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Microsegregation, macrosegregation and related phase transformations in TiAl alloys.

D. Daloz1, U. Hecht2, J. Zollinger1,2, H. Combeau1, A. Hazotte3, M. Založnik1

1 Institut Jean Lamour, Dép. SI2M, CNRS – Nancy-Université – UPV Metz, Ecole des Mines de Nancy, Parc de Saurupt, CS14234, F-54042 Nancy Cedex, France 2 ACCESS e.V., Intzestr. 5, 52072 Aachen, Germany 3 LETAM/LEM3, Université Paul-Verlaine Metz, Ile du Saulcy, 57012 Metz Cedex, France

Abstract

In the first part of the paper the influences of microsegregation on the microstructure

establishment in Ti-Al based alloys are described. Examples are taken concerning the primary

solidification phase, the grain refinement through boron addition, the occurrence of B2 phase

in as cast parts and the link between microsegregation and creep properties. In the second

part, a numerical model of macrosegregation devoted to centrifugal casting of TiAl alloys is

presented and the influences of the parameters of the model are discussed.

Keywords: A. Titanium aluminides, based on TiAl; B. Phase transformation; C. Casting; D.

Microstructure;

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1. Introduction

Due to the poor formability of TiAl based alloys, casting of TiAl parts is identified to be the

most cost-effective process [1] despite the microstructure variability resulting from

heterogeneities inherited from the solidification.

While the alloying and the processing route are developed to increase the properties of the

product (beta solidifying alloy, grain refinement through boron addition, hot isostatic

pressing, heat treatment via the massive transformation…), a thorough understanding of the

way segregation occurs during solidification should be a great help to further enhance the

reliability of the whole processing route. Inherent to the solubility difference between the

liquid and the solid phases, together with non-equilibrium solidification conditions, the

microsegregation (i.e. chemical heterogeneities at the scale of the microstructure) cannot be

avoided during casting. When associated with a relative movement between liquid and solid,

the microsegregation may lead to macrosegregation. Whereas heat treatments can decrease

the intensity of the microsegregation, the macrosegregation established during solidification

cannot be modified and may lead to different microstructural responses to subsequent heat

treatments.

The aim of the present paper is first to highlight some microstructures and properties of TiAl-

based alloys that are directly linked to microsegregation, and second, based on a modelling

study, to present the build up of macrosegregation during centrifugal casting of TiAl-based

alloys.

2. Microsegregation in TiAl based alloys

The composition ranges of TiAl-alloys of technological interest often involve the liquid + β

→ α peritectic reaction / transformation during the solidification. The β phase has an open

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BCC structure that allows a consequent amount of back diffusion upon cooling; on the

contrary very little back diffusion is observed in the α phase [2]. These two different

solidification behaviours also result in different characteristics, particularly with regard to the

grain size [3] and the texture [4]. Alloying elements influence the solidification stage by

stabilizing either the β phase (Nb, Cr, Mo, W, Ta) or the α phase (Si, C, N, O). In near-

equilibrium casting conditions, the primary solidification phase is mainly determined by the

thermodynamics of the alloy, i.e. by its composition. Once the primary solidification phase

nucleates, its subsequent growth strongly depends on the partition coefficient of the alloying

element. Table 1 gives the partition coefficient experimentally determined by the authors from

microsegregation analyses of different alloys produced in directional solidification

experiments. It appears that, although not strictly as a rule, an element that segregates

positively within the β phase (kβ/l >1) also segregates positively within the α phase (kα

/l >1). It

also appears that a β stabilizer can have a partition coefficient either greater than 1 (for

example Nb, Ta) or smaller than 1 (for example Cr), which will be detailed in paragraph 2.3.

Element Nb Cr Ta Si Re W O

Stabilize β β β α β β α

ks/l β 1.27-1.42 0.49 1.37 0.53-0.8 / / >1

α 1.08-1.17 0.34-0.55 / 0.29-0.45 0.78-0.82 1.28-1.37 1.13-1.29

Ref. [2-5] [5] [6] [7,8] * [9]

Table 1: studied alloying elements, their stabilizing effect; and the experimentally determined

partition coefficient ranges in both β and α phases. * present results

Due to the limited extents of diffusion, microsegregation leads to microstructural deviation

from the equilibrium that is affected by the casting conditions. This will be illustrated in the

following through: i) the influence of the thermal gradient GT and solidification velocity V on

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the occurrence of the peritectic reaction for the Ti-48Al-2Cr-2Nb GE alloy and on the

solidification path and occurrence of TiB precipitation in Ti-45Al-8Nb-0.2B, ii) experimental

evidence of the influence of microsegregation on the precipitation of B2 phase in GE alloy

and iii) the role of microsegregation on the creep properties of Ti-(47-49)Al-1Re-1W-0.2Si at

pct “G4” alloy.

2.1 Microsegregation and phase selection

A simple analytical model has been used to predict phase selection and microsegregation

during dendritic columnar growth and to interpret experimental results concerning the

occurrence of the peritectic reaction for the Ti-48Al-2Cr-2Nb alloy and on the solidification

path and occurrence of TiB precipitation in Ti-45Al-8Nb-0.2B.

For a given composition, thermodynamic databases developed by Saunders [10] for the Ti-Al-

Cr-Nb-O system and by Witusiewicz et al. [11-14] for the Ti-Al-Nb-B system, in conjunction

with the ThermoCalc© software, are used to determine partition coefficients, liquidus slopes

and phase stability. The tip undercooling, the secondary dendrite arms spacing and the back

diffusion are calculated for different solidification velocities and thermal gradients, following

the model developed by [15-17]. This allows a solidification map to be built with the main

assumption that there is no nucleation barrier for the secondary phase. Thermo-physical data

used for the calculation have been published in [18].

2.1.1 Ti-48Al-2Cr-2Nb (GE Alloy)

Whereas Cr and Nb are both known as β-stabilizers, the as-cast microstructures of the GE

alloy present large columnar grains with hexagonal symmetry of the dendrites, typical of α

solidification. From these observations it has been admitted that this alloy solidifies via the α

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phase only [19, 20]. However, Sankaran et al. [21] have proposed that very low textures

sometimes observed in as-cast GE alloys could be explained by a solidification path starting

with solid β phase. As mentioned above, Cr and Nb stabilize the β phase, which is the

primary solidification phase in a binary Ti-48Al alloy. Thermodynamically it is obvious that

the GE alloy crystallizes via the β phase. However, kinetic phase competition may also play a

role in the selection of the primary phase. The figure 1(a) shows the difference between the β

phase and the α phase dendrite tip temperatures evolution with solidification (dendrites)

velocity: the β phase remains the primary solidification phase for the velocity range

investigated (1 – 100.10-6 m/s). However, due to the high reactivity of Ti-Al alloy with O, the

effect of oxygen was evaluated with the same calculation, including 0.5 at. O (≈ 2000

wt.ppm) in the alloy. At low velocities, the thermodynamic effect can be appreciated: as an α-

stabilizer oxygen contamination increases the α phase liquidus and inversely decreases the β

phase liquidus, thus lowering the dendrite tip temperature. At higher velocities, the

temperature difference decreases but still not enough to promote the α primary solidification

phase.

Figure 1: Influence of the solidification velocity and of oxygen on (a) the temperature

difference between β and α tip temperature and (b) the amount of β phase formed when the

peritectic transformation starts.

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Once nucleation occurs, subsequent growth of the solid is governed by microsegregation.

Taking microsegregation into account, the figure 1(b) shows the amount of primary β phase

formed before the peritectic reaction / transformation starts. The fraction of primary β phase

formed varies weakly with the solidification rate; it evolves from 16 % at a velocity of 1 µm/s

to 12% at a velocity of 100 µm/s. The effect of oxygen is more pronounced since the

calculation predicts that the amount of β phase formed at 100 µm/s is below 2% with 0.5 O. It

is obvious that such a small amount of pro-peritectic β phase can hardly be observed in

castings and even in directional solidification, since oxygen contamination is unavoidable.

Therefore this could explain the fact that α dendrites are observed in the as-cast but with low

texture, due to β primary solidification.

2.2. Effect of microsegregation on grain refinement.

Grain refinement of Ti-45Al-(5-10)Nb-(0-0.2)B (TNB) alloys with low boron addition has

recently been reported [22] and appears to be rather promising. The following mechanism has

been identified by the authors: boron acts as an effective refiner, not concerning the beta

phase, but the alpha phase. During beta primary solidification, boron segregates into the

interdendritic liquid, where metastable titanium borides (NbB structure, Pearson symbol oC8,

spacegroup Cmcm, No.63) can precipitate. The authors suggest from their observation that to

be effective, the nucleation of borides should happen before the nucleation of peritectic α

phase. They proposed the following solidification path associated with grain refinement:

Liquid →Liquid + β → Liquid + β + MB → β + MB → α + MB (M = Ti,Nb)

While the grain refinement can be achieved by adjusting the composition of the alloy at given

growth conditions, it can also be controlled by adjusting the growth condition for one alloy

composition, e.g. by controlling the microsegregation. The model presented above was used

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to calculate the solidification paths in a Ti-45Al-8Nb-0.2B alloy. The results are shown on the

phase selection map on figure 2, which indicates the phases present for different solid

fractions and growth conditions. For a thermal gradient in the liquid of 20000 K/m the model

predicts that the grain refinement can be achieved at solidification velocities up to 67 µm/s;

beyond this limit the secondary solidification phase becomes the α phase, and the grain

refinement fails. These results are consistent with previous experiments [22].

Figure 2: Phase selection map of the Ti-45Al-8Nb-0.2B alloy. Note that for the lowest

gradient in the liquid (GL=5000 K/m), no alpha phase forms in the studied velocity range.

For lower thermal gradient in the liquid (5000 K/m) no formation of α phase is predicted and

only borides appear at the last stage of the solidification (solid fractions > 96%). The

calculations enable us to underline two behaviours:

- The solid fraction at which the borides precipitate depends weakly on the solidification

velocity. This is attributed to the limited back diffusion of boron, inherent to the very

low solubility limit of this element in the β phase.

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- The α phase precipitation is more velocity-dependent, which can be linked to the back

diffusion: increasing velocity decreases the amount of back diffusion of aluminium

and niobium.

Although theoretical, these results highlight the importance of taking into account the

establishment of segregation to adjust a processing route that guarantees the grain refinement.

2.2. Influence of microsegregation on solid state phase transformation: occurrence of B2

phase.

In order to check the influence of microsegregation on the microstructure, the casting route

has been compared to the powder metallurgy (PM) route before and after hot isostatic

treatment (hip) on the same Ti-48Al-2Cr-2Nb (GE alloy) [5].

Figure 3(a) represents the interdendritic microstructure of the Ti-48Al-2Cr-2Nb GE alloy in

the as cast state. During the solidification Nb partitions in the intradendritic region and Cr is

rejected in the interdendritic region. The resulting microstructure is only composed of α2 + γ

lamellae in the intradendritic region whereas γ monolithic grains and B2 phase are also found

in the interdendritic region [23]. The occurrence of B2 phase is often associated with the

ordering of residual β primary solidification phase. In this case, it appears as a white network

in back scattered contrast which is mainly located in the intradendritic region. In the GE alloy,

the observation of the B2 phase in the interdendritic region suggests that it forms differently.

During the hip treatment performed in the α + γ domain one observes that the B2 phase

coarsens and new monolithic γ grains appear (figure 3(b)). The volume fraction of the γ phase

increases from 97% to 98.5%, the volume fraction of α2 phase decreases from 2 to 1% and the

volume fraction of B2 decreases from 1% to 0,5%. Table 2 displays the composition of

monolithic γ grains and B2 phase before and after hipping.

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It appears that the formation of the B2 phase in the GE alloy is linked to the high level of Cr

content of the monolithic γ grains (γm) due to microsegregation during the solidification. This

high level stabilise the B2 phase that precipitates during cooling. During hipping Cr is

rejected outside the as cast γm. Coarsening of those grains and grain boundaries movement

may favour the redistribution in Cr towards the B2 whereas correspondingly Al leaves the B2

phase.

γ phase As-cast As-hipped

B2-Phase As-cast As-hipped

Ti 44,93 +/- 0.02 45, 83 +/- 0,25 40,55 +/- 1,02 51,2 +/- 0,45 Al 50,57 +/-0,15 50,72 +/- 0,16 42,63 +/- 1,22 36,53 +/- 0,51 Cr 3,43 +/- 0,12 1,74 +/- 0,32 16,10 +/- 1,03 10,40 +/- 0,9 Nb 1,08 +/- 0,3 1,71 +/- 0,23 0,73 +/- 0,12 1,87 +/- 0,23

Table 2: Chemical compositions of monolithic inter-dendritic γ grains and B2 phase in GE

alloy, in the as cast and as hipped state.

On the contrary, for the alloy elaborated via the PM route, the microstructural response to hip

treatment differs. Before hipping, the microstructure of the powder as determined via XRD is

composed of metastable α, γ and β phases (91,4% - 5.3% and 3,4% respectively). During

heating, the β phase transforms to γ below 550°C then α +γ (88% and 12%) transform to α2 +

γ (2% and 98%) between 650 and 750°C. After hipping, the structure is mainly of γ phase

(97,2%) with small amount of α2 phase (2,8%); no B2 phase is evidenced (figure 3(c)).

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Figure 3: SEM micrograph of inter-dendritic region of GE alloy in the as cast state a) and as

hipped state b) and (c) of as hipped PM alloy.

2.4 Influence of microsegregation on creep properties.

Since the third generation of TiAl alloys, β stabilizing elements are added to avoid the strong

casting texture observed with α primary solidification phase [4]. Among the different

elements, Re and W are very efficient β stabilizers, 2 at% being sufficient to promote β

primary solidification [24]. It gives way to the development of the Ti-(47-49)Al-1Re-1W-

0.2Si at pct “G4” alloy [25]. In order to determine the microsegregation behaviour of such an

alloy, investigation of the liquid/solid partitioning of the different elements has been

performed using quenching during directional solidification experiments. WDS microprobe

analysis has been done for different sections of the quenched bars corresponding to different

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solid fraction, from which cumulative distributions are reported in the figure 4(a). From these

measurements the partition coefficient has been determined (see the table 1). Concerning W

and Re, an opposite behaviour is noticed: kWs/l = 1,3 and kRe

s/l = 0,8. During solidification, Re

concentrates in the interdendritic region whereas W segregates in the intradendritic region.

This different behaviour is responsible for the high level of creep resistance (figure 4(b)) but

also for the high difference of creep resistance of the G4 alloy as a function of its preliminary

heat treatment reported in [26]: during high temperature hip followed by long term high

temperature heat treatment, intense homogenization leads to redistribute the interdendritic/

intergranular Re segregation. This results in a large decrease of the creep strength for the

structure that has been long term aged.

Figure 4: (a) Solute content as a function of cumulated fraction for Al, Si, W, and Re in G4

alloy and (b) creep resistance of the G4 alloy compared to IN738LC and GE alloys.

3. Macrosegregation

Microsegregation can lead to significant segregation at the macro-scale, whenever fluid flow

or solid grain motion occur. The phenomena responsible for macrosegregation in castings are

(i) fluid flow due to casting or stirring, thermosolutal natural convection and feeding of

solidification shrinkage; (ii) motion of free-floating equiaxed solid grains due to density

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differences (grain settling in TiAl) and due to entrainment by the liquid; and (iii) motion of

solid due to deformations of the packed solid network or the consolidated solid skeleton. At

the origin is the microsegregation, in TiAl-based alloys produced during the primary

solidification “Liquid → β(Ti)” and during the peritectic reaction, composed of two

transformations: “Liquid → α(Ti)” and “β(Ti) → α(Ti)”. As we saw above, it is however

possible that the peritectic transformation does not occur and the transformation continues as

only “Liquid → α(Ti)”. While the main phenomena are well identified, much less is known

about the interdependence and the respective importance of the individual macroscopic

transport phenomena (i-iii) in the formation of the macrosegregation in particular casting

processes. The combination of experimental and modelling research recently led to

significant progress in the understanding of macrosegregation formation in casting of steel

ingots and continuous casting of steel and aluminium alloys [27-30]. In modelling, multi-scale

approaches are used, which bridge length and time scales by averaging techniques and

simplifications [31-32]. A coherent mushy zone is a porous medium. The evolution of its

porosity and the convection-diffusion heat and mass transfer driven by the fluid flow in the

mush are strongly coupled. The macrosegregation patterns induced by the advection of solute

in the coherent mushy zone are well explained [30, 33]. On the other hand, more experimental

and theoretical research is required before we can fully understand the macrosegregation

formation in castings with fine equiaxed solidification structures [27,34]. Detailed research of

this mechanism started getting attention only recently [30, 31, 34] and is best studied in the

casting of steel ingots. In castings with a predominantly equiaxed structure, the transport of

the solute-lean equiaxed grains is a significant mechanism of macrosegregation formation

[27,30]. As the equiaxed grains settle, they accumulate into a coherent packed layer. As

recently shown [30,34], the morphology (dendritic/globular) of the equiaxed grains is the

decisive parameter for the packing of the grains and thus the accumulation of the solute-lean

solid phase. Globular grain morphology promotes the impact of grain settling on

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macrosegregation, while dendritic equiaxed structure limits it and promotes the influence of

the intergranular melt flow in packed layers. The grain growth and morphology development

is strongly coupled with nucleation, with columnar dendrite fragmentation (as a source of

growth seeds), with solute diffusion on the microscopic (grain/dendrite) scale, and with the

macroscopic transport of heat and solute [34].

Studies devoted to macrosegregation in Ti-Al alloys are scarce. The first of the two known

publications [35] reports an experimental study of macrosegregation in plasma arc melting of

γ-TiAl and relates the macrosegregation mainly to the homogeneity of the feedstock. The

model study by Noeppel et al. [36] discusses the solidification of Ti-35.2 mass%Al in a

Bridgman furnace in the presence of electromagnetic stirring. It accounts for a fixed solid

phase and a peritectic reaction and concludes that the forced convection has an important

influence on the segregation and the phase distribution.

Within the IMPRESS project we made first attempts to quantify the macrosegregation in

centrifugal casting of Ti-46Al-8Nb. Here we present a first modelling study as a part of an

integrated experimental/model approach. The modelling is used to identify the potentially

important physical phenomena in order to prepare the experimental part and to define the

required additional experimental inputs.

3.1 Micro-macro model

The numerical simulations are performed with SOLID, a 2D multiscale solidification model,

capable of modelling segregation in castings. We simulated a cylindrical sample with a

diameter of 8 mm and a length of 65 mm, solidifying in a ceramic mould. The mould is

rotated at 200 rpm in a horizontal plane with the outer radius of revolution of 470 mm. The

configuration and the boundary conditions are shown schematically in the figure 5. These

parameters correspond to the planned experiment.

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Figure 5: Schematics of the simulated casting sample. The model geometry was considered as axisymmetric.

Due to the limitations of the model to two dimensions, we considered an axisymmetric

geometry. For this assumption to be reasonable, the gravity acceleration and the Coriolis’

effect, both producing forces perpendicular to the revolution plane and thus breaking up the

axisymmetry per-se, have to be negligible compared to the centripetal acceleration. As shown

by our simulations, this is verified. We can roughly compare the influence of the three forces

by comparing the corresponding accelerations, as can be seen from Eqs. (1-3) in the table 3.

On the one hand, the centripetal acceleration is between grc!" 18~2ω (at the smallest radius)

and

€

~ 21 ! g (at the outer radius); and on the other hand the Coriolis’ acceleration is at most

grv cm!"" 4~2 2×ω . The largest Coriolis’ acceleration occurs in the case where we consider the

motion of equiaxed grains and the radial velocities reach up to 0.1 m/s.

SOLID is based on a volume-averaged Euler-Euler two-phase model that consists of two

parts: a macroscopic part with momentum, mass, heat, solute mass, and grain population

conservation equations, and a microscopic part that describes the nucleation and growth of

grains. A detailed derivation of the model equations and the solution algorithm are reported in

[32].

At the macroscopic level, the model accounts for heat and solute transport coupled with flow

driven by thermal and solutal buoyancy. Solidification shrinkage is not taken into account.

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Depending on the behaviour of the solid phase, we consider two flow regimes. The regime

depends on the local solid fraction, gs. If the local solid fraction is larger than the packing

limit (gs>gblock) the solid phase in the mushy zone is considered to be blocked or coalesced

and the flow of intergranular liquid through the porous solid matrix is described by a

momentum equation including a Darcy term to model the drag interactions. The permeability

of the porous matrix is modelled by the Kozeny-Carman law. At solid volume fractions

smaller than the packing limit (gs<gblock) the solid phase is considered to be in the form of

free-floating equiaxed grains and the motion of the grains is described by transport equations

for the solid phase. The macroscopic transport equations are derived from local continuum

equations using a volume averaging technique. Two phases, the solid and the liquid, are

considered separately in the model (two-phase model); each phase is described with an

Eulerian approach. In this way, the behaviour of a population of grains is locally described by

the behaviour of an averaged grain.

In the free-floating equiaxed regime (gs<gblock): total (solid+liquid) momentum balance

( ) ( ) ( )( ) ( )mcmllllllllll vrgvgpvvg

tvg !!!!!!!!

×−++∇⋅∇+−∇=⋅∇+ ωωρµρ∂ρ∂

22 (1)

Explicit expression for the velocity of the solid phase:

( )( )scsld

lgls vrgp

Cgd

vv !!!!!!×−++∇−+= ωωρ

µ2

Re34 2

2

(2)

In the porous flow regime (gs>gblock): liquid momentum balance

( ) ( ) ( )( ) ( )lcllll

lllllllllll vrgg

Kg

vgpgvvgtvg !!!!!!!!

×−++−∇⋅∇+∇−=⋅∇+ ωωρµ

µρ∂ρ∂

222

(3)

Table 3: Averaged momentum balance equations for the liquid and solid phases including the

centripetal and Coriolis’ accelerations. Note that gravity and Coriolis’accelerations were

assumed to be negligible in the simulations. vl, vs, and vm are the velocities of the liquid, the

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solid and the solid-liquid mixture respectively, ω is the angular velocity, and rc is the distance

from the axis of rotation.

The microscopic level is treated locally; within SOLID, which is based on the finite volume

method, this means within each control volume (CV). The formation of new grains by

nucleation is modelled by an instantaneous uniform volume nucleation law. Locally, a

predefined number of spherical nuclei per unit volume N0 = 6⋅1010 m-3 was activated when the

temperature dropped below the liquidus temperature. This density corresponds to a final grain

size of roughly 250 µm. This is a very rough approximation, since the grain size is difficult to

determine experimentally due to the secondary “β(Ti) → α(Ti)” transformation. In

experiments under similar conditions, the sizes of α colonies were between 175 to 200 µm.

Since multiple (e.g. two) colonies can form from one a, the size was taken somewhat larger,

i.e. 250 µm. At the microscopic level we further model phase change (solidification and

melting) that is controlled by solute diffusion in both phases at the grain scale, assuming local

thermal equilibrium and thermodynamic equilibrium at the solid-liquid interface. In the

present work the grains are considered spherical. With SOLID it is also possible to consider a

simpler phase-change model, such as the Lever rule or the Scheil law, which is a classical

approach in coupled micro-macrosegregation modelling. The alloy system was modelled in a

simplified way, as a binary Ti-46 at%Al (corresponding to Ti-29.6 mass%Al) with a partition

coefficient of kp = 0.9 [9] and a linearized liquidus slope of -14 K/mass%. The diffusion

coefficients in the liquid and the solid respectively were Dl = 4⋅10-9 m2/s [37] and Ds = 10-12

m2/s.

The motion of the free-floating grains is governed by a balance of buoyancy, drag, and

pressure forces. In this way, the solid and liquid phases have locally different velocities. In

particular, on one hand, the density of the solid phase is higher than that of the liquid and on

the other hand, the interfacial particle drag is considered dependent on the grain size. This

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produces the tendency that the larger the grains are, the stronger their tendency to settle;

contrarily, smaller grains are more easily entrained by the liquid motion.

3.2 The influence of the solidification kinetics and of equiaxed grain motion

We present three cases that allow us to estimate the effects of (i) the solidification kinetics

and (ii) the motion of equiaxed grains on the macrosegregation. So, in case B we employ a

simple solidification model, assuming local thermodynamic equilibrium (lever rule) and in

case A we account for the diffusion-controlled solidification kinetics. In both cases A and B

the solid phase is assumed to be fixed (columnar structure). In case C we account for the

motion of equiaxed grains, assuming a fully equiaxed structure with a globular grain

morphology and a packing solid fraction of gblock = 0.4.

The results are illustrated in the figure 6, where we show the liquid fraction and velocity fields

at 1.5 s from the beginning of solidification and the final segregation pattern. The fluid flow

in cases A and B is caused by the buoyancy force caused by thermal and solutal variations of

the liquid density in the centrifugal acceleration field (the gravity acceleration, perpendicular

to the plane is much smaller and is neglected). At the beginning, before the onset of the

solidification of the superheated liquid (initially by 16.5 K), the thermal buoyancy sets up a

flow in a closed loop outwards along the cooled outer side of the cylindrical sample and

inwards towards the centre of rotation along the centreline. During solidification the

microsegregation causes an enrichment of the liquid in aluminium in the mushy zone and thus

a decrease of the density. Within the mushy zone this solutal density variation is stronger than

the density increase with lowering temperature and the solutal buoyancy thus prevails. After

solidification has spread out the mushy zone, the flow direction reverses to inwards along the

outer side and outwards along the centreline. In case B the macrosegregation prediction is

classical and can be demonstrated by a classical analysis. The macroscopic transport equation

for the solute in the liquid phase and the consideration of mass conservation and of local

thermodynamic equilibrium in the liquid and solid phases in a binary alloy (Cl = (T-Tf)/mL, Cs

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= kp Cl, where Cl and Cs are the local liquid and solid concentrations, T is the temperature, Tf

is the melting temperature of the pure solvent, mL is the slope of the liquidus line and kp is the

equilibrium partition coefficient) give an expression for the variation of the average local

composition Cm = glCl + (1-gl)Cs

€

∂Cm

∂t= −∇⋅ gl

! v lCl( ) = −gl! v l ⋅ ∇Cl = −

1mL

gl! v l ⋅ ∇T , (4)

where gl is the liquid fraction and vl is the velocity of the liquid. So the heat transfer and the

direction of the flow circulation determine the observed segregation tendency. This

corresponds to a negatively segregated patch at the cooled outer end of the sample, created

during the initial stage of solidification, before the bulk flow changed direction. Later on, the

inversed solutally dominated flow created a negative Al segregation at the outer end and a

positive at the inner end.

In case A we take into account the finite diffusion at the grain scale that controls the phase

change. Due to the fast cooling rate (the solidification time is of the order of ~5 s) and the

limited solute exchange at the solid-liquid interface, considerable undercoolings are reached,

about 30 ºC at the beginning of solidification (during recalescence) and up to 15 ºC during

later stages of solidification. The liquid surrounding a growing grain has a concentration that

is much lower than that of the equilibrium concentration at the interface. Overall, the

segregation is decreased and certain tendencies, like the positive segregation at the centreline

at the outer end of the sample are changed due to the impact of the phase-change kinetics on

the macroscopic heat transfer via the modified solidification path.

In case C we take into account that the solid forms as equiaxed grains that can initially freely

move and are packed where the local solid fraction reaches 0.4. In the beginning of the

packed layer formation at the outer end of the cylinder, flow of intergranular liquid is still

possible and creates the positive segregation. Later on the layer of blocked grains becomes too

densely packed to permit any significant fluid flow between the grains. The solid phase has a

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higher density and the free grains thus have a tendency to migrate outwards under the

influence of the centrifugal acceleration. They entrain the liquid and most of the time control

the flow direction that is now directed outwards along the cooled wall, where the solid

fraction is higher. The grains are lean in solute and the settling phenomenon alone would

produce a negative Al segregation at the outer end of the casting. There are two mechanisms

of “attachment” to the coherent zone: by mechanical blocking at the outer end or by

coalescence due to grain growth at the vertical wall. Due to the fast phase change rate the

second one becomes important and the packing front is inclined (rather than perpendicular to

the axis). In their settling motion to the bottom of the packing layer the grains thus also move

towards the centreline. A negative segregation along the centreline is thus produced by the

motion of the solute-lean grains. The liquid “above” the packed layer becomes progressively

enriched and a positive segregation is created at the inner end of the sample.

20

Figure 6: Cases A (fixed solid phase and with diffusion-controlled growth), B (fixed solid

phase with lever rule solidification) and C (fully equiaxed with free-floating grains and

diffusion-controlled solidification). Left: liquid fraction and velocities (liquid streamlines for

cases A and B and solid velocities for case C) in the sample, packing limit for case C, all at

1.5 s from the beginning of solidification. Right: final segregation in mass%Al (note the

different scale for case C). The axis of rotation is perpendicular to the depicted plane and is at

y = -0.405 m.

21

4. Conclusions and perspectives

This article intends to explain how microsegregation occurs during solidification of TiAl-

based alloys and how it can affect the microstructure. While non exhaustive, it has been

shown how microsegregation can affect:

- the primary solidification phase,

- the grain refinement through boron additions,

- the nucleation / formation of the interdendritic B2 phase in the GE alloy,

- the redistribution of solutes responsible for high creep resistance in the G4 alloy.

Coupled to solid/liquid movement, microsegregation can lead to macrosegregation. The

modelling reveals the importance of several parameters on the macrosegregation in the

centrifugally cast sample. If the initial superheat is high enough, the thermal convection can

control the flow and determine the segregation in the part that solidifies first. The growth

kinetics can influence the intensity of segregation if high undercoolings are attained.

However, the extent of undercooling at comparable cooling rates (at the order of 20 K/s)

should be verified experimentally, to be able to refine the model and the conclusion in this

point. The motion of equiaxed grains leads to a very different macrosegregation, as settling of

the solute-lean grains becomes the preponderant segregation mechanism. However, here the

grain growth kinetics has an impact on the shape of the packing front and thus on the

segregation that the settling will induce. The guideline for a systematic casting experiment

should be to cast at different cooling rates ant different initial superheats, as well as to

experimentally determine the grain size.

Within the development of a new air-hardenable alloy through the massive γ transformation,

further work considering the coupling of micro and macro-segregation and its effect on the

reliability of the massive transformation is now required.

22

Acknowledgements

The authors would like to express their gratitude for financial support from the Integrated

Project IMPRESS, “Intermetallic Materials Processing in Relation to Earth and Space

Solidification” (Contract NMP3-CT-2004-500635) co-funded by the European Commission

in the Sixth Framework Programme and the European Space Agency.

23

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