Download - Dilatometry ppt
-
7/27/2019 Dilatometry ppt
1/41
Dilatometry
Measuring length-changes of yoursample
thermal expansion, magnetostriction,
Vivien ZapfNHMFL-LANL
-
7/27/2019 Dilatometry ppt
2/41
Heron of Alexanria !" # $%&%'
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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.
-
7/27/2019 Dilatometry ppt
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'
-
7/27/2019 Dilatometry ppt
7/41
&
7
&apacitive 7ilatometer!&artoon'
7
L
&apacitor
>lates
&ell
$oy
5ampleD
A
C o=
?xtra creit 6uestion)
+hy ont e put the sample .eteen the capacitor platesG
-
7/27/2019 Dilatometry ppt
8/41
ev% 5ci% Bnstrum% 77, /1IJ#K !1##3'George Schmiedeshoff,cciental &ollege
5ample
5ample
scre
Movea.le
capacitor plate
5tationary
capacitor plate
5pring
!&u$e plate'
Use of needle instead of plate on top of sample means
sample faces dont need to be perfectly parallel
-
7/27/2019 Dilatometry ppt
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 ('
-
7/27/2019 Dilatometry ppt
10/41
7ilatometer ors at various orientations to the magnetic fiel%
otators availa.le at LANL an (allahassee
H
-
7/27/2019 Dilatometry ppt
11/41
Capacitance bridge
(e.g. H 2!"" bridge
or GC 1#1$)
(o shiele, groune coax ca.les
Capacitance meas%rement
-
7/27/2019 Dilatometry ppt
12/41
ev% 5ci% Bnstrum% 77, /1IJ#K !1##3'
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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%
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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%
-
7/27/2019 Dilatometry ppt
21/41
Mounting mechanism
All titanium
&u .racet
2" +i,%tion fridge +i,atometer in -ac%%m
-
7/27/2019 Dilatometry ppt
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,,
-
7/27/2019 Dilatometry ppt
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%
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
27/41
?xample !Metals')
After +hite E &ollins, L(> !/JK1'%
Also) $arron, &ollins E +hite, Av% >hys% !/J4#'%
!latticeshon%'
Col
5ilver
&opper
Cruneisen parameter
-
7/27/2019 Dilatometry ppt
28/41
?xample !Heavy Fermions')
After eVisser et al% !/JJ#'
HF!#'
bi h iti
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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,
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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
-
7/27/2019 Dilatometry ppt
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'
-
7/27/2019 Dilatometry ppt
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