Download Lecture 10 - MyCourses

Thermometry
Definition of the temperature scale is more
arbitrary than for most basic quantities
The scale is based on agreement that the
triple point of water is 273.16 K
New proposed definition (Oct 2011)
sets fixed value for the Boltzmann
constant kB = 1.3806X . 10–23 J/K,
where X represents one or more
digits to be added
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
1
ITS-90
It is difficult to compare
two temperatures
far from each other
Various phase transitions
are defined as fixed points
over the scale
– These are agreed upon in an
international scale ITS-90
– The scale extends only
down to 0.65 K !
– No official scale exists
at mK-range
Provisional PLTS-2000
gives temperatures
From 1 mK to 1 K
in terms of the
melting pressure of 3He
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
2
PLTS-2000
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
3
PLTS-2000
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
4
PLTS-2000
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
5
Practical thermometry
For practical thermometry one may utilize any quantity x that
– depends on temperature (preferably monotonically)
– can be measured accurately, quickly, frequently, and easily
– is sufficiently sensitive, i.e. (Dx/x)/(DT/T) is large enough
using any probe that
– is in good thermal contact with the body to be measured
– reaches thermal equilibrium quickly
– has small thermal capacity
– does not produce intolerable heating
– does not change characteristics over time
It is desirable, that
– temperature dependence is simple
– x does not depend on other factors (such as magnetic field, pressure, etc.)
– method can be reproduced and transferred
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
6
Thermal contact
At mK-range (and below) it is hard to establish that the thermometer
and the sample are at the same temperature
– measurement produces heat
– thermal conductivity is low
– boundary resistance becomes an issue
– heat load from other sources may keep temperature up
– heat capacity may become an issue (magnetic measurements)
Often the temperature is deduced from the properties of the system itself, as
– 3He: viscosity, melting pressure, ...
– spin systems: polarization, entropy, ...
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
7
Primary thermometers
* x(T) can be calculated from known propertiess, no calibration needed
* Only few such methods are available
* Often these are slow, cumbersome, and/or have marginal sensitivity
– gas thermometer
– noise thermometer
– nuclear orientation
thermometer
– 2nd law
– Coulomb blockade
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
8
Secondary thermometers
* some easily measurable quantity depends on temperature
* as x(T) is not known a priori, there is more liberty for choice
* must be calibrated = > x(T)
For example:
– vapor pressure or melting pressure
p(T) → C(p) → V(C)
– resistance thermometers R(T)
(semiconductors or carbon compounds)
– other electric quantities (e.g. capacitance)
– susceptibility (paramagnetic salts, CMN, LCMN)
– NMR techniques (nuclear susceptibility
or relaxation measurements)
– superconductivity transitions
– oscillating bodies in helium fluids
(vibrating wires, quartz oscillators, etc.)
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
9
“Electron thermometry”
– resistance R (metals or semiconductors)
– thermal noise voltage or current
– magnetic susceptibility (CMN or magnetic impurities in metals)
– superconducting transitions
– Coulomb blockade
Resistance thermometry:
+ easy to measure, most applied method between 10 mK ... 300 K
– no generally applicable form for R(T) – must be individually calibrated
Metals:
R drops as function of T , saturates at T ~ 10 K
– commercial Pt-100, R(T) is linear between ~ 10 ... 300 K (100 W at 0 oC)
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
10
Semiconductors
R increases with decreasing T
doping gives suitable
range of conductivity, but
implies that the response
is sample specific
= > each device has to be
calibrated individually
commercially available, calibrated
sensors much more expensive
– doped Ge
– good reproducibility
– 50 mK ... 5 K or 0.3 ... 40 K ranges available
magnetoresistance has to be recognized !
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
11
Carbon resistors
* cheap
* R increases with decreasing T
* R(T) depends on the manufacturing process
= > has to be calibrated individually
* not available commercially calibrated as the reproducibility is sometimes
rather poor
* range of operation is determined by thermal contact:
– carbon is poor conductor of heat
– measurement produces heat (Joule heating)
= > resistor material cannot be cooled to below 1 ... 10 mK
* very low power for measurement must be used (<< 1 nA)
– ac resistance bridges tailored for this purpose are commercially available
* rf-interference must be eliminated by a cold filter
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
12
DIY resistance thermometer probe
1) take a bulk carbon resistor 50 ... 220 W
2) grind off the protecting surface layer to
expose the bare carbon material
3) sand away half of the cylindrical resistor
to make it flat from one side
4) use thin insulating layer (paper/kapton) and
glue (stycast 1266) to a piece of copper
5) sand the upper surface flat as well:
d < 0.1 mm, R ~ 1 ... 2 kW
6) attach the leads (2-w measurement, SC wires
in CuNi matrix) insulate the upper side
and fix in between copper plates
7) twist, anchor, and filter the wiring
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
13
Filtering
Before mounting to the cryostat:
– give it some thermal cycling between RT < – > LN2
– measure R(4K)
Filtering should be close to the probe at low temperature
– frequency low-pass should be at few 10 kHz
– measure the component values @ 4K before putting the filter together
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
14
Crude model
Resistance increases exponentially of the RESISTOR's temperature Tr
(T 0 /T r )
R(T r ) = Ri e
↑
resistance
when T → 
p
+ R0
↑
wires, filter
(no T -dep.)
bad thermal contact and heating (measurement + noise) produce difference
T nr −T n = nr Q̇
for metallic contact n ~ 2
for insulating contact
(phonon coupling) n ~ 4
n 1 /n p
[T 0 /(nr Q̇+T ) ]
R(T ) = Ri e
+R0
n/ p
1/n
R−R
0
T (R) = (T 0n /[ln(
)] −nr Q̇)
Ri
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
15
Noise thermometer
Brownian motion of conduction electrons causes voltage & current fluctuations
average over time
〈U 〉 = 0
2
〈U 〉 = 4 k B TR Δ f
or
or
measurement over the frequency range Df gives
〈I 〉 = 0
2
〈I 〉 = 4kBT Δ f /R
U rms = √ 〈U 〉
2
Fourier
transform
→
Voltages and currents due to thermal noise are extremely small at low T
*SQUID sensors must be used*
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
16
Noise
measurement
The best SQUID sensors have background noise levels of order 1 ... 2 mf0/√Hz
corresponding to ~ 1 pA/√Hz
For example R = 0.1 mW, Li = L ~ 1 µH = > t = L/R ~ 10 ms
Df = 1/(2pt ) ~ 15 Hz
Larger t => longer averaging, ~ 105 t corresponds ~ 0.5 h (indep. of T !)
Instrument noise bottom corresponds to T = RDf (1 pA/√Hz)2/(4 kB) ~ 2 mK !
Two problems:
– instrumental noise increases at low frequencies below 10 ... 100 Hz as 1/f
BGR-noise adds quadratically to the thermal noise
– sensor resistor may become thermally detached from the T to be measured
Best sensors have been used down to ~ 0.1 mK (correlation measurement)
Upper limit is set by the SC transition of SQUID or connecting wires !
Calibrate at one point (e.g. 4.2 K) and scale to any T (assumed: R indep. of T)
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
17
Commercial
device
Inductive coupling;
SQUID on the
low-T resistor
SQUID on the probe
generates heat
(~ 100 pW) = >
reliable down to
~ 5 mK
PHYS-E0551, Cryoengineering/Lecture 10/Thermometry - J. Tuoriniemi
18