Ekkes Brück Introduction Magnetic cooling Giant...

Magnetocaloric effect

1

materials for magnetic refrigeration

Ekkes Brück

Introduction

Magnetic cooling

Giant magnetocaloric effect

OutlookReview: E. Brück, Magnetic refrigeration near room temperature, Handbook of magnetic materials Vol 17 chapt. 4 (2007) ed. K.H.J. Buschow


2

spins lattice

Basic magnetocalorics

E

�Two energy reservoirs


3

�

E

Basic magnetocalorics

spins lattice


4

Domain movement


5

Magnetic cooling: Debye and Giauque 1926

61g Gd2(SO4)3·8H2O, ∆B=0.8T, 1.5K →0.25K Nobel prize 1949


6

Zeeman effect for state with total moment J

J

Jz210-1-2

B

• Ground state J is 2J+1 times degenerated: Jz=-J, -J+1, … J• Splits in magnetic field into sublevels• Spectroscopic splitting factor gLandee depends on L, S, and J• Splitting at B=1 Tesla in the order of meV• Atom behaves as if it has effective moment: µeff=-gLµBJ

BH zP ⋅−=⋅−= µBµ)1(2 )1()1(23 +

+−+−= JJ SSLLg Lande zzBLandeP BJgHE µ>==<zBL BgE µ=∆


7

When a system, in contact with a heat bath at temperature T can be in a state with energy E, the probability for this is given by the Gibbs rule:

where k is Boltzmann's constant. Z is called the partition sum,

Statistical physics description


8

Z is needed to have the proper normalization

The strength of statistical physics is that bycalculating Z a lot of information about the system can be derived.

The Helmholtz free energy is:

while the Gibbs free energy is:


9

Thermodynamic relations:

( )pBT

GpBTS

,

,, ∂∂−= , ( )

pTBG

pBTM,

,, ∂∂−= , ( )

BTpG

pBTV,

,, ∂∂−=

Differential of Gibbs free energy

Entropy Magnetization Volume

Differential of entropy

dppS

dBBS

dTTS

dSBTpTpB ,,,

∂∂+

∂∂+

∂∂=


10

VdpdBBSdTT

CdS pTpB α−

∂∂+= ,,Identification of terms

Adiabatic process at constant pressure

dBBS

CTdT pTpB ,,

∂∂−=

∫

∂∂=

B

Bm dB

TM

S 0∆Magnetic entropy

Maxwell relations BT TM

BS

∂∂=

∂∂


11Easy measurable

From definition of specific heat

S0 can be set to zero because it is not depending on field


12

BTT

BTMBTMBTS i ii iiiim ∆−−=∆ ∑

+

++ 111 ),(),(),(

Experimental determination from magnetic measurements


13

Continuous phase transition

In the absence of an external field, H=0, the system with exchange interaction J/k=1may spontaneously order.

T=0.3J/k

T=0.25J/k

T=0.2J/k

−= +m)(+m)-m)+((-m)(- NHm+NTNJmF21ln

21

21ln

21

21 2


14

First order phase transition

If interactions with quartets play a role this may result in local minima in the free energy.

−= +m)(+m)-m)+((-m)(- NHm+NTNJmF21ln

21

21ln

21

21 4

T=0.0225 J/k

T=0.025 J/k

T=0.02 J/k


15

MCE in iron

0T

3T

Cp

[J/m

ol ·

K]

T [°C]

T [K]

∆T [K

]

Magnetic ordering T

10

0

0.8T

3T

6T


16

Total entropy vs reduced temperature of gadolinium in low field (blue) and high field 9T (purple) (Gschneidner et al)

MCE in gadolinium


17

Magnetic entropy change (green left scale) and

Temperature change (red right scale)

Derived from specific heat data. (Gschneidner et al)

MCE in gadolinium


188.316-0.2-0.7-4-12~50aGd2In

8.3164.42.03718.5194Gd2In

8.4146.43.25529265Gd4Sb3

8.8346.43.24926273Gd4(Bi0.75Sb2.25)

9.2596.53.14724289Gd4(Bi1.5Sb1.5)

9.6796.83.74727308Gd4(Bi2.25Sb0.75)

10.0734.22.22715332Gd4Bi3

0-5T0-2T0-5T0-2TCompound

Dens.(g/cm3)

∆Tad(K)

-∆SM(mJ/cm3K)

TC(K)

Ilyn M I, Tishin A M, Gschneidner K A Jr, Pecharsky V K and Pecharsky A O 2001 Cryocoolers 11 ed R G Ross Jr (New York: Kluwer Academic/Plenum) p 457Niu X J, Gschneidner K A Jr, Pecharsky A O and Pecharsky V K 2001 J. Magn. Magn. Mater. 234 193

The magnetocaloric properties of selected binary intermetallic compounds

aTemperature at which ∆SM has the largest positive value and ∆Tad has largest negative MCE value


199.692-1.8c-0.4-131c-686.7dTmCu

9.6923.6c0.6118c25~10bTmCu

10.169-0.9c-0.4-55c-26~ 7aTmAg

10.1694.2c0.874c11~12bTmAg

8.7078.53.05722323Gd7Pd3

7.7974.01.94625325Nd2Fe17

0-5T0-2T0-5T0-2TComp.

Density

(g/cm3)

∆Tad(K)

-∆SM(mJ/cm3K)

TC(K)

Dan’kov S Yu, Ivtchenko V V, Tishin A M, Gschneidner K A Jr and Pecharsky V K 2000 Adv. Cryog. Engin. 46 397Canepa F, Napoletano M and Cirafici S 2002 Intermetallics 10 731 Rawat R and Das I 2001 J. Phys.: Condens. Matter 13 L379

The magnetocaloric properties of selected binary intermetallic compounds

aTemperature at which ∆SM has the largest positive value and ∆Tad has largest negative MCE valuebMaximum in MCE (no magnetic ordering observed at this temperature) cInterpolated dNéel temperature


20

The magnetocaloric properties of selected ternary intermetallic compounds.

7.961------17110010HoCoAl

9.3588.63.21424217GdPd2Si

7.619------1257037DyCoAl

7.649------804170TbCoAl

7.575------7937100GdCoAl

0-5T0-2T0-5T0-2TCompound

Dens.(g/cm3)

∆Tad(K)

-∆SM(mJ/cm3K)

TCa

Zhang X X, Wang F W and Wen G H 2001 J. Phys.: Condens. Matter 13 L747


21Temperature, T (K)0 50 100 150 200 250 300

Latti

ce h

eat c

apac

ity, C

L/R

0.0

0.2

0.4

0.6

0.8

1.0

ΘD = 150 K

ΘD = 350 K

ΘD = 250 K

Temperature, T (K)0 50 100 150 200 250 300

Latti

ce h

eat c

apac

ity, C

L/R

0.0

0.2

0.4

0.6

0.8

1.0

ΘD = 150 K

ΘD = 350 K

ΘD = 250 K

dimensionlless lattice heat capacity of three solids with different Debyetemperatures, ΘD, vs. temperature


22

Rules for magnetocaloric effect

Larger moment ⇒ larger ∆S & ∆T

Lower temperature ⇒ larger ∆S & ∆T

Smag ≈ J

Lower thermal agitation Lower heat capacity


23

Magnetic refrigeration:

External magnetic field changes entropy of magnetic moments

No CFCs, easy scalable, high efficiency, permanent magnets


24

Chubu and Toshiba Refrigerator 2003

Gd metal

Rotating magnet

0.76 T

Cooling power

60 W

T span 20 K


25


26(Rowe et al. 2006)∆T 50K2.0 (S)Gd , Gd.74Tb.26Gd.85Er.15reciprocatingUniversity of Victoria (Gao et al. 2006)COPT 252.18 (E)Gd spheres; Gd5(Si,Ge)4pwdr.reciprocatingXian JiaotongUniv. (Vasile et al. 2006)Torque 10 Nm1 (P)Gd platesrotaryNatl Inst. Appl. Sci. / Cooltech (Zimm et al. 2006)4 Hz1.5 (P)Gd, Gd-Er, spheres LaFeSiHparticlesrotaryAstronautics (Clot et al. 2003)COPR 2.20.8 (P)Gd foilreciprocatingLab. ElectricGrenoble (Richard et al. 2004)epoxy bonded pucks2 (S)Gd , Gd.74Tb.26reciprocatingUniversity of Victoria (Bohigas et al. 2000)Olive oil0.3 (P)Gd foilrotaryBarcelona (Zimm et al. 1998)COPT 105 (S)Gd spheresreciprocatingAmes Laboratory/ Astronautics Ref.RemarksMagnetic Field(T)AMRMaterialAMRTypeNameOther AMR prototypes


27

1990 FeRh (Nikitin et al.)1997 Gd5Si2Ge2（(Percharsky & Gschneidner Jr.)1998 RCo2 (Foldeaki et al. )2000-2002 La(Fe,Si)13 (Zhang et al., Fukamichi et al.) 2001 MnAs1-xSbx (Wada et al.)2002 MnFe(P,As) (Tegus et al.)2003 Co (S1-xSex)2 (Yamada & Goto)

Replace Gd with material with large MCE


28

Giant magnetocaloric effect in Gd5Ge2Si2

Magnetically dilute yet higher effect

double transition?

Pecharsky & GschneidnerPRL 78 (1997) 4494


29

Crystal growthCrystal growth

D=4mm Sphere was cut by spark erosion from as grown rod

Crystal was grown in a mirror furnace by means of traveling solvent floating zone method


30

� Extraordinary magnetic behavior: first-order character of the paramagnetic-ferromagnetic transition.

Unusual behaviorUnusual behavior

0 50 100 150 200 250 300 350 4000.0

0.5

1.0

1.5

2.0

2.5

3.0

Gd5Si

1.65Ge

2.35 Crystal

Sphere d=4mmB=0.05T Stepwise heating mode

a b c

M (

µ B /f

.u.)

T (K)

0 1 2 3 4 50

10

20

30

40

Gd5Ge

2.35Si

1.65 crystal

Sphere d=4mm at 5K

a b c

M (

µ B/f.

u)

B (T)

0 20 40 60 80 100 120 140 160 180 200 220 240 2600

50

100

150

200

250

300

350

400

450

500

550

600

C (

J/m

ol·K

)

T (K)


31

� The high temperature paramagnetic monoclinic phase transforms to the low temperature ferromagnetic orthorhombic phase. The low temperature phase has a higher symmetry than the high temperature, which is the opposite of what is normally observed for other polymorphic systems.


Crystallographic data comes from W Choe PRL v84, n20, p4617, 2000

>Tc: P1121/a, No.14<Tc: Pnma, No.62

bb


32

� Volume decreases when cooling through the transition, i.e., the cell volume in the low-temperature ferromagnetic phase is smaller ( ∆v>0.4%) than in the high-temperature paramagnetic one. This is in contrast with the general physical picture of the magnetovolume effects which are transtions from a low-volume low-moment to a high-volume high-moment state.


Normal:Unusual:


33Gd5Si4 based orthorhombic Pnma Ferro magnetQ.L.Liu et al.

� Recent XRD investigation reported that Gd5(SixGe1-x)4alloys form a completely miscible solid-solution crystallized in the Gd5Si4-type Pnma structure below TCregardless of the composition. Ground state is low temperature (Gd5Si4–based) orthorhombic ferromagnet� Temperature of structural phase transition always coincides with Curie temperature TC.



34x > 0.5 0.4 < x < 0.5 x < 0.3

Gd5Si4 type Pnma Gd5Si2Ge2 type P1121/a Gd5Ge4 type Pnma

T=Si, Ge (Gd3+)5(T26-)2(3e-) (Gd3+)5(T2

6-)1.5(T4-)(2e-) (Gd3+)5(T26-) (T2

6-)2 (1e-)

V. K. Pecharsky and K. A. Gschneidner, Jr., J. Alloys Compd. 260, 98-106 (1997)

b a

What is responsible for the unusual behaviors? What is responsible for the unusual behaviors?

Breaking and making bond RKKY or superexchangeBreaking and making bond RKKY or Breaking and making bond RKKY or superexchangesuperexchange


35

Magnetically driven 1st order structural transition below 270 K.

Gd5Ge2Si2 monoclinic above magnetic transition

orthorhombic below.

Anisotropy on X-tals. Exceptional coupling of lattice with s-state 4f-magnetism.

Hysteretic transition: locking of structure?Mechanical stability?

Summary Gd5Ge2Si2


36

Transition-metal compounds

High abundance (low price)

Intermediate magnetic moment (moderate MC effect)

Strong coupling to lattice (Simultaneous magnetic and structural transitions or metamagnetism)

other alternative


37

La(Fe,Si)13 compound

Cubic CaZn13 type of structure stabilized by addition of 10% Si(Kripyakewich et al. 1968)Invar type of behavior and unusual magnetic transition(Palstra et al 1983)Difficult to obtain single phase.


38

Concentration dependence of Curie temperature and moment

Palstra et al. 1983

Tc increase with dilution


39

LaFe13 system

APL Zhang et al 2000

Fujieda et al 2002

MCE decrease with dilution


40PRB Fujita et al 2003

Tc increase with hydrogen!

Sharp transition maintained!

LaFe13 system with hydrogen


41PRB Fujita et al 2003

LaFe13 system with hydrogen

MCE almost not affected with hydrogen


42

Field driven 1st order metamagnetic transition around 200 K .

La(Fe,Si)13 cubic above magnetic transition

cubic below

volume change 1.5%.

Low Tc can be increased by addition of Cobalt or Hydrogen.

Hysteretic transition: powder after hydrogenation?Mechanical stability?

Summary La(Fe,Si)13


43

MnFeP1-xAsx

Hexagonal Fe2P type of structure

Bacmann, JMMM 1994

Space group:

P62m

Mn 3g sites

Fe 3f sites

P/As 1b&2c sites

_


44

Sample preparation

Starting Fe2P, Mn2As3, Mn & P

mechanical alloying

sintering 1000oC

annealing 800oC


45

Temperature dependence of magnetizationwith different compositions

Tc tunable


46

Temperature dependence in different fields

Strong shift of T cwith field


47

Magnetization process near Tc

Field induced transition with small hysteresis


480.2 0.3 0.4 0.5 0.6 0.7

160

180

200

220

240

260

280

300

320

340

PM

FM

T (

K)

X

Concentration dependence of TC for MnFeP1-xAsx

Somewhat higher TC compared with lit.

Almost linear concentration dependence.


49

Comparison with Gd metal

Step-liketransition

first order

but very littlehysteresis


50

Comparison of magnetocaloric effect in different ma terials

Entropy changeconcentrated inrelevant T interval Tegus et al. Nature 415


51150 200 250 300 3500

5

10

15

20

25

30

35

2 T 5 T

x=0.35

x=0.5

x=0.25

x=0.65x=0.55

x=0.45

MnFeP 1-xAs x

- ∆∆ ∆∆S

m(J

/kgK

)

T (K)

MCE as function of composition

Broad T interval covered


52285 290 295 300 305 310 3150

1

2

3

4

5∆∆∆∆B = 1.45 T

MnFeP0.45

As0.55MnFeP

0.47As

0.53

Mn1.1

Fe0.9

P0.47

As0.53

∆∆ ∆∆Tad

(K

)

T (K)

Direct measurements MSU

Adiabatic temperature-change

Sample dependence need for careful preparation


53

Field driven 1st order magnetoelastic transition 150 K < Tc < 450 K .

MnFe(P,As) hexagonal above magnetic transition

hexagonal below.

Hardly any volume change( 0.1 %) but change of c/a.

Hysteretic transition: Hysteresis depends on grain size?High chemical stability allows As content?

Summary MnFe(P,As)


54

Conclusions

• First order magnetic transition common to the different systems!

• Structural transition may cause extra hysteresis.

• Control of hysteresis very important.

• Evaluation of entropy change needs care.

• Fe and Mn based systems with much lower materials costs.

• Relevant T range covered by La(Fe,Si)13Hx and MnFe(P,As,Si,Ge).

• Sample preparation simplest for MnFe(P,As) with As replaced by other element.


55

Cooltech current N°4 PrototypeIMPORTANT issues:1 – The AMRR Cycle (Active Magnetic Regenerator Refrigeration): with Gd inserts as cross-flow plate heat-exchangers.2 - Amplification of ∆Τ∆Τ∆Τ∆Τ by accumulation of cycles.3 - Reduction in torque (10 Nm) obtained by ensuring a ferromagnetic continuity on the disc.4 - Very low level of noise and vibrations (< 25 dB)5 - Creation of magnetic fields of 0.7 to 2 Tesla with standard permanent magnets.6 - Low thermal losses, completely separate “hot” and “cold” fluid circuits.

Registered Patents, Brand and Models

Outlook


56

Availability

60t?WW prod=90t, avail

10t ?GaNi0.501Mn0.227Ga0.258

4000

4000

none

WW prod=90t, avail 10t ?

1000

Estimated availability

7000tLaManganites

LaMnO3

22000tLaLathanum alloys

La(Fe13-xMx)

No limitation for an industrial production

none

Manganese alloys Mn(As1-xSbx)

MnFe(P1-xAsx)

140tGeGadolinium Silicon alloys Gd4(Si1-xGex)5

1000tGdGd metal

Total availability of MC material

Limiting ingredient

Data : Cooltech source and USGS.GOV


57

2520151050 0 20 40 60 80T (C0)

∆S (

J/K

·kg)

Increased T span with active magnetic regenerator containing different materials with tailored TC

Ekkes Brück Introduction Magnetic cooling Giant...

Documents

Transcript of Ekkes Brück Introduction Magnetic cooling Giant...