Tzero line paraequilibrium Experimental methods of phase diagram determination C D Composition a Schematic phase diagram b Thermal analysis of alloy X 2 c XRD of series of alloys phase boundaries from lattice parameter vs composition a diffusion couple X ID: 549438
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Slide1
The role of phase transformation kinetics in phase diagram determination and assessment
T-zero line, para-equilibriumSlide2
Experimental methods of phase diagram determination
C
D
Composition
a. Schematic phase diagram; b. Thermal analysis of alloy X
2
; c. XRD of series of alloys - phase boundaries from lattice parameter vs. composition; a. diffusion couple X
1
-X
4
– compositions determined at the interface
a
-
g
by EPMA; a. equilibration of X
3
alloy in two-phase field – compositions of phase
a
and
g
are determined by EPMA.Slide3
G
X
0
G
a
G
g
X
a
X
g
Composition
Gibbs
energy
Schematic diagram presenting variation of the Gibbs energy with temperature for stable and metastable phasesSlide4
Temperature dependence of the Gibbs energy
T
s-Tf range a+g
is equilibrium state; T
0
g
/
a
is T-zero line where Gg
=Ga;g
a
+
g
can occur by long-range diffusion.
When T<T
0
g
/
a g
a can occur forming a of the same composition as
g. This can be realised at temperature Ma, at which driving force D
Gg
a is large enough to initiate large nucleus. At T
f a becomes stable phase.
Phase a‘ is metastable martensite. Ga‘ is above Ga and T0g/a‘ is lower than T0g/a. Martensite transformation can occur at temperature Msa‘, at which driving force DGg a‘ is large enough to initiate martensite nucleus a’. If other metastable phases exist and their Gibbs energies are higher than for a’ they can form at temperature below Msa‘.The number of metastable phases increase with lower temperature.Equilibrium state is shown by heavy line.Slide5
Shifting of transformation start temperature on cooling and formation of metastable phase
Cooling transformation kinetics for
Ti
-Ag alloys showing variation of
b
a
transformation-start-temperature
Ts
with cooling rate and composition
Transformation temperature vs. cooling rate for Ag-Al and
Ti
-Cu alloysSlide6
Shifting of transformation-start temperature with heating rate
Transformation temperature vs. heating rate for pure
Ti
Transformation temperature vs. heating rate for Ti-5.25at%Mo alloy (a) showing shifting
b
/(
a
+
b
)
transus
with increasing heating rate; for Ti-4.6at.%Cr (b) showing shifting eutectoid temperature
a
+
a
TiCr
2
a+
b with heating rate.Slide7
a
/
a
Influence of formation of metastable phases to the results of
transus
determination on subsequent heatingSlide8
Dependence of transformation start temperature on heating/cooling rate and formation of metastable phase
Transformation-start temperatures
heating
cooling
heating, when
martensite
phase forms
heating
cooling
heating, when
martensite
phase
formsSlide9
Example: Fe-Ni system
Comparison of cooling and heating transformation start temperatures with equilibrium
g/(a+g)
transus
in Fe-Ni system
The heating transformation start temperature (A
s
) should be above
g
/(a+
g
)
transus
because heating always shift phase boundary to higher temperature. The fact that A
s
on heating is below the
transus
indicates that metastable structure has been
produced during the cooling. The As
is temperature of metastable phase transformation to g phase and has no direct relation to equilibrium transus.Slide10
Phase diagram of Co-Cr, miscibility gap (
Nishizawa
horn) is not identified by DTA.
Phase diagram of Co-Mo system;
Phase diagram Co-V system
Examples of deviation of phase boundaries obtained by DTA and equilibration
.Slide11
Concluding remarks
The specific high cooling and heating rate that cause significant deviation from equilibrium depends on the alloy, its composition, grain size, phase structure and temperature of the transus (relative to solidus).If high temperature phase is liquid the shifting of temperature during slow cooling and heating rate is less pronounced that that for solid-solid transformation, because it is easier to nucleate critical nucleus from liquid than from solid phase. DTA data for transformations including liquid are more reliable than for solid-solid transformation.
For high Fe-Ni alloys even few degree per minute is high cooling rate because diffusion is difficult.It is recommended to use the results of equilibrated alloys or diffusion couple to assess phase boundaries.It should be mentioned that transformation-finish temperature for cooling and heating (Mf, Af) has very little connection with equilibrium transus, because transformation start temperatures are already shifted away from equilibrium.If transformation temperature is below half of the homologous melting point, one need to pay special attention to potential problem associated with kinetics of phase transformation and shifting transformation temperature away from equilibrium phase boundaries.Slide12
Isopleth of the Cu-Ni-Sn system at 15 mass. %Ni (a); TTT diagram of the Cu-15Ni-8Sn alloy (b);
g
(D0
3
) is stable phase, L1
2
and D0
22
are metastable phases.
Decomposition of high temperature intermetallic compounds is very sluggish. Example Nb
-Si system:
a. Phase diagram, b. TTT diagram for Nb-19at.%Si.
Temperature of eutectoid reaction Nb
3
Si=bcc+Nb
5
Si
3
is 1679°C.
Isothermal phase transformation kinetics: time-temperature-transformation ( TTT) diagramsSlide13
Example: Phase diagram of Cr-
Nb
-Si system at 1000°C
Goldschmidt and Brand (1961):
220 alloys were arc-melted and annealed at 1000°C for 336 h (2 weeks)
Isothermal section based on the results of diffusion multiple (Zhao et al. 2003) annealed at 1000°C for 4000 h and all phases were formed by thermal inter-diffusion reaction without going through melting and solidification process. Therefore there no issue concerning kinetics of decomposition of high temperature phases at low temperatureSlide14
Example isothermal section of Nb
-Cr-Al system at 1000°C
a. Results based on melted and annealed samplesb. Results based on solid state reactions of fine powders (powder metallurgy) 168 hc. Results obtained from diffusion multiple annealed for 168 h.Both powder metallurgy and the diffusion multiples avoided the problem associated with slow decomposition of intermetallic compounds.Slide15
Kinetics and phase formation in diffusion couples/multiples
Advantages of diffusion couple
Formation of all phases at temperature of annealing without going to melting and solidification.
Formation of multiple phases in a single sample thus allowing multiple tie-lines to be extracted from the local equilibrium at the phase interfaces.
Disadvantages
Long time of annealing required to grow phases of sufficient thickness for quantitative composition analysis and structure identification
T
emperature limits – difficult to reach equilibrium at low temperatures
.
SEM/BSE image of diffusion couple
b) 1100°C (4000h)
c) 1150°C (2000h
)
bcc+Ti
5
Si
3
Ti
3
Si (1125°C) instead of 1170°C by DTA
Phase diagram of Ti-Si systemSlide16
Formation of
martensite
, T
0
-line calculation
The Schematic representation of the Gibbs energies of phases
a
and
g
, phase diagram and T
0
lines for
diffusionless
transformation of
g
a
and
g
a‘
Thé Gibbs energies of g,
a and a‘ (martensite
) and driving force of partitioning in stable assemblage and to a‘ (martensite
)Calculated portion of Fe-
Mn diagram along with T0-line of diffusion-less transformation gaSlide17
Fast diffusing elements, para-equilibrium
A schematic phase diagram for the ternary system Fe-C-2, where 2 is substitutional alloying element (e.g. Ni,
Mn, Cr etc.). The phase region limited by solid lines corresponds to full equilibrium (EQ); region PE limited by dashed lines and shaded corresponds to para-equilibrium.
Para-equilibrium is constrained local equilibrium in which mobile components are assumed to be freely redistributed between phases coexisting in the vicinity of transformation interface, while the less mobile components are assumed completely frozen in place during the passage of interface.
A schematic ray section (Fe/2 ratio is fixed) of isothermal Gibbs energy surfaces for ferrite and austenite. Deviation of local para-equilibrium
X
C
g
Pe
-X
C
g
i
results in driving force (approximately
m
g
S
-
m
a
S
). Driving force derives entirely from substitutional sublattice, while
mC is constant.Slide18
T0-line calculation and driving force to equilibrium partitioning
Equilibrium phase diagrams for the systems a. ZrO
2
-YO
1.5
; b. ZrO
2
-Gd
0.5
Y
0.5
O
1.5
; c. ZrO
2
-GdO
1.5
and calculated T
0
-lines for F-T and T-M diffusion-less transformations.
Calculated driving forces to equilibrium partitioning for quasi-binary systems and Gd(/Gd+Y)=0.25, 0.5, 0.75Slide19
Para-equilibrium diagrams for the Fe-Mn
-C system
Vertical section of Fe-
Mn
-C phase diagram at fixed
Mn
/(
Mn+Fe
) ratio 0.025
fcc+bcc
para-equilibrium is superimposed;
fcc+bcc
para-equilibrium and T
0
-lies are superimposed;
fcc+bcc
and
fcc+cementite
are superimposed.
a
c
bT0Slide20
Example: Fe-Mn-Si-C system
Vertical
section
of
Fe
-Mn-Si-C system
phase diagram for
1.5
mass
%
Mn
and
0.3
mass
.% Si together with T0-line
and para-equilibrium fcc+bccIsothermal
section of Fe-Mn-Si-C system
at 1000 K together with para-equilibrium fcc+bccSlide21
Scheil solidification with fast diffusing component (i.e. C) and without. Example: Fe-Cr-C
Vertical section of Fe-Cr-C system at 1
mass
.% C
a
b
Scheil
simulation of Fe-10%Cr-1%C solidification based on
Scheil
assumption with C as fast diffusing component and without fast diffusing components
Mole fraction of solid phases vs. Temperature
Micro-segragation
in the
fcc
phase