Phase diagram of the polymeric nitrogen
The results of theoretical prediction of the phase transition lines of molecular nitrogen into the polymeric phase at high pressure are presented. The role of the polymeric phase structure in the location of the transition lines on the phase diagram is considered. Possible configuration of the mel...
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irk-123456789-1279302018-01-01T03:03:02Z Phase diagram of the polymeric nitrogen Yakub, L.N. 10th International Conference on Cryocrystals and Quantum Crystals The results of theoretical prediction of the phase transition lines of molecular nitrogen into the polymeric phase at high pressure are presented. The role of the polymeric phase structure in the location of the transition lines on the phase diagram is considered. Possible configuration of the melting curve of the polymeric nitrogen solid forming the polymeric liquid is discussed. Predicted volumes of the coexisting phases are compared with experimental data and with results of the computer simulations. 2015 Article Phase diagram of the polymeric nitrogen / L.N. Yakub // Физика низких температур. — 2015. — Т. 41, № 6. — С. 576-581. — Бібліогр.: 26 назв. — англ. 0132-6414 PACS: 64.70.dj, 64.70.D–, 61.43.Bn http://dspace.nbuv.gov.ua/handle/123456789/127930 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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10th International Conference on Cryocrystals and Quantum Crystals 10th International Conference on Cryocrystals and Quantum Crystals Yakub, L.N. Phase diagram of the polymeric nitrogen Физика низких температур |
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The results of theoretical prediction of the phase transition lines of molecular nitrogen into the polymeric
phase at high pressure are presented. The role of the polymeric phase structure in the location of the transition
lines on the phase diagram is considered. Possible configuration of the melting curve of the polymeric nitrogen
solid forming the polymeric liquid is discussed. Predicted volumes of the coexisting phases are compared with
experimental data and with results of the computer simulations. |
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Article |
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Yakub, L.N. |
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Yakub, L.N. |
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Yakub, L.N. |
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Phase diagram of the polymeric nitrogen |
| title_short |
Phase diagram of the polymeric nitrogen |
| title_full |
Phase diagram of the polymeric nitrogen |
| title_fullStr |
Phase diagram of the polymeric nitrogen |
| title_full_unstemmed |
Phase diagram of the polymeric nitrogen |
| title_sort |
phase diagram of the polymeric nitrogen |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2015 |
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10th International Conference on Cryocrystals and Quantum Crystals |
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http://dspace.nbuv.gov.ua/handle/123456789/127930 |
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Phase diagram of the polymeric nitrogen / L.N. Yakub // Физика низких температур. — 2015. — Т. 41, № 6. — С. 576-581. — Бібліогр.: 26 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT yakubln phasediagramofthepolymericnitrogen |
| first_indexed |
2025-07-09T08:01:44Z |
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2025-07-09T08:01:44Z |
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1837155597798080512 |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6, pp. 576–581
Phase diagram of the polymeric nitrogen
L.N. Yakub
Thermophysics Department, Odessa National Academy of Food Technologies
112 Kanatnaya Str., Odessa 65039, Ukraine
E-mail: unive@icn.od.ua
Received February 24, 2015, published online April 23, 2015
The results of theoretical prediction of the phase transition lines of molecular nitrogen into the polymeric
phase at high pressure are presented. The role of the polymeric phase structure in the location of the transition
lines on the phase diagram is considered. Possible configuration of the melting curve of the polymeric nitrogen
solid forming the polymeric liquid is discussed. Predicted volumes of the coexisting phases are compared with
experimental data and with results of the computer simulations.
PACS: 64.70.dj Melting of specific substances;
64.70.D– Solid-liquid transitions;
61.43.Bn Structural modeling: serial-addition models, computer simulation.
Keywords: molecular solids, polymeric solid, polymeric liquid, melting, equation of state, phase equilibria.
1. Introduction
During last decades condensed systems consisting of
simple molecules with multiple bonds, which under strong
compression are able to form multiple coordinated atomic
structures with the redistribution of chemical bonds, were
intensively investigated [1]. Such substances allow at ex-
treme conditions accumulating many times larger amount
of energy than the high-energy-density materials used to-
day. An excellent example of such type of substances is
molecular nitrogen.
The first experimental evidence of the specific behavior
of strongly compressed nitrogen was the effect of the
“shock cooling” discovered on the Hugoniot curve of liq-
uid nitrogen at high temperatures [2], which was interpret-
ed as a molecular dissociation with the first-order transi-
tion in shock-compressed nitrogen fluid. Shock-wave
experiments indicated a first-order phase transition with
the volume jump of 1.5–2.0 cm3/mol.
Theoretical studies [3–5] have suggested that this transi-
tion may be associated with the dissociation of nitrogen
molecules into atoms (with breaking of the strong triple
chemical bond), accompanied by formation of a set of ordi-
nary chemical bonds between nearest neighbors. Such tran-
sition into an atomic (or polymeric [5]) phase was supposed
to be possible in both the liquid and solid state. The first
theoretical estimations [3,4] predicted that one of the most
stable at T = 0 K atomic crystalline lattices should have a
layered A7 (arsenic-like) structure. Such hypothetical transi-
tion into the stable polymeric nonmetallic structure was ex-
pected to occur at a pressure of about 77 GPa and have
a significant (about 35%) decrease in the volume [3].
Autors [5] reported a new ab initio calculations, which
predicted the spatial cubic gauche (CG) lattice, in which
all atoms are triply coordinated, to be the most stable pol-
ymeric structure and to have the total energy slightly lower
than the layered A7 structure. However, this theoretically
predicted transition of molecular N2 low-temperature solid
into the polymeric CG crystalline form was not observed
for years what was attributed to a large energy barrier sep-
arating phases.
This theoretically predicted dissociation of the nitrogen
molecules at high pressure in solid state has been con-
firmed experimentally relatively recently [6–9]. Only in
2004 Eremets and co-workers succeeded in synthesizing
the crystalline form of triply coordinated polymeric nitro-
gen directly from the molecular nitrogen [9]. Diatomic
nitrogen was first heated up to temperature above 2000 K,
compressed in the diamond anvils by pressure higher than
110 GPa, and then analyzed by x-ray diffraction and Ra-
man spectroscopy. A limited number of x-ray diffraction
peaks produced by the powder formed not allowed until
recently confirming the existence of CG structure, but the
x-ray diffraction on the single crystal obtained in Ref. 10
confirmed it. Thus, thanks to the long-lasting efforts of
experimenters the existence of the transition of highly
compressed molecular nitrogen into the nonmolecular
(polymeric) phase has been convincingly proved.
© L.N. Yakub, 2015
Phase diagram of the polymeric nitrogen
In the solid molecular nitrogen at least two high-
pressure phases, which can be directly transformed into the
polymeric phase are known [11]. One of them (ζ-phase),
may be in equilibrium with the polymeric solid phase of
nitrogen at low temperatures, the second one (ε-phase) —
at high temperatures, in the vicinity of the melting line.
These two phases differ from each other in the lattice
type and in the character of molecular rotation. In the
monoclinic ζ-phase rotational motion is suppressed (only
molecular librations are possible) and in the rhombohedral
ε-phase molecular rotation is relatively free. The type of
the crystalline structure of these phases has not been clear-
ly established for a long time, although the region of stabil-
ity of each was known [11].
In this regard a few ab initio calculations of energy and
relative stability performed for a number of crystal struc-
tures of the polymeric nitrogen in recent years [12,13]
should be noted. They predicted the relative stability of the
CG structure in the pressure range of 50 up to 150 GPa.
However, the estimates of the CG stability region cannot
be considered as completely reliable because they do not
agree with the experimentally studied in this pressure
range part of the phase diagram [7,8] and were performed
at T = 0 K relative to the high-temperature molecular ε-phase
instead of the low-temperature ζ-phase.
Thus, the configuration of the phase diagram of the ni-
trogen at elevated temperatures in the range of extremely
high pressure up to the present time remains unclear. This
gap has been partially filled by a number of theoretical
works [14–18], and computer simulations [19,20].
The aim of this work is to discuss the results of these
theoretical predictions concerning the region of coexist-
ence between molecular and polymeric solid and liquid
phases of nitrogen in a wide range of temperatures and
extremely high pressures and consider the role of the pol-
ymeric phase structure in the shape of the phase diagram of
strongly compressed nitrogen.
2. Equations of state for high-pressure phases
of solid nitrogen
The theoretical prediction of location of the transition
lines in the phase diagram is a task requiring usage of the
equations of state. In the case of transitions without the
change of symmetry (e.g., liquid-liquid transition), it is
possible to apply a single (common) equation of state for
both coexisting phases. For example, in [14] a single equa-
tion of state was developed on the basis of the modified
“soft dumbbells–sticky spheres” model and was applied to
the highly compressed nitrogen fluid.
Within this model the partially polymerized fluid was
represented as a mixture of diatomic molecules N2, which
were modeled by soft dumbbells (whose diameters and
lengths of bonds depend on the temperature), with a set of
different polymeric clusters modeled by sticky spheres
capable of forming up to three rigid bonds to each other.
However, such approach is not applicable to the predic-
tion of transitions between crystalline phases. Two differ-
ent expressions for the free energy of coexisting phases
(called canonical equations of state) are necessary here.
Prediction of the pressure dependence of the equilibrium
phase transition temperature T(P) of the molecular nitrogen
into the polymeric phase in [16–18] was made on the basis
of two separate canonical equations of state, one for the po-
lymeric, and other for the molecular high-pressure phase.
Due to small energy difference between two high-
pressure crystalline phases of molecular nitrogen mentioned
above, in a number of studies (particularly in [5,16]) it was
used an approximate (β-O2-like) representation of the mo-
lecular structure of the high-pressure phase, and both these
phases were described by a single equation of state.
This equation of state for molecular high-pressure phase
of nitrogen was based on the atom-atom force crystal mo-
del [16], which takes into account both the repulsion of
nonbonded atoms and “chemical attraction” of atoms
joined by the triple bond in the N2 molecule. Parameters of
this force model were calibrated on the results of ab initio
calculation of the molecular crystal energy [5].
Helmholtz free energy was presented in the form
mol
(id)
mol mol 0lat( , ) ( , ) ( ) ln .f
m
v
F T V F T V U R N kT
v
= + −
(1)
Here (id)
lat ( , )F T V is the energy of an ideal molecular lat-
tice gas as a function of temperature and volume,
mol 0( )U R is the energy of static lattice, 0R is the length of
the (triple) chemical bond, / mv V N= and mol
fv are
the specific and so-called molecular free volume, respec-
tively. In Eq. (1) the molecular free volume has been ex-
pressed within the quasi-harmonic approximation in terms
of the lattice and the potential parameters [16].
Potential models for the crystalline phases of polymeric
nitrogen having A7 or CG structure always assume that
since the transition of a molecular phase into the polymeric
phase is accompanied by breaking of the triple bond and
forming of three single bonds, each atom has the first co-
ordination sphere formed by exactly three neighbors. In the
case of A7 lattice it is a layered structure, and in the case
of CG — a spatial polymeric structure.
In the first case, the model expression for the interac-
tion energy has the form [16]
1
1 bonded
1 ( ) ( ).
2N ij ij
i j N
U r U L
≤ < ≤
= Φ +∑ ∑ ∑ (2)
The first summation here is taken over all pairs of at-
oms, the second one — only over those who are nearest
neighbors and are bound by single bonds ( ijL are the in-
stant lengths of these bonds). As the origin of the energy
here the energy of isolated atoms are used.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 577
L.N. Yakub
To calculate thermodynamic properties of the polymeric
nitrogen crystalline phase, having the structure A7, a ca-
nonical equation of the classical crystalline was used [16].
The expression for the free energy in the first-order theory
has a form similar to the above equation molecular phase:
(at)
(id)(at)
rep 1 0at
1
( ) ln .f
a
v
F F U U L N kT
v
= + + ∆ −
(3)
Here (id)
at ( , )F T V is the energy of an ideal atomic lattice
gas as a function of temperature and volume, 1 0( )U L∆ is
the energy of the А7 static lattice, 0L is the equilibrium
length of a (single) chemical bond, 1 / av V N= and (at)
fv
are the specific and atomic free volume, respectively. The
quantities 1 0( )U L∆ and (at)
fv in Eq. (3) were expressed in
terms of the lattice parameters and parameters of the inter-
action potentials in Eq. (2).
Using the explicit expression for the free energy Eq. (3)
and conventional thermodynamic relations, one can calcu-
late all thermodynamic functions, including chemical po-
tential and pressure necessary for the calculation of the
phase equilibria.
A slightly different approach was used to develop the
potential model for the polymeric CG crystalline structure
of the nitrogen observed in experiments. To describe the
nonbonded interactions of all pairs of nonbound atoms in
the crystal the same atom-atom force model as applied to
polymeric A7 structure was used. But the valence forces
acting between bound atoms were described more detailed
by a function depending both on the bond lengths and bond
angles between pairs of single bonds attached to atoms.
Parameters of such model were calibrated to reproduce the
results of testing the sensitivity of the CG crystal energy,
obtained in ab initio quantum mechanical calculations [5],
to the deformation of bonds and variation of bond angles.
This potential model was used in Monte Carlo computer
simulations [19] of polymeric CG solid (512 atoms in the
box and periodic boundary conditions). The simulation
results, in turn, were used in [18] to determine the parame-
ters of the equation of state for CG phase.
The results of Monte Carlo simulations [19] indicate
that the polymeric CG structure exhibits at high densities
the negative values of thermal expansion coefficient. This
specific behavior of thermodynamic properties cannot be
reproduced by the canonical equation similar to Eq. (3).
To describe the specific behavior of thermodynamic
properties, in particular the negative thermal expansion, in
Ref. 18 was suggested a new canonical equation of state
for CG polymer phase of solid nitrogen. Helmholtz free
energy was represented as a sum of two contributions, qua-
si-harmonic and anharmonic ones:
(at) ( ) (anh).hF F F= + ∆ (4)
The main contribution to the Helmholtz free energy in Eq.
(4) is the quasi-harmonic contribution ( )hF described by
the modified Mie-Grüeneisen model:
( )( )
1 3 ( ).CGh
a F DF U N kT D x= + (5)
Here ( )
1
CGU is the energy of the static lattice, / ,D Dx T= Θ
( )F DD x is Debye function, and DΘ is the Debye tempera-
ture. The Grüeneisen parameter ln / lnDd dγ = Θ ρ was
specified as a linear function of density: 0 0(1 / ).γ = γ −ρ ρ
This model contains two constants: 0γ and 0.ρ These con-
stants were determined using the above-mentioned Monte
Carlo data [19].
Anharmonic effects in the solid polymeric nitrogen at
high temperatures may be very significant [19]. The con-
tribution of anharmonic effects to the free energy (anh)F∆
was determined by the deviations of the specific heat from
the Dulong-Petit law, found in computer simulations [20].
3. Phase equilibria of the polymeric and molecular
phases in solid nitrogen
Equations of state for both molecular and polymeric
phases were used in Ref. 18 to determine T(P)-dependence
of the polymerization phase transitions. In the calculation
of the parameters of the phase transition, the conditions of
material equilibrium, i.e., the equality of the chemical po-
tentials (per atom) and mechanical equilibrium (equality of
pressure for both phases) were used. Because coexisting
phases were described by two separate equations of state
based on different potential models they must have a
common origin of energy. Therefore, the chemical poten-
tial of the polymeric phase was calculated by:
(at)
(at)
0
at
( , )( , ) .F T VT V
N
∂
µ = + ∆µ
∂
(6)
Here 0∆µ =–0.98 eV/atom is the difference in the ori-
gins of the polymeric and molecular phases [5].
Calculation of the phase equilibrium was carried out
numerically using the standard method of double tangent,
i.e., the equilibrium pressure of phase transition at a given
temperature P(T) was determined by the slope of the com-
mon tangent for to mol ( , ),F T V and (at)
0( , )F T V + ∆µ curves
versus volume and orthobaric volumes — by abscissae of
these tangency points.
Results of such calculations are illustrated in Fig. 1,
where two T(P)-curves for two types of polymeric struc-
tures — CG and A7 — are presented. As can be seen, the
equilibrium pressure of the transition into the A7 structure
increases monotonically with increasing temperature, and
P(T)-dependence in the case of CG structure is just the op-
posite. As it was shown in Ref. 18, these differences are
explained by the negative thermal expansion found in CG
phase.
In the case of the CG polymeric structure the phase
transition line T(P) intersects with the melting line at
578 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6
Phase diagram of the polymeric nitrogen
T ~ 1500 K and at a relatively low pressure of about
50 GPa. It is interesting to note that the hypothetical triple
point (solid molecular nitrogen-solid polymeric liquid ni-
trogen) predicted in Ref. 18 is approximately in the same
region, where, according to measurements of Mukherjee
and Boehler [23], as well as of Goncharov et al. [22]
the maximum of melting temperature was observed.
According to Ref. 18, the latent heat of polymerization
transition L into CG phase increases approximately line-
arly with temperature, like the case of the A7 structure but
has the opposite sign. This means that the entropy jump
∆S = L/T is almost constant. At the same time, unlike
the N2–A7 transition, heat of transition is negative. At
T ~ 1000 K the latent heat reaches L ~ –1.0 eV/atom, when
the predicted heat of transition in the structure A7 is about
0.7 eV/atom. There is also a significant difference in the
orthobaric volumes behavior of coexisting phases. In the
case of N2–A7 transition these volumes slightly decrease
with temperature. In the case of transition into the poly-
meric CG phase both orthobaric volumes mol ,V and poly ,V
and the jump in volume mol polyV V− increase with tem-
perature. Thus, in evaluating the thermodynamic behavior
of the molecular-to-polymeric crystal transition at nonzero
temperature the type of the structure of polymeric phase is
very important.
In Fig. 2 the calculated orthobaric volumes [18] are
compared with the experimental data [21] at room temper-
ature. This comparison shows that the calculated volumes
of both molecular and polymeric phases, although some-
what overestimated, are in reasonable agreement with ex-
isting measurements of Eremets et al. [9,10,21], obtained
in the diamond anvil cell at room temperature and pres-
sures up to 2 Mbar.
The predicted value of the volume jump is very close to
the measured. Eremets et al. found 22% of volume change,
theoretical result was about 21%. Predicted volume of the po-
lymeric phase agrees with the experimental value at room
temperature within 2% and the volume of the molecular
phase within 6%.
4. Evaluation of the melting line of polymeric nitrogen
The generality of the idea, which explains the phenome-
non of polymerization in the liquid and solid phases, allows
using canonical equations of state of two phases, to predict
the transition line where the crystalline polymeric nitrogen
melts forming polymeric liquid. Such a prediction was sug-
gested in Ref. 25 where two canonical equations of state: the
modified equation of Mie-Grüeneisen Eq. (5) for the solid
polymeric CG nitrogen, and the equation of state for the
liquid polymeric nitrogen proposed in Ref. 26 were used.
The parameters of the last equation of state were deter-
mined by reproducing the results of the recent ab initio
simulations of Boats and Bonev [20], including the pre-
dicted location of the liquid–liquid coexistence line in
highly compressed nitrogen.
The expression for the Helmholtz free energy of the
polymerizing liquid generalizes the canonical equation of
state for polymeric nitrogen fluid, proposed earlier in
Ref. 14. The expression for the Helmholtz free energy has
the following form:
(id) ( )
1 polypoly ( ) ( ) ( ).HD
LF F F F= α + ∆ η +α∆ η (7)
Here (id)
poly ( )F α is the free energy of an ideal mixture of
monomers (N2), dimers N4, etc., an explicit expression for
which was obtained in Ref. 26, and α is the degree of poly-
merization, (i.e., portion of all molecules bound in all types
of clusters). Functions ( )
1( )HDF∆ η and poly ( )LF∆ η ex-
press the correction on nonideality of the mixture of hard
Fig. 1. Calculated dependences of the equilibrium phase transi-
tion temperature of solid nitrogen from the molecular phase into
polymeric phase as a functions of pressure. Dashed line corre-
sponds to A7 and the dash-dotted line to CG structure.
Fig. 2. Comparison of the calculated orthobaric volumes of the
coexisting molecular and CG polymeric phases [18] with the
available experimental data at room temperature [21].
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 579
L.N. Yakub
dumbbells and the excess free energy of polymeric fluid [14],
correspondingly. Respectively, they are dependent on two
types of packing fractions: “molecular” 3
1 /3ndη = π and
“polymeric” 3 /3L Lndη = π ones, where d is the effective
molecular diameter and dL is the effective diameter of
an atom in the polymeric liquid. Parameters of this equa-
tion of state have been determined in Ref. 26 and repro-
duce the results of ab initio simulations [20]. In particular,
the liquid–liquid separation line in partially polymerized
nitrogen liquid with critical point at TC = 4890 K [26].
Equations of state Eqs. (7) and (3) were used in [25] to
find pressure dependence of the melting temperature Tm of
CG crystalline polymer, orthobaric volume of solid and
liquid phases, and latent heat of fusion. Results of calcu-
lating Tm(P) are presented in the phase diagram (Fig. 3)
in comparison with existing experimental data on melting
line of nitrogen [23,24]. As one can see in Fig. 3, near to
T = 1700 K and P = 70 GPa a triple point of the crystal poly-
mer–polymer liquid–molecular liquid-type is formed.
As it was already noted above, the equation of state for
the liquid polymeric nitrogen Eq. (7) was calibrated on ab
initio simulation data presented by Boats and Bonev [20]
in a temperature range 2000–5000 K. Therefore, the calcu-
lations in Ref. 25 were performed only within a reasonable
limited extrapolation to T < 2000 K and hence cover a lim-
ited range of temperatures and pressures.
Despite this limitations, an important qualitative feature
of the predicted Tm(P) dependence should be noted — it
decreases with increasing pressure, like the transition tem-
perature of molecular crystal into the polymeric CG phase.
Predicted melting temperature falls from 1750 K at 80 GPa
up to 1500 K at 95 GPa. This behavior is in agreement
with the recent measurements of Goncharov et al. [22],
who observed a maximum melting temperature in this
pressure range. The predicted value of the latent heat of the
CG crystal melting is also negative and its absolute value
increases with increasing temperature. At T = 1700 K, the
value of the latent heat reaches –2.0 eV/atom [25].
5. Discussion and conclusions
Phase transitions of simple highly compressed homo-
nuclear systems from the molecular into the nonmolecular
forms (dissociation, ionization, polymerization) have been
long attracted the attention of scientists as a promising way
for obtaining materials with high density of energy. Study
the conditions of formation of such high-energy-density
phases requires, inter alia, studying phase diagrams of such
systems at extreme pressures, where such transitions may
occur. In the recent decades, the main attention of experi-
mentalists in this direction was attracted to investigating
the possibility of polymerization of molecular nitrogen in
the crystalline state. However, the objective difficulties of
such research at ultrahigh pressures do not allow complete
solving of this problem using experimental methods only.
Theoretical study of these transitions and prediction of
their location in the phase diagram at high pressures and
temperatures is a problem which can be solved by invoking
canonical equations of state based on the ground of statisti-
cal physics. Successful development of such equations
of state depends on the underlying microscopic theoretical
models. Practical application of the theory is always strongly
dependent on the adequacy of potential models, used for
description of atomic and molecular interactions in a solid,
and on the possibility of their calibration on reliable ab ini-
tio quantum mechanical calculations.
A number of potential models, focused on the descrip-
tion of the specificity of the interaction in the studied sys-
tems have been applied to predict the positions of lines of
phase transitions accompanied by dissociation of nitrogen
molecules and formation of a spatial network of covalent
bonds between atoms.
Such potential models, calibrated on the limited ab ini-
tio calculations of the static lattice energy of systems stud-
ied, which correspond to their state at zero temperature,
can be successfully applied in conventional computer sim-
ulations (e.g. Monte Carlo or molecular dynamics), which
are able to predict the behavior of high-energy-density
systems at elevated temperatures. An example of a suc-
cessful application of this approach is the Monte Carlo
simulation of the spatially-polymerized CG nitrogen [20],
where the effect of the negative thermal expansion in the
crystalline and amorphous structures was discovered.
As it was revealed later [25], this fact plays an important
role not only in explaining the specific features of the thermo-
dynamic behavior in polymeric phase, but also in configura-
tion of the phase diagram of nitrogen at high pressures.
Fig. 3. Phase diagram of strongly compressed nitrogen. The solid
lines show the calculated transition line from the molecular to CG
polymeric phase, the melting line of the polymeric solid and
the transition line liquid–liquid in partially polymerized nitrogen:
1 are the computer simulation results [20], 2–4 are the experi-
mental data on the melting line.
580 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6
Phase diagram of the polymeric nitrogen
Pressure dependence of the transition temperature into
the spatial-polymerized high-pressure CG phase of nitro-
gen, having negative thermal expansion at high densities,
has a negative slope, while the same dependence of the
phase transition into the (hypothetical) layered polymeric
A7 structure will be monotonically increasing, if such
phase were stable.
It should also be noted that the effects of negative ther-
mal expansion is manifested also in the negative slope
the predicted pressure dependence of the melting tempera-
ture of the polymeric CG nitrogen shown in Fig. 3. Alt-
hough in some aspects the parameters of this phase dia-
gram differ from the predictions of some computer ab
initio calculations, in general, as shown above, they are in
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 581
1. Introduction
2. Equations of state for high-pressure phases of solid nitrogen
3. Phase equilibria of the polymeric and molecular phases in solid nitrogen
4. Evaluation of the melting line of polymeric nitrogen
5. Discussion and conclusions
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