Art Diamante

8/11/2019 Art Diamante

1/13

Pergamon

OOOS-6223 96)00170-O

Carbon Vol. 34, No. 2, pp. 141-153,1996

Copyright 0 1996 Elsevier Science Ltd

Printed in Great Britain.

All rights reserved

000%6223/96 15.00+ 0.00

REVIEW ARTICLE

THE PRESSURE-TEMPERATURE PHASE AND

TRANSFORMATION DIAGRAM FOR CARBON; UPDATED

THROUGH 1994

F. P. BUNDY,~ W.

A.

BASSETT,~ M. S. WEATHERS,~ R. J. HEMLEY,~ H. K. MAO~

and

A. F. GONCHAROV~

Retired General Electric R & D Center; Home address, 4607 Swallow Court, Lebanon, OH 45036-9541,

U.S.A.

bDepartment of Geological Sciences, Snee Hall, Cornell University, Ithaca, NY 14853-1504, U.S.A.

Geophysical Laboratory and Center for High-Pressure Research, Carnegie Institution of Washington,

5251 Broad Branch Rd, NW, Washington DC, 20015-1305, U.S.A.

(Recei ved 5

June 1995;

accepted

in

revi sed orm 12 Sept ember 1995)

Abstract-In recent years, important advances in our understanding of the pressure-temperature phase

and transformation diagram for carbon have occurred as a result of developments in both experimental

and theoretical techniques. Graphite, diamond, liquid and vapor remain the major thermodynamically

stable forms of carbon, However, due to the high activation energies for solid-state transformations and

the specific effects of reaction paths, other metastable forms and a wide spectrum of complex hybrid

forms may be generated, and possibly quenched-in, to survive metastably. This paper focuses primarily

on developments since the last review of the carbon phase diagram published in 1989, but also includes

references to the reliable older work. Some of the newer conclusions include the following: the Clapeyron

slope of the diamond melting line, dT,/dP, is positive; the liquid is metallic and there appears to be no

evidence for a transformation between electrically conducting and non-conducting forms; melted droplets

of carbon less than 0.2 pm in diameter quench to a giant fullerene structure even in the stability field of

diamond; graphite transforms to a transparent phase on compression at room temperature; this phase

reverts to graphite on decompression at this temperature from pressures as high as 100 GPa.

1. INTRODUCTION

The purpose of this article is to bring up to date

what is known about the thermodynamically stable

and metastable phases of elemental carbon and the

reaction dynamics among them over a very wide

range of pressure, temperature and reaction condi-

tions. Earlier reports of this type were published

[l&6] as new results, knowledge, and interpretations

of experimental results and theory developed. In

recent years new experiments and results, some of

which are unpublished, have been generated.

Therefore, it is deemed appropriate to present the

topic as an updated whole. The plan for this article

is to present the entire phase diagram as we currently

understand it and then discuss each part giving the

salient references and brief descriptions of the work

upon which it is based. For the new parts the

experimental background and results will be covered

in more detail.

The binding energy between atoms of carbon is

very large; for example, the cohesive energy of dia-

mond is 717 kJ/mol. This property is also demon-

strated by the extremely high melting temperatures

of its solid forms (- 5000 K). In addition, once carbon

atoms are locked into a given phase configuration,

typically a large amount of activation energy is

required to produce a different stable phase; in other

words, very high temperatures are often required to

initiate spontaneous transformations from one solid

phase to another. Recent work, however, has shown

that this is not always true: new pressure-induced

transformations have been documented at room tem-

perature, as discussed below.

In addition to the well known crystalline forms of

carbon, i.e. graphite and diamond, there are amor-

phous forms, such as glassy carbon and carbon

black, and possibly metastable solid forms referred

to as carbynes. The latter are believed to be solid

condensations of linear molecules of carbon but

remain controversial. Also, there are the more

recently discovered crystalline forms of pure carbon

molecules, the fullerenes such as ChO buckyballs and

C,, buckyfootballs. Because of the high cohesive and

activation energy, carbon polymorphs typically exist

metastably well into a T,P region where a different

solid phase is thermodynamically stable. For example,

diamond survives indefinitely at room conditions

where graphite is the thermodynamically stable form.

Conversely, except at very high temperatures, graph-

ite stubbornly persists at pressures far into the dia-

mond stability field. The same is true of fullerene and

amorphous carbons.

There are two preferred forms of electronic bonding

of carbon atoms in the solid state, viz.: (i) the sp

type in which a given atom is bonded to three

141


2/13

1 4 2 F

P. BUNDY et al

equidistant nearest neighbors 120 apart in a plane,

as in graphite; and (ii) the sp3 type in which a given

carbon atom is bonded to four equidistant nearest

neighbors arranged in tetrahedral symmetry, as in

diamond. The amorphous or glassy carbon forms are

thought to be micro-zonal mixtures exhibiting these

two types of bonding.

2 THE PHASE AND REACTION DIAGRAM

The T,P phase and reaction diagram over a wide

range of pressures for pure carbon is presented in

Fig. 1. The topology of stability fields of the thermo-

dynamically stable phases is quite simple: (i) the

boundary between the graphite and diamond stable

regions which runs from 1.7 GPa/O K, to the

graphite/diamond/liquid triple point at about

12 GPa/5000 K; (ii) the melting line of graphite

extending from the graphite/liquid/vapor triple point

at 0.011 GPa/5000 K to the graphite/diamond/liquid

triple point at 12 GPa/5000 K; and (iii) the diamond

melting line that runs to higher P and T above the

triple point. The graphite/liquid/vapor triple point,

and the graphite/vapor and the liquid/vapor phase

boundaries, which occur at pressures too low for the

scale of Fig. 1, will be shown and discussed later.

Other features illustrated in the diagram include the

thermal reaction rate thresholds for the solid-solid

transformations; these will also be discussed later.

In discussing the various features of the diagram

shown in Fig. 1, it is important to clarify that there

are two principal crystallographic forms of both

graphite and diamond: hexagonal and rhombohe-

dral graphite; and hexagonal and cubic diamond.

The basic chemical bonding is the same in both kinds

of graphite (i.e. sp) and the same in both kinds of

diamond (i.e. sp3). The slight crystallographic differ-

ences are the result of different sequences of layering

in the crystal. In each of the hexagonal types of

graphite and diamond the layering sequence is

ABABAB--; that is the third layer of atoms exactly

superposes the first layer. In rhombohedral graphite

and cubic diamond the layering sequence is

ABCABC-; that is the fourth layer exactly super-

poses the first layer. The two kinds of diamond and

hexagonal graphite will be referred to in the following

discussion of Fig. 1.

Region A in Fig. 1 is the T,P region utilized for

the high-pressure commercial synthesis of diamond

from graphite. Although the process starts with solid

graphite and ends with solid diamond, it is not a

truly solid-solid transition because in this process

carbon from the graphite source dissolves into the

ambient catalyst-solvent fluid metal layer and precipi-

I

J

I

I31

ND

F

I

I

E

\

\

.

LIQ.

GRAPHITE

I

0 00

Temperature K)

Fig. 1. P,T phase and transition diagram for carbon as understood from experimental observations through 1994. Solid

lines represent equilibrium phase boundaries. A: commercial synthesis of diamond from graphite by catalysis; B: P/7

threshold of very fast (less than 1 ms) solid-solid transformation of graphite to diamond; C:

P/T

threshold of very fast

transformation of diamond to graphite; D: single crystal hexagonal graphite transforms to retrievable hexagonal-type

diamond; E: upper ends of shock compression/quench cycles that convert hex-type graphite particles to hex-type diamond;

F: upper ends of shock compression/quench cycles that convert hex-type graphite to cubic-type diamond; B,F,G: threshold

of fast P/T cycles, however generated, that convert either type of graphite or hexagonal diamond into cubic-type diamond;

H,l,J: path along which a single crystal hex-type graphite compressed in the c-direction at room temperature loses some

graphite characteristics and acquires properties consistent with a diamond-like polytype, but reverses to graphite upon

release of pressure.


3/13

P T hase and transformation diagram

for carbon

143

tates out on the growing diamond sink. The activation

energy of solution is only about 125-165 kJ/mol, so

this process can proceed at relatively low temper-

atures and pressures at a rate useful for synthesis.

The B region on the dashed line B,F,G marks the

temperature/pressure threshold of very fast (< 1 ms)

and complete solid-solid transformation of graphite

to diamond. This transformation always yields cubic-

type diamond. Experimentally, it is done by pressuriz-

ing graphite above 12 GPa and heating the sample

with a pulse of electric current or laser radiation.

The shaded line, C, marks the temperature/pressure

threshold of very fast and complete transformation

of diamond to graphite. It is accomplished experimen-

tally by compressing diamond crystals embedded in

a graphite rod and then flash-heating the assembly

with a pulse of electric current to the threshold

temperature (or above). No graphitization of the

diamond specimen occurs unless the critical temper-

ature is reached, at which point graphitization is

complete.

Region D delineates the general area in which

single-crystal hexagonal graphite transforms grad-

ually to retrievable hexagonal-type diamond. This

transformation occurs when the graphite is subjected

to a deviatoric stress of at least 12 GPa with the

principal stress parallel to the c crystallographic axis

and annealing temperatures of 800-2000 K. Region

E marks the upper ends of shock compression/quench

cycles that convert hex-type graphite particles,

embedded in a metal matrix for thermal quenching,

to hex-type diamond. Note that there is an upper

limit on the temperature if hex-type diamond is to

be retrieved.

Region F designates the upper ends of shock

compression/quench cycles that convert hex-type

graphite (embedded in a thermal-quenching metal

matrix) to cubic-type diamond. The dashed line

B,F,G, marks the threshold of fast pressure/

temperature cycles that, however generated, convert

either type of graphite or hexagonal diamond into

cubic-type diamond. There have been a number of

relatively recent experimental results in this area

which will be described later in the article.

When single-crystal hex-type graphite is com-

pressed in the c-direction at room temperature along

the path H,I,J on the diagram, it maintains its com-

pressed graphite structure until, in the pressure region

H-I, it loses some of its graphite characteristics such

as reflectivity, conductivity and optical opacity. From

pressures of I (about 23 GPa) up to J and above, the

Raman spectrum is similar to that of amorphous

carbon. If such a specimen, under pressure, is heated

from region J to G, it very quickly organizes itself

into cubic-type diamond. The experimental evidence

indicates that the dashed line BFG, as noted above,

marks the activation energy threshold for the fast

transformation of compressed graphite, or hex-type

diamond, into the thermodynamically stable cubic-

type diamond. According to one theoretical study

[ 71 perfect single crystal graphite, compressed at zero

0.1

0

0 -

4000

5000 6000

Temperature (K)

Fig. 2. P,Tphase diagram for the lower pressure region. The

question marks following carbynes indicate that the exis-

tence of carbyne solid phases in this P,Tregion is controver-

sial (see text). The question marks in the liquid phase region

indicate that the newest more rigorous experimental results

do not support the earlier experimental interpretations that

a non-conducting liquid phase of carbon exists (see text).

K, could be compressed to a pressure of 80 GPa

before it would spontaneously transform to diamond.

These results are discussed in more detail in a later

section.

The low pressure part of the carbon T,P phase

diagram (O-O.3 GPa) is shown in Fig. 2. The major

features are the graphite (and carbyne?)/vapor line,

the liquid/vapor line and the graphite (carbyne?)

melting line. Evidence has been reported that the low

pressure liquid is electrically non-conducting whereas

the higher pressure liquid is conducting. Indeed, a

phase boundary between the two kinds of liquids has

been suggested, as illustrated in the figure. The

liquid/vapor line should end at a critical point which

has been estimated to be roughly in the vicinity of

0.2 GPa/6800 K. At high temperatures below melting

there is some evidence for transformations from

graphite to other solid phases which are proposed to

be carbyne (linear molecules) or chaoite-like [ S,9], -

but this remains controversial and unresolved [ 3, lo].

2.1. Diamond/graphite equilibrium line

The position of the diamond/graphite equilibrium

line has been quite accurately established by

thermodynamic calculations based upon the mea-

sured physical properties of graphite and diamond in

the temperature range from 300 to about 1200 K

[ 1 I-131 and by experiments on growing or graphit-

ization of diamond [ 14,151. The position of the

upper part of the line, where it approaches the

graphite/diamond/liquid triple point, is established

by the confluence of the lines B and C, Fig. 1, which

correspond to very fast transition of graphite to

diamond and the reverse, respectively [ 16-191.


4/13

144 F. P. BUNDY t u/.

2.2. Gruphite melting line and properties o iquid

carbon

The graphite melting line at low pressures is now

well established [20-261. However, there are differ-

ences of hundreds of degrees in the temperatures

reported in the region of the graphite/liquid/vapor

triple point. There are many difficulties involved in

obtaining reliable temperature measurements under

such high temperature conditions. With improve-

ments in pyrometric equipment and procedures over

the decades, the quality of the measurements has

become considerably better. The temperature

assigned to the triple point has been moved up from

about 4000 K in the 1940s to about 5000 K in recent

years. In Fig. 1 we show 5000 K as being the most

probable value for the temperature at the triple

point [ 271.

The graphite melting line has been investigated

experimentally by Bundy [ 161, Fateeva and

Vereshchagin [ 281 and Togaya er al. [ 191 using flash

electrical resistance heating of graphite specimens in

static high pressure apparatus. All studies found the

melting temperature to increase with pressure to a

maximum at 5-6GPa, then to decrease toward the

graphite/diamond/liquid triple point. The temper-

ature of the latter is about the same as that of the

graphite/liquid/vapor triple point. These studies dis-

agree, however, on the magnitude of the temperature

at the maximum. Fateeva and Vereshchagin [28]

reported that temperature at the maximum was

1200 K above the triple point, whereas Bundy [ 161

reported a temperature difference of 600 K and

Togaya et ~2. found 200 K. The study of Togaya et al.

[19] utilized the most sophisticated apparatus and

instrumentation, so it may be considered the most

reliable. In this work, the temperatures were based

on his measured values of enthalpy to melting, which

were then converted to temperatures by applying the

data of Scheindlin and Senchenko 1251 on enthalpy

versus temperature at conditions near the melting

point.

Experimental measurements of the heat of fusion

of graphite to liquid were reported by Bundy 1161,

Heremans et al. [26] and Baitin

et cd.

27]. The data

of Bundy [16] and of Heremans et al. [26] both

indicate a value of about 105 kJ/mol and the observa-

tions of Baitin et ul. [27] show it to be greater than

80 kJ/mol. These investigations, together with those

of Gathers er LI/.1231 and Togaya et ul. [ 191, indicate

that the enthalpy increase of graphite from room

temperature to melting. lies in the range of

92-t 15 kJ/mol. The value 115 kJ/mol is probably the

most reliable.

Observations on the electrical conductivity of

liquid carbon are varied and contradictory.

Experiments have been performed in which the speci-

men is confined by solid refractory walls and flash-

heated with a short pulse of electrical current through

the specimen itself [ 16,191. All such experiments at

higher pressures indicate that the resistivity of the

liquid phase is about 60-70s of that of the solid

graphite at the melting temperature. In Bundys [ 161

experiments at 4.8 GPa the resistivity of the liquid

carbon was observed to be about 350 @cm, whereas

the data of Togaya

et (II. [

191 at 5.6 GPa show about

460 @cm.

Experiments have also been performed in which a

rod or bar-shaped specimen is mounted in a chamber

with a high pressure atmosphere of an inert gas (such

as argon) to prevent vaporization and heated with

an electric current, usually in milliseconds or micro-

seconds [20,22,23,26]. These experiments yield

widely different values for the resistivity of the liquid

phase. Ludwig [ZO] and Jones [22] reported the

resistivity of the liquid formed from melting graphite

to be very high, practically an insulator. Gathers

et d. 1231 measured values of about 1000 @cm.

Heremans vt (II. [26] melted graphite fibers under

similar conditions and report values of 30-70 @2cm.

Vaporization and melting of graphite have also

been investigated by intensive surface-heating with

focused lasers. Both continuous wave and pulsed

experiments as short as 90 fs have been performed

[27.29%321. Among the objectives of these investiga-

tors were the determination of the optical, electrical

and thermal properties of liquid carbon. The results

tend to be contradictory, depending upon the energy

insertion time, the method of monitoring the sample

spot, etc. Experiments reported before 1988 are dis-

cussed by Bundy 143 and will not be treated further

here. Baitin et

al.

[27] found the emissivity of liquid

carbon at i=O.65 jtrn to be about 0.60; this is close

to values for liquid metals and is therefore consistent

with liquid carbon being metallic. Reitze

et al.

[32]

used 90 fs laser pulses which. due to inertial effects,

result in heating at constant volume. The sample

surface was probed with approximately 100 fs reso-

lution without interference from vaporized carbon.

According to the argument of Bundy [4] regarding

thermal pressure due to heating at nearly constant

volume (see Figs 3 and 4 in Ref. [4]), the pressure in

the zone of the sample melted by the laser would be

in the range of 5-10 GPa and the carbon melt would

be electrically conducting with a resistivity of about

400 &?cm. Optically derived d.c. resistivities from the

experiments of Reitze et ul. [32] are about 600 2cm.

which is in quite good agreement with the static

pressure results of Bundy [ 161 and Togaya

clt LI/.

[ 191. All of the results listed above, except for those

of Malvezzi et a/. [31], are consistent with liquid

carbon having semimetallic properties.

Consideration of all the reported experimental

observations brings up the question of whether there

is in fact an electrically insulating phase of liquid

carbon. In exploding wire types of experiments, a

wire or rod specimen is heated into the liquid state

very rapidly in a gas or vacuum environment. As

soon as the sample begins to melt, its physical shape

becomes unstable due to surface tension and electro-

magnetic forces, as demonstrated by stroboscopic

and streak camera photographic measurements. Even

in the most recent carbon melting experiments, in

which the best circuit control and diagnostic tech-

niques are used. it has not generally been possible to


5/13

P,T phase and transformation diagram for carbon

145

reach complete melting without disruptive instabilit-

ies occurring. In order not to lose the specimen by

disintegration, the power to the specimen may be cut

off at the instability point by crow bar shunt cir-

cuitry. There appears to be no firm evidence from

the most recent experiments that supports the exis-

tence of an electrically insulating form of liquid

carbon.

Recent first-principles calculations by Galli et al.

[33] indicate that liquid carbon at low pressure and

5000 K should have mainly two-fold and three-fold

coordination. Similar calculations for liquid carbon

at 9000 K and pressures above 100 GPa [ 341 predict

the coordination to be mainly four-fold. A simple

theoretical approach to modelling liquid carbon has

been to consider it as a pseudo-binary mixture of

graphite-like and diamond-like states in which the

composition changes smoothly with pressure [ 351.

This approach leads to a melting curve maximum, as

is found experimentally for graphite. On the other

hand, the first-principles molecular-dynamics calcula-

tions performed along high-density isochores indicate

that the melting curve of diamond should have a

positive slope, i.e. (dP/dT, >O) to above 100 GPa

[34]. In the section on melting of diamond, it will

be shown that there is some experimental evidence

that liquid carbon at pressures above the

graphite/diamond/liquid triple point does contain

graphite-like and diamond-like linkages [ 36,371.

2.3. The diamond melting line

Prior to the mid-1980s it was thought that the

behavior of cubic-type diamond would be analogous

to that of the diamond-structure forms of the heavier

Group IV elements Si and Ge. Experiments demon-

strated that diamond-structure Si and Ge melt to

form metallic liquids of higher density than the solid,

which requires dT,/dP to be negative. It was also

known experimentally that at higher pressures, dia-

mond-structure Si and Ge undergo transitions at

room temperature to denser, metallic phases [6,38].

By analogy, the earlier

T,P

phase diagrams for carbon

showed the melting line of diamond with a negative

slope, extending to a diamond/metallic solid/liquid

triple point at higher pressure and lower temperature.

The melting line of the (supposed) metallic solid was

believed to have a positive slope, as found in Si and

Ge [ 1,2].

This was the case in the first experimental observa-

tions of melting of diamond at pressures above the

graphite/diamond/liquid triple point reported by

Bundy [ 16,171. The data indicated that at the triple

point, the slope of the diamond melting line,

dT,JdP, is about zero. However, by analogy with Si

and Ge the melting line was thought to curve back

to give a negative slope at higher pressures.

Shaner, er al. [39] shock compressed pyrolytic

graphite and measured the sound velocity in carbon

at shock pressures from 80 to 140GPa and corre-

sponding shock temperatures of 1500 to 5500 K,

respectively. The sound derived velocities are close

to the elastic longitudinal wave in solid diamond,

which is much higher than that for a bulk wave in a

carbon melt. They concluded that the diamond

carbon had not melted even though the shock states

reached far into the supposed region of liquid carbon

and that the diamond melting line must therefore

have a positive slope. At this same time diamond-

anvil cell experiments indicated the stability of cubic

diamond to extend to at least 275 GPa [40]. These

experimental results are consistent with theoretical

calculations of the phase stability of diamond relative

to the possible metallic forms [41-431 which indi-

cated that the cubic diamond form of carbon would

remain stable relative to all the likely metallic forms

up to pressures in the range of 1300-2300 GPa and

that the diamond melting line must have a positive

slope. This difference in behavior between carbon

and Si and Ge is attributed to the absence of

p-electron states in the 1s atomic core which allows

the p-character sp3 bonding electrons in diamond to

be held close to the nucleus [41].

Gold et al. [44] melted diamond at high pressure

in a diamond anvil cell. Later, Weathers and Bassett

[36] reported detailed results of diamond-anvil cell

experiments of melting small particles of diamond or

graphite in a NaCl matrix at pressures of 5530 GPa

by a pulsed Nd:YAG laser. They found that liquid

carbon is immiscible with molten NaCl and that the

carbon specimens quenched to spherical particles

ranging in size from - 1 pm down to less than a few

nanometers (Fig. 3). For the samples melted at

30 GPa the larger spherules

(>

0.2 pm) were polycrys-

talline diamond with either a granular or radial

texture. The smaller spherules (< 0.2 pm) yielded

electron diffraction patterns with four diffuse rings

that correspond to the 002, 100, 004 and 110 d-

spacings of graphite - a pattern that is typical of

disordered graphite randomly oriented around the

c-axis. Dark-field electron microscope images pro-

duced by aperturing the 002 diffraction ring showed

that in the tiny spherules the c-axis had a radial

orientation. Also, it was found that the 002 and 004

(c-axis) spacings in quenched unloaded samples were

smaller in those samples that had been pulse heated

at higher pressures, while the 110 and 100 (a,b-axis)

spacings were insensitive to the pressure at the time

of pulse heating. This effect was interpreted to indicate

a graphitic structure with some sp3 diamond bond

stitching to hold the layers closer together on the

average and also that the diamond melt contains a

significant amount of sp2 as well as sp3 coordination

at pressures of 30 GPa. In 1993, after the fullerene

structures of carbon became well known and estab-

lished, Bassett and Weathers [ 371 re-interpreted their

1987 [ 361 results for the smaller

(

0.2 mm) solidified as polycrystal-

line diamond, it was interesting to note that the

spherules of borderline size commonly had a polycrys-

talline diamond core surrounded by an onion-struc-

tured fullerene-like mantle. This indicates that under

special circumstances the hybrid fullerene structure

can be energetically stable relative to diamond even

at conditions well within the diamond stability field.

Togaya [ 181 reported experiments in which speci-

mens of boron-doped semiconducting diamond were

melted at ambient pressures of 6-18 GPa by flash-

heating them with controlled current from a capaci-

tor. Although the behavior of the resistance was

complicated somewhat by changes associated with

the doping element, and at the lower pressures by

the transformation to solid graphite, there were clear

indications that the T, of diamond increases with

pressure. This result is consistent with Togayas obser-

vation, and that of Bundy [ 171, that at confining cell

pressures of 14-18 GPa (well into the diamond-stable

region) the central pocket of liquid carbon, enclosed

by a rigid shell of solid diamond always freezes to a

mix of diamond and graphite. The explanation is that

the strong container of solid diamond with its low

coefficient of thermal expansion serves as a nearly

constant volume space for the freezing process. The

first liquid freezes as diamond having a smaller

specific volume than the liquid. The chamber being

constrained to constant volume loses ambient pres-

sure until the equilibrium pressure for graphite is

reached after which the remaining liquid freezes as

graphite. According to the Clapeyron equation, a

solid of smaller volume than the melt requires

dT,/dP to be positive since the entropy of the melt

is always larger than that of the solid.

The positive slope of diamond melting is further

supported by the early observation of Bundy [ 161

that the threshold T P line for the fast transforma-

tion of diamond to graphite at pressures below the

graphite/diamond/liquid triple point (i.e. metastable

melting of diamond) has a positive slope (C in Fig. 1).

Additional experimental evidence that the slope,

dT,/dP, of the diamond melting line is positive was

obtained from an unpublished experimental study by

Bassett and Weathers. A mixture of Pt grains and

NaCl loaded in a diamond-anvil cell was brought up

to pressure and the individual Pt grains were heated

with a focused Nd-YAG laser. The temperature of

each grain was determined using spectroradiometric

techniques. After unloading, the Pt/NaCl specimen

was removed with the position of each Pt grain

indexed; the diamond anvil faces were then searched

for craters that would indicate melting of the diamond

face. The melt craters were observed and found to

correlate with adjacent Pt grains that were heated to

high temperatures.

In this manner, the P-T plot shown in Fig. 4 was

generated. The boundary line marks the minimum

temperature at which melt craters were observed.

This line is quite well defined and has a positive

slope. Note, however, that there is a large discrepancy

between the temperatures measured here and those

found for melting at the triple point graphite-dia-

mond-melt in quite different types of experiments;

this is shown by the dashed lines which are based on

the data presented in Fig. 1. Although the measure-

ment of absolute temperatures by this spectroradio-


7/13


147

Temperature, K

Fig. 4. Plot of relative temperatures of melting of carbon as a function of pressure. Solid circles represent P,Tconditions

at which a melt crater was formed in the diamond anvil surface when a millisecond laser pulse heated a platinum grain

embedded in NaCl a few micometers from the anvil surface. Temperatures were based on black-body spectra of incandescent

light and pressures were measured by the ruby method. The dashed line corresponds to the melt lines shown for graphite

and diamond in Fig. 1 (see text regarding the displacement).

metric method is subject to many technical difficulties,

the relative temperature measurements are probably

quite reliable. The significant point in this case is that

all the data points shown in Fig. 4 were taken with

the same physical and optical set-up and so the slope

of the indicated melting line for diamond should be

meaningful, especially the indication that the sign of

the slope is positive.

Theoretical studies of the phase stability of carbon

at extremely high

T,P

by Young and Grover [46]

indicate the melting line of diamond and the

solid/solid phase boundary between diamond and the

(supposed) BC8 metallic phase are as shown in Fig. 5.

The maximum pressures and temperatures in the

interiors of the outer planets Uranus and Neptune

are in the range of 600 GPa/7000 K; under these

conditions, calculations by Ross [47] indicate that

the elemental carbon there would be in the diamond

phase. Available data indicate that free carbon in the

Earths mantle (to 135 GPa, 250%3500 K) would

also be solid diamond phase as well.

1500

G

&

w 1000

2

9

8

PI

500

0

DIAMOND

IQUID

I

-I

5000

10,000

Temperature K)

I I

Fig. 5. P,Tphase diagram for carbon up to extremely high

pressures based on theoretical calculations [46].


8/13

148

F. P. BUNDY et al.

2.4. The graphite-diamond direct conversion line

The dashed line, B-F-G, in Fig.

1

marks the thresh-

old of very fast (i.e. ms-ii) transition of highly

compressed graphite, or its low temperature deriva-

tives, to cubic-type diamond. The lower pressure

portion of the line near the graphite/diamond/liquid

triple point was first explored by Bundy [ 171 by

millisecond resistance heating of specimens in a high

compression belt apparatus. Recently, this threshold

was investigated by Bassett and Weathers [unpub-

lished] up to 35 GPa using the laser-heated diamond-

cell technique like that described above. In these

experiments. a shutter was installed to chop the

continuous infrared laser beam (i= 1.06 mm) into

pulses of approximately 200 ms. The spectrum was

recorded as a function of time and fit to black-body

curves by a least squares method. The wavelength of

the fluorescence emission from a chip of ruby [48,49]

in the sample was used to measure the pressure before

heating. Measurement of the temperature and pres-

sure of the graphite-diamond transition is particu-

larly well suited for investigation by this technique.

When graphite is converted to diamond, the sample

becomes transparent (Fig. 6) and the absorption of

the infrared light ceases. Thus, the temperature rises

to the transition temperature and remains there while

the conversion is taking place.

Samples for this study were prepared by placing

graphite fibers c 1 kern in diameter in a sodium chlo-

ride matrix and compressing the mixture in a stainless

steel gasket between diamond anvils ranging from

0.3 to 0.5 mm in diameter. The fibers were provided

by Dr Gary Tibbitts of General Motors. Temperature

measurements on the graphite-diamond conversion

can be made quite accurately and repeatably with

the technique for two reasons: (1) the graphite

behaves as an excellent black body; and (2) the

temperature at the conversion ceases to rise when the

carbon is converted to the transparent diamond form

and no longer absorbs the infrared radiation from

the laser.

The direct conversion graphite-diamond boundary

extends from the graphite/diamond/melt triple point

along a nearly straight line to 2500 K/l5 GPa with

a negative slope. It then makes a sharp turn and

follows a nearly straight line with a gentle negative

slope to the highest attainable pressure point at

2000 K/35 GPa (Fig. 7). This line is in fairly good

agreement with that determined by Bundy [ 171.

The large number of new data points collected in

the vicinity of 20 GPa/2500 K indicate a rather

abrupt change in slope. Figure 7 shows this abrupt

change in slope along with the metastable room

temperature transition (discussed below) reported by

Hanfland rr al. [SO], Goncharov [ 5

I]

and Yagi rt trl.

[ 521. A metastable phase boundary may extend from

this room temperature metastable transition to the

point of abrupt slope change in our curve. resulting

in a metastable triple point there. The me&table

transition at room temperature is discussed in more

detail below.

The construction of a hypothetical phase line across

H,D,B (Fig.

1)

as a metastable extension of the graph-

ite melting curve would imply structural similarity, if

not thermodynamic continuity, between the liquid

and the diamond-like phase produced in the low-

temperature compression experiments. In other

words, such topology would suggest that the material

is glassy. The transition could then be analogous to

the pressure-induced amorphization of ice-1 [ 533 also

observed for other materials in which the melting

curve has a negative slope combined with a frustrated

10pm

Fig. 6. Optical micrograph showing conversion by laser heating of graphite fibers to diamond (circled) at pressures greater

than 12.5 GPa. The preservation of the morphology of the fibers indicates that the graphite (opaque) does not melt. but

undergoes direct conversion to diamond (transparent).


9/13

P T

phase and transformation diagram for carbon

149

PHASES OF CARBON

I

CJ

iamond

I

I

I

e:

transparent

a

w

metastable &

1

:

20

graphite

b.0 0

0 I

a

\

01.

I I. I. I,

t. I

0

1000 2000 3000 4000 5000 6000

Temperature K)

Fig. 7. P,Tplot of direct graphite-diamond conversion. The

dashed line separates

P T

oints of graphite fibers that

remained graphite (solid circles) from those at higher P,T

conditions that were converted to diamond by millisecond

laser heating pulses [Bassett and Weathers, unpublished].

solid-solid transition as in SiO, [54]. This inter-

pretation remains conjectural as the structural state

and thermodynamic properties of the carbon material

at high P-T(e.g. above the proposed metastable triple

point) has not been fully characterized. Alternatively,

the high temperature transition near 15 GPa (Fig. 7)

may be unrelated to the metastable extension of the

graphite melting curve, as indicated in Fig. 1.

Recent calculations of Zhang

et al

[55] on the

reaction rate of the direct transition of graphite to

diamond as a function of P and Tyield a fast reaction

line on a P,Tchart that is remarkably similar to the

BFG threshold of Fig. 1 and Fig. 7. This similarity

implies that the shape of the BFG threshold may be

determined mainly by the reaction kinetics.

We also point out that this behavior of carbon is

analogous to that of the iso-electronic case of boron

nitride which was investigated by Corrigan and

Bundy [ 561. These studies of boron nitride indicated

a reaction rate controlled threshold line between

wurtzite BN (like hexagonal diamond) and zinc-

blende BN (like cubic-type diamond) which is very

similar to that of BFG for carbon in Fig. 1 and Fig. 7.

2.5. Cool compression ofgraphite h,i,j, Fig. 1)

Aust and Drickamer [57] reported the first meas-

urements of the electrical resistivity behavior of single

crystal graphite compressed at room temperature

well into the lo-20 GPa pressure region. Compressed

in the c-direction and monitored in the a,b direction,

the graphite that they observed slowly underwent a

decrease of resistivity with increase of pressure to

- 12 GPa,

whereupon

the

resistivity rapidly

increased. In some of the better specimens the resistiv-

ity rise was more than a factor of 10, suggesting a

change of phase to a non-conducting form.

Bundy and Kasper [ 581 reported results of similar

experiments with additional arrangements for heating

the specimen while under pressure to moderate tem-

peratures up to about 1500 K. For the room temper-

ature experiments the same fast rise of resistivity as

reported by Aust and Drickamer [57] started at

about 12 GPa, but upon return to room pressure the

resistivity returned to its initial value and the reco-

vered specimen proved to be graphite. By contrast,

when the graphite specimen was compressed into the

higher resistivity state and then heated to around

1200 K the resistivity increased significantly and when

it was cooled and decompressed the resistivity

increased even more. The recovered specimen was no

longer shiny like graphite, but a dull gun-metal gray.

It would scratch sapphire the way diamond does and

its X-ray diffraction pattern showed it to be mostly

hexagonal diamond. In general, the static pressure

experiments indicated that in order to retrieve hexag-

onal diamond, it was necessary to subject the speci-

men to P,Tconditions in area D of Fig. 1.

When diamond anvil cells became available to

generate pressures of up to many 10s of giga-Pascals,

the behavior of very small specimens of graphite and

graphitic carbons could be monitored by optical,

Raman, and X-ray diffraction techniques in

situ

at

high pressure, in contrast to the previous experiments

which were limited to electrical conductivity measure-

ments using opaque tungsten carbide anvils. Of these

types of measurements, X-ray diffraction and Raman

are able to add significant structural and crystal

chemical information to our knowledge of the carbon

phases. The observed behavior of a given specimen

during compression depends upon its initial degree

of crystallinity, the direction and homogeneity of the

pressure field, the rapidity of compression and the

type of measurement performed. These effects are

illustrated by the experimental results of a number

of different workers, some of which follow.

Goncharov et al. [ 593, using a diamond anvil cell,

found that single crystal graphite transforms to an

optically transparent state at about 35 GPa. Although

this result suggested the formation of sp3 bonding,

the Raman spectra showed no hint of the diamond

Raman band and the spectral absorption edge was

too broad for that of diamond. Further work by

Goncharov [Sl] showed that the transition in single-

crystal graphite under hydrostatic conditions (He

medium) occurs at about 23 GPa, as indicated by an

abrupt change of the Raman spectrum and the open-

ing of the band gap. Specimens with less regular

stacking between hexagonal layers required higher

pressures (to 45 GPa) to achieve the same transition.


10/13

150

F. P. BUNDY

et al.

Goncharov [Sl] also found that the transition pres-

sure for single-crystal graphite can be lowered to

about 14 GPa under uniaxial stress directed along

the c-axis of the crystal. These Raman and optical

observations were corroborated by Hanfland et ul.

[60] and Utsumi et ul. [61].

Hanfland et u[. [SO] used X-ray diffraction and

Raman spectroscopy to explore the behavior of

graphite in diamond cells at pressures in the range

of 14 GPa where the previously reported increase in

electrical resistance and decrease of reflectivity occurs.

From the behavior of the widths and shifts of the

critical Raman bands and the X-ray diffraction pat-

terns, these authors concluded that the phase trans-

ition started at about 14 GPa. Yagi et ul. [ 521 used

a cubic anvil apparatus with sintered diamond piston

tips and X-rays from a synchrotron source to study

the compression of graphite. They reported that for

room temperature compression the behavior is sensi-

tive to the crystal texture of the specimen, but that

in general, graphite begins to transform at about

18 GPa.

Kertesz and Hoffmann [62] and Fahy et ul. [ 71

performed theoretical calculations of the structure

and energy of graphite during cool compression as it

approached the density of diamond. These studies

indicated that a very high activation energy is associ-

ated with transforming the strained graphite to the

diamond. In particular, the study by Fahy et al. [7]

indicated that a pressure of over 80 GPa (T=O K)

would be required to force a spontaneous transition.

From these experiments and calculations, it may

be concluded that when single-crystal graphite is

compressed along the c-axis at room temperature

(H,I,J of Fig.

1),

the material remains a good electrical

conductor in the a,b plane directions until about

12-14 GPa. At higher pressures decreasing electrical

conductivity and optical reflectivity and increasing

optical transmittance are observed. The fact that the

material remains transparent to visible light suggests

that it remains

electrically non-conducting.

Mechanically, the material is extremely strong and

was observed to fracture the faces of the single-crystal

diamond anvils that push against it [Hemley and

Mao, unpublished]. Heating this material causes the

sample to transform into coherent hexagonal dia-

mond crystallites as shown by the experiments of

Bundy and Kasper [SS] and by Utsumi and Yagi

C631

The changes in structure and other physical proper-

ties accompanying cool compression of graphitic

carbon are still not fully understood. It is likely that

sp3 bonding begins to develop at about 12-14 GPa,

thereby removing conduction electrons from the

system and decreasing the electrical conductivity and

optical reflectivity and increasing the optical transmit-

tance. The fact that decompression from this state

yields graphite implies either a martensitic trans-

formation or a small activation energy for the back

transformation. The latter is supported by very recent

observations of pressure quenching the transparent

form at low temperatures [Badding, private com-

munication]. It is also likely that small domains of

the high-pressure phase are formed initially on room-

temperature compression. Heat-annealing the mate-

rial may then cause the small domains to coalesce

and grow into coherent hexagonal diamond crystal-

lites that are large enough and stable enough to

survive decompression 158,631. Another explanation

is that the transparent high-pressure, room-temper-

ature phase is a new allotrope of carbon and perhaps

has the properties described here for reasons other

than sp3 bonding. Clearly further work is needed in

order to resolve this question.

2.6. Shock compression of graphites e,f; Fig. 1)

Both temperature and pressure rise during shock

compression. The rise of temperature with pressure

takes place with the compressional work done on the

specimen, the PdVwork. The greater the compress-

ibility and porosity of the specimen material the

greater the temperature rise for a given increase in

pressure. On Fig. 1, the T,P paths for shock compres-

sion of graphite would pass from room T,P toward

D,E,F. The T,P path is not reversible and unless fast

thermal quenching is provided, the temperature drops

much less rapidly than the pressure during the decom-

pression. In the commercial production of diamond

powder from graphite powder, the body to be shock

compressed consists of small particles of graphite

dispersed in a matrix of metal, such as iron or copper,

which is a good thermal conductor and less compress-

ible than graphite. During shock compression, the

graphite particles heat up more than the surrounding

metal matrix, transform to diamond, and are ther-

mally quenched during the decompression by the

adjacent cooler metal. The type and size of diamond

particles that can be produced by this method are

established and limited by the shortness of the reac-

tion time and thermal/geometry requirements

[64468].

Shock compression experiments of this type on

hexagonal graphite particles yield mostly hexagonal

diamond if the top of the cycle goes to the E region

(Fig. 1) and mostly cubic-type diamond if the top of

the cycle goes past the BFG line. To be retrieved as

diamond the specimen particles have to be at high

temperature long enough to allow coalescing of the

diamond domains into crystallites large enough that,

with thermal quenching, they can survive decompres-

sion without graphitizing. Only small particles of

diamond can be produced by this method because of

the very short time at high T,P and the necessity

for the individual carbon particles to be small in

order to satisfy the fast thermal quench requirements.

3. DIAMOND SYNTHESIS UNDER METASTABLE

CONDITIONS

As early as 1910 Tammann [69] proposed a T,P

phase diagram for carbon which included a large T,P

area at lower pressures and temperatures in which

there would be pseudo-equilibrium between dia-

mond and graphite. During this time, it also was


11/13


151

recognized that the free energy of carbon vapor was

far higher than in either the graphite or diamond

solid forms. The quantitative determination by

Rossini and Jessup [ 111 of the free energies of

graphite and diamond showed that their difference

at one atmosphere, 0 K, is only about 2.5 kJ/mol.

This difference is insignificant compared to

-712 kJ/mol of the vapor. Hence, with respect to

free energy, the condensation of carbon vapor to

graphite or diamond would be of nearly equal prob-

ability. By proper control of the reaction path and

the nucleation conditions it should be possible to

condense carbon vapor as diamond under low pres-

sure, metastable conditions.

The long history of attempts to accomplish this

include von Bolten [70], Ruff [71], Spitsyn and

Derjaguin [72], Oriani and Rocco [73], Eversole

[74], Angus

et al.

[75], Matsumoto et al. [76],

Kamo et al. [77] and Spitsyn

et al.

[78]. The method

was generally unsuccessful because of poor control

of graphite nucleation until the early 1980s when it

was found that carbon vapor deposition from a

plasma, which contained atomic hydrogen as well as

carbon vapor and hydrocarbon molecules, nearly

eliminated the competition of graphite nuclei [77].

This allowed only the diamond to exist and grow.

Under proper conditions it has become possible to

deposit films, and sheets, of polycrystalline diamond

which have commercial utility. Recent studies have

revealed that organic molecules in the vapor play an

important role by configuring the carbon to precipi-

tate as diamond [79].

4. FULLERENE CARBONS

Rohlfing

et al.

[SO] reported some curious results

from experiments with a cluster molecular beam

apparatus. They used a laser to produce puffs of

vapor from a carbon rod which was entrained and

cooled by expansion through a supersonic nozzle to

form small nanometer-size clusters of carbon atoms.

The relative abundance of clusters of different size

was examined on line by mass spectroscopy. In

addition to the usual 2-20-atom clusters studied

previously by numerous workers and different tech-

niques, carbon clusters in the 40-300-atom mass

range were observed. Interestingly, only even-num-

bered atom clusters formed.

In the following year, 1985, a similar apparatus

was set up by Kroto et al. [Sl] to synthesize and

study the chemical reactivity of the small 2-30-atom

clusters; in particular, to determine whether these

clusters had the same form as the long carbon linear

chains known to be abundant in interstellar space.

The study of the small clusters was successful, but

the most significant finding was that the C,, cluster

was outstandingly stable, as well as C,, and other

species. Thinking that the great stability might be

related to some kind of closed shell structure the idea

soon developed that C,, might be a truncated icosa-

hedral cage made up of hexagons and 12 pentagons

(like the markings on a soccer ball) with a carbon

atom at each intersection [ 811. Geometrically, it was

soon realized, 12 pentagonal defects convert a planar

hexagonal array of any size into a quasi-icosahedral

cage [ 823 as in C6,,, C240 and C,,,. C,, was visualized

as having 12 pentagons and 25 hexagons by Curl

and Smalley [83]. Kratchmer is credited with the

discovery that CeO and C,, are soluble in benzene.

That, together with Huffmans productive soot-

making apparatus [84,85] made it possible to pro-

duce macro amounts of C& and C,,, crystallize it

and determine the crystal structure. The lattice spac-

ings in the crystal were consistent with the presumed

size of the closed-cage molecules. The electronic and

vibrational spectra of the molecules had already been

probed by Curl and Smalley [S6] and, in these,

theory and observation agreed, indicating that the

closed cage structure of the molecules was correct.

The discovery and development of methods of

synthesizing and separating out bulk quantities of

fullerenes have opened up new fields in chemistry

and physics. No attempt is made to review these

large and rapid developments in this article. Earlier

in this article it was pointed out that Bassett and

Weathers now interpret the graphite-like spherules of

their quenched nanometer-sized carbon droplets as

being onion-layered giant fullerenes which formed in

the stability field of diamond. We note there have

been a number of studies of high-pressure trans-

formations of fullerenes. Some of the more interesting

ones are as follows: Duclos

et al.

[87] on the effects

of pressure and stress on C& fullerite to 20 GPa;

Samara et al. [ 881 on the pressure dependence of the

orientational ordering in solid C6,,; Regueiro et al.

[S9] on crushing of C,, to diamond at room temper-

ature; Chandrabhas

et al.

[90] on reversible pressure-

induced amorphization in solid (&; di Brozolo

et al.

[91] on fullerenes in an impact crater on the LDEF

space craft; Nunez-Regueiro et al. [92] on polymer-

ized fullerite structures; Wolk

et al.

[93] on pressure-

induced structural metastability in crystalline C,,. A

curious reaction difference is indicated for Cc0 versus

CT0 in that CT0 compresses at room temperature to

amorphous form, much like graphite and decom-

presses reversibly back to the C,, crystalline structure,

whereas the amorphous &,-derived material

decompresses to a more dense diamond-like form.

Such behavior illustrates once again how, for carbon,

the initial state and the reaction paths are important

factors in what the end product will be.

5. THEORETICAL STUDIES

In addition to the new results coming from

improved experimental methods, the large number of

increasingly accurate theoretical studies are providing

important new insights into the stability and physical

properties of known and predicted carbon poly-

morphs [94- 1041.


12/13

152

F. P.

BUNDY et (11.

6. CONCLUSIONS

Carbon, the lightest of the Group IV elements, is

certainly one of the most versatile, interesting and

useful of the chemical elements in respect of the

materials properties of its various phases and forms.

Although many new things have been learned during

the past few decades about its physical forms and

properties over a wide range of pressures and temper-

atures there is still much to be established accurately

and discrepancies to be resolved - possibly new

forms and properties to be discovered that may be

both technically useful and fundamentally important.

A deeper understanding of this important system will

surely emerge with the continued development of

experimental methods to probe higher pressures and

temperatures, with increasing accuracy, precision and

sensitivity, and with improving theoretical methods.

Acknowledgemmts~We thank John Badding for useful

comments and discussion. Work performed at the

Geophysical Laboratory and Cornell University was sup-

ported by the National Science Foundation.

1.

3

5:

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

REFERENCES

F. P. Bundy,

Koninkl, Nederl. Aknd. wn Wetenschap-

pen-Amsterdam-Proc. Series B 72, No. 5 1969).

F. P. Bundy. J. Geophys. Res. 85, 6930 (1980).

F. P. Bundy, In Solid Srute

Physics under Pressure

(Edited by S. Minomura), KTK Sci. Pub]., Tokyo

(1985).

F. P. Bundy, Phlsicn A156, 169

(

1989).

P. Gustafson, Carbon 24, 169 (1986).

D. A. Young, Phase Diagrams

of the Elements

niv. of

Calif. Press (1991).

S. Fahy, S. Ci. Louie and M. L. Cohen, Phys. Rev. B34,

1191 (1986).

B. V. Derjaguin. D. V. Fedoseev, V. P. Varnin and S. P.

Vnukov,

Nature

269, 398 (1977).

A. G. Whittaker, Science 200, 763

(

1978).

P. P. K. Smith and P. R. Buseck.

Science

216. 984

(1982).

F. D. Rossini and R. S. Jessup, J. Nut.

Bur. Stds.

C21,

491 (193s).

0. 1. Leipunskii, usp.

Khim 8,

1519 (1939).

R. Berman and F. Simon, Zeirs. Elektrochm. 59, 333

1955).

F. P. Bundy, H. P. Bovenkerk, H. M. Strong and R.

H. Wentorf, Jr, J. Chem. Phys. 35, 383 (1961).

C. S. Kennedy and G. C. Kennedy,

J. Geophys. Rex

81, 2467 (1976).

F. P. Bundy, J.

Chem.

Phys. 38, 618 (1963).

F. P. Bundy, J. Chem. Phys. 38, 631 (1963).

M. Togaya, In Science

and Technology ofNew

Diamond,

p.369. Tokyo, KTKiTSPC (1990).

M. Togaya, S. Sugiyama and E. Minuhara. In High

Pressure Sciewe und Technology, Proc. AIRAPT und

APS Cortf., Colorado Springs, CO (1993). p. 255.

A. Ludwig, Zuit. Elrktrochrm. 8, 273 (1902).

M. J. Basset, J. Phys. Radium 10, 217 (1939).

M. T. Jones, Nat. Carbon Res Lab. Report PRG

(1958).

G. R. Gathers, I. W. Shaner and D. A. Young, UCRL

Rpt., 51644 (1974); Phys.

Rev.

L t. 33, 70 (1974).

A. V. Kirillin, M. D. Kovalenko and M. A. Scheindlin,

Pisma Zh. Eksp. Tear. Fiz. 40, 452 (1980).

M. A. Scheindlin and V. N. Senchenko, Ser.

Phys.

Dokl.

33, 142 (1988).

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

J. Heremans, C. H. Olk, G. L. Eesly, J. Steinbeck and

G. Dresselhaus,

Phys. Rev.

L&t. 60, 452 (1988).

A. V. Baitin, A. A. Lebedev, S. V. Romanenko. V. N.

Senchenko and M. A. Scheindlin,

High Temp.

High

Pres.

22, 157 (1990).

N. S. Fateeva and L. F. Vereshchagin.

JETP Letr. 13,

157 1971).

T. Venkatesan, D. C. Jacobson, J. M. Gibson, B. S.

Elman, G. Braunstein, M. S. Dresselhaus and G. Dres-

selhaus, Phys. Rec. Lat. 53, 360 (1984).

J. Steinbeck. G. Braunstein, M. S. Dresselhaus, T.

Venkatesan and D. C. Jacobson.

J. Appl.

Phys. 58,

4374 (1985).

A. M. Malvezzi, N. Bloembergen and C. Y. Huang.

Phys.

Rrw.

Lert. 57, 146 (1986).

D. H. Reitze, H. Ahn and M. C. Downer, Phys. Rev.

B45, 2677 (1992).

G. Galli. R. Martin, R. Car and M. Parrinello. Phvs.

Rev. Lat. 63, 988 1989).

C.

Galli, R. M. Martin, R. Car and M. Parrinello.

Science 250, 1547

(

1990).

M. van Thiel and F. H. Ree,

Int.

J. Thermophy\. 10,

227

(

1989).

M. S. Weathers and W. A. Bassett, Phys. Chem. Minrr-

a/s

15, 105 (1987).

W. A. Bassett and M. S. Weathers. High Pressurr S ,i-

ewe and 7echnology. Proc. AIRAPT and APS Conf:,

Colorado Springs, CO ( 1993) p. 65 1.

F. P. Bundy. J. Charm. Phys. 41, 3809 (1964).

J. W. Shaner, J. M. Brown, C. A. Swenson and R. G.

McQueen, J. Phys. 45, 235 (1984).

K. A. Goettel, H. K. Mao and P. M. Bell. Rev. Sci.

Imtrum.56, 1420 (1985).

M. T. Yin and M. L. Cohen, Phys. Rer. Lctr. 50,

2006 (1983).

R. Biswas. R. M. Martin, R. J. Needs and 0. H. Nielsen.

Ph.r.s. Rw. B30, 3210 (1984).

R. Biswas, R. M. Martin. R. J. Needs and 0. H. Nielsen.

Phys. Rev. B35, 9559

(

1987).

J. S. Gold, W. A. Bassett, M. S. Weathers and J. M.

Bird, Science 225, 921

(

1984).

D. Ugarte, Nature 359, 707 (1992).

D. A. Young and R. Grover, In

Shock Waves in Con-

densed Mutter (Edited by Schmidt and Holmes), p. 13

1.

North-Holland, Amsterdam (1988).

M. Ross,

Noirturr

92, 435 (1981).

G. J. Piermarini, S. Block, J. F. Barnett and R. A.

Forman,

J. Appl. Phys.

46, 2774 (1975).

P. M. Bell, J. Xu and H. K. Mao, In

Proc. 4th Amer.

PI?xs. SM. 7~opical Conf. on

hock

Waws

in Condensed

Matter

(Edited by Gupta), p. 125. Plenum Pub]., NY

[

1986).

M. Hanfland. J. Z. Hu, J. F. Shu, R. J. Hemley, H. K.

Mao and Y. Wu, Bull. Amer. Phys. Sot. 35, 465

(

1990).

A. F. Goncharov, Zh.

Eksp. Tear. Fiz. 98,

1824 (1990).

T. Yagi, W. Utsumi, M. Yamakata, T. Kikegawa and

0. Shimomura.

Phys. Rru.

B46, 6031 (1992).

0. Mlshima. L. D. Calvert and E. Whalley,

Nature

310,

393 (1984).

R. J. Hemley, C. T. Prewitt and K. J. Kingma. In

Reriews irl Mineralogy (Edited by P. J. Heaney, C. T.

Prewitt and G. V. Gibbs), Vol. 29, p. 41. Mineralogical

Society of America, Washington, DC

(

1994).

Y. Zhang, F. Zhang and G. Chen,

Curhon

32, 1415

.^.

lYY4).

56. F. R. Corrigan and F. P. Bundy,

J. Chem. Phvs.

63,

3x12 (1975).

57. R. B. Aust and H. G. Drickamer, Scipnc,r 140, Xl7

(1963).

5X. F. P. Bundy and J. S. Kasper,

J. Chem.

Phy.s. 46,

2437 (1967).

59. A. F. Goncharov, I. N. Makarenko and S. M. Stishov,

Ser. Pkys. JETP 69, 380 1989).


13/13

P,T phase and transformation diagram for carbon 153

60. M. Hanfland, H. Beister and K. Syassen, Phys. Rev.

B39, 2598 (1989)

61. W. Utsumi, M. Yamakata, T. Yagi and 0. Shimomura,

In Hi gh Pr essure Science and Technology, Proc.

AIRAPT and APS Co Colorado Springs, CO

(1993), p. 535.

62. M. Kertesz and R. Hoffmann, J. Sol. State Chem. 54,

313 (1984).

63. W. Utsumi and T. Yagi, Science 252, 1542 (1991)

64. P. S. DeCarli and J. C. Jamieson, Science 133, 182

(1961).

65. Netherlands Patent Release No. 6506395, Nov. 22,

1965, E. I. duPont de Nemours and Company.

66. L. F. Trueb, J.

Appl.

Phys. 39, 4707 (1968).

67. V. I. Trefilov, G. I. Davvakin, V. V. Skorokhod and

A. F. Khrienko, Sou. Phys. Dokl. 23, 269 (1978).

68. N. Setaka and Y. Sekihawa, J. bZateria[s Sci. 16, 1728

(1981).

69. G. Tammann, Z. Phys. Chem. 69, 569 (1910).

70. W. von Bolton, Z. Elektrochenz. 17, 971 (1911).

71. 0. RulT, Z. Anorg. Allgem. Chem. 99, 73 (1917).

72. B. V. Spitsyn and B. V. Derjaguin, USSR Patent, issued

S/S/SO (filed 1956, issued 1980).

73. R. A. Oriani and W. A. Rocco, Gen. Elec. Memo No.

MA-36, Class IV (Aug. 1957).

74. W. G. Eversole, U.S. Patent, issued 4/17/62 (filed 1958,

issued 1962)

75. J. C. Angus, H. A. Will and W. S. Stanko, J. App2.

Phys. 39, 29 15 (1968).

76. S. Matsumoto, Y. Sato, M. Tsutsumi and N. Setaka,

J. Mater. Sci. 17, 3106 (1982).

77. M. Kamo, Y. Sato, S. Matsumoto and N. Setaka,

J. Cryst. Grow th 62, 642 (1983).

78. B. V. Spitsyn, L. L. Bouilov and B. V. Derjaguin, Prog.

Crysf. Growth and Charac. 17, 79 (1988).

79. W. A. Yarbough, In Meto

Di amond Science und Technof-

ogy (Edited by R. Messier, J. T. Glass, J. E. Butler and

R. Roy), p. 291. Materials Research Society, Pittsburgh,

PA (1990)

80. E. A. Rohlfing, D. M. Cox and A. Kaldor, J. Chem.

Phys. 81, 3322 (1984).

81. H. W. Kroto, J. R. Heath, S. C. OBrien, R. F. Curl

and R. E. Smalley, Nature 318, 162 (1985)

82.

83.

84.

85.

86.

87.

88.

89.

90.

91.

92.

93.

94.

95.

96.

97.

98.

99.

100.

101.

102.

103.

104.

H. W. Kroto, Science 242, 1139 (1988).

R. F. Curl and R. E. Smalley,

Sci. Amer

265,54 (1991).

W. Kratchmer, D. D. Lamb, K. Fostiropoulos and D.

R. Huffman, Nature 347. 354 (1990).

D. R. Huffman, Phys. Today 44, 22(1991).

R. F. Curl and R. E. Smalley, Science 242, 1017 (1988).

S. J. Duclos, K. Brister, R. C. Haddon, A. R. Kortan

and F. A. Thiel,

Nature 351, 380

(1991)

G. A. Samara, J. E. Schirber, B. Morosin, L. V. Hansen,

D. Loy and A. P. Sylwester, Phys. Rev. Lett. 67,

3136, (1991)

M. N. Regueiro, P. Monceau and J.-L. Hodeau, Nature

355, 237 ( 1992).

N. Chandrabhas, A. K. Sood, D. V. S. Muthu. C. S.

Sundar, A. Bharathi, Y. Hariharan and C. N. R. Rao,

Phvs.

Rev.

Lett. 73. 3411 (1994)

F. -R. di Brozolo, T. E. Bunch, R. H. Fleming and

J. Macklin,

Nature 369, 37 (1994)

M. Nunez-Regueiro, L. Marques, J. L. Hodeau, 0.

Bethoux and M. Perroux, Phys. Rev. Lett. 74, 278

(1995)

J. A. Wolk, P. J. Horoyski and M. L. W. Thewalt, Phys.

Rev. Let t. 74, 3483 (1995)

A. K. McMahan, Phys. Rev. B30, 5835 (1984).

S. Fahy and S. G. Louie, Phys. Rev. B36, 3373 (1987).

R. L. Johnston and R. Hoffmann, J. Am. Chem. Sot .

111, 810 (1989).

A. Y. Liu, M. L. Cohen, K. C. Hass and M. A. Tamor,

Phys. Rev. B43, 6742 (1991).

C. Mailhiot and A. K. McMahan, Phys.

Rev.

B44,

11578 (1991).

A. Y. Liu and M. L. Cohen, Phys. Rev. B45, 4579

(1992).

Y. Bar-Yam, T. Lei, T. D. Moustakas, D. C. Allan and

M. P. Teter, In MRS Symp. Proc. 242, W ide Band Gap

Semi conductors (Edited by T. D. Moustakas, J. I. Pan-

kove and Y. Hamakawajp. 335, (1992).

M. Teter. Phvs. Rev. B48. 5031 (1993).

K. Vogel and R. Nesper, J. Mol. Cat aL 82,467 (1993).

J. Crain, S. J. Clark, G. J. Ackland, M. C. Payne, V.

Milman, P. D. Hatton and B. J. Reid, Phys. Rev. B49,

5329 (1994).

J. Furthmuller, J. Hafner and G. Kresse, Phys. Rev.

B50, 15606 (1994).

Date post:	03-Jun-2018
Category:	Documents
Upload:	cris1104
View:	237 times
Download:	0 times

Art Diamante

Documents