Thermodynamic characteristics of the laser evaporation of amorphous
carbon nitride
Sergei I. Kudryashov,* Oleg V. Kravchenko, Nikita B. Zorov and Yurii Ya. Kuzyakov
Department of Chemistry, M. V. Lomonosov Moscow State University, 119899 Moscow, Russian Federation.
Fax: +7 095 431 3063; e-mail: serg@laser.chem.msu.su
A study of the thermodynamics of laser evaporation of amorphous carbon nitride makes it possible to predict the optimum
conditions for the laser deposition of crystalline films of superhard carbon nitride.
Numerous recent studies into the synthesis of nitrogen– carbon
materials, initiated by the prediction of the existence of a
superhard crystalline phase of b-C
3
N
4
,
1
touch on fundamental
problems of the thermodynamics of evaporation and condensation
of these compounds, such as the deposition temperature of
films, vapour composition, etc.
2– 4
However, such studies are
still really scant and generally not focused, thus on the whole
the problem of synthesising the crystalline phase of b-C
3
N
4
remains as yet unsolved.
In this work, we used laser evaporation and the photo-
acoustic method for detecting its parameters, to study over the
range 400–800 K the evaporation curve of amorphous carbon
nitride, a polymer with a symm-heptazine monomeric moiety
and a molecular formula C
3
N
4.25
. We also determined the
temperature dependence of the heat of evaporation of the
material and calculated the probable vapour composition. The
data obtained allowed us to make assumptions about the range
of optimum conditions for the laser deposition of crystalline
films of superhard carbon nitride.
Using the photoacoustic method,
5
the following physical
characteristics of an amorphous carbon nitride specimen
with a bulk density of r
s
=1.6gcm
–3
were determined: the
propagation velocity of acoustic waves, 2700± 300 m s
–1
; the
extinction coefficient,
a
(532 nm) = (1.0± 0.1)× 10
4
m
–1
; and the
dependence of mean crater depth
X
(
e
) per laser pulse on the
fluence (Figure 1). The reflection coefficient of the material,
R
(532 nm) = 0.07± 0.02, was determined by reflectometry.
In the case of pulse laser evaporation, the experimentally
measured crater depth per laser pulse,
X
, depends on the rate of
movement of the evaporation frontier in the target,
V
ev
, by a
differential equation:
On the other hand, the absolute rate theory gives the following
formula for the rate of movement of the evaporation frontier:
where
C
is a constant and
DnH
(
T
) is the evaporation heat of
amorphous carbon nitride.
The evaporation temperature for a weakly absorbing surface
can be calculated by the equation
in which the first term is the starting temperature of the
specimen (293 K), and the second corresponds to temperature
increase during a laser pulse with an increase in fluence,
e
(
t
), due to laser-induced heating (for a molar volume of
V
m
=8cm
3
mol
–1
and a heat of
C
p
=25Jmol
–1
K
–1
). Obviously,
due to the high absorption depth in the material studied, the
maximum evaporation temperature
T
(
t
) is achieved at the end
of the laser pulse (Figure 1).
Substituting equations (1) and (3) into (2), we obtained an
expression for the heat of evaporation
DnH
(
T
) of amorphous
carbon nitride in the form
Taking into account the fact that the experimentally measured
X
(
t
) is an integral value,
V
ev
was calculated through finite
differences of
X
and
e
for the average value
e
av
=(
e
i
+1
+
e
i
)/2
and temperature
T
(
e
av
)
where the physical meaning of the denominator in the middle
part of the equation corresponds to a laser pulse duration with
integral fluence
e
i
+1
, during which the crater deepens by
X
i
+1
–
X
i
as the fluence increases by
e
i
+1
–
e
i
. The calculated
magnitudes of
T
av
,
V
ev
(
T
av
) and
DnH
(
T
av
) are presented in
Table 1.
The heats of evaporation per atom of amorphous carbon
nitride in the temperature range 400– 700 K (Figure 2) correlate
with the heats of formation of C
2
N
2
molecules (300 kJ mol
–1
)
6
Table 1
Experimental and calculated parameters of the laser evaporation of amorphous carbon nitride.
e
/J cm
–2
T
(
t
)/K
e
av
/J cm
–2
T
av
/K
D
n
H
(
T
av
)/kJ mol
–1
vapour composition,
Z
/atoms per cluster
P
s
(
T
av
)/kbar
2.3± 0.2 367± 72 2.6± 0.2 376± 66 69± 56 4 0.14± 0.08
3.0± 0.2 388± 73 5.6± 0.4 472± 81 16± 11 22 0.41± 0.25
8.3± 0.6 557± 86 10.3± 0.7 622± 107 13 ± 11 26 0.92± 0.53
12.4± 0.8 689± 104 15.4± 1.1 786± 127 1.81± 1.10
18.5± 1.3 885± 152
V
ev
[
T
(
t
)] =
d
X
d
t
(1)
V
ev
(
T
)
»
C
exp[–
D
n
H
(
T
)/
kT
]
kT
h
(2),
T
(
t
)=
T
0
+
(1 –
R
)
a
V
m
e
(
t
)
C
p
(3),
10
8
6
4
2
0 5 10 15 20
900
800
700
600
500
400
300
laser fluence/J cm
–2
Crater depth/
m
m
M
a
x
i
m
u
m
t
e
m
p
e
r
a
t
u
r
e
/
K
Figure 1
Dependence of mean crater depth during an irradiation pulse
and maximum temperature on the surface of an amorphous carbon nitride
target on irradiation fluence.
D
n
H
(
T
)=
RT
2
()
d
V
ev
d
T
1
T
1
V
ev
(4)
V
ev
(
T
av
)= =
X
i
+1
–
X
i
t
[(
e
i
+1
–
e
i
)/
e
i
+1
]
e
i
+1
t
d
X
(
e
av
)
d
e
(5)
, 1998, 8(2), 73–74
– 73 –