Practical aspects of thermodynamic analysis Dynamic methods of phase equilibrium studies – DTA, HF-DSCa. Unary system; b. Binary and ternary systemsc. TGA; d. heat capacity measurements using DSC Isothermal methods (Phase equilibria, Diffusion couple); Influence of kinetics Applications

1. Classification of experimental methods2. DTA/DSC for unary systems 3. Temperature and enthalpy calibration4. Problems

Phase diagrams: relations to microstructure and properties

Eutectic phase diagram

Phase diagram with peritectic

Experimental methods used for phase diagram construction

Static methods Dynamic methods Metals Ceramics

Arc-meltingInduction melting

Solid state reactionsCo-precipitation and pyrolysis

DTA/TGADSCDilatometryHMA

Charactirisation methodsXRD – phase identification, phase boundary determinationSEM/EDX microstructure examination, phase composition determination (for identification)EPMA for more precise phase identificationEBSD for structure determination

Diffusion couples

HomogenisationHeat treatment:Natural cooling or quenching

Quenching or in-situ study

Thermal Analysis: Dynamic MethodsMeasurement 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

TW is furnace temperature, TC is temperature of crucibleTT is temperature of thermocouple, TS is sample temperature

Idealized curve Real curve

Steady –state condition DFSR – difference in heat flow rate, l – thermal conductivity

Heat is transferred between furnace, crucible, sample (reference) and thermocouple

DTA signal

Fr=L(Tm-TS)L is apparent thermal conductance to the sample, Tm is measured temperature, TS is sample temperature

𝑑Φ𝑟

𝑑𝑡=𝐿(𝑑𝑇𝑚

𝑑𝑡−𝑑𝑇 𝑆

𝑑𝑡 )b 0

𝑑Φ𝑟

𝑑𝑡=𝐿

𝑑𝑇𝑚

𝑑𝑡

𝑑Φ𝑟

𝑑𝑡𝑑𝑡𝑑𝑇𝑚

=𝑑Φ𝑟

𝑑𝑇𝑚

=𝐿

b is heating rate

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.

DTA signal for unary system

Temperature calibration

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.

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

Substance T, °C

Sn 231.928

Al 660.323

Ag 961.78

Au 1064.18

Pd 1554.8

Extrapolated T melting of Sn to b=0 for different sample mass

Temperature correction for Ga, In and Sn

Measured temperature of thermal event depends on mass and cooling rate b.

DT=Ts-Tref is difference between sample temperature and referenceRed line – DT vs. timeSolid black line - DT vs. Ts

Dashed line – DT vs. Tref

Tref=T0+bT

DTA melting of pure Ag at 10 K/minReference thermocouple Ttc

ref and sample thermocouple Ttc

sample vs. time

Plotting DTA signal vs. Temperature or time

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

𝑚𝑠𝑎𝑚𝑝𝑙𝑒∆𝐻 𝑠𝑎𝑚𝑝𝑙𝑒=𝐾 𝐻∫𝑡1

𝑡2

∆𝑇 (𝑡 )𝑑𝑡

KH is instrument sensitivity for Ga, In, Sn

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

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.

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.

Powder sample increase oxidation, reduce heat flaw

Solutions:Inert powder cover – to increase the thermal conduction to the sample cupLid – 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

Problems

Good praxis for DTA experiments

Calibration:Based on the melting point of pure substances. Crucible, standard material, heating rate, sample mass, atmosphere are kept constantCharacterisation:The composition of samples and crystal structure have to be investigated before and after the measurementCombination: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. DSCDTA DSC

Heat-flux Power compensation

DT between sample and reference

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

HF-DSC is more sensitive than DTA, possible to measure heat capacity

T and DH of transformation

T and DH of transformation, Cp measurements

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

DT