Magnetocaloric effect materials for magnetic refrigeration Ekkes Brück Introduction Magnetic cooling Giant magnetocaloric effect Outlook Review: E. Brück, Magnetic refrigeration near room temperature, Handbook of magnetic materials Vol 17 chapt. 4 (2007) ed. K.H.J. Buschow 1
Magnetocaloric effect Basic magnetocalorics Two energy reservoirs spins lattice � E 2
Magnetocaloric effect Basic magnetocalorics spins lattice � E 3
Magnetocaloric effect Domain movement 4
Magnetocaloric effect Magnetic cooling: Debye and Giauque 1926 61g Gd 2 (SO 4 ) 3 ·8H 2 O, ∆ B=0.8T, 1.5K → 0.25K Nobel prize 1949 5
Magnetocaloric effect Zeeman effect for state with total moment J • Ground state J is 2J+1 times degenerated: J z =-J, -J+1, … J • Splits in magnetic field into sublevels = − ⋅ = − µ ⋅ J z H µ B B P z 2 1 =< >= µ E H g J B 0 P Lande B z z J -1 ∆ = µ + − + E g B L B z -2 = − 3 L ( L 1 ) S ( S 1 ) + g Lande 2 2 J ( J 1 ) B • Spectroscopic splitting factor g Landee depends on L, S, and J • Splitting at B=1 Tesla in the order of meV Atom behaves as if it has effective moment: µ eff =-g L µ B J • 6
Magnetocaloric effect Statistical physics description 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, 7
Magnetocaloric effect Z is needed to have the proper normalization The strength of statistical physics is that by calculating Z a lot of information about the system can be derived. The Helmholtz free energy is: while the Gibbs free energy is: 8
Magnetocaloric effect Thermodynamic relations: Differential of Gibbs free energy G G G ∂ ∂ ∂ ( ) ( ) , ( ) S T B p M T B p V T B p = − = − = − , , , , , , T B p ∂ ∂ ∂ , B p T p T B , , , Entropy Magnetization Volume Differential of entropy S S S ∂ ∂ ∂ dS dT dB dp = + + T B p ∂ ∂ ∂ B p T p T B , , , 9
Magnetocaloric effect Identification of terms ∂ C = + − α S B , p dS dT dB Vdp ∂ T B T , p ∂ Adiabatic process at = − T S dT dB ∂ constant pressure C B ∂ ∂ B , p T , p = S M Maxwell relations ∂ ∂ B M ∂ B T T B S dB = Magnetic entropy m ∆ ∫ T ∂ B 0 10
Magnetocaloric effect From definition of specific heat S 0 can be set to zero because it is not depending on field Easy measurable 11
Magnetocaloric effect Experimental determination from magnetic measurements − ∆ = ∆ M ( T , B ) M ( T , B ) + + i 1 i 1 i i ( , ) S T B B ∑ − m T T + i i 1 i 12
Magnetocaloric effect Continuous phase transition In the absence of an external field, H=0, the system with exchange interaction J/k=1may spontaneously order. = − 1 1 1 1 1 2 F NJm - NHm+NT ( -m) ln ( -m)+( +m) ln ( +m) 2 2 2 2 2 T=0.2J/k T=0.25J/k T=0.3J/k 13
Magnetocaloric effect First order phase transition If interactions with quartets play a role this may result in local minima in the free energy. T=0.02 J/k = − 1 1 1 1 1 4 F NJm - NHm+NT ( -m) ln ( -m)+( +m) ln ( +m) T=0.0225 J/k 2 2 2 2 2 T=0.025 J/k 14
Magnetocaloric effect MCE in iron 10 6T 0T ∆ T [K] C p [J/mol ·K] 3T 3T 0.8T 0 T [K] T [° C] Magnetic ordering T 15
Magnetocaloric effect MCE in gadolinium Total entropy vs reduced temperature of gadolinium in low field (blue) and high field 9T (purple) (Gschneidner et al) 16
Magnetocaloric effect MCE in gadolinium Magnetic entropy change (green left scale) and Temperature change (red right scale) Derived from specific heat data. (Gschneidner et al) 17
Magnetocaloric effect The magnetocaloric properties of selected binary intermetallic compounds - ∆ S M ∆ T ad T C Dens. (mJ/cm 3 K) (K) (K) (g/cm3) Compound 0-2T 0-5T 0-2T 0-5T Gd 4 Bi 3 332 15 27 2.2 4.2 10.073 Gd 4 (Bi 2.25 Sb 0.75 ) 308 27 47 3.7 6.8 9.679 Gd 4 (Bi 1.5 Sb 1.5 ) 289 24 47 3.1 6.5 9.259 Gd 4 (Bi 0.75 Sb 2.25 ) 273 26 49 3.2 6.4 8.834 Gd 4 Sb 3 265 29 55 3.2 6.4 8.414 Gd 2 In 194 18.5 37 2.0 4.4 8.316 ~50 a Gd 2 In -12 -4 -0.7 -0.2 8.316 a Temperature at which ∆ SM has the largest positive value and ∆ Tad has largest negative MCE value 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 457 Niu X J, Gschneidner K A Jr, Pecharsky A O and Pecharsky V K 2001 J. Magn. Magn. Mater. 234 193 18
Magnetocaloric effect The magnetocaloric properties of selected binary intermetallic compounds - ∆ S M ∆ T ad T C Density (mJ/cm 3 K) (K) (K) (g/cm 3 ) Comp. 0-2T 0-5T 0-2T 0-5T Nd 2 Fe 17 325 25 46 1.9 4.0 7.797 Gd 7 Pd 3 323 22 57 3.0 8.5 8.707 ~12 b 74 c 4.2 c TmAg 11 0.8 10.169 ~ 7 a -55 c -0.9 c TmAg -26 -0.4 10.169 ~10 b 118 c 3.6 c TmCu 25 0.6 9.692 6.7 d -131 c -1.8 c TmCu -68 -0.4 9.692 a Temperature at which ∆ SM has the largest positive value and ∆ T ad has largest negative MCE value b Maximum in MCE (no magnetic ordering observed at this temperature) c Interpolated d Néel temperature Dan’kov S Yu, Ivtchenko V V, Tishin A M, Gschneidner K A Jr and Pecharsky V K 2000 Adv. Cryog. Engin. 46 397 Canepa F, Napoletano M and Cirafici S 2002 Intermetallics 10 731 Rawat R and Das I 2001 J. Phys.: Condens. Matter 13 L379 19
Magnetocaloric effect The magnetocaloric properties of selected ternary intermetallic compounds. - ∆ S M ∆ T ad a T C Dens. (mJ/cm 3 K) (g/cm 3 ) (K) Compound 0-2T 0-5T 0-2T 0-5T GdCoAl 100 37 79 --- --- 7.575 TbCoAl 70 41 80 --- --- 7.649 DyCoAl 37 70 125 --- --- 7.619 GdPd 2 Si 17 42 142 3.2 8.6 9.358 HoCoAl 10 100 171 --- --- 7.961 Zhang X X, Wang F W and Wen G H 2001 J. Phys.: Condens. Matter 13 L747 20
Magnetocaloric effect dimensionlless lattice heat capacity of three solids with different Debye temperatures, Θ D, vs. temperature 1.0 1.0 Θ D = 150 K Θ D = 150 K Lattice heat capacity, C L / R Lattice heat capacity, C L / R 0.8 0.8 Θ D = 350 K Θ D = 350 K 0.6 0.6 Θ D = 250 K Θ D = 250 K 0.4 0.4 0.2 0.2 0.0 0.0 0 0 50 50 100 100 150 150 200 200 250 250 300 300 Temperature, T (K) Temperature, T (K) 21
Magnetocaloric effect Rules for magnetocaloric effect Larger moment ⇒ larger ∆ S & ∆ T S mag ≈ J Lower temperature ⇒ larger ∆ S & ∆ T Lower heat capacity Lower thermal agitation 22
Magnetocaloric effect Magnetic refrigeration: External magnetic field changes entropy of magnetic moments No CFCs, easy scalable, high efficiency, permanent magnets 23
Magnetocaloric effect Chubu and Toshiba Refrigerator 2003 Gd metal Rotating magnet 0.76 T Cooling power 60 W T span 20 K 24
Magnetocaloric effect 25
Magnetocaloric effect Other AMR prototypes Magnetic AMR AMR Name Remarks Ref. Field Type Material (T) Ames reciprocatin (Zimm et COP T 10 Laboratory/ Gd spheres 5 (S) g al. 1998) Astronautics (Bohigas et Barcelona rotary Gd foil 0.3 (P) Olive oil al. 2000) epoxy University of reciprocatin (Richard et Gd , Gd .74 Tb .26 2 (S) bonded Victoria g al. 2004) pucks Lab. Electric reciprocatin (Clot et al. COP R 2.2 Gd foil 0.8 (P) Grenoble g 2003) Gd, Gd-Er, (Zimm et Astronautics rotary spheres LaFeSiH 1.5 (P) 4 Hz al. 2006) particles Natl Inst. Torque 10 (Vasile et al. Appl. Sci. / rotary Gd plates 1 (P) Nm 2006) Cooltech Gd spheres; Xian Jiaotong reciprocatin (Gao et al. COP T 25 Gd 5 (Si,Ge) 4 2.18 (E) g 2006) Univ. pwdr. ∆ T 50K University of reciprocatin Gd , Gd .74 Tb .26 (Rowe et al. 2.0 (S) Victoria g Gd .85 Er .15 2006) 26
Magnetocaloric effect Replace Gd with material with large MCE 1990 FeRh (Nikitin et al.) 1997 Gd 5 Si 2 Ge 2 （ (Percharsky & Gschneidner Jr.) 1998 RCo 2 (Foldeaki et al. ) 2000-2002 La(Fe,Si) 13 (Zhang et al., Fukamichi et al.) 2001 MnAs 1- x Sb x (Wada et al.) 2002 MnFe(P,As) (Tegus et al.) 2003 Co (S 1- x Se x ) 2 (Yamada & Goto) 27
Magnetocaloric effect Giant magnetocaloric effect in Gd 5 Ge 2 Si 2 Magnetically dilute yet higher effect double transition? Pecharsky & Gschneidner PRL 78 (1997) 4494 28
Magnetocaloric effect Crystal growth Crystal 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 29
Recommend
More recommend
