Moulson A.J., Herbert J.M. Electroceramics: Materials, Properties, Applications

Подождите немного. Документ загружается.

growth process must therefore be slow and so requires a precise control over

conditions over prolonged periods.

The formation of a solid phase at the freezing point of a liquid only occurs at

the surface of existing solids, e.g. dust particles in water at 0 8C. This process is

known as heterogeneous nucleation. Liquids free from solid particles can be

cooled to some extent below their melting points. Such a supercooled liquid

crystallizes through the spontaneous formation of ordered regions closely similar

to the solid in structure, and the growth of these nuclei leads to the rapid

formation of a large number of randomly oriented crystals. Single-crystal growth

can be obtained by providing nuclei in the form of a small single crystal (a ‘seed’)

and ensuring that the conditions conﬁne growth to the immediate vicinity of the

seed.

Where a seed crystal is not available or, by reason of the growth method,

cannot be utilized, advantage can be taken of the tendency for crystals to grow

more rapidly in one crystallographic direction than in others, as for instance in

the Bridgman–Stockbarger method outlined later. In the same way, if a thin

ceramic rod having the required stoichiometric composition is held vertically and

a small region near one end is fused by means of a laser beam and the molten

region is moved towards the other end of the rod, those crystals that grow fastest

along the axis of the rod will enlarge at the expense of those growing at angles to

it. By passing the molten zone up and down the crystal several times relatively

large single-crystal regions can be obtained. At the same time there will be a

zone-reﬁning eﬀect through which the impurities become concentrated at the

ends of the rod, thus leading to the growth of more perfect crystals.

Whilst every material presents its own problems in crystal growth, which must

be solved experimentally, there is a general thermodynamic principle that gives

an indication of how diﬃcult the process is likely to be. Since crystal growth

takes place reversibly, the Gibbs energy G must be constant and so, under

isothermal conditions,

DG ¼ 0 ¼ D H  TDS ð3:1Þ

where H is the enthalpy or heat content of the system, S is its entropy and T is

the thermodynamic temperature. Therefore

DS ¼

ð3:2Þ

If we take DH ¼ L

, where L

is the latent heat per atom, Jackson’s

dimensionless parameter a is deﬁned by

a ¼

ð3:3Þ

where k is Boltzmann’s constant and T

is the temperature of the change of

state. a represents the decrease in entropy on going from the disordered structure

122 PROCESSING OF CERAMICS

TEAMFLY

Team-Fly

in the liquid state to the ordered lattice structure of the solid state. Some values

of a are given in Table 3.2.

For a 5 2 crystals grow without facets and their shape is determined by the

isotherms in the melt. Many metals, e.g. iron and lead, are in this category. For

2 5 a 5 10, which covers the bulk of materials, facetting may occur during

growth as with germanium and silicon. For a 4 10 crystals nucleate readily so

that it is diﬃcult to avoid a polycrystalline structure. The value of a for the

growth of ice from water vapour at 0 8C is 20, which accounts for the low-density

polycrystalline character of snow. In contrast, a ¼ 2:7 for the growth of ice from

liquid water, and a dense material containing large crystals is readily formed.

An important consideration in the case of oxides containing several cations is

whether the melting point is congruent or incongruent. In the latter case crystals

cannot be grown from stoichiometric melts and a method must be found for

growth at a temperature at which the required compound is stable. A similar

diﬃculty occurs when the structure of the crystals formed at the melting point

diﬀers from that required. For example, silica yields cristobalite on solidifying at

1720 8C; cristobalite transforms into tridymite below 1470 8C and tridymite

transforms to b-quartz below 867 8C, while b-quartz transforms to a-quartz

below 573 8C. a-quartz must therefore be grown below 573 8C, as explained

below.

The following methods have been used to grow crystals of oxides.

1. From an aqueous solution by cooling.

2. From solution in an oxide or ﬂuoride ﬂux by cooling.

3. From the liquid phase by cooling:

(a) by ﬁrst freezing at the lowest point of a melt;

(b) by ﬁrst freezing at the upper surface of a melt;

THE GROWTH OF SINGLE CRYSTALS 123

Table 3.2 Values of Jackson’s parameter a

Substance

Change of

state

Temperature T

of change

of state

Latent heat

=kJ mol

1

at T

a ¼

Si Liquid–solid 1680 46.4 3.3

Ge Liquid–solid 1230 31.8 3.1

Fe Liquid–solid 1810 15.4 1.02

Pb Liquid–solid 601 4.77 0.96

O Liquid–solid 273 6.03 2.7

O Vapour–solid 273 45 20

4. (a) From the liquid phase kept at constant temperature by dipping a seed in

the surface and then withdrawing it into a cooler zone;

(b) from the liquid phase by deposition on a substrate of diﬀering

composition.

5. From the vapour phase by chemical reaction close to the surface of a seed

crystal.

These methods are illustrated by the following examples.

1. Quartz is grown from an alkaline solution in water under a pressure of about

150 MPa (1500 atm). Pure mineral quartz fragments are placed at the bottom

of a tall cylindrical autoclave that is 80% ﬁlled with either a 2.2% solution of

NaOH or a 5% solution of Na

. Seed crystals are held in wire frames near

the top of the autoclave. Because the base of the autoclave is kept at 400 8C

and the top is maintained at a temperature some 40 8C cooler, quartz dissolves

at the bottom of the vessel and is deposited on the seeds at the top. Crystals

weighing over a kilogram can be grown in a few weeks (Fig. 3.8). This

hydrothermal method is also of value for such materials as zinc oxide which

have high vapour pressures at their melting points.

2. Crystals of many compounds, of suﬃcient size for scientiﬁc purposes, can be

obtained by cooling a solution of the required compound in a suitable ﬂux.

BaTiO

crystals have been prepared by using a mixture of KF with 30 wt%

BaTiO

and 0.2 wt% Fe

[15]. A temperature of 1150–1200 8Cis

maintained for 8 h, and the mixture is then cooled slowly to 900 8C when

the ﬂux is poured oﬀ and the crystals are allowed to cool in the furnace to

room temperature. The crystals form as butterﬂy twins, i.e. as pairs of

triangular plates joined at one edge with an angle of about 608 between them.

The iron assists the formation of ﬂat plates of relatively large area that are

convenient for the investigation of the ferroelectric properties of BaTiO

small amount of iron, as Fe

3þ

, is incorporated in the BaTiO

lattice on Ti

4þ

sites. The charge diﬀerence is compensated by the replacement of an

equivalent number of O

2

ions by F



ions. This result is typical of ﬂux-

growth methods which frequently result in the incorporation of a small

proportion of the solvent in the crystal lattice.

Single crystal rods of a variety of compositions, including complex garnets

(see Section 9.5.4) can be grown by the ‘ﬂoating zone’ method. For example,

two sintered Bi-substituted garnet (BIG) rods of the chosen composition are

placed end to end with a single crystal ‘seed’ of the same composition

sandwiched between them. Halogen lamps are focused onto the join area as

the rods are rotated and provide suﬃcient heat to form a molten zone. If the

molten zone is moved into the sintered rod in a suitably controlled way then a

124 PROCESSING OF CERAMICS

THE GROWTH OF SINGLE CRYSTALS 125

Fig. 3.8 Hydrothermally grown quartz crystals.

high quality single crystal can be grown. The whole operation is carried out in

an oxygen atmosphere to ensure the iron is in the fully oxidized state. Very

high quality crystals of size 12 mm diameter 120 mm long suited to magneto-

optical applications can be grown.

In recent years strong interest has been shown in single crystals of the

relaxor ferroelectrics for actuator applications (see Section 6.4.3). Members of

this family of electroceramics exhibit exceptionally large electric ﬁeld-

induced strains. One such material has the composition approximately

0.9Pb(Zn

1/3

2/3

-0.1PbTiO

abbreviated 0.9PZN–0.1PT. The starting

materials are Pb

, ZnO, Nb

and TiO

. The constituents, in amounts

to give the required overall composition, are well mixed and then heated with

an excess of Pb

which serves as the ﬂux, in a sealed platinum crucible to

approximately 1150 8C. The melt is then slowly cooled at approximately

5 8Ch

1

when crystals with dimensions up to 20 mm grow. When the crucible

is cold the crystals are extracted with the help of hot nitric acid.

In order to form manganese zinc ferrite crystals using the Bridgman–

Stockbarger method (Fig. 3.9) a charge of the mixed oxides is melted in a Pt–Rh

crucible and kept just above its solidiﬁcation temperature. The furnace is

designed such that there is a sharp drop in temperature just below the bottom tip

of the crucible in its initial position. The crucible is lowered so that the tip enters

the colder zone causing the nucleation of crystals. The crystals grow fastest in

particular crystallographic directions and those growing at angles greater than

half the cone angle terminate at the walls of the cone; only those crystals

oriented so that growth is favoured in the axial direction persist into the bulk

of the charge as the crucible is lowered into the cooler zone. As a result the

upper part of the crucible ﬁnally contains either a single crystal or a few large

crystals.

There are a number of problems associated with growing manganese zinc

ferrite single crystals by the process outlined above. Temperatures close to

1800 8C are required to melt the oxides, and then there is rapid evaporation of

zinc and loss of oxygen from the Fe

resulting in the formation of FeO. These

diﬃculties have been largely overcome through the development of a high-

pressure version of the apparatus. The crucible, now in a sealed container so that

an oxygen pressure of up to 2 MPa (20 atm) can be maintained over the melt, is

heated indirectly by a surrounding thick cylindrical Pt–Rh susceptor. The

thickness of the inductively heated susceptor is suﬃcient to shield the melt from

the radiofrequency ﬁeld which would otherwise produce eddy current heating in

the melt, resulting in undesirable convective agitation.

A further problem arises owing to diﬀerences in composition between the

liquid and solid phases. The cation distribution can be optimized and the excess

FeO oxidized by annealing the crystal in a suitable atmosphere after cutting the

required shapes.

126 PROCESSING OF CERAMICS

Pure cubic BaTiO

cannot be grown from a melt of that composition because,

as shown in Fig. 5.41, the hexagonal form is in equilibrium with the liquid at the

solidiﬁcation temperature (1618 8C). It can, however, be grown from a

composition containing 35 mol.% BaO, 65 mol.% TiO

, which solidiﬁes below

1460 8C, the temperature below which the cubic form is stable. The melt is held

just above its solidiﬁcation point, a seed crystal is dipped into its surface and the

melt is then cooled at between 0.1 and 0.5 8Ch

1

. The seed crystal is attached to a

platinum stirrer which is rotated during growth so that the liquid near the crystal

does not become depleted in barium. Only a fraction of the melt can be obtained

as single-crystal BaTiO

since the whole of it solidiﬁes, forming a mixture of

cubic BaTiO

and Ba

, when the BaO content falls to about 32 mol.%.

The Verneuil ﬂame-fusion method illustrated in Fig. 3.10 is a well-established

but relatively crude method for growing refractory oxide single crystals,

particularly sapphire and ruby. In this case alumina powder is fed at a controlled

rate down a tube at the end of which it is melted by an oxyhydrogen ﬂame; it

then drips down into a shallow pool of liquid on top of the seed crystal. As the

crystal grows, it is lowered into the annealing zone. This method suﬀers from the

disadvantage of poor control over the growth environment, and the quality of

crystal produced is inferior to that obtained by crystal pulling. It is adequate,

however, for jewelled bearings.

Crystal pulling is one of the most widely exploited and successful processes,

and is generally termed the Czochralski method. Silicon, gallium arsenide,

alumina, lithium niobate, lithium tantalate and gadolinium gallium garnet are

all grown on a large scale by variants of this process which is applicable to

most materials that melt congruently. The melt is kept at a temperature just

THE GROWTH OF SINGLE CRYSTALS 127

Fig. 3.9 The Bridgman–Stockbarger technique (MP, melting point).

above its freezing point and a seed crystal, ﬁrmly ﬁxed to a rotating tube, is

lowered into the surface and then slowly withdrawn (Fig. 3.11). Air can be

blown down the tube to control the extraction of heat necessary to the growth

process. The crystal diameter can be varied by changing the rate of withdrawal.

128 PROCESSING OF CERAMICS

Fig. 3.10 The Verneuil technique.

Fig. 3.11 The Czochralski technique for pulling crystals.

Flaws and misoriented crystals can be eliminated by ﬁrst enlarging and then

diminishing the crystal diameter; misoriented regions are thereby terminated at

the crystal surface in much the same way as in a Stockbarger–Bridgman

crucible. In favourable cases nearly 90% of a melt can be obtained in single-

crystal form.

Smaller crystals can be grown from solutions by a similar method; for

example, a mixture of barium and strontium titanates containing a 28% excess of

TiO

can be melted at 1500 8C and crystals of (Ba, Sr)TiO

withdrawn on a seed.

The cubic crystals are stoichiometric in their ratio of SrþBa to Ti but contain a

substantially greater proportion of strontium than the liquid phase. Provided

that the mass of the crystals constitutes less than 1% of that of the melt, they

have a highly homogeneous composition despite the inevitable change in

composition of the liquid phase as the crystal forms.

In some applications only a thin ﬁlm of single-crystal material is needed on a

substrate that diﬀers in composition. In this case advantage can be taken of the

possibility of epitaxial deposition. A seed crystal of similar crystal structure but

diﬀering composition from the required ﬁlm can be used in place of a seed of

identical composition. The method is of particular value when the deposit has a

complex composition and a suitable substrate material is available. The

magnetic garnets that were used in the now obsolete ‘bubble’ memory stores

with complex compositions such as (Y

0:9

0:5

1:1

0:5

)(Fe

2:5

0:5

were grown by liquid phase epitaxy (LPE) on gadolinium gallium garnet

substrates.

The apparatus for LPE growth of garnet ﬁlm is shown schematically in

Fig. 3.12. The melt composition is typically PbO–B

in a 50:1 ratio by weight

to which suﬃcient garnet constituent oxides are added to form a saturated

solution between 950 and 1000 8C. A set of circular substrates is held in a

platinum holder above the solution which is attached to the rotatable spindle.

The melt is allowed to cool a few degrees so that it becomes supersaturated and

the substrates are then lowered into it and rotated for a suﬃcient time (some

minutes) for a ﬁlm of a garnet of the required thickness to grow. They are then

raised from the melt and spun rapidly to remove the excess liquid. The thickness

for bubble memories was usually about 4 mm, though ﬁlms of thickness up to

15 mm can be grown.

The growth of epitaxial layers from the vapour phase has been developed

extensively for III–V compounds for use in semiconductor and electro-optical

devices. The method most applicable to oxide systems is metal–organic chemical

vapour phase deposition (MOCVD). Metals form a wide range of volatile

organic compounds such as lead tetraethyl, (Pb(C

)

), silicon tetraethoxide

(Si(OC

)

) and titanium isopropoxide (Ti(C

), and these are readily

converted to oxide by reaction with oxygen or water and by thermal

decomposition. Mixtures of such compounds in vapour form can be reacted in

close proximity to heated substrates to form oxide deposits that interact to form

THE GROWTH OF SINGLE CRYSTALS 129

titanates, zirconates etc. Polycrystalline layers may be adequate for some

purposes, but with suitable substrates single-crystal layers are possible.

Problems

1. Estimate the density of a compact of uniformly close-packed alumina powder,

assuming a mean particle diameter of 25 mm. What would the density be if the close-

packed particles have a mean diameter of 10 mm? Estimate the compact density if

25 wt% of the powder has a small enough particle diameter for it to occupy the

interstices in the close-packed larger fraction (crystal density of Al

, 4000 kg m

3

[Answers: 2960 kg m

3

; 2960 kg m

3

; 3730 kg m

3

2. A sample of alumina powder has a mean ‘particle’ diameter of 25 mm. What is the

apparent speciﬁc surface area (SSA) of the powder? If each ‘particle’ is in reality an

agglomerate of ultimate particles of diameter 0.5 mm, estimate (i) the number of

ultimate particles per agglomerate and (ii) the true SSA of the powder. [Answers:

0.06 mg

1

;  10

;3m

1

3. A colloid in suspension in an electrolyte acquires a surface charge and an ‘atmosphere’

of oppositely charged ions. An inner part of the atmosphere moves with the colloid

130 PROCESSING OF CERAMICS

Fig. 3.12 Schematic diagram of a furnace for LPE growth of magnetic garnet ﬁlms.

and, together with it, constitutes an ‘electrokinetic unit’. If the net charge on the unit is

Q, and assuming that Stokes’ law applies, derive the equation

u ¼

4ez

where u is the electrophoretic mobility, e is the eﬀective permittivity of the electrolyte

in the immediate vicinity of the colloid, z is the zeta potential and Z is the viscosity of

the liquid. Write a brief account of the signiﬁcance of the zeta potential in determining

the stability of casting slips. (see [a], or similar)

4. The density of an aqueous alumina slip is 2.5 kg dm

3

. Calculate the concentration of

dry alumina in the slip on (i) a weight basis and (ii) a volume basis. [Answers: 80 wt%;

50 vol.%]

5. A pore-free polycrystalline solid contains two phases, A of density 4000 kg m

3

and B

of density 3000 kg m

3

. Calculate the density of the solid if it contains (i) 60 wt% of

phase A and (ii) 60 vol.% of phase A. [Answers: 3529 kg m

3

; 3600 kg m

3

]

6. As part of the characterization of an electrical porcelain the following weighings were

made at 25 8C using a balance which was accurate to the third decimal place:

single-piece sample of ‘body’ 15.234 g

sample saturated with water 15.408 g

saturated sample suspended in water 8.948 g

speciﬁc gravity bottle 22.432 g

bottle þ sample of ﬁnely ground dry ‘body’ 27.362 g

bottle þ powder þ water 75.379 g

bottle þ water 72.429 g

Calculate (i) the true density of the ‘body’, (ii) the bulk density of the ‘body’, (iii) the

open porosity and (iv) the total porosity (density of water at 25 8C, 997 kg m

3

[Answers: 2.482 Mg m

3

; 2.351 Mg m

3

; 2.7%; 5.3%]

7. Assuming a reasonable value for the surface energy of an oxide estimate the ‘negative

pressure’ tending to close spherical pores of radius (i) 1 mm and (ii) 0.01 mm during

sintering. Express your answer in megapascals and ‘atmospheres’. [Answers: 2 MPa

( 20 atm); 200 MPa (2000 atm)]

8. Compounds A and B interdiﬀuse a distance of approximately 1 mm in 1 h at 1000 8C. If

the activation energy for the rate-determining step is 3:2  10

19

J, calculate the

interdiﬀusion distance for a 10 h anneal at 1600 8C assuming the same diﬀusion

mechanism. [Answer: 58 mm]

9. A circular hole in an alumina plate at 20 8C is 1 cm in diameter. Calculate the diameter

at 1000 8C. If the density of alumina at 20 8C is 3980 kg m

3

, calculate the density at

1000 8C. Mean coeﬃcient of linear expansion over the temperature range 20–1000 8C

is 8.0 MK

1

. [Answer: 1.0078 cm; 3886 kg m

3

]

PROBLEMS 131