Thermal analysis heat capacity - ISU Sites
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Novel Materials and Ground States
Thermal analysis – heat capacity
590B F18
Sergey L. Bud’ko
Novel Materials and Ground States
Heat capacity
Cp = (dQ/dT)p = T(∂S/∂T)p Q – heat, S - entropy
Cv = (dQ/dT)v = T(∂S/∂T)v
Cp – Cv = TVβ2/kT β – volume thermal expansion, kT – isothermal volume compressibility
For solids Cp ~ Cv
Usually we measure Cp
Novel Materials and Ground States
Heat capacity – HOW?
•relaxation (QD PPMS)
Novel Materials and Ground States
Heat capacity – HOW?
•relaxation (QD PPMS)
simple
sample + platform
thermal conductance of wires
T of the bath
power of the heater
P0
0
solution: exponent with t = Ctotal/Kw
Novel Materials and Ground States
Heat capacity – HOW?
•relaxation (QD PPMS) more realistic
fit with two exponents
addenda
Novel Materials and Ground States
Heat capacity – HOW?
•relaxation (QD PPMS)
Addenda - simple model Sample – simple model
Novel Materials and Ground States
Heat capacity – HOW?
•relaxation (QD PPMS)
Sample – 2-tau model
Novel Materials and Ground States
Heat capacity – HOW?
•relaxation (QD PPMS)
- Good for flat relatively thin samples with reasonable thermal conductivity- Liquids: need thin-walled sealed container made out of material with
high thermal conductivity and low heat capacity. – personally did not try (yet?)
- Powders: - press a pellet (if has structural integrity); - mix with some metallic powder and press a pellet; - seal powder in aluminum DSC container (can be used for air-
sensitive powder samples as well, if assembled in a glove box)
Remember addenda!
Novel Materials and Ground States
Heat capacity – HOW?
•relaxation (QD PPMS)
calibrated heater and thermometer
sophisticated temperature control and fitting software
need to measure addenda (platform + grease) every time
need to calibrate heater and thermometer in magnetic field
need to shape your sample
vertical 3He platform may oscillate in magnetic field
remember about torque
assembly is fragile
measurements take long time
not good for 1st order phase transitions
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation
τ1 – sample to
bath;
τ2 – response
time of the sample
if τ2 << 1/w << τ1
Heat capacity – HOW?
•ac modulation
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation
after Andreas Rydh
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation Commercial chips with membrane
(this is a commercial thermal conductivity gauge)
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation Commercial chips with membrane
you are invited to play with it…
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation
after Andreas Rydh
differential cell
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation
after Andreas Rydh
differential cell
need to have (at least primitive) thin film technology and lithography
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation
fast
scalable, good for small sample
accurate (relative measurements)
easy to put on rotator
can use e.g. in pressure cells
hard to get absolute values
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation – under pressure
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation – under pressure
Bridgman cell-heater and thermometer are at ambient pressure
for DAC – laser heating with thermocouple as sensor
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation – under pressure
Novel Materials and Ground States
Heat capacity – HOW?
•ac modulation – under pressure
need to choose frequency
Novel Materials and Ground Statesafter Andreas Rydh
Novel Materials and Ground States
Heat capacity – WHY?
* Useful knowledge for useful (structural) materials – how easy to cool down
Novel Materials and Ground States
Heat capacity – WHY?
* To learn something about electrons and phonons
T -> 0: Cp = γT + βT3 (no magnetism)
γ ~ N(0)(1 + λ) - electronic density of states
λ - measure of e-e (and e-ph) interactions, m*/m0 = (1 + λ)
γ > 400 mJ/mol K2 – “heavy fermions” – an enormous, separate research field that entertains number of us
ΘD = (1944/β)1/3 - Debye temperature (use right units)
tells you something about stiffness of the lattice, helps to understand BCS superconductors [Tc ~ ΘD exp(-1/N(0)V)]
Novel Materials and Ground States
Heat capacity – WHY?
Novel Materials and Ground States
Lattice heat capacity – Debye and Einstein
Einstein – single frequency
Debye – elastic continuum
(T << ΘD)
(T >> ΘD)
Novel Materials and Ground States
Lattice heat capacity – Debye and Einstein
Debye
Einstein
One can also use realistic phonon DOS and calculate Cp
Einstein Debye
Blackman “realistic”
Novel Materials and Ground States
Lattice heat capacity –Einstein mode
Peak associated with the Einstein mode @ ~ QE/20
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about magnons
Ferro (ferri) magnets
isotropic
anisotropic
Antiferromagnets
isotropic
anisotropic
And need to remember contributions from electrons and phonons: Cp = γT + βT3
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about superconductors
Cs ~ exp(-1.76Tc/T) BCS
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about superconductors
RMP 62, 1027 (1990)
Strong coupling
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about superconductors
BCS value (3.53)
phenomenological (1970s)α-model:2Δ0/kBTc – fitting parameter;temperature dependence of SC gap – BCS;can calculate thermodynamic properties.
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about superconductorsMgB2
Two-gap superconductor
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about superconductorsMgB2
Two-gap superconductor
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about superconductors
four gaps
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about superconductors
BCS superconductors with paramagnetic impurities
BCS
PM impurities La-Gd
jump in specific heat
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about superconductors Kondo effect in SC
jump in specific heat
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about superconductorsIron-arsenides
ΔCp ~ Tc3
Smart person might be able to make sense out of this
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about phase transitions below superconducting Tc
Tc
TWFM?
TN
Novel Materials and Ground States
Heat capacity
Bulk, thermodynamic property
In case of “not so single phase” samples results:
-do not suffer from “M&M effect” in case of superconductors
-do not suffer from impurity SC or FM signal in magnetization (although for FM need to remember about entropy)
normal
Novel Materials and Ground States
Resistance
SC
normal bulk, superconducting shell
VI Will get R=0 below Tc of the shell
normal
Novel Materials and Ground States
Low field ZFC susceptibility
SC
normal bulk, superconducting shell
Will get complete flux expulsion below Tc of the shell
normal
Novel Materials and Ground States
Heat capacity
SC
normal bulk, superconducting shell
Will get complete jump of Cp at Tc of the shell proportional to the fraction of the SC phase, e.g. very small
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about crystal electric field (Schottky anomaly)
maximum:
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about spin glasses
Scaling hypothesis
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about spin glasses
1/T
Tmax ~ 1.5 Tf
Novel Materials and Ground States
Heat capacity – WHY?
•To learn something about magnetic transitions
HoNi2B2C
Also can play entropy game and evaluate degeneracy of the ground state
ΔSm = R ln N
Novel Materials and Ground States
Heat capacity – beware of fool’s gold
low temperature C = AT in insulators
Novel Materials and Ground States
Heat capacity – beware of fool’s gold
low temperature C = AT in insulatorsglasses - distribution of two level systems
Novel Materials and Ground States
Heat capacity – beware of fool’s gold
“fake” heavy fermions (apparently large Sommerfeld coefficient):
- (really) low temperature magnetic ordering
- low temperature spin glass behavior
One measurement technique, whatever sophisticated, is not enough
Novel Materials and Ground States
Reading:
Quantum Design Manual and refs therein
E.S.R. Gopal, Specific heats at low temperatures.
A.Tari, Specific heat of matter at low temperatures.
T.H.K. Barron and G.K. White, Heat capacity and thermal expansion at low temperatures.
Review of Scientific Instruments – search on “heat capacity…”
