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

No twodiamonds have exactly the same composition

and properties,

and any number of classification

schemes

can be devised.

However

only

one classification is universally

accepted.

It is based on the nature

and

amount of impurities contained within the structure

and consists of four

types.

These types, their

origin,

and their effect

on optical and other

properties are summarized

in Table

11.2

(some diamonds

may consist of

more than one type).

Table

11.2.

Classification

of Diamond

Type

Origin

Impurities

la

98% of all natural

App. 0.1 % nitrogen in

diamonds

small aggregates

Includes cl 0 % platelets

Not paramagnetic

lb

Rare in nature (~0.1%)

Nitrogen 0.05 % in lattice

Includes

most high-

Paramagnetic

pressure

synthetic

diamonds

Ila

Rare in nature

Few ppm of nitrogen

Usually clear

Ilb

Extremely rare in nature

Less nitrogen than Ila

Produced

by high-

Becomes

semiconductor

pressure

synthesis

by boron doping

Structure and Properties of Diamond

257

of testing

and

published

data are

still

limited.

These

problems

and

the

uncertainty

about

the

effect

of impurities

mentioned

above

contribute

to the

considerable

spread

in the

reported

values

often

found

in the

literature.

it

is generally

agreed

that

considerable

more

testing

and

evaluation

are

necessary,

particularly

in the

area

of synthetic

diamond.

The

properties

listed

in this

chapter

are

those

of

single-crystal

dia-

mond,

either natural

or synthesized

at high pressure.

4.2

Thermal

Sta biiity

As mentioned

above,

graphite

is the stable

allotrope

of carbon

and

is

one of the most refractory

materials

with

a sublimation

point above

4000

K

at one

atmosphere.

Diamond

has a different

behavior

and

is unstable with

respect

to graphite

with

a negative

free-energy

change

of 2.88

kJ/moi

at

room

temperature

and atmospheric

pressure.

Theoretically

at

least,

diamond

is

not

“forever”;

graphite

would

be

better qualified.

However,

in all fairness,

the

rate of the

diamond-graphite

conversion

is

infinitesimally

small

at

ordinary

temperatures

and,

for

all

practical

purposes,

diamond

is stable,

as

evidenced

by

the

presence

of

natural

diamonds

in some

alluvial

deposits

which

wereformed

over a billion

years ago and have not

changed

since.

The

carbon

phase

diagram,

illustrated

in Fig.

2.20

of Ch. 2, shows

the

relationship

between

these

two

allotropes

of carbon.

The free-energy

change

of the diamond-graphite

transition

decreases

with temperature

to

reach

-10.05

kJ/mol

at approximately

1200°C.

At that

temperature,

the

transition

to graphite

is observable

but still slow;

above

it,

it proceeds

with

a

rapidly

increasing

rate

as

the

temperature

rises.

For

instance,

a 0.1

carat

(0.02

g) octahedral

crystal

is completely

converted

to

graphite

in less

than

three

minutes

at 21 00°C.t4]

The

transformation

diamond-graphite

is also

a function of the environ-

ment.

It becomes

especially

rapid

in the

presence

of

carbide formers

or

carbon

soluble

metals.

For

instance,

in the

presence

of

cobalt,

the

transformation

can occur

as low as 500°C.

However,

in hydrogen

diamond

is stable

up to 2000°C

and

in a high vacuum

up to

1700°C.

The

opposite

transformation,

graphite-diamond,

is reviewed

in Ch. 12,

Sec.

3.3.

Specific

heat,

C,, J/mol:

at 300

K

6.195

at 1800K

24.7

at 3000

K

26.3

Effective

Debye

temperature,

OD:

273-

1100K

1860+

10K

OK

2220

+ 20 K

Thermal conductivity, W/m-K:

at 293

K Type

la

600 - 1000

Type

Ila

2000

- 2100

at 80 K

Type

la

2000

- 4000

Type

Ila

17,000

Linear thermal

expansion, 1c6/K:

at 193

K

0.4

f

0.1

at 293

K

0.8 + 0.1

at400-1200K

1.5 - 4.8

Standard entropy:

at 300

K, J/mol.K

2.428

Standard enthalpy of formation:

at 300

K, J/mol.K

1.884

Structure

and Properties

of Diamond

259

temperature

and approximately

five times

that

of copper.

This

conductivity is

similar

to that of the

graphite

crystal

in the

ab direction

(see Ch. 3, Table

3.6).

Mechanism

of

Thermal

Conductivity.

The

thermal

conductivity

in

diamond

occurs

by latticevibration.

Such

a mechanism

is characterized

by

a flow

of phonons,

unlike

the

thermal

conductivity

in metals

which

occurs

by electron

transportt13)t14t

(see

Ch.

3,

Sec.

4.3,

for

the

mathematical

expression

of thermal

conductivity).

Latticevibration

occurs

in diamond

when

the carbon atoms are excited

by a source

of energy

such

as thermal

energy.

Quantum

physics

dictates

that a discrete

amount

of energy

is required

to set

off vibrations

in a given

system.

This

amount

is equal

to the

frequency

of the

vibration

times

the

Plan&s

constant

(6.6256 x 1O-27ergs).

Carbon

atoms

are

small

and

have

low

mass

and,

in the

diamond

structure,

are tightly

and isotropically

bonded

to each

other.

As a result,

the

quantum

energies

necessary

to make

these

atoms

vibrate

is large,

which

means

that

their

vibrations

occur

mostly

at high

frequencies

with

a maxi-

mum

of approximately

40 x 101* Hz.nl)

Consequently,

at ordinary

tempera-

tures,

few atomic

vibrations

are present

to impede

the

passage

of thermal

waves

and

thermal

conductivity

is unusually

high.

However,

the

flow

of

phonons

in

diamond

is

not

completely

free.

Several

obstacles

impede

it by scattering the phonons

and thus lowering

the

conductivity.tJ3)

These

obstacles

include:

•

Hexagonal

diamond

inclusions

within

the

cubic

structure

and

the

resulting

stacking

faults they

may

create

.

Crystallite

boundaries,

lattice

defects,

and vacancy

sites

.

Other

phonons

(via

umklapp

processes)

.

Point defects

due to 13C carbon

isotopes,

normally

1.l

%

of all carbon

atoms

(See Ch. 2, Sec. 2.1 and Ch. 13, Sec.

3.6)

•

Point defects

due

to

impurities

When few of these obstacles

are present,

diamond

is an

excellent

thermal

conductor.

Effect

of

Impurities

on

Thermal

Conductivity.

Of all the

obstacles

to conductivity

listed

above,

a most

important

is the

presence

of impurities,

especially

substitutional

nitrogen.

The

relationship

between

thermal con-

ductivity

and nitrogen

is shown

in Fig.

11 .g.n5t

Nitrogen

aggregates,

found

Structure and Properties

of Diamond 261

Effect of Temperature on Thermal

Conductivity.

Fig. 11 -10 shows

the effect of temperature

on the thermal

conductivity of several types of

diamond.[13]-[151The conductivity reaches a maximum

at approximately

100 K and then gradually

drops with increasing

temperature. Below 40 K,

several materials such as copper have higher

conductivity.[14]

I

I

I

262 Carbon, Graphite, Diamond, and Fullerenes

5.3

Thermal Expansion

The

mechanism

of

thermal

expansion

in

a

crystal

material was

reviewed

in Ch. 3, Sec. 4.4.

Like

graphite

in the

ab directions,

diamond

is

a strongly

bonded solid

and,

as a result, it has a low thermal

expansion.

At

room temperature,

the coefficient

of thermal

expansion (CTE) is 0.8 ppm.“C

(in

comparison,

copper

is

17 ppm.“C and

graphite

in the

ab

direction

is

slightly negative).

Unlike

graphite,

diamond

has

an isotropic thermal

expansion

which

gradually

increases

with increasing

temperature

as shown

in Table

11.3.

The

specific

heat

of

diamond

is

generally comparable to that of

graphite

and is higher

than

most

metals (see Ch. 3, Sec. 4.3 and Table

3.5).

The specific

heat

of

diamond,

like

that

of all elements, increases

with

temperature

(see

Table

11.3).

It is now generally

accepted

that the term

“optics” encompasses

the

generation, propagation,

and

detection

of electromagnetic

radiations

hav-

ing wavelengths

greaterthanx-rays

and shorterthen

microwaves,

asshown

schematically

in Fig.

11.11.

These

radiations

comprise

the

following

spectra:

. Thevisiblespectrum

which can be detected

and identified

as colors

by the

human

eye.

It extends

from 0.4

to 0.7

Pm.

n The near-infrared

spectrum with wavelengths

immediately

above the

visible

(0.7 - 7 pm)

and the

far

infrared

(71_lm

- -1

mm).

IR radiations

are

a major

source

of heat.

. The

ultraviolet

spectrum

with

wavelengths

immediately

below the

visible

(CO.4 pm).

Most UV

applications are

found

in the

0.19

- 0.4 pm range.

Transmission

Mechanism.

The high transmittance

is related to the

nature and high strength

of the diamond bond. To break these bonds (by

exciting an electron across

the

bandgapl

requires

considerable

energy

since the bandgap is high (5.48

eV at room temperature).

This excitation can be accomplished

by the action of a photon of an

electromagnetic radiation.

The

energy of a photon

is proportional to the

frequency

of the

radiation

and,

as shown in Fig.

11 .l1, this frequency

increases

gradually going from the infrared to the visible

to the ultraviolet

and x-rays. The energy

in the lower-frequency radiations

such as infrared

and visible is too

low to excite

the diamond electrons across the high

bandgap

and,

as

a result,

diamond is capable of transmitting across a

unusually

broad spectral range from the x-ray region to the microwave and

millimeter

wavelengths

and has the widest electromagnetic

bandpass of

any material.

In the case of the visible light, virtually none is absorbed and

essentially

all

is transmitted

or refracted,

giving diamond

its unequalled

brightness.

Absorption

Bands.

Pure diamond (which has never

been found in

nature and has yet to

be

synthesized)

would have only two

intrinsic

absorption bands

as follows:t16)[17)