methods and problems in the characterization of ... scie… · ddmc 2011 r. burriel, october 24 -...

R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011

R. BurrielInstituto de Ciencia de Materiales de Aragón

CSIC – University de Zaragoza, 50009 Zaragoza, Spain

Methods and problemsin the characterization ofmagnetocaloric materials


We need reliable values for themagnetocaloric parameters

How reliable and how useful are the reported valuesfor ΔTS, ΔST , RC

How valid are for hysteretic transitionsResults from CB(T) : Good, but depends on the T rangeDirect measurementsResults obtained from M(B), M(T)Considerations in hysteretic compounds:

Mixed phase, irreversibility


Effect of a magnetic field change on T and S• Adiabatic temperature change, ΔTS• Isothermal entropy change, ΔST

TC,B

S (T)B

Ent

ropy

, S

Temperature, T

S (T)B = 0

TC,B=0

-ΔST

ΔTS

Magnetocaloric parameters


12)()( BBS STSTT −=Δ

∫−

=−=ΔT BB

BBT dTT

TCTCTSTSS

012

12

)()()()(

TC

S (T)B

Ent

ropy

, S

Temperature, T

S (T)B= 0

TC

ΔTSΔST

Specific heat

Calorimetric methods

∫=T

B dTTTC

TS B

0

)()(

Determination of ΔTS and ΔST


4.2 K – 350 K

Magnetic Field up to 9 T

Heat capacity:

Heat pulse method.

Continuous cooling and

heating thermograms.

Transition enthalpy.

Direct measurement of the

MCE parameters.

Adiabatic field cycles.

Adiabatic installation

Pt thermometer

Thermocouple

Adiabatic shield

Sample holder

CernoxTM

thermometers


0 100 200 3000

10

20

30 0T 1T 2T 3T 4T 5T

CB /

R

T (K)

Adiabatic calorimetryFields B = 1, 2, 3, 4, 5 TFirst-order transitionFerro Para

Heat pulse: Quasiestatic heat, C(T)B = Q/(T2−T1)

Mn1.18Fe0.82P0.75Ge0.25

Experimental techniques for ΔST and ΔTS


Thermograms

• Map the heat capacity of sharp transitions• Cooling and heating thermograms: Thermal hysteresis

dtdTTTC

TTTTdtdQ

dtdTC

dtdT

dTdQ

dtdQ

B

B

δσα

δσδα

)(

])[('

3

44

+≅⇒

−++=

==

Experimental methodδT = Tsample – Tadiabatic shield

0 10000 20000 30000 40000

300

310

320

330

T (K

)

t (s)

Heating thermogram Cooling thermogram

Tocado et al, J. Therm. Anal. Calorim. 84, 213 (2006)


295 300 305 310 315 320 325 33010

20

30

40 0T 1T 2T 3T 4T 5T

CB /

R

T (K)

pulse / cool

Mn1.18Fe0.82P0.75Ge0.25


290 300 310 320 330 340

8,8

9,6

10,4 heat cool 0T 1T 2T 3T 4T 5T

(S −

S0)/

R

T (K)

( )∫=T

BB dTTCTS0

)(

Mn1.18Fe0.82P0.75Ge0.25


• Good at low T

S(T)B=0 >> S(T)B=5Precision of ΔS T and S T are similar

• Low precision at high T

ΔS T < 5% of S TError in ΔS T > 20 times the error in S T

Pecharsky and Gschneidner, J. Appl. Phys. 86, 565 (1999)

Problems from specific heat determinations of S


Pecharsky, Gschneidner, J. Appl. Phys. 86, 565 (1999)

• Improvement combining CB with direct measurements• Avoids the need of CB at low temperatures• Without increased error at high T


Adiabatic systemPt thermometer

Thermocouple

Adiabatic shield

Sample holder

CernoxTM

thermometers

Direct measurements

Control of T, Q and B in the sample and in the surrounding shield


∫=T

H dTT

TCTS Hp

0

,)(

)(

TC

S (T)B

Ent

ropy

, S

Temperature, T

S (T)B = 0

TC

S(T)B

S(T)B=0

ΔTS

ΔTS = [TS(B2) - TS(B1)]

0

2

4

6

0 300 600 900

237,6

238,0

238,4

238,8

Temperature

ΔTS(6T-0)

ΔTS(5-6T)

ΔTS(3-5T)

ΔTS(1.5-3T)

t (s)

T (K

)

ΔTS(0-1.5T)

0T

6T

5T

3T

1.5T

B (T

)

Field

0T


∫=T

H dTT

TCTS Hp

0

,)(

)(

TC

S (T)B

Ent

ropy

, S

Temperature, T

S (T)B = 0

TC

S(T)B

S(T)B=0

-ΔST

ΔST = Q/T = [ST(B2) - ST(B1)]

200 400 600 800

-8

-4

0

4

80.0

1.5

3.0

4.5

t (s)

P (m

W)

B

(T)

0

2

4

6

δT (m

K)

Other methods: Peltier cellBasso et al, Rev. Sci. Instrum. 79, 63907 (2008)


∫+=T

TB

BB dTTTCTSTS

0

)()()( 0 )()()( 0000 TSTSTS TBB Δ+= =

Measured290 300 310 320 330 340

8,4

9,1

9,8

10,5

B = 0 B = 5T

330 332 334 336 33810.1

10.2

10.3

10.4

(S −

S0)/

RT (K)

(S −

S0)/

R

T (K)

direct ΔST

Combined CB(T)and direct ΔST

Entropy curves from- CB, unknown S0- Direct ΔST, common S0

Mn1.18Fe0.82P0.75Ge0.25 Solution to S calculation from CB(T)


260 280 300 3200

4

8

12

16

-ΔS T (

J/kg

·K)

T (K)

1T-0 2T-0 3T-0 5T-0

260 280 300 3200

2

4

6 0 - 1T 0 - 2T 0 - 3T 0 - 4T 0 - 5T

ΔTS (

K)

T (K)

Mn1.26Fe0.74P0.75Ge0.25

Full symbols: Results from direct measurementsContinuous lines: From CB


Magnetocaloric parameters from magnetic measurements

dBT

BTMSB

B

T ∫ ⎟⎠⎞

⎜⎝⎛

∂∂

=Δ0

),(

Gibbs free energyG = U – TS – BMdG = – S dT – MdB

Maxwell relation

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂=⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

∂BT

G TB

G 22

BT TM

BS

⎟⎠⎞

⎜⎝⎛

∂∂

=⎟⎠⎞

⎜⎝⎛

∂∂

[ ] dBTMTMTT

dBT

BTMSB

B

B

B

T ∫∫ −−

=⎟⎠⎞

⎜⎝⎛

∂∂

=Δ0 12

120

)()(1),(


Problem with derived “spikes” from Maxwell relation

The colossal effect for Mn1-xFexAsNature Materials 5, 804 (2006)


260 280 300 3200

20

40

60

0T 0T 0T 1T 1T 3T 3T 6T 6T 6T

C

p,B

/ R

T (K)

x = 0.01

Mn1-xFexAs (x=0.01)

Heat pulseHeating thermogramsCooling thermograms

G.F. Wang et al.Magneto-Science 2011,Shanghai


260 280 300 3200

10

20

30

40

1T 1T 3T 3T 6T 6T 6T 6T

-ΔS

T (J/k

gK)

T (K)

x = 0.01

260 270 280 290 300 310 3200

5

10

15

20

ΔTS (K

)

T (K)

1T 2T 3T 4T 5T 6T 1T 3T 6T 1T 3T 6T

x = 0.01

Mn1-xFexAs (x=0.01)

Symbols: from direct measurements. Dotted and solid lines: from heat capacityon cooling and heatingGiant MCE but not colossal

G.F. Wang et al.Magneto-Science 2011, Shanghai

R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011( )∫

=

=

Δ−=Δ

tB

B

BanPFex dB

HTCMMS

0 0

0)()(

0

1

2

3

4

5

6

7

8

9

220 230 240 250 260 270 280

T (K)

B (T

)

(dS)T

(dM)B

Para

Ferro

History

depe

nden

t

.

Hysteretic compounds

Mixed phase:

M = x·MP + (1-x)·MF

Calculation from M(B)T

ΔST = ΔS + ΔSex

∫ ⎟⎠⎞

⎜⎝⎛

∂∂

−=ΔtB

BPFex dB

TxMMS

0

)(

Tocado et al, J. Appl. Phys. 105, 093918 (2009)


220 240 260 2800

10

20

30

-ΔS

T (J/k

g.K

)

T (K)

cooling from M(B)

T

from M(T)B

Same results for ΔST from:• Field dependent magnetization M(B)T

with complete phase conversion• Temperature dependent magnetization

M(T)B• And also from Cp,B(T) and direct values

220 240 260 2800

10

20

30

40

50

60

70

80

-ΔS

(J/k

gK)

T (K)

ΔB=1T ΔB=2T ΔB=3T ΔB=4T ΔB=5T ΔB=6T ΔB=7T ΔB=8T ΔB=9T

Increasing Field

Results for ΔST from M(T)B, M(B)T, and M(B)T with cycling in T(same scale)


Heating process:• D A, Stable phase Ferro-• A B, Transition to Para-

Cooling process:• B C, Stable phase Para-• C D, Transition to Ferro-

A to C, unstable ∂S/∂T < 0

Phase equilibrium at TeqGE = GG

300 320

7.4

7.6

7.8

8.0

8.2

S/R

T(K)

Paramagnetic

Ferromagnetic

A

B

C

D Teq

E

F

GAACB

Entropy curve

Irreversibility: Entropy dS ≥ dQ/T


( )

A

BpACBA

A

BBBAAA

ACB

B

ABA

THS

dTTCHAHST

STHSTHSTH

ASdTGG

Δ>Δ⇒

=Δ>+Δ=Δ

⇔>Δ+Δ−=+−−=

==−

∫

∫

,

0

Estimation of the area AACB (as a triangle):

300 320

7.4

7.6

7.8

8.0

8.2

S/R

T(K)

Paramagnetic

Ferromagnetic

A

B

C

D Teq

E

F

GAACB

( ) )(21)(

21

CACAABACB TTSTTSSA −Δ=−−≅

CA

Aheatheat TT

TSS+

Δ≅Δ2'

Heating

Estimation of the real entropy jump

A

'

THS Δ

=Δwhere the pseudo-entropy


300 320

7.4

7.6

7.8

8.0

8.2

S/R

T(K)

Paramagnetic

Ferromagnetic

A

B

C

D Teq

E

F

GA

ACB

( )CA

CAcoolheat

B

Ccoolheat

coolBpA

D

heatBp

DAABBCCD

TTTTSSSS

TdTTC

TdTTC

SSSSSSSSdS

+−

Δ+Δ+Δ−Δ+−

≅−+−+−+−==

∫∫

∫''''

)()(

0

,,,,

Estimation of the real entropy jump

Similarly, on cooling

A

CADDC

TH

S

AGGΔ

<Δ⇒

=−

CA

Ccoolcool TT

TSS+

Δ≅Δ2'

Heating-cooling cycle DABCD


Error in the measurement of the entropy cycle

200 220 240 260

8

10

ΔS'cycle

ΔS'coolS'/R

T(K)

Pseudo-entropy by integration of Cp/T

Mn1.1Fe0.9P0.82Ge0.18TA

TC

ΔS'heatB = 6 T

( )coolheatcrit

coolheathys

crit

crit

hyscycle

TTT

TTTT

HS

TT

SS

+=

−=Δ

Δ=Δ

Δ−≅

Δ

Δ

2/1

'

''

It coincides with theexperimental value: 6%


Hysteresis: possible mixed phase

Wrong application of the Maxwell relation in M(B)T measurements

Unphysical “colossal” effect ΔSex

Irreversibility: Entropy dS ≥ dQ/T

Cycle of pseudo-entropy fromcalorimetric measurements

Effects of hysteresis and irreversibility

crit

hyscycle

TT

SS Δ

−≅Δ

Δ

''

( )∫=

=

Δ−=Δ

tB

B

BanompPFex dB

HTC

MMS0 0

0, )()(

Paramagnetic

Q

G

F

E

D

C

B

AEn

trop

y

Temperature

P

Ferromagnetic

GC < GBGA < GD


0

1

2

3

4

5

6

7

8

9

220 230 240 250 260 270 280

T (K)

B (T

)

Para

Ferro

History

depe

nden

t

Hysteretic compounds

Reduction of the efficientT region in practical cycles

Reduced effectiveparameters and coolingefficiency

R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011 0 20 40 60 80 1000

10

20

30

0

10

20

300

40

80

120

B (a

.u.)

B0

B1

Ferro

Para

Hystere

tic

ΔTS (a

.u.)

T (a.u.)

-ΔS T (a

.u.)

S (a

.u.)

S(B0)

S(B1)

Phase diagram• Ferro - para• First order• Hysteresis

Entropy curves at fields B0 and B1,heating and cooling

Derived entropychange ΔST

Derived temperaturechange ΔTS


Conclusions

Precise determination of the MCE parameters.

Measurement and control of: Q, T, and B ΔTS and ΔST

Determinations from CB, good at low T, no precision at high T.Solved with CB around Tc plus one direct measurement of ΔST.

Hysteretic compounds. Spike problem from M(B)T

Irreversible entropy. Small correction.

Hysteresis: reduces the effetive ΔTS, ΔST and RC


Contributors to this work at theInstitute of Materials Science of Aragon (ICMA)

Ramon BurrielElias PalaciosLeticia TocadoGaofeng Wang

methods and problems in the characterization of ... scie… · ddmc 2011 r. burriel, october 24 -...

Documents