DRIVING FORCE FOR SOLID STATE AMORPHISATION IN THE Fe-B SYSTEM

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DRIVING FORCE FOR SOLID STATE AMORPHISATION IN THE Fe-B SYSTEM

M. Clavaguera-Mora, M. Baro, S. Suriñach, N. Clavaguera

To cite this version:

M. Clavaguera-Mora, M. Baro, S. Suriñach, N. Clavaguera. DRIVING FORCE FOR SOLID STATE AMORPHISATION IN THE Fe-B SYSTEM. Journal de Physique Colloques, 1990, 51 (C4), pp.C4- 49-C4-54. �10.1051/jphyscol:1990405�. �jpa-00230765�

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COLLOQUE DE PHYSIQUE

Colloque C4, suppl6ment au n014, Tome 51, 15 juillet 1990

DRIVING FORCE FOR SOLID STATE AMORPHISATION I N THE Fe-B SYSTEM

M.T. CLAVAGUERA-MORA, M.D. BARO, S.

SURI'YNACH

and N. CLAVAGUERA*

Fisica de Materials, Department ~ f s i c a , Universitat ~ u t b n o m a de

?arcelona, SP-08193 Bellaterra, Spain

Department Estructura i Constituents de la Matgria, Universitat de Barcelona, Diagonal 647, SP-08028 Barcelona, Spain

Rdsumd

-

La force thermodynamique conductrice pour l'amorphisation en phase solide par rapport ii la cristalhation par broyage mkanique est calcul6e en fonction de la composition pour le syst4me Fe-B. Pour le Fe pur on intmduit l'amorphe i d k l comme celui qui a la transition vitreuse h la temp6rature h laquelle I'entropie du liquide eurlondu est 6gale ii celle du 7-Fe. L'6nergie libre de (%bbe de formation dea alliagea vitreux eat calcul6e et compade aux bnergies libres dee 46ments p u n et des c o m p d definis du ayateme.

On deduit l'acistence d'un domaine de formation de verre par daction en phase d d e qui s'6tend de 32 h 47

% at. B.

Abdraet

-

The thermodynamic driving force for the process of solid state amorphisation versus that of crystallieation by mechanical alloying is calculated as a function of composition in the Fe-B system. The ideal amorphous Fe is introduced as that one which has the glass tramition at the temperature for which the entropy of the supercooled liquid equals to that of 7-Fe. The Gibbs free energy of formation of the alloy glassea is calculated and compared with the free energies of the elemental components and stoichiometric compounds of the system. A glass forming range is predicted by solid state reaction in the range 32 to 47 at. % B.

I

-

INTRODUCTION.

In a solid state amorphieation, the reaction occurs from the elemental components directly to an amorphous, rather than crystalline, eolid solution. In general, this process is only pmible in a certain composition range. The use of metastable Gibbs free energy diagrams [l] is seen to provide a basis for clasdfyimg the poseible compcaition range in which solid date amorphiiation can proceed. A simple geometrical construction can be used to determine the maximum thermodynamic driving force for a particular reaction.

Here

maximum driving force refers to the maximum drop in chemical potential per atom in the solid state reaction.

Some djtliculties arise when treating the amorphous phase ae a metastable undercooled liquid 121. This is so becawe, in glaaa-forming systems, the heat capacity of the undercooled liquid is higher than that of the crystalline phase (or phases).

Aa

a consequence the entropy of the undercooled liquid decreaees more rapidly than that of the crystalline phases with lowering the temperature.

Now,

at the

TO

temperature (or the eutectic temperature) the Gibbs free energy of the crystalline phaaes is equal to that of the liquid and, furthermore, the entropy of the crystalline phases

is

lower than that of the liquid. Therefore, the entropy of the liquid remains higher than that of the crystalline phases when undercooling the liquid. Nevertheless, thii behaviour can be extrapolated only down to the bentropic temperature Ts

,

at which the undercooled liquid and the crystalline phases will have the same entropy. Below this temperature, in order to avoid the Kauzmann paradox 131, a drop in heat capacity hae to occut, the amorphous alloy is formed and d b i t e a heat capacity comparable with that of the stable crystalline phases.

The aim of this paper was t o calculate the driving force for the procees of non-crystalline mixing versus that of crystalhation as a function of composition for the Fe-B system. Rom phase diagram calculations [4], the thermodynamic properties of the liquid and crystalline phases were estimated over a wide temperature interval. Furthermore, the amorphous phase was considered as forming at

TS

and existing below thii temperature with a Gibbs f m energy and an enthalpy relative to the stable crystalline ph- constant and equal to that of the undercooled liquid at

Ts .

The Gibbs free energies and enthalpies of the equilibrium, metaetable and amorphous phases have been determined relative to the equilibrium elemental phaeee at the same temperature. The metastable multiphase equilibria were calculated by using the common-tangent rule to predict the composition ranges where the amorphiiation by eolid state reaction of the elements is thermodynamically favored. The driving force for the amorphiiation proceae has been w m p d with that of formation of the equilibrium crystalline phases.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990405

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C4-50 COLLOQUE DE PHYSIQUE

2

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RESULTS AND DISCUSSION.

The Gibbs free energy, enthalpy and entropy of the liquid with respect to the mixture of pure crystalline a-iron and rhombohedral boron at the same temperature were calculated form the thermodynamic porperties of the elements and the excess mixing functions asiwsed by Chart [S]. The thermodynamic properties of pure crystalline (rhombohedral) and liquid boron are tabulated in ref. [6]. The melting valuea

aaeeesed

in ref. [6]

were used too. The thermodynamic propertiae of a-Fe, ?-Fe and liquid iron are also given in ref. [6]. Fig.

1 shows the heat capacity of pure iron as a function of temperature. We assumed that the packing of the iron atoms in the amorphous structure is close to the close packed unit characteristic of 7-Fe. This aseumption permits to extrapolate the properties of the liquid down to the isentropic temperature Ts = 862K. Below this temperature both amorphous and ?-Fe will have the same heat capacity. That is, amorphous iron would have a sero entropy of formation relative to q-Fe (but not to a-Fe) and, therefore, its enthalpy and Gibbs free energy of formation relative to thase of 7-Fe would be independent of temperature. The heat capacity of the undercooled liquid and ideal amorphous Fe are plotted as a broken line in fig. 1.

To obtain the isentropic temperature of an alloy FeI-x Bx of any composition we proceeded similarly. In the range 0

5

^X

5

0.33 the undercooled liquid was aasumed to exist down to the temperature at which its entropy would be equal to the mixture of 7-Fe

+

^Fe2B.^In^{the range}^0.33

5

X 5 0.5 the liquid properties were extrapolated down to the temperature at which the entropy of the undercooled liquid would be equal to that of a mixture of &B and FeB. Finally, in the range 0.5

I

z

I

1 the andercooled liquid is assumed to exist down to the temperature at which its entropy would be equal to the mixture of FeB and (B). S i we use the mixing values tabulated in ref. 151, we neglect any influence coming from an excess heat capacity term in the undercooled liquid that could, for instance, come from the p r o p i v e chemical short-range ordering on decreasing temperaturea. Our neglect of an excess heat capacity term is a consequence of the fact that the heat capacity of the two stable intermediate compounds is very close to those of the mpective mixtures, with the aame compodtion, of 7-Fe

+

(B). The isentropic temperature is shown as a function of composition in fig. 2, s u p e r i m p d to the phase diagram asseased in reference 161.

Fig. 3 shows the enthalpy curves calculated for each of the stable elements and compounds, metastable q-Fe and undercooled liquid or amorphous alloy at 700K. As ahown in this figure, the calculation gives a cryetallisation enthalpy of 12.4 kJ/mol for amorphous iron. This value agreea with those that other authors [7,8] predicted by extrapolating the measured values of crystallisation enthalpies for low boron content metallic glasses of thie system. Our calculations agree with the results obtained by these authors in the whole range of boron content explorated experimentally if we assume that the crystallisation products of these glasses are a-& and FesB as it has been suggested 18-11) and if we assume that the enthalpy of the metastable compound FQB is that plotted with a dotted line in figure 3.

-

Fe liq.

Temperature ( K )

Fig. 1.- Heat capacity C, for pure crystalline and liquid (full curve) and extrapolated undemmled and amorphous (dashed curve) iron.

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Fig. 2.- Phase diagram (from ref. [5]) and isentropic temperature vs. composition in the Fe-B system.

The Gibbs free energy of all the stable and metastable phases as a function of composition is shown in fig. 4. Even if there are some eetimatea of the Gibbs fme energy of metastable FesB compound [12], these estimateshave not been included in this figure because the big discrepancies between the Gibbs free energy of F%B reported in ref. [l21 and those reported by other authors (7,131. The later are of the same order of magnitude of the o n e calculated here. It can be seen in figure 4 that a substantial drop in free energy occurs on forming a glass from the crystalline elements over a broad range of composition. The dashed lines represent the common tangent construction, neglecting the FQB and FeB wmpounda, of the terminal solutions with the amorphous phase. This construction allows to define three phase fields: two possible two-phase fields (a-Fe

+

amorphous all9 or (B)

+

amorphous alloy), and an hypothetical amorphous field region predicted as possible by solid state reaction of the elements. The range in composition of this amorphous field region extends from 32 to 47 at. % B. The relative position of the several curves is rather insensitive to changes of temperature of the order of 100K.

In ^fig.5 there is the plot of the e n t h a b of the several stable and metastable phases at W K . On comparing this plot with that of fig. 3 it can be concluded that, in the range of predicted glass formation by solid state reaction, roughly the crystallisation enthalpy of the hypothetical glasses is of the order of 2OkJ/mol at a temperature ranging from 300 to 700K. Comparatively, the crystallisation enthalpy of a low boron content glass is less than half this value (6.9kJlmol at 700K for a glass with 20 at. % B).

S i a r behaviour is expected for the Gibbs free energy difference between the crystallised material and the amorphous alloy if, as mentioned before, F e B appears as a crystallisation product in the low boron content glasses. Now, it is well known that the activation energy for homogeneous nucleation scales as the reciprocal of the square of the Gibbs free energy of crystallisation (see, for instance, ref. [Id]). Therefore, it seems that hypothetical glasses in the range 33.3 to 50 at. % B will not be very stable against crystallisation.

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64-52 COLLOQUE DE PHYSIQUE

line Fig. 3.- Calculated enthalpy curves for the different phases at 700K. The dashed hypothetical enthalpy of FeB metaatable compound.

5 0

-

,a-Fe

n

b

cir

\

7 0

Y

W

I

the

- -

50

Fig. 4.- Calculated free energy curves for the different phaeer~ at 300K.

I I I I

0.0 0.2 0.4 0.6 0.8 1 .O

at .f ract ion B

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Fig. 5.- Calculated enthalpy curves for the different phases at 300K.

3

-

CONCLUSIONS.

The thermodynamic functions of stable phasea in the

Fe-B

system at 300K have been evaluated. The thermodynamic functions of the metastable amorphous alloy phase have been evaluated by treating it as an undercooled liquid down to the kentropic temperature at which the entropy of the undercooled liquid will be equal to a mixture of crystalline phaaes. y-Fe inatead of a-Fe is taken to evaluate the isentropic temperature in the range 0

-

33.3 at. % B. Below

TS

the heat capacity of the amorphous alloy is supposed to be equal to that of the mixture of crystalline phases.

For the solid state amorphiisation of elemental powder mixtures, the assumption of a metastable equilibrium between the amorphous alloy and the elemental components describes the formation domain of amorphous phaee in the range 32 to 47 at. % B. This is the predicted glass formation range for mechanical alloying if the nucleation of the intermetdlic compounds FeB and FeB can be avoided during the milling procedure.

ACKNOWLEDGEMENTS.

The reae;rrch reported in this paper has been supported by CICYT, project no. MAT88-5439, which is acknowledged.

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COLLOQUE DE PHYSIQUE

REFERENCES.

[l] Johnson

W.L.

Progrees inMaterialsScience Vol. 30,

J.W.

Christian, P. Haasen and T.B. Massallri Ed. Pergamon 1986, p. 81

2 Clavaguera-Mora M.T. and Clavaguera N. J. Mater. Res. 4 (1989) 906 3 Kauzmann W. Chem. Rev. 43 (1948) 219

4 Kaulman L. and Bernstein H. Computer Calculations of Phase Diagrams (Academic Press, New

l l

York, 1970).

151 Chart T.G. Critical Assesement of Thermodynamic Data for the Iron-Boron Syetem, Nat. Phye.

Lab. of

U.K.

Middlemt, 1982 p.61.

[6] Barin I. Knacke 0. and Kubaschewski 0. Thermochemical Properties of Inorganic substances, Springer-Verlag 1977.

17) Cunat C. Notin M. Herte J. Duboie J.M. and Le Caer G. J. Non-Cryst. Solids, 55 (1983) 45.

8 Kem6ny T. Vincze I. Fogaraesy B. and Arajs S. Phya. Rev. B 20 (1979) 476.

9 Walter J.L. Mater. Sci. Eng. 39 (1979) 95.

I I

10 Weia J. Phys Stat. Sol. a79 1983 K117.

11 Kueller E. Z. Metallkde. 75

l 1

1984 698.

12 Ishihara K.N. and Shingu P.H. Mater. Sci. Eng. 63 (1984) 251.

13 Cunat C. Charles J. Hertz J. Dubois J.M. and Le Caer G. J. Phys. Colloque C9, suppl. au no. 12,

l l

⁴³(1982) CQ-191.

114) Thompson C.V. and Spaepen F. Acta Metall. 31 (1983) 2021.