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

36	Carbon,	Graphite,	Diamond,		and	Fullerenes
	In an sp*	structure	such as	graphite,		the delocalized			electrons	can
move	readily from one side of the			plane layer			to the	other but cannot		easily
move	from one	layer to another.		As a result,			graphite is anisotropic.			The
sp*-hybridized		structure	of graphite		will be reviewed			in more	detail in Ch. 3,
Sec.	1.2.

4.3The Digonal-sp Orbital and the sp Bond

The

sp orbital

(known

as a digonal

orbital) is a merger

of an s and

a p

orbital

which

consists

of two

lobes, one

large

and one

small,

as

illustrated

in Fig. 2.18. An sp bond consists

of two sp orbitals

which,

because

of mutual

repulsion,

form an

angle

of

180” and,

consequently,

the

sp

molecule

is

linear.

The

bond, like

all overlap

bonds,

is a sigma

(a) bond

and has high

strength.

The

sp orbitals account

for two of the electrons

of the carbon atom.

The othertwovalence

electrons

are free,

delocalized

pi (n) orbital

electrons

which are available

to form

subsidiary

pi (n) bonds

in a manner

similar to the

sp* hybridization,

Examples

of

molecules

having

sp bonds

are the

gas

acetylene,

HCGH,

and

the carbynes,

(GC),,

which

are

cross-linked

linear-chain

carbon

polytypes,

usually

unstable.t14t

2s Orbital

2P Orbital

SP (diagonal) orbitals showing overlap (sigma) bond

Figure 2.18.. Formation of the sp hybrid orbital and sp sigma bond.

The Element Carbon

37

4.4

The Carbon-Hydrogen Bond

The

carbon-hydrogen

bond

plays as important

part in the mechanism

of pyrolysis

of

carbon

compounds

and in the

formation

of graphite

and

diamond

(the pyrolysis

process

is reviewed

in Ch.

4).

The

energy

and length

of the carbon-hydrogen

bond

are related

to the

type

of hybridization of the

carbon

atom. The

hybridization

can be sp3, sp2

or sp as shown

in Table

2.8.i5)

Table 2.8.

Properties

of the Carbon-Hydrogen

Bond and

Effect

of Hybridization

Approximate

Hybrid

bond

Bond

bond energy*

length

Molecule

type

(kJ/mole)

(nm)

CH

radical

P

347

0.1120

CH,

(methane)

sp3

434

0.1094

C,H,

(ethylene)

sp2

442

0.1079

C,H,

(acetylene)

sp

506

0.1057

*Energy required to break one mole of bonds (Avogadro’s number)

5.0CARBON VAPOR MOLECULES

At

high

temperature,

carbon

vaporizes

to form

a gas.

This

gas

is a

mixture of single carbon atoms

and diatomicand

polyafomicmolecules,

that

is, molecules

containing

two, three, four, or more carbon

atoms.

These

gaseous

constituents

are

usually

designated

as C,,

C,, C,,

etc.

The understanding

of the

composition

and

behavior

of these

carbon

vapors,

the

accurate

measurement

of

their

heat

of formation,

and

the

precise

determination

of

their

ratio

are

essential

to

calculate the

heat of

formation

of organic

compounds,

i.e., the

energies

of all

bonds involving

carbon.

38

Carbon, Graphite,

Diamond,

and

Fullerenes

The

vaporization

of carbon

is a major

factor

in the

ablation

of carbon.

This

ablation

is

the

basic

phenomena

that controls

the

performance

of

rocket-nozzle

throats,

reentry

nose

cones

and

other

components

exposed

to extremely

high

temperatures

(see Ch. 9). The

rate of ablation

is related

to the

composition

of the

carbon

vapor

formed during

ablation

and to the

heat

of formation

of the various

carbon-vapor

species

and their

evaporation

coefficient.

Recent

and

accurate

mass-spectrographic

measurements

of

the

energy required

to vaporize graphite

to the monoatomic

gas C, give

avalue

of 710.51

kJ mot’

(171.51

kcal

mot ’ ). [15j Values

for the

heat

of formation

of the

molecular

vapor

species

of carbon

shown

in Table

2.9.

Table

2.9. Heat

of Formation

of Carbon

Moleculest15)

Heat

of Formation

Molecule

(kJ/mole)

c2

823

c3

786

c4

1005

c5

1004

C6

1199

c7

1199

cl3

1417

CQ

1396

C 10

1642

C,,

C,,

and

particularly

C,

are the

dominant

species

in the

equilibrium

vapor

in the temperature

range

of 2400

- 2700

K as shown

in the Arrhenius

plot

of the

partial pressure

of

these

species

in

Fig.

2.19.t15jt16)

The

contribution

of Cs and larger

molecules

to the

vapor

pressure

is small

and

generally

of

no

practical

import.

The

general

structure

of these

carbon

molecule

is believed

to consist

of double

carbon

bonds,

:C=C::::C=C:

(the

so-called cumulene structure)

which have

delocalized

bondings

and

an

axial

symmetry.

Larger

molecules,

i.e., thefullerenes,

are reviewed

below.

The Element Carbon

100

10

1

10-l

1o-2

g 10-3

z 10-d

2.f

3

g 10-S

2!

e 10-6

5; e

a 10-7

>

1O-8

1o-9

1O-10

10-l’

10-12	2000	2500	3000	3500	4000	4500	5000
1500

Temperature (k)

* Pressure observed if vapor is C, only

Figure 2.19. Vapor pressure of carbon species.

4-O Carbon, Graphite, Diamond, and Fullerenes

6.0THE CARBON ALLOTROPES

6.1The Carbon Phase Diagram

The carbon			phase	diagram		is shown	in Fig. 2.20.t6) Another		expression
of the T-P phase			diagram,		showing the		calculated total vapor		pressure		of
carbon,	is shown		in Fig. 3.7 of Ch. 3.
Carbon		vaporizes		at 4800		K at a pressure		of 1000 atmospheres,		which
is the	area	where diamond			is	stable.	The	high-pressure conversion			of
diamond from graphite				occurs at temperatures				of approximately	3000	Kand
pressures above			125 kbars		(in the absence of catalyst) and will				be reviewed
in Ch.	12.

I I I I I

100 -

1000

2000

3000

4000

5000

Temperature (k)

Figure 2.20. Carbon phase diagram.

The Element Carbon

41

6.2Allotropic Forms

In the

preceding

sections,

the

various

ways

that

carbon

atoms

bond

together

to form solids

were

reviewed.

These

solids are the

allotropes

(or

polymorphs)

of

carbon,

that

is,

they

have

the

same

building

block-the

element

carbon-but

with

different

atomic

hybrid

configurations:

sp3

(tet-

ragonal),

sp2 (trigonal)

or sp

(digonal).

These

allotropic

solids

can

be classified

into

three

major

categories:

(i) the

sp2

structures

which

include

graphite,

the

graphitic

materials,

amorphous

carbon,

and

other

carbon

materials

(all reviewed

in Ch. 3),

(ii)

the sp3 structures

which

include

diamond

and

lonsdaleite

(a form

detected

in meteorites),

reviewed

in Ch. 11,

and

(iii) the

Fullerenes

(see Ch.

15).

These

allotropes

are sometimes

found

in combination

such

as some

diamond-like

carbon (DLC)

materials

produced

by low-pressure

synthesis,

which

are actually

mixtures

of microcrystalline

diamond

and

graphite

(see

Ch. 14).

Recent

investigations

have

revealed

the

existence

of

a

series

of

diamond

polytypes

such

as the 6-H hexagonal

diamond.

The

structure

and

properties

of these

polytypes

are

reviewed

in

Ch. 11 .t171t1~ Also

under

investigation

is

a hypothetical

phase

of carbon

based

on a three-dimen-

sional

network

but

with

sp2

bonds.

This phase could be harder than

diamond,

at least

in theory. tlQj A carbon phase

diagram

incorporating

these

new polytypes

has

yet to be devised.

6.3The Fullerene Carbon Molecules

The

recently discovered

family of

fullerene

carbon

molecules

are

considered

another

major

allotropic

form

of carbon

that

combines both

sp2

and

sp3 bonds.

These

molecules

are still in the early

stages

of investigation

and

it will

be

some

time

before

practical applications

are found.

The

fullerenes

are

reviewed

in

Ch. 15.

42 Carbon, Graphite, Diamond, and Fullerenes

REFERENCES

1.Cram, D. J. and Hammond, G. S., Organic Chemistry, McGraw-Hill Book Co., New York (1964)

2.Jenkins, G. M. and Kawamura, K., Polymeric Carbons, Cambridge

University Press, Cambridge, UK (1976)

3.

Wehr,

M. Ft., Richards,

J. A.,

Jr.

and

Adair, T. W.,

Ill,

Physics ofthe

Atom, Addison-Wesley

Publishing

Co., Reading,

MA

(1978)

4.

Van

Vlack,

L. H., Elements of Materials

Science

and

Engineering,

4th

ed.,

Addison-Wesley Publishing

Co.,

Reading,

MA

(1980)

5.

Eggers,

D. F., Gregory,

N. W.,

Halsey,

G. D., Jr. and

Rabinovitch,

B.

S.,

Physical

Chemistry,

John

Wiley & Sons, New

York (1964)

6.Cotton, F. A. and Wilkinson, G., Advanced inorganic Chemistry,

Interscience Publishers, New York (1972)

7. Handbook of Chemistry and Physics, 65th ed., CRC Press, Boca Raton, FL (1985)

8.Press, F. and Siever R., Earth, W.H. Freeman & Co., San Francisco (1974)

9. Asimov, A., Understanding Physics, Vol. 3, Dorset Press (1988)

10.Ceramic Bull., 69(10):1639 (1990)

11.

Krauskopf,

K.

B., introduction

to Geochemistry,

McGraw-Hill

Book

Co., New

York

(1967)

12.

Huheey,

J. E.,

Inorganic

Chemistry,

3rd. ed., Harper

& Row,

New

York (1983)

13.

March, J., Advanced

inorganic

Chemistry,

John

Wiley

& Sons,

New

York (1985)

14.

Korshak,

V. V., et al,

Carbon,

25(6):735-738

(1987)

15.

Palmer,

H. B. and Shelef,

M.,

Chemistry and Physics

of Carbon, (P.

L. Walker,

Jr.,

ed.), Vol.4, Marcel Dekker, New York (1968)

16.

Mantell,

C. L.,

Carbon and Graphite

Handbook,

Interscience,

New

York (1968)

17.

Spear,

K. E.,

Phelps,

A. W.,

and

White,

W.

B., J.

Mater.

Res.,

5(1 I):2271

-85

(Nov. 1990)

18.Bundy, F. P. and Kasper, J. S., J. ofChem. Physics, 46(9):3437-3446

(1967)

19. Tamor, M. A. and Hass, K. C., J. Mater. Res., Vol. 5(11):2273-6 (Nov.

1990)

3

Graphite Structure and Properties

1.0THE STRUCTURE OF GRAPHITE

1.l

General Considerations

and Terminology

The

origin

of the

word

“graphite” is the

Greek word

“graphein” which

means

“towrite”.

Indeed,

graphite

has been

used

to write

(and draw) since

the dawn

of history

and the first pencils

were manufactured

in England

in the

15th century.

In the 18th century,

it was

demonstrated

that

graphite

actually

is an

allotrope

of carbon.

Graphite

is remarkable

for

the

large variety

of materials

that

can be

produced

from its basic form such as extremely

strong

fibers,

easily

sheared

lubricants,

gas-tight

barriers,

and gas adsorbers.

All these

diverse

materials

have

one

characteristic

in common:

they are all

built

upon

the trigonal

sp*

bonding

of carbon

atoms.

Strictly

speaking,

the

term

“graphite”

by

itself

describes

an

ideal

material

with

a

perfect

graphite

structure

and

no

defects

whatsoever.

However,

it is also

used

commonly,

albeit incorrectly,

to describe

graphitic

materials.

These

materials

are either

“graphitic carbons”,

that

is, materials

consisting

of

carbon

with

the

graphite

structure,

but with

a number

of

structural

defects,

or”non-graphitic

carbons”,

that

is, materials

consisting

of

carbon

atoms

with

the

planar hexagonal

networks

of the graphite

structure,

but lacking the

crystallographic

order

in

the

c

direction.t’t

This

is

a

fundamental

difference

and these

two

groups

of

materials

are

distinct

in

many

respects,

with

distinct

properties

and

different

applications.

43

44	Carbon,		Graphite,		Diamond,			and Fullerenes
As		a reminder		and	as mentioned			in Ch. 1, the term “carbon” by			itself
should	describe		the element			and	nothing		else.	To describe a material,	it is
coupled		with	a qualifier,			such	as	“carbon		black,” “activated carbon,”
“vitreous carbon,”				“amorphous carbon,”					and others.

1.2Structure of the Graphite Crystal

Graphite		is composed		of series of stacked			parallel	layer	planes shown
schematically		in Fig. 3.1, with the trigonal				sp*	bonding	described		in Ch. 2,
Sec. 4.0.	In Fig.		3.1 (and	subsequent	figures		of the carbon		structure), the
circles showing		the position		of the carbon		atoms do not represent				the actual
size of the	atom.		Each atom, in fact,		contacts		its neighbors.

p atoms (in open circles) have no direct neighbors

In adjacent planes

A Plane

B Plane

0

a atoms (in full circles) have neighbors directly above and below In adjacent planes

\

e

A Plane

Figure3.1. CrystalstructureofgraphiteshowingABABstackingsequenceand	unit
cell.

Graphite

Structure

and

Properties

45

Within

each

layer

plane,

the

carbon

atom

is

bonded

to

three others,

forming

a series

of continuous

hexagons

in what

can

be considered

as an

essentially

infinite

two-dimensional

molecule.

The

bond

is covalent

(sigma)

and

has a short

length

(0.141

nm)

and

high strength

(524 kJ/mole).

The

hybridized

fourth

valence

electron

is paired

with

another

delocalized

electron

oftheadjacentplane

byamuchweaker

vanderWaa/sbond(asecondary

bond

arising

from

structural

polarization)

of only

7 kJ/mol

(pi bond).

Carbon

is the

only

element

to

have

this particular

layered

hexagonal

structure.

The spacing

between

the

layer

planes is relatively

large

(0.335 nm)

or

more

than

twice

the

spacing

between

atoms

within

the

basal

plane and

approximately

twice

the

van der

Waals

radius

of carbon.

The

stacking

of

these layer planes occurs in

two

slightly

different

ways:

hexagonal

and

rhombohedral.

Hexagonal

Graphite.

The

most common

stacking

sequence

of the

graphite

crystal

is hexagonal

(alpha) with a -ABABAB-

stacking

order,

in

otherwords,

where the carbon

atoms

in every other

layer

are superimposed

over

each

other

as shown

in Fig. 3.1.

Atoms

of the alpha

type,

which

have

neighbor

atoms in the

adjacent

planes directly above and below,

are shown with

open

circles.

Atoms

of the

beta type, with no corresponding

atoms

in these

planes,

are shown

with

full

circles.

A view

of the

stacking

sequence

perpendicular

to the

basal

plane

is given

in

Fig.

3.2.

	Plane	A
------	Plane	B
Figure 3.2. Schematicof hexagonalgraphite	crystal. View is perpendicularto basal
plane.