Binary systems Equilibrium example SnBi system Binary system Equilibrium Example SnBi system Scheil Solidification Fast diffusion in liquid Slow diffusion in solid Local equilibrium Latent heat Equilibrium vs ID: 539164
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Slide1
Analysis of DTA data for binary alloysSlide2
Binary systems
Equilibrium: example Sn-Bi systemSlide3
Binary system
Equilibrium:
Example Sn-Bi systemSlide4
Scheil Solidification
Fast diffusion in liquid
Slow diffusion in solid
Local equilibriumSlide5
Latent heat: Equilibrium vs. Scheil
solidification
Equilibrium solidification
Scheil
solidificationSlide6
Example: Ag-Cu system
Phase diagram of Ag-Cu system and calculated
dH
S
/
dT
S
for compositions 1, 5, 9, 15, 23, 28 mas.% Cu.Slide7
Example: Ag-Cu system
Solid lines equilibrium calculations, dashed lines
Scheil
simulation.
Phase diagram of the Ag-Cu system.Slide8
Example: Ag-Cu system. Comparison of calculated
dH
S
/
dT
S
with DTA results
DTA results at different heating rates: black -15 K/min, red – 10 K/min, blue – 5 K/min.
Phase diagram and calculated
dH
S
/
dT
S
for 1 and 5 mass.% Cu.
dH
S
/
dT
S
(J/
kg
K
)Slide9
Example: binary system Ag-Cu
Comparison of experimental DTA with calculated
dH
S
/
dT
S
for alloys with 9, 23 and 28 mass.% Cu:
Black line – heating rate 15 K/min, red – 10 K/min, blue 5 K/min.
dH
S
/
dT
S
(J/
kg
K
)Slide10
General DTA curve analysis for binary system
Alloy Ag-15%Cu:
dH
S
/
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.Slide11
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].
Problems with
liquidus
determination on heatingSlide12
Problems with liquidus
determination on heating
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.
Liquidus solidus separation by cycling near the liquidus Slide13
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 red Slide14
Comparison of Sb-10%Bi with k<1 (a) and Bi-10%Sb with k>1 (b).
dH
S
/
dT
S curves are computed for equilibrium conditions.Alloys with k<1 and k>1
Phase diagram of the Bi-Sb system. Slide15
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 . Slide16
Eutectic reactions (L
a
+
b
) vs. Peritectic reactions (L+b
a)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
La and Lb
. 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.Slide17
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 eutecticd – Chinese script
Different types of eutectic microstructuresSlide18
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 is usually surrounded by a phase resulting in coarser two phase microstructure than eutectic one.Slide19
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.
DTA signal for eutectic and
peritectic reactions
Part of the phase diagram for the Au-Sn system.
DTA signal for Sn-25%Au alloy.Slide20
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 Sn-25%Au calculated for equilibrium (black) and Scheil (red) conditions
. Slide21
Example: Au-Sn system
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).
(e)Slide22
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 temperatureLiquidus 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.