dilatometry ppt

7/27/2019 Dilatometry ppt

1/41

Dilatometry

Measuring length-changes of yoursample

thermal expansion, magnetostriction,

Vivien ZapfNHMFL-LANL


2/41

Heron of Alexanria !" # $%&%'


3/41

(oay) Applications too numerous to list

* +e still use thermal expansion for everything from carengines to nuclear poer plant cooling regulation

* Affects esign of sieals, .riges, cryostats,

Thermal expansion within a solid phase is much smallerbut can be an invaluable tool for probing fundamental physics


4/41

-#%#/#

-#%##0

#%###

#%##0

#%#/#

#%#/0

#%#1#

#%#10

# 1 2 3 4 /# /1 /2

$ !('

L/L(%)

Magnetostriction

Hc1

Hc2

LcLa

c

a

H

Ni&l1-25&!NH1'1) an antiferromagnetic 6uantum magnet


5/41

7ilatometry

* () thermal expansion) 8/9L!L9(': ; 8 ln!V'9(

* H) magnetostriction) < 8 =L!H'9L

* >) compressi.ility) 8 ln!V'9>

* ?) electrostriction) @ 8 =L!?'9L

* etc.


6/41

Ho to measure 7ilatometry

* Mechanical !pushro etc.)

* ptical !interferometer etc%'%

* ?lectrical !Bnuctive, &apacitive, 5train Cauges'%

* 7iffraction !D-ray, neutron'%* thers !a.solute E ifferential'


7/41

&

7

&apacitive 7ilatometer!&artoon'

7

L

&apacitor

>lates

&ell

$oy

5ampleD

A

C o=

?xtra creit 6uestion)

+hy ont e put the sample .eteen the capacitor platesG


8/41

ev% 5ci% Bnstrum% 77, /1IJ#K !1##3'George Schmiedeshoff,cciental &ollege

5ample

5ample

scre

Movea.le

capacitor plate

5tationary

capacitor plate

5pring

!&u$e plate'

Use of needle instead of plate on top of sample means

sample faces dont need to be perfectly parallel


9/41

+hy a capacitive ilatometerG

* Fantastically sensitive

5u.-Angstrom resolution of length changes on a mm-sie

sample

* Versatile) ie range of signal sies, sample sies an

shapes

* ecall Al.erts tal on noise) no intrinsic noise in a

capacitance measurement

* seful for the ranges of ( an H at the magnet la.

!1# mO to "I# O, # to 20 ('


10/41

7ilatometer ors at various orientations to the magnetic fiel%

otators availa.le at LANL an (allahassee

H


11/41

Capacitance bridge

(e.g. H 2!"" bridge

or GC 1#1$)

(o shiele, groune coax ca.les

Capacitance meas%rement


12/41

ev% 5ci% Bnstrum% 77, /1IJ#K !1##3'


13/41

&ali.ration* se sample platform to push

against loer capacitor plate%

* otate sample platform !P',

measure &%

* Aefffrom slope !ege effects'%

* Aeff 8 Aoto a.out /QGR

* SBealT capacitive geometry%

* &onsistent ith estimates%

* &MADUU &) no tilt correction%

&MAD30 pF

perating

egion


14/41

&ell ?ffect

CuCuCellCellSampleSampledT

dL

LdT

dL

L += ++

11

High magnetic fiels) se e%g% titanium instea of &u .oy to

create less ey currents in magnetic fiels

High temperatures) se 6uart9sapphire !see or of ohn

Neumeier'Slide courtesy G. Schmiedeshoff


15/41

&ther bac'gro%nds

7ielectric constant of li6ui helium .eteen capacitor plates

Magnetic impurities in commercial titanium

(hese effects are small compare to some

samples !.ut not allR'

C% M% 5chmieeshoff, S(hermal expansion an magnetostriction of a nearly saturate IHe-

2He mixtureT, accepte >hil Mag% 1##J%


16/41

(ilt &orrection

* Bf the capacitor plates are truly parallel then & W as 7 W #%* More realistically, if there is an angular misalignment, one can sho that

* & W &MADas 7 W 75H(!plates touch' an that

>ott E 5chefy !/J44'%

* For our esign, &MAD8 /## pF correspons to an angular misalignment of a.out #%/o%

* (ilt is not alays .a) enhance sensitivity is exploite in the esign of otter et al.!/JJ4'%

+=

2

MAX

o

C

C

1C

A

D

Slide courtesy G. Schmiedeshoff


17/41

Oapton $a !thans to A% eVisser an &y peil'

*eplace Oaptonashers ith alumina%

*Ne cell effect scale%

*Bnvestigating sapphire

ashers%

Slide courtesy G. Schmiedeshoff


18/41

(or6ue $a

* (he ilatometer is sensitive to magnetic tor6ue on the sample!inuce moments, permanent moments, shape effects'%

* Manifests as irreprouci.le9hysteretic ata

* 5olution

/% Clue sample to platform !(X1# O'

1% Crease the sample scre -U grease freees at lo

temperatures

I% &hoose a goo sample shape

Coo gly$a


19/41

(hermal graients .a

You are measuring the ifference .eteen thermal expansionof cell an sample% (emperature of cell is importantR

7ilatometer cell originally esigne to .e immerse in li6%ui

helium

5ample is mounte on a scre that is notell-thermalie to the .oy of the cell

+orarouns)

&ontrol temperature of .oth top an .ottom of ilatometer

&onnect thermaliation ires from top to .ottom

Bmmerse in li6ui helium

(his part relatively thermally isolate%

At LANL, e mae a moifie scre that contains

heater, thermometer, an attachment points forthermaliation ires


20/41

$u..les are .a

Li6ui helium .u..les as it .oils, especially hile you

are pumping on it%

$u..les cause .ig umps in the capacitance%

Dilution fridge, immersed in liquid) no .u..les !.ut

.eare of fiel-epenence of helium ielectricconstant, an of the HeI-He2 .ounary line crossing

the capacitor'

Dilution fridge, vacuum: No .u..les, .ut nee to

thermalie the cell, sample%

Liquid helium 3) Lots of .u..les% 7ont o this%

Liquid helium 4) .elo 1%1 O !superflui helium has

no .u..les'

Helium gas) +ors if you thermalie the cell%


21/41

Mounting mechanism

All titanium

&u .racet

2" +i,%tion fridge +i,atometer in -ac%%m


22/41

Sample

Thermometer 2

(20mK 4 K)

Zero field region

Thermometre 1

(20 mK 4 K)

Heater

MixingChamber

2" * +i,%tion fridge +i,atometer in -ac%%m

HML * LL

ield !enter

Thermal lin"# to

the mixing !hamber

i

di,atometr0

ce,,


23/41

Ho to get goo ilatometry ata

Avoi torque) &hoose non-tor6uey sample shape, glue sample to

ilatometer, grease the scre

Thermalize the ilatometer, put a thermometer near the sample

CalibrateE Measure the cell .acgroun

5tic to low temeratures !unless you have a 6uart ilatometer'

Avoi !aton

Avoi heliumbubbles

&orrect for ielectric constant of meium .eteen capacitor plates !a.out

0Q'

Mount ilatometer so as to avoi thermal contraction9expansion stresses .y

mounting mechanism on ilatometer%


24/41

rigins of thermal expansion

* Mie!/J#I') First microscopic moel%

* Grneisen!/J#4') ;!('9&!(' " constant

A funamental thermoynamic propertythat is often proportional to the specific heat

+hat creates length-changes in samplesG

First theories) effects of thermal vi.rations


25/41

Cr[neisen (heory

1

L

dL

dT

= (T)

(T)V0Cv (T)T

3

(T) =dlnL

dP

+rite on Free energy of the vi.rations of a

soli !a set of harmonic oscillators'

se this free energy to compute the specific

heat% r the thermal expansion

7e.ye theory) assume a max% cutoff

fre6uency of the vi.rations

compressi.ility

(hermal expansion

Cr[neisen parameter

Thermal pressure due to

vibrations


26/41

Cr[neisen (heoryApplies to other thermal vi.rations

eff V0(T)(T)

C(T)= eff(T)

C

i(T)i

Ci(T)

i

= (T)

Examples: Simple metals: e =2

3+dln(m*)

dln(V)

e.g.:phonon, electron,

magnon, &?F, Oono,

OOY, etc.

?lectronic Cr[neisen parameter pro.es effective mass

2


27/41

?xample !Metals')

After +hite E &ollins, L(> !/JK1'%

Also) $arron, &ollins E +hite, Av% >hys% !/J4#'%

!latticeshon%'

Col

5ilver

&opper

Cruneisen parameter


28/41

?xample !Heavy Fermions')

After eVisser et al% !/JJ#'

HF!#'

bi h iti


29/41

>hase (ransition) (N1nrer >hase (ransition,

?hrenfest elation!s')

p

N2M

c

N2

CTV

p

T

=

c

d

d

S

)(V

S

V

p

TM

N1

=

L

L

cd

d

/strer >hase (ransition,

&lausius-&lapyeron ?6!s'%)

robing hase ransitions


30/41

Limitations of Cr[neisen (heory

an other thermoynamic approaches to thermal expansion

*Bsotropic thermal expansion only

*nly treats vi.rational effects

*Limite treatment of elastic effects


31/41

-#%#/#

-#%##0

#%###

#%##0

#%#/#

#%#/0

#%#1#

#%#10

# 1 2 3 4 /# /1 /2

$ !('

L/L(%)

Magnetostriction

Hc1

Hc2

LcLa

c

a

H

An anisotropic, elastic example)

& t ,,i 5 t M t


32/41

/1 /2

iC,234SC(H2)2

&rgano3meta,,ic 5%ant%m Magnet

Meta,

Ni1\

58/

5uperexchange

coupling)AFM

&rganic)

thiourea provies structure

i S 6 1

c

a

a

chain/'86 2.2 9

p,ane/'86 ".1: 9

C,


33/41

#

#%1

#%2

#%3

#%4

/

/%1

# 1 2 3 4 /# /1 /2

Magnetocaloric effect

5pecific heat

H !('

;< M/8=C

8ose3=instein Condensation of i s0stem

8oson n%mber contro,,ed b0 magnetic fie,d

T

T!

cc

"

1

I7 $?&) 8 I91

I7 Bsing) 8 1

17 $?&) 8 /

he 5%ant%m art


34/41

#

#%1

#%2

#%3

#%4

/

/%1

/%2

#

#%1

#%2

#%3

#%4

/

/%1

# 0 /# /0

?xperiment]uantum Monte &arlo

H !('

+e have a pretty goo unerstaning

of this material)

$ut a complete unerstaning re6uires incluing


35/41

$ut a complete unerstaning re6uires incluing

the spin-lattice coupling

Capacitance

itani%m +i,atometer

(design b0 G. Schmiedeshoff)

C%8e

spring

>. S. ?apf et a,@ h0s. Ae-. 8 77@ "2"4"4(A)

(2"":)

Hc

a

-#%#/#

-#%##0

#%###

#%##0

#%#/#

#%#/0

#%#1#

#%#10

# 1 2 3 4 /# /1 /2

$ !('

L/L(%)

Hc1

Hc2

6 2$ m9

H BB c

Lc

La

Moeling the Magnetostriction


36/41

Moeling the Magnetostriction

!to First rer'

"ssume: Lattice has linear spring response ith Youngs moulus #

"ssume: #ero temperature $measurements at T % &' m()

$eglect:&rystal fiel effects changing ith pressure

$eglect:Magnetic effects along a-axis

M(H)

=

L/L

Magnetic stress

5train along c-axis

i

i

(

)c

S1S2

rigin of Magnetic stress

Youngs Moulus)

#6


37/41

Hm =D Siz( )

2

i

gBB Sizi

+ J

Si < i,j>

S j

Magnetic Hamiltonian)

el +em( )=0

= 1

EV

Jc

Si Si+1

ml eee +=

2

2

1Ee

l=

1

11+== iicmm SSJ

VH

NVe

Lattice energy9volumeMagnetic energy9volume

Minimie the energy)

?nergy ensity) lattice an magnetic

- epenence

= 2

2

1kx

Minimie the energy

M(H)

=

L/L

Youngs Moulus)

#6

1 J


38/41

1

1

+

= iic SS

J

EV

-#%#/

-#%##0

#

#%##0

#%#/

#%#/0

#%#1

#%#10

# 1 2 3 4 /# /1 /2

H !('

c-axis Magnetostriction

?xperiment

(heory

L

L!Q'

H ^^ c

1+= ii SSk

(810mO

5%ant%m Monte Car,o sim%,ations

( )011)0(

)0()(=++

=HiiHii

SSSSkL

LHL


39/41

= c

J

EVk 1

-#%#/

-#%##0

#

#%##0

#%#/

#%#/0

#%#1

#%#10

# 1 2 3 4 /# /1 /2

H !('

c-axis Magnetostriction

?xperiment

(heory

LL

!Q'

H ^^ c

1+= ii SSk

(810mO

Significance

+e can measure the spin-spin correlation functionR

&an extract the spatial epenence of resulting from

the Ni-&l-&l-Ni superexchange .on


40/41

-#%#/#

-#%##0

#%###

#%##0

#%#/#

#%#/0

#%#1#

#%#10

# 1 2 3 4 /# /1 /2

$ !('

L/L(%)

Magnetostriction

Hc1

Hc2

LcLa

c

a

H

Ni&l1-25&!NH1'1) an antiferromagnetic 6uantum magnet

Acnolegements !7(N'


41/41

Acnolegements !7(N'

Aesonant D,traso%nd

&ristian >antea, on $etts, Al.ert Migliori,

*!+,-,*,

>aul ?gan, /0lahoma State

=SA

5ergei Zvyagin, ochen +osnita,

1resden igh !agnetic +ield ,ab

ure Oryste, *!+,-Tallahassee

HML3LL7iego Zocco, Marcelo aime, Neil Harrison,

Alex Lacera

HML3a,,ahassee

(im Murphy, ?ric >alm

Cr0sta, groEth and magnetiFation

Armano >auan-Filho

Universidade de Sao 2aulo3 4ra"il

ne,astic e%tron diffraction

M% Oenelmann, $% % Hansen, &% Nieermayer,

2aul Scherrer 5nstitute and 6T3 #7rich3 Swit"erland

Magnetostriction

Victor &orrea, 5tan (oer,

*!+,-Tallahassee

5%ant%m Monte Car,o

Mitsuai (suamoto, Naoi Oaashima

University of To0yo

heor0

>inai 5engupta, &ristian $atista, ,*,

NSF NHMFLDOE

dilatometry ppt

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