H.O. Pierson. Handbook of carbon, graphite, diamond and fullerenes. Properties, processing and applications. 1993

Structure

and

Properties

of Diamond

247

The

Raman

scattering

efficiency

for sp2 bonds

is more than

fifty

times

the efficiency

for

sp3 bonds for

graphitic

domains

smaller

than

10 nm.

As

a result,

the

technique

is capable

of detecting

minute

amounts

of graphite

bonds

(such

as may

present

in some

diamond-like carbon). However, it

must

be recognized

that

the

techniques

cannot

readily

define

the

state

of

aggregation

of the

constituents.

Diamond

Characteristics.

It is generally

accepted

that,

for a material

to be recognized

as diamond,

it must

have

the

following

characteristics:

. A crystalline

morphology

visible

by electron

microscopy

. A single-phase

crystalline

structure

detectable

by x-ray

or

electron

diffraction

. A clear

diamond

Raman spectrum

with

a sharp

peak

at

1332 cm

2.2

Atomic

Structure

of Diamond

In Ch. 2, Sec. 3, the

hybridization

of the

carbon

atom

from the

ground

state

to the hybrid

sp3 (or tetragonal)

orbital

state

is described.

It is shown

that

this

hybridization

accounts

for

the

tetrahedral

symmetry

and

the

valence

state

of four

with

four

2sp3

orbitals found

in

the

diamond

atomic

structure.

These

orbitals

are

bonded

to

the

orbitals

of four

other

carbon

atoms

with a strong

covalent

bond

(i.e., the

atoms

share

a pair of electrons)

to form

a regular tetrahedron

with

equal angles

to each

other of 109” 28’, as

shown

in Fig.

11.2

(see

also

Fig.

2.10

of Ch.

2).

Diamond is a relatively

simple substance

in the sense

that

its structure

and

properties

are

essentially

isotropic,

in

contrast

to

the pronounced

anisotropy

of graphite.

However,

unlike

graphite,

it has

several

crystalline

forms and

polytypes.

Cubic

and Hexagonal

Diamond.

Each diamond

tetrahedron

com-

bines with four other tetrahedrato

form strongly-bonded,

three-dimensional

and

entirely

covalent

crystalline

structures.

Diamond

has

two

such

struc-

tures, one with

a cubic

symmetry

(the more

common

and

stable) and one

with

a hexagonal

symmetry

found in nature as the

mineral

lonsdaleite

(see

Sec.

2.5).

Structure

of

Cubic

Diamond.

Cubic

diamond

is

by far

the

more

common

structure and, in order to simplify the terminology,

will

be referred

to as simply “diamond”.

The

covalent

link

between

the

carbon

atoms

of

diamond

is characterized

by asmall

bond

length

(0.154

nm) and a high bond

energy

of 711

kJ/mol

(170 kcal/mol).t*]

Each

diamond

unit cell

has

eight

atoms

located

as follows:

l/8

x 8 at the

corners,

l/2

x 6 at the

faces

and

4

inside

the

unit

cube.

Two

representations

of the structure

are shown

in Fig.

11.3,

(a) and

(b).t21t31

The

cubic

structure

of diamond

can

be visualized

as a stacking

of

puckered

infinite

layers

(the{1

11) planes)

or as atwoface-centered

interpen-

etrating cubic lattices, one with

origin

at O,O,O,and the other

at l/4,1/4,1/4,

with

parallel axes,

as shown

in Fig. 11.3(c).

The

stacking

sequence

of the (111)

planes

is ABCABC,

so that every

third

layer

is identical.

Density

of

Diamond.

With its fourfold

coordinated

tetrahedral

(sp3)

bonds,

the diamond

structure

is isotropic

and,

except

on the (111)

plane,

is

more

compact

than

graphite

(with

its

sp*

anisotropic

structure

and

wide

interlayer

spacing).

Consequently

diamond

has

higher density

than graph-

ite (3.515

g/cm3

vs.

2.26

g/cm3).

Diamond has

the

highest

atom density of any

material

with

a molar

density

of 0.293 g-atom/cm 3.

As

a result,

diamond

is the stiffest,

hardest

and least compressible

of all substances.

In comparison,

the

molar

density

of graphite is 0.188

g-atom/cm

3.

The atomic and crystal structure

data of

diamond

are summarized in Table

11 .l .I41Also included

in the table

are the

data for

hexagonal

diamond (see

Sec. 2.5).

(100) Plane

(110) Plane

Cubic {loo}

Dodecahedron (110)

Structure

and

Properties

of Diamond

253

The cubic diamond

nucleus

is slightly

more stable than the hexagonal

with an energy

difference

between

the

two

of only 0.1 - 0.2 eV per carbon

atom.

Because of this

small

energy

difference,

the

growth

mechanism

leading

to the

hexagonal

structure

instead

of cubic can readily occur. The

inclusion

of hexagonal

diamond

in a cubic

diamond

structure

is equivalent

to

having

a

stacking

fault

at

every

two-atom

layer

and

is

generally

detrimental

to

optical

and

other

properties.

Hexagonal

Diamond

Occurrence.

The

formation

of hexagonal

diamond

is usually favored where

high

carbon

supersaturation

is prevalent,

a condition

commonly found during

CVD

synthesis

and

occasionally

during

high-pressure

synthesi@lt9)

(see Ch. 12). Natural

diamond

grows at much

lower

supersaturation

levels

and consequently

natural

hexagonal

diamond

is rarely

found.tlO)

The

natural

hexagonal

diamond

is known

as the mineral

lonsdaleite.

Some meteoriies

contain

diamond

such

as the

one

found

in Canyon

Diablo in Arizona.

The

diamond

is in the form

of polycrystalline

compacts

made

up of submicron

crystals.

These

crystals

are

mostly

cubic

although

the

hexagonal

form is also

found.

6H

Diamond.

Recent

investigations

have

revealed

the existence

of

another

intermediate

diamond

polytype

known

as

6H

diamond.t5)

This

material

is believed

to belong

to a hypothetical

series

of diamond

typeswith

structures

intermediate

between

hexagonal

and cubic.

The membersofthis

series

are

tentatively

identified

as

4H,

6H, 8H,

10H.

The

series

would

include

hexagonal

(2H) diamond

on one end and cubic

(3C) diamond

on the

other

(the digit

indicates

the number

of layers).

The existence

of 4H, 8H and

1OH diamonds

has yet to be confirmed.

The

6H

structure

has

a

mixed

six-layer

hexagonal/cubic

stacking

sequence

AA’C’B’BC,

shown

schematically

in Fig.1 1.7.p)

It may exist

in

CVD

diamond.

The properties of diamond

are susceptible

to impurities and the presence

of even

a minute

amount of a foreign element

such

as nitrogen can

cause

drastic

changes.

It is therefore

important to

know

the composition

of the

Structure

and Properties

of Diamond

255

material

being tested

as

accurately

as possible

in order

to obtain

a true

evaluation

of the

measured

properties.

Types of Impurities.

Diamond,

synthetic

or natural,

is never completely

free of impurities.

These

impurities

are

divided into two

different

types:

1.

Lattice

impurities

which

consist

of

foreign

elements

incorporated

in the

lattice,

the

foreign

atom replacing

a

carbon

atom.

2.

Inclusions,

which

are

separate

particles

and

not

part

of

the

lattice,

usually

consist

of

silicates

of

aluminum,

magnesium,

or calcium

such

as olivine.f”j

The two major lattice impurities

found

in diamond

are nitrogen

and

boron.

These

two elements

are the neighbors

of carbon in the periodic

table.

They

have small

atomic

radii

and

fit

readily

within

the

diamond

structure.

Other

elemental

impurities

may also

be present

but only

in extremely

small

amounts

and

their effect

on the

properties

of the

material

is still

uncertain

but

probably

minor.t12]

Nitrogen.

Nitrogen

impurity

in diamond

is detected

and characterized

by

IR absorption

and

paramagnetic

resonance.

The majority of nitrogen

atoms

within

the

diamond

structure

are

arranged

in pairs as shown

in Fig.

11.8.[“] Isolated nitrogen atoms are

rarer.

Nitrogen

platelets

are

also

present and can be represented

as a quasi-planar

structure

within the cube

(100)

plane of the diamond

crystal.

Their

exact

form is still controversial.