As a result the following states of the ferromagnet and their stability conditions are found. (1) Cubic paramagnetic phase (M = 0, e2 - e.~ - 0). (2) Tetragonal paramagnetic phase ( M - O, e2 = O, e3:#0). (3) Cubic ferromagnetic phase ( M J p [ l l l ] . e2 = e3 = 0). (4) Tetragonal angular ferromagnetic phase (M changes its direction fi'om [1 11] to [ 0 0 I], e2 = 0, e3 :# 0). (5) Tetragonal collinear ferromagnetic phase (MIll0 0 1], e2 = 0, e~ ¢ 0). in order to compare the results of calculations with experimental data, the or-a-phase diagram can be represented on T - X coordinates. For this purpose we assume simple linear dependencies:
08 1
T~I = TMo -- 2b2/19cao) - B2/Iqao) + icX,
3
06
T c = Too - 7X,
where TMo and Tco are the temperatures of martensitic and ferromagnetic phase transitions for the stoichiometric composition (X = 01. The lines of the main phase transitions on T - X coordinates are
04
02 L
O0
150
1 - X=0.00
2 - X=005
3 X=010 5 - X=016
4 - X=O 13 6 - X=0.19
200
250
300
350
400
( 1)<=>I2):T = TMo -- Be/{qao) + ,',:X:
T IK)
Fig. 2, Low-field AC magnetic susceptibility Mnl xGa, X = 0-0.2.
of Ni_~.x
~c4.4(e 4 1 2 + e52 + eg)' 1
+ lbe3(e2 - 3e2) + ¼c(e2 + e2) 2 + ~ B l e l
\/'3
F + B2/~-~ez(m7 - m22) + ~ e 3 ( 3 m 2 kv/2 x/6 1
,
me
l
--
D/2}
J
+ B3(e~.mlm2 + e s m 2 m 3 + e6m3nq)
+~6(m~
mE
m~):
2
+ K(m~m~ + m~_m3+ m~m~).
I1)
Here ei are the linear combinations of the deformation tensor e2
components
( e : , , . - ey~,)/x/-' e3
eik:
( 1)¢:>(3):T = Too -- "/X: {3)<:>(4):T = TMo + tcX.
for a cubic crystal of space group Oh experiencing at cooling ferromagnetic and structural phase transitions is given by F = ½(q i + 2Cl2)e~ + 2aIe~l~ + e~) +
(21
e~ = (exx + e~,~.+ e=)/v/3, (2e-: -- e,-~ -- e>,), e4
e,-,.,
The analytic equations for the remaining phase transitions lines is too complicated to be presented here [5]. The phase diagram on T (temperature) and X (composition) coordinates is shown in Fig. 3. In general, the results of these experimental studies correspond to each other and establish the general tendency of martenstitic temperature TM to increase and Curie temperature Tc to decrease with Ni excess in Ni2MnGa. It appears that the characteristic temperatures in Ni2+xMn~ xGa merge at X = 0.18-0.20. In the samples of this composition range the profiles of the observed singularities changed qualitatively. It can be shown that the experimentally obtained T - X phase diagram is in a qualitative agreement with the calculated one (Fig. 3). The detailed comparison of theory with experiment can be made on the basis of low-field magnetic susceptibility measurements. It can be seen that different sequences of phase transitions can be realized in Ni2 +xMn~ - x G a of different compositions. According to Figs. 2 and 3 the temperature of magnetic-phase
A. Vasil'ev et al. / Journal of Magnetism and Magnetic Materials 196-197 (1999) 837-839
839
low-field magnetic susceptibility at T ~ 260K for stoichiometric composition (Fig. 2) can be ascribed to the transition from the cubic ferromagnetic phase 3 to the tetragonal angular phase 4. The sharp drop of Z at T ~ 202 K is due to orientational transition from phases 4to5.
400-
1
300-
This work was supported by the Russian Foundation for Basic Research Grant-in-Aid 96-02-19755.
5
~0 K F
I
0.1
0.2
x Fig. 3. Calculated T - X phase diagram of Ni2+xMnl_xGa. transition from the cubic paramagnetic phase 1 to the cubic ferromagnetic phase 3 linearly decreases with concentration X. The temperature of the phase transition from the cubic ferromagnetic phase 3 to the tetragonal ferromagnetic phases 4 and 5 increases with concentration X. The appearance of an additional anomaly of
References [1] P.J. Webster, K.R.A. Ziebeck, S.L. Town, M.S. Peak, Philos. Mag. 49 (1984) 295. [2] T. Kanomata, K. Shirakawa, T. Kaneko, J. Magn. Magn. Mater. 65 (1987) 76. [3] A. Zheludev, S.M. Shapiro, P. Wochner et al., Phys. Rev. b 51 (1995) 11310. [4] J. Worgull, E. Petti, J. Trivisonno, Phys. Rev. B 54 0996) 15695. [5] A. Vasil'ev, A. Bozhko, V. Khovailo et al., JETP, 1998, submitted.