CAVITATION OF INTERPHASE INTERFACES AT ELEVATED TEMPERATURES

HAL Id: jpa-00230324

https://hal.archives-ouvertes.fr/jpa-00230324

Submitted on 1 Jan 1990

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

CAVITATION OF INTERPHASE INTERFACES AT ELEVATED TEMPERATURES

R. Raj

To cite this version:

R. Raj. CAVITATION OF INTERPHASE INTERFACES AT ELEVATED TEMPERATURES.

Journal de Physique Colloques, 1990, 51 (C1), pp.C1-393-C1-401. �10.1051/jphyscol:1990161�. �jpa-

00230324�

COLLOQUE D E PHYSIQUE

Colloque Cl, suppl6ment a u n O l , Tome 51, janvier 1990

CAVITATION OF INTERPHASE INTERFACES AT ELEVATED TEMPERATURES

R. R A J

Department of Materials Science and Engineering, Bard Hall, Cornell University, Ithaca, NY 14853, U.S.A.

Abstact

-

Intergranular fracture in high temperature structural materials, for example, stainless steels and superalloys, is often precipitated by the nucle- ation of microcavities between the metal and the ceramic particles such as oxides and carbides that are present at grain boundaries. A thermodynamic model for the nucleation of cavities is presented. The most critical parameter is the interfacial energy of the metal ceramic interface. The work is extended to the stability of thin films of one material on a substrate of another material where poor wetting is shown to lead to the breakdown of the film by cavity nucleation and by mass transport through solid state diffusion. Ex- amples include thin films of zirconia on sapphire and copper on sapphire.

INTRODUCTION

Nucleation and growth of voids at interphase interfaces is often the rate limiting factor in the longevity of engineering materials developed for high temperature structural applica- tions. In stainless steels and nickel base superallnys these cavities form at interfaces between the metal matrix and small ceramic particles which are frequently either oxides or carbides. Nearly always, the cavities form at grain boundaries, especially where the

particle and the grain boundary form a triple junction. Thus, the ceramic particles that are added to iapart creep resistance to the material, also become the cause of cavity nucleation.

Since the spacing of the cavities in the grain boundaries is determined by the spacing be- tween the particles, which is often of the order of 1 ym, once formed the cavities quickly grow and link with each other forming a continuous fracture path. As a result fracture can occur at strains of 1% to S % , leading to the phenomenon of creep embrittlement. An inter- granular fracture surface of a copper polycrystal showing the nucleation and growth of cavities at small particles of silica is shown in Fig. 3. The lenticular shape of the particles is a characteristic of particles that form at grain boundaries. A high voltage transmission electron micrograph showing the nucleation of cavities at a triple junction be- tween the matrix and a ceramic particle in copper is shown in Fig. 2 [ l ] .

In this paper I will derive a condition for the nucleation of cavities at hetero-interfaces betweer, two materials A and B that depends upon two factors: (i) the interface energy of the interface, and (ii) the geometrical characteristics of the nucleation site.

It is interesting to compare the phenomenon of cavity nucleation in the solid state to the concepts of wetting between a liquid and a solid. A poorly wetting liquid quickly forms beads on the solid surface if the contact angle 0, shown in Fig. 2, is large; if Q + 0 then the liquid film becomes continuous and stable. It is likely that the nucleation of cavities in the solid state also depends on the contact angle; the difference, as I will illustrate later, is that a polycrystalline film has interfaces that a liquid film does not. Junctions between the grain boundaries in the film and the hetero-interface become the preferred sites for cavity nucleation. The other point is that while cavitation at both liquid-solid and solid-solid interfaces requires mass transport, the transport occurs by viscous flow in the liquid and by solid state diffusion in the crystalline film.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990161

Cl-394 COLLOQUE DE PHYSIQUE

In the following sections we begin with the description of a thermodynamic criterion for cavity nucleation at internal interfaces under an applied stress. In this analysis it is shown why cavity nucleation by mass transport occurs at stresses that are much smaller than the ideal tensile stress of an interface. This work is then extended to the breakdown of a thin film of one material that is deposited on another material. Finally experimental re- sults from recent work with films of zirconia on sapphire and copper on sapphire are pre- sented. The readers are cautioned that a different mechanism for breakdown of a film, one that depends upon surface grooving of the film at grain boundaries has also been proposed in the literature [2,3]; this concept is different since it does not depend upon the wetting between the film and the substrate. These two different approaches to the breakdown phe- nomenon can be distinguished experimentally by studying cavitation in a film that is sand- wiched between two substrates since that will eliminate the possibility of surface grooving.

To my knowledge these experiments have not yet been done, although they are planned.

THERMODYNAMIC CRITERION FOR CAVITY NUCLEATION AT HIGH TEMPERATURE

A thermodynamic approach to fracture entails the interaction between the mechanical work done on the system, which provides a driving force for the growth of a crack or a cavity, and the increased surface energy which opposes crack growth. In his classical work Griffith [4] de- veloped a simple theory for brittle fracture by considering the difference in the free energy between the two states shown in Fig. 4. The crack in state I1 is larger than the one in state I, and therefore has a higher surface energy. If the experiment is done at constant load then the difference in the mechanical energy is given by the difference in the change in the poten- tial energy of the load P and the increase in the stored elastic energy in the body. If all deformation is elastic then the stored elastic energy is given by the area under the triangle ABC in state I and ADE in state 11, the difference between these two states (in the first order) being equal to the area in the triangle ABC. Note that the reason why the line AD lies below the line AB is because the growth of the crack increases the compliance of the specimen. The change in the potential energy of the load is simply given by PAL which is equal to the area CBDE. Thus the net mechanical driving force for crack growth is the dif- ference between the area CBDE and ABD which is equal in magnitude to one of half of the area CBDE. The balance between this driving force and change in the surface energy of the crack leads to the following condition for Griffith fracture:

where a is the critical stress for fracture for a flaw size c. E is the Young's modulus and y is thg specific surface energy. Note that the Griffith derivation does not allow any mass transport. Also if the crack is very small, of the order of the atomic spacing then it can be shown that oc S E/20 which approaches the ideal tensile strength of the interface.

In contrast, we now consider the formation of a cavity by mass transport, that is creation of a cavity of finite volume. This new situation is illustrated in Fig. 5. Here the decrease in the potential energy of the load P is much larger, being equal to the volume of the cavity multiplied by the applied normal stress on a per cavity basis. Thus while the change in the

stored elastic energy which opposes nucleation, and which is equal to only a fraction of the area A'B'C' from the discussion of Fig. 1, is small the change in the potential energy which favors nucleation is much larger than in the Griffith theory of brittle fracture. As a result nucleation of cavities is possible at stresses that are much lower than the Griffith fracture stress provided that mass can be transported by solid state diffusion to create a cavity of a finite volume. It can be shown that the probability of cavity nucleation by this mechanism, p, is given by the following equation [5]:

where

v = ~ r ' C V C and where

:'ere G i s the a~plied tensile stress, r is the radius of curvature of the critical nucleus,

")

and y is the surface enesgy. The quantifly v is the volume of the cavity of critical size;

it is proportional to r and to a shape factor F which depends on the site of cavity nucle-

ation. v

The above result can be visualized by considering a cavity that is drawn at an interface such that all its surfaces have a uniform radius of curvature r and such that all the dihedral angles in the cavity satisfy equilibriu~ between the surfaces that bound the cavity. Tke smaller the volume of this cavity the higher the probability of nucleation. Note that the applied stress determines the radius of curvature of the cavity through Eq. ( 4 ) , while the site of nucleation controls the shape factor F

.

The importance of the site of nucleation is illustrated in Fig. 6, where it can be apprecixted that even for a much larger radius of cur- vature (and therefore, for a much smaller applied stress) the volume of the critical cavity is smaller at the triple junction between an inclusion and the grain boundary than at the inclusion-matrix interface (type B versus type A in Fig. 5 ) . Vote that in type B nucleation, E is equal to (n-81, where 0 Zs the contact angle; thus if $ + n , that is if the inclusion is non-wetting, then nucleation is spontaneous since the volume of the cavity goes to zero.

CAVITATION AT A FLAT XWERFACE BETWE?ZN A THIN FILY AND A SUBSTRATE

Thin films that are supported on thick substrata are often unstable when annealed at a temperature where solid state diffusion occurs fast enough to produce spheroidization or beading. The diffusion distances for the breakdown of the film are of the order of the film thickness: as a result in films that are about 0.1 um thick spheroidization can occur in less than 1 hour at one half of the melting point.*

Because of their large surface area thin films are intrinsically unstable unless the wetting between the film and the substrate is ideal, that is when the contact angle is equal to zero.

However, even if the contact angle is greater than zero, kinetic barriers may be able to main- tain a continuous film over very long periods of time. The nucleation of cavities at the film-substrate interface may be one of these kinetic barriers. We now apply the criterion for nucleation described in the first section to the possibility of spontaneous nucleation of voids at the interface [6]. The stability of the interface can be considered in terms of voids of equilibrium shapes that are constructed where a triple junction line in the film meets the interface. This construction assumes that the triple lines are normal to the plane of the interface; this is reasonable since breakdown of films appears to occur only after the grain size in the film grows larger than the thickness of the film. [ 3 , 7 ] .

The construction of the void described just above for two cases, one for a large contact angle and one for a small contact angle, is shown in Fig. 6. The void is enclosed by four sur- faces: by the substrate free surface at the bottom and by the surface of three grains in the film that meet at the triple junction. The apex of the void is the tip of the triple junc- tion line. The voids in Fig. 7 are drawn such that surfaces of the film have a uniform curvature and the two dihedral angles, one the contact angle with the substrate equal to 8, and the other the grain boundary to free surface dihedral angle in the film itself denoted by

a , are equal to the equilibrium values. The condition for the stability of the void is then

given by the direction of the radius of curvature of the surfaces. If the radius of curva- ture points outwards, as shown on the left, then the void will grow spontaneously; if it points inwards then the void will try to sinter and will present a thermodynamic barrier to nucleation. The transition between the stable and the unstable case is then given by the geometry of a tetrahedra with flat surfaces. This case then gives a condition on the dihedral angle and the contact angle for a stable to an unstable void. Straightforward geometrical analysis then leads to the following condition for spontaneous nucleation of voids at the interface:

(*) The approximate time and temperature for spheroidization can be estimated by applying equations of diffusional creep by interface diffusion and replacing the grain size by the thickness of the film, and the applied stress by the stress created due to surface curvature which is equal to 2y/r, where r, the radius of curvature is equated to one half of the film thicknes~. These substitutions lead to the following equation for the breakdown of the film:

t = kTh /(l76 n6D ) , where tb is the time for the completion of the beading process, h is the initial film tkickness, Q is the atomic volume, y is the surface energy, and 6Db is the boundary width times the grain boundary diffusion coefficient. It is also possible that the kinetics of the beading process is controlled by surface diffusion; in that case a similar equation will be obtained except that 6D will be replaced by 6 D that is, the surface dif- fusion cross section multiplied by the surface diffusion coeffi~i&t. b The noteworthy result is that the rate of growth of the instability is inversely proportional to the fourth power of the film thickness.

COLLOQUE DE PHYSIQUE

-1 4 sin 2 a

-

^1)1/2

8 > n

-

^cos

_{( 7}

where cavitation occurs spontaneously if the above condition is satisfied. A plot of equation (5) is given in Fig. 8.

In initial stages of the nucleation of voids in thin films of zirconia on sapphire and copper on sapphire are shown in Figs. 9 and 10. Full description of the experiments and the results are contained in Refs. 6 and 7. The thickness of these films ranges from 50 nm to 250 m.

The two cases show the contrast between a case where nucleation occurs spontaneously at many triple junctions in the film, and where nucleation occurs at processing defects in the film which can be seen in Fig. 10, presumably these are non-wetting dirt particles that caused in- complete cohesion between the film and the substrate during deposition. The contact angles for copper-on-sapphire were measured and were found to lie within the stable regime in Fig.

8. In the case of zirconia films it can be seen that nucleation occurs preferentially at the grains that are brighter presumably because their greater surface curvature, and therefore a larger contact angle, reflects more electrons in the scanning electron microscope.

DISCUSSION

Heterointerfaces are extremely common in engineering materials. Examples of such interfaces in structural as well as electronic materials are shown in Fig. 11. Four categories of materials are considered: metals, ceramics (including oxides, carbides, etc.), intermetallics

(including silicides, aluminides, etc.), and glasses. Stainless steels are precipitate strengthened with metal carbides and metal-carbide interfaces are of critical importance in intergranular fracture. Nickel based superalloys contain nickel aluminide and carbides: ex- perience shows that the metal-aluminide interfaces are more resistant to cavitation than are metal-ceramic interfaces but a fundamental and definitive study of this phenomenon is not available. In silicon-nitride the use of additives that promote sintering produce thin films of a glass phase at grain interfaces and triple junctions and cavitation frequently occurs in these triple junctions. In integrated circuits metals and intermetallics are used to make interconnects with glass and silicon and the stability of these interfaces is important fn processing as well as in the long term reliability of electronic devices.

The purpose of this paper is to stimulate the use of thin films techniques to study the re- actions and cavitation at heterointerfaces. The interfaces between intermetallics and other materials, especially ceramics, are of considerable technological interest in the new genera- tion of high temperature structural materials. Reactions at intermetallic-interfaces need to be understood as a function of the activity of environmental species, particularly oxygen.

The film methods and techniques are a simple way to develop a fundamental understanding of these reactions.

The research has been supported by the Air Force Office of Scientific Research under the direction of Dr. A. H. Rosenstein.

REFERENCES

1. R.G. Fleck, D.M.R. Taplin and C.J. Beevers, Acta Metall.,

2,

415 (1975).

2. K.T. Miller and F.F. Lange, Acta Metall., 3J[5], 1343-1347 (1989).

3. D.J. Srolowitz and C.V. Thompson, Thin Solid Films,

139

133-141 (1986).

4. A.A. Griffith, Trans. ASM Quart.,

3,

861 (1968).

5. R. Raj, Acta Metall.,

2,

995-1006 (1978).

6. C.M. Kennefick and R. Raj, Acta Metall., x[11], 2947-2952 (1989).

7. D.C. Agarwal and R. Raj, Acta Metall., X[?], 2035-2038 (1989).

Fig. 1.

-

Intergranular fracture at elevated temperature in copper where cavities have nucleated at particles of silica.

Fig. 2.

-

^A high voltage transmission electron micrograph showing the nucleation of cavities in copper at the triple junctions between a grain boundary and ceramic particles.

GOOD WETTING POOR WETTING

Fig. 3.

-

The wetting of one material on the substrate of another can be described by the contact angle. A large contact angle implies greater susceptibility to cavitation and instability.

COLLOQUE DE PHYSIQUE

Fig. 4.

-

A schematic illustration of Griffiths theory of brittle fracture. The difference in the free energy of state I and I1 consists of three terms: the increase in the surface energy, the decrease in the potentia1,energy of the weight P because of greater elastic compliance of state 11, and the increased stored elastic energy in state IT.. The third term is given by the area ABD while the second term is equal to the area CBDE.

Fig. 5.

-

The nucleation of a cavity differs from the Griffith approach because the cavity has a finite volume which is accommodated by diffusional matter transport. Here the two important terns in the change of free energy are the increase in the surface area and decrease in the potential energy of the weight P. The latter is given by C'B'D'E', which, in contrast to the case of brittle fracture, is much greater than the change in the stored elastic energy. The elastic energy term is therefore neglected in this approach.

L~

TYPE A

BOUNDARY

ye ^-

"&P' 2 TYPE B

Fig. 6.

-

Construction of voids of equilibrium shape at heterointerfaces. The volume of the void is site dependent. For example the type B void has a smaller volume and is therefore more likely to nucleate than type A void.

UNSTABLE High 8

STABLE Low

e

Fig. 7.

-

Construction of voids of equilibrium shape at the intersection of triple junction in a thin film and the substrate. The triple junction line is assumed to be normal to the plane of the interface. The curvature of the void surfaces depends upon the contact angle, 0, and the dihedral angle, a.

COLLOQUE DE PHYSIQUE

Fig. 8.

-

The relationship between the contact angle, 8 , and the dihedral angle, a, for spontaneous nucleation of voids at the interface. In the stable region there is a thermodynamic barrier for void nucleation and the breakdown in the film should occur by a different mechanism.

180

160

140

120 m

Fig. 9.

-

Nucleation of voids in a 500 nm thick film of zirconia deposited on sapphire after annealing at 1528 K in air. Pictures correspond to annealing times of 15 min, 110 min, 248 min and 2700 min.

-

-

UNSTABLE

-

STABLE

2

8 0 - 2

S

60 -

40

20

0

-

-

0 20 W 6 40 6 0 8 0 90 DIHEDRAL ANGLE, a

COLLOQUE DE PHYSIQUE

0 20 W6 40 60 80 90

D I H E D R A L ANGLE, a

Fig. 8.

-

The relationship between the contact angle, 8 , and the dihedral angle, a, for spontaneous nucleation of voids at the interface. In the stable region there is a thermodynamic barrier for void nucleation and the breakdown in the film should occur by a different mechanism.

Fig. 9.

-

Nucleation of voids in a 500 nm thick film of zirconia deposited on sapphire after annealing at 1528 K in alr. Pictures correspond to annealing times of 15 min, 110 min, 248 min and 2700 min.

Fig. 10.

- ^A

breakdown of a thin film of copper on sapphire begins from processing defects in the film in the form of non-wetting inclusions. The instability then radiated outwards from these defects ultimately consuming the entire film.

y l y ' Superalloys

METALS INTERMETALLICS

Si3N4

CERAMICS 1 W GLASS

Glass Ceramics

Fig. 11.

-

Different types of heterointerfaces encountered in engineering materials.