Combustion, Explosion, and Shock Waves, Vol. 38, No. 3, pp. 358 359, 2002
Phase Diagram of Ultrafine Carbon
A. L. Vereshchagin1 UDC 548.7
Translated from Fizika Goreniya i Vzryva, Vol. 38, No. 3, pp. 119 120, May June, 2002.
Original article submitted May 3, 2001; revision submitted October 23, 2001.
A three-dimensional phase diagram of carbon has been built in the coordinates
 pressure temperature dispersivity on the basis of the published data on detonation-
diamond properties.
Key words: three-dimensional phase diagram, detonation diamond, nanoscale dia-
mond particles, ultrafine carbon.
The interface of phases in the carbon state dia- point with a higher degree of dispersivity. This effect is
gram has long been the subject of constant refinement characteristic of all the substances in the ultrafine state.
in the range of superhigh pressures and temperatures. (Since there are no graphic data in [6, 7], the results of
The last variant was updated [1] for the interface be- these studies have not been used in state-diagram con-
tween liquid carbon and diamond; it was shown that struction.)
liquid carbon near the interface with crystalline dia- A state diagram of carbon is constructed using yet
mond has a lower density. Recently, however, new meth- scarce experimental data on detonation diamonds. A
ods developed for the production of ultrafine diamond state diagram of carbon in a massive state is located
gave grounds to a conclusion that this diagram of state in the horizontal plane [1], and the vertical axis shows
cannot be used to consider the process of synthesizing the size of system particles, which is a thermodynamic
nanoscale diamond particles in a detonation wave [2]. parameter for disperse materials [8]. In the horizontal
As early as in [3, 4], it was noted that the diagram plane, the particle size is assumed to be 100 nm (which
of state of a one-component ultrafine system would be makes it possible to neglect the surface phenomena con-
different from the state diagram of a massive substance tribution to the properties of a material). The mini-
by the phase equilibria line positions in passing from the mum size of diamond particles produced by detonation
disperse solid state to the liquid state or from the amor- is 1.8 nm [9 11]. Therefore, in the vertical plane, the
phous to the crystalline state. The positions of phase domain of existence for the diamond phase extends to
equilibria lines can be estimated in the approximation 1.8 nm. The position of the carbon triple point changes
allowing for the change in the entropy of the ultrafine with changing particle size. The vertical plane was con-
system and the excess surface energy [5]. structed on the basis of the data from [12, 13], where
There are two well-known opposite approaches to it was shown that spherical diamond particles with an
the construction of phase diagrams. The first approach average size of 4 nm are produced from the liquid state
consists in measuring thermodynamic characteristics at a temperature of 3000 K. Therefore, it was assumed
followed by the calculations using thermodynamic laws that the position of the carbon triple point may shift
and the model employed. The second approach involves from 5000 to 3000 K in passing to 4 nm particles. Un-
the experimental construction of a phase diagram using der those conditions, the interfaces of solid phases of
methods of physical and chemical analysis. graphite and diamond will also change. As is reported
The construction of a phase diagram of ultrafine in [14, 15], for a particle size of 2.5 3.0 nm, diamond is
carbon based on thermodynamic calculations was stud- more thermodynamically stable than graphite. There-
ied in [6, 7]. These studies report a shift in the lines of fore, there is only a diamond phase in the upper part
phase equilibria and a decrease in the carbon melting of the state diagram in the range of particle sizes less
than 3 nm.
1
Biisk Institute of Technology, It follows from the constructed three-dimensional
Altai State Technical University, Biisk 659305;
diagram that part of the space bounded by the surfaces
[e-mail].
358 0010-5082/02/3803-0358 $27.00 © 2002 Plenum Publishing Corporation
Phase Diagram of Ultrafine Carbon 359
4. I. D. Morokhov, L. I. Trusov, and V. N. Lapovok,
Physical Phenomena in Ultrafine Media [in Russian],
Énergoatomizdat, Moscow (1984), p. 195.
5. A. I. Bublik and B. Ya. Pines,  Phase transition under
thickness changes in thin metal films, Dokl. Akad. Nauk
SSSR, 87, No. 2, 215 218 (1952).
6. S. B. Viktorov, S. A. Gubin, and I. V. Maklashova,
 Thermodynamic calculations of the state diagram of
disperse carbon phases, in: Physical Chemistry of
Ultrafine Systems: Proc.of the IV All-Russian Conf.,
Moscow (1999), pp. 195 196.
7. S. B. Viktorov, S. A. Gubin, and I. V. Maklashova,
 Equations of state for ultrafine graphite and diamond
particles, in: Physical Chemistry of Ultrafine Systems,
Proc. of the V All-Russian Conf., Eng.-Phys. Inst.,
Moscow (2000), pp. 49 50.
Fig. 1. Phase diagram of ultrafine carbon:
8. Yu. G. Frolov, Course of Colloid Chemistry. Surface
OBTT1T1a is the existence domain of the graphite
Phenomena and Disperse Systems [in Russian] Khimiya,
phase, OTT1T1a is the interface between the graphite
Moscow (1982), p. 83.
and diamond phases, BTT1 is the interface between
9. I. Yu. Mal kov,  Formation of the ultrafine diamond
the liquid carbon and graphite phases, and TT2L1L is
phase of carbon at detonation of heterogeneous mix-
the interface between the liquid carbon and diamond
phases.
ture compositions, Fiz. Goreniya Vzryva, 27, No. 5,
136 140 (1991).
10. I. Yu. Mal kov  Analysis of factors determining effi-
OT1aT1B, is the stability range of graphite, and the
ciency of diamond formation by detonation, in: Ultra-
remaining part is the domain of diamond existence.
fine Powders, Materials, and Nanostructures [in Rus-
The properties of ultrafine carbon have not yet
sian], State Univ., Krasnoyarsk (1996), pp. 47 48.
been studied in sufficient detail; therefore, many ele-
11. S. V. Pershin, E. A. Petrov, and D. N. Tsaplin,  In-
ments of this state diagram will have to be significantly
fluence of the molecular structure of explosives on the
refined in future.
rate of formation, yield, and properties of ultradisperse
diamond, Combust. Expl. Shock Waves, 30, No. 2, 235
238 (1994).
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