Nucleation studies on undercooled refractory metals … · Unité qui présente / Réf présentation 03-08-28 1 Nucleation studies on undercooled refractory metals and alloys: a review

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03-08-28 1Unité qui présente / Réf présentation

Nucleation studies onNucleation studies on undercooledundercooledrefractory metals and alloys: a reviewrefractory metals and alloys: a review

Bernard Vinet

CEA-DRT-Département des Technologies pour les Énergies Nouvelles

Service Matériaux et Procédés

17 rue des Martyrs, 38054 Grenoble, Cedex 09 (F)

Nucleation Workshop, ENS – Mines de Saint-Etienne

DRT/DTEN/SMP - Nucleation Workshop June 17-18th (2003)

1. Experimental approach - containerless processing

2. Nucleation studies on pure refractory metals

q statistical analysis on nucleation events

q comments on the limit to crystal nucleation

3. Metastable phases

q pure metals

q Refractory alloys (Re-W and Re-Ta systems)

4. Conclusion – acknowledgments - references


1. Experimental approach: liquid undercooling (1)

The state of liquid undercooling is discovered by Fahrenheit (1724) on water when working on the thermometer ; observed by Cavendish in Hg protected by nitric acid and fats (bef. 1800).

Undercooling water down to – 20°C, Despretz noticed a rapid solidificationthat caused the destruction of the glass vessel (ard 1820).


Temperature

nucleation

solid-liquid

equilibrium temp.

undercooling

liquid

solidrecalescence

liquid

thermocouple

inorganic glass

slag, oil, etc

crucible

atmosphere

encasement methods

origin, limit, phase selection ?


The French word “germination” is introduced by Gernez (1865), a student of Pasteur: nucleation is favoured by introducing isomorphous solidparticles ; Van Riemsdyk (1880) observed the detrimental effect of stirring and discontinuous cooling.


1. Experimental approach: heterogeneous nucleation (2)

heterogeneous nucleation

extraneous interfaces (e.g. impurities, container walls)

homogeneous nucleation

favourable thermodynamic fluctuations in the bulk utheoretical limit

impurities

stirring

?containerless processing

free-fall methods


1. Experimental approach: dispersion methods (3)


Mendenhall and Ingersoll (1908) obtained very large undercoolings on minute particles of Pt (375 K) placed upon the surface of a Nernst glower, whose temperature could be controlled with suitable rheostat and examined with a microscope of low power.

Vonnegut (1948) demonstrated that heterogeneous nucleation sites can be isolated by dividing the melt into small particles : suitable way to investigate the undercooling behaviour.

dispersion & emulsification methods

Turnbull, Perepezko, Bosio, Rasmussen, Skripov,…


1. Experimental approach: containerless processing (4)


Containerless processing is introduced by Shiraishi and Ward (1964) for thermophysical properties measurements. Based on the monitoring of temperature/time profiles, it is well suited for undercooling experimentson high-temperature and refractory materials (uuuufree-fall conditions).

aerodynamic lev. : CRMHT – Orléans (F. Millot)

electrostatic lev. : NASDA – Tsukuba (J.F. Paradis)

electromagnetic lev. : DLR – Cologne (D.M. Herlach)

1st drop-tube : NASA – Huntsville (W.H. Hofmeister)

space transfer of containerless processing

ESA-EML

48-m high G

renoble drop-tube


1. Experimental approach: refractory metals (5)

Au1064°C

19.3fcc

Pt1772°C

21.4fcc

Ir2443°C

22.5fcc

Os3045°C

22.4hcp

Re3180°C

21.0hcp

W3410°C19.30

cc

Ta2985°C16.65

cc

Hf2231°C

13.3cc/hcp

Ag962°C10.5fcc

Pd1552°C

12.0fcc

Rh1960°C

12.4fcc

Ru2250°C

12.4hcp

Tc*2172°C

11.5hcp

Mo2617°C10.20

cc

Nb2468°C

8.40cc

Zr1852°C

6.50cc/hcp

Cu1083°C

8.96fcc

Ni1453°C

8.9fcc

Co1495°C

8.90hcp

Fe1535°C

7.87cc

Mn1244°C

7.43A12

Cr1857°C

7.19cc

V1890°C

6.10cc

Ti1660°C

4.54cc/hcp

4d-

5d-

3d-

Undercooling experiments have essentially dealt with elements ranging between Hg and Fe in melting temperature, thus considering in a common approach elements characterized by very different physical and chemical properties (e.g. Fe, Al, Si, Bi, Au, etc.).


Importance of transition refractory metals:

xxxx fundamental: correlation with the periodic table (atomic number)

xxxx practical: outstanding properties (severe environments), new alloys

03-08-28 7Unité qui présente / Réf présentationDRT/DTEN/SMP - Nucleation Workshop June 17-18th (2003)

Gibbs proposed in 1873 a thermodynamic analysis of phase stability. In the case of classical nucleation, metastability corresponds to the situation where a critical size exists within a localized fluctuation beyond which growth occurs. Through the capillary formalism, the Gibbs free-energy difference of a spherical nucleus in the melt is the sum of:

1 nm

250 atoms

solid-liquid interface energy

radius r

“surface”

“volume”

growth

Gib

bs

free

en

erg

y ∆∆

G

LS2r4 σσππ

V3 Gr

34

∆∆ππnegative free enthalpy change in forming a unit volume of solid from the liquid

activation barrier ∆∆G*

critical radius r*

2. Nucleation studies: critical nucleus (1)


Improving the Volmer and Weber approach (1926) for nucleation in a supersaturated vapour, Becker and Döring (1935) assumed that embryos of critical size are formed by a sequence of bimolecular processes involving vapour molecules and subcritical embryos, some of which aredissolved. A theory of the rate of homogeneous nucleation in condensed systems is realized by Turnbull and Fisher (1949).

2. Nucleation studies: nucleation rate (2)

J : frequency of the formation of crystal nuclei per unit volume of an undercooled liquid (nucleation rate)

∆∆−−==

Tk*G

expKJB

V 2V

3LS

G316

*G∆∆σσ

ππ==∆∆

TSG mV ∆∆∆∆==∆∆∆∆Sm : entropy of fusion

∆∆T : liquid undercooling

m

mm T

HS

∆∆==∆∆

mTT∆∆

==ΘΘ

models


2. Nucleation studies: undercooling results (3)

Turnbull and Cech (1950) remarked that the normalized amounts of undercooling (θθ = ∆∆T/Tm) are roughly constant (0.18 ±± 0.02). The systematic use of a scaling of ∆∆T against Tm allows comparisons between experiments but promotes the speculation of a defined, relatively unique, θθ limit for metals.


0 1000 2000 3000 4000

1000

800

600

400

200

0 HgGa

BiSn

Pb

Mg

Sb

Ag CuAu

Pd

NiCo

Fe

Melting temperature ( K )

Zr

Ir

Nb

MoTa

W

Re

Ge

18% Tm

30% Tm

Un

der

coo

lin

g ∆∆

T(

K )

the highest absolute amount of ∆∆T

drop-tube experiments

Liquid undercooling…

Water : 40°C (15%)

Nylon 6 : 99°C (20%)

Si : 450°C (27%)

Re : 860°C (28%)


2. Nucleation studies: Cn-θ scaling (4)

Assuming the classical assumptions, the critical nucleus is unique (JVt = 1) and Kv ≈≈ 1039 s-1.m-3, a graphic interpretation for homogenous nucleation using a new Cn-θθ scaling shows that the absolute limit is an intrinsic property of the material under consideration.

Cn

ααLS(fcc)= 0.86

ααLS(bcc)= 0.71

1

0 2 4 6 8 10

2/3

KV* = 3.1031

V ≈≈ mm3 to cm3

KV* = 2.1027

V ≈≈ µµm3

0.2

0.4

Transition metals

ααLS= 0.45

Turnbull Spaepen’s analysis

size effect

θ

(( ))3LS

m

2B

V

BV

BV

RS

316

Cn

1Cn

TkÄG

LogK

1 Tk

ÄG- exp K

1 Tk

ÄG-expVt KJVt

αα∆∆

ππ==

θθ−−θθ====

==

==

==

∗∗∗∗

∗∗∗∗

∗∗

LSm

3/12m

LS H

)V( σσ

∆∆==αα

N


2. Nucleation studies: statistical analysis (5)

The determination of KV is considered the clearest way to distinguish properly between homogeneous and heterogeneous processes. This can be undertaken by studying the effect of sample size on nucleation or, by analysing the full width at half maximum of the distribution of nucleation events (Skripov, 1977) uuevidences for refractory metals*

2873 ±± 3 K

(2,9 ±± 0,3 ) 105 K/s

t = 0,224 ±± 0,022 s

3128 ±± 13 K

(2,0 ±± 0,3 ) 105 K/s

3223 ±± 22 K

3263 ±± 15 K

xxxx Statistical analysis on a double recalescence phenomena: A15 metastable phase in the Re-W system (see page 16).

A15A15

75 droplets

8 K

∆∆T = 440 K

10

20

30

01020 1030 1040

KV

FWH

M (

K)

Nb

Temperature

Nu

mb

er o

f d

rop

lets

*See also Hoffmeister’s work


2. Nucleation studies: correlation for σσLS (6)

As for numerous physical properties, the solid-liquid interface energy σσLS

derived from undercooling experiments is found to be correlated with the atomic number (not ααLS) . The trends are identical to those obtained for the liquid-vapour surface energies σσLV. A classification of the elements into different groups is obtained by considering the σσLS/σσLV number, the main division being between metals and nonmetals.


xxxx Solid-liquid interface energy (J.m-2)

Zr

Rh

Pd

Os

Ir

Pt

Au

Hg

Ti

V Cr

Mn

FeCoNi

Cu

Zn

Nb

MoTc Ru

Ag

Cd

Hf

Ta

W Re

0.0

0.1

0.2

0.3

0.4

0.5

Ti

V

CrMn

FeCo

Ni

Cu

Zn

Zr

Nb

Mo

TcRuRh

Pd

Ag

CdHf

TaW

ReOs

IrPt

Au

Hg

0.9

1.1

1.3

1.5

1.7

xx Size in nm of the critical nucleus

V

Ti

3d- 4d- 5d- 3d- 4d- 5d-


2. Nucleation studies: dimensionless αLS (7)

Structure Elements

A4 Ge, Si 0.40 0.5

bcc (A2) Cr, W, V, Nb, Mo, Ta 0.43 8.6

bcc � hcp Ti, Zr, Hf 0.47 1.5

fcc (A1) Al, Pt, Pd, Cu, Ni, Ir, Rh, Au, Ag, Pd 0.48 12

hcp (A3) Cd, Zn, Ru, Os, Tc, Re 0.50 8.6

ααLS ∆∆ (%)

others In (A6), Ga (A11), Hg (A10) 0.65 5

The majority of transition metals are around the classical value of 0.45. Clear correspondances are found with the cristallographic structure. The average values for the compact fcc and hcp structures are in excellent agreement with the recent simulationfrom molecular dynamics* (i.e. 0.51 for fcc).

*R.L. Davidchack & B.B. Laird, Phys. Rev. Lett. 85 (2000) 4751


Spaepen analysis:fcc (0.86), bcc (0.71) !


3. Metastable phases: pure metals (1)


The nucleation of metastable phases of pure metals (f.c.c.-Re and A15-Ta) is observed through favourable heterogeneous nucleation events. The melting temperature of the metastable phase is the only property that can be both measured or calculated, especially by first-principles calculations (FPLMTO and pseudopotential methods)

Sig

nal

(V

)

1 1.02 1.04 1.06

5

4

32480°C

2620°C

3020°C

2660°C

Tantalum

Free-fall time (s)

60

40

20

-20

0

- 40

Structural energy differences

Ta W Re Os

fcc

hcpbcc

σσσσχχ

A15

∆∆E x

-cfc

(kJ.

mo

l-1)

2630°C

A15


3. Metastable phases: sequences (2)

A systematic study is carried out for both 4d- (Nb, Mo, Tc and Ru) and 5d- (Ta, W, Re and Os) metals: the sequence of phase appearance is bcc ÒÒÒÒ A15 ÒÒÒÒ σσ ÒÒÒÒ χχ ÒÒÒÒ fcc ÒÒÒÒ hcp when increasing ∆∆T (reverse for a hcp metal). With a common origin (atomic coordination and level-splitting of the d-like states), this sequence is also observed with composition in many binary metallic systems based on refractory metals (e.g. Os-Nb).


(Os)(Nb)

Liq

bcc Α15 σ χ Α15 σ χ hcp

A15 and σσ t.c.p. (Franck-Kasper) phases

A15A15 A (Z14)

B (Z12)CrCr33SiSi

σσσσA (Z12)B (Z15) C (Z14)D (Z12)E (Z14)

CrFeCrFe


3. Metastable phases: Re-W system (3)

(+4.6)

hcp cc

(-4.2)σσ(-3.2)

χχ(-1.6)

(+8.6)

(+15.3)

cfc (+6.2)

6

2

0

Time (s)0.84 0.94 1.04

2600

2990

28552950

3186°C

2950

2390

3422°C

1300

(Re)

χχ

σσ(W)

Liq

Tn

δδt ≈≈ 0.22 s

3/4

Weak heteroatomic interactionsfavour the formation of solid solutions (entropic effects). The A15 phase shows a metastable behaviour in a tremendously wide range of composition (two sublattice description to simulate order-disorder phenomena).

A15E

(k

J.m

ol-1

)


3. Metastable phases: Re-Ta system (4)


Alloying effects are stronger in the Re-Ta system, which promote the stability of t.c.p. phases. The (Ta) solid solution is affected by the metastable behaviour displayed again by the A15 phase as well as by a primary nucleation of the σσ-phase around 15 at% Re due to an uncommon site inversion between its two 12-fold coordinated sites*.

CB

A D

E

0 20 40 60 80 100

1

bcc

0 20 40 60 80 100

At% Ta

hcp

χχ

σσA15

σσ

-20

χχ (Ta)σσ

At% Ta

E (

kJ.

mo

l-1)

Equilibrium

Metastable σ ?σ ?

Ato

mic

fra

ctio

n T

a

*Cluster Variation Method calculations have been performed by M. Sluiter (University of Sendai)


4. Conclusion (1)


“Nucleation, essentially, the initiation of a phase transformation, is of central importance in physics, chemistry, biology and materials science. Many of the pioneers in the study of nucleation processes were metallurgists…”*

The study of undercooled refractory metals leads to establish that the solid-liquid interface energy can be connected to the position of the element in the periodic table. No significant unexplained anomaly is identified making believe that the classical theory furnishes a robust support to describe crystal nucleation. The 5d-series, that does not present any physical anomaly, shows the most perfect parabolic trends for dimensional properties. This context allows to develop an experimental strategy for studying alloys.

*From a lay report of the discussion meeting 6-7 June 2002 on “Nucleation Control” (The Royal Society, London)


4. Conclusion (2)

Kinetics measurements are of a central importance when dealing with alloys, due to the possibility in getting significant variations of Kv

(complex phases, multicomponent alloys). First-principles based calculations of the structural stability have been successfully developped to identify the intervening metastable phases (sequences).


0 10 20Atomic percentage

0

- 200

- 400

Hf

TaNb

W

Mo

Ir

xxxx Atomic size mismatch effect on Re (relative effect) (coll. Fecht)

∆∆T

Re 1.28 Å28

32

36

40

1 3 5 7 9

xxxx Homophase Fluctuation Mechanism (effect of the number of constituantson Kv, Desré, 2001) -

Lo

g10

Kv


Acknowledgements


The drop-tube experiments have been performed within an agreement betweenCNES and CEA. The author is indebted to Pierre Jean Desré (LTPCM-Saint-Martind’Hères) and Alain Pasturel (LPNSC/CNRS) for their invaluable help. Many thanks to

Cécile Berne : Solidification hors équilibre et apparition de phases métastables dans les séries de transition 4d- et 5d-, Ph-D Thesis INP-Grenoble (2000),

Emmanuel Cini : Contribution à l’étude de phénomènes de germination, de démixtion et de métastabilité morphologique, Ph-D Thesis, INP-Grenoble (1997),

Sandrine Tournier : Étude de phénomènes de métastabilité dans des alliages Rhénium-Tungstène et Rhénium-Tantale élaborés en tube à chute libre, Ph-D Thesis, INP-Grenoble (1996),

Laurent Cortella : Étude de la germination des métaux réfractaires élaborés dans le tube àchute libre de Grenoble, Ph-D Thesis, INP-Grenoble (1993).

Investigations with European teams have also received a financial support from ESA. Many thanks to Hasse Fredriksson, Lena Magnusson (KTH - Stockholm), Lindsay Greer (University of Cambridge), Hans Fecht (University of Ulm), Dieter Herlach (DLR - Cologne), Wolfgang Löser (IFW - Dresden) and László Gránásy (ISPPO, Budapest) for their scientific collaboration.


Related work (1)

1. Last overview, process

B. Vinet; Solidification of undercooled refractory metals and alloys by containerless processing, Special Issue: Emerging process in metal casting, science and technology, International Journal of Materials Product and Technology (2003), in press.

W. Loser, A. Garcia-Escorial, B. Vinet; Metastable formation in electromagnetic levitation, drop tube and gas atomisation techniques: a comparative study, International Journal of Non Equilibrium Processing 11 (1998) 89.

2. Nucleation studies / pure metals

B. Vinet, L. Magnusson, H. Fredriksson, P.J. Desré; Correlations between surface and interface energies in transition metals with respect to crystal nucleation, Journal of Colloid and Interface Science 255 (2002) 363.

C. Berne, B. Vinet, A. Pasturel, M. Sluiter; Ab initio study of metastability in refractory metal-based systems, Physical Review Letters 83 (1999) 1621.

L. Cortella, B. Vinet; Undercooling and nucleation studies on pure refractory metals processed in a ultrahigh vacuum drop-tube, Philosophical Magazine B 71(1995) 11.

L. Cortella, B. Vinet, P.J. Desré, A. Pasturel, T. Paxton, M. Van Schilfgaarde; Evidences of transitory metastable phases in refractory metals solidified from highly undercooled liquids in a drop-tube, Physical Review Letters 70 (1993) 1469.

B. Vinet, L. Cortella, J.J. Favier, P.J. Desré; Highly undercooled W and Re drops in an ultrahigh vacuum drop tube, Applied Physics Letters 58 (1991) 97.


Related work (2)

3. Phase selection phenomenon in refractory alloys (Re effect)

B. Vinet, B. Marie, I. Touet, B. Drevet ; Undercooling experiments on Nb-Re alloys from drop-tube processing, Scripta Materialia 48 (2003) 1991.

C. Berne, M. Sluiter, Y. Kawazoe, T. Hansen, A. Pasturel; Site occupancy in the Re-W sigma phase, Physical Review B 64 (2001) 144103-1/8.

C. Berne, B. Vinet, E. Rolland, A. Pasturel; Comparative study from drop-tube experiments and ab-initio calculations of the nucleation of the sigma phase in the Re-W systems during solidification far from equilibrium, Journal of Metastable and Nanocrystalline Materials 8 (2000) 3.

S. Tournier, B. Vinet, A. Pasturel, I. Ansara, P.J. Desré; Undercooling-induced metastable A15 phase in the Re-W system from drop-tube processing, Physical Review B 57 (1998) 3340.

S. Tournier, M. Barth, D.M. Herlach, B. Vinet; Competitive formation of bcc and s phases in undercooled Co-V and Re-W melts, Acta Metallurgica et Materialia 45 (1997) 191.

4. Multicomponent systems

P. J. Desré, E. Cini, B. Vinet; Homophase fluctuation mechanism of nucleation in multicomponent liquid alloys and glass forming ability, Journal of Non Crystalline Solids 288 (2001) 210.

E. Cini, B. Vinet, P. J. Desré; A thermodynamic approach to homogeneous nucleation via fluctuations of concentration in binary liquid alloys, Philosophical Magazine A 80 (2000) 955.


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Nucleation studies on undercooled refractory metals … · Unité qui présente / Réf présentation 03-08-28 1 Nucleation studies on undercooled refractory metals and alloys: a review