Grain boundaries in ceramics. Grain boundaries Grain boundary: interface between two crystals (grains) of the same phase but different orientation. Regions

Grain boundaries in ceramics

Grain boundaries

Grain boundary: interface between two crystals (grains) of the same phase but different orientation.Regions with:

- lower density- different coordination of atoms/ions- relaxation of atomic positions- often different composition (segregation of impurities, dopants, lattice

defects)- different properties (charge and mass transport, dielectric, optical, etc.)

Small angle tilt boundary: misfit accommodatedby formation of dislocations Low energy tilt boundary: coincidence of lattice positions

Dislocations

Edge dislocation

Screw dislocation

Line defects originated by the relative shearing of two parts of a crystal (plastic deformation).

Non-equilibrium defects, can not be treated by thermodynamics.

Grain boundaries

Left. HRTEM image of the 5.4 [001] (010) symmetrical tilt grain boundary in SrTiO3. Right. Strain field around the dislocation cores evaluated from the HRTEM image. The size of the lozenges reflects the unit cell size in the respective area.

Simulated image. Half oxygen atoms were removed from one O column on the g.b. (white arrow). The oxygen deficiency produces a higher brightness in this position ().

O Sr-O

Imaging of oxygen sublattice and grain boundary structure in SrTiO3 by HRTEM

Central dotted lines connect CSL positions(CSL: coincidence site lattice)

Tilt grain boundary of SrTiO3

The intensity profile along the g.b. shows that the intensity of the O column s is variable. Column with oxygen vacancies

110

Observed displacements and grain boundary expansion in agreement with first-principle calculations (0.06 nm expansion). Expansion related to Ti-Ti repulsion and existence of O vacancies on the g.b.

Relaxation of atomic positions near the grain boundary

Expansion compared to perfect lattice

Differences of Ti-Ti spacing along the direction perpendicular to the g.b. The spacing closer to the g.b. is smaller. Increased separation of the two Ti columns facing each other at the g.b.

Differences of Sr-Sr spacing along the direction perpendicular to the g.b. The spacing closer to the g.b. is larger. Decreased separation of the two Sr columns facing each other at the g.b.

Differences normal to the g.b. of Sr-Sr spacings located on CSL sites. The first spacing is increased meaning that there is an expansion of the g.b. (0.043 nm, 1% lattice parameter).

Decreased spacing

Increased spacing

Ti-Ti Sr-SrSr(CSL)-Sr(CSL)

Segregation at grain boundaries

Surface tension or surface energyinPT

rev

A

G

dA

dw

,,

Natural tendency to minimize the surface energy of a system by redistribution of the components. Components which lower the surface/interface energy tend to concentrate at the surface/interface (adsorption, segregation). Oxygen is strongly surface-active in liquid metals and non-oxide ceramics. Segregation at surfaces and grain boundaries in ceramics is determined by the different formation energies of defects at interfaces than in bulk.

Segregation in alumina ceramics as visualized by SIM

250 ppm MgO 1000 ppm La2O3250 ppm CaO

bulkMMseg EEH ,sup, OOAl VOMgMgO2

122 '

OAl OLaOLa 332

Segregation modifies the energy of the different crystallographic surfaces and, consequently, the equilibrium shape of crystals

Segregation in alumina ceramics – atomistic simulation

Equilibrium morphologies of undoped -alumina (a) front and(b) top view. Equilibrium morphologies of 10 ppm Y-doped -alumina at 1600°C seen again from (c) front and (d) top view.

Wulff’s theorem for the equilibrium shape

i

i

hhh

.....

2

2

1

1 i: surface tension of ith facehi: distance from the center

Surface energies of pure and Y-doped -Al2O3

Basal plane

Interfacial energies of pure and Y-doped -Al2O3

.)(int.)(2 surf

Predicted grain boundary structuresFor highly symmetric (left) and more general case (right).

Calculated grain boundary structure showing a regular La pattern resulting from segregation.


Enthalpy of segregation for La in alumina


Calculated and experimental solubility limit of MgO in alumina as a function of grain size

bulkMMseg EEH ,sup,

Grain boundary phases and films

In many cases, solid phases located at grain boundaries result from the solidification of a liquid phase formed during sintering. The grain boundary phase can form a continuous film, pockets at the triple junctions or discrete particles.

Wetting of a liquid on a solid

SLSVLV cos

> 90°: nonwetting < 90°: wetting

= 0°: spreading

Necessary condition for spreading: SVLV

SL θ

LV

SV

Wetting of grain boundaries

2cos2

SLGB

Liquid phase forming additives in ceramic oxides: SiO2, glass, alkaline oxides (Li2O, Na2O, K2O), alkaline-earth oxides (CaO, SrO, BaO), TiO2, B2O3, CuO, ZnO, V2O5

Distribution of liquid/amorphous phase at grain boundaries

(1)

(3)

(4)

(2)

(1)Y2O3:ZrO2

CaO:Si3N4

AlN

(3)Y2O3:ZrO2

(2)Si3N4

(4)AlN

SL

GB

2

1

2cos

“Special” grain boundaries show little segregation and are free of an amorphous grain boundary layer

Criterion for film formation: GBCA 2

Special (A) + random (B) grain boundaries

Random grain boundary

Grain boundaries in SrTiO3 ceramics

Distribution of liquid/amorphous phase at grain boundaries

2A: interfacial energy of a gb containing a wetting amorphous phase

GBC: interfacial energy of a clean gb

No grain boundary layer

GBC

(rotation)

A

A

Distribution of secondary phase at grain boundaries

Ordered grain boundary phase in Ti-rich BaTiO3 ceramics

Segregation and space charge at grain boundaries

The defect formation energies and defect chemistry at the grain boundaries is, in general, different from that of the bulk. Preferential segregation of charged defects in ionic solids leads to net charge at the grain boundary core which is compensated by a space charge cloud of opposite sign adjacent to the boundary, with formation of an electrostatic Schottky barrier.The thickness of the space charge layer is of the order of the Debye length.

220

2 Fzc

RTr

r: relative dielectric constantz: number of charges on defectc: defect concentration in the bulk

Schematic diagram of a positively charged grain boundary (segregation of oxygen vacancies) and compensating space charge (acceptor impurity). The region adjacent to the grain boundary will be depleted in oxygen vacancies.

OSrOTiSrTiO OSrVFeOFeSrO 5222 '

323

2

2

1exp

)(

)(

Lx

c

xc

O

O

V

V L is the width of the space-charge layerL = 2.5 nm in Y-doped ZrO2.

Segregation and space charge at grain boundaries

Transport through a polycrystal. Due to anisotropy of grain boundaries and their specific topology, different situations are encountered: (a) parallel effects, (b) perpendicular effects and (c) e flux constriction.

The effect of grain boundaries on the properties of ceramic

oxides

The segregation of oxygen vacancies in acceptor-doped oxygen conducting electrolytes (Y:ZrO2, Gd:CeO2. Fe:SrTiO3) leads to positively charged grain boundaries cores and a depletion of oxygen vacancies in the adjacent space charge layer. The combined effect of the electrostatic potential barrier (Schottky barrier) and the depletion layer determines a decrease of the oxygen conductivity at gbs (blocking gbs). In doped zirconia ceramics with clean boundaries the resistivity of gbs is at least two orders of magnitude higher than the bulk resistivity. A size effect is expected for grain dimensions in the nanoscale region (grain size <4λ).

Ionic conductivity in oxides: the effect of grain boundaries and grain size

Specific bulk and grain boundary conductivity in 3 mol.% Y2O3 doped ZrO2 (oxygen conductor)

At present, the minimum grain size (30-40 nm) of dense Y:ZrO2 ceramics is still >> 4λ and strong size effects on ionic conductivity are not observed.

OOZrZrO VOYOY 322

32Oxygen conduction in Y-doped ZrO2

Dopant segregation: decreasing effective bulk dopant concentration

Space charge effect

Because of the high density of gbs in nanoceramics, the total conductivity (not shown) is dominated by the resistive grain boundaries.

D

[VO••]

[VO••]∞

+++

+++ D

[VO••]

[VO••]∞

+++

+++

2

D

[VO••]

[VO••]∞

+++

+++

Mesoscopic fast ion conduction in thin-film heterostructures

Parallel ionic conductivity in CaF2-BaF2 thin-film heterostructures with overall thickness L comprising of N layers of thickness d. The overall thickness (L) is approximately the same in all cases.

d = L/NBlack lines: reference single phase films;Green lines: semi-infinite space-charge zones (period >8)Red lines: overlapping space-charge regions (period <8)

σT versus 1/T

Variation of ionic conductivity with the density of interfaces, N/L.

Nanosize effect. Loss of individuality of the single compounds.

interface effect

d < 8λ

d > 8λ

d=50nm

20nm

16nm

430nm

d

d

FMF

F VFF '2


Impedance spectroscopy

Y axis

Fourier transform

v(t) V(ω)i(t) I(ω)

v(t) = v0sin(ωt)

i(t) = i0sin(ωt+θ)

v: voltagei: current: angular frequencyθ: phase difference

Time domain

V(ω) = I(ω) Z(ω)Z(ω) = 1/(C ω j)

Z: impedanceC: capacitancej = 1

V(ω), I(ω) and Z(ω) are complex quantities

Frequency domain

ωp R1 C1 = 1

Simple RC circuit

ω R1 C1 = 1

R0R0+R1

R1

ω

Solid materials can be described by one (homogeneous single crystal) or more (ceramics, composites) semicircle in the impedance plot. Each semicircle is described by one resistive and one capacitive component.

d

S

d

SC r 0 d

S


Proton conduction in Y-doped BaCeO3

Sintered 1250°C/2h; gs: 0.38 μm Sintered 1500°C/48h; gs: 5 μm

Trivial size effect. The lower conductivity (left) of the fine grained ceramic is only due to the higher density of resistive grain boundaries. The specific conductivities (right) are the same irrespective of grain size.

OHOHOV

OVYYBaOOYBaCeO

OO

OOBaCeBaCeO

2

52223

3

2

''32

Total conductivity

grain interior

grain boundary

Intrinsic conductivity

Ionic conductivity in oxides: the effect of the grain boundary phase

Impedance spectra

Bulk resistivity

Grain boundary resistivity

freq.(a)

(b)

ZrO2: 3 mol % Y2O3

(a)

Continuous grain boundary phase

ZrO2: 6 mol % Y2O3

(b)

Lenticular grain boundary phase + clean boundaries

Colossal permittivity in CaCu3Ti4O12 : the role of interfaces

TiO6 octahedra

Ca

Cu

• Perovskite-like, non polar structure

• Not a ferroelectric relaxor

• Ab-initio calculations: r = 40

• Processing-dependent properties

tan0 rac tanδDielectric lossDissipation factor

Ceramic

102 Hz

106 Hz

Rel

ativ

e di

elec

tric

con

stan

t

Step-like behaviour of dielectric constant observed in ceramics as well as in single crystals. Strong frequency dispersion

l

S

l

SC r 0 l

S

The dielectric constant (real part of dielectric permittivity) is calculated from the measured capacitance C taking into account the sample geometry:

Single crystal

20 Hz

106 Hz

Rel

ativ

e di

elec

tric

con

stan

t



Insulating gbs

Semiconducting grains

Semiconducting core

Insulating skin

semiconducting ceramic

insulating layer

electrode

- semiconductive grain interiors; - more insulating grain boundaries and related interfacial polarization - insulating layer at the electrode-ceramic interface; - insulating surface skin

} IBLC effect – only for ceramicsMaxwell-Wagner relaxation

} also exist in single crystals

Brick layer model of a ceramic

Apparent colossal dielectric constant is of extrinsic oringin and is associated to the electrical heterogeneity of the samples and the contribution of different interfaces:


The step-like behaviour of the dielectric constant and all other electrical properties can be reproduced by using equivalent circuit models.

l

S

l

SC r 0

l

S

lR

bbR

bbC

gbgbgb xR 3

1

gb

b

gb

gbgb xx

C 33

b

gb

gb

b

C

C

D

d

Cgb>>Cb

Cb depends only on composition

Cgb depends on microstructure

Intrinsicbehaviour

1V

Vx bb

1V

Vx gbgb

D

d

ρgb >> ρb; gb = b

S


Inhomogeneous conduction probed by atomic force microscopy (AFM)

Vceramic

conductingtip

electrode

Current image Topograpicimage

Fracturesurface

Insulting grain boundaries (brown) Strongly nonlinear

current-voltage properties

Influence of grain size on the dielectric constant of ferroelectric BaTiO3 ceramics

Progressive depression of the dielectric constant with decreasing grain size when d1< 1 micron

d1

d2

ε 2

ε 1 >> ε 2

ε 2 ε eff ε 1

ε 1

The microstructure of BaTiO3 ceramics corresponds to ferroelectric grains with high dielectric constant (ε1 = 3000-5000) separated by non ferroelectric (ε 2 100) grain boundaries (“dead layer”). The NFE gbs do not necessarily imply a second phase grain boundary layer.d2 = 1-3 nm depending on ceramic preparation method.

“clean” boundary

2

2

1

11

x

gx

eff

εi ≡ Ki’

grain

grain boundary

Relative dielectric constant (298 K, 10 KHz) of dense BaTiO3 ceramics, 1998-2006

0

1000

2000

3000

4000

5000

6000

10 100 1000 10000

Grain size (nm)

Rel

ativ

e d

iele

ctri

c co

nst

ant

Arlt et al., HPSFrey & Payne, IPRandall et al., CSMRandall et al., HPSTakeuchi et al., SPSZhao et al., SPSBuscaglia et al., SPSDeng at al., SPSZhu et al., SPSWang, 2SS

Dead layer effectDomain size and

mobility effect

HPS: hot pressingIP: pseudo isostatic pressing in a multi-anvil cellCSM:combined sintering methodSPS: spark plasma sintering2SS: two-step sintering

Influence of grain size on the dielectric constant of ferroelectric BaTiO3 ceramics

Dispersion of experimental values related to processing (purity and stoichiometry of powders, sintering method) and microstructure (porosity, second phase grain boundary layer)

Documents

Grain boundaries in ceramics. Grain boundaries Grain boundary: interface between two crystals (grains) of the same phase but different orientation. Regions