THEORETICAL STUDIES AND DEVICE APPLICATIONS OF SOLUTE SEGREGATION AT CERAMIC GRAIN BOUNDARIES

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THEORETICAL STUDIES AND DEVICE

APPLICATIONS OF SOLUTE SEGREGATION AT CERAMIC GRAIN BOUNDARIES

M. Yan

To cite this version:

M. Yan. THEORETICAL STUDIES AND DEVICE APPLICATIONS OF SOLUTE SEGREGA-

TION AT CERAMIC GRAIN BOUNDARIES. Journal de Physique Colloques, 1986, 47 (C1), pp.C1-

269-C1-283. �10.1051/jphyscol:1986140�. �jpa-00225569�

JOURNAL DE PHYSIQUE

Colloque Cl, suppl6ment au n02, Tome 47, fgvrier 1986 page cl-269

THEORETICAL STUDIES AND DEVICE APPLICATIONS OF SOLUTE SEGREGATION AT CERAMIC GRAIN BOUNDARIES

M.F. YAN

Bell Laboratories, 600 Mountain Avenue, Murray H i l l , New Jersey 0 7 9 7 4 , U . S . A .

RCsumi

-

Les Ctudes t h b o r i q u e s e t l e s a p p l i c a t i o n s p r a t i q u e s de l a s C g r C g a t i o n aux j o i n t s de g r a i n s , d 1 e s p 8 c e en s o l u t i o n s o l i d e dans l e s cCramiques s o n t p r k s e n t k e s . Les p o t e n t i e l s d ' i n t e r a c t i o n e n t r e l e s i o n s s o l u t C s e t l e s i n t e r f a c e s de l a c i r a m i q u e s o n t i d e n t i f i C s comme r C s u l t a n t -1) d ' i n t e r a c t i o n s C l e c t r o s t a t i q u e s e n t r e espkces s o l u t C e s c h a r g e e s e t i n t e r f a c e s ; 2) de l f C n e r g i e C l a s t i q u e due au dCsaccord s t C r i q u e du s o l u t C dans l a m a t r i c e e t 3) de l ' i n t e r a c t i o n d i g o l a i r e e n t r e des l a c u n e s de s o l u t e e t l e champ C l e c t r i q u e dans l a r e g i o n i n t e r f a c i a l e . Des d i s t r i b u t i o n s n o n - u n i f o r m e s du s o l u t k & p r o x i m i t e de l ' i n t e r f a c e , r e s u l t a n t de c e s p o t e n t i e l s i n t e r a c t i f s s o n t c a l c u l e s numeriquement p o u r u n systSme modClisC. Oans c e r t a i n e s c o n d i t i o n s , l e s i n t e r a c t i o n s C l a s t i q u e s a u s s i b i e n que d i p o l a i r e s p e u v e n t m o d i f i e r de f a s o n s i g n i f i c a t i v e l e p o t e n t i e l C l e c t r o s t a t i q u e B p r o x i m i t t ? de l f i n t e r f a c e . Les c a l c u l s m o n t r e n t que l a s8gr;gation auw i n t e r f a c e s d ' u n s o l u t C a l i o v a l e n t p e u t a t r e m o d i f i g e p a r l a p r k s e n c e d l u n a u t r e s o l u t t ? a l i o v a l e n t mais p r C s e n t a n t u n e f f e t s t C r i q u e d i f f e r e n t . Pour une c e r t a i n e c l a s s e de p r o c e s s u s c i n i t i q u e s ou de c o n d i t i o n s t r a n s i t o i r e s , l e temps n C c e s s a i r e h l a r e d i s t r i b u t i o n des s o l u t i s a u t o u r de I t i n t e r f a c e n ' e s t pas a t t e i n t a l o r s que l a m i g r a t i o n de l a c u n e s p e u t d t r e r a p i d e . Des d i s t r i b u t i o n s de p o t e n t i e l s , a u t o u r d e s i n t e r f a c e s , dans d e s c o n d i t i o n s d l C q u i l i b r e s s t a t i o n n a i r e s , 03 il n l y a pas r e d i s t r i b u t i o n des s o l u t C s , s o n t c a l c u l C e s . L e s d i f f g r e n c e s q u i en r C s u l t e n t p a r r a p p o r t l ' e q u i l i b r e c o m p l e t s o n t montrbes. De p l u s , nous avons a n a l y s e l e temps c a r a c t e r i s t i q u e n d c e s s a i r e p o u r a t t e i n d r e l a d i s t r i b u t i o n n a t u r e l l e d e s l a c u n e s , c e l l e du s o l u t e , e t d e s l a c u n e s associCes e t l a s C g r C g a t i o n du s o l u t e B I ' d q u i l i b r e . L ' a p p l i c a t i o n de l a s e g r e g a t i o n des s o l u t C s aux j o i n t s de g r a i n s dans l e s c g r a m i q u e s C l e c t r o n i q u e s s o n t i l l u s t r e e s p a r des Ctudes r e c a n t e s e f f e c t u e e s d a n t n o t r e l a b o r a t o i r e . Des e x e s p l e s i n c l u a n t l e s f e r r i t e s dopCes au Ca, d o n t l ' o b j e t e s t de d o n n e r de f a i b l e s p e r t e s p a r c o u r a n t dlEddy B h a u t e - f r e q u e n c e e t une f o r t e r e s i s t a n c e mCcanique, s o n t donnCs. Le c a s des cbramiques de t i t a n a t e s dopkes au 8a q u i p o s s 6 d e n t une f o r t e c o n s t a n t e d i e l e c t r i q u e e t des p r o p r i C t i s de c o n d u c t i v i t e C l e c t r i q u e non l i n C a i r e s e s t trait;. L e s p r o p r i C t 6 s d e c e s composants s o n t r e l i C e s aux c o m p o s i t i o n s en dopant, aux c o n d i t i o n s de p r C p a r a t i c n e t aux c a r a c t k r i s t i q u e s des j o i n t s dc g r a i n s .

A b s t r a c t

-

T h e o r e t i c a l s t u d i e s and d e v i c e a p p l i c a t i o n s o f s o l u t e s e g r e g a t i o n a t c e r a m i c g r a i n b o u n d a r i e s a r e r e v i e w e d . The i n t e r a c t i o n p o t e n t i a l s between s o l u t e i o n s and i n t e r f a c e s i n c e r a m i c s a r e i d e n t i f i e d a s ( l ) t h e e l e c t r o s t a t i c i n t e r a c t i o n between t h e c h a r g e d s o l u t e s and i n t e r f a c e s ; ( 2 ) t h e e l a s t i c energy due t o t h e s i z e m i s f i t o f s o l u t e s i n t h e m a t r i x , and ( 3 ) t h e d i p o l e i n t e r a c t i o n between t h e s o l u t e - v a c a n c y d i p o l e s and t h e e l e c t r i c f i e l d i n t h e i n t e r f a c e r e g i o n . Non-uniform s o l u t e d i s t r i b u t i o n n e a r t h e i n t e r f a c e r e s u l t e d f r o m t h e s e i n t e r a c t i o n p o t e n t i a l s a r e c a l c u l a t e d n u m e r i c a l l y i n a model system. Under c e r t a i n c o n d i t i o n s , b o t h t h e e l a s t i c and d i p o l e i n t e r a c t i o n s can s i g n i f i c a n t l y m o d i f y t h e e l e c t r o s t a t i c p o t e n t i a l n e a r t h e i n t e r f a c e . C a l c u l a t i o n s a l s o show t h a t t h e i n t e r f a c i a l s e g r e g a t i o n o f an a l i o v a l e n t s o l u t e can be a l t e r e d by a n o t h e r a l i o v a l e n t s o l u t e o f a d i f f e r e n t s i z e m i s f i t w i t h t h e m a t r i x . F o r a v a r i e t y of k i n e t i c p r o c e s s e s o r t r a n s i e n t c o n d i t i o n s , t h e r e i s i n s u f f i c i e n t t i m e f o r s o l u t e r e d i s t r i b u t i o n

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986140

JOURNAL DE PHYSIQUE

around t h e i n t e r f a c e , while the vacancy migration may be r a p i d . P o t e n t i a l d i s t r i b u t i o n s around i n t e r f a c e s under constrained e q u i l i b r i a of no s o l u t e r e d i s t r i b u t i o n a r e c a l c u l a t e d and shown t o be d i f f e r e n t from t h a t f o r complete equilibrium. Furthermore, we have analyzed t h e c h a r a c t e r i s t i c times required f o r f r e e vacancy e q u i l i b r i u m , solute-vacancy equilibrium and s o l u t e segregation equilibrium. Device a p p l i c a t i o n s of s o l u t e segregation a t grain boundaries of e l e c t r o n i c ceramics a r e i l l u s t r a t e d by the r e c e n t s t u d i e s a t our l a b o r a t o r i e s . Examples include Ca doped MnZn f e r r i t e s t o give low Eddy c u r r e n t l o s s a t high f r e q u e n c i e s , and high mechanical s t r e n g t h ; and Ba doped t i t a n a t e ceramics t o give high d i e l e c t r i c constant and nonlinear e l e c t r i c a l c o n d u c t i v i t i e s . Device p r o p e r t i e s of these e l e c t r o n i c ceramics a r e r e l a t e d t o dopant compositions, processing conditions and grain boundary c h a r a c t e r i s t i c s .

I - INTRODUCTION

Solute segregation near interfaces (free surfaces and grain boundaries) has been observed in ceramics. Many electrical, dielectric, magnetic and mechanical properties of polycrystalline ceramics are critically dependent on the type and amount of solute segregation at interfaces. For example, the device properties of varistors, PTC materials, grain boundary layer capacitors and inductors are directly related to solute segregation at interfaces.

In this paper, we will give a summary of our theoretical studies on interfacial segregation in ceramics.

Furthermore, we will describe some recent,applications of the grain boundary phenomena in electronic ceramic devices in our laboratories. On theoretical studies, we will describe the driving forces leading to solute segregation.

These driving forces are due to the elastic, electrostatic, and dipole interactions between interfaces and solutes. Then we will describe the distributions of solutes and point defects resulted from these interaction potentials under conditions of complete equilibrium and during kinetic processes. More detailed analyses have recently been reported elsewhere.('-') On device applications, we will describe the effects of solute segregation on the

mechanical,'* dielectri~'~,~) and electricalfs) properties of ferrites and titanates.

I1

-

THEORETICAL STUDIIB 1. Driving Forces

We have identified three driving forces leading to solute segregation at ceramic interfaces. These driving forces are due to the elastic, electrostatic and dipole interactions in the interface regions, described in the following sections.

(a) Elastic Interactions

The first driving force is due to the elastic energy associated with the size misfit between solute and the matrix.

We have proposed that the elastic energy has a certain spatial dependence and it has a range of about two lattice constants as expected from the coincidence model of the grain boundary structure.(9) The magnitude of the elastic energy, U,, is related to the size misfit, Ar, of the solute, the bulk modulus, B, of the solute and the shear modulus, a, of the matrix.(lO) U,, is given as

where r is the radius of tne matrix ions of the sublattice into which the solute is substituted. Table 1 shows the magnitude of the elastic energies in KCl, Ti02 and BaTi03. In all cases, the elastic energies increase rapidly with the size misfit. For example, the elastic energy in KCI, increases from 0.0005 eV to 0.5 eV when the size misfit of solute increases from 1.5% to 51%. In general, oxides have a larger elastic energy because of their larger shear modulus. For example, a barium substitution in T i 0 2 could lead to an elastic energy of 7.6 eV. It also appears that solutes in BaTi03 have a smaller elastic energy probably because there are two cation sublattices in BaTi03 and solutes tend to dissolve in the more appropriate sublattice to minimize the elastic energy.

(b) Electrostatic Interactions

The electrostatic interactions between solutes and ceramic interfaces are due to the space charge regions in such interfaces. The existence of space charge regions near interfaces in an ionic solid was first postulated by ~renkel,(") and the charge distribution models have been formulated by several researchers.""'" In an ionic solid, the vacancy concentrations a t the interfaces are determined by the innate free energies of formation. The cation and anion vacancies usually have different formation energies. For example, in KCI, the energy required to form a cation vacancy is about 36% less than that required to form an anion vacancy. However, the vacancy concentrations in the bulk are determined by the condition of charge neutrality and usually they are different from those a t the interfaces.

Table 1: Magnitude of the Elastic Energies iu Selected Cenmies DEFECT DISTRIBUTION CHARGE DENSITY POTENTIAL OISTRIBUTION

KCI: Solute U, (eV)

Mg 0.5

Ca 0.2

Sr 0.05

Ba 0.0005

Fig. 1. A schematic diagram of the defect distribution, [ l, the charge density, p, and the potential distribution,

+,

in the interface region of KC1 doped with several hundred ppm of a divalent solute.

Thus, the vacancy concentration changes as a function of distance from the interface. Usually, the vacancies in ionic solids are charged defects. Spatial distributions of these charged defects lead to a distribution of the charge density and thus a potential difference between the bulk and the interface. This potential difference induces the interface segregation of the charged solute ions, e.g. divalent cation solutes, I i , in KCl. Figure 1 shows a schematic diagram of the defect distribution, [ l, the charge density, p, and potential distribution, @, in the interface region of KC1 doped with several hundred ppm of a divalent solute. The electrostatic interaction energy U,, is given as U,

-

1 / 2 ~ 9 .

Furthermore, t h e c h a r g e distribution is also resulted from the segregation of charged solutes due to other non- coulombic interactions, e.g. the elastic interaction. Thus, both the electrostatic potential and elastic interactions are coupled to each other. These two driving forces must be included to evaluate their net effect on interface segregation in ceramics.

(c) Dipole Interactions

Charged solutes in most ceramics tend to combine with defects of the opposite charge. For example, they form solute-vacancy complexes and this association of defects decreases the free energy. In simple cases, these complexes are electrically neutral, but they have a dipole moment. The electric field gradient in the space charge region exerts an attractive force on the dipoles of solute-vacancy complexes. The dipole interaction energy, Ud, between the electric field, E, and dipoles with a moment, p, is Ud

- ^-

^{112 E}

^.

^p.

Poisson's equation relates the electrostatic potential to the concentration of these complexes. Furthermore, these associated defects may also have an elastic interaction with the interface. When they are redistributed by the elastic interaction, a new electrostatic potential results. Thus, all interaction potentials resulting from electrostatic, elastic and dipole interactions are effectively coupled to each other.

2. Quilibrium Solute Distributions in Interface Region

After we have identified the driving forces leading to solute segregation, we can calculate the electrostatic potential and the equilibrium solute distributions in the interface region. Our approach is first to formulate the free energy, including the formation energies of the lattice defects; the elastic, electrostatic and dipole interactions; and the configurational entropy due to the statistical arrangement of lattice defects in the interface region.

The free energy in the interface region is then minimized by the method of calculus of variations to obtain the equilibrium solute distributions, subject to the constraints of electrical neutrality and the conservation of solute ions

Fig. 2. Potential distributions in the interface region due to the coupled effects of the electrostatic space charge and the elastic interaction at 500'C. which is

o / above the isoelectric temperature, To. At

this temperature, M,

-

^{-0.053 eV and}

0 1 2 3 4 5

RECUCEO DISTANCE FRIil GRBN ~ X I N ~ ~ R T I L ~ ) r 6

-

^{1 1 . 1 nm.}

C l - 2 7 2 J O U R N A L DE PHYSIQUE

within the sample. It is obvious that the equilibrium distributions of the charged defects and solutes depend on the electrostatic potential in the interface region. Thus, it is necessary to solve Poisson's equation to obtain the electrostatic potential. Results of our analyses on the equilibrium solute distributions will be summarized in the following sections.

(a) Coupled Effects of Elastic and Elech.ostatic Interactions

We have performed numerical solution of Poisson's equation to obtain the potential distributions in the interface region due to the coupled effects of the electrostatic and elastic interactions. Our analyses have shown that enhanced solute segregation can result from an attractive elastic interaction due to the size misfit between the solutes and matrix ions. While this interaction is non-Coulombic in origin, it can significantly affect the electrostatic potential distributions.

The solute and defect distributions are determined by the sum of the elastic and electrostatic interaction energies.

When both interaction terms are large the distributions will be very different than for either individual case.

Furthermore, the solute elastic interaction has a significant effect on the electrostatic potentials when ( ~ J e & l >> 1. However, when

IuJ~&(

G 1, the electrostatic potential is similar to that derived from Kliewer and ~ o e h l e r ( ' ~ ) considering only electrostatic effects. The changes in electrostatic potential induce changes in the distributions of other defects. For example, an attractive elastic interaction for the solute leads to significant increases in the cation vacancy concentration near the interface. When the electrostatic potential is small, e.g. near the isoelectric temperature, To, a large elastic term can change the polarity of the electrostatic potential in some parts of the space charge layer, andfor cause changes from segregation to repulsion of a charged species within the charge cloud.

Figure 2 shows the effect of elastic interactions on the electrostatic potential at 500°C in KCl. This temperature is above the isoelectric point and the bulk potential, @,, is negative. In the absence of any elastic interaction the charge solutes, Ii( are repelled from the interface region a t this temperature. When U, < 0, the elastic interaction tends to attract solutes to the interface which counter-act the electrostatic effect, and nf(0)/nr(m) > 1 when U, < &, < 0. Thus, within the charge cloud the space charge potential is increased by an attractive elastic interaction. When U, << e& < 0, solutes become significantly segregated at the interface owing to the elastic interaction. This changes even the polarity in part of the space charge layer near the interface. Numerical solutions show that when U, 6 0.2 eV a t 500'C and U, d -0.05 eV at 450°C, solute segregation induced by the elastic energy leads to a positive potential. For example, Figure 2 shows 4(x)/I$, < 0 a t part of the space charge region.

Calculations for the repulsive elastic energies, i.e. U, > 0, are also shown in Figure 2 and the results were discussed elsewhere.(')

At temperatures below the isoelectric point, the bulk potential, G,, is positive, and in the absence of any elastic interactions, the electrostatic potential leads to solute segregation. Figure 3 shows the effect of elastic interactions on the electrostatic potential at 400'C. When U, < 0, the solutes are also attracted by the elastic interaction and the additional segregation increases the electrostatic potential. At temperatures close to the isoelectric temperature, a large attractive elastic energy, e.g. U,

-

-0.2 eV, increases the electrostatic potential to several times the bulk potential a t a distance less than one Debye length, 6.") At lower temperature, e.g. 400'C, 4, becomes larger, and Figure 3 shows that the solute segregation induced by the elastic energy has less effect on the electrostatic potential.

Figure 4 shows the distribution of [V;] and [II;;] at 400 to 500'C in the interface region when U,

-

^{-0.2 eV.}

Comparison with the case without elastic interaction can be seen by observing the values of [v,(o)~ in Figure 4 and recalling that these values are independent of the elastic interactions and that without elastic interaction nf(x)/nr(-)

-

n+(-)/n+(x)

-

exp[-(@-e,)/kTI, and that the curves of log(nf(x)/nf(m)) or log(n+(x)/n+(w)) versus ^X would reflect the approximately exponential decay in +(X) with X. The solute segregation near the interface is significant at all three temperatures and most, if not all, of it is due to the attractive elastic interaction energy. In addition, a t all three temperatures the vacancy concentration near the interface is higher than for the purely electrostatic case due to the increased solute concentration. In solving Poisson's equation we assumed that U,'

-

⁰

when X > 2a. Thus, the solute distribution for X > 2a is determined by the electrostatic potential alone. When T > To and I$, < 0, solutes are depleted from this part of the space charge region if e41/c$, < 1. However, at a lower temperature, when T < To and 4, > 0, solutes are depleted only if @/&, > 1. For example, Figure 4 shows that when U,

-

-0.2 eV the elastic energy-induced solute segregation near the interface leads to solute depletion in a region further away from the interface at temperatures near or above the isoelectric point.

(b) Segregation of Multiple Solutes

Multiple solutes usually are found in ceramics. These solutes usually have different elastic interaction energies with the interface and different segregation profiles. Because of the electrostatic coupling, the segregation profiles for the two solute species will not be independent. A case of particular interest is that when a minority solute has a large elastic interaction energy and so segregates strongly to the interface. In this case the segregation of the majority solute will be significantly suppressed. The majority solute may even be depleted under the same conditions where there would be segregation where the minority solute is not present.

R E W E D DISThNCF FROM MA111 B W N W I X I S I

Fig. 3. Potential distributions in the interface region due to the coupled effects of the electrostatic space charge and the elastic interaction at 400'C. which is below the isoelectric temperature. At his temperature, e9, = 0.044 eV and d

-

^{1.22 nm.}

Fig. 4. Unassociated solute, I, ions and K vacancy distribution profiles, under the electrostatic and elastic interactions.

For illustrative purposes, we have analyzed the interface segregation of two divalent cation solutes having different elastic terms UI and U2 respectively in KCl. Figure 5 shows the distributions of these two divalent solutes a t temperatures of 400, 450, and 500°C. In particular, we assume that KC1 is doped with two types of solutes: the majority solute with a concentration of 49.5 ppm and the minority solute with 0.5 ppm. We further assume that both solutes have identical probabilities of association to form solute-vacancy complexes. More importantly, we assume that the majority solute does not have any elastic interaction energy with the interface i.e. UI

-

0, while the minority solute has a large attractive elastic energy, U2

-

^-0.5(1

^-

x/2a) eV. In KCl, U,

-

-0.5 eV is appropriate for MgK. Figure 5 shows that the minority solute is 100 times less concentrated than the majority one in the bulk.

However, the elastic interaction leads to enhanced segregation of the minority solute such that it becomes 20 to 50 times more concentrated than the majority solute a t the interface. The dotted lines in Figure 5 show the distributions of the majority solute as if the minority solute does not exist. At the lower two temperatures, the strong segregation of the minority solute significantly reduces the amount of majority solute near the interface relative to that expected when only the majority solute is present. At 450aC, where @, is very small, there is appreciable depletion of the majority solute from the interface region. At SOO'C, which is above the isoelectric temperature, adjustments of the free vacancy concentration is evidently sufficient that there is only a minor change in the electrostatic potential and the distribution of the majority solute.

Significant Ca segregation has been found a t grain boundaries of MgO-doped A1203. For a Ca concentration less than 0.01% in the bulk, a high Ca concentration of 2% was found on these grain boundaries. Hmever, little Mg was found segregated at the grain boundaries even though the A1203 was doped with 0.3% M~.(''-'~) This is probably because Ca has a much larger size misfit than Mg in an A1203 matrix. It is estimated using Eq. (1) that the elastic energy, U,, of Ca is probably 5 times larger than that of Mg. Both Ca and Mg have the same valence and thus identical electrostatic effects. Because of the electrostatic coupling, it is possible that MgO could be segregated near the boundary in purer samples but depleted in samples with Ca impurity.

(C) Effects of Dipole Interaction

In general, the electrostatic potential does not affect the segregation profile of the solute-vacancy and vacancy- vacancy complexes, which are electrically neutral. However, the dipole interaction between these complexes and the electrical field may lead to certain modification in the electrostatic potential and the distribution profiles of these neutral complexes. We have solved Poisson's equation, with an explicit consideration of the polarization term.

Figure 6 shows the electric field, -d@/dx, in the interface region. The dashed line in this figure shows the electric field calculated as if the dipole interaction does not exist. The results of the calculations shown in this figure and others for higher temperatures demonstrated that the correction term due to dipole interactions has very little effect on the electric field for KC1 with 50 ppm solute a t 200°C and even less at higher temperatures. In fact, the calculated electric field is nearly identical to that derived by Kliewer and ~ o e h l e r ( ' ~ ) who have neglected the dipole interactions in their analysis. We have shown that the dipole contribution can be neglected except at high solute concentration andlor low temperatures, such that the electric field is very large in the interface region and the probability of association to form solute-vacancy complexes is very large. For example, Figure (6) shows that even when 91% of the solutes form (I~v;()' dipoles a t 200'C, the dipole interaction has only a very small effect on the

JOURNAL DE PHYSIQUE

Fig. 5. Coupled etTect on the distributions of two divalent cation solutes at 400'C in (a), 450'C (b) and 500'C (c). The analysis is for KC1 with 49.5 ppm of the majority solute, which does not have any elastic interaction; and 0.5 ppm of the minority solute, which has a very strong elastic interaction. The dotted lines show the solute distributions calculated from the space charge theory for 50 ppm solute without any elastic interaction.

electric field. Thus, it is usually a good approximation to use the electrostatic potential evaluated without any dipole interaction to calculate the distribution of solute-vacancy complexes at this or higher temperature.

Figure 7 shows the concentrations of solute-vacancy complexes (I~v;()' near the interface. When the dipoles have a net moment resolved in the electric field direction, e.g. parallel, m3, and anti-paral!el, m;, their distributions are non-uniform in the interface region. However, dipole without any net moment in the field direction, e.g. m*, have a uniform distribution.

REDUCED DISTANCE FROM GRAIN BOUNDIRY 11/81

Fig. 6. Effects of dipole interactions on the space charge electric field distribution in the interface region at 200'C. The dotted line shows the distribution without dipole interactions. At this temperature, e4,

-

0.21 eV and 6

-

^2.45

nm.

R E W E D DISTANCE FRM BOUNDARY. X I S

Fig. 7. Distributions of vacancy-solute dipole complexes in the interface region. M;, M2 and M; denote the concentration of dipoles with the resolved dipole moment antiparallel, perpendicular and parallel to the electric field respectively. The dashed line represents the distribution of dipoles with different moments.

Usually the dipole interaction causes only a small amount of solute segregation at interfaces. However, it-is important to observe that the dipole interaction always leads to enhanced solute segregation and that the dipole interaction also affects the diffusivity and ionic mobility of solutes in the interface region.(") Furthermore, at T > To, only the associated solutes, which do not carry a net charge, segregate at interfaces. However, at T < To, most of the segregated solutes are charged defects. The charges carried by the segregated solutes usually affect the interfacial electrical properties. Thus, the temperature from which a sample is quenched affects the device properties in ceramics. Furthermore, when the polarization term is large there will be more total dipole segregation and the field will penetrate further into the bulk.

3. Solute Distribution During Kinetic Processes

There are certain transient situations or kinetic processes during which it is difficult to achieve complete equilibrium around interfaces because diffusion of solutes or defects is too slow. However, partial solute segregation, defect redistribution or development of a space charge cloud can often occur during these processes. When solute are aliovalent, any solute redistribution leads to changes in both the charge density and the electrostatic potential.

Material transport is required to redistribute the charged species. Complete treatments of the kinetics in such cases would be desirable but are generally not available. Thus, it is of interest to develop approximate solutions which are applicable to such problems.

Examples of these problems include creation or migration of interfaces and rapid changes of temperature or ambient atmosphere. For instance, quenching will lead to a new equilibrium state near interfaces, usually involving an increase in solute segregation. Similarly, changing stoichiome'try, in response to an atmosphere change, involves defect diffusion into the lattice from an interface. Since defect diffusion is significantly more rapid than solute diffusion, it may be possible to significantly change the stoichiometry without being time for the interfacial solute segregation to adjust to the new conditions. Creation of new surfaces, such as by cleaving an ionic crystal or deposition of thin films at low temperature may give interfaces in which there is initially no segregation or space charge. Finally, during grain boundary, or phase boundary, migration, segregated solutes maintain an asymmetrical distribution in the boundary region.(18) The total amount of excess segregant decreases relative to the static case, and the solute must diffuse to maintain this situation. When a grain boundary moves faster than a critical velocity, the solutes cannot keep pace with the boundary. Then the solutes have a nearly uniform distribution in the frame of reference of the moving boundary.(")

The atomic mobilities determine the kinetics for achieving the new equilibrium distributions. There are several constituents, e.g. cation and anion vacancies, unassociated solute and associated defect complexes, in the space charge region. These species can have significantly different mobilities. Thus, there can be a wide range of conditions under which the electrostatic potentials and defect distributions are kinetically determined. In general, vacancies have a much higher mobility than the unassociated solutes and defect complexes.

We have studied two limiting cases in which the solutes are relatively immobile. To treat the first problem, case A, we make the following specific assumptions: 1) vacancy creation and migration are rapid and so metastable equilibrium distributions of free vacancies are obtained, 2) solute diffusion is negligible and so the total solute concentration profile remains fixed, and in particular is taken to be uniform in most examples, and 3) solute-vacancy association and dissociation are rapid and so local equilibrium in the degree of association is obtained. For the second case, B, we keep assumptions 1) and 2) and take as 3) solute-vacancy association and dissociation are negligibly slow and so no change occurs in the degree of association.

Numerical calculations have been performed to give the electrostatic potential and defect distributions in these two limiting cases. Our calculations showed that at high temperatures and above the isoelectric temperature, the calculated electrostatic potential for either case A or B is very similar to that given in Kliewer and ~oehler('~) for a fully equilibrated interface. However at lower temperatures, the calculated potential can be significantly different from that of the equilibrium case. It is because at temperatures below the isoelectric point, the free solutes constitutes most of the charge density. Thus, the conditions of uniform solute distribution have a larger effect on the electrostatic potential. Figure 8 shows that at 200'C the potential distribution near an interface with a constrained equilibrium involving a fixed total solute distribution is up to 30% different from that near the equilibrated interface and the charge cloud is somewhat wider. For the constraint on both solute species, case B, the potential is morechanged; a significant space charge extends at least twice as far into the bulk. The bulk potential is positive, i.e.

-

0.21 eV, at this temperature, and Figure 8 shows that the electrostatic potential near a partially

,/ ,,..,,.' Fig. 8. Comparison of electrostatic potential

[l.Im, distributions near a KC1 interface at 200°C for

f o s ---COMUTE EWIL

: -VKANCIBCCMZEX,, ,. vacancy plus complex equilibrium, case A, free

Z.4

:guaaNCI

^{/ ,.:} vacancy equilibrium, case B, and complete

WIL ,,/

02 equilibrium. At this temperature, c+, is 0.21 CV

.. , ... .. ... ^. .... . in KC1 with 50 ppm divalent solutes.

9 10

REDUCED DISTANCE FRCU GRIUNBDUMVVn l&/%)

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T = 200.C

-.-.- vncnmr a ~ F I E ~ EOUlLlBRlUM F R E EVaCnNCI

REDWED DISTANCE RIoM GRAIN B(XMIDRIk/8l

Fig. 9. Comparative distribution of divalent solute ions, IK, and K vacancies near a KC1 interface at 200'C for complete' equilibrium vacancy plus complex equilibrium, case A, and free vacancy equilibrium, case B.

.- _. I

c . e . r s o L u r e

A ,,...,-

^/

E O U I L I B R I U M

Fig. 10. Typical values of T,, tb and T, as functions of temperature for KC( with 50 ppm Sr solutes. The time-temperature regions are delineated to show which metastable equilibrium cases are applicable.

equilibrated interface is lower than near a fully equilibrated one. This is because the conditions of uniform solute distribution restrict the positively charged solutes from segregating to the interface region as strongly as they would at equilibrium.

Figure 9 shows a comparison of the defect distributions in the three cases. The Ii( concentration near the constrained interface approaches but never exceeds the total solute concentration for case A and cannot change from the bulk value in case B. However, the Ii( concentration near a fully equilibrated interface is free to exceed the total bulk solute concentration and frequently does so. For example, in the fully equilibrated interface the Ii(

concentration at X

-

0 is 20 times higher than the bulk solute content at 200'C.

The metastable equilibrium cases treated in this paper are directly applicable to describing the space charge cloud which would form at a surface cleaved at an intermediate or low temperature. Often, the potential would be as described for one of the two metastable cases, or intermediate between these, under conditions for which solute segregation were negligible and vacancy diffusion were rapid enough to form a charge cloud. The case A would obtain when solute association were rapid and case B when it were slow. The times, t, for which these situations would obtain can be estimated as follows. For a very shbrt time, there will not be any electrostatic field or space charge if t < ^T,, where 7" is the characteristics time for vacancy equilibrium. The conditions of free. vacancy equilibrium, as described in case B, will be applicable if 7, < t < rb, where ^sb is the characteristic time for solute vacancy association. The conditions of vacancy and complex equilibrium, as described in case A, will be applicable if

~b < t < ^{T ~ ,} where T, is the characteristic time for solute segregation. Finally, complete equilibrium can be achieved if 7, < t. These characteristic times are related to the appropriate diffusivities and the material or defect transport distances required to achieve the equilibrium.

We have calculated the characteristic times for vacancy, solute and complex equilibria in KC1 with 50 ppm Sr.

Figure 10 shows these characteristics times as a function of the reciprocal temperature. In this figure, we have delineate the time-temperature regions within which the different metastable equilibrium cases are applicable. In general, complete equilibrium can be achieved at either high temperature or for a very long time. Over a wide range of time and temperature, the metastable cases of vacancy-complex equilibrium and free vacancy equilibrium are appropriate. However, at low temperature and for a short equilibriation time, space charge may not exist. Thus, in order to analyze the problem of solute segregation, we must determine the equilibrium condition applicable to the experimental conditions, and our analyses shown here can provide general guidelines for such a determination.

111 - DEVICE APPLICATIONS

Solute segregation and oxidation at grain boundaries or interfaces have significant effects on the device properties of many electronic ceramics. In this paper, we will describe several recent research activities in our laboratories in the development of electronic ceramic devices with novel grain boundary or interface properties. These devices include ferrites with a low eddy current losso4) and a high mechanical strength;(') and titanate ceramics with high dielectric constant,(@ and a non-linear electrical

(1) Low Loss Ferrite for High Frequency Applications

In the design of switching power supplies, the trend is towards higher operating frequencies, approaching 200 kHz, and towards miniat~rization.(~) Thus, the core losses of the transformer become significant to power supply designers. Recently, Ghate, Sundahl and ~ ~ u ~ e n ( ~ ) have developed MnZn ferrites with a much lower power losses than the conventional transformer materials, such as silicon-irons or the permalloys, for high frequency applications.(4) The classical expression for the eddy current losses, P=, per cycle and per unit mass of a composite materials made up of individual elements is

where d is the element size; f, frequency; B, peak flux density; p, material resistivity and A is a geometrical factor.

Thus, the eddy current losses can be reduced by decreasing the element size and/or increasing the resistivity. Data of loss per cycle as a function of frequency for single-crystal, hot pressed and sintered polycrystalline samples of MnZn ferrite are shown in Figure 11. The hot pressed and sintered samples were prepared at 1100 and 1300°C respectively. Figure 11 shows that within the frequency range studied the core loss per cycle increases linearly with frequency; and this frequency dependence confirms the eddy current contribution to the core loss. The larger slope of the single crystal specimens is probably due to the larger element size, d, which is approximately same as the sample size in a single crystal. However, the element size, d, in the polycrystalline specimens is approximately same as the grain size. Furthermore, the hot pressed samples have a larger hysteresis loss, probable due to the stress gradients and compositional inhomogeneities resulted from a lower processing temperature; and the hysteresis loss per cycle is independent of frequency and thus has a constant contribution in Figure 11. More importantly, the data show that a small amount (0.07 wt%) CaO dopant reduces the core loss by 30% because the CaO addition increases the resistivity of the ferrite.

For example, Figure 12 shows the resistivity of undoped and CaO-doped MnZn ferrites. In fact, both S i 0 2 and CaO dopants are effective in increasing the resistivity. The resistivity of CaO-doped ferrites shows a frequency dispersion as illustrated in Figure 12. Such dispersion suggests that the polycrystalline ferrites consist of fairly conducting grains separated by resistive grain boundaries as proposed by ~ o o p . ( ' ~ )

Auger analyses of fractured grain boundary surfaces of MnZn ferrites, given in Table 2, show that both CaO and SiOl have a significant grain boundary segregation.(3) Segregation profiles of the solutes and the major constituents in the MnZn ferrite were derived from these data and shown in Figure 13, with the assumptions that the fractured surface had a mean distance of 0.5-0.6 nm from the actual boundary and that the bulk composition was attained a t a distance of 104 nm from the fractured surface. Solute segregation is expected from the large difference in the ionic sizes between Ca (0.099 nm) and Si (0.041 nm) and Mn, Zn or Fe (0.064

-

0.08 nm). Furthermore, the electrostatic potential in the grain boundary region of ferrites may exert a rather large driving force on the tetravalent Si. Apparently, the segregation of Ca and Si increases the grain boundary resistivity as shown in Figure 12 and thus reduces the eddy current loss. In contrast, Sn does not show much enhancement at ferrite grain boundaries because its ionic size (0.071 nm) matches the matrix ions fairly well. A slight depletion of the major constituents is probably caused by the electrostatic repulsion from the strongly segregated Ca and Si solutes in the boundary region, similar to those shown in Figure 5.

Fig. 1 1. Power loss versus frequency for Fig. 12. A. C. resistivity of MnZn MnZn ferrites, showing the effects of ferrites showing the effect of CaO grain boundaries. After Ref. (4) additive. After Ref. (4)

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Table 2. Auger analysis of an M n Z n ferrite containing SnOZ. CaO, and ~ i 0 ~ ' ' '

0.1 I I ^{I I}

0.1 1 10 102 1 0 3 104

MEAN DISTANCE FROM GRAIN BOUNOARY (nm)

Fig. 13. Segregation profile of solutes and major constituents in the grain boundary region of MnZn ferrite.

Element M n

%n Fe 0 Sn Ca Si K

(2) Improved Mecbanica1 Strength of Ferrite

103,

Mn zn Ferrlte I

Grain boundary composition (at.%*) Bulk

cornp.

9.52 3.04 30.09 57.1 0.18 0.047 0.015 CO.01

In the manufacture of spinel ferrites the compositional and processing control are usually exercised to tailor the magnetic properties; and relatively little concern is given to their mechanical properties.(5) However, outright breakage can occur during manufacture, handling, grinding, or assembly into spring-loaded inductor or transformer hardware. Chipping or cracking can occur again during handling and particularly during grinding, a step crucial for mating cores for the manufacture of transformers or inductors.(') Thus, it becomes desirable to study the critical parameters affecting the mechanical properties of these spinel ferrites. Johnson et alO) have shown that a control of the p02 in the cooling atmosphere during sintering of ferrites can markedly affect their mechanical properties. In particular, Johnson has observed that samples, cooled in an oxygen excess atmosphere, were mechanically weak because of the oxidized layers on specimen surfaces. The fracture path was largely transgranular through the oxidized layers of about 500 pm thick a t the specimen surfaces and was mostly along grain boundaries in the specimen interior. However, in samples with a higher strength, intergranular fracture was observed throughout the specimens, Figure 14.

Recently, ~ o h n s o n ( ~ ) have shown that Ca dopant improves the mechanical strengths of MnZn ferrites. Figure 15 shows the modulus of rupture in MnZn ferrites versus the CaO dopant. Furthermore, the fracture mode in the ferrites changes from the transgranular fracture without CaO to the grain boundary fracture with CaO as illustrated in Figure 14.

After 42-nm sputter etch

8 37 2.98 25.34 60.15 0.38 0.48 2.29 Freshly

fractured 4.93 2.59 16.82 53.48 1.3 10.98 8.21

1.68

It is hypothesized that grain boundary fracture occurs because the large cations, Ca2+ and FeZ+, on the grain boundaries cause a locally distorted structure which is an easy fracture path. Despite the easy fracture path, the total fracture energy is increased for this fracture mode due to crack branching, leading to dead end cracks with their consequent increase in the total fracture energy.($)

After 3-nm sputter etch 5.94 2.77 22.1 8 59.36 0.59 4.30 4.56 0.3 1

WT X COO no ( ' a 0

Fig. 14. Modulus of rupture, by three Fig. 15. SEM micrographs of fracture point bending tests, increases with CaO surfaces of MnZn ferrite showing largely addition in MnZn ferrites. After Ref. transgranular fracture without CaO and

(5) grain boundary fracture with CaO. After

Ref. (5)

(3) Grain Boundary Layer Capacitors

In recent years, the sale of ceramic capacitors enjoys a fast growth rate parallel to that of integrated circuit chips, because capacitors are required to decouple the high frequency transients. Miniature ceramic capacitors are particularly popular for electronic applications. There are four basic types of ceramic capacitors depending on the electrode arrangement and ceramic microstructures. Table 3 lists the capacitance obtained in these four types of capacitors.

Multilayer capacitors are prepared by W-sintering a stack of thin ceramic layers screen-printed with electrode coatings. Because of their large capacitance value and volumetric efficiency, multilayer capacitors have essentially replaced the wnventional discs capacitors in most integrated circuit applications. In grain boundary layer capacitors, thin insulating layers are formed a t grain boundaries of semiconductive grains and their capacitance is a factor of G16 larger than the wnventional disc capacitors with a uniform ceramic microstructure. Despite their large effective dielectric constant, the grain boundary layer disc capacitors have difficulty in competing with the multilayer capacitors in providing a large capacitance value of 20.05 pF. However, it has been proposed that the next plateau in the volumetric efficiency of ceramic capacitors might well be by combining the grain boundary layer and multilayer concepts.(20)

There are three basic methods to prepare the grain boundary layer capacitors. In the first method, two separate firings are required. During the first firing, donor doped BaTi03 or SrTi03 ceramic is densified a t high temperatures in a reducing atmosphere to give a large grain size and a high electrical conductivity. After the first firing, a mixture of low melting oxides is deposited on the surfaces of sintered discs, and then reannealed in an oxidizing atmosphere at a lower tenperature. During the second firing, the oxide coating melts and penetrates the grain boundaries to form thin dielectric layers between the semiconductive grain lattice. This method is probably most widely used by most manufacturers of grain boundary layer disc capacitors.(21) However, this method cannot be readily modified to prepare grain boundary layer capacitor in a multilayer configuration.

The second method, which was developed by Payne and ark,^^-^" involves liquid phase sintering of a high temperature calcined semiconductive powder. Donor doped powders, e.g. Nb or W doped SiTi03, was calcined a t a high temperature to give a high wnductivity. The calcined powder is then mixed with a low melting oxide, e.g.

Pb5Ge3011, and is densified by liquid phase sintering a t a temperature well below the calcination temperature of the semiconductive powder. Since sintering takes place at a lower temperature than calcination, the grain lattice preserves its high conductivity; and the low melting oxide simply coats the grain boundaries to provide thin dielectric layers.

In the third method, thin dielectric layers are prepared by solute segregation a t the grain boundaries.

Appropriate solutes are included in the ceramic composition. One solute is a donor dopant to increase the lattice wnductivity; and another solute is chosen such that it is an acceptor dopant and it also has a large elastic energy when substituting in the lattice at sintering temperatures. However, during cooling the elastic energy is relaxed by solute segregation at grain boundaries. The segregation layers are depleted of electrons and form thin dielectric layers. Both the second and the third methods involve only a single step sintering and they can be modified for the processing of multilayer capacitors.

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Table 3: Capacitance Value in Four Basic Types of Ceramic Capacitors*

Ceramic Microstructure

Uniform

1

Grain Boundary Layer

*A and T are the area and thickness respectively of a capacitor sample; n is the number of electroded ceramic layers in a multilayer capacitor; G and 6 are grain size and grain boundary thickness respectively; and KO and K, are the dielectric constants in the grain lattice and grain boundary

CO- -.

-

region.

I ^{I I I I} I

0 200 4M) 600 800 MOO 1200

ELECTROW ENERGY. *V

Fig. 16. Resistivities of 0.1% Ba-doped Fig. 17. Typical Auger spectrum of an TiOz versus the Nb dopant content. intergranularly fractured surface from

(Nb, Ba) doped Ti02.

Recently, we have prepared T i 0 2 grain boundary layer capacitors, using Ta or N b as a donor dopant and Ba as a segregation dopant. Ta and Nb are used as electron donors because they have S+ valence. Furthermore, they have ionic sizes (0.073

-

0.070 nm) similar to Ti (0.068 nm). Figure 16 shows the electrical resistivity of TiOz versus the Nb content. Data show that the resistivity of TiOl decreases by 10" by an addition of 0.1% Nb.

Barium segregation is expected because it has a much larger ionic size (0.133 nm) than Ti. Figure 17 shows Auger energy pattern in intergranutarly fractured (Nb, Ba)-doped Ti02 sample. The Ba concentration a t grain boundaries is about 150 times higher than the bulk value. Furthermore, Ba compensates for Ta and forms dielectric layers a t grain boundaries.

Figure 18 shows the effective dielectric constants of (Ba, Ta)-doped TiOz versus composition. Data show that these titanate ceramics have high effective dielectric constants in excess of 50,000. However, the dielectric constant and loss of T i 0 2 capacitors show dispersive properties as shown in Figure 19. Such dispersive properties are characteristics of many grain boundary layer capacitors. According to K O O ~ , ( ' ~ ) it is desirable to decrease the lattice resistivity such that the dispers~ve properties can be shifted to a high frequency.

While these T i 0 2 grain boundary layer capacitors are promising, further development is necessary to prepare them in a multilayer configuration. High sintering temperatures of the titanates, the compatibility between the ceramic and metal electrode, and the high frequency dispersion and losses are the major technological issues yet to be resolved.

Low voltage varistors are used to equalize the direct current from central switching facilities to telephone sets on customer premises located at different circuit path lengths. S i c is the conventional material used to prepare these varistors. The quality of SIC powder from commercial sources is very sensitive to the trace impurities and dopants introduced during powder processing. Furthermore, during processing of S i c varistors, clay from natural sources was

Fig. 18. Effective dielectric constants are Fig. 19. Dielectric constant and loss are plotted versus, Ba and Ta dopant plotted versus frequency showing a composition in TiOz ceramic. dispersive effect.

Fig. 20. Photograph showing a large size reduction of Ti02 varistors versus S i c varistors.

Fig.21. Schematic voltage-current relation showing the resistivities at the low and high current limits and the transition between these limits.

used as a binder and filler material; and graphite was used as a reduction agent. These material sources and processing technique pose a difficult challenge to the quality control. These considerations led to the investigations of an alternative to S i c for low voltage varistor applications.

Recently, varistors based on ZnO have been developed. However, these varistors operate at -100-200V. which are 10-100 times larger than the voltage used in the telephone circuit. Thus, ZnO is not a viable candidate for low voltage varistors, except for few special cases.

In our laboratories, we have developed low voltage varistors based on Ti02 ceramic with similar compositions as described in T i 0 2 capacitors. Figure 20 shows a photograph to illustrate a significant size reduction of the T i 0 2 varistors versus the B C varistors. Empirical model, similar to that proposed by ~ o o ~ , ( ' ~ ) has been constructed to understand the varistor properties of T i 0 2 ceramics and a schematic voltage-current relation is given in Figure 21.

In this model, we assume that at low current density, the voltage is too low for electron tunneling through the grain boundaries and the specimen resistivity is due to the high grain boundary resistivity. However, in the limit of high current, the voltage is sufficient to tunnel through grain boundaries and the grain boundary resistivity becomes small and approaches the lattice resistivity. Thus, the specimen has a lower resistivity at high current. It is the transition from the high resistivity limit at a low current to the low resistivity limit at a high current that gives a nonlinearity, a, in the voltage, V, and current, I, relation of I

-

KVa as shown schematically in Figure 21. Voltage-current relation and cu value of a typical Ti02 varistors are shown in Figure 22.

Figure 23 shows the resistivity as a function of current for T i 0 2 samples sintered at different atmospheres. In oxygen sintered samples, the resistivity decreases rapidly as the current increases, which is consistent with the schematic model shown in Figure 21. Sintering in an atmosphere with a lower p 0 2 tends to give a smaller resistivity difference. Thus, the nonlinearity index, ^a, decreases with a decrease in the p 0 2 of the sintering atmosphere as illustrated in Figure 24.

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Fig. 22. DC voltage-current relation and Fig. 23. Resistivity versus current in a values of a typical Ti02 varistors. Ti02 varistors sintered at different p02.

l , , , , , , , , , ]

XI mo tm ~ z w rxo m

A m w w TmFcmTw m1

Fig. 24. Nonlinearly index, a, of TiOl Fig. 25. Nonlinearity index, ^a, of Ti02 varistors versus the p02 of the sintering varistors versus the annealing

atmosphere. temperature in 0 2 .

Some nitrogen sintered samples were re-annealed in oxygen for 2h a t different temperatures. Varistor properties were acquired during the oxidation anneal. The a values of ^{0 2} annealed .samples are shown versus the annealing temperatures in Figure 25. Data show that the a value gradually increases with the annealing temperature. This corresponds to an increasing degree of oxidation. Since the a value can be significantly increased by a relatively low temperature oxidation, the oxidation kinetics is probably achieved through grain boundary diffusion. If it is assumed that a

-

^2.8 is equivalent to the full oxidation in this composition, one can estimate from the specimen dimensions and the annealing time that the grain boundary diffusivity of oxygen in Ti02 can be as high as 2.2 X 10-S cm2/s a t 1100°C.

IV

-

CONCLUSION

We have reviewed the theoretical studies on solute segregation and device applications at ceramic grain boundaries. Elastic, electrostatic and dipole interactions between solute and grain boundaries are the major driving forces in solute segregation in ceramics. These driving forces are usually coupled to each other. Equilibrium solute distributions in the boundary region are analyzed. We also show that the segregation profile of a solute species is usually affected by the presence of other solutes with a different valence and/or ionic size. Furthermore, the degree of solute segregation is also affected by the kinetic processes involved in the experimental conditions. We have analyzed the appropriate equilibrium times required for the segregation of solute and other defect species. Device applications of solute segregation a t grain boundaries of electronic ceramics are illustrated by recent studies on ferrites and titanates. It is shown that a low eddy current loss and a high mechanical strength in MnZn ferrites can be achieved by Ca dopant; and a high dielectric constant and a nonlinear electrical conductivity can be obtained in Ba doped Ti02. In both cases, solute segregation and oxidation are important to the device properties.