Practical aspects of thermodynamic analysis
 Dynamic methods of phase equilibrium studies – DTA, HF-DSC
a. Unary system; b. Binary and ternary systems
c. TGA; d. heat capacity measurements using DSC
 Isothermal methods (Phase equilibria, Diffusion couple);
 Influence of kinetics
 Applications
1.
2.
3.
4.
Classification of experimental methods
DTA/DSC for unary systems
Temperature and enthalpy calibration
Problems
Phase diagrams: relations to microstructure and properties
Eutectic phase diagram
Phase diagram with peritectic
Experimental methods used for phase diagram construction
Dynamic methods
Static methods
Metals
Ceramics
Arc-melting
Induction melting
Solid state reactions
Co-precipitation and pyrolysis
Homogenisation
DTA/TGA
DSC
Dilatometry
HMA
Heat treatment:
Natural cooling or quenching
Quenching or in-situ study
Diffusion couples
Charactirisation methods
XRD – phase identification, phase boundary determination
SEM/EDX microstructure examination, phase composition determination (for identification)
EPMA for more precise phase identification
EBSD for structure determination
Thermal Analysis: Dynamic Methods
Measurement of physical property of a substance as a function of temperature
using controlled temperature program
Method
Measured property Application
Differential
Thermal Analysis
(DTA)
Temperature
difference
Phase reactions,
phase
transformations
Differential
Scanning
Calorimetry (DSC)
Heat flow
Specific heat, Heat
of transition
Thermal
Gravimetric
Analysis (TGA)
Mass Change
Reactions with the
gas phase,
decomposition
reactions
Dilatometry
Size Change
Phase
transformations,
Thermal expansion
Thermomechanical
Analysis (TMA)
Mechanical
properties
Materials testing
DTA/Heat-Flux DSC
The temperature is not measured in the sample, but at the bottom of crucible.
Temperature calibration is necessary.
DTA/HF-DSC signal is difference between sample and reference thermocouples. It
is usually given in mV. For some devices it is given as temperature difference; this
means that reference table or equation was used by instrument to calculate
temperature from voltage difference.
The DTA Signal
Heat is transferred between furnace, crucible,
sample (reference) and thermocouple
𝐴𝜆
Steady –state condition ∆Φ𝑆𝑅 = − Δ𝑙 Δ𝑇𝑆𝑅 = −𝐾Δ𝑇
DFSR – difference in heat flow rate, l – thermal conductivity
TW is furnace temperature, TC is temperature of crucible
TT is temperature of thermocouple, TS is sample temperature
Idealized curve
Real curve
DTA signal
Fr=L(Tm-TS)
L is apparent thermal
conductance to the sample,
Tm is measured temperature,
TS is sample temperature
𝑑Φ𝑟
𝑑𝑇𝑚 𝑑𝑇𝑆
=𝐿
−
𝑑𝑡
𝑑𝑡
𝑑𝑡
≈b
=0
b is heating rate
𝑑Φ𝑟
𝑑𝑇𝑚
=𝐿
𝑑𝑡
𝑑𝑡
𝑑Φ𝑟 𝑑𝑡
𝑑Φ𝑟
=
=𝐿
𝑑𝑡 𝑑𝑇𝑚 𝑑𝑇𝑚
DTA signal for unary system
DTA responses to melting and freezing of pure substance: a- onset temperature, b- peak at
temperature c . Due to dynamic character of experiment, the temperature distribution is
never completely homogeneous. The temperature is not measured in the sample, but at the
bottom of crucible. That is why temperature correction is necessary.
Temperature calibration
Measured temperature vs. time and associated DTA plot for melting of pure
Sn. Black is measurement with instrument thermocouple, red is results from a
thermocouple immersed directly in the Sn sample.
Temperature calibration: establishment of relation between measured temperature
Tmeas indicated by the instrument and the true temperature Ttr.
At least three substances (usually pure metals) with melting temperature covering
temperature range of interest should be selected.
Mass should be corresponded to recommended mass for measurement in this
instrument. Measurement should be done with different heating range b and
extrapolated to b=0.
Temperature calibration
Measured temperature of thermal event depends on mass and cooling rate b.
Extrapolated T melting of Sn to b=0
for different sample mass
Substance
T, °C
Sn
231.928
Al
660.323
Ag
961.78
Au
1064.18
Pd
1554.8
Temperature correction for Ga, In and Sn
Plotting DTA signal vs. Temperature or time
DTA melting of pure Ag at 10 K/min
Reference thermocouple Ttcref and
sample thermocouple Ttcsample vs.
time
DT=Ts-Tref is difference between sample
temperature and reference
Red line – DT vs. time
Solid black line - DT vs. Ts
Dashed line – DT vs. Tref
Tref=T0+bT
DT vs. time is necessary for quantitative
determination of enthalpy. DT vs T sample is
better for determination of temperature of
thermal event.
Enthalpy calibration
KH is instrument sensitivity for Ga, In, Sn
𝑡2
𝑚𝑠𝑎𝑚𝑝𝑙𝑒 ∆𝐻𝑠𝑎𝑚𝑝𝑙𝑒 = 𝐾𝐻
∆𝑇 𝑡 𝑑𝑡
𝑡1
Recommended values of temperatures and enthalpies of
melting of metals
Element
Tmelt (°C)
DHm(J/g)
Ga
29.764
80.07
In
156.598
28.62
Sn
231.928
60.38
Zn
419.527
108.09
Al
660.323
399.87
Ag
961.78
104.61
Au
1064.18
64.58
Enthalpy calibration factors for each
calibration substance are represented
as a function of transition temperature.
Provided the dependence on heating
rate b and sample mass are negligible
(within scatter of individual
experiments) the enthalpy calibration
factor KH(Ttr, m, b) give the enthalpy
calibration function KH(T).
Problems
Influence of mass and heating rate:
Larger mass and larger heating rate produce larger peak, but make detection of
closely spaced thermal events more difficult.
Blue 5 K/min, red-10 K/min, black – 15 K/min
Problems
Sample shape is typically not conform to the shape of the sample cup. The thermal
contact area between the sample and crucible will change during melting process.
Possible solution is second heating. However in case of complicated phase diagram
and not equilibrium freezing different phase assemblage can be present in the sample
before second heating.
Undercooling problem with liquidus determination on cooling
Measured temperature vs. Time (a) and DTA signal vs. Temperature for freezing of
pure Sn. The instrument thermocouple readings are black and from thermocouple
immersed directly into Sn sample are red. For the immersed thermocouple the
temperature reheats up to melting temperature as heat of fusion is released rapidly.
Many metals and alloys are prone to undercooling before the nucleation of solid
phase start from melt. Nucleation temperature can differ from liquidus up to 100
or more degree depending on nature of alloy system and other factors.
Determination of melting on heating is more reliable.
Problems
Powder sample increase oxidation, reduce heat flaw
Solutions:
Inert powder cover – to increase the thermal conduction to the sample cup
Lid – to reduce material loss and contamination of the instrument, to prevent
sample radiation loss and maintain an isothermal sample
Atmosphere. Commercial purity inert gas is no adequate. Use of high purity inert
gas to a Ti getter is recommended. Helium (He) has higher thermal conductivity
than Ar; the choice can alter thermal transport rates in DTA instrument.
Calibration should be performed with the same gas as used for samples
Crucible selection/reaction. High purity Al2O3 is standard DTA crucibles
for metals investigation. Use of ZrO2 and Y2O3 crucibles can be
recommended for highly reactive metals. Carbon crucibles can be
recommended for metals not forming carbides. Pt, W crucibles can be
used for ceramic materials
Good praxis for DTA experiments
Calibration:
Based on the melting point of pure substances. Crucible, standard material,
heating rate, sample mass, atmosphere are kept constant
Characterisation:
The composition of samples and crystal structure have to be investigated
before and after the measurement
Combination:
DTA experiments tell us that something is happening at a specific
temperature. They usually do not tell us, what is happening. Combination
with other methods like X-ray diffraction, spectroscopy, microscopic
investigation and composition analysis (e.g. Electron probe microanalysis)
are required to interpret the results
DTA vs. DSC
DTA
DSC
Heat-flux
Power compensation
DT
DT between sample
and reference
T and DH of transformation
DT between sample
and reference
More robust, measurements
can be done in wider T range,
in more aggressive
environment (oxidation
atmosphere), possible
combination with TGA to
measure mass change
T and DH of
transformation, Cp
measurements
HF-DSC is more sensitive
than DTA, possible to
measure heat capacity
Power compensation
to keep the same
temperature in both
furnaces
T and DH of
transformation, Cp
measurements
More effective,
since response
time is shorter
than in HF-DSC