DTA/HF-DSC analysis of ternary systems, heat capacity measurements using DSC, Other dynamic methods Phase diagram of ternary system and DTA Application of DTA for vertical section construction TGA mass change measurement Heat capacity measurement using DSC Dilatometry

DTA analysis of ternary systems Composition 1: Al-0.5%Fe-6 % Cu Equilibrium solidification - black line LL+fccL+fcc+aL+fcc+a+b(U) L+fcc+b Scheil solidification – red line L+fcc+bL+fcc+b+(E) Composition 2: Al-0.5%Fe-20 % Cu Equilibrium and Scheil (the same sequence of transformations) LL+fccL+fcc+bL+fcc+b+(E)

Types of reactions in ternary system Sn E2: LAg3Sn+(Sn)+Cu6Sn5 U5:L+Cu3Sn  Ag3Sn+Cu6Sn5 P2: L+(Ag)+Cu10Sn3  Cu3Sn

DTA for ternary systems: Example Al-Fe-Cu (composition Al-6%Cu-0.5%Fe) L+fcc+b L+fcc+a L+fcc+b L+fcc+a+b L+fcc+a L+fcc L+fcc+b+q L+fcc DTA and dHs/dTs plots under equilibrium conditions DTA and dHs/dTs plots under Scheil conditions

DTA for ternary systems: Example Al-Fe-Cu (composition Al-20%Cu-0 DTA for ternary systems: Example Al-Fe-Cu (composition Al-20%Cu-0.5%Fe) L+fcc+b+q L+fcc+b 1. Ternary invariant transition reactions (U-type) may have quite different DTA signal compared to ternary eutectic reaction. This depends how cooling occurs by equilibrium or non-equilibrium procedure. 2. Microstructure investigation before and after melting can help to interpret DTA results L+fcc DTA and dHs/dTS plots for Al-20%Cu-0.5%Fe under equilibrium conditions

Example: system Ag-Cu-Sn Part of liquidus surface U5 L+Cu3Sn=Ag3Sn+Cu6Sn5, E2 L=Ag3Sn+(Sn)+Cu6Sn5 Phase fraction diagram Sn-25%Ag-10%Cu Vertical section at 25 mass% Ag Latent heat release in equilibrium Latent heat release in Scheil conditions dH/dT in equilibrium

Example Ag-Cu-Sn Phase fraction Sn-25%Ag-27%Cu Latent heat release in equilibrium dHS/dT in equilibrium Latent heat release in Scheil conditions

Vertical section construction using DTA/DSC

Vertical section construction using DTA/DSC

Concluding remarks Temperature of sample thermocouple is different from sample temperature. The temperature ranging from on-set to peak is not due to kinetics but due to heat transfer between sample, crucible and thermocouple. The deviations from full equilibrium can and do occur during the melting and freezing of alloy sample at the rates encountered in DTA. The loss of full equilibrium is due to slow rate of solute diffusion in alloys and can be modelled by Scheil approach. Using DTA temperature and heat effect of melting or solid phase transformation of alloys/compound can be determined. Interpretation of DTA results for multicomponent system is very complex task especially taking into account non fully equilibrium processes. Combination with other methods like XRD and SEM/EDX before and after DTA is necessary to interpret the results obtained by thermal analysis.

TGA: Thermo Gravimetric Analysis Determination of the mass as function of temperature. It is applicable for all reaction involving gas phase Decomposition reactions Vaporization and sublimation Desorption Oxidation and reduction Corrosion Small sample Gas flow essential Different temperature modes Linear heating, isothermal, stepwise isothermal

Solid lines- TG, dashed lines - DTG

DTA/TGA combination Identification of intermediate reactions Determination of reaction temperature Temperature calibration of the instrument Example : the ZrO2-MnO-Mn2O3 system Pure MnO sample 778°C 3Mn2O3  2aMn3O4+0.5O2 1167°C aMn3O4  bMn3O4 1458°C bMn3O4  3MnO+0.5O2 ZrO2-30%MnO Below 1000°C F  M and Mn2O3  aMn3O4+O2 1122°C aMn3O4bMn3O4 1200°C beginning bMn3O4  MnO+O2 1193°C M  T 1295°C T  F 1404°C end of bMn3O4  MnO+O2 1573°C melting L  MnO+F

Differential Scanning Calorimetry (DSC) Linear heating rate  Stationary heat flow (FFS, FFR F –furnace, S- sample, R –reference) A thermal reaction causes a deviation from stationary conditions Evaluation is possible if reaction heat flow rate Fr ~DTSR Conditions Fr << FFS, FFR 𝑄 𝑟 =−𝑘 𝑇 𝑡1 𝑡2 ∆ T 𝑆𝑅 𝑇 𝑑𝑇 Φ 𝑟 = 𝑑 𝑄 𝑟 𝑑𝑡 =−𝑘(𝑇)Δ 𝑇 𝑆𝑅 (𝑇) Qr is heat of reaction, k(T) calibration factor

DFSR=b(CpS-CpR)=-k´DT

Peak area integration KQ 𝐾 Φ 𝑇 = 𝐶 𝑃 𝑇 𝛽 Φ 𝑚 𝑇 − Φ 0 (𝑇)

Heat capacity measurement using DSC: classical three-step method Empty crucible measurement F0(T) Calibration substance measurement (e.g. synthetic sapphire, Pt) 𝐶 𝑃,𝑐 𝑚 𝑐 𝛽= 𝐾 Φ (𝑇)( Φ 𝑐 − Φ 0 ) KF(T) – calibration function Sample measurements 𝐶 𝑃,𝑆 𝑚 𝑆 𝛽= 𝐾 Φ (𝑇)( Φ 𝑆 − Φ 0 ) All three measurements have to be performed under exactly the same conditions Good thermal contact between sample and crucible is required 𝐶 𝑃,𝑆 = 𝑚 𝑐 𝑚 𝑠 ∆Φ 𝑆 ∆Φ 𝑐 𝐶 𝑃,𝑐 DFS=FS-F0, DFc=Fc-F0, - heat flow rate difference between substance S / calibration substance c and zero-line F0(T), mc-mass of calibration substance, ms – mass of sample, CP,c –heat capacity of calibration substance

1. Possible source of errors The quasi-steady-state conditions in the scanning and final isothermal regions are not reached immediately after change in scanning program but with a certain delay. The measured heat flow rate (with zero-line subtracted may be smaller than ideal (theoretical) one. The isothermal level tstart and tend differ from each other and from run to run. These discrepancies results from finite thermal conductivity of path between temperature sensor and sample and from limited thermal conductivity of sample. dT (thermal lag) can be estimated and corresponding correction can be done. Thermal leg can be reduced by sample preparation and correct positioning of the sample in DSC. The difference in isothermal level must be corrected to common level (zero). If isothermal heat flow rate with temperature can be approximated by straight line Fiso(T) the offset correction is: Φ 𝑖𝑠𝑜 𝑡 = Φ 𝑖𝑠𝑜,𝑠𝑡 + Φ 𝑖𝑠𝑜,𝑒𝑛𝑑− Φ 𝑖𝑠𝑜,𝑠𝑡 𝑡 𝑒𝑛𝑑 − 𝑡 𝑠𝑡 (𝑡− 𝑡 𝑠𝑡 ) Fcorr(t)=Fexp(t)-Fiso(t) 2. The „Absolute“ dual step method If temperature dependent KF(T) is stable in time and determined carefully the CP can be calculated as: 𝐶 𝑃,𝑆 = 𝐾 Φ (𝑇)( Φ 𝑆 − Φ 0 ) 𝛽 𝑚 𝑆

Discontinuous method The total temperature range is divided to narrow intervals with isothermal periods in between. The same operation should be repeated with empty crucible. CP is calculated from heat Qi proportional to area between sample and zero-line 𝐶 𝑃,𝑆 ( 𝑇 𝑗 )= 𝐾 Q ( 𝑇 𝑗 ) Q 𝑗 Δ𝑇 𝑚 𝑆 Advantages is using of integration method for heat determination, no correction for thermal leg is required if temperature calibration is precise. Disadvantage is long measuring time. Accuracy is not higher for continuous technique. Discontinuous method for determination of heat capacity (upper curves: sample run, low curves: zero-line).

Summary: Dynamic standard methods DTA, DSC and TGA are standard methods for characterisation of the thermal behaviour of materials. Many commercial instruments are available Scientific use is focused on investigation of phase diagrams, the analysis of thermal reactions and the measurements of thermodynamic properties Usually, the combination with other methods is required for an unambiguous interpretation of results. Industrial use is for characterisation and quality control.

Dilatometry Measurement of the thermal expansion of solid samples during controlled temperature-time program Thermal expansion coefficient a 𝛼= 1 𝑙 0 𝑑𝑙 𝑑𝑇 𝑃 Investigation of: Thermal expansion of polycrystalline and single crystalline material Phase transitions Change of microstructure Re-crystallisation Thermal treatment of lattice distortions and stress Manufacturing processes (sintering etc.) Dilatometry results for steel (C-0.59%, P:0.024,%, Mn:0.92% S:0.033%, Si:0.25% in mass%) Measurement modes: isothermal or temperature program

Concluding remarks All considered dynamic methods need calibration. The considered methods are based on measuring of property under temperature-time program. Differential thermal analysis (DTA) measures DT between sample and reference crucibles. Temperature and enthalpy of transformation can be measured by DTA. Differential scanning calorimetry (DSC) measures DT (or heat flow rate) between sample and reference crucibles in case of heat-flux DSC and power to compensate temperature difference between sample and reference crucibles in power compensation DSC. Temperature, enthalpy of transformation and heat capacity can be measured by DSC. Thermal gravimetric analysis (TGA) measure mass loss/gain. Temperature and mass loss/gain for the reaction including gas phase can be measured. Dilatometry measures thermal expansion. Thermal expansion coefficient and temperature of transformation can be determined.