1. Analysis of DTA data for binary alloys

2. Binary systems
Equilibrium: example Sn-Bi system

3. Binary system
Equilibrium: Example Sn-Bi system

4. Scheil Solidification
Fast diffusion in liquid
Slow diffusion in solid
Local equilibrium

5. Latent heat: Equilibrium vs. Scheil solidification
Equilibrium solidification
Scheil solidification

6. Example: Ag-Cu system Phase diagram of the Ag-Cu system.
Solid lines equilibrium calculations, dashed lines Scheil simulation.

7. Example: Ag-Cu system
Phase diagram of Ag-Cu system and calculated dHS/dTS for compositions 1, 5, 9, 15, 23, 28 mas.% Cu.

8. Example: Ag-Cu system. Comparison of calculated dHS/dTS with DTA results
Phase diagram and calculated dHS/dTS for 1 and 5 mass.% Cu.
dHS/dTS (J/kgK)
DTA results at different heating rates: black -15 K/min, red – 10 K/min, blue – 5 K/min.

9. Example: binary system Ag-Cu
Comparison of experimental DTA with calculated dHS/dTS
for alloys with 9, 23 and 28 mass.% Cu:
Black line – heating rate 15 K/min, red – 10 K/min, blue 5 K/min.
dHS/dTS (J/kgK)

10. General DTA curve analysis for binary system
Alloy Ag-15%Cu: dHS/dTS vs. TS using equilibrium enthalpy. Delta function is eutectic, vertical jump is liquidus.
DTA scan for melting and freezing at 5 K/min for Ag-15%Cu alloy:
Important points are labeled by i, not important by n.

11. Problems with liquidus determination on heating
Effect of hold time prior melting
The temperature at which a solid alloy begin to melt depends on the history of material.
Cast alloys often begin melting at temperatures below solidus (incipient melting). Reasons are existence of compositional gradients within individual phases or presence of extra phases in the alloy microstructure.
DTA for Inconel 718 showing effect of annealing time [91Cao]. With the annealing (Fe,Cr)2Nb Laves phase is dissolved and onset of melting increases from 1163 to 1247°C [91Cao].

12. Problems with liquidus determination on heating
Liquidus solidus separation by cycling near the liquidus
Results for Ni-base super-alloy a) Normal DTA scan on heating; b) Normal DTA on cooling; c) Cycling DTA to determine the liquidus temperature
If there is no endothermic effect the sample is in liquid state. If endothermic effect is present a partially solid state is implied.

13. Alloys with k<1 and k>1
The partition coefficient k <1 if liquidus/solidus separation (freezing range) increases with temperature decrease, while k>1 if liquidus/solidus separation decreases with the temperature decrease.
a) Phase diagram; b) dHS/dTS for k<1 is black line and for k>1 is read

14. Alloys with k<1 and k>1
Phase diagram of the Bi-Sb system.
Comparison of Sb-10%Bi with k<1 (a) and Bi-10%Sb with k>1 (b). dHS/dTS curves are computed for equilibrium conditions.

15. Errors caused by using extrapolated melting onset
In case of unary metal or eutectic in binary system linear extrapolation has physical ground: the onset is sharp and DTA curve is linear after the onset. The DTA curve for alloys with no eutectic has no linear portion near onset .

16. Eutectic reactions (L a+b) vs. Peritectic reactions (L+a b)
Both reactions take place at fixed temperature and exhibit an isothermal jump in enthalpy at the transition temperature. However they are quite different in their diffusion kinetics. For eutectic solidification both phases form directly from liquid; i.e. locally one has La and Lb. Thus the necessary solute redistribution occurs in the liquid ahead of the individual interfaces, which are in close proximity. Redistribution of components occurs through diffusion in liquid.

17. Different types of eutectic microstructures
More complex arrangements of the two phases occurs if interface attachment kinetics are sluggish (usually encountered for crystals that grow from liquid with crystallographic facets). Then two solid phases grow independently from the melt with very little communication of the solute fields in the liquid. This leads to much coarser mixture of the two solid phases (divorced eutectic).
a - globular eutectic
b – acicular (needle-like) eutectic
c - lamellar eutectic
d – Chinese script

18. Peritectic reaction L+ba
It requires the complete disappearance of b phase, a process that involves solute diffusion in two solid phases at peritectic temperature. The kinetics is different from eutectic because the diffusion rate is very different in liquid and substitutional solids. If only interstitial diffusion is required the peritectic reaction occurs more easily.
If one assume that no diffusion occurs in the solid upon cooling, solidification merely switch from freezing of high temperature phase L b to freezing of low temperature phase L a. Then b phase usually surrounds a phase resulting in coarser two phase microstructure than eutectic one.

19. DTA signal for eutectic and peritectic reactions
When the eutectic portion of a microstructure melts, both solid phases melt very close to common temperature, because phases usually exist as a fine two-phase intermingled microstructure. The melting DTA signal looks like that of a pure material. For peritectic alloy the two solid phases are not intermingled as closely as they would in eutectic alloy. The melting response of two phase microstructure can occur over a range of temperatures due to requirement of solid diffusion. The DTA response, as in freezing, again depends of the rate of solid diffusion with equilibrium and Scheil enthalpies representing the extremes of behaviour.
Part of the phase diagram for the Au-Sn system.
DTA signal for Sn-25%Au alloy.

20. Phase diagram with eutectic and peritectic reactions
Example Au-Sn system
Sn-rich part of Au-Sn phase diagram. Hs and dHs/dTs curves for An-25%Au calculated for equilibrium (black) and Scheil (red) conditions.

21. Example: Au-Sn system
(e)
Calculated freezing (c) and melting curves (d). The peak for peritectic reaction at 252°C is much smaller when the Scheil enthalpy is used. Experimental melting and freezing curves at 5 K/min (e).

22. Major points
Melting onset depends on metallurgical state of sample prior analysis.
Slow cooling and heating rates do not necessarily guarantee an equilibrated sample at each instant.
NIST recommendation: The melting onset during heating should be determined by first deviation from baseline. Extrapolated onset can be used for transformations in pure substances or for eutectics. In other cases DTA scans do not have linear section.
Annealing of samples in instrument prior to melting is sometimes required to obtain the thermodynamic solidus.
Peak temperature on heating with small freezing ranges may overestimate the liquidus temperature. Cycling experiments can be used to obtain a true liquidus temperature
Liquidus temperature determination on heating for alloys with partition coefficient k>1 is more difficult than for alloys with k<1
Peritectics do not produce as sharp melting peak as eutectics
Not all temperatures that can be extracted from DTA for alloy scan have meaning with regards to the alloy.