Deformation- induced phase separation icon

Deformation- induced phase separation




НазваDeformation- induced phase separation
Дата16.03.2013
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Deformation- induced phase separation

Yaroslav Korol, Andriy Gusak

Cherkasy National University, Ukraine

king@cdu.edu.ua


Deformation may change not only the structure of the alloy but as well the phase state and spatial distribution of components. Plastic deformation of tin-lead solder, within broad range of deformation rates, does not form the metastable solutions but, instead, accelerates the decomposition of supersaturated (quenched) solid solutions. Creep of the same alloy leads to spatial separation of phases in two-phase mixture (“squeezing” of tin).

Keywords: solid solution, decomposition, two-phase alloy, plastic deformation, creep


1. Introduction

Influence of deformation on the phase transformations involving separation of phases has been studied for many years. Yet, so far there is no clear understanding of these phenomena. In this presentation we will consider two kinds of phase separation:

(1) decomposition of solid solution under fast or slow plastic deformation,

(2) spatial separation of already existing phases under creep in multiphase alloys.

Actually, deformation can lead to two competing effects of opposite direction. On one hand, steady deformation process generates the thermally non-activated atomic displacements (“ballistic jumps” – as called by George Martin, Bellon Pascal and others [1,2]). Clearly, such ballistic jumps do not obey the thermodynamics of equilibrium systems – therefore one should expect the shifts of equilibria lines at the phase diagrams. Thus, one might expect that deformation can form the metastable solid solutions beyond the solubility limits. On the other hand, deformation practically always generates the excess vacancies and therefore should lead to ACCELERATION of all diffusion-controlled processes, and in particular, to acceleration of diffusional decomposition. In this part we consider this, second possibility.

Decomposition of solid solutions induced by plastic deformation had been observed in [3]. It is already known that plastic deformation accelerates the diffusion, and anomalous mass-transfer is observed across the interface [4,5]. Anomalous masstransfer (if any) and formation of metastable solutions under plastic deformation are, most probably, interrelated. To observe the maximal possible extent of metastable phase formation, one needs not only fast transfer but as well as large contact zone as possible.


^ 2. Deformation-induced decomposition

Well-known alloy Pb-62%Sn forms eutectic which can be considered as the wide-spread interface between tin-based ( – phase) and lead-based (α – phase). At that content of tin is 24at.% at temperature 183°С, and 3 аt.% - at the room temperature Our aim is to study the influence of deformation magnitude and rate on the phase content and structure. The XRD study was performed by difractometer (fig.1, FeKα – radiation) and by Debye-Scherrer camera (fig.2, CuKα – radiation).

Concentration of tin in α-phase was determined according to modified composition dependence of the lattice constant:

а0=4,9508 - 0,00135с0 (Ǻ).

Samples were quenched with the cooling rate about 2000 К/s from the temperature 175°С. At that, phase partially decom­posed, and profiles of Bragg peaks were becoming bimodal. One of the modes corresponded to initial composition, and another one – to equilibrium concentration of tin at 20°С in a solid solution. Values of tin concentrations corresponding to two modes, are given in table 1.

No intermediate compo­sitions were observed – initial peak shrinked and peak of equilibrium composition grew instead (Fig. 1).



Table 1.

Deformation, %

First component

cSn, at%

Second component

cSn, at%

0

5,5

28,0

3

4,9

26,8

8

3,4

24,9

20

2,8

22,6






Fig.1. Profiles of (331) line for

α-phase of the quenched alloy Pb-62%Sn after deformation

To take into account the natural aging, a decomposition kinetics of α-phase at 20°С was investigated (Fig.3). One can see that within first one hour a structure is not changed significantly.

We investigated influence of deformation at various magnitudes and rates.

Main results:

1


Fig. 2. Debye patterns of Pb-Sn alloy just

after quenching (a) and after plastic
deformation by 30%
.
Plastic deformation induces decomposition of lead-based solid solution with formation of almost pure lead. Extent of decomposition linearly depends on the total deformation magnitude (until the moment of full decomposition).

2. Extent of decomposition does not depend on the deformation rate at fixed deformation magnitude, at least within rates interval 5*103 - 5*10-4 s-1.

3. Extent of decomposition does not depend on the history of deformation (single stage, two-stage, three stage …) but only on eventual deformation.

4. In the quenched sample the tin crystallites (-phase) have much greater size than those of α-phase. Deformation leads to refinement of grains.

Naive model of the above mentioned results can be suggested, based on the analysis of extra vacancies generation proportional to the velocity and density of dislocations and vacancy relaxation proportional to the magnitude of vacancy supersaturation.

. (1)

Here vacancy generation rate coefficient A can be estimated from elementary picture of vacancy generation by moving dislocations [6,7] (Hirsch, Mott, Nabarro et al):

, (2)

where is a Burgers vector magnitude is the fraction of forest dislocations, s  e = /2

is the density of screw dislocations,  is the total dislocation density, is the fraction of vacancy producing jogs on a gliding screw.

In the steady-state regime








Fig.3 Time dependences of two modes intensity of the (421)-line of α-phase at 25°С natural ageing.

Fig.4 Deformation magnitude dependences of two modes intensity of the (421)-line of α-phase at 25°С.

■ – new structure mode, ● – old structure mode
If (and estimations according to eq.(2) show that such situation is quite possible), then vacancy concentration and, respectively, diffusivity are proportional to the deformation rate.


In case of cellular decomposition the growth of transformed region proceeds, in average, with constant velocity, proportional to diffusivity in the moving interface. Thus, the total fraction of the transformed phase should be proportional to the integral which correlates with our experimental findings.

Thus, steady state analysis gives the decomposition magnitude proportional to deformation time and deformation rate which immediately gives the linear dependence on total deformation magnitude.


^ 3. Creep-induced phase separation in multiphase alloy.

I
Fig.5. Simplified scheme of the experimental set-up.

Dot-line – sample boundary prior to deformation

t is well-known that action of external field (electric current, thermal gradient) on solid solutions and on two-phase mixtures (solders) is drastically different. In solid solution such action typically leads to very weak redistribution of components, because the drift generated by external field is very effectively opposed by the arising gradient of chemical potential (determined by concentration gradient). In two-phase mixtures the gradient of coarse-grained concentration is not anymore the driving force of diffusion – it means just the gradient of molar fractions of the phases which remain in equilibrium with each other. Therefore, if one neglects Gibbs-Thomson effect, the redistribution of components due to external force is not opposed by equilibrating diffusion, so that this force can eventually lead to full spatial separation of phases. If one neglects the solubility of lead in tin and of tin in lead, the velocity of spatial separation of two-phase mixture can be roughly evaluated as where are the diffusivity of i-th component and an external force acting on the atoms of this component.



Table 2

Composition of sample in the center (EPMA)

Element

O

Si

Sn

Pb

Wight %

6.38

0.54

42.37

50.72



This is very well known for electromigration in solders [8, 9]. High current density of about 100 millions amperes per square meter passing through solder bump leads to full separation of tin and lead. The same happens under temperature gradient. It is well-known that action of external field (electric current, thermal gradient).




Fig.6.Top view of the sample after 170 hours of creep.



Fig. 7. Radial distribution of components after 170 hours of creep under load of 3kg at temperature 160C. Double dot-line indicates the position of margin before deformation.
It seems natural to assume that the gradient of mechanical stress ( with being an atomic volume for i-th phase and - one-third of Spur of stress tensor) as well can be an external force leading to separation of phases in the macroscopically homogeneous two-phase alloys. This hypothesis was checked at the solder Pb-Sn with eutectic composition. Superplastic alloys of such type, under constant loading and high temperature, demonstrate creep [10].

Cylindric sample (diameter 10 mm and height 12 mm) was subjected to long-term loading in the special device (simplified scheme of experimental setup is shown at Fig. 5) Temperature was kept constant (20°С). Load was constant determining the constant deformation rate 15 mm/hour. Deformation was measured during experiment and reached 20%. Phase redistribution at the top of the sample was determined by EPMA. Composition of the central part is given in Table 2.

Character of deformation at the top and at the bottom appeared to be quite different. Upper part transformed into “mushroom” of the height 10mm and hat of diameter 14mm. At that, the new-formed annular region had optical contrast typical for tin.

Radial concentration profile measured by EPMA are shown at Fig.7. One can see very distinct change of phase content ratio: - annular region contains much more tin-based phase than the sample in average..


4. Summary.

Plastic deformation of tin-lead quenched alloy accelerates the decomposition of tin solution in lead. Extent of decomposition (if far from complete one) is proportional to the total resulting deformation in within broad interval of deformation rates.

Creep of the tin-lead two-phase alloy leads to spatial phase separation


Acknowledgment

The work is supported by The State Fund for Fundamental Researches of Ukraine (Project F40.7/040).


Referenses

  1. Enrique Raúl A.; Bellon Pascal Phase stability under irradiation in alloys with a positive heat of mixing: Effective thermodynamics description Phys. Rev. B 60, 14649 (1999)

  2. Andriy O. Koval\'chuk, D.S. Gertsriken, Andriy Gusak, V.F. Mazanko// Models of Mutual Solubility Increasing under the Pulse Loading // Defect and Diffusion Forum (Volume 277) April, 2008 p.69-74

  3. S.D. Gertsriken, I.Ya. Dehtyar, Diffusion in Metals and Alloys, Fizmatgiz, Moscow, 1960.

  4. L.N. Larikov, V.M. Falchenko, V.F. Mazanko, Fiz. Met. 49 (1975).

  5. D.S. Gertzricken, V.F.Mazanko, V.M.Tyshkevych, V.M.Falchenko. Mass-transfer in Metals at Low Temperatures Under External Actions, Kiev 1999, NASU Publ.

  6. F R N Nabarro, Z S Basinski, D B Holt: Advances in Physics 1964 50 193-323.

  7. B.B.Khina. http://www.ariel.ac.il/sites/conf/mmt/mmt-2008/service_files/papers/session_1/1_42-51.doc

  8. K.-N. Tu., Solder Joint Technology: Materials, properties, and reliability, Springer, 2007.

  9. A.M. Gusak et al, Diffusion-Controlled Solid State Reactions, in Alloys, Thin-Films, and Nano Systems, Wiley-VCH, 2010.

  10. Physical metallurgy Ed. by R.W. Cahn // Chapter XIII-XX. 1965. Amsterdam.

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