[Springer Series in Materials Science] Magneto-Science Volume 89 || Magneto-thermodynamic Effects

4 Magneto-thermodynamic Effects

The magnetic energy of a substance is usually very much smaller than the thermal energy at room temperature or activation energy in a chemical reaction. Therefore, for many years it was believed that magnetic field could not affect chemical equilibrium. However, this is not always correct. Magnetic energy is proportional to the square of magnetic flux density. Thus the physical and chemical phenomena which cannot be observed at 1 T become observable at 10 T, especially when ferromagnetic substances are involved.

In this chapter, MFEs on hydrogen reaction with metals and martensitic transition of ferrous alloys, magnetic treatments of ferromagnetic alloys and magnetic controls of diamagnetic molecular assemblies and gels are described.

4.1 Magnetic Field-induced Effects on Hydrogen Reaction with Metals

4.1.1 The Metal-Hydrogen System

Some intermetallic compounds and alloys consisting of three-dimensional transition and rare earth metals uptake reversibly a large amount of hydrogen. "" ^ Such a metal hydride works as a hydrogen-absorbing alloy and is used practically as the negative electrode of secondary batteries. Generally, a cobalt-rich alloy indicates a ferromagnetic property. The saturation magnetization of the ferromagnetic metal hydride depends strongly on the hydrogen composition.^^ The equilibrium state changes to form the hydride with large magnetic moment under the influence of magnetic fields because the magnetic free energy tends to be stable. In this section, the magnetic field effects are described for the ferromagnetic hydride LaCosH, as a typical material of ferromagnetic metal hydride. The relationships between the chemical equilibrium and the change in magnetic free energy are investigated theoretically and experimentally.

Hydrogen is stored in and released from the metal hydride of the coexistence region between low and high concentration hydride phases. The low composition hydride MH« reacts with hydrogen gas to form the

142 4 Magneto-thermodynamic Effects

high composition hydride MH/, (b > a) according to Eq. (1).

- ^ M H , - f H2 » - ^ M H , (1) b-a b-a

The equilibrium hydrogen pressure increases with increasing hydrogen composition, but the pressure is almost constant in the two-phase coexistence region, that is, the plateau pressure becomes almost constant in the plateau region. On the other hand, the plateau pressure is sensitive to the temperature and increases with increasing temperature. The linear relation between the logarithmic equilibrium hydrogen pressure P and the inversed temperature \IT is explained thermodynamically by the van't Hoff relation, Eq. (2).

RT R

where R is gas constant and T is absolute temperature. Thermodynamic parameters A// as the standard change in enthalpy and A5 as the standard change in entropy can be obtained experimentally from the gradient and the cross section of the linear relation.

4.1.2 Magnetic Field Effect on Equilibrium States

The change in magnetic free energy g^""^ in the magnetic field is written as

^c") = 2HOH'^'^^-^^ = 2BAM. (3) b-a

where Ho is the permeability of a vacuum, H and B are the magnetic field strength and the magnetic field density, respectively, and m« ' and mt^^ are the saturation magnetization for the solid MH^ and MH , respectively. The AMs is defined as the change in magnetization per hydride of 1 kg per desorbed hydrogen atom of 1 mol. The magnitude of the magnetic field effect on the chemical equilibrium depends on Eq. (3) for the metal-hydrogen system. The magnitude of the magnetic field effect on the chemical equilibrium is determined by the magnitude of AMs and B. However, the direction of the magnetic field effect is determined only by the sign of AMs.

Figure 4-1-1 shows the pressure composition isotherm (PCT curve) and the saturation magnetization of the LaCosHr system at 293 K. The LaCosH c system has two plateau regions; the a -1- (3 and (3 + y regions have a low and high plateau pressures, respectively.^^^ The saturation magnetization is decreased linearly with increasing hydrogen composition for each plateau region, as shown by the broken or dotted line in Fig. 4-1-1. The AMs corresponds to the gradient of the line and the values are equal to 16.4 and 8.7 JT"' kg-'(molH)-' for the a + p and (3 + y regions, respectively, at r = 293 K.

4.1 Magnetic Field-induced Effects on Hydrogen Reaction with Metals 143

100 tr

1 2 3 4 Hydrogen composition, X

Fig. 4-1-1 PCT curve and saturation magnetization for the LaCosHt system at T = 293 K. The open and closed circles denote the equilibrium pressure at B = 12 T and B = 0 T at 7 = 293 K.

4.1.3 Magnetic Field Effect on the Electrochemical System

The experimental value g '" in Eq. (3) can be observed directly from the electrochemical system using the metal hydride electrode. The change in free energy AG corresponds to the change in the electrode potential A£ according to Eq. (4).

AG = ~2FAE (4)

where F is the Faraday constant. The electrode potential depends strongly on the temperature, but the change in the electrode potential is independent of the temperature. According to Eqs. (3) and (4), the change in the electrode potential is proportional to the magnetic field density, ^

AE = -BAM, I F (5)

In the experiment, the electrochemical cell consisted of the hydride negative electrode, Ni positive electrode and SSE reference electrode. They were soaked in acid solution with a thermocouple. Then the magnetic field was applied up to B = 15 T at constant temperature T = 293 K. The temporal variations of the magnetic field and the corresponding change in the electrode potential are shown in Fig. 4-1-2. ^ The equilibrium potential responding to the applied magnetic field was decreased by AE = -1.6 mV under the influence of a magnetic field of B = 15 T. Fig. 4-1-3 illustrates the relationship between the applied magnetic field and the change in the electrode potential.^^ The change in the potential decreased with increasing magnetic field. The linear relation was observed in the fields below 10 T,


2 4 6 Time, / / min

Fig. 4-1-2 Time variations of magnetic field and changes in the electrode potential for LaCo5H, at T-293 K.

-i -0.5-

^ -1.0-

-1.5^

U -2.0-0 5 10 15

Magnetic field, Bll

Fig. 4-1-3 Magnetic field effect on the electrode potential of LaCosHr at T = 293 K. The broken line was observed theoretically according to Eq. (5).

but the gradient tends to become large in the fields above 10 T. The observed change in the potential A£ = -1.6 mV at ^ = 15 T did not agree with the value A£ = -1.0 mV calculated according to Eq. (5) with AMs = 6.4 JT^ kg" (molH)"^ The difference between them is due to the increase in the AMs in high magnetic fields. The value of the saturation magnetization Ms does not depend on the hydrogen composition and magnetic field below a few Tesla. However, the magnetic measurement showed that the AA/s becomes large with increasing magnetic fields above 10 T because of the increase in the Ms. Theoretical values were recalculated using the averaged Value AMs = 8.7 JT"'kg"^ (molH)"^ in the magnetic fields and plotted by the broken line in Fig. 4-1-3. Both decreases in the electrode potential agreed qualitatively. The magnetic field energy was converted directly into electrochemical free energy.^ ' ^


4.1.4 Magnetic Field Effect on Phase Diagram

The PCT curve is an equilibrium phase diagram of the soHd and gaseous phases. The magnetic field influenced experimentally the PCT curve as shown in Fig. 4-1-1. ^^ The open circles denote the equilibrium pressure of LaCo5HX3.6 <x< 4.6) under the influence of a magnetic field of ^ = 12 T. The PCT curve shifted to the high pressure side. The increase in the pressure is explained as follows. The change in free energy of the system consists of that for the solid phase g"""^ and that for the gaseous phase RT ln(P/Po), In the equilibrium state, the total must be zero at any magnetic field as described by Eq. (6). Accordingly, the magnetic field effect on the equilibrium pressure is explained by Eq. (7).

g - + /?rin(^-^j = 0 (6)

{PoJ RT

where P and Po are the equilibrium pressures in the presence and in the absence of the magnetic field. Eq. (7) means the logarithmic change in the pressure ratio is proportional to the magnetic field B when the parameter AMs, the hydrogen composition and the temperature Tare fixed. " ' ^

4.1.5 Magnetic Field Effect on Hydrogen Pressure

In the experiment, a large amount of LaCos alloy and a small space of gaseous phase were prepared; for example, W= 30.9 g and V= 31.9 ml.* ^ The relatively small volume avoids the change in hydrogen composition. The hydrogen pressure for LaCo5H4.i in the p + y region increased with increasing magnetic fields, as shown in Fig. 4-1-3. Finally, the hydrogen pressure of Po= 153.5 kPa increased io P= 186.6 kPa at a magnetic field of B = 14 T. The pressure was increased by 1.22 times and the logarithmic pressure change LPC was equal to 0.195. The theoretical LPC was calculated to be 0.189 according to Eq. (7) with AMs= 16.4 JT-'kg"' (molH)"' for the p + y region. Both LPC values agreed well. The closed circles in Fig. 4-1-4 denote the equilibrium points.'^^ These points are plotted as a function of the magnetic fields in Fig. 4-1-5. A linear relation between the LPC and the magnetic field was observed below 14 T according to Eq. (7) as plotted by closed circles in Fig. 4-1-5. The increase in the equilibrium pressure was investigated for LaCo5H4.2 under the influence of a high magnetic field of up to 26 T. The equilibrium pressure was increased by 1.50 times at a magnetic field of 26 T. This increase corresponded to a decrease in the equilibrium constant of 33%. However, the gradient increased in high magnetic fields as shown by the closed squares. The same tendency appeared in the electrochemical system described in section 4.1.3. It was understood that the reason was the


20 40 Time, 11 min

Fig. 4-1-4 Magnetic field response to the hydrogen pressure of LaCosHa i at 7= 293 K.

-0.1

-0.2

^t^^. -A--A*-

_ GdCo.H:.

(T-n r: 288.2 K)

Y:C07H2 5

(7^=348.2 K) 10 15 20 25

Magnetic field, BIT

30 35

Fig. 4-1-5 Magnetic field effects on equilibrium hydrogen pressure for various metal hydrides. The broken line denotes the theoretical LPC for LaCo5H4 at Tm = 293 K.

increase in MlJ^^ The magnetic field effects on the equihbrium pressure were investigated for other ferromagnetic or ferrimagnetic hydride systems, such as SmCosHi.g, PrCo5H43, GdCo5H25 and Y2C07H2.5, as shown in Fig. 4-1-5. The magnetic field effects were classified into two groups according to the direction of the changes in the equilibrium pressure. The hydrides with positive AA/s showed a positive change in the hydrogen pressure, as shown by the closed marks. In contrast, the hydrides with negative AMs showed a negative change in the pressure, as shown by the open marks. ^ This experiment suggests that equilibrium pressure and equilibrium constant can be controlled by the magnetic field.


4.1.6 Magnetic Field Effect on Hydrogen Composition

The increase in the pressure is accompanied by the release of hydrogen from the hydride. The hydride releases hydrogen until the change in the free energy of the gaseous phase balances the magnetic free energy. When the volume of the gaseous phase is large enough compared to the small amount of the hydride, the hydrogen composition of the hydride must be influenced by the magnetic field. The plateau pressure is not flat but shows a gradient for the hydrogen composition. The gradient was defined as plateau factor Fp= d\nP(x)/dx. Assuming a constant plateau factor, the magnetic field effect on the hydrogen composition is expected to decrease according to Eq. (8),

Ax = 2 BAM, F,RT

(8)

In the experiment, the magnetization was measured using an extraction method to determine the hydrogen composition because of the controlled hydrogen pressure.'^^ The hydrogen composition was estimated from the relationship between the magnetization and the hydrogen composition. The hydrogen composition was adjusted to be JC = 1.88 as the midpoint of the a + p region at a magnetic field of B = 2.0 T at a temperature of 7= 313.2 K. This initial composition corresponded to the p-phase mol fraction of k^ = 0.54. Then the stepwise field was applied to the system up to 14 T under the controlled pressure P = 11.2 kPa. The hydrogen composition decreased with increasing magnetic field as shown in Fig. 4-1-6. ^^ Hydrogen was released from the metal hydride in high magnetic fields and the hydrogen composition of the solid phase shifted toward the a-rich phase in the a + p region. Under the influence of a magnetic field of 14 T the hydrogen composition decreased to ^ = 0.96 (k^ = 0.26), and the change in the hydrogen composition reached Ax = -0.92

o a E o

1.8h

1.6^

1.4-

1.2-

.0-0.25

0 5 10 15

Magnetic field, B/T

Fig. 4-1-6 Magnetic field effect on hydrogen composition for LaCosH^ at 7= 313 K.


(A/:p = -0.28) at a magnetic field of J5 = 14 T. The expected value was calculated to be Ax = -0.89 according to Eq. (8) with AMs = 8.7 JT"'molH'' and Fp = 0.09 for the a + p regions of LaCosHt. The experimental result agreed with the calculated one. This experiment demonstrates that the hydrogen composition of the metal hydride is controllable by a magnetic field.

4.1.7 Magnetic Field Effect on Thermodynamic Parameters

The heat of reaction A// , the entropy of reaction AS and the free energy of reaction ACf are significant thermodynamic parameters for understanding metal hydride-hydrogen systems. The magnetic field effect on the free energy change AG has been described above for the electrochemical system. Therefore, the magnetic field effects on the enthalpy change Mf and the entropy change A " are discussed here. The thermodynamic consideration gives rise to the existence of magnetic field effects on the thermodynamic parameters. The magnetic field effects on the changes in parameters were concluded as follows,

5// = 25AMs -2BTd B(^^^^] (9)

5 . = - 2 ^ r d ^ ( ^ ) (10)

The ratios of the thermodynamic parameters r« and Ts were defined as Eqs. (11) and (12), respectively.

5H

„ 85 n = ^ (12)

The values bH and 85 were estimated according to Eqs. (9) and (10) using the magnetic properties of LaCosH,. The ratios of the parameters FH and Ts were calculated according to Eqs. (11) and (12) and the results listed in Table 4-1-1.^^^ For example, the expected value TH was calculated to be +0.5% at a magnetic field of 28 T according to Eqs. (9) and (11). Meanwhile, the magnetic field effects on the thermodynamic parameters were observed experimentally by measurements of the equilibrium hydrogen pressure in high magnetic fields.'^ ~' van't Hoff relations were measured for the LaCosHx of the a + p and p + y regions at various temperatures, as shown in Figs. 4-1-7 and 4-1-8.'^^ According to Eq. (2), the gradient or the cross section gives the parameter Aff or AS in zero field and 6// or 5S in magnetic fields. The value FH was obtained experimentally to be +0.4% at a magnetic field of 28 T. The experimental and calculated values agree well, as shown in Table 4-1-1. The magnetic field effect on the thermodynamic parameters was remarkable for the LaCosH c of the p + Y region. However, the negative sign of the magnetic field effect was opposite to the a + P region reflecting the magnetic


Table 4-1-1 Magnetic field effects on thermodynamic parameters

Region

a+p

r/K

286-343 293-323

BIT

28 14

T„-'^9c

+0.5 -5.6

r^^^'^^^r

+0.4 -6.4

Tr''%

+0.8 -2.1

pôbs^^

+0.8 -2.1

100 F

cu

5=28 T

10 r 5=0

a + p Region

1 r i_

2.8 3.0 3.2 3.4 3.6

Inverse temperature, 1000/7/ K"'

Fig. 4-1-7 van't Hoff plots for the a + p region of LaCo^H,.

a.

9 -8 -7 -6 -

5 -

5=14T

0.1 ^ 3.0 3.1 3.2 3.3 3.4 3.5

Inverse temperature. 1000/r/ K '

Fig. 4-1-8 van't Hoff plot for the p + y region of LaCosHt.

properties. In any case, good agreements between theoretical and experimental values were observed qualitatively and quantitatively.

In this section, magnetic field effects on chemical equilibria for metal hydride-hydrogen systems have been discussed. Changes in chemical equilibrium were explained perfectly by the thermodynamics and magnetic properties. The magnetic field controls the equilibrium states, such as electrode potential, pressure, composition and thermodynamic parameters.


References

1. M. Yamaguchi, I. Yamamoto, Dynamic Spin Chemistry (S. Nagakura, H. Hayashi, T. Azumi, eds.), Chapt. 5, KodanshaAViley, Tokyo (1998).

2. M. Yamaguchi, S. Ozeki, Bunshi Jisei (K. Itoh, ed.), p.448, Gakkai Shuppan Center, Tokyo (1996) (in Japanese).

3. F. A. Kuijpers, Phillips Res. Kept. SuppL, 2, 1 (1973). 4. M. Yamaguchi, I. Yamamoto, F. Ishikawa, T. Goto, S. Miura, / Alloys. Compd.,

253/254, 191 (1997). 5. F. A. Kuijpers, J. Less-Common Met., 11. 27 (1971). 6. M. Yamaguchi, H. Nomura, I. Yamamoto, T. Ohta, T. Goto, Phys. Lett., 126A/2, 133

(1987). 7. M. Yamaguchi, T. Katamune, T. Ohta, / Less-Common Met., 88, 195 (1982). 8. I. Yamamoto, M. Yamaguchi, T. Goto, S. Miura, Sci. Repts. Res. Inst., Tohoku

University, A-42, 309 (1996). 9. M. Fujino, I. Yamamoto, M. Yamaguchi, T. Goto, S. Miura, J. Alloys. Compd., 231,

631 (1995). 10. I. Yamamoto, H. Tega, M. Yamaguchi, Trans. Mat. Res. Soc. Jpn., 18B, 1201 (1993). 11. M, Yamaguchi, I. Yamamoto, T. Goto, S. Miura, Sci. Repts. Res. Inst., Tohoku

University, A-38, 390 (1993). 12. I. Yamamoto, M. Fujino, M. Yamaguchi, F. Ishikawa, T. Goto, S. Miura, / Alloys.

Compd., 239/295, 251 (1999). 13. I. Yamamoto, M. Yamaguchi, T. Kobayashi, T. Goto, S. Miura, I. Mogi, Jpn. J. Appl

Phys., 2S, 2629 {\9S9). 14. I. Yamamoto, M. Yamaguchi, T. Goto, T. Sakakibara, Zeit. Phys. Chem. N. F., 163,

671 (1989). 15. M. Yamaguchi, H. Nomura, I. Yamamoto, T. Ohta and T. Goto, Phys. Lett., 134A,

504(1989). 16. I. Yamamoto, M. Yamaguchi, T. Goto, S. Miura, J. Alloys. Compd., 231, 205 (1995). 17. I. Yamamoto, M. Yamaguchi, T. Goto, S. Miura, / Less-Common Met., 172/174, 79

(1991). 18. I. Yamamoto, M. Yamaguchi, M. Fujino, F. Ishikawa, T. Goto, S. Miura, Physica B,

216,399(1996). 19. I. Yamamoto, M. Yamaguchi, N. Deguchi, S. Miura, Materia, 36/12, 1296 (1997). 20. I. Yamamoto, N. Deguchi, M. Yamaguchi, Y. Shimazu, F. Ishikawa, Physica B,

246/247,404(1998). 21. I. Yamamoto, M. Yamaguchi, K. Ishikawa, S. Mizusaki, T. Takamasu, Proc. 6th

Japan-Korea Joint Symp. '01 Hydrogen Energy, 145 (2001).

4.2 Magnetic Field Controls of Molecular Assemblies and Gels

Various kinds of magnetic fields are available for use in chemistry: steady magnetic field, gradient magnetic field, pulsed magnetic field and electromagnetic field, which are homogeneous or inhomogeneous in space and time. Magnetic fields may affect chemical reactions, chemical equilibria, structures and physical properties of materials ' " ^ via direct effects such as quantum mechanical, thermodynamical and mechanical

4.2 Magnetic Field Controls of Molecular Assemblies and Gels 151

effects and indirect effects such as convection, concentration changes and temperature changes.

The structure of organized molecular assemblies of surfactants and lipids can be controlled by flow and an electric field. Use of a magnetic field is also a potential method for aligning molecules and domains; it has the advantage that any material can in principle be aligned by magnetic fields. It is well established that diamagnetic assemblies having magnetic anisotropy will become oriented in a steady magnetic field so as to achieve the minimum-energy state. Gaffney and McConnell"^^ and Maret and Dransfeld,^^ using the electron spin resonance (ESR) and the Cotton-Mouton effect, respectively, showed that phospholipid molecules could be oriented by a magnetic field. The magnetic orientational energy (Er) of a diamagnetic lipid domain containing A molecules (volume A v), whose long molecular axis is at an angle cp io H and which have the diamagnetic anisotropy, Ax, and the magnetic susceptibility perpendicular to //, x^^ is given by the following equation \*

Er =-(//V2)ai+A;fcos»A^v (1)

The long molecular axis of lipid molecules in a domain can be cooperatively aligned in the direction of averaged (p, ^ when H is as large as Er that overcomes the thermal energy. For example, orientational effects are expected when A is on the order of 10 for Aj - -1 x 10^ cm^mol' (for long chain hydrocarbons) under 10 T and 318 K or when // = 4.0 T for a 200-nm diameter liposome with a 5-nm membrane thickness.^^ Another example for magnetic field effects on a bilayer membrane comes from the elastic properties of the membrane. Helfrich predicted theoretically the magnetic deformadon of phospholipid liposomes from a sphere to an ellipsoid, which was shown experimentally by Tenforde and Liburdy. ^

In this section, the molecular orientation of diamagnetic organic molecules, which may lead to the magnetic deformation of micelles and lipid membranes and the phase shift of surfactant mesophases, is introduced.

4.2.1 Micelles and Surfactant/Silicate Hybrids under Steady Magnetic Fields

Amphiphilic molecules will form micelles of various shapes and sizes. Since rodlike micelles have a persistence length of about 20 nm or are flexible, long rodlike micelles behave like wormlike micelles. Adding salicilate ions to a rodlike micellar solution, very long wormlike micelles or threadlike micelles are formed. The threadlike micelles will be entangled. Can a steady magnetic field extend the rod and thread and promote micellar growth?

Amphiphiles also form various mesophases such as hexagonal and lamellar structures in the higher concentration region. Since mesophases


include many molecules, the molecules in the mesophase tend to be oriented toward a magnetic field. Therefore, surfactant/silicate hybrids having hexagonal structure were ordered under steady magnetic fields in order to prepare higher order mesoporous silicas which were prepared by calcination of surfactant molecules in the hybrids. ^ This method made it possible to align a silica skeleton through the magnetic orientation of a surfactant mesophase of hexadecyltrimethylammonium bromide (CTAB) used as a template. The mesoporous silicas comprising a honeycomb structure have homogeneous, straight pores of narrow size distribution. Therefore, potential materials have been the focus of attention from the viewpoint of both fundamentals and application. It is, however, desirable that the oriented domain of a honeycomb structure be much larger than that of conventionally synthethized mesoporous silicas. In general, however, since magnetic ordering of surfactant molecular assemblies is reversible, we must fix the memory under a magnetic field using some method. One of those methods is the sol-gel method, in which the gradual production of silicate ions makes it possible for silicate ions to polymerize slowly after the formation of a surfactant mesophase. ^

A. Magnetic Deformation of Micelles CTAB forms rodlike micelles in water. The addition of NaBr and sodium salicylate (NaSal) makes the micelles wormlike (or longer) and threadlike, respectively. Magnetic fields align rodlike micelles in the parallel direction and may promote micellar growth.

Light scattering intensity at scattering angle 90° from CTAB/NaBr and CTAB/NaSal aqueous solutions decreased by applying a 10-T magnedc field (Fig. 4-2-1). The radius of gyrafion RG of the micelles, estimated by the angular dependence of light scattering intensity, increased at more than 5 T. In both systems, the wormlike micelles having RG of more than 120 nm grew by magnetic fields, i.e., RG of micelles in 50 mM CTAB and 100 mM NaSal solution changed from 145 nm to 168 nm upon application of a 10-T magnetic field.

B. Magnetic Control of Surfactant/Silicate Hybrid Structures The hybrids were prepared from ethanol-water mixtures containing tetraethyl orthosilicate (TEOS) and CTAB at 298 K under magnetic fields.^^ The acidic and basic systems containing TEOS, H2O, HCl or NH3, EtOH and CTAB showed one-phase and two-phase regions. A hexagonal structure developed with a magnetic field in a one-phase system. Fig. 4-2-2(A) shows an example of the magnetic field effect on a hybrid from a basic mixed solution. An amorphous-like hybrid at zero field was transformed into a typical hexagonal phase by a 28-T magnetic field. The N2 adsorption isotherms for the mesoporous silicas at 77 K and their pore size distributions were consistent with the XRD patterns, as seen in the

4.2 Magnetic Field Controls of Molecular Assemblies and Gels

15

153

5000 s CsaSal / m M

- 10

OX)

Time, t

Fig. 4-2-1 Changes in scattering light intensity from aqueous solutions of 20 mM CTAB containing sodium salicylate with application of magnetic fields.

Steps in Fig. 4-2-2(B). The silicas prepared from hybrids changed from microporous at zero field to mesoporous ones with increasing magnetic field. The increase in adsorption of N2 and the step-like increase at around moderate pressure suggest more homogeneous mesopores in the hexagonal structure. When hexagonal and lamellar phases coexisted, a 28-T magnetic field depressed almost perfectly only the growth of a lamellar phase to lead to a pure hexagonal phase.

By contrast, in two-phase systems the hexagonal structure in the bottom phase was depressed with increasing magnetic field. The hexagonal peak intensities in X-ray diffraction (XRD) decreased with increasing magnetic field, as indicated by the disappearance of the steps in the N2 adsorption isotherms and decrease in pores with increase in magnetic field. The hexagonal depression was accompanied by composition changes in the bottom (hexagonal) and upper (lamellar) phase.

The great dependence of the magnetic field-induced structural changes on the compositions seems to arise from the stability and domain size of the surfactant mesophases. pH especially may affect hybrid structure via polymerization of silicate ion, because an acid and a base are hydrolysis and polymerization catalysts, respectively. Moreover, when magnetically anisotropic molecules are added to the system, the magnetic field may lead to the hexagonal structure. For example, 5% anthracene induced the amorphous-hexagonal transition by a 10-T magnetic field. Thus, steady magnetic fields can control indirectly the pore size, pore volume and pore direction of mesoporous inorganic polymers via organic mesophases as the template.


^^^ 2000

1500-

> 1000

ler

(B) 600

28 T . 0.3

0.25-

:< 0.2-

1 0.15-

1 0.1 -

0.05-

°10

,1

15

|28T

K

;1 \ lOT

/ '

\ . OT

20 25 3 r(A)

0.2 0.4 0.6 0.8 1 Relative pressure p I /?„

Fig. 4-2-2 (A) XRD patterns of the hybrids prepared from the basic mixed solution (TEOS: H2O: NH3: EtOH: CTAB = 1: 40: 2: 1.8: 0.03) under steady magnetic fields at 298 K. The typical hexagonal phase developed with increase in magnetic field at 298 K. (B) N2 adsorption isotherms at 77 K and pore size distribution for mesoporous silicas obtained by calcination of the hybrids.

4.2.2 Magnetic Regulation of Lipid Membranes

There are many reports on magnetic field effects on biological systems: structural changes in organisms,'^^ catalytic activities,^ ' ^ material transport,^^^ etc. Since biological cells contain many components and elementary processes, the magnetic responses of such complex biological systems may often be contradictory to each other. To elucidate the magnetic effects on biosystems, those on each elementary process should be examined. For this purpose, an artificial lipid bimolecular membrane


called the black lipid membrane (BLM), and unilamellar and multilamellar vesicles (liposomes) have been used as models for biomembranes, although such thermodynamical lipid membranes are too simple.

There are many studies on electromagnetic field effects on model systems as well as living systems because it is generally believed that an electromagnetic field should be more effective for biological systems than a steady magnetic field. On the other hand, studies on steady magnetic field effects on model membrane systems are relatively limited. In this section, the great effects of relatively low, steady magnetic fields less than 0.5 T to high magnetic fields of up to 30 T on the membrane potential (*P) and resistance (R) of BLMs are presented. Moreover, magnetic field-induced fusion and division of vesicles are demonstrated. Such significant magnetic responses in membrane functions and structures are not familiar, although it is well known that diamagnetic lipid assemblies as well as liquid crystals and macromolecules tend to align under steady magnetic fields.'-'^

A. Steady Magnetic Field Effects on Black Lipid Membranes The membrane potential and resistance of BLMs, comprising didodecyl phosphite (DP), dipalmitoylphosphatidylcholine (DPPC) and dioctadecyldimethylammonium chloride (DODAC), changed remarkably under low, steady magnetic fields of less than 0.5 T.' ^^^ The electrical properties seem to be affected not via the Lorentz force on the ion flux, but via a cooperative orientation of lipid molecules. Under high magnetic fields, another magnetic field effect on a bilayer membrane comes from the elastic properties of the membrane. Helfrich predicted theoretically the magnetic deformation of liposomes from a sphere to an ellipsoid,'^^ and Tenforde and Liburdy showed experimentally the magnetic undulation of membrane deformation.^^ Moreover, Ozeki and coworkers found that the magnetoundulation of membranes brought about magnetofusion and magnetodivision of vesicles and great responses in the electrical properties of BLMs. ' '

The BLM in aqueous solutions was formed at 298 K for DP and 311 K for DPPC and DODAC in the hole (ca. 0.8 mm diameter) of a thin Teflon sheet (0.5 mm thickness) which divided the Teflon cell into two compartments.^^^ *F arising across a BLM by maintaining a 10-fold difference in the NaCl concentration (1 x 10"" and 1 x 10"' mol dm'^) was measured with a couple of Ag-AgCl electrodes. The dilute side of the solution was taken as being negative. /? of a BLM in a 1 x 10" mol dm"" NaCl solution was measured by means of two platinized Pt electrodes. BLM-forming solutions were prepared by mixing 20 ppm of DP or DPPC with (3 + 2) octane-dodecane.

Figure 4-2-3(A)^^^ and (B) show typical examples of changes in *F and /? of a BLM of DPPC and DODAC, respectively, with the application


(A)

>^

500 s ^J ^" ^WVW%10^^

:0.5

(B)

Stepwise

-30 900 1800 2700 3600 4500

Fig. 4-2-3 (A) Typical examples of the time course of changes in membrane potential "F of a black lipid membrane (BLM) of DPPC with the application of various magnetic fields (upper) perpendicular to the membrane at 318 K. No magnetic field parallel to the membrane, H//, affected f (lower). (B) Magneto-responses in /? of a BLM of DODAC containing 50 mol% perylene at 318 K as a function of H.

of magnetic fields (//i) perpendicular to the membrane. The general features in the magnetic response {Af=fH-fo, where/is I *P| or /?, and the subscripts 0 and H mean H = 0 and H, respectively) are its reversibility, the maximum response (A/max) at around 0.2 T (// = Hc\) and the reverse response at // > 0.4 T. *F for DPPC membranes changed by ca. 2 mV even at 0.025 T. The changing rate (100 A/T/b) in "F and R reached more than -50 and 4% (13 mV and 20 MQ) at 0.2 T and 20 and -2% at 0.45 T. These


magnetic responses seem to be notably large from the viewpoint that, for example, the magnetic field theoretically required to produce a 10% reduction in the conduction of a nerve impulse was roughly 24 T.' ^

It is assumed that magnetic fields should modify the apparent fixed charge density (a) of the membrane, e.g., a modification of the distribution of small ions around the head groups and/or in the membrane and inherent charge-bearing ability of head groups. In order to discuss qualitatively from the viewpoint of cr, a theory^^^ for a thick membrane was applied to our systems because, to our knowledge, no theory exists for a BLM. The features in the experimental magnetic responses of *P and R for DP membranes seem to be consistent with the theory.' ^ [*P(mV), /?(MQ)] from the theory is estimated [-20, 520], [-10, 546], and [-24, 503] for a (10-^ mol dm-^) = 6.4 at // = 0, 4.3 at // = //d, and 7.4 at // = 0.45 T, respectively. The changing rates in *F and R from the estimated values are -50 and 5% at He] and 20 and -1.9% at 0.45 T, respectively, which are consistent with the experimental rates of -50 and 4% at Hd and 20 and - 2 % at 0.45 T. Thus, the a values may be used as a measure for an effective fixed charge density of the BLM. Fig. 4-2-4(A) shows that the estimated a changed with magnetic field through a minimum (cTmin) at around 0.2 T.' ^

//=o o<//<//„ / / = / / c l //>//„

Fig. 4-2-4 (A) Apparent fixed charge density a of the BLM estimated from the f values as a function of the magnetic field (//). a changes with the magnetic field through a minimum (cTmm) at Hci. (B) A possible model for the magnetic responses in the membrane potential and resistance is depicted schematically.


When a magnetic field (////) was parallel to the lipid membrane, i.e., perpendicular to the direction of ion flow, no magnetic effect was observed at 0.5 T, suggesting that an ion flow would not be directly affected by the Lorentz force. Thus, the change in a due to magnetic fields may be brought about by the molecular orientation, which leads to changes in the molecular density (area per molecule) at the membrane surface. If H and/or N in Eq. (1) is large enough, the long molecular axis tends to align in a direction perpendicular to // (0 = n/2) because of the negative diamagnetic anisotropy {Ax < 0). Under 1 T and 298 K, significant orientational effects are expected when A is on the order of 10 for A; ~ -1 x 10" (for lipids), at which the magnetic orientational energy is comparable to the thermal energy if other energies associated with orientadonal changes, such as surface energy, intermolecular interaction energy and elastic energy for membrane deformation, are neglected. It seems possible that such a domain exists in the BLM used comprising 10' molecules, as is known in insoluble monolayers.

When a lipid molecule tilts under a magnetic field, the occupied molecular area increases monotonically with 0; thus a would also decrease monotonically with magnetic field. On the other hand, with increasing 0, the hydrocarbon/water interface at the membrane surface should increase and destabilize the tilted structure. Thus the critical tilt angle (0ci) must exist at the first critical magnetic field Hc\. Then one possible way to increase cr or | *F | at higher magnetic field than He would be to introduce membrane deformation in a plane surface, e.g., a small displacement of the head groups in the direction perpendicular to the surface, like a nematic liquid crystal. From these considerations, a possible model for the magnetic responses under low magnetic fields is depicted schematically in Fig. 4-2-4(B). Such deformation would lead to a reduction of the hydrocarbon/water interfacial energy.

Over 0.15 T, ^ decreased across 0 at 0.3 T with an increase in //, and reached a plateau (-8 mV) in the range 10 to 12 T, followed by a steep decrease in the range 12 to 20 T, then approached -18 mV at 28 T. The steep *F change at around 12 T seems to correspond to vesicle growth, suggesting that the large change in *F should arise from modification of the membrane structure. The membrane deformation out of a plane surface, i.e., undulation, may be expected so as to relax the orientational defects among domains having different orientation at a tilt angle under higher magnetic fields larger than a few T. This should lead to a ripple-like structure. In fact, DPPC liposomes, which were cooled down from 318 to 303 K under a high magnetic field (11.7 T), showed a proton nuclear magnetic resonance (500 MHz) pattern very similar to its ripple phase. ^^ At least, the undulation structure must be frozen or stable under a 11.7-T magnetic field in the cooling process. Such irreversible deformation has been observed by means of phosphorus ( 'P) and deuterium ( H) NMR. ^


B. Magnetofusion and Magnetodivision of Vesicles A high steady magnetic field should induce membrane deformation. Then, one interesting question is whether or not deformation in the diamagnetic molecular assemblies due to high magnetic fields can induce fusion among vesicles and division of a vesicle.

The bilayer membrane is not a homogeneously curved surface if it has different elastic properties because of, for example, orientational defects. The Helfrich theory for the magnetodeformation, silr^, of a spherical bilayer vesicle of radius ro, in which the domains in the bilayer have a local curvature co, gives the equation

S2/ ro = rQÂxbH^^ 13k, (6 - Coro) (2)

where Z? is a measure of the thickness of the bilayer and kc is the curvature-elastic modulus. " Then, the total energy (£"(ro)) of a vesicle which initially has radius ro comprises the curvature-elastic (Ec) and magnetic energies (£H),

Liposome growth from radius ro to r with the association of n vesicles under a magnedc field may be possible when the following relation is satisfied^^ :

£"(ro)>(l/Ai)£"(r) (4)

When association occurs without changes in the vesicle surface area, r is simply given by

r = n^^'ro (5)

When H is large enough (-10 T) (case 1) or the shape of a liposome is exactly an ellipsoid of revolution (case 2), the following relation is obtained if co is unchanged during the size change' \*

6(\-n)-Coro(n'^''-n)>0 (6)

This relation was derived from Eqs. (2), (3) and (4) using the two equations (Ec and En) in ref. 14 for case 1 or the following two equations for case 2:

^c=(8;r/5)/:c(6-Coro)(52/ro)' (7)

£H =-(16;r/15)A;t:^//Vo52 (8)

Solving Eq.(6) and adding the condition Ax (6 - coro) > 0, possible association in vesicle having radius ro may be estimated for a given radius of curvature p(= 1/co), as shown in Fig. 4-2-5. ^^ The shadowing in the figure illustrates the regions of magnetofusion (n> I) and magnetodivision {n< 1) for p = 25 nm. When « = 1, a vesicle of size ro is stable against or


7

6

400 600 800 To/nm

1000 1200

Fig. 4-2-5 Comparison between experimental and theoretical association number (n). Possible association number (n) in vesicles having initial radius ro by applying magnetic fields (10-30 T), which was estimated from Eq. (6) for a given radius of curvature p (= 1/co). Shading in the figure illustrates the regions of magnetofusion (n> \) and magnetodivision (n < \) for p = 10 nm. When « = 1, a liposome of size ro is stable against or insensitive to a certain magnetic field. Theoretical: p = 10 (shaded region) and 20 nm (oblique line).

insensitive to a certain magnetic field, that is, the apparent Ax of a whole vesicle should be zero. a. Steady magnetic field effects on vesicles Vesicles were prepared from chloroform solutions of DPPC by the Bangham method. The average vesicle size was determined as a sphere from the Einstein-Stokes equation by dynamic light scattering at 298 K under no magnetic field. Vesicles grew when they were exposed to high magnetic fields of more than 12 T at 318 K for 3 h, e.g., from 160 nm to 275 nm in radius by applying a magnetic field of 20 T; this may be referred to as magnetofusion. ^^ Small vesicles of less than 500 nm were grown by a 10-T magnetic field. However, the larger vesicles were reduced in size by magnetic fields, i.e., magnetodivision of vesicles was induced. Fig. 4-2-5 summarizes the experimental ratio of r to ro or square root n as a function of ro. A comparison of the theoretical to the experimental vesicle size under magnetic fields shows that almost all experimental points drop in the theoretical region for po = 20 nm.

Figure 4-2-6(A) shows changes in the size distribution for DODAC vesicles containing 20 mol% anthracene or pyrene with the application of a 10-T magnetic field and 30 T at 318 K for 1 h. Different size distributions were obtained depending on the kind of additive employed: magnetofusion for the anthracene system and magnetodivision for the pyrene system. b. Magnetodeformation of vesicles by pulsed magnetic fields The dynamical process in magnetofusion and magnetodivision is quite


(A)

Anthracene ^ 6

2 r

0 60 71.8 98.17 156 282.7 560.4 1169

ro/nm

8 -

6 -

60 71.8 98.17 156 282.7 560.4 1169

r /nm

in

rene

(R)

o

^

10 h i i 1

200

15 -

394.8 865.4 1897

ro/nm

-

4160

-

10 -

5 '

0 ~-^ 200 394.8

20 T( pulse)

15 -

865.4

r /nm

1897

-

4160

-

80 122.5 212.7 394.1758.9 1493 2969 5200

ro/nm

80 122.5 212.7 394.1 758.9 1493 2969 5200

r /nm

Fig. 4-2-6 (A) Changes in the size distribution for DPPC vesicles containing 20 mol% anthracene or pyrene with the application of 10 T (magnetofusion) and 30 T (magnetodivision), respectively, at 318 K. (B) Change in the vesicle size distribution during the exposure time of 10 ms to a 20-T pulsed magnetic field.

unclear. The vesicle size distribution strongly depended on the exposure time for a steady magnetic field within 1 h. Even when the time of exposure to a steady magnetic field was very short marked changes were observed: 5-s exposure to a 10-T magnetic field induced a bimodal distribution for vesicle size. Furthermore, just a 10-ms pulse of a 20-T magnetic field promoted significant magnetodivision of vesicles, changing from a monomodal size distribution to a typical bimodal one (Fig. 4-2-6(B)).


4.2.3 Structure and Functions of Chemically Cross-linked Hydrogels Prepared under Steady Magnetic Fields

Hydrogels have been investigated not only from the viewpoint of purely scientific interest but also technological aspects such as drug delivery and actuator. Thus, it is very important to investigate the methodology for control of structures and physical properties of gels. Although the magnetic energy of a nonmagnetic molecule in magnetic fields is much less than the thermal energy, macromolecules having high molecular weight and magnetic anisotropy can be oriented by high magnetic fields. Therefore, magnetic fields may provide a useful method for the structural control of gels. Magnetic anisotropy of a monomer or a polymer chain is not enough to respond to magnetic fields, but polymer chains produced in the polymerization process may orient cooperatively. When the oriented polymer chains are cross-linked, a structured gel may be obtained. Gel properties depend on polymer chain distribution, cross-link density and hydration. If we can control these factors by magnetic fields, a novel gel would be generated.

NIPA and AAm gels were prepared from aqueous solutions of 700 mM A^-isopropylacrylamide (NIPA) or acrylamide (AAm) monomer and A^,7V'-methylenebisacrylamide (BIS) of various concentrations (CBIS = 4.3, 8.6, 17.2, 25.8, and 34.4 mM) in a thin glass capillary (inner diameter: 0.4 mm) at 278 K. The radical polymerization was initiated by potassium peroxodisulfate and accelerated by A ,N,A^Â '-tetramethylethylenediamine. Steady magnetic fields (< 30 T) were applied perpendicular (Hi) or parallel (H//) to the capillary for 60 min (during polymerization) using a superconducting magnet and a hybrid magnet. Then the capillary remained at rest under zero field at 278 K for 24 h. Cylindrical gels prepared were taken out of the capillaries, washed repeatedly by temperature swings in a large amount of fresh distilled water, then dried in air at room temperature.

The volume of NIPA gels prepared under steady magnetic fields increased (Fig. 4-2-7(A)), and their volume phase transitions were much more significant, as shown in Fig. 4-2-7(B). Magnetic fields increased the diameter of the gels in the swelling state, but decreased the diameter in the shrinking state.'^^ The diameter of gels in the swelling state increased linearly with increase in magnetic field below 10 T, and became about 40% larger at 30 T and 298 K than that of a zero-field gel.' ^ The volume phase transition temperature did not change by magnetic field. When NIPA gels were prepared at high / ' ^ (= CBIS/CNIPA, where CNIPA = 700 mM), the diameter in the swelling state decreased continuously, i.e., no volume phase transition appeared. However, when they were prepared under magnetic fields, the diameter changed discontinuously at 33.8°C; the volume phase transition appeared. The discontinuity in the volume phase transition of the NIPA gels became more significant with increasing


(A)

(B) 0 .6-

: 30 ! •

0.5 u 10TO

B t B

^ 0 . 4 - O T A

° „ \

.2 0.3 [

0.2 [

0.1

tt»6 6 i

20 25 30 35 40 45

Temperature, T/°C

Fig. 4-2-7 (A) Optical microscopic photographs of NIPA gels prepared under 0 T and 30 T. (B) Volume phase transition of NIPA gel prepared under various magnetic fields.

magnetic field intensity. The plots of the diameters of swelling and shrunken gels at the volume phase transition temperature vs. magnetic field intensity give the swelling line and the shrunken line, between which the volume phase transition occurs. The swelling lines indicate that the diameter was not saturated even at 30 T. The swelling and shrunken lines of the gels were prepared at various q^'^ close at each magnetic field intensity, /fv, where no volume phase transition occurs. In other words, magnetic fields higher than //v induced the volume phase transition of NIPA gels. The same phenomenon was observed in AAm gels, which are well known as a nonvolume phase transition gel. Since the diameter of gels increased with decreasing BIS concentration in preparation, it is inferred that the decrease in gel diameter due to magnetic fields should be ascribed to the reduction of cross-linkage in gels prepared under magnetic fields. The effective degree of cross-linkage (q^^) was estimated by comparing the diameter of gels prepared at different degrees of cross-linkage and zero-


field with that of gels prepared under magnetic fields. Magnetic fields reduced the effective cross-linkage, e.g., from / '^ = 0.0123 to q^^ = 0.004 at 10 T; generally q^^ < 1/3 / '^ over 15 T. Considering no change in C/N ratios of gels estimated by elemental analysis with magnetic field, dangling chains would be increased by magnetic fields. Also, the average number of residues between cross-linking points increased with increasing magnetic field intensity, which was estimated by the equation given by Flory. The above findings suggest that magnetic fields reduced the network density of gels to soften the gels.

Volume phase transition is subject to diffusion of the polymer network in medium. ^^ The diffusion depends on polymer concentration and cross-link density. Therefore, the decrease in the network density under magnetic fields seems to induce the volume phase transition of high q^'^ gels. However, considering that no volume phase transition was observed even when AAm gels were prepared at low ^P' the volume phase transition induced must also be subject to factors other than the network density. The volume changes of Hi gels were much larger than those of H// gels, suggesting that magneto-orientation of polymer chains in gels made the gels anisotropic. The structural anisotropy led to a difference in the iodine diffusion rate in H± and H// gels, which were about 10% faster and 20% slower than that of a zero-field gel, respectively.

4.2.4 Conclusion

Steady magnetic fields of less than 0.1 T brought about significant responses in membrane potential and resistance. Deformation in lipid membranes led to the magnetofusion and magnetodivision of the vesicles and large changes in the electrical properties of their black membranes under steady magnetic fields of up to 30 T. Pulsed magnetic fields also affected lipid membranes very effectively. Micelles were deformed by steady magnetic fields. Also, surfactant/silicate molecular assemblies were effectively regulated by steady magnetic fields via orientation of surfactant molecules used as template, leading to specific pore structures and adsorptivity of mesoporous silicas. In these systems, magnetically anisotropic molecules can effectively control the magnetoresponses in structures and functions of molecular assembly systems. Chemically cross-linked gels were also modified by magnetic fields in preparation and regulated by applying external magnetic fields. These examples demonstrate the potentiality of various magnetic fields that can regulate the function, structure and size of artificially organized molecular assemblies. This will lead to extensive applications for sensors, electric devices, material transport, structure-controlled materials preparation, drug release and numerous other uses.

4.3 Magnetic Field-induced Martensitic Transformation in Ferrous Alloys 165

References

1. Magnetic Field Effect on Biological Systems (T. S. Tenforde, ed.), Plenum Press, New York (1979).

2. Biophysical Effects of Steady Magnetic Fields (G. Maret, N. Boccara, J. Keipenheuer, eds.), pp.2-51, Springer-Verlag, Berlin (1986).

3. B. J. Gaffney, H. M. McConnell, Chem. Phys. Lett., 24, 310 (1974). 4. G. Maret, K. Dransfeld, Physica, 86-88B, 1077 (1977). 5. J. Seeling, F. Borle, T. A. Cross, Biochim. Biophys. Acta, 814, 195 (1985). 6. T. S. Tenforde, R. P. Liburdy, J. Theor. Biol, 133, 385 (1988). 7. S. H. Tolbert, A. Firouzi, G. D. Stucky, B. F. Chmelka, Science, 278, 264 (1997); A.

Firouzi, D. J. Schaefer, S. H. Tolbert, G. D. Stucky, B. F. Chmelka, J. Am. Chem. 5oc., 119,9466(1997).

8. S. Ozeki, K. Iguchi, Y. Kojima, K. Nakamoto, Y. Imai, K. Yajima, Riken Review, 44, 153 (2002); S. Ozeki, M. Yamamoto, K. Nobuhara, Characterization of Porous Solids IV (B. McEnarney et al., eds.), p.648, The Royal Society of Chemistry, London (1997).

9. W. Haberditzl, Nature, 213, 72 (1967). 10. S. Ueno, M. Iwasaka, J. Appl. Phys., 79, 4705 (1996). 11. T. Higashi, A. Yamagishi, T. Takeuchi, M. Date, Bioelectrochem. Bioenerg., 36, 101

(1995). 12. H. R. Khan, S. Ozeki, J. Colloid Interface 5c/., 177, 628 (1996). 13. S. Ozeki, H. Kurashima, M. Miyanaga, C. Nozawa, Langmuir, 16, 1478 (2000); H.

Kurashima, H. Abe, S. Ozeki, Mol. Phys., 100, 1445 (2002). 14. W. Helfrich, Phys. Lett., 43A, 409 (1973); Zeit. Naturforsch., 28C, 693 (1973). 15. S. Ozeki, H. Kurashima, H. Abe, J. Phys. Chem. B, 104, 5657 (2000); S. Ozeki, H.

Kurashima, Encyclopedia of Surface and Colloid Science (A. Habbard, ed.), p.3109. Marcel Dekker, New York (2002).

16. J. P. Jr. Wisco, J. P. Barach, IEEE Trans. Biomed. Eng., BME-27, 722 (1980). 17. T. Ueda, N. Kamo, N. Ishida, Y. Kobatake, J. Phys. Chem., 76, 2447 (1972). 18. S. Ozeki, I. Ohtsuka, A. Miyazawa, H. Kawasaki, H. Maeda, Abstracts of

International Conference on Biological Physics, Kyoto, p. 120 (2001). 19. S. Ozeki, I. Ohtsuka, Magnetoscience (K. Kitazawa, S. Ozeki, Y. Tanimoto, M.

Yamaguchi, eds.), p. 184, IPC Press, Tokyo (2002) (in Japanese). 20. T. Tanaka, D. J. Fillmore, J. Chem. Phys., 92, 1214 (1979).

4.3 Magnetic Field-induced Martensitic Transformation in Ferrous Alloys

4.3.1 Effect of Magnetic Field on Martensitic Transformation Temperature

Martensitic transformation, which occurs in many Fe-, Cu- and Ti-based alloys and ceramics, is a typical first-order structural phase transition without atom diffusion and has been widely studied to determine its characteristics from physical, metallographical and crystallographic viewpoints/^ In addition, the martensitic transformation has also been studied from a technological viewpoint, partly because fine martensite


Structures formed in quenched ferrous alloys and steels are effective for strengthening and are thus used as structural materials, and partly because the shape memory effect and pseudoelasticity effect appear in relation to the thermoelastic martensitic transformation, and these effects are useful for practical purposes as functional materials.

According to studies by Patel and Cohen^^ and Otsuka et al., ^ some aspects of martensitic transformation such as transformation temperature, crystallography and the amount and morphology of the product martensites are strongly influenced by external fields, such as temperature, hydrostatic pressure and uniaxial stress. To clarify the effects of these external fields on martensitic transformation it is very important to understand the essential matters of the transformation such as thermodynamics, kinetics and the origin of the transformation. Magnetic field is one of such external fields because some difference in magnetic moment between the parent and martensite states exists. ^

How the transformation temperature is influenced by the magnetic field is shown schematically. Fig. 4-3-1 shows the temperature dependence of the Gibbs chemical free energy of the parent phase (G^) and the martensite phase (G""). At high temperature, the Gibbs chemical free energy of the parent phase is lower than that of the martensite phase so the parent is stable. When the parent phase is cooled, martensitic transformation does not occur at equilibrium temperature, To, but occurs at Ms, which is below To. This is because the interfacial energy and strain energy are needed to initiate the transformation, and this additional energy is supplied by the excess cooling from To to M^. When the magnetic field is applied to the system, the Gibbs chemical free energy of the martensite decreases mainly due to the magnetostatic energy (change in Gibbs

AG(MJ

M,

AG(AJ

c

! i

1 1 1

j j i

1 1 ^ \ T \

1 1 !

^^ G"'(H=0)

(//=0, H^ 0)

M: To r,,' A:

Fig. 4-3-1 Schematic Gibbs chemical free energy as a function of temperature under a magnetic field.


chemical free energy of the parent is neglected here for simplicity). Therefore, the equilibrium temperature under the magnetic field increases as shown in the figure. Also, the Ms, under the magnetic field increases to Ms' if it is assumed that the martensitic transformation under the magnetic field occurs at the temperature where the change in Gibbs chemical free energies under the magnetic field, (G""- G ), is the same as that under no magnetic field at Ms. This assumption on the effect of the magnetic field is analogous to that on the effect of uniaxial stress and hydrostatic pressure made by Patel and Cohen.^^ The validity of the assumption has been confirmed by many researchers, that is, the effect of uniaxial stress on Ms calculated by the assumption is in good agreement with the experimental one in many materials.

In the following, the results of more detailed studies concerning the effect of the magnetic field on the transformation temperatures in many ferrous alloys are discussed. The samples used are three Invar Fe-Ni alloys, disordered and ordered Fe-Pt Invar alloys and non-Invar Fe-Ni-C and Fe-Mn-C alloys. ' ^ Their structural changes are basically those from fee to bcc. High-field magnetization measurements were performed at the Research Center for Materials Science at Extreme Conditions, Osaka University, the magnetic field used in the study being a pulsed one with maximum strength of 31 MA m"^ Details of the ultrahigh magnetic field instrument are reported elsewhere.^^ Fig. 4-3-2 shows typical magnetization curves (M(t)~H(t)) for Invar Fe-31.7Ni and non-Invar Fe-24.7Ni-1.8C and Fe-3.9Mn-5.0C (at%) alloys, where Ar represents the temperature difference between a set temperature T and Ms (AT = T - Ms). In the figure, an abrupt increase in magnetization is recognized for all the alloys at a certain strength of the magnetic field as indicated by an arrow. The magnetic field, H^ at the abrupt increase in magnetizafion is the critical one for inducing the martensitic transformation at r. That is, the set temperature is interpreted as the martensitic transformation start temperature, Ms', under the strength of magnetic field of He. The relations thus obtained between the critical magnetic field and the shift of Ms, AMs (= Ms'-Ms), are shown in Fig. 4-3-3 with solid circles for several alloys. It is known from the figure that AMs increases with increasing magnetic field for all the alloys examined, and the rate of the increase against the magnetic field depends on the alloy system.

We have proposed^^ the following equation to estimate the relation between the critical magnetic field and the transformation temperature:

AG(Ms)-AG(Ms') = -AM(Ms')//c--;C///c '+ôf^l//c^ (1)

where AG(Ms) and AG(Ms') is the difference in Gibbs chemical free energy between the parent and martensite phases at Ms and Ms' temperatures, respectively, AM(Ms') is M"^(MS')-MP(MS') (where M" and M^ are the


10 20 Magnetic field / MA m '

Fig. 4-3-2 Magnetization curves of Invear Fe-31.7Ni (at%) alloy (a), non-Invar Fe-24.7Ni-1.8C (at%) (b) and non-Invar Fe-3.9Mn-5.0C (at%) (c).

spontaneous magnetization of the martensite and parent phases respectively), X"^ the high magnetic field susceptibility in the parent phase, Co the volume change associated with martensitic transformation, co the forced volume magnetostriction and B the parent bulk modulus. The first term on the right-hand side of Eq. (1) represents the energy due to the magnetostatic effect, which was already proposed by Krivoglaz and Sadovsky." ^ The second and third terms are introduced by the author's group and represent the energies due to the high-field susceptibility and forced volume magnetostriction effects, respectively.

The second term in Eq. (1) is related to the induced magnetic moment in the parent phase by applying a magnetic field and is originally the same as the magnetostatic energy like the first term. Strictly speaking, the moment induced in the martensite must be considered, but its value is smaller than that of the parent phase in many Fe-based alloys. So we neglect the value of induced moment in the martensite.

The third term in Eq. (1) is quite effective for the Invar alloys because co in Invar alloys are larger by one order than those of non-Invar alloys. Here, we will simply show how to derive the third term. It is well known that Invar alloys have a large forced volume magnetostriction as mentioned before. This means that 3co/3// is quite large in Invar alloys. The value of 3co/3// is isotropically positive, that is, the austenite is subject to


(a) t (c)

60 ^ / ^ ! Fe-31.7at%Ni /

- 80

li Fe-3.9 Mn-5.0C (at%) /

m

r 20 y y • Fe-32.5 at%Ni g

. ' ' ' ^ ' ' 1^# Fe-24 at%Pt ' ^^ .-'' ^

0 10 20 30 0 10 20 30 Magnetic field / MA m ' Magnetic field / MA m '

(b) V 100

h 80 Fe-24.7Ni-1.8C

^ h60 1

40 y 20 •-''

0 10 20 30 Magnetic field / MA m~'

Fig. 4-3-3 AMs vs. H^ relation for Invar Fe-Ni and Fe-Pt alloys (a), non-Invar Fe-Ni-C (b) and Fe-Mn-C (c). Solid marks are measured values and dotted lines are calculated relations.

volume expansion, and it is about 10"' m A' for Invar alloys and about 10" ' m A" for non-Invar alloys. Microscopically the volume expansion comes from the Pauli repulsion in the induced magnetization. Phenomenologically, it can be regarded as a negative hydrostatic pressure for the austenite. The effect of hydrostatic pressure on transformation start temperature was quantitatively studied by Patel and Cohen^^ and they proposed the equation

AG(Ms,0)- AG(Ms' ,0) = -E^P (2)

where AG(Ms, 0) represents the difference in Gibbs chemical free energy between austenite and martensite phases under no pressure at Ms (transformation start temperature under no pressure), AG(Ms\ 0) that at Ms' (transformation start temperature under pressure P), and eo the volume change associated with martensitic transformation. When the negative pressure (i.e., isotropic expansion) is produced by the forced volume


magnetostriction effect, the negative term -e^P in Eq. (2) must be replaced by the positive term £o(d(x)/dH )HB, since (dco/dH )HB corresponds to the hydrostatic pressure P.

The calculated relation between AA/s and magnetic field based on Eq. (1) are shown in Fig. 4-3-3 by dotted lines, which are in good agreement with the experimental ones for all the alloys. We also show the calculated magnetic field dependence of transformation temperature for each term in Eq. (1) in order to learn which term is effective in changing the transformation temperature by magnetic field. Typical calculated results for Invar Fe-31.7 at% Ni alloy and Fe-24.0 at% Pt alloy with S = 0.8 are shown in Fig. 4-3-4, where the dotted lines denoted by M.S.E., H.F.E., F.M.E. and (M.S.E. -\- H.F.E. -h F.M.E.) are the //c vs. Ms' relations calculated for the magnetostatic, high field susceptibility, forced volume magnetostriction and their total effects, respectively. As seen from the figure, the calculated relations (M.S.E. + H.F.E. + F.M.E.) are in good agreement with the experimental ones for both alloys. It should be noted that the shift of Ms due to the forced magnetostriction effect is nearly of the same order as that due to the magnetostatic effect for both alloys, and the shift of Ms due to this effect is a decrease in the ordered Fe-Pt alloy, but an increase in the Fe-Ni alloy. This difference is due to the fact that the volume change associated with the martensitic transformation in the ordered Fe-Pt alloy is negative, but positive in the Fe-Ni alloy.

Incidentally, in Eq. (1) we neglect the energies due to the well-known effects of magnetocrystalline anisotropy and the shape anisotropy since the

^

i 1 II

^

1 : (a)

I 1 ^60 Fe-31.7 at%Ni ^ Z

[ • / c a l . M.S.E.

cal. M.S.E.+ H.FE.«y' y'

+ F.M.E 1 •' r > .'-''

1 yi ..'-' , , - ' ' ' cal. EM.E.

\ .'••.'''''-'''' y-^:'-''"' 10 20 30

^ cal. H.F.E. ~-~-

;

40 (b)

- Fe-24 at^cPt , , - ' " ' cal. M.S.E. ,.'"'

20 , > ' c a l . M.S.E. + H.EE.

, , ' " ' " + F.M.E .

-~ ---j__ cal. H.F.E.

cal. EM.E. ~~~~~~--._ ~~~-~-.

Magnetic field, H1 MA m '

Magnetic field, H / MA m '

Fig. 4-3-4 Shift of Ms as a function of magnetic field for Invar Fe-31.7Ni (a) and Invar ordered Fe-24Pt alloys (b). Solid marks are measured values and dotted lines are calculated relations, where M.S.E., H.F.E. and F.M.E. mean the effects of magnetostatic energy, high field susceptibility and forced volume magnetostriction, respectively.


energies due to these effects are smaller than those due to the effect shown in Eq. (1) under high magnetic fields. Recently, however, the magnetocrystalline anisotropy was found to play an important role in magnetic field-induced martensitic transformation in a Co-Fe alloy' ^ and a Ni-Mn-Ga alloy.''^ Furthermore, this anisotropy is important for the rearrangement of martensite variants, which will be described later.

4.3.2 Magnetoelastic Martensitic Transformation

In alloys exhibiting a thermoelastic martensitic transformation, each martensite crystal grows or shrinks with temperature cycling, that is, it responds elastically to temperature to maintain the balance between thermal and elastic energies. If a uniaxial stress is applied to such an alloy at a temperature above Af (reverse transformation finish temperature) and released, the forward and reverse transformations occur by a loading cycle. Thus the martensite is induced only while the stress is loaded and reverts to the parent phase when the stress is released. Considering this behavior, it is expected that if a magnetic field is applied above Af to an alloy which exhibits a thermoelastic martensitic transformation and removed, martensite can be induced only while the magnetic field is applied and reverts to the parent phase when the magnetic field is removed. We found this type of martensitic transformation in an ausaged Fe-31.9Ni-9.8Co-4.1Ti (at%) shape memory alloy and gave it the term magnetoelastic martensitic transformation'^^ in analogy to the thermoelastic transformation. The term "ausage" means that the alloy is aged at a temperature where its austenitic phase is stable.

Figure 4-3-5 shows the spontaneous magnetization of the parent and the martensite phases as a function of temperature obtained by magnetization measurements under low magnetic field. The difference in spontaneous magnetization between the two phases is about 0.3 //e/atom at Ms, which is of the same order as that in a previous Fe-32.5 at%Ni alloy. Ms and Af shown with arrows are determined to be about 127 and 159 K, respectively and As is 60 K. A pulsed high magnetic field was applied to a sample at a temperature above Af, 163 K (AT= (T-M,) = 36 K) and typical M(t)-H(t) curves obtained are shown in Fig. 4-3-6(a) and (b). It is noted in Fig. 4-3-6(a) that there is no hysteresis in magnetization when a pulsed magnetic field of 22.22 MA m"' is applied and removed. This means that 22.22 MA m"' is lower than the critical field He for inducing the martensitic transformation, and therefore no martensitic transformation occurs under a magnetic field of 22.22 MA m ^ A higher magnetic field was then applied, and the M(t)-H(t) curve obtained is shown in (b), revealing a hysteresis of magnetization. That is, when a magnetic field is applied, the rate of increase of magnetization against the magnetic field changes at He = 23.08 MA m"\ as indicated by an arrow, and when the magnetic field is removed, the increased magnetization returns to the


A.60K

100 200 Temperature / K

300

Fig. 4-3-5 Spontaneous magnetization as a function of temperature in an ausaged Fe-Ni-Co-Ti alloy.

1.4- (a)

3- 1.0

22.22 MA m '

r=163K(r>Af)

10

23.08 MA m"

7=163 K(r>Af)

20

Magnetic field / MA m~'

Fig. 4-3-6 M{t)-H{t) curves for an ausaged Fe-Ni-Co-Ti alloy at 163K above Af. Magnetic field-induced transformation starts at He in the field applying process, and reverse transformation finishes at //f in the field removing process.

initial value at about //f = 5 MA m~\ indicated by another arrow. This means that martensitic transformation is induced at He and its reverse transformation is completed at //f. These observations show that the magnetoelastic martensitic transformation is realized in the ausaged Fe-Ni-Co-Ti alloy.


4.3.3 Effect of Magnetic Field on Morphology and Arrangement of Martensites

Figure 4-3-7 shows optical micrographs of thermally-induced martensites formed by cooling to slightly below the Ms temperature in Fe-Ni-C alloys ((a), (d) and (g)) and those of magnetic field-induced martensites ((b), (c), (e), (f), (h) and (i)). The formation temperature r, ^T (= T-M,) and H are shown below each photograph. Despite the different formation temperatures, the Fe-28.7Ni-1.8C mass% alloy exhibits thin plate morphology and the two other alloys show lenticular morphology. It is noted that the martensite morphology is different even if the martensites are formed at nearly the same temperature, as seen from a comparison of (c) and (d). This result is contradictory to the proposition that the martensite morphology in Fe-Ni-C alloys is decided only by the formation temperature. " ^ The reason for this difference is not yet known. The same results (the morphology of a magnetic field-induced martensite was the same as that of a thermally-induced one irrespective of the formation temperature and the strength of magnetic field) are obtained for Fe-Ni^ and Fe-Mn-C^ alloys.

Fe-28.7Ni-1.8C, (A) Fe-29.0Ni-1.4C, (B) Fe-24.7Ni-1.8C, (C)

(a) fc£ "': ^ (d) j s ^ " :~ (g)

T^^ „» ^ '

T=123K . a d t i 7=223 K --* ' _ 7=273 K Ar=30K, / /=l l . l lMAm- ' A7=30 K,//= 17.46 MA m ' Ar=50 K,//= 15.87 MA m '

_ _ _ ^ ^ - > - ' _ ^ • r = 1 8 1 K | K « / ^ V 7 ^ 2 5 8 K . v d H a H H 7 =317 K

Ar=88 K, //=30.16 MA m ' Ar=65 K, //=28.97 MA m ' Ar=94 K, //=30.16 MA m '

Fig. 4-3-7 Optical micrographs of thermally induced martensites ((a), (d), (g)) and magnetic field-induced martensites ((b), (c), (e), (0, (h), (i)) in Fe-Ni-C alloys. Transfomiation temperature r, Arand H for the magnetic field-induced martensites are shown below each photograph.


Figure 4-3-8 shows optical micrographs exhibiting the entire view of a thermally-induced martensite in Fe-31.6Ni (at%) alloy single crystals (a) and magnetic field-induced martensites (b)-(d). Crystal orientation, formation temperature, strength of the applied field and its direction are

r :(a)

.i

1 mm

7=163 K

>â6»4

• ( b )

<100>, AT=1 K, 172 K, //=3.89 MA m '

V ^. V i , JV , ( / -r

^^^ ^

<110>, Ar=10 K, 173 K, //=4.98 MA m ' , - ^ ^ - « , ^ _ _ - ., .(^^

\ ^ ^ ^ ^ - r ; 1*^1 ' ^~^-

<111>, Ar=13K, 173K.//=4.98MAm

r. *^î»l ^ , " ^ 4

Fig. 4-3-8 Optical micrographs of a thermally induced martensite (a) and a magnetic field-induced martensite (b),(c), (d) in Fe-31.6Ni (at9'c) single crystal. The temperature and magnetic field is shown below each photograph, (e) is an enlargement of the framed area of (c).


inscribed below each photograph. It is known from (b) and (c) that several martensite plates grow neariy parallel to the direction of magnetic field and run from one end to the other end of single crystals. Such directional growth of martensite plates does not appear in thermally induced martensite, as shown in (a). Therefore, directional growth appears to be a characteristic of magnetic field-induced martensites. Fig. 4-3-7(e) is an enlargement of the framed-area of (c), from which it is seen that one plate grows lengthwise along the direction of the magnetic field and that other plates terminate at the directionally grown plates. This means that the directionally grown plates were formed first and followed by the other plates. The reason for this lengthwise growth of martensite plates under magnetic field is not clear, but shape magnetic anisotropy effect appears to play an important role.

4.3.4 Giant Magnetic Field-induced Strain in Ferromagnetic Shape Memory Alloys

Sections 4.3.1 to 4.3.3 above discuss the magnetic field-induced martensitic transformation. In this and following sections, another effect of magnetic field on martensite phase is described. In some ferromagnetic shape memory alloys (FMSMAs), the arrangement of martensite variants can be controlled by a magnetic field. As a result, a giant magnetic field-induced strain (MFIS) of several percent arises in these alloys.

Before describing MFIS behavior, the shape memory effect related to MFIS is explained. When the martensite phase of a shape memory alloy is induced thermally, it is usually composed of several variants (crystallographic domains). For simplicity, we consider the case in which the specimen is composed of two variants, as schematically shown in Fig. 4-3-9. When a shape memory alloy is cooled below the transformation temperature, all variants will be equivalently formed naturally and they are arranged so as to minimize the total shape change associated with transformation (Fig. 4-3-9(a) -^ (b)). The interfaces of variants are twinning planes, which can be moved easily by the application of external stress T. As a result, rearrangement of variants occurs and a large strain appears (Fig. 4-3-9(b) -^ (c)). This strain recovers by heating to the parent phase (Fig. 4-3-9 (c) -^ (a)). This is the conventional shape memory effect of shape memory alloys.

In ferromagnetic shape memory alloys, magnetic domains in addition to variants exist, and the magnetic moment m will be aligned along the easy axis of each variant, as shown in Fig. 4-3-9 (b). The easy axis of one variant is nearly parallel to the hard axis of another variant. When a magnetic field is applied along the hard axis of one variant which corresponds to the easy axis of another variant, the magnetic energy of the former variant becomes higher than that of the latter variant. As a result, a magnetic shear stress Tmag will act across the twinning plane. The twinning


(a) Parent

Cooling

Twinning -^MMMM^ __ txttlXj ^ plane s \ \ \ \ -^ ~~ fX^TyfCTj y ^

^^ ^^ -> Cxt^xtj/H Twinning - - ^ ^ J L J ^ ^ Stress / (X^txXX)

plane D L X ^ ' ^ X O I ) magnetic field C X X X X X )

Martensite Martensite (multi-variants) (single variant)

Fig. 4-3-9 Schematic illustration showing twinning plane movement by shear stress r and by magnetic field H.

plane will move if Tmag becomes larger than the shear stress required for the twinning plane movement Treq, resulting in a large field-induced strain (Fig. 4-3-9(b) -> (c)). The maximum energy difference between the two variants is the magnetocrystalline anisotropy constant, and it is attained when the magnetic moment becomes parallel to the hard axis for one variant.

Considering the above mechanism, a large magnetocrystalline anisotropy constant and small treq are essential to realize a giant MFIS in ferromagnetic shape memory alloys. Based on this criterion, several ferromagnetic shape memory alloys have been studied. The first report of a giant MFIS was made by Ullakko et al. ^ in a Ni-Mn-Ga alloy. After that, a giant MFIS was also found in Fe-Pd alloys'^' ' ^ and in FesPt.' ^ In the following, we describe the MFIS in Fe-31.2Pd (at%), Fe3Pt and Ni2MnGa, and in the subsequent section, we show that the relation rmag>rreq is clearly realized in Fe-31.2Pd.

All three alloys (Fe-31.2Pd, Fe3Pt, Ni2MnGa) exhibit thermoelastic martensitic transformations. The Fe-31.2Pd alloy transforms from the Al-type structure (a quenched phase) to a tetragonal structure (so-called f.c.t.); the FeaPt with degree of order of about 0.8 transforms from the Lh-type structure to the L6o-type structure; and NiiMnGa transforms from the L2i-type structure to the 10 M martensite with a pseudotetragonal structure. The martensitic transformation temperature is 230 K for Fe-31.2Pd, 85 K for FesPt and 202 K for Ni2MnGa. Fig. 4-3-10 shows the lattice parameters of these alloys as a function of temperature. The lattice parameters of the martensite phase in Fe-31.2Pd and Fe^Pt change gradually as temperature


decreases, but the change in NiiMnGa is small. Common to the three alloys, the tetragonality {da) at 77 K (for FesPt at 4.2 K) is about 0.94. The easy axis of the Fe-31.2Pd is the a axis and that of the FeaPt and the NiiMnGa is the c axis. Considering that the martensite phase is tetragonal, there are three corresponding variants in the martensite phase. The interface of these variants is {101}M ( M stands for the martensite phase) type twinning plane. The [001]? direction (P stands for the parent phase) corresponds to the c axis for one variant and to the a axis for the remaining two variants. The Curie temperature is about 650 K for Fe-31.2Pd, about 450 K for FeaPt and 376 K for NisMnGa. Fe-31.2Pd and FesPt are also known as Invar alloys.

Figure 4-3-11 shows the MFIS obtained in single crystals of the three alloys. The strain was measured along the [001]? direction by a capacitance method under a magnetic field applied along the [001]? direction after the

0.39

0.38

0.37

0.36

0.35

-(a)Fe31.2Pd

a ••

'

-c ••

1

• •% • ^

. ' •

^ -i

^ • • i

-1

-]

^

1

0.39 - (b) Fe,Pt

0.38 - • • . V. .

0.37 -

0.36 f\

0.35 h

0.61 r (c)Ni2MnGa

0.60 r a • MMM • • •

0.59-

0.58 -

0.57-

0.55 -

0 100 200 300 0 100 200 300 Temperature, TIK

0 100 200 300

Fig. 4-3-10 Temperature dependence of lattice parameters of Fe-31.2Pd (a), FesPt (b) and NizMnGa (c).

(a)Fe-31.2Pd

2h

0 ^ — ^

0.0

r=77 K

0.5 1.0 / / / M A m '

(b) FejPt r (c) Ni.MnGa

0.5 1.0 / / / M A m '

Fig. 4-3-11 The longitudinal magnetic field-induced strain along the [001]P direction of Fe-31.2Pd at 77 K (a), Fe3Pt at 4.2 K (b), and Ni2MnGa at 77 K (c). Measurements were made after cooling to these temperatures under zero magnetic field. The marks A to F in (b) indicate the sequence of the measurement.


Specimen was cooled to 77 K (4.2 K for Fe3Pt) under zero magnetic field. For all specimens, the strain starts to appear at a field of about 0.25 MA m"' and then saturates. The saturated strain is larger than 2% for all alloys. The specimen expands along the magnetic field in Fe-31.2Pd but contracts in FcsPt and Ni2MnGa. This difference is due to the difference in the easy axis. By using the strain and lattice parameters, we can evaluate the fraction of the variant whose easy axis lies along the field direction. This fraction is about 100% for Fe-31.2Pd and Ni2MnGa, but it reaches only 70% for FeaPt. One more characteristic feature of the FesPt alloy is the appearance of reversible MFIS. That is, as seen in curve B of Fig. 4-3-11(b), part of the field-induced strain (about 0.6%) recovers in the field removing process, and a strain of about 0.6% repeatedly appears in the subsequent field applying and removing processes (curves C-F in Fig. 4-3-11(b)). This reversible strain is larger than the magnetostriction of TERFENOL-D, which is known as a super magnetostrictive material. The strain recovery in Fe^Pt will be caused by the accumulation of elastic energy, but the reason is not yet known. The reversible strain exhibits significant temperature dependence and reaches about 1 % at 20 K.

4.3.5 Energy Evaluation for Twinning Plane Movement by Magnetic Field

Since the twinning plane moves under a magnetic field as mentioned above, a kind of shear stress, imag, should act across the twinning plane under a magnetic field. In the following we evaluate Tmag and compare it with the stress required for the twinning plane movement Treq for the case oftheFe-31.2Pd alloy.

In evaluating Tmag, we must know the magnetic energy difference per unit volume AUmag between the two states before and after the movement of the twinning plane. The magnetic shear stress will be expressed as Tmag = AUmag/s, where s is the amount of twinning shear. Assuming that the magnetic energy is mainly composed of magnetocrystalline anisotropy energy and Zeeman energy, the maximum of AUmag is the uniaxial magnetocrystalline anisotropy constant | Ku I when a magnetic field is applied along the [001]? direction. The value of [KJ is obtained from the area surrounded by the two magnetization curves along the hard axis and along the easy axis. In the case of the Fe-31.2Pd alloy at 77 K, the value of \KU\ is obtained to be 180 kJ m"\ The amount of twinning shear is expressed as ^ = {1 - (c/af }l{cla). By substituting the lattice parameters shown in Fig. 4-3-10, s is obtained to be 0.124 for Fe-31.2Pd at 77 K. Using the above values of | ATu I and s, the maximum of Tmag is calculated to be about 1.5 MPa for Fe-31.2Pd at 77 K. On the other hand, the value of Treq Is obtalucd from tensile tests using a single-crystalline specimen and found to be between 0.6 and 1.2 MPa at 80 K.

Comparing Tmag and Treq mentioned above, it is obvious that the value

4.4 Control of the Solidification Process by High Static Magnetic Field 179

of Tmag is larger than ireq. In this way, the reason for twinning plane movement by magnetic field is explained by energy evaluation. The condition Tmag > treq Is also confirmed to be satisfied for stoichiometric NizMnGa (at about 80 K, r ag: 3.4 MPa, Treq: 1.2-2.2 MPa, k u l : 420 kJ m-^5 = 0.124).

References

1. Z. Nishiyama, Martensitic Transformations, Academic Press, New York (1978). 2. J. R. Patel, M. Cohen, Acta MetalL, 1, 531 (1953). 3. K. Otsuka, H. Sakamoto, K. Shimizu, Acta MetalL, 24, 585 (1976). 4. M. A. Krivoglaz, V. D. Sadovsky, Fizika Metal MetalL, 18, 502 (1964). 5. T. Kakeshita, K. Shimizu, S. Funada, M. Date, Acta MetalL, 33, 1381 (1985). 6. T. Kakeshita, T. Shimizu, S. Funada, M. Date, Trans. Jpn. Inst. Met., 25, 837 (1984). 7. T. Kakeshita, K. Shimizu, S. Kijima, T. Yu, M. Date, Trans. Jpn. Inst. Met., 26, 630

(1985). 8. M. Date, Physics in High Magnetic Fields (S. Chikazumi, N. Miura, eds.), p. 44,

Springer, Berlin (1981). 9. T. Kakeshita, K. Shimizu, Proc. ICOMAT-86, p. 230, Nara, Japan (1986).

10. T. Tanaka M. Takahashi, S. Kadowaki, Mater. Trans. JIM, 41, 950 (2000). 11. J-h. Kim, T. Fukuda, T. Kakeshita, Materials Science Forum, 512, 189 (2006). 12. T. Kakeshita, K. Shimizu, T. Maki, I. Tamura, S. Kijima, M. Date, Scripta MetalL,

19,973(1985). 13. T. Maki, M. Shimooka, M. Umemoto, I. Tamura, J. Jpn. Inst. Metals., 35, 1073

(1971). 14. K. Ullakko, J. K. Huang, C. Kantner, R. C. O'Handley, V.V.Kokorin, AppL Phys.

Lett., 69, 1966(1996). 15. R. D. James, M. Wuttig, PhiL Mag., Ml, 1273 (1988). 16. T. Sakamoto, T. Fukuda, T. Kakeshita, T. Takeuchi, K. Kisho, J. AppL Phys., 93,

8647 (2003). 17. T. Kakeshita, T. Takeuchi, T. Fukuda, M. Tsujiguchi, T. Saburi, R. Oshima, S. Muto,

AppL Phys. Lett., 11, 1502 (2000).

4.4 Control of the Solidification Process by High Static Magnetic Field: Application to YBaCuO Superconductors

Since the synthesis of the superconducting YBaCuO phase in 1987 by Wu et al., ^ many efforts have been made on processing it to obtain a material suitable for high current applications. The superconducting properties of the orthorhombic YBa2Cu307 are highly anisotropic, and in particular, critical currents are much larger in the ab plane of the lamellar structure (Cu02 planes) than along the perpendicular c axis. Grain boundaries are weak electrical junctions, and local measurements confirm that superconducting magnetization currents loops only flow inside individual grains. For high current applications, such as large monodomains for superconducting magnetic bearings or long conductors for current limitation devices, it is necessary to process large grained samples with controlled crystallographic orientation.


4.4.1 YBaCuO Growth

The YBa2Cu30^ (123) phase incongruently melts at 1015°C in air to form the mixture of a Ba- and Cu- rich Hquid and of the YzBaCuOs (211) solid phase (so-called "green phase"). During cooling, the 123 phase is formed by a peritectic reaction between the hquid and the 211 phase. In a typical peritectic recombination, the 123 phase should nucleate at each 211/liquid interface on cooling, thus leading to a small-sized multigrain material, since many green phase 211 particles are dispersed in the liquid above 1015°C. However, using high temperature optical microscopy, Rodriguez et al. ^ demonstrated the nucleation of the 123 phase directly in the liquid. Cima et al. ^ and Izumi et al.^' proposed a model where yttrium is dissolved from 211 phases and diffuses to the 123/liquid interface to feed the 123 growth. Following Nakamura et al.,^' the growth speed is then governed by yttrium diffusion in the melt and also by growth kinetics at the interface. The growth is a slow process and typical values of the growth speed have been experimentally measured below 1 mm h"^ The resulting material is an YBa2Cu307 matrix (superconducting phase) including finely dispersed insulating Y2BaCu05 particles.

4.4.2 Magnetic Texturation Feasibility

A. Mechanisms High static magnetic fields induce magnetic alignment of solidifying crystals. Two mechanisms, magnetocrystalline anisotropy and shape anisotropy, account for this effect where in each case, a magnetic torque acts on 123 nuclei freely suspended in the melt. If a solidifying single crystal possesses a magneto-crystalline anisotropy, then its magnetization M is generally not parallel to the applied field B. The sample is then submitted to a torque r = VM AB^ with V the crystal volume, and rotates in order to align its major (algebraic value) susceptibility axis parallel to the field. In the case of a shape anisotropy, the demagnetizing field and hence the magnetization depends on the angle between the field and the particle orientation. The sample tends to rotate in order to maximize its magnetization (so that it minimizes its internal demagnetization field) and hence aligns its longest direction parallel to the field, whatever the sign of the susceptibility may be.

In both mechanisms, the critical parameter for the occurrence of magnetic alignment is the difference in magnetic energy between the aligned and misaligned crystal as compared to the thermal disordering energy kT (where k is the Boltzmann constant and T the temperature). For a single crystal with magnetic anisotropy Ax, the necessary relation is:

R~ AEanisotropy = ^X ' V > ^T ( 1)

2^0


For an elongated shape with a demagnetizing factor n (0 < n < 0.3), this relation becomes:

4 2^0

A second limiting factor is the orientation time within the solidification time. The orientation kinetic has been mathematically derived and experimentally observed for a suspension of fibers in a viscous fluid. ' ^ It is found that the tangent of the angle between the applied field and an orientation axis of the particle follows a decreasing exponential law with a time constant T: tan(^) = ian{eo)e~''^. The time constant T is given for both magneto-crystalline and shape anisotropy mechanisms as 7 = A/(2A£'), where A is a viscous coefficient defined as the ratio between the viscous torque and the rotation speed. As both A and AE are proportional to the volume of the particle, T is independent of its size. A rough estimation can be given for a sphere (A = 8 j^rir\ with r the radius and n the fluid viscosity), then T = ^"^ must be much lower than the solidification time.

AXB'

B. Magnetic Alignment of YBaCuO As the anisotropy of Cu02 planes of the lamellar structure could lead to a magnetic orientation at high temperature, the melting of precursors and the growth and magnetic orientation of bulk YBaCuO material was then tested in a high field and high temperature facility. A mixture of Y2BaCu05, BaCu02 and CuO was heated to 1050°C, maintained for two hours in a 5-T magnetic field, then cooled at 20°C h" to recombine the YBa2Cu307 phase through the peritetic reaction.

After processing. X-ray diffraction pole figures were measured on surfaces cut parallel and perpendicular to the applied field Ha. On the surface perpendicular to Ha, (007) peaks are located in a very small area parallel to Ha, while they are very weak in the other direction. These results indicate that the resulting microstructure of the magnetically processed YBaCuO sample consists of highly orientated crystals with the c axis parallel to the applied field. ^ This structure is also evidenced by SEM micrographs showing a layered structure where 10 micron-thick platelets following the ab planes are stacked together.

During the recombination, nuclei of the YBaCuO phase have been magnetically aligned in the surrounding liquid. Orientation by a shape mechanism is rejected since the resulting microstructure should have led to platelets aligned parallel to the applied field. The actual mechanism is then the existence of a remaining magnetic anisotropy at the peritectic temperature, with a larger value along the c axis.

C. Nuclei Size and Orientation Time The magnetic anisotropy of the YBaCuO phase is associated with the


CUO2 planes of the structure. The room temperature value A;f(300 K) is about lO"'* emu mole"\ and is expected to decrease slowly with the temperature because of the strong correlations in the Cu-0 layers. ^ The critical volume for the magnetic orientation of a crystallite (A£ = kT at the solidification temperature) is much smaller than 1 jim^: at 1500 K, assuming a temperature independent anisotropy and with a 5-T magnetic field, the value of the ratio Ê /kT is then about 5000. ^ The time constant T is about 1 s in 5 T, even for a viscosity 10,000 times larger than that of water. Considering the slow speed of the solidification process, the orientation time should not be considered as a limiting factor.

D. Improvement of Magnetic and Superconducting Properties of Bulk YBaCuO

First, magnetization cycles from zero field cooled state were measured from 0 t o 6 T a t 4 K o n a 2 x 2 x 2 mm^ cube cut from the center of the magnetically aligned sample and from a sample processed without field. The sample processed without magnetic field shows no differences between vertical and horizontal sample orientation in the measuring field, in agreement with a disordered polycrystalline structure. The measured remnant magnetization is then about 0.5 T. In contrast, a large anisotropy is observed for the field processed sample, with a larger cycle when the measuring field is parallel to the field applied at high temperature, confirming the c axis orientation. Moreover, even the magnetization cycle width measured in the perpendicular direction for this sample is larger than the one of the zero field processed sample: the remnant magnetization reaches 1.6 T along the direction of the alignment field and is still about 1 T in the perpendicular direction.

These figures demonstrate that the magnetic alignment enhances the superconducting critical current density (which is proportional to the magnetization cycle width) by taking advantage of the alignment of the c axis and hence of the ab plane, which can carry larger currents. This alignment also provides a better connection between grains, since both anisotropic values are larger than in the disordered sample processed without field.

However, these grain boundaries are still weak, limiting junctions for large-scale superconducting current, and the number of grains needs to be reduced, possibly to a single one, to obtain very large magnetizations or long length conductors. In order to improve growth and reduce the nucleation rate, the process has been optimized with the help of in situ magnetic measurement at high temperatures.

4.4.3 In situ Magnetic Susceptibility in High Fields

A. Experimental Setup When a sample of susceptibility x is placed in a magnetic field B gradient


region, it is then submitted to a force:

2jUo

Hence, by measuring the magnetic force exerted on an YBaCuO sample during its processing, it is then possible to measure in real time its magnetic susceptibility at high temperature and quantitatively determine the phase transitions encountered.

A specially designed tubular furnace has been inserted in the vertical room temperature bore of an Oxford Instrument superconducting magnet. The high temperature zone of the furnace exists in a working alumina tube surrounded by either a SiC machined tube heater or a heating wire embedded in high temperature cement. The heater is insulated from the exterior by a thin alumina/silica wool insulator, and the overall system is inserted in a water-cooled jacket to remove heat and protect the magnet cryostat.

The sample in its crucible is held on top of an alumina thin tube that is put on the plateau of an electronic balance placed far below the magnetic field. The sample temperature and magnetic weight are continuously recorded by computer during the process. The device is conveniently used for 25 g pellets, but larger samples of up to 200 g can also be processed in a similar device. Due to the sample weight, the field gradient and the balance quality, the magnetic susceptibility can be measured with a sensitivity of about 10"' emu g"\ i.e., 10" S.I.

B. Standard MTG Process The standard Melt Texture Growth (MTG) occurs in the slow cooling from the partial melting state above the peritectic temperature as described below.

The starting material is a pressed pellet of a mixture of YBa2Cu307, Y2O3, Ag20 and PtOi powders. Y2O3 is added to provide excess Y2BaCu05 particles, which maintain the sample shape and are known to increase critical currents. Ag20, which transforms into metal silver, is known to reduce cracks, and Pt02 also enhances critical currents by reducing the coarsening of the Y2BaCu05 particles. The sample is rapidly heated to 1100°C to transform all YBa2Cu307 and Y2O3 into a liquid phase containing Ba and Cu and Y2BaCu05 solid particles. It is rapidly cooled to 1020°C and slow cooling (TC h ' ) is then applied down to 890°C to promote the peritectic recombination of the 123 phase.

C. Magnetic Signature of Melting, Solidification and Oxygen Exchanges The magnetic susceptibility recorded during this process is shown in Fig. 4-4-1. On heating, a small increase is seen at 900°C and this is due to the sintering of the system, together with a first transformation of Y2O3 into


6,5 10-

6 10-'

5,5 10-'

5 10-' -

4,5 10-' -

4 10-' 600 700 800 900 1000

Temperature / °C

1100 1200

Fig. 4-4-1 Magnetic susceptibility recorded during a standard Melt Texture Growth process of an YBaCuO sample. All phase transformations and evolution can be monitored: sintering (a), melting (b to c), Curie-Weiss susceptibility decrease and oxygen loss in the liquid state (c to d), irreversibility due to poor oxygen uptake on fast cooling (d to e), large oxygen uptake during slow cooling (e to f), main YBaCuO solidification (f to g), remaining phases solidification (h to i).

YiBaCuOs. Melting is then evidenced by a large increase, the liquid containing more magnetic Cu ^ ions. This increase takes place in a large temperature range (from QGO 'C to 1020°C) due to the high heating rate. The susceptibility then decreases due to the Curie law behavior of the paramagnetic liquid combined with a change in the copper valence. On heating, the ionic liquid loses oxygen so that magnetic Cu ^ is transformed into nonmagnetic Cu^ following

2[Cu^tg„et.c - O ^ - ] - ^ [ (Cu; , , , , g , e t i c ) " O ^ " ] + ^ O 2 ( 4 )

On cooling, the susceptibility increases, but a large hysteresis is observed since oxygen uptake in the sample has a slow kinetic. From 1020°C, the increase is enhanced, the slow cooling applied at that time allowing more oxygen uptake. Solidification takes place in a very narrow temperature window, as seen from the rapid susceptibility decrease. At lower temperatures, the remaining BaCu02 and CuO phases solidify and are responsible for the new susceptibility increase.

D. Anomalous Solidification In order to reduce the overall time spent in the liquid state (to avoid reactions with the crucible and parasitic nucleations) but still promote growth by slow cooling, the heat treatment has been modified as follows: rapid cooling was maintained down to a few degrees above the previously determined solidification point and the slow cooling applied only from that


7 10- — — — „ ^ _ „ - , _ _ - ^ _ _

Reference process

Short process

4 10-: ^ '800 850 900 950 1000 1050 1100 1150

Temperature / °C

Fig. 4-4-2 Anomalous solidification observed by magnetic susceptibility when no slow cooling is applied from 1020°C prior to solidification. Compared to the standard MTG process, the susceptibility increases slowly from (a) to (b) due to poor oxygen uptake. Rapid solidification is then evidenced by a sharp kink in the susceptibility curve. The rapid increase from (b) to (c) was correlated by thermogravimetric measurements with a very fast and anomalous oxygen uptake prior to the solidification.

lower temperature. As seen in Fig. 4-4-2, the magnetic susceptibility exhibits a sharp anomalous increase prior to the solidification. The same experiment was conducted without magnetic field to allow a mass measurement only of the oxygen exchanges, and a rapid uptake of oxygen was observed at the same temperature as the anomalous susceptibility rise. Moreover, the susceptibility change calculated from the oxygen mass uptake and the resulting copper valence change (Aj = 1.1 x 10" emu g~*) was in very good agreement with the actual change (1.3 x 10~ emu g~ ).

In both samples, the microstructure consists of very small spherulitic grains, indicating rapid nucleation and poor growth. Although the mechanism remains unclear, we suggest that since the rapidly cooled sample was far from oxygen equilibrium, oxygen uptake occurred too rapidly at that time, triggering a very fast and multiple nucleation as the equilibrium peritectic temperature increased with oxygen content.

E. Double Dwell Process In order to obtain both equilibrium oxygen and very large growth in a reduced time, a double step process has been defined: the heating remains unchanged, rapid cooling is still applied but at a few degrees above the experimental solidification point, and the sample is maintained at constant temperature until oxygen equilibrium is reached. Slow cooling of a few degrees is then applied and a second temperature dwell is maintained until complete solidification. In this process, the completion of oxygen equilibrium and then peritectic recombination are evidenced in real time by the magnetic susceptibility, as seen in Fig. 4-4-3.


6,5 10-' —~~

6,0 10 '

4,5 10 ' 900 950 1000

Temperature / °C

1100

Fig. 4-4-3 Magnetic susceptibility during the "double dwell" process. On cooling, the sample temperature is stabilized at 955°C until the oxygen uptake evidenced by the susceptibility increase is complete. A further temperature step is maintained at 946°C until the solidification evidenced by the susceptibility decrease is complete.

In this figure, both the standard MTG process and the double dwell process are presented for comparison. From 1020°C to about 955°C, the susceptibility slope remains constant since almost no oxygen uptake is allowed by the fast cooling, while a larger increase was seen for the slow cooling of the standard MTG process. At 955°C, the susceptibility rose at a constant temperature until it become saturated at a constant value, indicating that oxygen had reached its equilibrium. Compared to the standard process, the same susceptibility values were attained at that temperature. The susceptibility increased again at the slow cooling until the second dwell was applied at 946°C. Then after a few hours, solidification occurred and the slow cooling was applied again after the susceptibility decrease had stopped.

The resulting microstructure of the sample indicated a 17-mm diameter single grain, and magnetic flux trapping confirmed the circulation of the magnetization currents in a single loop at the scale of the full sample.

The magnetic field has been used with two advantages in this study: all phase transformations could be magnetically monitored to optimize the growth process, and the single orientation was controlled by the magnetic alignment.

4.4.4 Supercooling Behavior of the Powder

A. Precursor Effect In the double dwell process, the temperature profile was determined following the magnetic susceptibility behavior of the material. A large supercooling was observed in this case, with onset of the solidification


< :

—^*

^r:^ ^ 1 —

r ;

900 950 1000 1050 Temperature / "C

1100 1150

Fig. 4-4-4 Magnetic susceptibility versus temperature for three precursor batches. The melting and solidification is strongly dependent on the precursor batch used for the starting powders, as seen from the magnetic susceptibility measured in three samples with the same composition and the same heat treatment but from three different YBaCuO powder batches. The arrows indicate the different solidification points.

near QSC'C. This supercooling behavior is strongly dependent on the composition and the kind of process used. Even keeping the same composition and thermal process, strong changes in this supercooling behavior can be evidenced when similar starting materials, but from different providers, are used.

As seen in Fig. 4-4-4, a particular composition using three different YBaCuO powder batches from two different providers exhibits a different solidification temperature when the same cooling process is applied after melting (heating at 240°C \f\ step at 1100°C for 30 m, rapid cooling to 1020°C, then slow cooling at PC h ' ) .

Defining a successful solidification process then requires careful analysis of the magnetic susceptibility for each new precursor batch in order to adapt the temperature profile to the supercooling behavior.

B. Overheating Effect The supercooling behavior for a given batch and a given process is also very sensitive to the maximum temperature reached in the liquid state. A classical Melt Textured Growth process was applied at two different maximum temperatures in the liquid state. A 45°C increase in the overheating temperature induced an IPC reduction of the solidification temperature.

C. Solidification Nuclei above the Melting Point The solidification temperature dependence on the starting material and on the overheating temperature suggests that the liquid phase, prior to the


solidification, retains some information about the history of the sample. In several systems (YBaCuO, BiSrCaCuO and SmCo), it was found that magnetic orientation was also very sensitive to the maximum temperature reached in the liquid state: a higher overheating leading to a larger supercooling and a worse orientation.'^'

It has been suggested'^' that nuclei of the solid phase could survive above the melting point of the bulk phase and that those nuclei may control the solidification and orientation. With a low overheating above the melting point, the nuclei remain in the liquid, are freely oriented by the magnetic field and trigger the solidification with a small supercooling. However, if a large overheating is applied, the nuclei are dissolved and hence a larger supercooling is necessary to nucleate from heterogeneous phases, such as the crucible walls, that cannot be magnetically aligned.

4.4.5 Conclusion

Bulk YBa2Cu307 superconductors can be textured by solidification through a peritectic reaction performed at high temperature in high magnetic field (7 T). The superconducting properties of the material are improved due to the alignment of the ab planes and to a better connection between grains.

The high temperature magnetization of the sample in the high magnetic field can be monitored in real time, following all phase transformations in the bulk sample. An optimized process can then be defined after determining the solidification temperature, which is strongly dependent on the process and the starting materials. In an optimized double dwell process, the oxygen equilibrium in the first temperature dwell above the solidification point is probed by the magnetic susceptibility. The solidification itself is then monitored during a second step a few degrees below. A large oriented grain with improved superconducting properties is then obtained.

High temperature, high field magnetization measurement is a powerful tool to study the general phenomenon of solidification. Relations between overheating, supercooling and magnetic orientation can be experimentally investigated in order to test for the existence of soUdification nuclei above the melting point.

References

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Haggerty, J. Appl Phys., 72, 179 (1992). 4. T. Izumi, Y. Nakamura, Y. Shiohara, / Mater. Res., 7, 1621 (1992). 5. Y. Nakamura, Y. Shiohara, J. Mater. Res., 11, 2450 (1996). 6. T. Kimura, M. Yamato, W. Koshimizu, M. Koike, T. Kawai, Langmuir, 16, 858

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7. B. Michaud, E. Beaugnon, A. Sulpice, R. Toumier, J. Claverie, Mater. Trans., JIM 41, 8 (2000).

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[Springer Series in Materials Science] Magneto-Science Volume 89 || Magneto-thermodynamic Effects