UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Microstructure of Ceramic Materials

Proceedings of a Symposium

April 27-28, 1963

Held under the auspices of the Ceramic Educational Council of the American

Ceramic Society, with the cooperation of the National Bureau of Standards, and

under the sponsorship of the Edward Orton Junior Ceramic Foundation and the

Office of Naval Research. The Symposium took place at the 65th Annual Meeting

of the American Ceramic Society in Pittsburgh.

National Bureau of Standards Miscellaneous Publication 257

Issued April 6, 1964

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402

Price 31.75 (Buckram)
Library of Congress Catalog Card Number: 64-60020
Contents

troduction

Geometry of Microstructures

Lawrence H. Van Vlack

Department of Chemical and Metallurgical Engineering

University of Michigan

Ann Arbor, Michigan

Experimental Techniques for Microstructur e Observation

Van Derek Frechette

Alfred University

Alfred, New York

The Effect of Heat Treatment on Microstructure

Joseph E. Burke

Research Laboratory

General Electric Company

Schenectady, New York

Correlation of Mechanical Properties with Microstructure

Robert J. Stokes

Research Center

Minneapolis-Honeywell Regulator Co.

Hopkins, Minnesota

Microstructure of Magnetic Ceramics

A. L. Stuijts

Philips Research Labs.

Eindhoven

Netherlands

Microstructure of Porcelain

Sten T. Lundin

Royal Institute of Technology

Stockholm

Sweden

iii
Introduction

In all materials, the physical and even the chemical properties of a polycrystalline body are not exactly the same as those of a single crystal of the same materials.

Many materials are anisotropic - their properties depend upon the orientation of the

measuring system with respect to the crystallographic axes - and the polycrystalline

properties are some form of an average over the crystal directions. Thus the dielectric constant, elastic constants, index of refraction, magnetic susceptibility,

and many other "bulk" properties depend to some extent on the microstructure of the

specimen

.

Beyond this, some properties depend on the motion of various entities through

the material-transport of atoms and ions in diffusion, transport of phonons in thermal conduction and electrons and ions in electrical conduction, motion of dislocations

and other defects in plastic deformation and of domain walls in ferromagnetic and

ferroelectric switching, and even the propagation of cracks in fracture. In these

transport processes, the grain boundaries between the crystals in a polycrystalline

body behave differently from the bulk material, and their presence markedly affects

the resulting properties. Diffusion is usually faster at grain boundaries, especially at low temperatures, so that diffusion is enhanced in polycrystalline bodies.

Electrons and phonons are scattered by grain boundaries, so that electrical and thermal conduction tends to be lower in the polycrystals . The movements of dislocations

across grain boundaries are impeded, so that plastic deformation is inhibited by

their presence, and polycrystalline bodies tend to be stiffer and less ductile than

the corresponding single crystals.

Finally, the presence of grain boundaries not only modifies the behavior, but

sometimes even introduces new elements. Thus in brittle fracture the grain boundaries provide sources of cracks, making polycrystals weaker in general than single

crystals. The presence of strain and of impurities at grain boundaries raises the

local free energy, so that chemical effects, such as etching rates, are enhanced.

It is clear, then, that a knowledge of the microstructure of a polycrystalline

body is essential in any attempt to study and control its properties. This is particularly important in the field of ceramics, where the overwhelmingly important

form is the polycrystalline body. In order to review the problems involved in

specifying and studying microstructure in ceramics and the factors involved in the

interaction between microstructure and physical properties of ceramics, this

Symposium on Microstructure of Ceramic Materials was held. The papers presented are published in this volume. Primary responsibility for their technical content must

rest, of course, with the individual authors and their organizations.

In the first two Chapters, Prof. Van Vlack reviews the geometry of microstructures and how they can be specified and Prof. Frechette describes the principal

experimental techniques by which observations of microstructures are made. In

Chapter 3, Dr. Burke then describes the factors controlling the development of the

microstructure during heat treatment of the ceramic, and their relation to the

processing variables of time and temperature.

In the next two Chapters, Dr. Stokes discusses the influence of microstructure

on the mechanical behavior, and Dr. Stuijts describes the influence on the ferromagnetic properties of ferrites. In the last Chapter, Prof. Lundin examines in

detail the microstructure of one material, porcelain, and its ramifications.

Ivan B. Cutler, Chairman

University of Utah

Joseph E. Burke

General Electric Company

William D. Kingery

Massachusetts Institute of

Technology

Willis E. Moody, Co-Chairman

Georgia Institute of Technology

Alan D. Franklin, Editor

National Bureau of Standards

iv
Geometry of Microstructures

Lawrence H. Van Vlack

1. Introduction

The internal structure that a material possesses on a microscopic scale is generally called mic ro s true ture . This presentation is concerned with the geometry of

such microstructures as encountered in ceramic materials.

A study of microstructures does not involve the study of atomic coordination as

it exists in various crystalline and amorphous phases. However, it does involve the

phase and grain relationships at the lower end of the electron microscopic range, and

extends through the size spectrum up to and well into the "hand lens" range. Examples

at the lower end of the mic ro struc tural size range include the nuclei which start the

crystallization of glass and therefore introduce a heterogeneity of structure. Microstructures at the coarse end of the size range are found in ceramic products which can

be illustrated by abrasive grinding wheels. These products contain a distribution of

specific sizes and shapes of abrasive phases that are bonded with a silicate or similar

material and include closely controlled porosity.

The geometric variations which are encountered in microstructures include

(1) size, {?.) shape, and (3) the preferred orientation of constituent grains-'- (Fig. 1). In addition, when more than one phase is present, there can be the added variables:

(li) amount of phases, and (5) the distribution of phases among each other (Fig. 2).

Item above is most closely related to the chemistry of the ceramic product because

the amount of phases depends directly upon the composition. The other structural

variables are less closely related to the composition and depend more specifically

upon factors of processing and service history. Each of the preceding five microstructural variations involves grain boundaries and the consequent crystal structural

discontinuities.

Many ceramic materials possess porosity. From a micro struc tural point of view,

pores can be considered as an additional phase of zero composition. Of course this

"phase" is a very important feature in the microstructure, because the pores markedly

affect the micro struc tural dependent properties.

As will be pointed out in later presentations, the microstructures and therefore

the consequent properties of the ceramic are not static in behavior, for they may be

altered by external factors such as mechanical forces, thermal conditions, chemical

environments, and electric or magnetic fields. Therefore, a microstructure may be

varied by processing factors and servicing conditions. This presentation will first

consider the characteristics of internal boundaries, then single phase microstructures,

and finally polyphase microstructures.

2. Internal Boundaries

The most general characteristic of a microstructure is the presence of its

internal boundaries which separate the grains and phases within the material. Whether

these internal boundaries are between the disoriented grains of one phase, between

grains of different phases, or between electrical and magnetic domains of one grain,

they represent a specific change in the internal structure of the ceramic. Internal

boundaries are thus an important feature in a ceramic and have significant effects on the properties of the material.

It is possible to characterize boundaries as grain boundaries, domain boundaries,

phase boundaries, or surfaces. However, such characterization is usually unnecessary

for a general discussion, because each of the above boundaries may be considered to be

a surface or zone of crystalline mismatch. Boundary discontinuities in a microstructure

x The term, grain, as used in the discussion of microstructure denotes a single

crystalline volume. This is in contrast to grog grains which are usually 1-10 mm in

size and contain numerous small crystals.

1
represent locations of higher atomic energies; therefore a "driving force" exists

which tends to reduce the boundary areas with consequential boundary movements.

2.1. Boundary Structure

The atomic structure of a grain or phase boundary must be inferred because it is currently impossible to view the involved atoms directly. However, several conclusions

may be made about these boundaries as a result of indirect experimental evidence and on the basis of appropriate models. In doing so, several types of boundaries can be

cited. The first of these is the small-angle boundary which consists of aligned dislocations as illustrated in Fig. 3- Experimental evidence strongly supports this

structure. For example, since dislocations are revealed by etching, it is a simple

procedure to determine the angle of this boundary from the spacing of the etch pits

and lattice dimensions. An independent and corroborative check of the angle can then

be made by diffraction measurements. Figure l\ reveals such etching pits along small

angle boundaries in LiF. Similar boundaries have been observed in other materials

such as AlpO-^ and TiOj and have received specific, interest in view of their indication

of deformation and its consequences [1,2].^

Large-angle boundaries are most simply represented by Fig. 5. This can be considered to be typical of most of the boundaries which are found between grains and

phases within various materials. Again it is impossible to be specific about the

structures' along these boundaries except by inference. However, substantial evidence

does imply that the boundaries represent a zone of mismatch in atom spacings with a consequence that the atoms at the boundary are at a higher energy level than those

within the grain proper. Furthermore, the mismatch produces relatively large interstices between the atoms for grain boundary diffusion and for impurity absorption.

Because such boundaries possess atoms with higher energies, it comes without surprise

that the boundary is frequently the site for nucleation and subsequent crystalline

growth

.

Twins, a not uncommon feature of mineral phases, represent a special large angle

boundar;/- situation, in which the adjacent grains are coherent with one another (Fig. 6). The only mismatch involves second-neighbor and more distant atoms. Coherent boundaries may arise between unlike phases as represented in Fig. 7. As

with twin boundaries, coherency between phases is favored by specific crystallographic

orientations in which the atoms along the boundary are part of the two adjacent phases.

The oresence of these boundaries leads to Widmanstatten-type structures as shown in

Fig. 8.Domain boundaries are often categorized separately from the above boundary types.

However, there is no specific reason for such separation because they also represent

surfaces or zones of mismatch between adjacent groups of coordinated atoms. This is indicated in Fig. 9 where separate parts (domains) of a single crystal will have

opposing polarity as a result of inverted unit cell alignments. The boundary between

these areas is shown schematically in Fig. 10 as a transition zone which possesses

higher energy because of the changing alignment.

2.2. Boundary Energies

The interatomic spacings within equilibrated phases are such that the atoms

possess the lowest total energy. Higher energies exist when the interatomic spacings

are either increased or decreased. The major part of the boundary energy arises from

the variation in the spacing of adjacent atoms at the boundary. Additional but smaller

energies are required for the mismatch of second-neighbor or more distant atoms. It may be deduced from the above that the large-angle boundaries have high energies, while

small-angle boundaries, twin boundaries, and coherent phase boundaries have lower

energies. This conclusion may be verified by calculations and by experiments.

Since the small-angle boundary is a series of aligned dislocations, its energy may

be calculated as a summation of the energy associated with each of the individual

dislocations. As such, it possesses energies ranging from 0 to 100 ergs/cm3

. The energies of several large-angle metallic boundaries are indicated in

Table 1 [31. The determination of these energies commonly involves the experimental

use of dihedral angle measurements which are illustrated in Fig. 11 as a vectoral

balance [!(.]. Since the boundary area requires extra energy, there is a natural

8 Figures in brackets indicate the literature references at the end of this paper.

2
tendency for this area to be reduced. Thus the angle along grain and phase edges

undergoes an adjustment which is mathematically equivalent to the result of a surface

tension in the following relationship:

Y 1/3 Y 1/2 Y 2/3

sin s ^ n ^3 s ^ n &i

When two of the boundaries are comparable, Eq. 1 reduces to

i/a = 2 Ya/b Y „ /„ = 2 Y„ /u cos — (2)

as shown in Pig. 11(b). The dihedral angle, 0, is a special case of the edge angle 0.

The energy of the boundary or interface between two grains or phases is represented

by Y. It is necessary to use statistical methods to determine the two dihedral angles

accurately if the observed angles are on a random 2-dimensional plane through the

usual 3-dimens ional micro structure [5]. However, a reasonably accurate approximation

is obtainable from the median angle of a small number of observed angles [6], Thus,

comparative values may be made of the boundaries of several types.

The energy of boundaries between adjacent grains of the same phase will vary with

the relative orientation of the two adjacent grains. The extreme case is that of two

grains with identical orientation in which the boundary disappears and the energy drops

to zero. As the adjacent grains are rotated out of alignment, the boundary energy is

increased until there is a maximum amount of mismatch between the structures of the two

grains [7]. The specific orientation with these higher energies will vary with the

structure of the grains and with the direction of rotation. However, for many materials

it can be concluded that most boundaries have energies close to the maximum and only a few favored low angle and twin orientations diverge significantly from the maximum

energy values.

2.3. Boundary Movements

The average grain size of a single-phase ceramic will increase with time if the

temperature is such as to give significant atom movements. The driving force for such

grain growth is the free energy released as the atom moves across the boundary from

the convex surface to the concave surface where the atom becomes coordinated with the

larger number of neighbors at equilibrium atom spacings (Fig. 12). As a result, the

boundary moves toward the center of curvature (Fig. 13), and the larger grains will

grow at the expense of the smaller grains. This is true in both single phase microstructures and polyphase mic rostruc tures , as will be indicated later. The net effect

is less boundary area per unit volume.

Boundary movements are influenced by grain size, temperature, and the presence of

insoluble impurities. Smaller grain sizes provide a greater driving force for atom

movements across the boundary as indicated in the previous paragraph. Beck [8] has

provided the relationship:

dD/dt = k/Dm

, (3)

where D is the index to grain diameter, t is time and k and m are constants. Since

experimental data indicate the value of m is close to 1, this equation integrates to:

D

2

- D

2 = 2 kt . (/j.) Therefore the change in cross-sectional area of the grain is nearly proportional to time, or if the initial size may be assumed to be zero, the diameter increases with the

square root of time. The value of k_ in Eq. 3 an.d tj. is usually an exponential function

of temperature in which k reflects the activation energy for the atom movements shown

in Fig". 12.

The most obvious limitation to grain growth occurs as the grain size approaches

the dimensions of the ceramic product, and therefore grain growth is inhibited. A less

obvious, but equally important, limitation occurs in the presence of an inhibiting

second phase as shown in Fig. 14. In general, the boundary as seen in two-dimensions

must be increased and the curvature reversed locally before a boundary can move beyond

the dispersed particles, thus inhibiting grain growth. Zener [9] has presented the

following relationship for the limitation of boundary movements:

R/r « l/f (5)
R and r are the radii of curvature for the grain surface and the dispersed phase res- pectively. The volume fraction of the dispersed phase is given as f. Such grain

growth inhibitors have been used in various ceramic materials such as k\~p^ and MgO

The movements of domain boundaries are accentuated by the introduction of an externally applied field. This is achieved by the inverting of the polarity of the

cells within and adjacent to the boundary zone so as to expand the favorably aligned

domains and reduce the volume of the unfavorably aligned domains (Fig. 15>) . These

boundary movements are reversible as the external field is inverted. Domain boundary

movements, like grain boundary movements, are influenced by the oresence of external

surfaces and by impurity particles.

3. Single Phase Micro structures

It was pointed out previously that a single phase micro structure may have

variations in grain size, grain shape, and preferred orientation of the grains. These

are not wholly independent because grain shape and grain size are both consequences of

grain growth. Likewise, the grain shape is commonly dependent on the crystalline

orientation of the grains during growth. In the simplest situation the grain may be

considered to be uniform in size, equiaxed in shape, and random in orientation. This can be illustrated in Pig. 16 for periclase (MgO).

3.1. Grain Size and Boundary Area

The grain size as shown in Fig. 16 does not indicate the true grain size distribution inasmuch as that figure reveals a random 2-dimensional section through a 3-dimensional solid, and very few grains show a maximum cross-sectional area. A theoretical

distribution of grain size areas for uniform grain size would provide a median area of

about 0.8 of the maximum area. Since the various measurements in ceramics reveal that

the median area is less than the above figure, it is to be concluded that there is a distribution of grain sizes. This is to be expected since the process of grain growth

requires that certain grains decrease in size and disappear (Fig. 13). Burke [10] has

shown that this does not proceed uniformly for any one grain because of the complex

boundary network around any disappearing grain. Smith [11] used a soap bubble as a model for grain growthand boundary movement. Since the analogy is theoretically sound,

qualitative comparisons are justified. This procedure provides the suitable means of

studying changes in 3- dimensional solids.

Abnormal grain growth may occur in materials. Burke [10] explains such growth in

metals by noting that if an individual grain is favored to become significantly larger

than the balance of the grains, then it possesses an additional advantage for still

further grain growth by virtue of sharper boundary curvatures (Figs. 17 and 18) . The

circumstances which produce the Initial size advantages for specific grains can only be surmised. However, factors such as impurities, the distribution of inhibiting particles, location of nucleants, and the oxidation of adjacent grains are undoubtedly

important

Grain size has commonly been indicated as the grain diameter. Also, an ASTM

procedure assigns a number, n, to a grain size where,

N = 2n-1

(6)

and N is the number of grains observed in 0.0001 sq. in. of a 2-dimensional section

(i.e., 1 in. ^ at a magnification of X100). These are appropriate for those microstructures in which it may be assumed that all grains are spheres with identical

diameters. Since microstructures seldom if ever meet these conditions, diameters and

grain numbers are at best only an index of size.

Statistical procedures are available which take into account a distribution of

actual sizes, as well as a distribution of observed sizes in a microstructure which

arises because the grains are not cut through their greatest diameter [12,13]. Such pro

cedures require a knowledge of shape and size distributions before they are meaninfgul.

An alternate index of grain size is that of determining the grain boundary area in a microstructure without regard to shape or size distribution. This area is often more

important than the grain size per se , because the amount of area influences the

properties which arise out of the microstructures. Several workers [12,lii] arrived

independently at the following extremely simple relationship:

i = 2 N

V L

In this equation, B„ is the boundary area (mm")2 per unit volume /I(mirr) , and is the

4
number of grain boundaries traversed per millimeter by a random line. The several

derivations of this equation are cited by Underwood [13] and Saltykov [12]. The significant feature about Equation 7 is the fact that the boundary area is measurable without determining the grain size and may be determined for materials with non-uniform

grain sizes. The only requirement is that the sample lacks grain size gradients or

grain shape heterogeneities.

The use of the random line technique is illustrated in Pig. 19 for the MgO of

Fig. 16. Several lines give a figure of about 85 grains/mm, thus indicating a boundary area of 170 mm2/mm3.

It is possible in a single phase material to relate the number of grains per unit

volume, Ny, to the boundary area, By, in that volume, if some assumptions are made

concerning the grain shapes.

Ny = (By/F)3 (8)

where F is a shape factor equal to 3-0, 2.86, 2.67, and 2.66, respectively for cubes

hexagonal prisms, rhombic dodecahedrons, and truncated octahedrons, i.e. cube-octahedrons [15]- Underwood [1^] concludes that the latter are most appropriate in

equiaxed microstructures . Thus Equation 8 reduces to Ny = bJ/19 (8a)

N

v

= 0.1+2 (8b)

As a result, the MgO ceramic of Fig. 16 would contain about 260,000 grains per mm^.

Although this number could be converted to an equivalent grain 'diameter," it is not

recommended because assumptions would have to be made concerning grain shapes.

3 . 2 Grain Shape

Although it is common to speak of grain size in terms of diameter, it is obvious

that grains of single-phase, nonporous ceramics are not spherical. Rather, they must

completely fill space and also maintain a minimum in total boundary energy. Thus,

they have an irregular shape at best. The term, equiaxed, is used for those grains

that have approximately equal dimensions in the three coordinate directions. This is

the case for the periclase (MgO) of Fig. 16. In other cases there can be an elongation in one direction as indicated for U0-3 in Fig. 20. The grain shape in a single phase material may be described by a length/width

ratio. Thus both the schematic micro structure of Fig. 1(c) and the actual microstructure of Fig. 20 would possess an L/W ratio between 3/1 and l|/l, depending on whether maximum or typical widths are used. Here, as with grain size, we also

encounter the question of 3-dimensional sizes vs. 2-dimensional observations. As a result it may be desirable to utilize a statistical calculation of shape when there is an elongation to the structure. However, instead of using the random lines of

Equation 7, lines are intentionally aligned in the two principal coordinate directions.

An elongation, E, may be calculated.

E = i—ll (9)

(NL )j_ + (TT/2-1) (NL )jj As before, is the number of grain boundaries traversed per mm; || and I indie ate

the two principal coordinate directions; and E is the degree of elongation [13]. The

degree of elongation for Fig. 1(c) is about This is in contrast to zero elongation for the other three sketches of Fig. 1, and 1.0 for perfect elongation.

Microstructures may possess patterns of elongation of the grain shapes other than

those shown in Fig. 1(c) where it is implied that the elongation in one direction is

greater than the other two, i.e., (Nt) & < (Nt) d = (%,)<,. Other possibilities include

(NL ) a = ( nl) d < ( NL^cJ and ( NL)a < ( NL)b < Because of these possibilities,

it is not safe to draw conclusions about the grain shape and mic rostruc tural elongation on the basis of one section only. As the minimum, it is necessary to examine

two perpendicular sections.

At this point it should be noted that there Is a major contrast between metals and

ceramics. Because the grain shapes in single-phase metals normally tend to be equiaxed,

5
elongated grains in metals are generally achieved as a consequence of processing

factors such as deformation and recrystallization . In contrast, it is not uncommon to have considerable anisotropy in the growth rates of ceramic grains with mic rostruc tures,

and as a rule, deformation and recrystallization are not important factors.

3.3- Preferred Orientation of Grains

The crystalline orientation of the various grains in single-phase ceramic products

is typically quite random. Unlike metals, these ceramic products are not subject to mechanical deformation, which favors an alignment of the individual grains both before

and after recrystallization. However, ceramic products with a preferred orientation

are possible and will undoubtedly have increased significance in the future. Grains

in a ceramic which are nucleated at an external surface to produce columnar recrystallization commonly will have a preferred orientation with the fastest growth direction

aligned with the grain length (Pig. 20). Those grains which were nucleated so they

grew in other orientations were soon overtaken by the more favorably oriented grains.

Other factors, such as electrical or magnetic fields, become important in grain orientation if they are present at the time when the product is made. This subject will

undoubtedly be covered in subsequent lectures.

Preferred orientation (Pig. Id) may be indicated geometrically as the direction

favored for the normals to specific crystal planes. Thus the preferred orientation of

UO2 in Fig. 20 is <100> , which was the direction of the thermal gradient during

solidification. This orientation is obviously not perfect, because if it were there

would be no remaining boundaries of mismatch, and only a large single crystal would

result. Quantitative measures of the amount of preferred orientation are difficult.

However, pole figures do provide an indication of the amount [16].

I4. Polyphase Mic rostruc tures

I4.I. Introduction

The microstruc tural variations of polyphase (and porous) materials involve not

only the previously cited (1) grain size, (2) grain shape, and (3) preferred orientation, but also the geometric relationships of the phases. Included are: the

relative amounts of the phases, and (5) the mutual distribution of the two or more

phases which are present.

An analysis of the first three geometric factors for polyphase microstruc tures

may be approached much as they were for single-phase micros true tures. Equation 7 may

be used to describe the amount of any type of interface per unit volume. Thus, Pig. 8 can be shown to have 900 mm /mm3 of coherent UC-UC2 interface. Likewise, the domain

boundary area of Fig. 9 is about 700 mm^/mm3. Since the latter microstruc ture

contains dispersed domains within continuous matrix (also a domain) , it is possible to determine the average size of the dispersed areas from their numbers [15] . Also,

relatively simple micrographic procedures permit a determination of the distribution of

true plate thicknesses and spacings of the UC-TJC2 mic rostruc ture shown in Fig. 8. The

reader is referred to Gahn and Fullman [17] for further elaboration.

The energy of a phase boundary, like the energy of a grain boundary, is a driving

force which promotes grain growth in polyphase ceramics. Figure 21 illustrates the

changes which occur with added time and elevated temperatures [19]. The relative

amounts of the two phases are identical in the two examples, thus indicating chemical

or phase equilibrium. However, geometric equilibrium has not been fully attained, and

in fact will not be as long as there is an opportunity for further grain growth. In effect, the growth process which is shown in Fig. 21 requires steps of solution (of

grains with small radii of curvature), diffusion, and precipitation (onto grains with

larger radii of curvature). Thus, unless the atomic mobilities and surface energies

are high, the growth process is slower in polyphase materials than in single phase

microstruc tures where the atoms simply move across the grain boundary (Fig. 12).

The grain shape analysis of single phase microstruc tures (Equation 9) may be used

only if there is an alignment of the grain shapes. Even so, it is possible to obtain

information concerning the shapes of dispersed grains which are not equidimensional

.

For example, the mullite grains which are present in a siliceous glass in Fig. 22 are acicular, or needle-like prisms with an euhedral outline of a%b <c. Hence we generally observe only the small cross-section. Occasionally, a grain lies in such a manner that its major elongation is revealed. Likewise, the corundum of Fig. 23 (also

present in a siliceous glass) develops a plate-like grain which commonly reveals an elongated trace on the 2-dimensional microsection. This arises because a«b> c, In this example, however, the third dimension is not as markedly different from the two

6
as it was in Fig. 22, so the plate-like characteristics are less commonly revealed.

i|.2. Amounts of Phases

It is assumed that the reader is familiar with the relationships between relative

amounts of two or more phases and the compositions of ceramic materials as indicated

by a phase diagram. Therefore, that subject will be passed with only a mention of

references [18,20].

There are several procedures for determining the quantity of a selected phase

within a micro structure. They all provide volumetric answers; so, of course, subsequent calculations are required if weight percentages' are desired. Point analyses

and linear analyses are the most widely recommended procedures (Pig. 2i|) . Point analyses utilize the following relationship:- a random point in a microstructure has a probability of lying within each phase which is equal to the volume

percent of that phase within the micro struc ture . The linear analysis is based on a similar probability, viz., a random line will be within any phase in proportion to the

amount of that phase. It can be shown that a point analysis can be slightly more

accurate than the linear analysis for a given amount of effort on the part of the

mic rographer. In each case, special efforts must be maintained to avoid any-nonstatistical selection of points or lines, and care should be taken so that one phase is

not preferentially lost during sample preparation. On the other hand, if the microsection is representative, microporosity can be determined by either of these two

methods simply by determining the volume of the pore space as a fraction of the total

volume

Assuming that the microscopic section is representative of the whole structure,

and statistical randomness has been maintained, the binomial accuracy standard

] deviation of the data is given by the following relationship:

a v

= ^F(1.0 - F)/N , (10) or the fraction may be estimated from: - F = (lWl - 4Nov)/2 . (10a)

Within these equations, a

v is the standard deviation of analyzed volume fractions from

successive samplings, F is the estimated true fraction, and N is the number of randomly

selected observation points.

k.3. Distribution of Phases

The mutual distribution of two or more phases within a microstructure can be a result of (1) changes in chemical equilibrium which modify the relative amounts of

phases, and (2) geometric equilibrium which arises from boundary energy relationships.

Changes in chemical equilibrium introduce solution and precipitation. This can be illustrated by Fig. 25 where tridymite is present in a silica-saturated iron oxide

liquid. During the active growth of the tridymite crystals, there was an euhedral

development of the crystal faces so that the boundaries are regular between the two

phases

Geometric equilibrium often develops more slowly than chemical- equilibrium. This

is demonstrated when Pig. 26 is contrasted with Pig. 25. The two have the same composition and the same volumetric phase ratios. However, with time at temperature, there

has been a partial anhedralization which reduces the total interface area (and energy).

The degree of anhedralization varies with the material. The microstructures of Fig. 21

do not show euhedral growth of wustite (FeO) In the times indicated. However, some crystal faces are developed on the grains when saturation Is exceeded during a quench.

The distributional variations of phases become most noticeable when one of the

phases is a liquid. .The schematic presentation of Fig. 2 is illustrated in actual

microstructures in Figs. 27 and 28. In the simplest case, it is possible to have a liquid phase penetrate along the grain boundaries (Fig. 27). Under such a condition

there is negligible solid -to-solid contact at the elevated temperatures with consequent

effects upon properties [21]. Also, subsequent effects may be realized at lower

temperatures as indicated in Pig. 29 where the fracture path follows the silicate phase

which was originally distributed as a high temperature liquid.

A contrast to the foregoing conditions is shown In Fig. 28 where solid-to-solld

contact was maintained between cristobalite grains by a finite dihedral angle [22].

7
Thus, although there are channels of liquid distributed through the micro s true ture

,

there remains a solid skeleton which maintains significant strength at high liquid

contents.

The microstruc tural differences between Figs. 27 and 28 must be accounted for

through the relative interfacial energies as indicated in Equation 2. In general, it

may be concluded that the phase boundary energy is least when the compositions of the

two adjacent phases are most similar (other things equal). In Fig. 28, there is a markedly greater dissimilarity in the compositions between the cristobalite (SiOo) and

the liquid than there is between the wustite (FeO) and liquid in Fig. 27. Furthermore,

all evidence would suggest that the grain boundaries between two cristobalite grains

would have a relatively low energy as contrasted to the energy between two wiistite

grains because the cristobalite has a low packing factor and therefore has additional

degrees of freedom to compensate for the mismatch which accompanies the boundary.

5. Conclusions

The internal structure of a material may be analyzed on a basis of geometry with

factors such as grain size, grain shape, grain orientations being important in singlephase micro structures . Polyphase microstruc tures will include these variables plus

the variation in the quantities of the individual phases and their juxtaposition or

dis tribution

.

While there are both qualitative and quantitative data on the factors which affect

geometric equilibrium and microstruc ture s , it has been impossible in this presentation

to present comparable information on the kinetics, or rate of obtaining geometric

equilibrium within the micros true tures . This is a more complex consideration with

only a smattering of analytical information. At the same time it may be a major consideration because relatively few microstructures within ceramic materials will have

gained full geometric equilibrium at the time of their us e in engineering applications.

6. References

[1] R. Scheuplein and P. Gibbs, Surface

Structure in Corundum: I. Etching of

Dislocations, J. Am. Ceram. Soc. ZQ, 458 (1960).

[2] W. M. Hirthe and J. 0. Britton, Dislocations in Rutile as Revealed by the

Etch Pit Technique, J. Am. Ceram.

Soc. 45, 546 (1962).

[3] D. McLean, Grain Boundaries in Metals , p. 77, Clarendon Press (Oxford , 1957)

.

[4] C. S. Smith, Grains, Phases and Interfaces: An Interpretation of Microstructure, Trans. AIME , 175 , 15

(191+8).

[5] D. Harker and E. Parker, Grain Shape

and Grain Growth, Trans. ASM _3j£, 156 (1945).

[6] 0. K. Riegger and L. H. Van Vlack,

Dihedral Angle Measurement, Trans.

AIME 218, 933 (I960) .

[7] C. G. Dunn and F. Lionetti, The Effect

of Orientation Difference on Grain

Boundary Energies, Trans. AIME 185,

125 (1949)

.

[8] P. A. Beck, Effect of Recrystallized

Grain Size in Grain Growth, J. Appl.

Physics 19, 507 (1948).

[9] C. Zener, Grains, Phases and Interfaces: An Interpretation of Microstructure, Trans. AIME 175 , 4 8 (1948).

[10] J. E. Burke, Recrystall Izat ion and

Grain Growth, Grain Control in Industrial Metallurgy , p. 1, Am. Soc. Metals (Metals Park, 0., 1948).

[11] C. S. Smith, Grain Shapes and Other

Metallurgical Applications of Topology, Metal Interfac es , p. 65,

Am, Soc. Metals (Metals Park, 0.,

195D.

[12] S. A. Saltykov, Stereometricheskaya

Met alio grafiya , Literatury Po Chernoy

i Tsvetnoy Metallurgii (Moskva, 1958).

[13] Ervin E. Underwood, Surface Area and

Length in Volume, Quantitative

Metallography , New York, McGraw-Hill,

to be published.

[141 C. S. Smith and L. Guttman, Measurement

of Internal Boundaries In ThreeDimensional Structures by Random

Sectioning, Trans. AIME 197, 8l

(1953)

•

[15] Ervin E. Underwood, Quantitative Metallography, Metals Engineering Quarterly, 1, [3] 70 (Aug., 1961). Also

see 2, [4] 62 (Nov., 1961) for

Part 2 of the article.

[16] B. D. Cullity, Elements of X-ray

Diffraction , o. TJT', Addison-wesley

Pub. Co. TReading, Mass., 1956).

8
[17] J. W. Cahn and R. L. Fullman, On

the Use of Lineal Analysis for

Obtaining Particle Size Distribution Functions in Opaque Samples,

Trans. AIME 206 , 610 (1956)

[18] E. M. Levin, H. F. McMurdie, and

F. P. Hall, Phase Diagrams for

Ceramists , Am. Ceram. Soc.

(Columbus, Ohio, 1956)

[19] L. H. Van Vlack and 0. K. Riegger,

Microstructures of Magnesiowiistite [(Mg,Fe)0] in the Presence

of SiOa , Trans. AIME 224 , 957

(1962) .

[20] L. H. Van Vlack, Physical Ceramics , Addison-Wesley Pub. Co. (Reading, Mass., 1964).

[21] 0. K. Riegger, G. I. Madden, and

L. H. Van Vlack, The Microstructures of Periclase When Subjected to Steel-Making Variables,

Trans. AIME (1963), in press.

[22] L. H. Van Vlack, The Microstructure of Silica in the Presence

of Iron Oxide, J. Am. Ceram.

Soc. 43, 140 (1960)

Table 1. Enerp;ies of Metallic Boundaries "

Boundary Energy

Conner 6i(.6 ergs/cm

Iron (y) 850

Silver I4OO

Conner twin 19

Iron twin (11?) 187

Aluminum twin 120

Adapted from D. Mclean, Grain Boundaries in

Metals , p. 77, Clarendon Press (Oxford, 1957).

FIGURE 1. Microstructural variables

(single-phase materials) . (a vs. b)

Grain size. (a vs. c) Grain shape,

(b vs. d) Preferred crystal orientation . (Schematic .

)

FIGURE 2. Microstructural variables

(polyphase materials). These are in

addition to those of fig. 1. (a vs. b)

and (c vs. d) Amounts of phases,

(a vs. c) and (b vs. d) Distribution

of phases. (Schematic).

9
FIGURE 4. Small-angle boundary.

FIGURE 3. Small-angle boundary Example: Etch pits in LiF (X225).

(schematic) . This discontinuity in Each etch pit is the site of an edge

the microstructures consists of a dislocation. The angle of the boundseries of aligned edge dislocations. ary can be ca icu iated from the spacing

of the dislocations.

•v.v.*.*.y. :::::::::::: (courtesy a. s. Keh.)

FIGURE 5. Large-angle grain boundary.

Although this schematic representation

probably oversimplifies the grain

boundary structure, it does indicate

the major mismatch of structure which

results

FIGURE 7. Coherent boundary (schematic)

The adjacent phases have a closely

matching repetition in structure.

FIGURE 6. Twin boundary (schematic)

The mismatch does not involve firstneighbor atoms

FIGURE 8. Example

[Chang

,

Widmanstatten structures.

UCa (bright) in UC (X281).

R. , and C. G. Rhodes, "HighPressure Hot-Pressing of Uranium Carbide Powders and Mechanism of

Sintering of Refractory Bodies," J. Am. Ceram. Soc. 4_5, 379 (1962].

FIGURE 9. Domains. Example: BaTi03 aligned with the c-axes perpendicular

to the figure (X5625). Etched by

H3 P04

. The positive ends etched more

rapidly than the negative ends.

[Belitz, R. K. , "Differential Etching

of BaTi03 by H3 P04

, " J. Am. Ceram. Soc. 45 , 617 (1962) ] .

J / \ \ I f

J / / \ \ f f

J / / \ \ f f

J / / N \ f r

J / / \ \ f r

J / / \ \ 1 r

J / / ,\ \ r r

J / / \ \ r ;

J / / \ \ f \

J / / \ \ i \

J / / \ \ f t —-r

FIGURE 10. Domain boundaries (schematic)

The realignment across the boundary

requires energy. Therefore, there is

a driving force to reduce the boundary

area.

10
FIGURE 11. Energy balances. (a) Three

unlike boundaries eq (1) . (b) Dihedral angle between two like grains

eq (2) .

FIGURE 12. Boundary movements. Less

energy is required to move an atom or ion from the surface of the grain with

a convex surface to a grain with a con- cave surface than in the opposite

direction. Therefore the boundary

moves toward the center of curvature.

FIGURE 13. Grain growth. The movement

of boundaries toward their centers of

curvature produces grain growth and a disappearance of the smaller, more

spherical grains.

FIGURE 14. Growth inhibition. Second

phases generally retard boundary movements because they introduce reversals

in boundary curvature.

i A V t

J \ I *3rr

J J t * r

J 1 x K r

J \ t \ r

J ] X

4'

r

J i JC r

J i I / *v f

1 J X / <v f

J I X / «v r

J J X / X r <

FIGURE 15. Domain boundary movements.

The partially aligned dipoles along

the boundary (fig. 10) are pulled into

orientation with the external field,

thus shifting the boundary zone.

A.

iS

1 —*o

FIGURE 16. Equiaxed grains. Example:

periclase (MgO) . (approx. X140). This

microstructur e corresponds to that in

fig. 1(a). [R. F. Gardner and G. W. Robinson, Jr., "Improved Method of

Polishing Ultra-High Density MgO,

Am. Ceram. Soc. 45, 46 (1962)].

11
FIGURE 17. Abnormal grain growth

(schematic) . Abnormally large grains

(A) have faster growth rates than nor- mal grains (N) because the radii of

curvature of their boundaries are smaller

.

FIGURE 19. Boundary measurement.

Example: random line technique.

Eq (7) applies. (See fig. 16 for

references) . (approx. X140).

FIGURE 21. Grain Growth in polyphase microstructures . Example:

Wustite (FeO) growth in an iron

oxide saturated silicate liquid

(approx. X84). (a) Four hours

at 1200°C (2190°F). (b) 64 hours

at 1200°C [19]. W - wustite;

S - silicate liquid.

FIGURE 18. Abnormal grain growth.

Example: corundum (Al3 03

) heated to

1900 °C (X281).

(courtesy R. L. Coble.)

FIGURE 20. Grain elongation. Example:

Uranium dioxide grains (approx. X42).

The U0e had been melted and then

solidified within a temperature gradient. [J. R. MacEwan and V. B. Lawson, "Grain Growth in Sintered

Uranium Dioxide: II, Columnar Grain

Growth," J. Am. Ceram. Soc. 4_5, 42

(1962)].

FIGURE 22. Grain shape (acicular)

.

Example: mullite (AlsSi3 013 ) in

an alumino-silicate glass (X281).

Most crystals of mullite are seen

in cross-section only, in this

reflected light microsection

.

The elongation is observed in

the few which are aligned parallel to the surface. M - mullite;

S - silicate glass.

12
FIGURE 23. Grain shape (plates). Example:

corundum (A1S 03 ) in an alumina-saturated

silicate glass (X281). The elongated shapes

are cross-sections of the plate. Those

plates which lie parallel to the surface are nearly equidimensional in the microsection

.

C - corundum; S - silicate glass.

FIGURE 24. Volume analyses. (A) Point

analysis. (B) Linear analysis. The

probability that a point or a line

falls within a phase in a microsection

is equal to the volume fraction which

is present.

FIGURE 25. Euhedral growth. Example:

tridymite (SiOa ) in a silicasaturated iron oxide liquid (XI 69).

In many situations the rate of growth

is sensitive to crystal direction.

T - tridymite; S - silicate glass.

FIGURE 26. Anhedralization. Example:

tridymite (Si03 ) in a silica-saturated

iron oxide liquid (XI 69). With time

at the equilibrating temperature, the

surface area is minimized. (Cf.

fig. 25.) T - tridymite; S - silicate

glass

.

13
FIGURE 27. Grain separation. Example: periclase (MgO) and an MgO-saturated calcium

silicate liquid (approx. X140).. Although

less than 10 percent liquid is present, it

allows only a negligible quantity of solidto-solid contact (Cf. fig. 28, fig. 2c, and

fig. lib.) [21] P - periclase; S - silicate

liquid

FIGURE 28. Solid contact. Example: cristobalite (Si02 ) and a silica-saturated iron oxide

liquid (XI 69). Although more than 25 percent

liquid is present, a large dihedral angle

(fig. lib) provides solid- to-solid contact and

structural rigidity at high temperatures.

(Cf. fig. 27 and fig. 2b.) C - cristobalite

;

L - silicate glass.

w

FIGURE 29. Microstructural-controlled

behavior. Example: wustite (FeO) and

a silicate matrix. This matrix was

liquid at the equilibrating temperature

and subsequently has crystallized to fayalite (FeaSi04

) and more wustite

(approx. X84). The crack is in the

silicate matrix, but is closely associated with the silicate-wustite boundary.

W - wustite; S - silicate liquid;

Arrow - crack.

14
Experimental Techniques for Mlcrostructure Investigation

V. D. Frechette

1. Introduction

The study of microstructures is concerned essentially with the ability to distinguish between materials having different chemical composition, structure or orientation and to distinguish between details separated by only small distances.

Techniques for revealing microstructural features are almost all based either on the

action of their details on incident radiation or on the quality and intensity of the

radiation emitted by them when appropriately excited. Working treatments of the

principles governing the resolution of microscopic details are available in standard

works [1-*+] and only the briefest review will be given here in order to identify the

effects involved.

When a homogeneous object is viewed in transmission, i.e. by means of radiation

transmitted through it, details corresponding to greater thickness may be revealed by

their greater absorption as dark regions in the image. At constant thickness, details

having greater absorption coefficients also yield darker images and, if the

absorptions differ sufficiently for different light wavelengths, they may yield image

color differences also.

Refraction effects at a boundary between grains may change the light path,

thereby darkening the corresponding region of the image and brightening adjacent

regions. The effect is intensified when the object is slightly out of focus and when

the illuminating aperture is restricted. Boundaries may also be revealed by the

scattering of light which takes place there to an extent which depends on the ratio

of the refractive indices of the bordering phases. With illumination of the bright

field type, i.e., when the light in the absence of any object in its path illuminates

the entire field of view, the boundary layer shows up in the image as a darkening

because the light is scattered by it and is lost to the true image. Under dark field

conditions, in which illumination is arranged to just miss the field of view in the

absence of an object in its path, scattering provides a mechanism by which details

are rendered luminous and they form a bright image in a dark field.

Polarization-interference effects, which occur when an object is examined

between crossed nicols or other polarizing elements with or without the aid of

accessories, may be extremely valuable and the subject has been treated in numerous

works 15-7 ]• Crystalline solids, except those of the cubic system, and stressed

solids of any structure split plane-polarized light into two rays vibrating

perpendicular to one another which travel along essentially the same path but with

different velocities. During passage through a mineral grain one of these is

retarded behind the other owing to its slower velocity; when the two rays emerge from

the mineral and pass through the analysing nicol prism they interfere to an extent

determined by that retardation and by the wave length of the light. Under crossed

nicols, therefore, a mineral grain displays colors, corresponding to retardation,

which are determined by the thickness of the grain and by its effective birefringence

(birefringence is the difference between the refractive indices of the two rays) for

the orientation in which it lies. Not only may grains be distinguished from one another by this process but their identity and their orientation may be inferred,

particularly with the aid of interference figures formed in the back opening of the

objective lens under strongly converging transmitted light.

In reflected light, details may be distinguished through operation of all of

the above effects [8]. In addition differences in reflecting power characterize

those materials whose refractive indices differ sufficiently as indicated by Fresnel's

formula, stated for normal incidence:

15
where R is the fractional amount of light reflected and N is the refractive index.

Under both transmission and reflection conditions, the light beam passing

through the grain or being reflected from its surface is retarded somewhat behind

those light rays which pass around it, or encounter materials of other refractive

index. In the phase contrast microscope [9] an annular diaphragm is inserted in the

condenser, while a second annular plate is set at the conjugate plane of the

condenser ring, to introduce an additional small phase shift. Interference between

these two in the image plane provides sharp contrast between details which vary only

very slightly from their surroundings. The phenomenon of interference is applied

also in the so called interference microscope [10-19] for the determination of

surface contours. In the simplest arrangement of this type the light rays reflected

downward by a semi-silvered mirror are partly reflected by an optically flat plate,

while those which are transmitted through the plate are reflected from the surface

of the specimen. These two are tipped slightly with respect to one another so that

there is seen in the field of view, for a perfectly flat specimen, a series of

parallel bright lines, or interference fringes. Each bright line is the locus

of those points on the specimen surface which are at a constant distance from the

optical flat, this distance being precisely an odd number of half wave lengths of the

light employed. Consequently any excursion of the specimen contour from the plane

of its surroundings results in a displacement of the fringes. The test is an extremely sensitive one and make possible surface contouring of a specimen to within

a small fraction of the wavelength of light, i.e., to about a hundredth of a micron,

although lateral resolution is still confined to the usual limit of the lens system

or about 0.2 microns for visible light.

2. Optical Microscopy

A tremendous increase in the use of the optical microscope on ceramics [20-2^]

and other materials in recent years has acted as a spur to and has itself been

accelerated by the development of instruments and accessories [3,25] • Most

notable are the new microscopes of the universal type featuring permanently aligned

illuminators of high intensity and stable operation, conveniently mounted apparatus

for photography including automated cameras for films, plates and Polaroid, and

rapidly-interchangeable accessories for bright- and dark-field examination in

transmitted and reflected light with the option of phase contrast and interferometric

optics. A growing list of polarizing accessories extends the range of optical

measurements that can be made and new mechanical devices facilitate particle size

measurement and quantitative analysis. Inclined binocular eyepieces reduce operator

fatigue to negligible proportions and high eyepoint eyepieces permit spectacles to be worn without sacrificing breadth of visible field, an advantage to observers

having pronounced astigmatism. At lower magnifications zoom- type optics contribute

significantly to speed and convenience.

The limit of resolution of the .microscope is approximately 0.6X /N.A. where

is the wavelength of the light used and N.A. is numerical aperture of the X illumination and objective lenses. For visible light this is approximately 0.2

microns. Ultraviolet light microscopy using photographic registration of the

(invisible) image extends the resolution by a factor of two but at great loss of

convenience

3.' Electron Microscopy

Very much shorter wavelengths (about .015 millimicrons) are associated with a beam of electrons. The electron microscope [26-37] uses an incandescent filament as

a source of electrons, accelerates them to high velocity by means of an electric

field, and focuses them with magnetic or electrostatic lenses in much the same way

as an optical microscope focuses light beams. In practice it is particularly

distinguished from the optical microscope by the very poor penetrating power of the

electron beam, which limits the object to extremely thin sections unless a reflecting technique is to be employed. It is significant that the effectiveness of the

electron microscope has grown directly in proportion to the development of methods

of specimen preparation and particularly the replica techniques. Useful

magnifications up to about 2 x 10-> are routinely employed, (although most work is under

2 x 10 ) and under special conditions dislocations themselves may be directly

observed by it through diffraction effects [38,391- While the optical crystallography

of materials, based on refractive indices and polarization effects, does not apply in

the electron microscope, many instruments are provided with means for obtaining

electron diffraction natterns of individual grains located in its field and thus

phase identification and orientation may be studied.

16
The poor quality of reflected electron images has been overcome in an ingenious

way in the scanning electron microscope [31] . In this instrument the electron beam

is brought to a fine focus on a very small region of the sample and the scattered

electrons are picked up in a fixed detector whose signal is fed to a cathode ray- oscilloscope. The beam is swept across the surface of the sample in synchronization

with the sweep of the oscilloscope which accordingly traces an image of the specimen

whose brightness corresponds to the atomic number and density of atoms in the

specimen components. Useful magnification by this method is not great and does not

exceed that of the optical microscope. The depth of focus, however, is very much

greater than that of the optical microscope at corresponding magnification, and

excellent photographs of fracture surfaces of aluminum oxide have been obtained with

itPfO].

3. Electron Probe X-Ray Analysis

The high speed electrons of the electron microscope impinging on the sample

excite the atoms to emit X-rays. These X-rays may be analyzed with respect to wavelength and intensity to yield spectra from which the constituent elements may be

identified both qualitively and quantitatively. If the electron beam is confined to

a very small area of the sample, a few square microns, complete chemical analysis

of the small area may be obtained, excepting only those elements under atomic number

eleven, whose emitted X-rays are so long in wavelength that they are easily lost.

If the electron beam is swept across the surface while the X-ray detector is set to record a wavelength characteristic of a particular element, a plot may be obtained

on an oscilloscope sweeping in syncronization with the electron beam; brightness

in the oscilloscope image corresponds to points in the specimen where the element is

to be found in abundance. Instruments of this kind are termed electron probes or electron micro-probe X-ray analyzers [^1]. While few of these have seen application

on ceramic materials up to the present, a few studies show the method to be effective

and highly promising U+2 ,^3 1 • Indeed the application of the electron probe to problems of ion species segregation in polycrystalline materials is one of the most

exciting on the present scene.

h. Emission Microscopes

Professor Castaing has suggested another way of imaging the specimen surface.

If it is bombarded with a beam of ions of appropriate energy, it may be excited to give off secondary ions which may be focused with electro-magnetic lenses, passed

through a mass spectrometer set to select a particular ion species, and brought to focus on an image converter which releases electrons to be focused in turn on a photographic plate.

Other emission type microscopes have been developed [29, 3^+1 and have been

extremely successful with certain metals, but their use with ceramic materials has

been limited V+k ]

.

5- Microradiography and X-ray Microscopy

Specimens containing radioactive elements may be photographed by simply pressing

them against the photographic emulsion for an extended period of time. The resulting

autoradiograph Is not usually sharp enough to permit much magnification but it is a valuable technique for indicating concentration gradients as in the case of experiments

on diffusion and especially self -diffusion. Cyclotron activation techniques extend

the method to include a wide variety of elements and it should prove useful in

specialized structural studies.

The use of X-rays to disclose structural features is well known. When the

X-ray source is very small the radiograph attains high resolution [hj] ; in theory it

is that of the electron microscope but practical difficulties are formidable and it

is limited in the present state of development to the limit of the optical

microscope [^6]and little work is done beyond 100X. Except in particularly favorable

cases good contrast in the image is difficult to obtain [V7]. Neutron microradiography [V8-50] seems to be a promising alternative, since the light elements which

are so frequently of interest in ceramic problems are extremely opaque to thermal

neutrons

.

Two principal techniques are in use. Contact microradiography consists in

obtaining the image by radiography in which the specimen is in contact with a photographic plate and enlarging it photographically. In point projection X-ray

microscopy the specimen is some distance away from the plate so that it casts an enlarged shadow upon it.

17
6. Specimen Preparation

The above are by no means the only methods for obtaining highly resolved images

of a specimen, but they represent those whose present state of development seems to offer most promise for use on ceramic materials. It is especially significant that

the vastly increased knowledge of the microstructure of ceramics which has come during the past decade has been accompanied and has been largely the result of

greatly improved techniques in the preparation of specimens for examination.

Thin sections of specimens, fine-ground to flatness, cemented on a glass slide,

and ground down to a thickness of 30 microns, more or less, [20,21] are suitable for

the examination of course-grained materials, using the transmission optical microscope. With the aid of polarized light accessories these are capable of yielding

structural information including grain orientation by the petrographic methods

(petrofabric analysis) originated in connection with petrological problems [51] • For fine grained materials the thickness of these sections implies the overlapping

of a number of grains in the image so that information concerning both detail and

orientation are lost. Recently a method for making very much thinner sections has

been suggested [52,53] • A shallow well is etched with hydrofluoric acid in the

surface of the microscope slide. The specimen cemented in the bottom of this well

is protected by the glass down to the last stages of finish grinding, so that sections

6 microns in thickness can be produced with care. The technique restores the thin

section to an extremely useful place in the microscopy of ceramic materials. At the same time the ultra-microtome [5*+- 57] employing a diamond knife, has been used

successfully to get sections thin enough for direct electron microscopy although

they are small in area. Splinters and chips of materials can be produced easily by simply crushing

materials under proper conditions and these have given results in optical and

electron microscopy [58] . In the case of porcelain enamels this may involve only

bending the specimen in the direction of the enameled surface. Thin scales may be

pulled from surfaces by applying a concentrated gelatine solution or certain glues

and drying in an oven. Specimens for direct transmission electron microscopy may be prepared by special

fabrication and heat treatment. Glasses and enamels have been prepared by blowing

very thin bubbles followed by etching [591- Sinterable materials may be prepared

by sintering a little of the very fine powdered material on a metal grid [60].

Polished sections, while yielding meager optical information, offer strong

advantages in quantitative studies, since they represent a single plane through

the specimen and so yield textural information with less quantitative ambiguity.

Distinction between the phases rests less on the optical properties of the phases

themselves, and more on particular treatments to which some of the constituents of

the specimen are more susceptible than others. On the one hand, this involves

attack by chemical or physical agents, while on the other hand, it may involve the

receptivity of certain details to decoration. The problem of preparing an initially

flat polished surface has largely been solved with the advent of impregnation

techniques to fill pores and diamond dust as the polishing medium, either fixed in

rotating laps or used as a paste on an appropriate surface [21] . In every case,

however, there is a certain art in the choice of the backing surface, the lubricant,

polishing speed, pressure, and time [61-651.

In order to enhance the contrast between grains in a specimen, to distinguish

phases from one another, and to reveal internal structure in the grains themselves,

such as dislocations, an etch is usually helpful A variety of procedures are in use

as the partial list in Table 1 indicates. The superb results obtained with portland

cement clinkers and basic refractories [21] and with metallurgical slags [103] in

differentiating between constituents of complex mixtures is a spur to more persistent

efforts. An almost complete lack of discussion of the reasons for the selection of

procedures lead to the suspicion that very much is still to be learned on this subject.

It would be surprising if there are not far more effective etching proceedures still

to be found. In the face of the difficulty of choosing an appropriate specific

chemical etch, there is of course a hope for a universal etchant. Three are claimed

in the field of ceramics. Thermal etching, i.e., raising the temperature of the

polished specimen in a furnace with an oxy-acetlyne torch or in an arc image, has

been found successful in bringing out grain boundaries in many cases. Examples are given in Table 2, which includes also examples of the relief polish and ion

bombardment techniques.

18
Material and Reagent

Aluminum Oxide

85% H PO, 3

*+ H PO. cone.

3 ^

Table 1. Some Chemical Etchants for Ceramics

Conditions Comments Reference

KHSO

K^S 0

2 2 7 H SO. 2 h

K

3A1F

6 Dry H

2 Barium Ferrite

5% HC1

HC1

Barium Titanate

Few drops HF in 5 ml.

HC1, 95 ml. H2

0 HF-HNO.-H^O

O.^HF in HNO

Boiling 5

_ 10 min.

Boiling •+ min.

2100c. 11-16 min.

1+25°C. 120-180 sec. Polish (0001)

Melt 3~l5 sec. 675°C. 15-20 sec. Etch (0001)

675°C. 135 sec. Etch (1120)

300°C. 3 min.

2000C. 20 min. to 270°C. 5 min.

1000°C. 30-60 sec 1-2 min.Polish (1120)

1700°C

1% HF

3

20 sec.

1-7 min

During polishing

1-g- min.

'2iC

2

w

5 iFe 2

0I+ -I

% H

3 P0^ 100°C.

Beryllium Oxide

HF VWT

Calcium Fluoride

20$ HC1

50$ HC1

2% sulfamic acid in water

Calcium Fluoride - Sodium Fluoride

H2

S0i+ Calcium Oxide

h% picric acid in methyl alcohol

Cadmium Manganese Ferrite

HF (h8%)

Cadmium Niobate

HF

Carbon( Diamond)

1 hr.

10 sec. 5 min. near boiling 5-10 sec. boiling 5 min. to polish

40-50 min.

10 sec. - 2 min.

°2

Chromium Sesquioxide

KHSO^

Glasses

0.05$ HF

Acetic Acid

HF (dilute)

NH^F (sat'd sol'n)

+ NH^HF

2 2h% HF

Lead Titanate Zirconate

Few drops HF in 100 ml.

5% HC1

Hot

melt 3-15 sec

2 min.

Several hours

15 sec.

enamel

Na

2 0.2Si0

2 To bring out

cracks from

microindenter

Lithia glass

Houle [62]

Gardner [63]

Warshaw [66]

Alf ord r67

Houle [62]

Alford [67]

Alford [67]

Warshaw ICC 1 [66]

McVickers [6h]

Alford [67]

Houle [62]

Goto [68]

-.Goto

7 [68]

Kulcsar [69]

DeVries [70]

Tennery [71]

DeVries [72]

Belitz [73]

Liy

Houle [62]

Burn [7^]

Burn 17^]

Phillips [75]

Kingery [76]

Daniels 177]

Eichbaum [78]

de Bretteville[7<

Frank [80]

Gualtieri [81]

Houle [62]

Yee [59]

Parikh [82]

Argon [83]

Jaccodini [8h]

Rindone [85]

Kulcsar [69]

19
Table 1. Material and Reagent

Lithium Fluoride

2 x 10- 4 mol % FeF ln H2°

Magnesium Ferrite

SnCl 2 -HCl

Magnesium Oxide

2,0% HC1, 10% sat'd sol'n

of NHi,Cl , 60% water

HNO^ '

H

2 S0^

Comments

Some Chemical Etchants for Ceramics (Cont'd)

Reference

Gilman [86]

Carter

Conditions

1 min.

in H

2

0 1:1

5-20 min.

1-5 min

(dilute)

H^PO^ (Dilute)

Magnesium - Manganese Ferrites

(Thermal etch)

Mullite - Glass

10% HF 3 sec. Porcelain

HF

Plutonium-Carbon System

Acetic acid-HNO-^-E^O,

equal parts

Plutonium Monocarbide

H20 Strontium Titanate

5 parts HF, 10 parts HNO^

,

10 parts H2

0 Titanium Carbide-Molybdenum

Alkaline Ferricyanide

Titanium Carbide-Nickel

Alkaline Ferricyanide

Titanium Dioxide (Rutile)

KOH

85% E

3 POk

E2

S0\

+ Tungsten Carbide-Cobalt

Alkaline Ferricyanide

Tungsten Carbide-Copper

Alkaline Ferricyanide

Uranium - Uranium Nitride

(Electrolytic

)

Uranium Carbide-Plutonium Carbide

HN0

3 Uranium Dioxide

80 ma. /cm 30 sec. (electrolytic etch)

1+00 0 C 20 min.

Boiling 2-g— 3 min.

hot 10-30 min. (preferred)

1-5 min.

9 Parts

1 Part

Uranium Dioxide - Lanthanum Oxide

HNOy Water 1:1

H

2

0

2 H

2 S0^

H

3 P 0l+ Uranium Sulfide

T0%~R~S0^~

"

Yttrium Iron Garnet

HC1

HC1

20$ HC1

Zirconium Dioxide

HF (W°)

Boiling

Boiling 1 hr.

H hr.

2i hr.

1-5 min.

Gorum

Houle

Daniels

Daniels

Palmer

Studt

Lundin

Kruger

Lied

Waugh

Parikh

Parikh

Hi r the

Hi r the

Hirthe

Parikh

Parikh

Accary

Lied

Houle

Fuhrman

Hill

Shalek

Rudness

Lefever Lefever Houle

[87]

[88]

[62]

177]

177]

[89]

[90]

[91]

[92]

[931

[9M

[83]

[83]

[96]

[96]

[96]

[82,95]

[82,951

[97]

[93]

[62]

[98]

[99]

[100]

[101 ] [102]

[102]

[62]

20
Table 2. Universal Etch Techniques

Material and Technique Conditions

RELIEF POLISH

Aluminum Oxide

Glass-metal Seals

Comments

0.1 micron AI2O3 on Microcloth

0.2 micron A12 0^

Reference

Angelides

Cole

lioh]

[10?]

THERMAL ETCH

Aluminum Oxide 1700°C. in dry R" 2 1-2 min.

1900(-) C. oxyacetylene torch

2-5 sec. Beauchamp [106]

Uranium Dioxide-Lanthanum Oxide

Incipient fusion in arc image furnace

ION BOMBARDMENT

Aluminum Oxide

Porcelain

Uranium oxide

Aluminum - aluminum oxide

Titanium carbide - nickel

Cobalt silicide - titanium carbide

Titanium diboride

PUO. UO,

Evans

Bierlein

Bierlein

Bierlein

Bierlein

Bierlein

Bierlein

Bierlein

Keig

Pyrolytic graphite Coy

[107]

[108]

[108]

[108]

[108]

[108]

[108]

[108]

[1091

[110]

Thermal etching may develop surface detail by at least three processes [111] . It may involve transfer of material by surface diffusion from high surface energy

to low surface energy regions and , therefore , away from grain boundaries. It may

involve loss of material by sublimation, and it may involve evaporation-condensation,

developing growth figures.

Relief polishing, involving a polishing step with a softer abrasive, .develops

a surface relief indicative of the abrasion resistance of the constituents at the

surface. Like the chemical etch, this is sensitive to grain orientation as well as

to the differences in hardness among phases and at grain boundaries.

Ion bombardment of the polished specimen surface is also promising as a universal etch [108] . The specimen is placed in a chamber evacuated to 30-50

microns krypton pressure and is made the cathode with respect to a potential drop

of about ^000 volts across the chamber. Exceptionally fine etches have been

obtained on a variety of materials by this method, but experimentation is necessary

in every case to find the appropriate gas pressure, voltage, and time for best

results

The decorating of surfaces before or after an etching treatment has not been

sufficiently explored. Important results with decoration by sodium vapor to reveal

cracks in glasses [112, 113] , decoration of sodium chloride with gold particles [llh]

resulting from the decomposition of gold chloride, decoration of magnetic materials

with Fe 202and the use of small charged particles in crack location and polarity

determinations [115, 116] all suggest that decoration is well worth exploring

further

The study of fracture-exposed surfaces [117-120] to disclose fracture origins,

grain orientation through cleavage traces and negative crystals and the path of

fracture, whether through grain boundaries or through the grains themselves, has

proved rewarding and shows great usefulness in connection with materials testing,

trouble shooting of fabrication problems and service failures, as well as microstructural details on which recent revisions of glass atomic arrangement have been

partly based [127-132] .

21
7. Replication

In order to preserve the advantages of the polished section or fracture

surface without the difficulty of reflecting type instruments the surface in

question may be replicated as a thin film which preserves its topographical details.

The process may be as simple as the technique of pressing a plastic tape, softened

with an appropriate solvent , against the surface and stripping if off [133] • The

result is a negative replica, i.e., high points in the sample correspond to hollows

in the replica. This method has been valuable in examing surface damage in enamels

with the optical microscope [13^1 • The replicating process for electron microscopy

usually involves several stages [21, 26, 28; 135-150] . The high resolution

technique of Bradley [136] will serve as an example. A film of Formvar is first

coated on the specimen as a 1 or 2% solution in chloroform. This is backed with a 7% solution of a soluble resin, Bedacryl, in benzene. The replica is then stripped

from the surface. In vacuum carbon is coated on the surface from a carbon arc. The Bedacryl backing resin is then dissolved with acetone and the Formar removed

with chloroform. The film is then ready for examination.

To enhance contrast in such replicas and to provide a relief effect giving

three dimensional information, the replicas are generally shadowed by evaporation

of a metal such as platinum, palladium, gold or chromium at a glancing angle so that the metal accumulates on the near side of positive details, while the far

sides are sheltered. The appearance of such shadowed replicas in the electron

microscope gives the impression of illumination at a glancing angle and throws

details into strong relief.

8. Conclusion

Of the many instruments and techniques discussed, none should be considered

"best" but each has its own particular applications. Most dangerous of all would be

the temptation to rely on one technique alone, for each has its "blind spots" and

areas of confusion where spurious effects can lead to error. Most problems profit

from complementary observations with two or more methods and in almost every case optical microscopy, not neglecting the stereoscopic microscope at lower magnifications,

should be one of these.

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106 Edwin K. Beauchamp, "The Etching; of

AI2O3 Grain Boundaries", J. Am."

Ceram. Soc. 4_3_, 224 (i960).

107 P. E. Evans, "Interpretation of

the System U02-Zr02", J. Am. Ceram.

Soc. 44, 631 (1961)

.

108 T. K. Bierlein, H. V. Newkirk, Jr.,

and B. Hatel, "Etching of Refractories and Cermets by Ion Bombbardment", J. Am. Cer-m. Soc. 41, 196-200

(1958).

109 G. A. Keig and H. R. Haines, "The

Cathodic Etching of Plutonium

Ceramics" , Trans. Brit. Ceram. Soc.

62, 363-73 (1963).

110 W. J. Coy, "Electron Microscope

Study of Pyrolytic Graphite", J. Am. Ceram. Soc. 4j5_, 223-25 (I962).

111 Hayne Palmour III, John Duplessis

and W. Wurth Kriegel, "Microstructural Features and Dislocations

on Thermally Etched Sapnhire Surfaces

J. Am. Ceram. Soc. 44, 400-404 (I96I)

112 E. N. Andrade and L. C. Tsien,

"Surface Cracks in Glasses", Proc.

Royal Soc. (London) A 159 , 346-55

(1937).

113 W. C. Levengood and E. B. Eutler,

"Relationship of Surface -Structure

of Glass to Residual Laminar Stresses

J. Am. Ceram. Soc. 36, 257-62 (1953).

114 S. Amelinckx, "Dislocations in Ionic Crystals. I. Geometry of

Dislocations" in Mechanica

1

Properties of Engineering Ceramics , W. W. Kriegel and H. Palmour III,

ed., Interscience (New York, I96I).

115 F. A. Petersen, R. A. Jones and

A. W. Allen, " A New Method for

Studying Fractures of Porcelain

Enameled Specimens", J. Am. Ceram.

Soc. 3_1, 186-93 (1948).

116 J. H. Lauchner and D. G. Bennett,

"Thermal Fracture Resistance of

'Ceramic Coatings Applied to Metal:

I Elastic Deformation", J. Am. Ceram. Soc. 42, 146-50 (1959).

26
11? W. L. Phillips, Jr., "Effect of

Environment and Surface Condition

on Strength of Lithium Fluoride

Single Crystals", J. Am. Ceram.

Soc. 44, 395-400 (I96I).

118 V. K. Zworykin and E. G. Ramberg,

"Surface Studies with the Electron

Microscone ", J. Appl. Physics 12 , 692-5 (19^1).

119 Robert Scheuplein and Peter Gibbs,

"Surface Structure in Corundum:

II Dislocation Structure and

Fracture of Deformed Single Crystals"

J. Am. Ceram. Soc. 4_5_, 439 (1962).

120 W. Schatt and D. Schulze, "Einige

Elektronenmikroskopische

Beobachtungen an Freien Sinterkorundoberf 13 chen " . Ber deut.

keram. Ges._J_6, 364-67 (1959).

121 A. F. Prebus and J. W. Michener,

"Electron Microscope Investigation

of Glass", Ind. Eng. Chem. 56,

147-53 (1954).

122 K. H. Kim and F. A. Hummel, "Studies

in Lithium Oxide Systems: VI Progress Reoort on the System

Li20-Si02-Ti02" , J. Am. Ceram. Soc.

42, 286-91, (1959).

123 B.S.R. Sastry and P. A. Hummel,

"Studies in Lithium Oxide Systems

VII Li20-B2 03-Si02" , J. Am. Ceram.

Soc. 42, 23-33 (i960)

124 F. A. Hummel, T.Y. Tien and K. H. Kim, "Studies in Lithium Oxide

Systems. VIII Application of

Silicate Liquid Immiscibility

to Development of Ooaoue Glazes",

J. Am. Ceram. Soc. hj ,"192-97 (i960 )

125 T. Y. Tien and F. A. Hummel,

"Studies in Lithium Oxide Systems

XI Li„0-Bo 0,-P o 0 c

", J. Am. Ceram.

2 2 j 2 0 Soc. 44, 390-9^ (1961).

126 M. Krishna Murthy, "Influence of

Platinum Nucleatlon on Constitution of and Phase Separation in

Sodium Phosphate Glasses", J. Am.

Ceram. Soc. 44, 4l2-4l7 (1961).

127 T. F. Bates and M. V. Black,

"Electron Microscope Investigation

of Opal Glass", Glass Ind. 29_,

487-92, 516, 518 (19^8).

128 Muneo Watanabe, Haruo Noake and

Takeshi Aiba, "Electron Micrographs of Some Borosilicate

Glasses and Their Internal

Structure", J. Am. Ceram. Soc. 4_2,

593-99 (1959).

129 I. Warshaw, "Structural Implications

of the Electron Microscopy of

Glass Surfaces", J. Am. Ceram. Soc.

42, 4-9 (I960).

130 Stanley M. Ohlberg, Helen R. Golob,

and Charles M. Hollabough,

"Fractography of Glasses

Evidencing Liquid in Liquid

Colloidal Immiscibility", J. Am. Ceram. Soc. 4_5_, 1-4 (1962).

131 Georges Zarzycki and Rene Mezard,

"Etude de la Structure Fine du

Verre", Compt. Rend. 25_4,

1755-56 (1962).

132 V. J. Moran, "Structure in the

Fracture Surface of Silicate

Glass", J. Am. Ceram. Soc. 46,

102-103 (1963).

133 A. W. Allen and A. L. Friedberg,

"Application of Replica Techniques

to the Study of Ceramic Surfaces

with the Optical Microscope",

J. Am. Ceram. Soc. 31. 83-88

(19^8).

134 J. C. Richmond and A. C. Francisco,

"Use of Plastic Replicas in

Evaluating Surface Texture of

Enamels", J. Res. Nat. Bur. Stds.

42, 449-460 (19^9).

135 R« D« Heidenreich, "Methods in

Electron Microscopy of Solids",

Rev. of Scientific Instruments

21, 583-95 (1952).

136 D. E. Bradley, "High Resolution

Evaporated Carbon Replica

Technique for the Electron

Microscope" , J. Inst. Metals 83 . 35-38 (195^).

137 D. E. Bradley, "An Evaporated

Carbon Replica Technique for Use

with the Electron Microscope and

its Application to the Study of

Photographic Grains", Brit. J. Appl. Phys. 5, 96-98 (195^).

138 Yoshio, Iida, "Sintering of HighPurity Nickel Oxide", J. Am.

Ceram. Soc. 4l , 397-^06 (1958).

139 R. Dallendorfer , "Licht-und

Elektronenmikroskopische

OberfISchenuntersuchungen an Keramischen Werkstoffen"

,

Silikattechn.9_, 510-13 (1958).

140 V. J. Tennery and F. F. Anderson,

"Examination of Surface and

Domain Structure in Ceramic

Barium Titanate", J. Appl. Phys.

22,755-758 (1958).

27
ihl H. E. Simpson, "Study of Surface

Structure of Glass as Related to its Durability", J. Am. Ceram.

Soc. hi, h^-hO (1958).

lh2 W. Heister, "Einfluss der

Sintertemperatur auf die

Magaetischen Eigenschaften and

das Kristallgeftlge von Mn-Zn

Ferrites", Ber. deut. keram. Ges.

31, 2>+9-258 (1958).

1^3 J- Kainz, "Die Dielektrischen

Eigenschaften des Systems

Barium-Strontium__Lanthanum

Titanate", Ber. deut. keram. Ges.

31, 69-77 (1958).

ihh B.S.R. Sastry and F. A. Hummel,

"Studies in Lithium Oxide Systems

III Liquid Immiscibility in the

System Li20-B2 03Si02" , J . Am. Ceram. Soc. hg, 81-88 (1959).

1^5 Joseph Comer, "Electron

Microscope Studies of Mullite

Development in Fired Kaolins",

J. Am. Ceram. Soc. i+3, 378-81+, (I960).

14-6 K. Schtlller, "Untersuchungen

uber die Geftlgeausbildung im

Porzellan", Ber. deut. keram. Ges.

38, 150-157; 208-11; 2^1-^6 (1961)

1^7 J. Drobek, W. C. Bigelow and

R. G. Wells, "Electron Microscopic Studies of Growth

Structures in Hexagonal Ferrites",

J. Am. Ceram. Soc. hj_, 262-6^ (1961)

lh8 M. Navey, C. Sella, H. Gervais and

J. J. Trillat, "Appareillage pour

La Realisation Sous Vide de

Repliques et d'Empreintes pour

la Microscopie Electronque"

,

Vide 6,91-97 (1961).

1^9 J. J. Comer, "New Electron-Optical

Data on the Kaolinite-Mullite

Transformation", J. Am. Ceram. Soc.

M+, 561-63 (1961).

150 T.Y. Tien and W. G. Carlson,

"Effect of Additives on Properties

of Lead Titanate", J. Am. Ceram.

Soc. h$_, 5&7-571 (1962).

28
The Effect of Heat Treatment on Micros tructure

J. E. Burke

1. Introduction

At some stage during processing, most ceramics are heated to an elevated temperature, held for a time and then cooled. During this heat treatment, many profound

changes in structure may occur and the final micros tructure is established. For

example, the identity, amount, composition, perfection, size, geometrical arrangement

or crystallographic orientation of the phases initially present may change. The composition of the whole body may change if volatile species evaporate or are picked up

from the heat treating atmosphere. Our goal in this paper is to set down some simple

general principles governing the effect of heat treatment on micros true ture . Some of

the principles are concerned with establishing, from phase stability studies, what

phases are stable at the heat-treating temperatures. Some are concerned with the influence of forces such as surface tension upon the geometry of phases. These aspects

have been well covered by other speakers in this series, and I should like to concern myself with the problem of relating temperature to the rate at which the approach to

equilibrium is made. This is not a new branch of science, although it has developed

rapidly over the past 20 years. Furthermore, this is not intended as an elegant treatment, but rather as a practical one, to provide a way of thinking about reactions in

solids, with enough information so that semiquantitative calculations can be made. For more quantitative treatment, the reader is referred to the standard texts.

2. Diffusion

Undoubtedly the most important single reaction which may occur during heat treatment is the diffusional transport of individual atoms through the solid from their

initial positions to new positions of greater thermodynamic stability. It is by such

transport that concentration gradients are smoothed out, that phases form and disappear,

and that shrinkage and pore elimination during sintering is accomplished.

The elementary mathematics of the diffusion process was first formulated over 100

years ago, and during the ensuing period many measurements of diffusion rates of certain

atomic species in various solids have been made, and quite detailed knowledge of the

mechanisms by which diffusion occurs now exists. There are many review papers on the

subject, particularly in metals, and man^ textbooks of metallurgy and ceramics have

extensive treatments of the subject [11. In spite of all this work, it should be

mentioned that a complete understanding of diffusion does not yet exist, particularly

in ceramic materials, and it is an active field of research at the present time. In

this section an attempt is made to establish only the most elementary concepts so they can be used in later discussions.

1 Figures in brackets indicate the literature references at the end of this paper..

29
Let us consider a system in which there is a sudden change in composition with

distance, such as might exist if a piece of pure aluminum oxide were to be welded to a ruby which contains a small amount of dissolved C^O^ replacing some of the A1_0„ . It has been established that in Al^O^ tb.| oxygen ions form a relatively rigid framework,

so that upon heating, some of the Cr ions will diffuse into the sapphire and this

diffusion will be compensated by a counter -diffusion of Al ions into the ruby. The

situation is presented schematically in Fig. 1, where the solid line shows the concentration gradient assumed to exist initially and the two dotted lines show the concentration gradients after two successive times of heat treatment.

The general law governing this process, and the law from which the shape of these

penetration curves can be explained, at least in principle, was formulated by Fick in

1855. In its simplest form it states:

J -

"D § <»

the quantity J of diffusion substance which passes per unit time through a unit area

of a plane at right angles to the direction of diffusion is proportional to the con- centration gradient of the diffusing substance 9C/3X. The negative sign appears to compensate for the fact that the slope of concentration versus distance curve which

favors diffusion is negative. The proportionality constant, D, is called the diffusion

coefficient, and its absolute value serves to characterize the diffusion rgte of the

diffusing species in that substance. Commonly it is stated in units of cm per second.

The larger is the value, the shorter will be the heat-treating times necessary to accomplish a given amount of diffusion. The value of D can be measured in many ways,

typically from measurements of concentration - distance curves of the type presented

in Fig. 1.

It will be immediately evident from an examination of the literature that the

above description is greatly over-simplified. In particular, the value of D is not

independent of composition, and if a phase boundary is involved, it is possible for

diffusion of an atomic species to occur from one phase where its concentration is low

(but its thermodynamic activity is high) to another phase where its absolute concentration is higher (but its thermodynamic activity is lower). In spite of this, we shall

consider here that the diffusion constant has a single value for a given diffusing

species in a given material, at constant temperature.

Darken [1] has pointed out a simple relationship which can be very roughly used to compute minimum heat treating times, and which permits a feeling to be obtained for the

absolute values of diffusion coefficients.

Diffusion is substantially complete when

t = £ 2

/T> (2)

where t is the diffusion time in seconds and H is the radius (or minimum dimension of

the particle concerned) in centimeters. Thus, if one were concerned with determining

the minimum heat-treating time necessary to cause homogenization in an aggregate of 2|j. radius particles a^a temperature where the diffusion coefficient for the diffusing

species is 1 X 10 cm sec he would find

fc = (2 X 10 ) = 4 x 1Q 2 seconds

1 X 10" u

If the particle size were doubled, the time would be increased by a factor of 4. In practice, the actual times might be very much longer than those computed in this way

because pores and imperfect contacts between particles reduce the effective inter30
diffusion area and increase the diffusion distance. On the other hand, if the

necessary time for one particle size is known, the increase in time for an increase

in particle size should be given reasonably well by this relationship, assuming that

the two systems are geometrically similar.

There are many factors which may influence the diffusion rate in ceramics. Undoubtedly the most important one is temperature, and this is discussed in some detail

in a following section.

Most theories of diffusion assume that the atoms move by utilizing crystallographic

defects, particularly unoccupied lattice sites, to accomplish the rearrangement. A

major effect of increasing the temperature is to increase this number of defects, so

that diffusion is speeded up. The addition of impurity atoms, particularly those of a different valence, may also cause the format^m of unoccupied lattice sites. For

example, if Ca ions are substituted for Zr ions in ZrO^, one unoccupied oxygen

site is formed for each such substitution. With large substitutions many such sites

are formed and the diffusion coefficient for oxygen ions is tremendously increased.

Many impurity additions may operate in a similar way to increase diffusion

coefficients and thus to increase the rate of heat-treating reactions, but it is not

assured that increasing the diffusion rate of one ionic species in a compound will

I necessarily increase the reaction-rate

Two categories of diffusion reactions may be considered -

1) In the example cited above, the oxygen framework remains fixed, and the

| chromium and aluminum ions interchange. Any factors influencing the diffusivity of

i these ions will influence the velocity of the homogenization of the two crystals.

2) In reactions such as sintering, both atomic species must move. If the

objective of the heat -treatment were to cause sintering of aluminum oxide particles,

the diffusion rate of the oxygen ion would be all-important since it is slower moving

and rate controlling. Any factor, such as an impurity, that would modify the oxygen ion

mobility, would greatly speed up the sintering rate. If the rate of aluminum ion

diffusion alone were affected, the sintering rate would be unchanged.

It is commonly observed also that diffusion at grain boundaries in polycrystalline

solids is greatly enhanced. There is presently some obscurity in determining whether

or not this is universally true, or whether only the slower moving species are speeded up. More work needs to be done, but at the present time there are strong

indications that the behavior of ceramics does not parallel that of metals

Most chemical reactions are observed to increase rapidly in rate as the temperature

is increased. The so-called Arrhenius relationship is that:

3. Factors Influence the Diffusion Rate

4. Effect of Temperature on Reaction Rates

Rate = K e -Q/RT

(3)

or

or In Rate = InK - Q/RT

log Rate = log K - 2.3^

31
where the pre -exponential proportionality constant and the exponent Q (the activation

energy) are characteristic of the reaction concerned. R is the gas laws' constant, and T the absolute temperature.

In chemical usage, quantities are expressed in moles, or gram formula weights of

the reacting substances, R, the gas laws' constant, is expressed in calories per

degree (1.986 « 2.0), and Q has the dimensions of calories per gram formula weight.

Frequently, the computation is done on a per atom basis. Then the Boltzman gas constant k is used in place of R, and it is commonly expressed in electron volts per

degree C (8.6 X 10~4 ). Q has the dimension of electron volts per atom. Approximately

1 ev per atom = 23,000 cal per gram atom.

The diffusion coefficient D is a measure of the rate of the diffusion reaction.

Its temperature dependence is commonly determined, and presented in the form

D = D 0 e"

C^RT

(4)

If the value of D 0 and Q are given, the value of the diffusion coefficient at any

temperature may be computed. A typical value of D 0 is unity and reported values range

at least from 10-4 to 104 cm

8 per second. Occasionally very much larger or smaller

values for D e are published, but these should be viewed with caution. Values for Q are not so variable. They range typically from 10,000 calories per mole for rapid

reactions which will occur at an appreciable rate at room temperature to 150,000 or even 200,000 calories per mole for reactions in refractory materials that are observable only at temperatures above 1000°C. A few typical values are listed in Table 1. TABLE 1 . Typical values for some diffusion coefficients

Matrix Diffusing

Substance Ion

Do cm2 /sec

Q

KCal/Mole Remarks Reference

Ala 03 0

= 1.9 X 103 152 Single Crystal [3]

Al8 03 0

=

2 X 10° 110 Polycrystal [3]

A1E 03 Al+3 2.8 X 10 1 114 Polycrystal [4] uos 4.3 X io-4 88 Stoichiometric U0S [5]

U02 0

= 1.2 X 103 65 Stoichiometric U0S [5]

UO

s 0

= 2.7 X io-3 29.7 Non-Stoichiometric U02-0s [5]

'Ca+ + 4.1 x io-1 100 12 and 16 mol 7„ CaO [6]

CaOStabilized < Zr+4 2.1 x io-1 100 12 and 16 mol % CaO [6]

ZrOs 1 X io-2 28.1 15 mol % CaO [7]

4a. Isothermal Reaction Rates

We have just seen that the use of the Arrhenius relationship relating reaction

rate to temperature provides a compact means of describing the diffusion rate of one substance in another. The same approach may also be used to predict the effect of a change of temperature upon the time necessary for a given amount of reaction if the

value of the activation energy, Q, is known or can be determined. This approach works

well only in those cases where the driving force for the reaction is not strongly influenced by temperature, as is commonly the case in sintering, viscous flow, homogenization by diffusion or grain growth. If a phase change is involved in the reaction the

situation may be more complicated, as is discussed below.

32
It is common, for development purposes, to determine a proper firing temperature

for a ceramic by conducting a series of ISOCHRONAL observations . firing for a given

time at a series of temperatures, and presenting the results, for example, as a plot

of density, or grain size versus firing temperature. Fig. 2 presents such a plot, in

which for purposes of illustration, an arbitrary parameter V, having the dimensions of

length and representing a phenomenon such as a length change, has been plotted against

firing temperature.

Such an approach assumes that temperature is of primary importance in characteriz

ing the heat -treatment , and that changing the time of heat -treatment has little effect

It is apparently justified if one plots, on ordinary graph paper, the results of

measurements of the property concerned as a function of time. As is shown in Fig. 3,

the properties appear to reach more or less stable values at each temperature.

In Fig. 4, log V has been plotted versus log time, and it can be seen that the

reaction is continuing at each temperature in the same way. Only the time scale has

been shifted. Figure 3 incorrectly implies that the amount of reaction is controlled

by the temperature. It is controlled by temperature only if the same annealing time

is used at each temperature.

If one is concerned with commercial processing, and is limited to a period such

as an hour for heat treating, then such conclusions are correct. In those cases, heat

ing a specimen to an elevated temperature will effectively stabilize it against change

j with respect to short time heat -treatments at lower temperatures. On the other hand,

' if one is concerned with long term stability, as in creep, then comprehension of the

I fact that reaction may continue indefinitely even at low temperatures is of great

importance.

The curves in Figures 2-4 were computed from the relationship

V = kt 1/2

and k was assumed to vary with temperature as

k = k exD (-100,000)

This equation is reasonably representative of many of the structure -control ling reactions in ceramics.

In diffusion-controlled reactions, the thickness of a diffusion layer or the

thickness of an oxide film or reaction product formed by diffusion will be given, at

least approximately, by the relationship

Thickness = kt 1^ 2 (5)

which gives rise to the so-called parabolic rate law for most tarnishing reactions.

The rate constant k is characteristic of that of a thermally activated process, and

increases exponentially with increasing temperature.

The rate of grain growth in most materials is found roughly to be inversely

proportional to the grain size S, thus:

£ - kr <«

33
2 2 and S -S 0 = kt

where S 0 is the grain size at t =0. Assuming it to be much smaller than S, one can

deduce the commonly used grain growth equation

1/2

S = kt1'^

(7)

where k varies with temperature according to the Arrhenius relationship.

Sintering in many systems is observed to obey a similar law. The fractional

shrinkage in the initial stages 'can commonly be approximated by

^ = kt2/5

(8)

where again the rate constant k varies exponentially with temperature.

Many of the reactions tend to be self -limiting in this way. If the concern is

with having a reaction go to completion for processing reasons, times at low temperatures may become excessively long, and the only practical way to attain more complete

reaction is to use higher processing temperatures. On the other hand, if the concern

is with long term stability, say resistance to plastic deformation by creep, lowering

the temperature will lower the rate, but deformation will continue.

4b. The Effect of Heating Rate

It is obvious that many different reactions may go on simultaneously during heat

treatment. The question sometimes arises: can one of these be favored over the other

by changing the heating rate or the heat-treating temperature? For example, can

shrinkage be accomplished with less grain growth by raising the temperature to speed

up sintering and keeping the time short so that not much grain growth occurs? The answer in general must be "no". The precise answer is shown by the relative values

of the activation energy, Q in equation 3 for the two competitive processes concerned.

If the Q for each process is about the same, (as it usually is) than raising the

reaction temperature or changing the heating rate will affect each of the processes

equally, and the only effect will be to change the time necessary for reaction. If,

however, for example, the activation energy for grain growth were to be higher than

the activation energy for sintering, then indeed, raising the temperature would

increase the rate of grain growth faster than it would increase the rate of sintering.

A fine grained body would be obtained in that case by firing at the lowest temperature

consistent with the available heat treatment time.

Usually, the activation energies for the independent processes are not known, and

the effect of temperature on the relative rates of two identifiable competing reactions

is best determined by examining microstructures of specimens heated at two different

temperatures for times which are adjusted to cause comparable amounts of reaction at each temperature.

5. Determination of Activation Energies

It is conventional to determine activation energies by evaluating some specific

rate constant in the reaction law, such as the diffusion coefficient D in equation 1, at several temperatures. Then, a plot of the logarithm of the rate constant versus

the reciprocal of the absolute temperature should give a straight line whose slope is

Q/2.3R.

34
This is readily seen from the rearrangement

D = D c e-Q

/RT

(9)

In D = 2.3 log D = (h + In D c R T Rigorously speaking, this method is valid only if it can be independently demonstrated

that the sole effect of changing the temperature has been to change atomic mobility.

In practice, the existence of a straight line relationship on such a plot is usually

taken as evidence that the procedure is valid

In Fig. 5, the data from Fig. 4 have been replotted to permit a determination of

the value of Q. A measure of the reaction rate, the reciprocal of the time necessary

to produce a given amount of reaction, has been plotted against the reciprocal of the

absolute temperature. The activation energy can be determined from the slope as indicated

. -1 -1 -Q slope = ^ = IJ = 23^"

5.64 X 10^ - 5.18 X 10 4.6 X 10 J *

Q = 100,000 cal/gram formula weight.

It will be noticed that the value of the activation energy does not depend upon

the stage in the reaction at which the temperature dependence of the rate is determined.

When the law governing the process at hand is complex, it is sometimes difficult

to evaluate a rate constant with precision. Under these conditions the following

relationship will be found useful:

2.3 log = |

Ojr- - (10)

where t^ and are the times at Kelvin temperatures T^ and T^. If the reaction

occurring at different temperatures is essentially the same one, all of the curves on

a plot of the type shown in Fig. 4 should be parallel (although they may not be

straight lines) and it should be possible to superimpose them by the use of an appropriate multiplying factor computed with the aid of equation 10. Such techniques

provide an approach to the selection of heat-treating times which should produce

comparable amounts of reaction if the temperature is changed.

In determining activation energies, proper selectivity must be exercised in

determining the value of the rate. It is not permissible to state a shrinkage rate

as a certain percentage shrinkage per unit time, because the value of this rate will

depend upon the time period considered, and upon the shrinkage which has previously

been accomplished. On the other hand, it is permissible to measure the time necessary

for a reaction to cause a property to change from a given initial value to a given

final value as a function of temperature, as was done for Fig. 5, and to plot the

reciprocal of this time versus 1/T to obtain a value for the activation energy. For

example, one might measure the time necessary to produce 57o shrinkage and plot its

reciprocal versus 1/T.

6. Phase Transformation

The discussions presented above assumed that the driving force for the reaction

was not profoundly altered by temperature, so the rate would depend almost entirely

35
upon atomic mobility. When a phase transformation occurs, there are problems in forming

nuclei of the new phase, and the driving force for the reaction increases with supercool

ing while atomic mobility decreases. It is therefore sometimes difficult to predict

whether a change in temperature will increase or decrease the rate of the reaction.

6a. Nucleation

The problem of nucleation of a hew phase is well understood, and the kinetics of

the process have been studied in great detail. Discussions of the phenomenon may be

found in several reviews [2].

In these theories, the driving force for the transformation is the free energy

decrease associated with the transformation of a volume of the phase 4/3irr3 to the more

stable modification. When this new phase forms, an interface of area kin? is formed.

Thus the total energy change associated with the process is

AF = - j/rr3 AFv + 4-jrr 2 r (11)

where aFv is the decrease in free energy per unit volume associated with the transformation and r is the surface free energy of the interface per unit area.

The important geometrical parameters are set forth in Fig. 6 and a plot of this

behavior is shown in Fig. 7.

Most of the theoretical studies of nucleation and phase transformation have dealt

with the problem of describing the factors influencing the rate of nucleation. We shall

not attempt to reproduce these here, but shall merely qualitatively describe the conclusions. The stable nucleus must grow by the addition of atoms in the stable configura

tion. In a pure system this is an energetically unfavorable process at temperatures

close to the transformation temperature, so considerable undercooling may be required,

and the rate of nucleation increases with increasing undercooling.

The need to supply an interface of energy 4iTrs y , eq. (11), when a new phase forms

constitutes a nucleation barrier which can be greatly modified by impurities. If

impurities are in solid solution they may adsorb at the new interface, decrease the

interfacial energy y , and thus facilitate nucleation. If they are present as second

phase inclusions, they may serve as nucleation catalysts since the interfacial energy

between the inclusion and the new phase may be less than between the new phase and the

original matrix.

6b. Rate of Phase Transformations

Once nucleation is established, the rate of the phase transformation will be controlled by two parameters, the driving force, which increases with the supercooling

below the transformation temperature, and the atomic mobility, measured for example by

the diffusion coefficient. Thus

Rate = Const, f(g)- Doe"^7 *1

(12)

At the transformation temperature, Te, aT =0 and the reaction rate is low. As aT

increases the reaction rate will increase until it begins to be limited by the decreasing atomic mobility at lower temperatures, when the rate will again fall. A schematic

presentation of such behavior is given in Fig. 8.

36
Reactions of this type are well known in the heat treatment of metals, where their

understanding provides the basis for the control of the heat -treatment of steel. Probably the most striking example in ceramics is the devitrification or controlled crystalli

zation of glass. At both high and low temperatures the transformation rate is low, and

I at intermediate temperatures it is high. It is self-evident that although reactions of

this type are indeed thermally activated, one cannot compute activation energies in the

conventional way, nor can he without additional information predict the effect of

temperature on reaction rate.

7. Applications

Examples of the applications of these principles might be given almost without end.

In practically no case can they be applied without thought, however. This will be

illustrated by reference to the factors controlling the rate of sintering in an essential

ly pure single phase oxide.

It is reasonably well demonstrated that sintering is accomplished by the diffusional

transport of atoms from grain boundaries to pores. The pores are filled, and the space

left at the grain boundaries is closed by moving the grains closer together and thus

accomplishing shrinkage. What factors may influence the sintering rate?

1) The sintering temperature, because with other conditions constant it will

control the rate at which the atoms move.

2) The initial particle size, because it will control the distance atoms must

move to accomplish shrinkage, and thus the time required for movement.

3) The possible occurrence of grain growth during sintering. This can be detected

only by microscopic examination, but it will alter the necessary diffusion distance just

as certainly as changing the particle size. In either case, doubling the particle size

will quadruple the sintering time.

4) The presence of an impurity in the starting material - it may do at least

three different things:

a) Modify the diffusion rate of the slower moving species, and thus modify

the sintering rate.

b) Inhibit grain growth, and thus control the diffusion distance and hence

the sintering time.

c) Cause the appearance of a liquid phase which can completely modify the

shrinkage mechanism.

5) Reaction with the atmosphere. This may modify the stoichiometry of the

sintering material, and thus diffusion coefficients and reaction rates. Or the

atmosphere may become entrapped in pores and mechanically prevent shrinkage.

There is no simple road to understanding the effect of heat -treatment on. microstructure. To understand what is going on, and to be able to predict what effect changes

in processing conditions will have on structure and properties, the experimentalist will

however find it helpful to follow the process by measuring the changes in some sensitive

parameter in a series of isothermal heat treatments made at a sequence of times at a variety of temperatures and at the same time, follow the changes in micros tructure which

occur as a consequence of these heat treatments. In this way, he should be able to at

least describe the process in quantitative terms, and under favorable conditions he

should be able to understand what is going on in a fundamental way.

37
References

[1] See for example:

L. S. Darken and others, in Atom Movements, A.S.M. (Cleveland, Ohio,

1951).

W. D. Kingery, Introduction to Ceramics,

p. 217, John Wiley & Sons, Inc. (New

York, 1960).

Ling Yang, and M. T. Simnad, in Physicochemical Measurements at High Temper- [5]

atures, edited by J. O'M. Bockris,

J. L. White, and J. D. Mackenzie,

Butterworths Scientific Publications,

p. 295 (London, 1951).

[2] S. D. Stookey and R. D. Maurer, Progr.

Ceram. Sci. 2, 77 (1961).

J. E. Burke and D. Turnbull, Progr. in

Metal Phys. 3, 254 (1952).

J. H. Hollomon and D. Turnbull, Progr.

in Metal Phys. 4, 336 (1953).

W. D. Kingery, Introduction to Ceramics

p. 296, John Wiley & Sons, Inc. (New

York, 1960).

A. B. Auskern and J. Belle, in Uranium

Dioxide: Properties and Nuclear

Applications, edited by J. Belle,

USAEC, p. 309, U. S. Government

Printing Office, Washington, D. C. (1961).

W.'D. Kingery, J. Pappis, M. E. Doty,

and D. C. Hill, J. Am. Ceram. Soc. 42, 393 (1959).

[3] Y. Oishi and W. D. Kingery, J. Chem.

Phys. 33, 480 (I960)

[4] A. E. Paladino and W. D. Kingery, J. Chem. Phys. 37, 957 (1962).

[6] W. H. Rhodes and R. E. Carter, Bull.

Am. Ceram. Soc. 41, 283 (1962).

5 <-> or

oo

A

//

t» >t, >t f

FIGURE 1, Schematic representation

of diffusion. Upper diagram represents exchange of Cr+3 and Al+3

ions between ruby and sapphire.

Lower diagram shows Cr+3 concen- tration gradient at various

times

800

700

600

500

400

300

200-

100

EFFECT AT TEMPERATURE

ON V - I HR. ANNEAL

1500 1700 1900 TEMPERATURE °K

2100

FIGURE 2. Isochronal reaction curve showing variation of extent of reaction, V, with temperature at constant annealing time.

38
TIME- MINUTES

FIGURE 3. Arithmetic plot of isothermal reaction data. Apparent cessation

of reaction at each temperature is misleading, and consequence of reaction

law.

tures

FIGURE 5. Method of computing

activation energy,

log rate log 1/t = (-) so slope is -Q/2.3R.

39
PHASE I

FIGURE 6. Geometrical parameters

in nucleation, see eq. (11)

= r ergs/cm

FIGURE 7. Plot of conditions for

formation of stable nucleus of

radius r*.

RADIUS OF NUCLEUS —

TRANSFORMATION TEMPERATURE

FIGURE 8. Rate of transformation versus undercooling,

see eq. (12)

40
Correlation of Mechanical Properties with Microstructure

Robert J. Stokes

1; Introduction

The last review article on this subject was prepared by Coble in 1956 and was subsequently published in 1958 DO 1

• Since that time, a number of conferences on allied

topics have been held and the proceedings published but no review specifically on the

effects of microstructure has appeared. The period 1956 to the present has been particularly productive since it corresponded at the start with the beautiful etching ex- periments on dislocations in lithium fluoride by Gilman and Johnston [2] and the demonstration by Gorum et al.D] that single crystals of magnesium oxide could be deformed

plastically at room temperature. The implication from this latter work that certain

ceramic materials might possess ductility led to increased research activity in the

field of the mechanical behavior of ceramics. Most of the early effort concentrated

on the behavior of dislocations in single crystals of a relatively few substances,

particularly those having the cubic rock salt structure. More recently the field has

broadened considerably to include a wider range of single crystal ceramic materials and

the earlier work on the rock salt structure has been extended to include the effects of

microstructure.

In this paper the influence of microstructure on the following aspects of mechanical behavior will be considered in turn, (1) elastic deformation, (2) anelastic behavior,

(3) plastic deformation, (4) brittle fracture, (5) high temperature deformation and

creep. In addition to the familiar variables such as grain size and the presence and

distribution of porosity or a second phase, the term microstructure will be considered

broadly enough to allow discussion of the role that fundamental variables such as crystal

structure, bond character and crystalline defects such as impurities, vacancies and dislocations play in determining mechanical behavior. By necessity the paper is concerned

almost exclusively with the simple oxide ceramics since these materials have been the

most extensively studied.

2. Elastic Deformation

Purely elastic deformation of a single crystal corresponds to the variation in

spacing between atoms under stress. Thus, elastic extension is directly related to the

forces between atoms and the binding energy of the structure. Similarly the elastic

modulus, the ratio of stress to the extension it produces, is related to bond strength

and character. A simple way in which this correlation may be appreciated is to consider

the elastic moduli of a number of materials as a function of their melting temperature.

The points all fall within a fairly narrow band for which the elastic modulus increases

as the melting point increases [4] . Materials of similar type and structure fall in a much narrower band.

1 Figures in brackets indicate the literature references at the end of this paper.
The principal effects of microstructure on elastic modulus arise through the pre- sence of a second phase. There are a considerable number of theoretical analyses re- lating the elastic modulus of heterogeneous systems to the amount of second phase.

Each calculation leads to a slightly different relationship enjoying a different degree

of success in describing the experimental results. In the simplest case, where the

bond between the matrix (the continuous phase) and the inclusions remains continuous

and the two phases have the same value for Poisson's ratio, the resultant modulus (E)

is given by the simple relationship:

E = ED (l-c) + Ejc.

or

E = E0

- c (Eq-E-l) (1)

where ED is the modulus for the matrix, E]_ is the modulus for the included second phase,

and c is the volume fraction of the second phase. This gives a linear relationship

between the modulus of the two end components as indicated in figure 1.

In general the elastic modulus of a two-phase solid does not vary linearly and the

value is always less than that predicted by the linear relationship. Probably the most

successful analyses for predicting the modulus of heterogeneous solids are the recent

ones by Paul [5] and Hashin [6j and the modification to Hashin's analysis by Hasselman

and Shaffer [7] . These authors consider the more general case where values for Poisson's

ratio of the two phases are not the same and examine the influence of particle shape.

Both Paul [5] and Hashin [61 used the system tungsten carbide-cobalt investigated by

Nishimatsui and Gurland [8] and others for verification of their equations, obtaining

good agreement with experiment. In later work, Hasselman and Shaffer [7] and

Hasselman [9j applied these equations to their measurements on the variation of elastic

modulus for zirconium carbide containing graphite. These results are reproduced in

figure 1, where it appears that Hashin's equation, in particular the lower boundary,

shows the best agreement. The equations for shear or bulk modulus derived by Hashin [6] can be written in the general form:

A E E = En

- c(ED -E1 ) 9— n (2)

° 1 ED + B[EX + TVElTcJ

where A = B + 1 is a numerical constant.

For the case where the second phase is porosity, i.e., E]_ = 0, equation (2)

reduces to

E - E0 t 1 - iHp] «i

where P is the porosity. Other simplified theoretical relationships for the dependence

of modulus on porosity are

E = Ec [l - 1.9P + 0.9P 2

] (4)

when y (Poisson's ratio) = 0.3 derived by MacKenzie[ 10] for an elastic solid containing

spherical holes and

E = Eo [ rTT~-~p273J (5)

derived by Paul [5] for a solid containing holes of cubic shape. Pores of both shapes

can be seen in a ceramic body depending upon their location and the crystal structure.

The equation due to MacKenzie has been applied by Coble and Kingery [llj to their

measurements on sintered alumina with excellent agreement.

42
In addition, the relationship:

E = E0 e~ kP (6)

where k is a numerical constant, has been devised on a purely empirical basis by- Murray et al.[l2] , to describe experimental results on the effect of porosity on the

modulus of beryllium oxide. A similar relationship for alumina was suggested by

Spriggs [13] , and investigated by Knudsen [14] who accumulated all the available data on this material and showed that the exponential relationship gave a very adequate re- presentation out to 1+0% porosity with k = k- Spriggs et al.|15] have also used it for

magnesia containing up to 25% porosity; their results are reproduced in figure 2. Use

of the empirical exponential relationship in equation (6) has been criticized by

Hasselmann [16] on the grounds that it does not have any fundamental basis and does not

satisfy the boundary condition E = 0 when P = 1, he suggests that equation (3) due to

Hashin[6] can be used with equal success and is more flexible.

In fact the exponential function when expanded takes on a form similar to

equation (4) apart from the numerical factor which depends on k. All of the equations

(3) through (6) give a fairly adequate representation of the modulus dependence on porosity and it is difficult to make a critical choice among them. Obviously the

microstructural variables from specimen to specimen make it virtually impossible to define a practical ceramic in terms of a mathematical model. It is highly probable

that the size, shape and location of the pores as well as the total porosity governs

the success of any particular equation.

Other microstructural parameters such as grain size or texture have little or no effect on the elastic modulus. In their studies on alumina and magnesia, Spriggs and

Vasilos [17] found the dynamic modulus to be relatively insensitive to variations in

grain size for specimens having the same porosity. Although no specific studies have

been made, the major effects of texture (alignment of the grains in an extruded body

for example) are to be expected in those materials of non-cubic crystal structure

possessing strongly anisotropic elastic constants.

In conclusion, it may be stated that for purposes of mechanical strength and

rigidity the maximum elastic modulus is generally desirable and this is obtained in

material of the highest density, in structures where the solid phase is continuous

and the pores are closed and spherical.

3. Anelastic Behavior

When a stress is applied to a body in the elastic region it does not necessarily

come to equilibrium immediately but approaches the total strain value asymptotically

with time. This so-called "anelastic" effect [18] becomes particularly important when

a periodic stress is applied since the resulting hysteresis loop causes energy to be

dissipated by the solid.

The magnitude of the energy dissipated at a particular temperature, generally

referred to as the internal friction, depends on the strain amplitude and frequency of

the imposed vibrations. With the amplitude constant, the internal friction goes through

a maximum when the frequency is varied, as shown in figure 3« The time interval at this critical frequency corresponds to the relaxation time for the particular process

responsible for the peak. At the same frequency, the dynamic elastic modulus changes

discontinuously, increasing as the frequency is raised through the critical range be- cause the relaxation process then has insufficient time to contribute to the "elastic"

strain. This is also illustrated in figure 3. For experimental purposes it is

generally more convenient to use the natural frequency of a specimen and to vary its

temperature. In this case the internal friction goes through a peak at a characteristic

temperature and there is usually an accompanying inflexion in the dynamic modulus versus temperature curve. By studying the displacement of the peak along the temperature scale

for different specimen frequencies it is possible to estimate the activation energy for

the relaxation process.

43
Studies of the internal friction spectrum as a function of temperature, strain

amplitude and microstructure have provided powerful research tools for understanding

internal structure and atomic movements in solids. But internal friction is also

important from a practical viewpoint in that it constitutes the damping capacity of a freely vibrating solid; depending on the particular application, one may desire either

a very high or a very low rate of damping. In the remainder of this section we will

review briefly the effect of microstructure on the internal friction, or damping

capacity, -of ceramics.

The most important microstructural effect is that associated with the presence of

grain boundaries. Figure 4 due to Chang [19] shows the difference in internal friction

between monocrystalline and polycrystalline alumina as a function of temperature. The

internal friction peak at 1100°C is observed only in the polycrystalline material and

has been attributed to grain boundary sliding by Wachtman and Maxwell [20] and Chang [19] . Correspondingly Wachtman and Maxwell [20] have shown that the dynamic elastic modulus

drops off in value very rapidly at this temperature due also to intergranular relaxation. By measuring the shift in the peak for different frequencies, Chang [19] was able

to measure the activation energy for this relaxation process. The value, 200 K cals/mole,

agreed fairly well with other measurements obtained from creep studies (see later) and

the activation energy for self-diffusion of aluminum or oxygen ions in alumina. The

implication was that the internal friction peak corresponded to diffusion controlled

grain boundary sliding.

The grain boundary relaxation peak in alumina has been the subject of extensive

investigation, particularly into the effect of purity. Conventional alumina shows the

peak around 1100°C, but for high purity alumina it has been reported as high as 1400 C C [21] . The deliberate addition of impurity lowers the temperature of the internal

friction peak at a given frequency considerably. Figure 5> taken from the work of

Crandall et al.[22] , shows how the addition of just 1% Si02 introduces a new peak around

700°C. Similarly, the addition of small amounts of Cr203 or La20o result in the

appearance of internal friction peaks at lower temperatures [l9>23j • Also, the addition

of 1% MgO has been shown to increase the damping capacity of beryllium oxide at low

temperatures [23] . The general interpretation is that impurities tend to enhance

grain boundary sliding in ceramic materials, a phenomenon the opposite to that normally

observed in metals. The reason for the lower viscosity is not fully understood, it may

be associated with the precipitation of a complex or glassy phase in the grain

boundaries or it may be associated with the introduction of a non-equilibrium concen- tration of vacancies necessary to maintain electrical neutrality when impurity ions of

a different valence are added. Obviously, the damping capacity of ceramics at low

temperature is exceedingly sensitive to purity.

Other microstructural features are known to be responsible for internal friction

peaks in solids. These include, stress induced phase tranformations, stress induced

ordering, and relaxation phenomena associated with the presence of incoherent interfaces (inclusions) and the motion of twin interfaces [24J . While these processes have

been studied extensively in metallic solids there has been little research in this

area on ceramic systems. Chang [23] has suggested that an internal friction peak

observed in zirconium hydride around 100°C may be due to twin interface motion.

Another microstructural effect on internal friction at low temperatures is that

associated with defects introduced by plastic deformation. Again this is a field which

has been investigated primarily in metals [24] and internal friction peaks due to dislocation motion (the so-called Bordoni peak) have been identified. Of the ceramic

materials, sodium chloride has been studied in most detail [25,26] , although a limited

amount of work has been done on lithium fluoride [27] , maenesia [2§, 29] and alumina[293 . In general the damping increases with the amount of plastic deformation and is observed

so long as the dislocations are mobile. Thus procedures to lock dislocations by heat

treatment or X-irradiation [25] result in a decrease in the damping capacity. The

effect of plastic deformation on the internal friction spectrum of magnesium oxide is

illustrated in firure 6. In this material plastic deformation enhances the damping

capacity around room temperature. The equivalent dislocation damping peak is not observed in alumina until around 1500°C and, as Chang [29] has pointed out, this difference

in behavior is a reflection of the relative dislocation mobility in these two solids

(see later). In this respect the damping capacity of a single crystal at a certain

temperature is influenced by its crystal structure, and similarly the damping capacity

may be regarded as a useful indicator as to whether dislocations are mobile in a particular solid at a given temperature or not.

44
4. Plastic Deformation

Plastic deformation in crystalline solids at low temperatures (ie.<^0.5Tm) is due

! to the generation, motion, and multiplication of dislocations. The previous seminar

I in this series [30] has dealt with some of the more sophisticated aspects of dislocation

theory and dislocation interactions in crystalline solids. However, it is important

to emphasize here that the properties of dislocations in ceramics are quite different

from those in metals. The reasons for this are the short range nature of the bonding

forces, the presence of two or more ion species of different size and a more complicated

crystal structure. Furthermore, the behavior of dislocations differs from one ceramic

material to another and it is dangerous to generalize between them. In this section

we shall be concerned with the influence of structural and microstructural elements on

the availability and mobility of dislocations and thus on the plastic properties of

ceramic materials.

4.1. Single Crystals

4.1.1. Crystal Structure and Bond Character

A dislocation line represents the boundary line between slipped and unslipped

portions of a crystal plane. The direction in which slip occurs and the plane selected

depend on crystallographic factors, the primary factor being that the slip (or Burgers)

vector should correspond to the shortest displacement resulting in crystalline identity.

The slip plane is generally the closest packed plane. However, in purely ionic solids

there is the additional restriction that displacement should occur in a direction or over a plane which does not cause like ions to be forced into juxtaposition at any

stage of the displacement. It is for this reason that magnesium oxide slips in the

[110] direction over {110} planes rather than the more densely packed {001} planes [3l] . For similar reasons the slip direction of caesium chloride type crystals changes from

[ill] to [lOO] as the bonding changes from metallic to ionic in nature [32] . Thus bond

character is important in determining the slip elements.

Crystal structure also plays a very important role in determining the dislocation

configuration, in general the more complex the crystal structure, the more complex the

dislocation configuration. Consider alumina for example: the shortest direction of

crystalline identity is a [1120] , but as Kronberg [33] has shown, it is energetically

favorable for this displacement to be achieved in a series of four shorter displacements where the ions ride through the saddle points in the structure. The passage of

one of these shorter displacements, or partial dislocations, results in the formation

of a planar stacking fault. Thus dislocations in alumina should consist of four

partial dislocations linked by three stacking fault layers. Dislocations in the

basal plane of the layer silicates similarly dissociate into four partials and this has

been observed directly in talc by the electron transmission technique[34,35] • Stacking

faults linking partial dislocations have been observed directly in a number of other

layer structures [34,35] , and in rutile [36] . In magnesium oxide the structure is relatively simple and the dislocations can be thought of as being made by the insertion of

two supplementary (110) surfaces of positive and negative ions. The two surfaces are necessary to maintain charge balance and they must remain adjacent to maintain

continuity. Any tendency for them to dissociate would force like ions into juxtaposition and consequently form a very high energy stacking fault.

The combined influences of bond character and crystal structure have their greatest effect on the relative mobility of dislocations in various ceramic materials.

When a dislocation moves, bonds, ionic and covalent, must be broken and remade and in

the case of dissociated dislocations the partials must also be moved along together.

While the breaking of bonds due to the movement of dislocations is a relatively low

energy process in metals, in covalent solids it can be very high. The situation is

further complicated in alumina, for example, by the fact that when the dislocation

moves the aluminum ions and oxygen ions in the dislocation core must move in different

directions, referred to by Kronberg [33] as "synchro-shear". Only at high temperatures

where ion mobility is high and the motions easy to synchronize can dislocations move

easily in alumina. It is for this reason that it is necessary to go to extremely high

stresses or high temperatures [37,3^,39] (greater than 1000°C) to observe plastic deformation in single crystals of this material. It also explains the strong temperature

dependence of the yield strength of alumina [39] • In the case of rutile the movement

of dislocations requires the rupture of predominantly covalent bonds and this probably

explains the inability of this material to deform plastically below 600°C [36] . By

contrast the predominantly ionic nature of the bond and the relative simplicity of the

dislocation configuration in magnesium oxide makes it possible to deform this material

even at liquid nitrogen temperature.

45
As mentioned earlier, the difference in dislocation mobility between alumina and

magnesia is reflected by their relative damping capacity [29] , it is also responsible

for many of the other contrasting features of their mechanical behavior as we shall

discuss in the following sections. Similarly, the effects of microstructure on the

mechanical properties of other ceramic materials at a given temperature are conditioned

by the relative ease with which dislocations can move.

It is important to realize that the conventional yield strength of a solid

corresponds to a stress level at which large numbers of dislocations are moving with

quite a high velocity. The plastic strain rate of a crystal may be written as:

£ - n b v (7)

where n is the number of mobile dislocations per unit area, a factor which increases

rapidly due to dislocation multiplication [40J ; b is the Burgers vector; v is the

average velocity of the dislocations, a factor which is very sensitive to the local

stress. Direct measurements of the velocity-stress dependence by Johnston and

Gilman [41] have shown that the velocity of dislocations in lithium fluoride increases

approximately as the twenty-fifth power of the stress. Macroscopic yielding occurs when £ , equation (7) , is approximately equal to the imposed strain rate of the testing

machine. With sensitive techniques however, it is possible to detect plastic deformation well below the conventional yield strength in the so-called microstrain region.

In particular etch pit techniques [42] can be used to measure the stress required to

get dislocations moving. This stress is defined as the microscopic yield stress.

Thus, to summarize, the plastic properties of a solid depend critically upon the

number of dislocation sources (n) and the mobility of dislocations (v). Dislocation

mobility is influenced fundamentally by bond character and crystal structure. All of

these parameters must be borne in mind when considering the extra effects due to

microstructure

4.1.2. Solid Solution and Precipitation Hardening

First, we discuss the effects due to impurities. Impurities can be present either

in solid solution or in the form of precipitate particles and can act in two main ways

to change the plastic properties of a crystal. First, they can lock dislocations in

place, preventing them from participating in plastic flow and thus reducing the initial

value of n in equation (7); and second, they can impede the motion of dislocations

through the crystal lattice and thus reduce v in equation (7). Either way the crystal

increases in strength.

The most direct example of dislocation locking by impurity is that demonstrated

by Stokes [43] on magnesium oxide single crystals. He showed that crystals specially

treated to contain only "aged" or "grown in" dislocations supported stresses as high

as 140,000 psi in a purely elastic manner without yielding. In this case all of the

dislocations were immobilized and n in equation (7) was zero at all stress levels.

On the other hand, crystals containing "fresh" dislocations (ie. dislocations generated

at the surface at room temperature and therefore free from any contamination by

impurity) deformed plastically at a yield stress of approximately 10,000 psi. The

"fresh" dislocations could move and multiply fast enough at this stress level for the

plastic strain rate (e ) to keep up with the testing machine. Similar differences in

mechanical behavior between crystals containing "fresh" and "aged" dislocations,

although on a less spectacular scale, have been noted in lithium fluoride by Gilman

and Johnston [2]

"Grown in" dislocations in magnesium oxide have been observed directly by the

electron transmission technique and are found to have precipitate particles strung all

along their length [44] as illustrated in figure 7- The particles have been identified

as zirconium dioxide [45] , although considering the purity of the crystals there are likely to be other oxides precipitated on the dislocations too. The mechanism by

which these particles lock the dislocations is not entirely understood, but it

probably involves an elastic interaction between the impurity ions and the stress

field of the dislocations.

46
One of the characteristic features of impurity locking is that it represents a metastable condition. As soon as a single dislocation escapes from its impurity

environment it can move and multiply rapidly and the stress level needed to sustain the

imposed strain rate falls. Such catastrophic drops in strength at the onset of yielding

have been observed in magnesium oxide [43] •

The great difference in mechanical behavior between these two conditions in

magnesium oxide has proved to be extremely useful in understanding the origin of brittle

fracture in polycrystalline material. We shall return to this point later in connection

with table 2.

It is now generally agreed that the permanent strengthening associated with

impurities must arise from an increased resistance to dislocation motion through the

lattice, ie., by decreasing the velocity v for a given stress [46]. Local fluctuations

in the internal stress field due to the presence of impurity ions impede the dislocations

and cause the strengthening. Although the exact differences between solid solution and

precipitation hardening are by no means well understood, the stresses due to a coherent

precipitate are generally regarded as a much more effective impediment than those due

to impurities in solid solution. However, the situation is further complicated in ionic

solids by the requirement that electrical neutrality must be maintained at all times and

the valency of impurity ions going into solid solution must be taken into consideration.

There are, therefore, at least three conditions to be considered, (i) simple solid

solution with ions of the same valency, (ii) simple solid solution with ions of different

valency, (iii) precipitation.

When the valency of the added impurity ion is the same as that of the ion it is

replacing, simple solid solution strengthening is observed. This has been observed in

silver chloride, for example, hardened by the addition of silver bromide [473 and in

potassium chloride hardened by the addition of potassium bromide [48] . The stress

strain characteristics of silver chloride-sodium chloride alloys |_49J are compared

with the phase diagram in figure 8 and simple solid solution strengthening is observed

at the two extreme ends (Le., up to 10 mole percent and above 85 mole percent sodium

chloride) of the composition scale.

When the valency of the added impurity ion going into solution is different from

the ion it is replacing, then an equivalent number of vacancies must be introduced into

the host lattice to maintain electrical neutrality. This condition has a remarkable

strengthening effect. The influence of divalent alloying elements on the mechanical

properties of sodium chloride was studied extensively in Germany in the early 1930*

and this work is reviewed in the book by Schmid and Boas [50] . While the solubility

of divalent cations is very restricted, marked hardening is observed for additions in

the range 10 -6 to 10 -4 mole fractions. Thus, 0.02% calcium chloride in sodium chloride

raises the strength fivefold. Similarly, the addition of minute quantities of magnesium

fluoride to lithium fluoride result in a tenfold increase in strength [51] • Eshelby

et al [52] have proposed a mechanism to account for this strengthening in which they

take into consideration the electrostatic attraction between charged dislocations and

the charged vacancies, so that the dislocation lines become surrounded by a vacancy

cloud which restricts their motion. Other evidence concerning the role of vacancies

and point defects in the strengthening of ionic solids is reviewed in the paper by

Pratt [53] .

There are very few clear cut examples of precipitation hardening in ceramic systems.

The best example to date is that observed in the middle composition range of the sodium

chloride-silver chloride system illustrated in figure 8. Sodium chloride-silver chloride

alloys show a miscibility gap between 10% and $0% sodium chloride at room temperature

and in this same range the strength increases by 50 to 100-fold over that of the end

components [49] • However, even in this system rules of precipitation hardening are

not strictly followed in that solution heat-treated crystals are equally as strong as fully precipitated crystals, and it is not certain whether internal stresses due to

co-precipitation of the two equilibrium phases are the true source of hardening or not.

47
As a result of their studies on the effect of heat treatment and temperature on the strength of commercial magnesium oxide crystals, Gorum et al. [54], May and

Kronberg L55] and Stokes [56] concluded that a precipitation hardening type of mechanism

was occurring. Crystals in the as-received (fully precipitated) condition containing

many "fresh" dislocation sources were approximately twice as strong as those annealed

above 1200°C, as shown in figure 9 curve A; however, the higher strength could be re- stored by a subsequent anneal around 800°C, figure 9 curve B. Presumably the anneal

above 1200°C dissolved the precipitate particles initially present into solid solution

making it easier for the dislocations to move at room temperature. The subsequent

anneal at 800°C forced them to reprecipitate again. Unfortunately, this work is

currently lacking direct experimental evidence concerning the nature and distribution

of the second phase.

Deliberate alloying of magnesium oxide single crystals with small quantities of

impurity can lead to remarkable changes in strength, although the strengthening

mechanism, i.e., whether due to solid solution, precipitation or point defect hardening,

has not yet. been identified. Satkiewicz [57] showed that single crystals doped with

0.5% Cr20o raised the compressive strength fivefold to 80,000 psi, a value which

dropped by one-half on subsequent vacuum annealing. Liu et al [58) have found a similar strength (80,000 psi) for magnesia containing a few mole percent of MnO, and

a strength of 40,000 psi for alloys containing only five mole percent NiO. In the

latter case microscopic studies indicate that the nickel ions are in solid solution.

There is a need for further work in this area with emphasis on the control of

stoichiometry, and the manipulation of microstructure through heat treatment based on complete phase diagrams.

4.2. Polycrystals

Next, we consider the effect of grain boundaries on the plastic deformation of

ceramic materials. As was pointed out many years ago by von Mises [59J and by

Taylor [60] , for a fine grained polycrystalline solid to undergo plastic deformation

each of the individual grains must be capable of a perfectly general change in shape.

To satisfy this condition, each of the crystalline grains must possess five independent

slip systems. If not, then voids are likely to develop within the solid where the

individual grains cannot conform to the change in shape of their neighbors. Groves

and Kelly [ol] have recently examined the observed crystallographic slip systems for

a number of common ceramic materials to determine whether they allow the- required

general change in shape or not. Their results, reproduced in Table 1, are most interesting. They find that none of the common ceramic materials is capable of a great

amount of plastic deformation at low temperatures (we shall discuss the high temperature case later).

TABLE 1. The number of independent slip systems for

s ome common ceramic crystal structures

Structure Crystallographic

Slip Systems

Number of

Independent Systems

NaCl (Low Temperatures)

(ag. MgO)

{110} <110> 2

NaCl (High Temperatures)

(eg. MgO)

{110} <U0> and

{001} <110>

5

Hexagonal

(ag. Graphite, AI2O-3

{0001} <1120> 2

CsCl {100} <010> 3 CaF2 (Low Temperatures)

(eg. U02 ) {001} <110> 3

CaF2 (High Temperatures) {001> <110> and

{110} <110>

5

Ti02 {101} <10T> and

{110> <001>

4

48
One of the consequences of this failure to satisfy the von Mises criterion is

demonstrated by the marked effect of grain size on the plastic properties of ionic

solids at low temperatures. Figure 10 reproduces stress strain curves obtained on polycrystalline sodium chloride at room temperature [62] . As can be seen, decreasing

the grain size has a comparatively small effect on the proportional limit, but a very

large effect on the rate of work hardening. By the time there are three to five grains

in the cross- section, the rate of work hardening has increased tenfold over that of

the cubic orientation single crystal and for the finest grain size tested (.035 mm) it

has increased thirtyfold over the single crystal. Similar effects have been found in

polycrystalline silver chloride [63] and lithium fluoride [64] at low temperatures.

These observations may be interpreted as follows:

(i) Since "grown in" sources are not completely immobilized in these ionic solids

there are plenty of sources for slip over {110} planes. The stress to start these dislocations moving is relatively insensitive to grain size. In fact the slight dependence

noted in figure 10 would probably disappear with the use of higher sensitivity microstrain techniques.

(ii) As slip propagates and the whole polycrystalline matrix attempts to deform

plastically, constraints develop at the grain boundaries due to the fact that there are only two independent slip systems (table 1). Consequently the material as a whole can- not deform plastically and hardens at a rate almost determined by the elastic constants.

(iii) As the stress increases the constraints can be_relaxed somewhat by local

slip on additional systems. In particular slip on -(j001}<110> has been observed in the

vicinity of grain boundaries in polycrystallire lithium fluoride at room temperature as shown in figure 11. This additional slip permits the small amount of plastic deformation

observed in the stress strain curves of figure 10. Unfortunately the applied stress

required to promote general slip throughout a grain on this -C00]J <llO> system is far

too high, for example in sodium chloride it is four times [65] and in lithium fluoride

at least eight times [66] the stress to promote slip on the -{110} <Cll0> system at room

temperature. Consequently the material as a whole cannot deform plastically by any

great amount at least until the applied stress reaches this level.

(iv) The actual rate at which the stress increases, ie. the rate of work hardening,

is dependent on the grain size since the smaller the grain size the greater the grain

boundary surface area and the greater the volume of constrained material wherein shear

cannot take place. The exact relationship between grain size and the rate of work

hardening under these conditions has neither been considered theoretically nor determined experimentally.

The situation in magnesium oxide is even worse than in the simple halides. The

stress to promote slip on the £001)- <110> system at room temperature is approximately

one hundred times higher than that to cause slip on the {110J- <110> system [67J so that

even local deformation of the kind illustrated in figure 11 cannot be expected until

extremely high stresses are reached. Thus, polycrystalline magnesium oxide shows

virtually no plastic deformation at room temperature even though dislocations are quite

mobile and the equivalent single crystals ductile. At higher temperatures the difference

in stress level for slip on the two systems is reduced and at 1000°C is down to a factor of ten, equivalent to the situation in lithium fluoride at room temperature. A

slight amount of plastic deformation has been observed in compression in this temperature range [67] .

Again it must be emphasized that this discussion does not really apply to the low

temperature mechanical behavior of ceramic materials in which dislocations are immobile

(ag. AI2O0, TiOj, TiC, etc. at room temperature). In these materials the lattice

resistance to dislocation motion is so high that the cohesive strength of the crystalline planes is exceeded before any plastic deformation is possible. The extent to

which it may apply at high temperatures when these materials become plastic will be

considered later in section 6.

49
5. Brittle Fracture

In most of the preceding sections attention has been drawn to the plastic

properties of ceramic materials, yet the fact remains that the most notorious mechanical

property of a ceramic, particularly at low temperatures, is its brittleness. The

strength of a ceramic is always limited by brittle fracture. In this section we shall

examine some of the aspects of brittle fracture in ceramics and shall show that in

many instances the fracture strength can be related to the plastic properties described

so far.

It is well known that the fracture strength of a brittle material falls far short

of the theoretical strength (E/10) expected from simple estimates of interatomic forces.

Equally familiar is the" work of Griffith [68] who showed that the critical tensile

stress (o~) to propagate a crack of length c is given by;

where E is Young* s modulus and X the surface energy of the fractured faces. It is

important to realize that equation (8) applies specifically to propagation in a purely

elastic medium and assumes the pre-existance of cracks. It was for these reasons that

Griffith was so successful in applying equation (8) to the strength of glass fibers,

since, in glass, surface flaws are nucleated spontaneously by chemical reaction with the

environment.

The nucleation, growth, and propagation of brittle fracture in crystalline solids

is a vastly more complicated phenomenon. In the absence of pre-existing surface or internal defects a crack nucleus must be generated in some way and it has now been

clearly demonstrated in a number of ceramic materials that crack nucleation can occur

as a direct consequence of the limited amount of plastic deformation which precedes

fracture [30,69] . However, the cracks nucleated by these various mechanisms are often

too small to propagate catastrophically under the existing applied tensile stress and

either the stress must increase or the cracks must grow to reach the critical dimension.

Again it has been found that crack growth is assisted by local plastic deformation

[70,71]. When finally the crack reaches the critical dimension the condition for

propagation is dictated by a modified form of the Griffith equation due to Orowan [72] ;

where ^ represents the energy consumed by plastic deformation in the highly stressed

region ahead of the propagating crack. This term Jfp * s particularly important since

its magnitude determines whether the solid is ultimately brittle or not. When Xp is

large a crack may be stalled for an indefinite period but when $p is small propagation

may proceed without resistance. The value of jp ^ s strongly dependent on the plastic

properties of the solid. For most ceramic materials )(p is inherently small and they

are naturally brittle materials. Since much cannot be done to remedy this latter

situation most of the attention in ceramics has been focussed on the early stages of

fracture. In particular fracture nucleation has been studied intensively and is

probably the stage where improvements in the fracture characteristics are most likely

to be implemented. Next, we shall discuss the role of structure and microstructure

in the nucleation of brittle fracture in ceramics.

(8) .

cr (9)

50
5,1. Crack Nucleation Due to Slip at Grain Boundaries

Crack nucleation has been studied most extensively in magnesium oxide. The

essential feature is that cracks nucleate wherever groups of dislocations are obstructed

either by other slip bands [73,74] or by grain boundaries [75,76,77,78]. The primary

j reason why these observations can be made so readily in magnesium oxide is that shear

occurs at room temperature over flat {110} planar surfaces in discreet slip bands.

Thus the deformation is distributed very inhomogeneously and when a slip band is

blocked by a microstructural barrier, such as a grain boundary, the stress concentration

due to the dislocation pile up [79, SO] cannot be dissipated by secondary slip in the

surrounding material. Instead a crack forms. Figure 12 shows a cleavage crack

generated where a slip band intercepts the grain boundary in a magnesium oxide bicrystal under compression. Under tension such a cleavage crack switches into the intergranular surface and propagates immediately for fracture [78]

There are two possible ways to prevent the crack nucleation event recorded in

figure 12. Either slip within the grains should be made more homogeneous to relax the

j local stress concentration at the tip of the dislocation pile up or slip should be

I avoided altogether.

Efforts to make shear homogeneous have indeed resulted in a considerable improvement in the ductility of magnesium oxide single crystals [74] but similar attempts

with bi-crystals and polycrystalline material have not been successful [78] . There

are a number of reasons for this but the most general and important one for the

present discussion arises from the fact that there are only two independent slip

systems as indicated in table 1 [61] . Even when homogeneous slip does occur the high

stresses developed in the boundary regions due to the incompatability of the grains

eventually exceeds the intergranular strength at certain points causing cracks to

open up and the specimens to fracture. It is significant that the source of fracture

under these conditions is always intergranular [62] . Thus in polycrystalline sodium

chloride and lithium fluoride at room temperature, where slip is homogeneous and there

is some measurable plastic deformation (see figure 10) brittle fracture always

originates from an intergranular source.

On the basis of these observations Stokes and Li [62,78] have concluded that the

ability of magnesium oxide, or any other ceramic material for that matter, to slip at

low temperatures is in fact an undesirable feature, and they have shown how the

fracture strength of fully dense magnesia may be improved when steps are taken to

eliminate slip.

Table 2 summarizes recent results comparing the strength of polycrystalline

magnesia in the presence and absence of active slip sources [78] . The tensile fracture

strengths quoted in the right hand column represent the strength when "fresh" dislocation sources (introduced by the simple expedient of sprinkling the surface with

fine silicon carbide powder [42] ) are known to be present; the left hand column

represents the strength when all possible precautions have been taken to remove

surface dislocations by a chemical polish. It is instructive first to compare the

fracture strength of bi-crystals with the yield strength of single crystals under the

two extreme conditions discussed earlier in connection with dislocation locking

(section 4.1). The extremely high fracture strength of the bi-crystal obtained in

the absence of slip (compare results 1 and 3) and the close agreement between the

fracture strength and yield strength when slip sources are present (compare results

2 and 4) indicate that it is not the presence of the grain boundary per se but the

interaction of slip with it which is responsible for the low fracture strength of the

bi-crystal in result 4.
TABLE 2. Tensile strength of magnesium oxide in the absence and

presence of "fresh" surface dislocations

Tensile Strength

Result Material

"Fresh"

ulOXUvduIUXlO

ABSENT

"Fresh"

U X OlUCd 0 lUilO PRESENT

1 Single Crystal 140,000 psi

2 10,000 psi

3 Bi-Crystal 110,000 psi

4

n 8,000 psi

5 Fully Dense (100$), As-received

noxi rresseu roxycrysoaxj-ine

(Grain size 20yu )

28,000 psi

6

n 18,500 psi

7 Fully Dense (100$), Annealed,

Hot Pressed Polycrystalline

(Grain size 75p. )

19,500 psi

8

n 15,000 psi

9 99.7$ Dense, As-received,

noT> rresseu roxycrysi^axxxne

(Grain size 30yu,

)

12,000 psi

10 it 9,000 psi

11 99.7$ Dense, Annealed,

Hot Pressed Polycrystalline

(Grain size 50^,)

11,500 psi

12 n 12,500 psi

52
When similar care is taken to eliminate "fresh" dislocations from the surface of

fully dense (100$) fine grained polycrystalline magnesia the tensile strength can be

increased markedly, exceeding 30,000 psi in some cases. Again the average value

(26,000 psi, result 5) for such specimens drops down to 18,500 psi when dislocations

are reintroduced into the surface. It is believed that this remarkable surface

sensitivity is due to the fact that fracture originates in these fully dense polycrystalline magnesia specimens by the slip dislocation mechanism of figure 12.

Obviously this discussion of slip interaction with grain boundaries applies only

to those solids in which dislocations can move easily at low temperatures. The extreme

sensitivity to surface condition described in the previous paragraph is not likely to

be found in materials such as alumina or rutile. The effect of surface damage on

these materials will be discussed later.

When just a slight amount of porosity is present the magnitude of the difference

in strength in Table 2 due to the presence or absence of surface dislocation sources

is much less. For example, annealing the fully dense hot pressed material at 2000°C

causes grain growth and the appearance of slight residual porosity in the grain

boundary interface. The strength of polished material is then reduced to 19,500 psi

(result 7) and drops further only by one quarter (to 15,000 psi, result 8) when surface

dislocations are introduced [78]. In more conventional material of lower density

(99.7%) the tensile fracture strength is much lower (12,000 psi) and the value is then

apparently independent of surface treatment (results 9 through 12). These observations

have been interpreted by assuming that the pores themselves provide stress concen- trations which either initiate slip or nucleate intergranular failure directly. Thus,

porosity in excess of 0.1 to 0.2% tends to override any effects due to surface dislocations and the brittle fracture strength is more dependent on the amount and distribution of porosity.

It has long been realized that the strength of ceramics is sensitive to porosity

and that the greatest changes occur following small departures from theoretical

density. Ryshkewitch [81] and Duckworth [82J first demonstrated that the transverse

bend strength (S) of alumina, zirconia, and silicate porcelain decreased exponentially

with porosity as in equation (10);

The form of this equation should be compared with equation (6). It is found

experimentally that the value of k is generally one half the value found for b. A similar dependence has been established for thoria [83] , uranium dioxide [84] , and

magnesia [85] . While the empirical relationship holds quite well when the porosity

exceeds 0.3%, for values less than this the strength is determined by other variables.

In particular equation (10) makes no allowance for the distribution and location of

pores. It is to be expected that the stress concentration effect will depend critically

upon whether the pores are interconnected (open) or isolated (closed) in any particular

intergranular region at low porosity.

Similarly it is well known that decreasing the grain size increases the strength

of a ceramic material. Knudsen [83] has suggested that the combined effects of grain

size (d) and*porosity (p) can be represented by equation (11);

5.2. Effect of Porosity and Grain Size

S = S0 e~ bP (10)

S = S0d- a e" bP (11)

I The value of a varies from 1/2 to 1/3 for a variety of materials and the equation has

j been found adequate to describe results of thoria [83] , uranium dioxide [84J , magnesia [85] and alumina [22,85,86] and for beryllium oxide [87] with a = 1.

53
Unfortunately most of this data on the transverse bend strength of ceramics as a function of grain size and porosity has been obtained on specimens of variable surface

perfection. By surface perfection here we do not necessarily mean the presence or absence of surface dislocations considered earlier with respect to magnesia, but gross

imperfections in the form of intergranular or cleavage ruptures generated by mechanical

preparation techniques. Surface perfection is extremely important, for the presence

or absence of flaws determines to a great extent the subsequent mechanical behavior and

certainly contributes to the statistical nature of the strength of ceramics [86].

Harrison [89] has emphasized how surface flaws and damage introduced during grinding

and lapping operations can lower the strength of polycrystalline magnesia. It follows

that the empirical relationship of equation (11) may well represent the stress required

to propagate existing surface defects through the microstructure rather than the stress

to initiate cracks. In this case when a = 1/2, equation (11) corresponds to the

Griffith equation (8) with the condition that c is related to the grain size d in some simple manner. In order to determine the effects of porosity and grain size systematically much more attention should be paid in the future to surface condition.

It is not easy to anticipate what the fracture strength dependence on grain size

will be in the absence of surface flaws. Certainly it will depend on whether dislocations are mobile or not. When dislocations are mobile then the grain boundary

interactions discussed in the previous ^ section are important and the fracture strength

dependence on grain size may follow a d ? relationship of the type developed by Petch

and Cottrell [.90] for brittle metals. When dislocations cannot move the fracture

strength will be limited by internal stresses developed during firing and heat treatment.

The internal stresses may be added to the applied stress and will be particularly severe

in the boundary regions of anisotropic materials. All in all it seems reasonable to

anticipate that the greatest low temperature fracture strengths will be obtained in

materials of high density, fine grain size, perfect surface condition, in which dislocations cannot move. It is encouraging to note that transverse strengths in alumina

in excess of 100,000 psi can be obtained under these conditions.

6. High Temperature Deformation and Creep

At elevated temperatures, two factors become important to change the dependence of

mechanical properties on microstructure. First, dislocations become more mobile on existing slip systems and new slip systems become possible, and second, the diffusion

of point defects is enhanced to the point where they begin to contribute to the

deformation.

6.1. Plastic Deformation and Ductile Fracture

The increased mobility of dislocations at high temperatures is reflected by a further drop in strength of single crystals of materials such as magnesium oxide [67]

which are already plastic at low temperatures. It is also responsible for the onset

of plasticity at reasonable stress levels in single crystals of materials like alumina

[37,38,39], rutile [36,91], and titanium carbide [92] which are not plastic at low

temperatures. For the most part these newly plastic ceramic materials slip on simple

systems and the restrictions on polycrystalline ductility discussed earlier still

apply.

The possibility of slip on multiple systems has more interesting consequences

particularly for materials having the rock salt structure. As indicated in Table 1,

slip becomes possible over ^100} planes in addition to the [110} planes at high

temperatures. The occurrence of {100} slip contributes an additional three independent

slip systems, making a total of five, thereby satisfying the condition for polycrystallin

ductility. Stokes and Li [62] have shown that polycrystalline sodium chloride undergoes

appreciable extension above 150°C, the temperature at which "wavy" or multiple slip is

first observed. Under these conditions constraints do not develop in the grain boundary

region and brittle fracture does not occur, instead the specimens extend continuously

and neck right down to a point, giving a type of ductile fracture. The influence of

grain size and porosity on ductile fracture has not been studied in sufficient detail

yet to allow any conclusions to be drawn from the behavior of sodium chloride. However,

similar work on silver chloride [63] in the temperature range where it exhibits wavy

slip has shown that grain size has little or no effect on the rate of work hardening,

again consistent with the fact that grain boundary constraints have been completely

relaxed.

54
6.2. Creep and High Temperature Fracture

Unfortunately, the temperature range where a multiplicity of slip systems becomes

available in most oxide ceramics is so high that additional complications come into

play and the occurrence of plastic deformation by the simple movement of dislocations

is never observed. Deformation at elevated temperatures is always enhanced by the

diffusion of point defects and by the onset of viscous sliding at grain boundaries.

The diffusion of vacancies or interstitial ions contributes to each of the three basic

processes considered responsible for creep; dislocation climb, vacancy migration under

stress, and grain boundary sliding. These will be described briefly in turn.

Dislocation climb occurs when vacant lattice sites condense on or escape from edge

dislocations causing them to be displaced vertically in a direction perpendicular to

the slip plane. The climb process permits unlike dislocations to move together and

annihilate and it also permits dislocations to detour around obstacles in the slip

plane. Thus, dislocations trapped in a pile-up against obstacles such as sub-grain

or grain boundaries can escape by climb and rearrange themselves, the relaxation of the

back stress enables the dislocation source to resume operation and deformation continues.

When the rate of dispersion of the dislocations is approximately equal to the rate at

which they are pumped into the pile-up a steady state creep rate is established. The

rate controlling step in this process is vacancy diffusion, a fact which has been wellestablished for all metals for which accurate data is available [93] • In a derailed

analysis of the climb mechanism, Weertman [94] has shown that the creep rate ( E ) varies with the applied stress (o~) and temperature (T) according to the following

relationship;

where U is generally the activation energy for self diffusion. In ceramics the presence of two ion species having different activation energies for self diffusion and

the possibility that diffusion may occur in pairs makes the interpretation of U more

difficult.

The remaining creep processes do not involve the motion of dislocations and apply

specifically to polycrystalline material. In vacancy migration under stress , deformation results from diffusional flow within each crystal away from those boundaries

where there is a high local compressive stress towards those boundaries having a high

local tensile stress. This is generally referred to as Nabarro-Herring type creep and

it has been estimated by these authors [95,96] that the creep rate is related to the

stress, temperature and grain size (d) by;

where D is the diffusion coefficient and

d^T

(13)

D = D

0 e" U /KT (14)

It should be noted that the relationship for t in (13) differs from that in (12) by the

power of the stress dependence and by the appearance of a grain size term. The linear

relationship of E and cr in equation (13) gives rise to a viscous type of flow, at a rate determined by vacancy diffusion.

55
The exact mecha

boundary sliding , is

boundaries in ionic

Whether this increas

an impure glassy pha

motion through the d

to note that the ere applied stress but s volume it varies inv

nism of the third contributor to high temperature creep, grain

not known. It has been shown that the shear strength of grain

materials can fall off catastrophically at high temperatures [97,98] . ed viscosity in the grain boundary region is due to the presence of

se or whether it is controlled by vacancy diffusion or dislocation

isordered boundary region has not been determined. It is important

ep rate due to this process is also roughly proportional to the

ince it is dependent on the grain boundary surface area per unit

ersely as the grain size, ie.

EOC.f (15)

Obviously, all three of these mechanisms occur together, to a certain extent, during

high temperature creep. It is possible to distinguish which is the controlling

mechanism by measuring the dependence of the creep rate on temperature, stress and

grain size as may be appreciated by comparing equations (12) (13) and (15). This

procedure is generally followed by workers in the field. There is comparatively little

systematic work on the effect of structure and micro structure on the creep of ceramics.

Probably the earliest work on this subject is that by Wygant [99] who compared the

creep rates of different ceramic materials. Data for materials of similar grain size

or porosity at the same temperature and stress level are almost impossible to obtain,

but Table 3, compiled by Kingery [4] gives some indication of the effect of crystal

structure when most of these other variables have been fixed.

TABLE 3 Comparison of torsional creep rate

for different polycrystalline ceramic materials

The most detailed studies of the effect of microstructure have been conducted on

alumina, although even here the agreement amongst workers is varied. Tests have been

performed on materials of different purity, porosity and grain size with different

methods of loading. However, an attempt to interpret the results in a logical manner

will be made with the help of Table 4. First, we compare the work of Rogers et al [100]

and Kronberg [39] on single crystals in the temperature range 900-1700°C, (results 1 and 2 in Table 4). Although these tests were performed under different loading con- ditions, the activation energy for flow in both cases is approximately the same,

85 Kcal/mole. Since in Kronberg' s tests the specimens were known to be deforming by

simple slip on the basal plane, this may be regarded as the activation energy to

initiate dislocation motion, i.e., to operate the synchro-shear mechanism [33] in

single crystals.

Material

Creep Rate at 1300°C

1800 psi (in/in/hr.)

A12 0

3 0.13 x 10' 5 !

Zr02 3.0 x 10-5

1 MgO (hydrostatic pressed,

2% Porosity)

3.3 x 10-5

1

i

MgO (slip cast, 12% porosity) 33.0 x 10"5

1 BeO 30.0 x 10"5 i

if Th02 100.0 x 10~5

56

1
At higher temperatures (above 1800°C) Chang [lOl] found single crystals to exhibit

steady state creep at a rate dependent upon stress to the power 4.5 as in equation (12),

indicating that it was controlled by the dislocation climb mechanism (result 3). The

activation energy, 180 Kcal/mole, for dislocation climb, compares fairly well with the

activation energy for diffusion of either the aluminum or oxygen ion determined by other

means. The steady state creep rate of the alumina crystals was reduced by four orders

of magnitude with the addition of 2% C^O, as shown in figure 13, but the activation

energy for the process remained unchanged. The interpretation here is that the impurity

is restricting motion of the dislocations over the slip plane, but does not change the

rate at which they can climb.

With the introduction of grain boundaries there is an increase in the creep rate

and a change in the creep mechanism from one controlled by dislocation climb to vacancy

migration under stress. Studies on high density, fine grained alumina (Lucalox) by

Warshaw and Norton [102] and Folweiler [103] illustrate this point. Both find the

creep rate to vary linearly with the stress between 1500°C and 1800°C and the activation energy has been measured to be 130 Kcal/mole (results 4 and 5). Similarly

Chang [19] has also found a viscous behavior although with a higher activation energy

(result S) in this temperature range. Paladino and Coble [l05l have taken these

results and estimated the diffusion coefficients (D in equation (13)) using the exact

form of the Nabarro-Herring [96] equation. They have then compared them with the selfdiffusion coefficient for the aluminum ion determined by independent means. The

excellent agreement illustrated in figure 14 confirms that the Nabarro-Herring mechanism

is operating and indicates that the diffusion of aluminum ions is the rate controlling

process. A similar correlation has now been established between the beryllium ion

diffusion coefficient and the creep diffusion coefficient for beryllia [105,106], and

between the magnesium ion diffusion coefficient and the creep diffusion coefficient

for magnesia at low stresses [107].

Folweiler [103] studied the effect of grain size on the creep rate of Lucalox

alumina and found a dependence inversely proportional to the square of the grain

diameter, again consistent with the Nabarro-Herring theory as can be seen from

equate :n (13). Thus, large grained material has a higher creep resistance than fine

grained material.

At higher temperatures ( 1800°C-1900°C ) and larger grain sizes the creep rate of

alumina was found to increase at a rate more rapid than predicted by the vacancy

migration theory (results 6 and 7). Warshaw and Norton [102] studied the stress

dependence and found it to vary as the fourth power and on this basis suggested that

a dislocation climb mechanism was rate controlling; however, in a more recent examination of this accelerated creep, Coble and Guerard [104] have suggested that grain

boundary sliding has taken over. Their reasoning is based on the fact that an addition of Cr^Oj increases the creep rate even further; an observation also reported

by Chang [19] for polycrystalline material (result 8). If dislocation climb is the

controlling mechanism, then an addition of C^O^ should lower the creep rate as observed on alumina single crystals [101] and reproduced in figure 13. If grain

boundary sliding is the controlling mechanism then, as is known from anelasticity

studies [19,22] (figure 6), the viscosity is lowered by the addition of impurities,

and the creep rate should increase consistent with the experimental observations.

These observations on alumina may be summarized briefly as follows; single crystals

creep by the dislocation climb mechanism and impurities lower the creep rate; polycrystals creep in the range 1200-1800°C by the migration of vacancies under a stress

gradient and above 1800°C by grain boundary sliding, in both cases impurities raise the

creep rate. There is a need for further experiments on bi-crystals to determine the

stress dependence of grain boundary sliding and the effect of impurities on grain

boundary viscosity.

57
TABLE 4. High temperature deformation and creep

of single and polycrystalline alumina

Result

No. Material

Temperature

Range

Rate Controlling

Deformation

Mechanism

Activation

Energy

Kcal/mole Author

± oingie crystal basal o±ip °5 Rogers et al»

[100]

2 Single Crystal 1200-1700°C Basal Slip 85 Kronberg [39]

3(a) Single Crystal 1800°C Dislocation Climb 180 Chang [101]

3(b) Single Crystal

plus 2% Cr20o

1800 °C Dislocation Climb 180 Chang [101]

4 Polycrystalline

Lucalox, High

Density, 5-15k

grain size '

1600-1800°C Vacancy Migration 130 Warshaw and

Norton [102]

5 Polycrystalline

Lucalox, High

Density, 5-3 5/^ grain size

1600-1800°C Vacancy Migration 130 Folweiler [103]

6 Polycrystalline

97% Density,

50-100/^

grain size

1600-1800°C Grain Boundary

Sliding

185 Warshaw and

Norton [102]

7(a) Polycrystalline

High Density,

lOOyU. grain

size

1750-1900°C Grain Boundary

Sliding

280 Coble and

Guerard [104]

7(b) Same as 7(a),

plus C^O^

1750-1900°C Grain Boundary

Sliding

280 Coble and

Guerard [104]

8(a) Polycrystalline 1400-1700 °C Vacancy Migration

and Grain Boundary

Sliding

200 Chang [19]

8(b) Same as 8(a),

plus 1% Ct2 0^

1400-1700 °C Vacancy Migration

and Grain Boundary

Sliding

200 Chang . [19]

8(c) Same as 8(a),

plus 0.25$

^a 2^3

1400-1700°C Vacancy Migration

and Grain Boundary

Sliding

200 Chang [19]

58
Probably the reason why polycrystalline alumina creeps by the diffusion controlled

mechanism rather than by dislocation climb is a consequence of the number of independent

slip systems available. There are only two independent slip systems in alumina so long

as basal slip predominates (Table 1) and, even taking into account the additional flexibility afforded by climb, polycrystalline material cannot deform by slip without the

generation of intergranular constraints. The constraints can be relieved somewhat at

high temperatures by the migration of vacancies but will eventually result in the

appearance of intergranular voids in the regions of locally high tensile stress.

Figure 15 shows the occurrence of grain boundary voids and sliding in polycrystalline

alumina deformed at 1600°C. In magnesia, on the other hand, at a sufficiently high

temperature and a high enough stress level, wavy slip occurs and recent tests in our laboratory [108] have shown that high density polycrystalline magnesia can be deformed

substantially at 2000°C without the formation of intergranular voids. Under these

conditions the creep rate might be determined by dislocation climb although this

remains to be confirmed. At lower stress levels or slightly lower temperatures, slip

in magnesia remains confined to -0-10} planes and the two independent slip systems are

not then sufficient for creep to proceed by slip alone. Coble [107] has recently

shown that under these conditions creep is controlled by vacancy migration under

I stress, although whether intergranular voids then open up remains to be determined.

Certainly the high temperature behavior of magnesia as a function of stress, temperature and microstructural variables is a subject for more systematic and detailed

investigation. The fact that fully dense material deforms without intergranular

I separation may make it superior to alumina for certain high temperature applications.

An increase in creep rate with porosity has long been recognized. Wygant [99] showed

that the creep rate of a 2% porosity hydrostatically pressed magnesia was approximately

one-tenth the creep rate of a 12% porosity slip cast material as shown in Table 3«

Coble and Kingery [109] studied the effect of porosity on the creep rate of sintered

alumina up to almost 50$ porosity; their results are reproduced in figure 16.

At temperatures where the deformation process is controlled by the migration of

point defects, it is to be expected that stoichiometry will play an important role.

Scott et al [110] showed that stoichiometric uranium dioxide (UO2) could not be deformed

until the temperature reached 1600°C, whereas a deviation in stoichiometry to

UO2.06 allowed plastic deformation around S00°C. The non- equilibrium cation

vacancies are considered to contribute to creep at the lower temperatures. Similarly,

Hirthe and Brittain [111] have shown that the activation energy for steady state creep in

rutile changes gradually from 63 Kcal/mole at stoichiometric composition to 33 Kcal/mole

for reduced material.

7. Conclusions

This paper has attempted to correlate the mechanical properties of ceramics with

fundamental microstructural variables. By necessity the discussion is limited to the

simple alkali halide and pure oxide ceramics, but from this fundamental background it

is to be hoped that a better appreciation of the mechanical behavior of more conventional

ceramics can ultimately be attained. The salient points may be summarized as follows.

1) The maximum elastic modulus is obtained in material of highest density, in

structures where the solid phase is continuous and the pores closed and spherical.

The addition of a second phase of higher modulus causes the resultant modulus of the

heterogeneous mixture to be increased.

2) The damping capacity of a ceramic single crystal at a particular temperature

depends on the density and mobility of dislocations. The introduction of grain

boundaries raises the damping capacity in a certain characteristic temperature range,

this range can be broadened and extended to lower temperatures by the addition of

impurity.

59
3) Ceramic materials deform plastically at the stress level and temperature at

which dislocations are sufficiently mobile. The mobility of a dislocation can be re- duced by impurities in a number of ways, (a) direct elastic interaction with impurity

ions to lock the dislocation line, (b) indirect elastic interaction of the moving dislocation line with internal stress fields due to impurity ions in solid solution or precipitate particles, (c) electrostatic interaction of the dislocation line with

charged point defects introduced to maintain neutrality. Each of these mechanisms leads

to an increase in strength.

4) Plastic deformation of polycrystalline ceramics at low temperatures is prohibited by the lack of sufficient independent slip systems. At high temperatures some ceramic materials (eg. MgO) slip on additional systems and macroscopic polycrystalline

ductility then becomes possible.

5) The tensile fracture strength at low temperatures is a maximum in fully dense,

flaw free specimens of a ceramic material in which dislocations cannot move (eg. AI2O3).

In the presence of porosity or surface damage the strength is determined by the critical

stress to propagate a preexisting flaw. In the absence of porosity and surface damage

brittle fracture occurs in those ceramics in which dislocations can move (eg. MgO) by

the interaction of slip with grain boundaries, and in those ceramics in which dislocations cannot move the strength is limited by internal stresses developed in fabrication.

6) High temperature creep of ceramic single crystals occurs by dislocation motion

and climb. Impurities hinder dislocation motion and thereby lower the creep rate of

single crystals.

7) High temperature creep of polycrystalline ceramics generally occurs by vacancy

migration under stress and grain boundary sliding. Impurities lower grain boundary

viscosity and thereby increase the creep rate of polycrystals. Plastic deformation by

dislocation motion and climb is generally restricted by lack of sufficient independent

slip systems even at high temperatures.

Even with simple ceramic materials the above interpretations of mechanical behavior

are still quite flexible and there remains a great need for critical theoretical and

experimental work. Current developments of fully dense polycrystalline ceramics by

novel fabrication techniques are providing the experimentalist with a good opportunity

to perform quantitative experiments on well defined systems. The next few years should

be particularly productive with respect to understanding the mechanical properties of

polycrystalline material.

Acknowledgments

It is a pleasure to acknowledge the Office of Naval Research and Aeronautical

Systems Division, U. S. Air Force for their sustained support of this work. The

author has benefited from discussions with colleagues at Honeywell Research Center,

in particular the criticism of Dr. C. H. Li has been very helpful in arranging the

material for presentation. I am grateful to Drs. G. W. Groves and A. Kelly and

Professor R. L. Coble for making their manuscripts available before publication.

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62
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,

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63
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101 R. Chang, J. Appl. Phys. 31,

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106 R. R. Vandervoort and W. L. Barmore,

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100 W. A. Rogers, G. S. Baker, and

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110 R. Scott, A. R.Hall, and J. Williams,

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Ill W. M. Hirthe and J. 0. Brittain,

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64
LINEAR

'PAUL

'HASHIN (UPPER BOUND)

HASHIN (APPROXIMATE)

100 VOLUME CONTENT GRAPHITE (PERCENT)

Figure 1. The variation in elastic modulus of a two phase solid. Comparison of

theoretical and experimental relationships for the system zirconium carbide

plus carbon. (After Hasselman and Shaffer [7] ).

60 0

50.0

at * 40.0

1O

* 30.0

3

o

o

5

o

<

I

COQ

Z

<

UJO

t-

</) <

20 0

10.0 9.0

8.0

7.0 6.0

5.0

10

— 4 74 P E^46,080,000e (psi)

G«20,240,000e 490P (psO

• SPRIGGS H P. LANG CP. O SCHWARTZ S.C. a WACHTMAN CP. O TINKLEPAUGH H P. e WYGANT S C.

8 12 16 20

POROSITY VOLUME. PERCENT

24 28

Figure 2. Effect of porosity on elastic (E) and shear (S) moduli of polycrystalline

magnesia at room temperature. Letters after author names are fabrication

codes, H.P. - hot pressed, CP. - cold pressed and sintered, and S. C. - slip cast and sintered. (After Spriggs et al. [15] )• 65
A X

3 TO O Q. o

£ £ .« c

.2 £

Ul (tl a

0.001

Elastic modulus —

0.1 1 10

Frequency, tw

1000

Figure 3, Change in damping capacity (internal friction) and dynamic elastic modulus

with frequency. Amplitude and temperature constant.

0.04

0.03 z

o

U

£ 002

<

crui- 0.01

SINGLE CRYSTAL AL 203 (o SOLID LINE)

POLYCRYSTALLINE AL 20,

(o DOTTED LINE)

200 400 600 800 IOOO 1200

TEMPERATURE (°C)

1400

Figure 4 The internal friction spectrum for single crystal and polycrystalline alumina.

(After Chang [19] ).

66
17.5 -

x 15.0

<z

CELU

I12.5- o

I-o

o: 10.0

LL

7.5

5.0

2.5

_ 1 1 i i i P

(

i

-o—o—o- ALUM IN A, ~ 5000 cps

l

-0--0---0-- ALUM N A -

i 1% SILICA ,~ 15,000 cps

I

|

I

—

if

i

i

i

iii 4 \

1 v /

/ » /

-

1 \ 1 1, J

^-o-.-o.a* / -

g._^__-0---0 -oT° ft—4/7 * 1 o ' 1 i 200 400 600 800

TEMPERATURE. °C

1000 1200

Figure 5 Effect of impurity on the internal friction spectrum of polycrystalline

alumina. The addition of lfc Si02 introduces a new low temperature internal

friction peak. (After Crandall et al. [22] ).

10

0.9

0.8

0.7

0.6 o

0.5

0.4

0.3

0.2

0.1

-80

2 A UOWER CURVE : AS HEAT TREATED

28 MIDDLE CURVE: COLD WORKED BY COMPRESSION ~0.4% AT 130° C 2C UPPER CURVE: COLD WORKED BY COMPRESSIONS l.7%ATI30° C FREQUENCY: 27 Megacycles/second

-40 -20 0 20 TEMPERATURE (°C)

60

Figure 6, Effect of plastic deformation on the internal friction spectrum of magnesium

oxide single crystals. (After Chang [29] ).

67
Figure 7 "Grown in" dislocations in magnesium oxide. Note the impurity precipitate

particles spaced at fairly regular intervals. (Electron transmission

micrograph courtesy G. W. Groves).

900

O 10 20 30 40 SO 60 70 80 90 100 AgCI MOLECULAR PERCENT NaCI

(a)

Figure 8 Solid solution and precipitation hardening in the silver chloride-sodium

chloride alloy system.

(a) The AgCl-NaCl phase diagram

(b) Compression stress strain curves for AgCl-NaCl alloy single crystals.

68
Figure 9. Effect of heat treatment on the room temperature yield strength of commercial

purity magnesium oxide single crystals.

ar - room temperature yield strength in as-received (fully precipitated)

condition.

oz - room temperature yield strength after annealing.

ELONGATION

Figure 10, Tensile stress strain curves for polycrystalline sodium chloride at room temperature illustrating the effect of decreasing the grain size on the

proportional limit and rate of work hardening.

69
Figure 11, Slip distribution in the vicinity of grain boundaries in lithium fluoride

deformed at room temperature. Note very local slip on {001} planes near

triple point. Slip revealed by etch pit technique, (courtesy V/. D. Scott

and J. A. Pask)

Figure 12 Nucleation of a cleavage crack due to dislocation pile up at a grain boundary.

Magnesium oxide bi-crystal deformed in compression. Slip revealed by etch

pit technique.

70
-IS

4.8 5.0 5.2 I/T(I04/°K)

Figure 13 Effect of purity on the steady state creep rate of alumina. The addition

of 2% C^C^ lowers the creep rate by 10^. (After Chang [lOl] ).

Temperature (°C)

10-12] I I I I I I I

'

I 0.46 0.48 0.50 0.52 0.54

1000 /T (°rC')

Figure 14. Comparison of the diffusion coefficient measured for self diffusion of the

aluminum ion with the diffusion coefficient calculated from creep data of

alumina using the Nabarro-Herring equation. (After Paladino and Coble [105] )

71
Figure 15. Generation of intergranular voids during torsional creep of high density

alumina. (courtesy R. L. Coble).

40,000

0 0.1 0.2 0.3 0.4 0.5 VOLUME FRACTION PORES

Figure 16. Effect of porosity on the torsional creep of sintered alumina at 1275°C.

The stress to promote a constant creep rate and the creep rate at a constant

stress are both plotted as a function of the porosity. (After Coble and

Kingery [109] )•

72
Microstructure of Magnetic

A.L. Stuijts

Ceramics

1. Introduction

Electrical engineering has made enormous; strides since the beginning of this

century. Advances in the field of telecommunication and high-frequency techniques have stimulated the development of the required high-frequency insulating,

dielectric and magnetic materials.

Important developments in the field of magnetic oxides were started in our laboratories in the late thirties by J.L. Snoek [1] %, Although other investigators had

realized the potential importance of ferrites for high-frequency applications, it was Snoek and his collaborators who took the fundamental step to obtain control of

these materials so as to make their properties useful to the electrical engineer.

They were also able to explain a number of fundamental aspects of the high-frequency behaviour of ferrites.

Simultaneously pioneering work was done to gain further knowledge of the ionic

structure of these ferrites [2] . These studies made it possible to explain the semiconducting properties, and the basis was laid for a further interpretation of the

magnetic behaviour.

The French scientist L. Ne"el succeeded in predicting the magnitude of the magnetic moment as well as its curious temperature dependence [3]. He introduced the name ' ncompensated anti-ferromagnetism" or "f errimagnetism" , since, as opposed to

the Case in ordinary ferromagnetic alloys, the exchange forces orient the magnetization vectors of neighbouring spins antiparallel . The predictions of Ne"el have

been confirmed by the experimental work of Guillaud and Gorter [4],

After 1950 a new period in the development of magnetic oxides set in. New systems of magnetic oxides were discovered and developed, such as the hexagonal permanent-magnet material BaFe ^0 ^g, the ferroxplana materials and the garnets. On the

other hand new developments in electronics occurred, thanks to the application of

such specific properties of magnetic oxides as their gyromagnetic effects and their

ability to store information.

An essential feature of the magnetic ceramics is the combination of moderate

magnetic permeability with high volume resistivity (from 10 up to 10 10 ohm. cm).

Thus eddy-current losses in an alternating field of high frequency can be very low.

The development of magnetic oxidic materials has many different aspects involving physicists, chemists and engineers. Most of the properties are very sensitive to variations in chemical composition, ionic distribution over different lattice sites, ionic ordering phenomena, etc. Furthermore the shape of the product is

of importance for the application. Although magnetic oxides can be formed in any

shape by ceramic techniques, there are considerable problems in combining an exact

control of the chemistry with control of the microstructure of the shaped ceramic

product. It is with these problems that the present paper is concerned.

Although considerable progress has been made in the last decade with respect to fundamental aspects of chemical reactions and sintering, we are still far from

being able to control the microstructure even in simple oxides. There is, however,

an overwhelming amount of information on the importance of such control. The main

part of this paper will deal with a number of obvious examples of the importance of

microstructure in the development of "tailor-made" magnetic ceramics.

Figures in brackets indicate the literature references at the end of this paper

73
2. Crystal Structure and Intrinsic Magnetic Properties

2+ 3 + The mineral magnetite, Fe Fe,, 0^, was already used in antiquity for its magnetic properties. The magnetic ceramic materials now used in electronics are found

in a limited range of crystal structures. The cubic ferrites have the spinel structure with the general formula MeFe

2 0^, in which Me is Mn, Ni, Co, Fe% +

, Mg, Zn, or

a combination as for instance Li i++Fe 3+

. Moreover Fe 3+ can be substituted by e.g.

Al- or Cr-ions. Thus a great variety is possible in the chemical composition of ferrites with spinel structure [5] . The large oxygen ions form a close-packed structure,

in which two kinds of interstitial sites are occupied, viz. tetragonal sites and

twice as many octahedral sites. Some metal ions, like Zn and Cd, have a strong preference for the tetrahedrally-surrounded sites; others, like Fe 2 * and Ni, for the

octahedrally- surrounded ones. The spins of neighbouring ions in these oxides are oriented anti-parallel by the exchange forces. These forces, however, are strongest

for the interaction between the magnetic ions in tetrahedral and octahedral sites

mutually. When the sum of the magnetic moments at tetrahedral sites differs from

that at octahedral sites, a net magnetic moment can result. In the case of ferrous

ferrite, for example, in which Fe 2+ contributes four Bohr magnetons and Fe3 + five:

Fe 3+ Fe 2+ Fe 3+

0/ 5 4 5 u4 there is a net magnetic moment of four Bohr magnetons per formula unit.

The study of the distribution of the constituent metal ions over the different

types of lattice sites is very important. The intrinsic magnetic properties, and

to a large extent also the technologically important properties, are intimately re- lated to detailed aspects of the crystal chemistry of these compounds.

The same holds for the ferrites based on the structure of the mineral garnet,

for which the prototype is Y

3 Fe 5°^2* In tnis case the ionic distribution over the

tetrahedral and octahedral lattice sites has also been studied, but garnets are very often used unsubstituted.

Next there is a group of ferrites with closely related hexagonal crystal structures. These compounds are found in the diagram of figure i, the corners of which

represent the oxides BaO, MeO and Fe^Og. In the same way as in the spinel structure,

a great number of ions can be introduced. One of the compounds, BaFe.

2 0^ Q or barium

hexaferrite, has become a technically important permanent-magnetic material. Some of

the other hexagonal compounds, e.g. BagCOgFe^O^ (Co

2 Z) or Ba

2 Zn2 Fe i2 022 (Zn2 Y),

have interesting high-frequency magnetic properties.

As for the chemistry of magnetic oxides, we will limit the description of the

intrinsic magnetic properties to the most essential points. For further study re- ference may be made to the original literature in this field, which is readily ac- cessible (see e.g. [ 6]).

A ferromagnetic material is characterized by its spontaneous magnetization,

originating from the magnetic moments of the magnetic ions. The exchange interaction which aligns the magnetic moments of the electron spins parallel or antiparallel is opposed by thermal agitation. Thus the spontaneous magnetization has a characteristic temperature dependence, which disappears at the Curie point.

There are several factors binding the magnetization vectors to certain directions : 1. The crystalline anisotropy. The spin of the electron which causes the magnetic

moment is coupled with the orbit of that electron; the electron orbit is in its

turn fixed by the symmetry of the crystal lattice. As a result of this spin-orbit

and orbit-lattice coupling, the magnetic moment has a preference to be directed

along certain crystallographic directions. These- directions are called directions

of easy magnetization and are related to the symmetry of the crystal lattice. Work

has to be supplied to rotate the magnetization into a difficult or hard direction,

the energy being the crystalline anisotropy energy E

c

. In most spinels the easy direction is the cube diagonal. By the substitution

of a sufficient amount of Co-ions it changes into a cube edge. Most of the hexagonal compounds have large crystalline anisotropy energies, with the preferential direction of magnetization either parallel to the c-direction, within the basal plane

perpendicular to the c-axis, or on a cone lying in between the c-axis and the basal

plane

.

74
2. When a body of a ferromagnetic material is magnetized its length changes.

The origin of this linear magnetostriction X = — is closely related to that of the

crystalline anisotropy, Conversely, external stresses act on the direction of magnetization by virtue of the presence of magnetostriction, and this strain anisotropy energy is proportional to the linear magnetostriction \ st and the external

stress o : E K \ o . s s For the further considerations in our paper we shall assume the crystalline

anisotropy to be predominant, since a similar treatment applies for both anisotropics. In many cases it is convenient to express the binding force to a certain

direction as an anisotropy field HA

, proportional to K/M , where K is the absolute

value of the anisotropy constant.

3. Permeability and Hysteresis Loop

An externally applied magnetic field will cause the magnetization to turn toward

the field direction (see figure 2). The change in magnetic induction, A B, for an applied field, AH, is the permeability of the material:

A B

M = "ZTh The magnetic induction B is simply the sum of the magnetization 4 ttm and the external magnetizing field H;

B = 4 tt M+H

If there were no opposing forces, the permeability would be infinite. The forces . which bind the magnetization vector to certain directions (the anisotropy field BT^) cause the external field necessary to obtain a given value of A B to have a definite value and thus the permeability to be finite.

The initial permeability, for a small value of AB, is proportional to the . saturation magnetization M and inversely proportional to the anisotropy field Br:

s M M

2

The presence of anisotropy, and thus a finite permeability gives rise to a hysteresis loop when the magnetic induction B is measured as a function of a magnetic field H, the field being varied from a large negative to a large positive

value and back. The value of B for H = 0 is the remanence or retentivity B

r> A

magnetic material has thus two equally large, but oppositely directed remanence

values (see figure 3).

When a specimen is cycled around the hysteresis loop, energy is expended which

is liberated as heat - the hysteresis losses. Ferromagnetic materials generally are divided into "hard" and "soft" magnetic materials. The basis of this division is

the magnitude of the coercivity or coercive force H . This is the field necessary

to bring the induction, in the direction of the fie?d, to zero. One would expect

the value of the coercive force to be closely related to the anisotropy field H^.

This is indeed the case in permanent or "hard" magnetic materials, where high

coercivities are an essential property. For "soft" magnetic materials, with low

coercive forces and narrow hysteresis loops, the magnetization changes direction in

an external field which is generally much smaller than the anisotropy field HA„ Also the permeabilities found are several orders of magnitude higher than calculated

with the formula given above. This has to be explained by a different magnetization

process

4. Domain Theory

Pierre Weiss introduced his domain theory at the beginning of this century [7] to explain e.g. the non-magnetic state of a ferromagnetic material. He postulated

the existence of local regions in which the magnetization vectors are parallel. The

different regions are magnetized in different directions, as shown in an oversimplified way in figure 4. The uniformly magnetized regions are called Weiss domains.

The basic reason for the formation of domains is the reduction. of the magnetostatic energy which arises from the external surface of the specimen. See Figure 5a. Such a uniformly magnetized domain possesses induced magnetic poles at the surface.

75
The stray fields arising from these poles cause a high value of magnetic energy of

this system. By division of this body into two domains, as shown in figure 5b, the

magnitude of the magnetostatic energy arising from the poles is reduced to one half.

It is even possible to eliminate the magnetostatic energy completely by the formation,

of closure domains, as shown in figures 5c and 5d. In these cases no magnetic flux

leaves the structure.

The geometric configuration of the Weiss domain structure which actually is

formed is determined by the requirement that the total energy must be minimum. A

number of energies have to be taken into account, the most important of these being I the energy of the boundary between the domains, the domain wall energy. Bloch 8 showed that the magnetization does not abruptly shift direction at the boundary,

but changes direction gradually from atom to atom, as shown in figure 6. As a result

of a competition between exchange energy and crystal anisotropy there is a given minimum thickness of the domain wall, the energy of which is the sum of both energies.

The energy associated with the total domain wall area competes with the gain

in demagnetizing energy, thus giving rise to a specific width of the domains. Also

the magnetoelastic energy comes into play. Given a finite magnetostriction, strains

are set up in a configuration! Work has to be done to fit the domains together, causing the configuration of figure 5d.with more closure domains to be energetically more favourable.

There are several methods of making the Weiss domain structure visible under

the microscope. With a colloidal solution of magnetic Fe^O^ the so-called powder

pattern or Bitter pattern can be made visible. Figure 7 gives an example of this.

Owing to stray fields at the surface of the crystal the powder coagulates at the

position of the Bloch walls. For optically transparent crystals the Weiss domains

can be seen by making use of the optical Faraday-effect [9], A third method is based

on the magneto-optical Kerr-effeet [ 10] . In an external applied field H, and starting from the unmagnetized state, the

energy can be lowered in two ways (see figure 8):

1. Rotation processes, in which the magnetization is turned into the direction

of the applied field.

2. Domain wall movement 9 by which the domain having the magnetization vector

nearest to the field H grows at the expense of its neighbour.

In the same way as indicated in a preceding paragraph a permeability caused

by wall movement would be infinite, if there were no opposing forces. However, the

permeability caused by domain wall movement is limited by the fact that the domain

wall configuration gives a minimum value for the magnetic energy of the system which

is measured [11]. Further it is at this point that the mierostructure comes into

discussion. Any imperfections in the material — nonmagnetic inclusions or voids, dislocations, concentration fluctuations, internal stresses - will hinder wall movement. If we limit our discussion to non-magnetic inclusions and holes it can be

stated that domain walls prefer to contain the inclusion. In figure 9 such a situation is shown. The effect is a decrease in magnetostatic energy, for the same reason

as discussed above in regard to the external surface of the specimen. The wall area

too, and thus the total wall energy, is reduced. The microstructural characteristics

therefore cause the walls to be bound with a certain stiffness to their positions of

equilibrium, limiting the wall mobility.

The magnetization curve can be discussed in terms of these two magnetization

processes (see figure 10). The initial slope of the curve, starting from the un- magnetized state, is completely reversible. The domain walls are fixed at the imperfections in the material and reversible wall displacements predominate. At larger

field strengths the slope increases, the walls then being pulled loose from the imperfections. The walls can travel relatively large distances, but irreversibly, until all domain walls have disappeared. A further increase in induction occurs by

rotation of the magnetization vector into the field direction until complete saturation is reached.

Generally the magnetic field necessary^to obtain irreversible wall movements

is small compared to the anisotropy field H . Consequently the coercive force nor- mally measured in any magnetic material is small.

as shown in figure 5c. In this configuration

76
5. Single-domain particles. Permanent magnets.

The most straightforward relation between microstructure and magnetic properties is found in the permanent magnet materials based on single-domain behaviour of

their constituent particles.

We have seen that the basic reason for the formation of domains is the reduction in magnetostatic energy. When the diameter of a magnetized particle decreases

(see figure ll), the magnetostatic energy drops of f as the cube of the diameter D of

the particle. The domain wall energy, however, drops off only as the square of the

diameter. The effect will be that below some critical diameter, D , no magnetic

| energy is gained by dividing the particle into Weiss domains. Below D single domain

I particles exist in which no stable Bloch walls can be formed.

In the absence of domain walls demagnetization can only occur by rotation of

the magnetization vectors of the particles against the anisotropy forces. Thus, for

high anisotropy fields high coercive forces can result, with H

e of the same order of

magnitude as HA , a necessary condition for permanent magnetic properties.

The critical size, D , can be calculated for simple geometrical configurations,

giving approximate values [12] . For soft magnetic materials, with low magnitude of

the wall energy and thus a relatively large wall thickness, D is small. For nickel

ferrite a value of 0.08 M can be calculated [13], In hard magSetic materials, with a large anisotropy, the wall energy is high and thus the value of D relatively large.

For the hexagonal compound BaFe^O^g a D

cr

of about 1 micron is calculated [14].

The origin of the permanent magnetic properties of BaFe^O^g (or Ba0.6Fe

2 03

) is

the pronounced uniaxial magnetic anisotropy, with the preferred direction of the magnetization parallel to the c-axis. A large single crystal of this compound has low

coercivity, owing to the formation of Bloch walls. For permanent magnetic properties

I the constituent crystallites must be made smaller than the critical diameter. In

figure 12 the coercive force H is plotted as a function of grain size for some materials, showing the increase in coercive force when the mean grain size decreases.

For a permanent magnet the demagnetization curve, which is the part of the hysteresis loop where B and H are opposite, is of ynp^ortance . The quality of a permanent magnet is described by its energy product B«H, which reaches a maximum somewhere on the demagnetization curve. It is clear that a high energy product also

calls for a high induction. But the induction is roughly proportional to the apparent

density of a material, and thus a sintering process is applied in order to increase

the density, in which growth of the constituent particles above D has to be avoided

[15], This requirement can only be partly fulfilled, as heat treatment is generally

associated with grain growth. In figure 13 two hysteresis curves are drawn, one for

an optimally fired specimen (curve l), the other for a specimen with low coercive

force resulting from grain growth during sintering (curve 2).

Much work has been done on studies of grain growth phenomena during sintering,

and the effects on magnetic properties. As the value of D (about 1 micron) is just

within the range where the magnetic ceramics normally hav§rtheir mean particle diameter before sintering, fabrication is consequently critical. Much attention has

been given to the development of additions to aid in a better control of the manufacturing procedure, e.g. by retarding grain growth during sintering. Most of these

additions are only of value for the specific procedure used by the manufacturer

(raw materials, furnace, etc.).

The most disastrous effect on the magnetic properties arises from discontinuous

grain growth during sintering. Owing to the magnetic interaction of the domains in

adjacent grains, flux reversal in one grain will directly influence its surroundings

and finally introduce an avalanche-like effect, lowering the coercive force considerably. Discontinuous grain growth in this material is characterized by the high

growth velocity. In the hexagonal material under discussion the g rowth velocity in

the different crystallographic directions is of especial importance. The growth velocity is largest in the basal plane, causing the crystals to be thin plates, with

the c-axis perpendicular to the plate. This is shown in figure 14. The ratio of

diameter to thickness is about 2 for crystallites of about 1 micron diameter, and

appears to increase linearly to about 15 for discontinuously grown crystals of 500

microns diameter (figure 15). Magnetically this plate shape has significant consequences, as the effective demagnetizing field is very large for these thin plates.

Another aspect of microstructure is that the constituent particles can have

77
an orientation texture. In remanenee the magnetization vectors of a uniaxial ma- terial like barium hexaferrite will lie in the easy direction nearest to the sa- turating field under the influence of the anisotropy forces. (See figure i6.)This

decrease in induction, and thus in energy product, will not occur when the con- stituent particles are aligned with their c-axis parallel to the magnetizing field.

By a special procedure, in which use is made of the magnetic anisotropy field of

the material, this can actually be achieved and thus the maximum energy product increased considerably [ 16] . In figure 17 hysteresis curves are given for barium hexaferrite, relating to an isotropic and a crystal-oriented sample. Figure 18 shows a photomicrograph of the crystal-oriented sample.

I Other interesting aspects of microstructural events during sintering, e.g. in- crease of texture during sintering and anisotropic shrinkage, are not discussed in

this paper.

6. Single Crystals vs Polycrystalline Materials

I In the preceding section an example was given where a polycrystalline material

was essential for the hard magnetic properties. A single crystal can be considered

as the other extreme. Domain wall processes are favoured over rotations, which is

essential for soft magnetic materials. Apart from economic considerations, many difficulties arise in preparing single crystals with a controlled chemical constitution.

Moreover, no satisfactory techniques have yet been developed in which single crystals

of cubic materials can be grown from fluxes, as they generally contain inclusions.

Owing to the lack of a reference, e.g. a single crystal , the definite influence

of small v ariations in the material, unknown interactions between domains and a num- ber of other factors, it is often difficult to decide whether the microstructure ae- i tually found is essential for the physical properties measured. Therefore we will

show in the following paragraphs only examples where gross effects in the physical

properties are related to microstructural variations.

7. Initial Permeability and Coercive Force

The initial permeability and coercive force of a material are closely related,

as both are determined by the two basic proc'esses for magnetization. Thus they are very sensitive to porosity, size and distribution of the pores, the average size

of the grains, and whether a s econd phase is present.

The initial permeability is determined by rotation processes or by reversible

bulging of the domain walls, without changing the Weiss domain pattern as a whole.

The coercive force is a mean critical field, governed by irreversible rotation processes or by irreversible domain-wall displacements. As rotation processes are determined predominantly by intrinsic properties of the material, they are fairly independent of microstructural variations and can be calculated with good approximation. It is found that the initial permeabilities of sintered specimens are much

higher and the coercive forces much lower than one can expect from rotation processes alone. Thus wall displacements do contribute appreciably.

In figure 19 the initial permeability is given as a function of the porosity p

of a series of nickel ferrites and of nickel-zinc ferrites [17] . The value for p=0

in this figure is the result measured on a nickel ferrite single-crystal. The value

of the permeability which has been calculated for p=0 when only rotation processes

occur, is about 8. It appears that the increase in permeability with decreasing porosity of the material must be attributed to an increase in the contribution of wall

displacements. Also the coercive force becomes smaller with decreasing porosity, as shown in figure 20. The linear dependence found is as expected for domain-wall displacements. Presumably the sharp increase at the highest values of p is caused by

the fact that single-domain behaviour is approached.

The samples with varying porosities were obtained by sintering at different

temperatures. Sintering is accompanied as a rule by grain growth, which also affects

permeability. In figure 21 the measurements of Guillaud [ 18] have been given for the

initial permeability u as a function of grain size for manganese zinc ferrites

with constant chemical 8omposition. There are two inflections in the curve. The

lower inflection, at about 5-6 microns, is attributed to a change from rotational

permeability in small grains to a permeability due to wall displacements for larger

grains. However, from recent results published by Paulus [19] on this system, it

appears that also an appreciable increase in density occurs in the same region of

grain sizes (see figure 22). Thus one cannot unambiguously attribute the increase

78
in permeability to either the decrease in number of pores or the increase in grain

size. Owing to the fact that the chemical composition is very sensitive to changes

in the oxygen content of the atmosphere and to evaporation of zinc oxide, ceramic

technology has so far failed in this respect, as measurements should be made in a range of porosities for a given constant grain size. Also the mean pore size has to

be taken into account, as the blocking of domain walls at pores is determined by the

ratio of pore size to wall thickness. In the manganese-zinc ferrites an appreciable

increase in the mean pore size occurs during the heat treatment.

The same considerations presumably hold for the measurements on nickel-zinc

ferrites, made by the same authors. However, no measurements on one and the same chemical composition have been published.

The effects of discontinuous grain growth have not been investigated thoroughly.

Guillaud [18] attributes the upper limit of the permeability in figure 21 to the appearance of pores in the crystals. According to [19] discontinuous grain growth

starts in this system at about 10 microns. This can just as well be the reason for

densif ication to stop, as is known from theories on sintering [20] . We have studied

this phenomenon in a nickel-zinc ferrite, Ni

Q „.ZnQ

64: Fe 2^4' us * n§ a material which

was known to give discontinuous grain growth during ' sintering . In figure 23 results

are given of measurements on samples made from prefired powder. The samples were heated at a constant heating rate of 250 C per hour up to the temperature given,

and next rapidly cooled to 900 C. From 900 C to room temperature the samples were

slowly cooled. Dp to a temperature of 1200 C grain growth was very small, all grains

being smaller than one micron. Sintering was appreciable, as a density of about

97.5% of the X-ray density was obtainei. After 1200°C grain growth could be seen under

the microscope, up to 1 or 2 microns, and above this temperature discontinuous grain

growth started. A very sharp break in the density-temperature curve is seen at this

temperature. In figure 24 photomicrographs are given of the etched samples after

a) the temperature of 1200°C, where grain growth is clearly visible,

b) the temperature of 1210°C, where discontinuous grain growth has started; and

c) at a much higher temperature where the new equilibrium grain size is formed.

There is no break in the permeability curve. We believe that the main effect on the

initial permeability n is the decrease in porosity. A further increase in permeability, when the density is constant, is obtained by the gradual disappearance of

the very small grains. Apparently the domain-wall mobility which favours a high permeability is more hindered when the pores are located on the grain boundaries of

the grains than when the pores are trapped within larger grains.

A second phase or inclusion should have the same influence on u and H as a

pore or void. However, because of the difference in thermal expansion of thS two phases, stresses are set up in the ferrite matrix. When the material has a certain

value for the magnetostriction, a stress anisotropy energy can be formed which can

be relatively high with respect to the other anisotropies . This effect has been

studied by Carter in magnesium ferrite [21] . The second phase was formed by partly

reducing the ferrite, as the solubility of the metal oxide phase MeO in the spinel

phase is generally very low. At a high content of the reduced oxide phase, stresses

were high enough to crack the ferrite crystals around the inclusion.

The decrease in initial permeability and the increase in coercive force found

by us in the nickel-zinc ferrites (Ni

Q „Jn0 67°^1 ^ Fe 2°3^1- for x>0 » as shown

in figure 25, has to be attributed to the same effect. In tnesFe ferrites the crystalline anisotropy is very low, whereas the magnetostriction has a value still high

enough to cause a sufficiently large stress anisotropy to affect the permeability

and coercive force. In the range measured the volume fraction of the second phase,

a divalent metal oxide, is far too low to account for the decrease in M D and the

increase in H , All these specimens have a density differing from the X-ray density

by less than 0.25%. Both u and H show a perfect inverse behaviour in this case.

o c By a special method the internal demagnetization caused by pores can be determined experimentally. In figure 26 the internal demagnetization coefficient

has been plotted as a function of the porosity p. Curve a was measured for a cubic spinel ( f erroxcube ) . The value of goes to zero for p=0.

A typical effect of microstructure occurs in the hexagonal ferroxplana materials, in which the basal plane is a preferential plane for the magnetization

79
[22], In a polycrystalline sample, with random orientation of the crystallites, a large demagnetizing effect arises from the strong forces which hind the magnetization

vectors to the preferential plane. In figure 27 the lines of force have been drawn

for a schematic situation in which the preferential planes lie within the plane of

the figure, except for one crystal. The lines of force bend around this crystal,

which therefore acts as an air gap. From measurements of N. it appears that in isotropic ferroxplana materials an appreciable value f or remains when p=0 (curve b. Fi

26.) Thus, even in a fully dense hexagonal ferrite a virtual porosity is present, cor- responding to a cubic ferrite of 30% porosity.

It is possible to give the crystallites a preferred orientation by utilising

the magnetic anisotropy forces. This can result either in a "fan" texture, in which

the c-axes of the crystallites lie at random in a plane (see figure 28), or in a

texture as shown for barium hexaferrite (see figure 18), in which the c-axes are oriented more or less parallel. Measurements on specimens with an increased degree

of orientation f , in which f = 0 for random and f = i for parallel orientation of

the c-axes, show the expected decrease of N. , as shown by curve c in figure 26. The

technically important effect is a large increase of the permeability, mainly resultin;

from this decrease of N. , as shown in figure 29.

Dp till now we have only discussed the static magnetic properties of magnetic

ceramics. Except for the permanent magnets, their practical usefulness is at high

frequencies and we shall discuss some of the microstructural aspects of the highfrequency behaviour. We shall limit our discussion to the properties up to radio

frequencies

.

A sinusoidal field gives an induction that lags behind the field in time. This

time lag gives rise to losses, expressed as the loss angle tan 6. In low-induction

applications one is primarily interested in the quality factor 0 = l/tan 6. The losses can be divided into hysteresis, eddy-current and residual losses. Because of the

complexity of the physical relation between these losses and the microstructural

characteristics of the ferrite, only some view-points will be brought forward.

For low hysteresis losses a homogeneous structure seems to be necessary. With

less uniform grain size distribution and with grains having pores enclosed, the

hysteresis losses are greatly increased [18], [23] . The eddy-current losses in most ferrites are negligible, unless the ferrous

content is high. Ferrous ions lower the resistivity of ferrites considerably. In

manganese-zinc-ferrous ferrites, which have the most useful properties for many applications (especially for telecommunications) up to frequencies of about lMc/s, the

ferrous content is essential for the specific magnetic properties desired. The low

resistivity, about 10-100 f2*cm, caused by this ferrous content results in eddycurrent losses which are relatively high, compared to the other magnetic losses. A

peculiar effect is the decrease in the eddy—current losses when Ca-ions are added in

a quantity of about 0.1 mole—% [18,24] . The preference for the Ca-ions to be located

at grain boundaries was concluded from several experiments. It was also shown that

the resistivity measured within the individual grains is lower than the resistivity

measured across the grain boundaries; when Ca—ions are present the difference is

much larger (Fig. 30). During cooling of these ferrites a reoxidation occurs. The

addition of Ca-ions apparently brings about the appearence of an open porosity, so that quick reoxidation can also occur at the core of the specimen. Although the re- oxidation of the bulk of the crystals is increased as compared with specimens in

which no Ca-ions are present, the main effect is the high state of oxidation at the

grain boundaries if Ca-ions are present.

Little effective work has been done on the influence of microstructure on re- sidual losses. Among many other factors, domain-wall relaxation processes definitely seem to have an influence, especially when inhomogeneities are present. The same holds for the losses in those applications where high inductions are used (transformer cores) and thus irreversible wall movements play a preponderant role.

It appears that every group of materials has its optimum frequency range where

it can be used. The upper frequency limit is given by the so-called natural resonance frequency, where the losses increase sharply. In fig. 31 the relative -loss factor tan 6 / u is given for different classes of ferrites, as n function of frequency.

8. High-Frequency Behaviour

80
The very soft manganese-zinc-ferrous ferrite show excellent magnetic properties

in the lower frequency range. The high permeability in these materials is caused, by

a large contribution from wall movements [18]. In this lower frequency range, wall

mobility is apparently high enough to cause no losses.

In the higher frequency ranges, however, wall mobility is generally not sufficiently high. To obtain reasonably low losses at these high frequencies only moderate permeabilities can be used, in which no large contribution from domain wall

movements is present. Although both small grain size and a finely divided porosity

within the grains are effective to make low-loss materials for these high frequen1 cies, the most effective way to obtain low losses is by completely freezing the domain walls by the substitution of a few percent of cobalt ions.

9. Conclusion

The world production of magnetic ceramics is rapidly increasing. It is now about 12,000 tons a year with a value of about $30,000,000. In the foregoing the

j discussion has been limited to several groups of magnetic ceramics, in which the microstructure had a clear influence. This relationship is most straightforward in the

ceramic permanent magnetic materials. A clear relationship is also found with the

properties of the static hysteresis loop. For the magnetic properties measured under

dynamic conditions, the number of other factors influencing these properties in- creases. As many of them are physically not well understood, it is more difficult to establish a clear relationship between these phenomena and the microstructure

Ceramic technology can supply the methods and tools necessary for achieving

certain required microstructures , also for fundamental studies of the physical phenomena. Hot-pressing undoubtedly is one of these methods [25] . There are several other applications in which specific properties of ferrites

form a keypoint. Ferrites for radar and microwave communication components require

a very low porosity [26] . The same holds for ferrites used in magnetostrictive transducers. In recent times the study of ferrites with square hysteresis loops, as used

in memory cores, has been directed to the microstructure with more success than before [27J . Further studies of the fundamental aspects in those fields of the technology of magnetic ceramics, which determine the microstructure, will certainly help

both to provide a better understanding of the physical properties and a better control of their fabrication.

The author thanks his collegues Dr. G.H. Jonker, Dr. E.W. Gorter, van Groenou and C. Kooy for critically reviewing the manuscript.

Broese

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et de Manganese et de Zinc, Compt.

Rend. Ac. Sc. Paris, 230 , 1458-1460

(1950)

C. Guillaud and M. Sage, Propri^t^s

Magnetiques des Ferrites Mixtes de

Magnesium et de Zinc, Compt. Rend.

Ac. Sc. Paris, 232, 944-946 (1951)

E.W. Gorter and J. A. Schulkes, Reversal of Spontaneous Magnetization as a Function of Temperature

in LiFeCr Spinels, Phys .Rev. , 90

(3), 487-488 (1953).

[5] E.W. Gorter, Some Properties of Ferrites in Connection with their

Chemistry, Proc. I.R.E. 43, 1945-

-1973 (1955).

81
[6] J. Smit and H.P.J. Wijn, Ferrites, [19]

Philips Technical Lihrary, 1959.

[7] P. Weiss, L

r Hypothese du Champ Mole*- culaire et la Proprie'te' Ferromagne"-

tique, Journ. de Phys. 6, 661-690 [20]

. (1907)

[8] F. Bloch, Zur Theorie des Austauschproblems und der Remanenzerscheinung [ 21]

der Ferromagnetika , Zeit „ f . Physik, J_4 295-335 (1932).

[9] C. Kooy and V . Enz , Domain Configuration in Layers of BaFe^O^gi Philips [ 2 2] Res.Repts. 15 (l), 7-29 (I960).

[10] I. Hanke und W. Metzdorf, Ahhildung

magnetischer Bereichs-strukturen von [23]

Ferriten mit Hilfe des magnetooptischen

Kerr-Eff ekts , Z. angew. Phys.i_5 (2),

191-192 (1963).

[24]

[11] A. Broese van Groenou, private communication .

[12] C. Kittel, Phys. Theory of Ferromagnetic

Domains, Rev.Mod . Phys . 2JL (4),

541-583 (1949).

[25 ] [13] S.L. Blum, Microstructure and Properties

of Ferrites, J . Am . Ceram . Soc . 4_1 (ll),

489-493 (1958).

[14] J.J. Went, G.W. Rathenau, E.W. Gorter

and G.W. van Oosterhout, Ferroxdure,

a Class of New Permanent Magnet Materials, Philips Techn. Rev. 13 , 194-208 (1951/52). [26 ,

[15] A.L. Stuijts, Sintering of Ceramic Permanent Magnetic Material, Trans. Brit.

Ceram. Soc. 5_5, 57-74 (1956)

[16] A.L. Stuijts, G.W. Rathenau and G.H.

Weber, Ferroxdure II and III, Ani- [27] sotropic Permanent Magnet Materials,

Philips Techn. Rev. 16, 141-147 (1954).

[17] Reference [6] page 245.

[ 18] C. Guillaud, The Properties of ManganeseZinc Ferrites and the Physical Processes Governing Them, Proc , Inst . Electr

Engrs.l_04B, 165-173 (1957).

M„ Paulus , Influence des pores et des

inclusions sur la croissance des

cristaux de ferrite, Phys . Stat . Sol

2, 1325-1341 (1962)

J.E. Burke, Role of Grain Boundaries in,;

Sintering, J .Am. Ceram . Soc . , 40, 80-

-85 (1957).

R.E. Carter, Effect of Oxygen Pressure

on Microstructure and Coercive Force

of Magnesium Ferrite, J. Am. Ceram. Soc

41 (12), 545-550 (1958).

i A.L. Stuijts and fl.P.J. Wijn, Crystal-Oriented Ferroxplana, Philips

Techn. Rev. 19, 209-217 (1957/58).

W. Heister, Magnetic Properties and

Grain Structure of Mn-Zn Ferrites,

J.Appl.Phys. 30 (4), 22S-24S (1959)

M. Paulus et Ch, Gaullaud, Structure

Granulaire et Proprie'te's des Ferrites, J. Phys. Soc. Japan, 17 , Suppl. B-I, 632-640 (1962). Proc.

Int .Conf. Magnetism and Crystallography, 1961, Kyoto.

W.W. Malinofsky and R.W. Babbitt,

Fine-Grained Ferrites. I. Nickel

Ferrite, J.Appl.Phys. 32. (3),

237S-238S (1961).

W.W. Malinofsky, R.W. Babbitt and

G.C. Sands, Fine-grained Ferrites,

II, Ni

1 _x

ZnxFe

2 04

. J. Appl.Phys.

33 (3), 1206-1207 (1962).

A.L. Stuijts, J. Verweel and H.P.

Peloschek, Dense Ferrites and

Their Applications, Proc. Intern.

Conf. on Nonlinear Magnetics,

Washington, April 17-19, 1963;

I.E.E.E. Spec. Publ. T-149.

J.E. Knowles, Philips Techn. Rev.,

24, 242-251 (1962/63).

P.D. Baba, E.M. Gyorgy, and F.J.

Schnettler, Two-Phase Ferrites

for High-Speed Switching. J.Appl.

Phys., 34 (4), 1125-1126 (1963).

E.A. Schwabe and D.A. Campbell,

Influence of Grain Size on SquareLoop Properties of Lithium Ferrites, J.Appl.Phys., 34 (4),

1251-1253 (1963).

82
BaO MeO

FIGURE i. Composition diagram for the FIGURE 2 0 Change of the direction of

ferromagnetic ferrites. Me is a di- the magnetization vector M

g in an apvalent ion or a combination of diva- plied field H„

lent ions.

FIGURE 3„ Hysteresis loop of a magnetic FIGURE 4„ Weiss domains in a ferromagmaterial. netic material, Unmagnetized state.

83
FIGURE 5. Examples of Weiss

domain configurations.

N NNN

t ssss =^7 <

\ \

\ \ I

—'/

nn|ss

tjl

SSjNN

s /

FIGURE 7. "Bitter" powder

pattern on crystals of

BaFe13 019 , embedded in a glassy phase (courtesy of

G. H. Jonker)

84
UNMAGNETIZED MAGNETIZED MAGNETIZED

BY DOMAIN BY DOMAIN

ROTATION GROWTH

FIGURE 80 Magnetization Processes:

(a) unmagnetized state: (b) magnetized

by domain rotation; (c) magnetized by

domain growth.

o

'.'.YAW/

TEZZEZZZZZZZk

FIGURE 9. Decrease of demagnetization

energy when a domain wall intersects

a pore or inclusion.

INDUCTION

B

ROTATION

PROCESSES

IRREVERSIBLE

WALL MOVEMENTS

REVERSIBLE

WALL MOVEMENTS

FIELD STRENGTH H

FIGURE 10. Different magnetization processes along the magnetization curve. FIGURE 11. Magnetization in a small particle without and with a Bloch wall.

85
FIGURE 13. Upper half of the

hysteresis loop for

BaO-6Fe

20

3 with random

crystal orientations.

-4000 -2000 0 2000 4000 6000

»- H (oersted)

86
20

16

g

* 8

0

C-AXIS

MUI T FIGURE 15. Ratio of diameter to thickness

of discontinuous grown grains in sintered BaO„6Fe

2 0 as a function of grain

diameter D. 3

0 100 200 300 400 500 600

GRAIN DIAMETER D (MICRONS)

H=0, 4TTI=0

A

A

vH ==0,4lTl=Br I

r

TV

H=0,4rtl=0

a H=0,4irI=Br=4TtIs c FIGURE 16, A sintered mass of barium hexaferrite a) unmagnetized, b) magnetized

in a field H and c) converted into a permanent magnet.

Upper row: crystallites in random orientation; bottom row: parallel-oriented

crystallites

FIGURE 17. Demagnetization curves of barium

hexaferrite for a) isotropic and b) crystal-oriented sample.

ANISOTROPIC

ISOTR 0PIC

4000

(GAUS!

4TTIt 3000

2000

1000

-5000 -4000 -3000 -2000 -1000 0 H (OERSTED)

87
FIGURE 18. Photomicrograph of a crystaloriented harium hexaferrite sample,

thermally etched.

10 (SINGLE

CRYSTAL)

(CALCULATED)

F1GDRE 19. Variation of the initial permeability ft with the porosity p for

NiFe.,0^ and Ni„ .Zn„ Je^O,. (After

10

Hc (0e)

t

i Zn

0.5 Fe2°4

o

0-1 0.2 0.3 0-4 0.5

FIGURE 20. Variation of the coercive

force H with the porosity p of a se- ries of nickel-zinc ferrites. (After

Smit and Wijn [6] ) .

'2^4 " i 0.5""0.5 1 Smit en Wijn [17] )

'2 4'

88
5000

4000

>

m

<

LU

Q_

3000

2000

1000

5 10 15 20

CRYSTAL DIAMETER IN MICRONS

FIGURE 21. Variation of the initial permeability H- with grain diameter in

manganese-zinc ferrites. (After

Guillaud [18] ).

10 _ 15

-*-d 3

IN MICRONS

MGURE 22. Density of manganese-zinc ferrite, with the same chamical composition

as; those in fig. 21, as a function of

the mean diameter of the grains. (After Paulus [>9] )

700

=£600

3 500 _j

m

I 400

<

Y- 200

100

X-rav n "MQITVf

GRAIh . —LARGE GRAIN?

' WITH PORES

DENS ITYV >

-o—Qc

-o—0— -o

O

j -/ c

Ni

(].36 Zn

0

5.3 8

5«2 q.

CO

5.1 £

2

uQ -45

1160 1200 1240 1280

temperatureCC)

FIGURE 23. Initial permeability and density as a function of the temperature

to which the samples have been heated.

Heating-rate 250 C/hr.

89
FIGURE 24. Photomicrographs of samples from fig. 23 at a) 1200°C,

b) 1210°C and c)~1270°C.

f0.5

FIGURE 25„ Initial permeability H- , coercive force H and density for a range of nickel-Sine ferrites with

excess metal oxide. All the specimens

are very near to X-ray density0.25

0-20

0.15

0.10

0JD5

b/

o // o

// /; //

(i

i

a 1

/

*'

h=o

:

).22

/

| xO.60 k 0.78 p

f

0.91

0 0.10 0-20 0.30 0.40 0-50 *-p

S04- £5.3

0.3

0.1

54

5.2

c 0.2 - Q 5-1

- 5.0

33^067 ^

i 7 \

DENSITY-'' 7\

/ \

/A

' INITIAL 1 PERMEABILITY

i

l

1

1 COERCIVE FORCE

1 \ 1

1

1

l

2500

2000 q

1500f

1000

;

500

0-04 CW2

FIGURE 26. Internal demagnetization co- efficient N . as a function of the porosity p: a) for ferroxcube; b) for

isotropic ferroxplana; c) for crystaloriented Co

2 Z with different degree

of orientation f.

90
FIGURE 28. Photomicrograph of a ferroxplana material with "fan" texture. The c-axes

of the crystallites lie at random in the plane of the figure (thermally etched)

91
FIGURE 29. Initial permeability H- of

Co

2 Z (Ba

3 Co2 Fe 240 41 ) with different

degree of orientation f.

OHMS

10000

1000

100

10

0.147

v. N \ \ \ \ ^ \ \ AGGREG^

WITH Cc

\

TE

\ \ \ 1

-\

\

I \

\ V

\ AGG

t V"WIT

REGATE

HOUT Ca

INSIC CRY

WIT

E THE

3TALS:

'H Ca^

HOUT Ca

V \.

"""^ WIT

49 51 53 55 *-7°Fe2 03

57

FIGURE 30. Resistivity of manganese-zinc

ferrites, with and without Ca-addition,

as a function of the Fe„0„-content

„

(After Paulus and Guillaud [24] )

FREQUENCY IN CYCLES PER SECOND

FIGURE 31. The relative loss factor

tan S//x for different groups of ferrites as a function of frequency.

92
Micros true ture of Porcelain

Sten T. Lund in

1 . Introduction

The principal raw materials in the manufacture of porcelain are kaolin clay, feldspar and quartz. The primary purpose of these three components may be described rather

roughly in the following way. The clay gives the body the necessary plasticity during

forming and cohesion during drying. The feldspar acts as a flux and glass former in the

firing, and the quartz is a filler material ensuring less shrinkage and more stability

to the body during firing.

The bodies pass through several processes on their way to the final product, the

most important being forming, drying and firing. The composition of a body is not

determined only by the desired properties of the material in the finished product, but

also by the properties required of the body during the different phases of manufacture.

The composition of the body may vary considerably according to the purpose of the

product [j3j 1 . However, we will not discuss the differences between various types of

triaxial whiteware bodies here, but will deal with the common characteristic features

of their microstructure.

We are interested in the microstruc ture of the porcelain as it determines the

material properties. The things we want to know about the microstructure are the nature,

quantity and distribution of phases and pores. We also want to know the degree of inhomogeneity in the glass phase, and the structural stresses present in the different

phases

I will here give a review of our present knowledge and at the same time also try

to explain why the microstructure looks the way it does.

In table 1 the normal composition range of the raw body is given together with the

chemical composition of the fired bodies. If the raw materials in the bodies are pure

kaolinite , potash feldspar and quartz, the total system after dehydration can be

these three components, and these minor constituents are important, for they have a great influence on the changes during firing. In the absence of data on the multicomponent systems, Slielton has suggested converting the extra components to equivalent

contents of the main components similar in character £l 7]

The phases occurring in triaxial whiteware bodies are normally mullite

3AI2O3 • 2SiC>2 , quartz and a glass phase. In addition cristobalite may sometimes be

present as a fourth phase in bodies with a high percentage of quartz. The nature and

percentages of the crystalline phases can be determined by X-ray diffraction analysis.

As a rule technical porcelain contains about 10 - 25 per cent mullite, 5-25 per cent

quartz, and 65 - 80 per cent glass. The glass phase is thus the major part of the

porcelain. In addition, there are always pores in whiteware bodies. Even when the bodies

are fired to impermeability, a porosity of 4-8 per cent remains as closed pores.

Figures in brackets indicate the literature references at the end of this paper.

2. Composition of Porcelain

93
TABLE 1 Composition Range of Porcelain

Components in the raw body

per cent

China clay -, Q _ 6q Ball clay J Feldspar 25 - 35

Quartz 10-40

Chemical composition of the fired body

per cent Shelton's grouping

Si02 70 - 801 Ti02 < if R02 A1 20 3 15-25 A1 2 0

3 K20 2 - 5] Na20 1 - 2 CaO < 1 > R2 0

MgO < 1 Fe 20

3 < 1j Phase composition of the fired body

per cent

Mullite 10 - 25

Quartz 5-25

Cristobalite 0-10

Glass 65 - 80

3. Appearance of the Microstructure in the Optical Microscope

The microstructure of porcelain may be studied by different methods, but the

replica technique on polished and etched specimens is the simplest one and gives the

best results. A photomicrograph of an electrical insulator porcelain is shown in figure

1. This is a general picture with a magnification of about 400x taken on a collodion

replica with transmitted light. The micrograph shows that porcelain is a very heterogeneous material with the crystalline phases rather unevenly dispersed in a continuous

glass matrix.

Reminiscences of the original boundaries of the quartz and feldspar grains in the raw body can be distinguished in the micrograph. In this porcelain an extensive dissolution of the quartz grains has occurred as shown by the wide solution rims. Of the

mullite phase, only the larger of the crystals which have grown in the feldspar relicts

can be seen. No formation of cristobalite is found in this sample. The pores of the

porcelain are indicated by black areas in the micrograph.

The occurrence of cracks around and even within the quartz grains can easily be seen. Most or nearly all of these cracks do not exist in the untreated porcelain

material but are formed during the preparation of the specimen in the grinding and

polishing operations by the release of microstresses within the quartz grain and the

surrounding glass phase. These stresses are due to the great difference in the thermal

expansion coefficient between the crystalline quartz and the glass phase.

The information obtained from this type of micrograph is mainly concerned with the

grain size distribution of the quartz and feldspar components and their blending in the raw body, the degree of dissolution of the quartz, and the orientation effects present.

Figure 2 shows the microstructure of another electrical insulator porcelain with

a higher quartz percentage and less quartz solution, and figure 3 the structure in a vitreous sanitary ware at higher magnification. The firing temperatures have here been

too low to give an appearence of the individual mullite crystals.

In figure k, showing the structure of a porcelain fired at higher temperature,

mullite crystals can be seen in the feldspar relicts but not in the clay matrix. Some

of the quartz grains have started transformation into cristobalite.

4. Appearance of the Microstructure in the Electron Microscope

Only a small part of the mullite phase can be observed by the optical microscope,

owing to the extremely small size of the mullite crystals.. In order to determine the

quantity and distribution of the mullite phase the replica method has to be used in

connection with the electron microscope.

94
Figures 5a and 5b show electron micrographs of an electrical porcelain at a magnification of about 2500. We see here still more strikingly that the original

composition of the raw body with respect to quartz, feldspar and clay determines the

distribution of the crystalline . phases in the fired product. The appearance of the

mullite phase in the feldspar relicts is as distinct as can be desired, for the mullite

crystals isolated by the etching have stuck to the replica. The mullite phase in the

original clay fields has a different appearance. The mullite crystals are here present

in more compact aggregates, and the isolated crystal layer in the surface does not

stick to the stripped replica, which, therefore, has an uneven surface at these places.

The mullite crystals in the original feldspar and clay fields are different in

size, shape and degree of aggregation. This is due to the different formation conditions

of the mullite phase in these two types of fields. In order to understand this, we must

study the reactions during the firing of the body.

5. Changes during Firing

First a short survey will be given of the different processes that occur in the

structure during the firing of the body. Then the high temperature changes resulting in

the mullite phase distribution, the quartz grain dissolution, and cristobalite formation

will be discussed in connection with the ternary diagram, K20-Al203~Si02

In the raw body, relatively large quartz and feldspar grains are surrounded by

clay crystal plates and stacks. Thus the contact surfaces consist of quartz-kaolin and

feldspar-kaolin, but only exceptionally of quartz-feldspar. Then the potash feldspar

always contains some albite or soda feldspar.

When the body is heated, the chemically bound water in the kaolin clay is expelled

at 5O0-6OO°C giving a metakaolin phase Al 2 03«2Si02 flj . The next change occurs at

700-1000°C in the feldspar, where the mixed alkali feldspars are transformed into the

homogeneous high temperature form sanidine [12J.

Brindley and Nakahira [2] showed in their excellent work (1959) that the metakaolin phase at 925-950°C condenses to a spinel type phase 2Al3 0 3 -3SiO2 and amorphous

silica.

A melt phase begins to form in the same temperature interval by boundary reaction

between sanidine and the amorphous silica in the clay relicts. For a potash feldspar

with 20 per cent albite this occurs already 60° below the eutectic temperature of 985 C in the ternary system K^O-A^Oo-SiOg [llj« But at these low temperatures the diffusion

rates are very low, and thus the melt formation proceeds very slowly in the beginning.

The alkali liberated in the feldspar reaction starts diffusing into the clay relicts.

The sintering of the body also starts with the melt formation, very slowly at first,

but accelerating as the proportion of melt increases and its viscosity is lowered.

At about 1000-1050 C the mullite phase begins to develop in the clay phase relicts

from the spinel type phase with further discarding of silica. At a somewhat higher

temperature the mullite phase also begins to develop in the feldspar relicts by crystals

growing from the boundaries.

At about 1200°C the mullite phase is completely developed in the clay relicts and

normally also in most of the feldspar relicts. During the continued firing at higher

temperatures, recrystallization of the mullite phase continues resulting in larger

crystals

The quartz phase has a very low reactivity and the grains are not noticeably

affected by the other components below 1200°C. But about this temperature the dissolution of the quartz grains begins developing solution rims of cr}'stal-free glass. If

enough quartz is present to saturate the melt, the quartz dissolution stops and the

quartz begins to transform into cristobalite.

When the temperature is decreased during the last part of the firing, there is a small increase in the mullite content due to crystallization from the melt. No other

crystallization occurs, and the melt new forms the glass phase in the porcelain.

6. The Use of the Phase Diagram K

2 0-Al2 0^-Si02 Several attempts have been made to describe the changes occurring during firing

and also to explain the microstruc ture , starting from the equilibrium diagram of

K20-Al 20-j-Si02

, and using Shelton's grouping [3, 5, 11, 17].

95
Equilibrium concerning the total system in a triaxial whiteware body is never

attained at any point in the current firing schedules. Not even the polymorphic forms

of the silica corresponding to equilibrium are present at high temperatures. Nor does

the melt crystallize to tridymite and potash feldspar during the cooling of the body.

However, the proportions of mullite phase and melt can be estimated satisfactorily from

the diagrams. This fact, combined with a consideration of the relative rates of the

different process elements, makes the diagram very useful for describing some of the

reaction changes at high temperatures.

But trying to predict from the ternary diagram the quantity of melt in the body

at temperatures below 1100 - 1200°C gives great divergence from experimental data.

There are two reasons for this. First the active phases do not correspond to the

equilibrium phases (the presence of the spinel phase and the absence of a leucite phase)

and second the presence of Na 2 0 lowers the liquidus surfaces appreciably. At these

temperatures the melt formation is not an equilibrium state problem but instead a rate

problem.

It is not until the feldspar phase has disappeared and the mullite phase formed

that the changes in the phase composition of the body can be represented advantageously

in the ternary diagram. Here the use of the diagram will be demonstrated for two cases,

(a) an explanation and estimation of the mullite content in different fields and (b)

for describing the change in melt composition during the quartz grain dissolution £l ij

7. Formation and Distribution of the Mullite Fhase

The diffusion processes within the reaction layer between the feldspar and the

clay relict will be determined by the concentration gradients and the diffusion rates

of the components.

The formation of the mullite phase and its distribution between the clay relicts

and the feldspar relicts will thus be determined by the relative magnitude of the

diffusion rates of K 20 and Al 20-j components, and by the contact stirface and diffusion

distances, i.e. the grain size and grain distribution of the feldspar phase.

The alkali, which diffuses over to the clay phase relicts, there accelerates the

formation of the mullite phase. The mullite phase is formed first within the clay phase

relicts beginning at about 1050°C by discard of silica from the cubic spinel phase.

When the alkali content in the melt of the feldspar relicts is reduced sufficiently and

the melt becomes supersaturated with mullite, the mullite phase in the feldspar relicts

begins to form from nuclei and already existing mullite crystals at the original grain

boundary feldspar-kaolinite . The growth is determined here by the type and direction of

the crystal surfaces. The growth is most rapid on [00lj surfaces directed toward the

inner part of the feldspar relicts, and the mullite phase within the feldspar fields

thus acquires its characteristic appearance of a great number of crystal needles running

outwards from the original grain boundary toward the inner parts of the feldspar relicts

( figure 6a)

On the basis of the simplifying approximation that the mass transfer of A1 2 0^ may

be ignored compared with the mass transfer of alkali over the grain boundaries, the

distribution of the mullite phase between the clay and the feldspar relicts after

completed reaction can be estimated from the equilibrium diagram.

Let us study the conditions in a particular body, consisting of 50 per cent

kaolinite, 25 per cent potash feldspar and 25 per cent quartz, corresponding to traditional European hard porcelain. After dehydration of the clay the composition of

the total system is represented in the ternary phase diagram by the point P1 (figure 7).

The total system now consists of the three reactants , potash feldspar, dehydrated clay

and quartz, with the corresponding composition points W (K 20 • AI0O3 • 6Si0 2 ) , P3

(Al 2

0-j • 2Si02 ) and Si0 2

. The solution of the quartz grains bel ow*~ 1 200°C can be neglected,

and the quartz phase be regarded as an isolated system, which does not affect the

remaining sub-system feldspar-clay relicts.

When the alkali content of the feldspar relicts is decreased, their composition

point moves from W toward the point Al 2 02«6Si02

. At the same time the alkali content of

the clay relicts is increased, which causes their composition point to move toward

K20.Al 203«2Si02

. When the firing temperature increases from 1100° to 1200°C the reaction rate of

the mullite formation increases very rapidly. At 1200°C the mullite formation may be

regarded as completed in both the clay and feldspar relicts, if the feldspar grains are not too large. At this temperature the sub-system contains only mullite and melt in

96
equilibrium. The melt will have the composition marked, by a square point in the diagram

and the compositions of the feldspar and clay relicts are given by the points Ph and P5

respectively. This corresponds to a mullite content of 12 per cent in the feldspar

relicts and of 52 per cent in the clay relicts. The mullite content within the clay

relicts should thus be about four times as great as within the feldspar relicts. This

agrees well with the picture of the mullite phase distribution obtained from electron

micrographs of etched surfaces and of grains where the glass phase has been dissolved

with? hydrofluoric acid.

8. Size and Shape of the Mullite Crystals

It is very difficult to describe quantitatively, and simply, the mullite phase of

a body as to size, shape and distribution of the crystals. The electron micrographs of

etched surfaces give some idea, but local variations are so great that it is difficult

to obtain a reliable evaluation of the entire mullite phase (figures 6b and c). The

best way is to grind the sample and then isolate the mullite phase by treating with

hydrofluoric acid. From the large aggregates of mullite crystals obtained the individual

needles can be loosened without any extensive damage and dispersed in water by the action

of a colloid mill (figure 8).

In this way the mullite phase from different kinds of porcelain may be investigated

and compared, giving the result that mullite phase in tecfvnical porcelains fired at

different temperatures or with different feldspars may differ considerably as to mean

size and size distribution. But we still know very little about the effect of these

variations on the properties of the porcelain.

The mullite crystals have throughout the characteristic prismatic needle shape.

The length of the needles may be very great in the feldspar relicts. The present author

has observed mullite needles 0.05 p- wide and 10 p long, that is to say, with a proportion of about 200 times between length and width.

As a result of the growth conditions, the crystals may, within small zones,

occasionally lie parallel to each other. The mullite aggregate in figure 9 illustrates

part of such a feldspar relict. The sample is taken from a ground electrical porcelain

and the glass phase in the grain dissolved in hydrofluoric acid. In stereo this picture

gives a good idea of the mutual positions of the mullite crystals in the glass. One is

inclined to make a comparision with the reinforcing bars used in a concrete structure.

We also notice how non-uniform the width of the crystals is, even within this small

section. In the same picture can also be seen some smaller crystal aggregates which

come from the original clay fields. These aggregates are much more compact, and are made up of small and shorter mullite needles.

Comer has shown the orientation of mullite crystals in three preferred directions

120° to each other in kaolinite flakes fired at low temperatures [^J • In the clay

relicts in porcelain these orientation effects cannot be distinguished with certainty.

The explanation must be that the kaolinite relicts become deformed by viscous flow,

and this hexagonal outline destroyed or disordered.

9. The Dissolution of the Quartz Phase and the Formation of Cristobalite

When discussing the appearance of the quartz grains in the microstructure it is

best first to analyze the limiting equilibrium conditions.

It follows from the ternary diagrams, that if a homogeneous melt with the composition point P1 should cri'stallize under equilibrium conditions, mullite is the primary

phase starting crystallization at about 1800°C. When the temperature lias decreased to 1230°C, the melt also becomes saturated with tridymite. The melt composition point then

follows the boundary line with simultaneous crystallization of mullite and tridymite down

to the eutectic at 985°C, where also feldspar starts crystallizing. In solid state

there follow two transitions in the silica phase, first to high temperature quartz at

870°C and then to low temperature quartz at 573°C.

There are two important deviations from this equilibrium schedule; (a) the only

silica forms that have been observed in technical porcelains are quartz and cristobalite, (b) no crystallization from the melt of either silica or feldspar occurs during

the cooling, but a glass phase is formed instead.

When the body is fired, the reactions between clay and feldspar are relatively

rapid compared with the dissolution of the quartz grains in the melt. The formation

of the mullite phase is mainly completed before the dissolution of the quartz grains

becomes noticeable. At the beginning of the dissolution, therefore, the quartz particles

97
are in a matrix of mullite and melt, where the melt has, on the whole, the same composition. »

! The composition of the melt phase in a porcelain is determined by the presence of j mullite, the temperature, and the amount of quartz dissolved. Starting from the

proportion 2:1 of kaolinite and potash feldspar, and assuming that the melt is always

saturated with mullite, the composition point of the melt will move during an isothermal

quartz dissolution at 1300°C along the corresponding isotherm within the mullite field

(figure 10). Experimental data where the quartz and mullite percentages have been

determined by X-ray diffraction analyses and then the mean composition of the melt

calculated confirm this [1 1 J

The total mullite content is changed only slightly during the dissolution of the

quartz. If there is so much quartz in the system that the phase boundary line to the

tridymite field is reached just when the quartz has been completely dissolved, the

mullite content of the total system will be changed from 23.7 per cent at the beginning

of the quartz dissolution to 22.7 per cent at the completion of the dissolution. The

dissolution of the quartz is thus attended by a slight decrease in the total mullite

content

.

If enough quartz is present, the melt will become saturated and the dissolution

stops. Then the transformation of the remaining quartz into cristobalite begins. More

precisely, the cristobalite phase begins to form when the rate of transition to cristobalite at the phase boundary is greater than the rate of quartz dissolution. The

cristobalite phase forms an outer zone round the quartz, and the transformation is

apparently a solid state reaction starting from the surface of the quartz grain

( figure 11).

The quartz content at the start of the cristobalite formation may be estimated in

the following way. At this point, the phase boundary composition of the melt, and after

a certain time also the total composition of the melt, correspond to the saturation

point of cristobalite. This value is unknown, but may be approximated by the saturation

value of the tridymite according to the phase diagram, which gives a somewhat too high

result. The difference in temperature between the stable tridymite liquidus surface and

the metastable cristobalite surface is only small according to Schairer and Bowen [15j • The dissolution of quartz is a transfer process where alumina and alkali diffuse

in the direction towards the quartz surface and there is a mass flow in the melt in the

opposite direction. Further, the rate-determining step in the dissolution process is

probably the alumina transfer through the crystal-free dissolution zones around the

quartz grains. The absence of mullite crystals in the solution rims is due to the fact

that the mullite phase in the matrix was already fully developed before the solution of

the quartz grains started, and then the solution of the quartz also involves a con- sumption of alumina resulting in a dissolution of the mullite crystals nearest the

quartz grains.

10. Pores and Fracture Surfaces

Sometimes it is of interest to study the appearance of the pores in the fired and

sintered body. This is almost impossible with the optical microscope, but the electron

microscope, with its greath depth of field, is an excellent tool, and the stereoscopic

technique can be used with great advantage in the interpretation of the micrographs

[lO, 16, 18], These circumstances will be illustrated by a few pictures.

The first, figure 12, shows closed pores in an unetched fracture surface of a normal insulator porcelain. Information about the size, shape and other characteristics

of the pores can be obtained from such micrographs. In this case, for example, a faint

image of mullite crystals can be seen on the inside surface of the pores. This reveals

a beginning bloating effect in the porcelain. If the porcelain is overfired, an in- crease in porosity is obtained, due to the release of gases solved in the melt. In the

resulting bloating pores, the melt has been forced back and the mullite crystals are left bare, as shown in figure 13. In the same way, studies of the microstructure of fracture surfaces of whiteware

bodies are possible only with the aid of the electron microscope. My own investigations

confirm what can be expected from an ocular inspection of the shard. A smooth, highsheen fracture surface shows that the fracture runs practically independently of the

crystal structure, and a grainy surface shows that the fracture runs principally along

the old grain boundaries.

98
In this connection only one especially interesting illustration will be given, fig ure 14. It is a picture of an unetcbed fracture surface from a test loaded rod and

shows a pore in more unusual surroundings. In one direction the pore merges into a zone with a structure markedly different from both the appearance of the pore and the rest

of the fracture surface. This zone was first assumed to be a drying crack, i.e. a local

crack formed during drying, and which later was not completely cured in firing. This

zone, however, has exactly the same structure as is found on delayed fracture surfaces

in porcelain (figure 15) > that is, cracks which, under constant or slightly varying

stress grow from an outer surface at a very low speed so that the total fracture time

might be a matter of years. This may imply that figure 14 illustrates the first stage

in the progress of a fracture, beginning at a pore in the material.

11. Degree of Inhomogeneity in the Glass Phase

The porcelain in its entirety is a very heterogeneous material with crystalline

phases and pores dispersed in a glass matrix. The distribution of the mullite phase is

very uneven between the clay and the feldspar relicts, which emphasizes the heterogeneity by giving the different regions different properties.

However, the most important phase is the continuous glass phase, which gives

porcelain its fundamental properties. What we want to know about the glass phase is its

local composition or degree of inhomogeneity. The direct experimental study of this in

the glass phase is subject to great difficulties.

A common mistake made earlier was to draw conclusions regarding the homogeneity of

the glass phase from values of the diffraction index measured on thin sections observed

in the optical microscope. As a matter of fact these observations have not been made on

a glass phase, but on a two phase system, glass and mullite, with varying mullite

content. This has given rise to the opinion that the glass phase in fired porcelain is

most inhomogeneous , having different compositions in different regions. The high

viscosity of the system has also contributed to this opinion, but on this point it must

be remembered that the high apparent viscosity can only partly be traced back to the

melt phase, for the dispersed mullite phase increases it most efficiently.

Instead conclusions regarding the homogeneity of the glass phase must be drawn

indirectly from a combination of (a) quantitative phase determinations, (b) rate

measurements, and (c) electron microscopic observations of the phase distribution.

Such studies have indicated that the melt phase is not at all so inhomogeneous as previously believed, but instead has its composition regulated by the presence of the

mullite phase. The kinetic data provide evidence that at temperatures above 1200°C,

equilibrium conditions between melt and mullite phase are approximately reached. This

is also true of the feldspar regions once the mullite phase is formed there. The high

transfer rates are due to the high specific surface of the mullite phase, giving short

diffusion distances in the melt phase.

The greatest degree of inhomogeneity in the glass phase is caused by the dissolution of the quartz grains. The rate determining step is here assumed to be the alumina

diffusion from the adjacent mull'ite crystals, causing the essential part of the concentration gradient to fall within the crystal-free solution rims around the quartz grains

Within the types of porcelain in which a cristobalite phase is formed, this

concentration gradient has disappeared, too. The highest degree of homogeneity in the

glass phase will thus be reached in porcelain bodies with no quartz phase or with such

high quartz content that the melt has become saturated and cristobalite formed,

12. Internal Microstresses

Due to the great difference in the thermal expansion coefficient between the

crystalline quartz and the glass phase, high internal microstresses arise in the

porcelain during the cooling of the body.

A knowledge of the kind and magnitude of these stresses is very important when

studying and explaining the influence of microstructure on such properties as thermal

expansion and mechanical strength. This knowledge has to be gained by theoretical

analyses combined with experimental measurements on thermal expansion behavior and on

the induced strain in the lattice of the crystalline phases.

The quartz grains strive to contract more than the glass matrix during the cooling

of the body. As a result tensile stresses arise in the quartz grain. In the surrounding

glass phase radial tensile stresses and tangential compression stresses are formed,

both having their largest value at the boundary to the glass phase and then rapidly

99
decreasing with incereasing distance from the quartz grain. The analysis also shows

that the tensile stresses within the quartz grains decrease with increasing quartz

content, and that they are independent of the grain size at constant quartz percentage

[11].

For example, experimental strain measurements on a particular porcelain body with

6 per cent quartz gave a mean tensile stress in the quartz phase of about ^200 kg/cm2

. This value may be compared with the normal range for the modulus of rupture of porcelain,

500-1000 kg/cm2

, and the estimated flow point of silicate glasses 20,000 kg/cm2

. The question now arises whether these internal stresses are of such a size that

they may cause local fractures, with microfissures within or around the quartz grains

as indicated in the micrographs (figure 16). The modulus of rupture for porcelain is

much lower but refers to much larger volumes and gives, therefore, no information in

this case, owing to the statistical nature of strength. Measurements of the strain in

the quartz phase, and of the temperature dependence of the thermal expansion, indicate

that the stress state is the normal and dominant one, but they do not exclude the

existence of microcracks [l l]

Microfissures of this kind are believed to exist in porcelain bodies [6 , 7» 9]

but no reliable data on their frequency have yet been forthcoming. If they do exist,

they must be weak points in the material and presumptive starting points for growing

cracks when the body is mechanically loaded. A decrease in the grain size of the quartz

is known to give an increase in both mechanical strength and thermal expansion coefficient, and these effects could then be explained by the decrease in size and frequency

of the microfissures.

If microfissures do not exist, but only the microstresses , what does that mean to the mechanical strength? The existence of high tensile stresses in the quartz grains

and of high radial tensile stresses in the surrounding glass phase must be a weakness

especially regarding the crack nucleation during loading. The existence of the tangential

compression stresses must, on the other hand, make the crack nucleation in these directions and crack propagation in the glass phase more difficult. Which of these two effects is the most important is very much disputed [l3 f 19J« An increase of the quartz

content in the porcelain usually means an increase in mechanical strength, and this

effect might be explained by the decreased proportion of the weaker glass phase combined

with higher mean tangential compression stresses in the glass phase.

13. The Micros true ture of Porcelain - an Exhausted Field of Research?

There is always a need for improving the limiting properties of a material, and

porcelain is no exception. In technical porcelains, for instance, mechanical strength

is frequently the limiting property. In order to improve it in an efficient way, we must

aquire a much better understanding of the influence of the microstructure than we have

at present.

The electron microscope and the X-ray diffraction technique have given us a clear

picture of the microstructure as far as the percentages and phase distributions are concerned. But we have to go further and investigate structural details in the con- tinuous glass phase, such as concentration gradients, pores, microfissures and solved

gases, in order to elucidate the effects of these different factors. The main interest

will be centered around the glass phase, and around the crystal phases mostly as modifiers of the glass phase properties.

As to mechanical strength, special attention must also be paid to the surface

structure and the chemical conditions there. We do not yet know the nature of the weak

points in the porcelain, nor the nucleation mechanism of the cracks in the fracture, or if there is a possibility of stopping a crack once it has started. We have only some empirical rules to follow but no real understanding.

The microstructure of porcelain and its influence on the material properties is

thus far from being an exhausted field of research, and there is still scope for

significant future developments and improvements in this ancient and highly appreciated

material

.

100
[1]

[2]

[3]

w

[5]

[6]

[7]

[8]

[9]

G. W. Brindley and M. Nakahira , J Ceram. Soc . 40, 346 (1957).

G. W. Brindley and M. Nakahira, J. Am. Ceram. Soc. Mi 311 (1959).

G. W. Brindley and D. M. Maroney , J. Am. Ceram. Soc, 4J3, 511 (1960).

J. J. Comer, J. Am. Ceram. Soc. 43 , 378 (1960).

Re ferences

Am. [11

A. Dietzel and N. N. Padurow, Ber.

deut. kerarn. Ges. 21 » 7 (1954).

V. H. Earhart, Ohio State Univ. Eng.

Sta. News J_2, 25 (1940); Ceram.

Abstr. 206 (1940).

R. F. Geller, D. N. Evans and A. S. Creamer, Bur. Standards J. Research

11. 327 (1933).

W, D. Kingery , Introduction to Ceramic s . p. 148, John Wiley & Sons

(New York, i960)

I. M. Lachman and J. 0. Everhart , J. Am. Ceram. Soc. 22» 30 (1956).

[10] S. T. Lundin, Trans. 4th Intern. Ceram. Congr. Florence, p. 383 (1954).

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

S . T . Lund in , Studies on Triaxial

Whiteware Bodies , Almqvist & Viksell (Stockholm, Sweden, 1959).

V. S. MacKenzie and J. V. Smith, Am.

Mineralogist 40, 707 (1955) i ibid

4_L, 405 (1956).

R. Masson, Trans. 8th Intern. Ceram.

Congr. Copenhagen, p. 393 (1962).

J. F. Schairer and N. L. Bowen, Am.

J. Sci. 24j>, 193 (1947).

J. F. Schairer and N. L. Bowen, Am.

J. Sci. 2J52, 681 (1955).

K. Schiiller, Ber. deut. keram. Ges,

38 , pp. 150, 208 and 241 ( 1 96 1

)

G. R. Sheltoh, J. 21, 39 (1948).Am. Ceram. Soc.

H. Stager and H, Studer, Tech. Mitt.

42, 170 (1956).

A. Winterling, Ber. deut. keram.

Ges. J38, 9 ( 1961 ).

MZ'2

FIGURE 1. Electrical insulator porcelain FIGURE 2. Electrical insulator porcelain with extensive quartz grain dissolution with low quartz grain dissolution

(etched 10 sec, 0 °C, 407o HF, collodion (etched 10 sec, 0 °C, 407= HF, collodion replica). replica).

101
FIGURE 3. Vitreous sanitary ware (etched

10 sec, 0 °C, 40% HF, collodion replica).

a

FIGURE 5. Two examples (a and b) of

insulator porcelain (etched 10 sec,

FIGURE 4. Vitreous triaxial whiteware

body fired at 1300 °C (etched 20 min,

50% NaOH, 100 °C, collodion replica).

b

electron micrographs of electrical

0 °C, 40% HF, silica replica).

102
103
3AIJOJ-2SIO!

FIGURE 7. Portion of the phase

diagram for the system

Kg 0-Als 03 -Si02 after Schairer

& Bowen [14,15]. The composition points correspond to, Pl=

total system. P2 = sub-system

clay and feldspar, P3 = metakaolin, P4 = feldspar relicts,

and P5 = clay relicts.

FIGURE 8. Isolated and dispersed

mullite phase of an insulator

porcelain .

FIGURE 9. Stereoscopic views of a part (the large aggregate) of the

mullite phase from a feldspar relict region showing the magnitude

and relative position of the mullite crystals. To the left some smaller, more compact aggregates from clay relicts can be seen.

104
K 1585*10 *C

L 1470 ±10 *C M 985 ±20-0 N 1140 i 20

v start matrix

o melt

K70

Al20,-2Si02 50

FIGURE 10. The change in melt

composition during the quartz

dissolution, when the melt is

saturated with mullite.

FIGURE 11. Quartz grain partly

transformed into cristobalite

(etched 20 min, 50% NaOH,

100 °C, silica replica).

FIGURE 12. Stereoscopic views of closed pores in an unetched fracture

surface (aluminium replica).

105
FIGURE 13. Closed pore with mullite

crystals in an overfired body

(unetched fracture surface,

aluminium replica).

FIGURE 15. Surface structure of a delayed fracture in an electrical

porcelain insulator (aluminium

replica)

FIGURE 14. Pore with crack in an unetched fracture surface (aluminium replica)_

106 * U S GOVERNMENT PRINTING OFFICE : 1964 O - 720-834