Roberto Bini et al- High-pressure phases of solid nitrogen by Raman and infrared spectroscopy

8/3/2019 Roberto Bini et al- High-pressure phases of solid nitrogen by Raman and infrared spectroscopy

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High-pressure phases of solid nitrogen by Raman and infrared spectroscopy

Roberto Binia)

Dipartimento di Chimica dellUniversita di Firenze, Via G. Capponi 9, I-50121 Firenze, ItalyLENS, European Laboratory for Non-linear Spectroscopy, Largo E. Fermi 2, I-50125 Firenze, Italy

Lorenzo Ulivib)

Istituto di Elettronica Quantistica, Consiglio Nazionale delle Ricerche, and INFM Via Panciatichi 56/30,I-50127 Firenzo, Italy

Jorg Kreutzc)Fachbereich Physik, Universitat Kaiserslautern, E. Schrodinger Str., 67663 Kaiserslautern, Germany

Hans J. Jodld)

Fachbereich Physik, Universitat Kaiserslautern, E. Schrodinger Str., 67663 Kaiserslautern, GermanyLENS, European Laboratory for Non-linear Spectroscopy, Largo E. Fermi 2, I-50125 Firenze, Italy

Received 5 November 1999; accepted 24 February 2000

Raman and infrared spectra of solid nitrogen have been collected between 25 K and room

temperature up to 41 GPa. A careful analysis of the spectral band transformations occurring across

the high pressure transitions among the , loc , , and phases allowed to define the phase diagram

in the whole P-T region investigated. In particular, the transition between the and phases has

been observed in the range 30230 K and the corresponding phase-boundary drawn. A significant

metastability region spanning about 10 GPa in pressure hinders the transformation between the

and phases when pressure is varied at low temperature. Group theory arguments suggest acentrosymmetric structure for the phase and the number of Raman and infrared 1 and 2components can be reproduced both with cubic and tetragonal structures. An appreciable coupling

among neighboring molecules is observed, at room temperature, only in the phase where the

relative orientations of the molecules are fixed. 2000 American Institute of Physics.

S0021-96060001219-8

I. INTRODUCTION

Diamond anvil cells are extensively used to study the

properties of simple molecular solids in the high-pressure

regime.1 Among this class of crystals nitrogen is considered

in many respects a model system.2,3

This is attested by thelarge number of experimental and theoretical investigations

carried out on condensed nitrogen. Five solid phases , ,

, , have been identified at pressures up to 10 GPa and

temperatures below 300 K see Fig. 1. Recent infrared

results4 have complemented previous Raman data5,6 allowing

the characterization of a sixth structural modification (loc)

discovered in the P-T plane between the and the phases.

The complete vibrational analysis, based on group theoreti-

cal arguments, allowed to propose a cubic structure for the

loc phase which closely recalls that of the phase. The

disklike molecules of the phase have fixed orientation in

the loc phase and the amplitude of the fluctuations around

the new positions progressively decrease lowering the tem-perature.

Spectroscopic experiments on solid nitrogen have been

performed at room temperature up to more than 100 GPa,712

x-ray data, available up to 50 GPa, agree on a phase transi-

tion at 16.5 GPa which was assigned to the phase

transition.8,10 Recent x-ray experiments using synchrotron ra-

diation revealed another transition at 11 GPa between the

cubic phase and a new phase which is probably coincident

with the already described loc phase.13 More contrasting are

the results derived from Raman experiments. At room tem-

perature, two transitions were detected by Reichlin et al. at20 and 66 GPa.9 Later, Schneider et al. fixed the stability

limit of the phase between 17 and 20 GPa, and another

phase was supposed to exist above 20 GPa up to 4050

GPa.7 These results were recently contradicted by a line

shape analysis of the internal Raman bands up to 30 GPa. 14

At lower temperature 30015 K the pressure range inves-

tigated is much smaller ( P30 GPa),5,6,1521 furthermore

below 100 K only Raman19 and infrared up to 7 GPa4,21

experiments have been performed above the phase

boundary 2 GPa.

As to the phase, the results are consistent with a mul-

tisite rhombohedral R3

c structure having eight moleculesper cell. Six molecules are located on sites with C2 symme-

try while the other two molecules are on sites with a S 6symmetry. The stretching modes relative to the two sites are

indicated, according to the terminology used for the phase,

as 2 and 1 , respectively. On the basis of group theoretical

arguments one Raman band of symmetry A 1g is expected

for the 1 mode while three bands, two Raman, of symmetry

A1g and Eg , and one infrared, of symmetry Eu , are pre-

dicted in the 2 region. In the low-temperature Raman spec-

trum only two peaks one for each the 1 and the 2 were

aElectronic mail: [email protected] mail: [email protected] mail: [email protected] mail: [email protected]

JOURNAL OF CHEMICAL PHYSICS VOLUME 112, NUMBER 19 15 MAY 2000

85220021-9606/2000/112(19)/8522/8/$17.00 2000 American Institute of Physics


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observed below 21 GPa. Above this pressure a splitting of

the 2 Raman band was detected.19 This observation has

been interpreted as due to a phase transition to a new rhom-

bohedral structure , which was speculated to have a R3c

symmetry. In the infrared spectrum one band is observed in

the 2 region, up to 7 GPa.21 Recently the infrared analysis

was extended up to 9 GPa confirming this observation.4

In this paper we report on an extended study of both

infrared and Raman spectra of solid nitrogen up to 40 GPa

between room temperature and 25 K. Several isobaric and

isothermal cycles were performed in order to clarify the sta-

bility range of the loc and of the phases. According to

these results we were able to establish the phase diagram

below 295 K and 40 GPa.

II. EXPERIMENT

High-pressure infrared and Raman spectra of solid nitro-

gen were measured using a membrane diamond anvil cell

MDAC. The crystals were produced by loading the cell

either cryogenically, or with gaseous N2 (purity99.99%)by means of an high-pressure gas loading equipment. A ruby

chip was inserted in the sample and the pressure determined

from the peak wavelength of the R 1 ruby fluorescence band.

The uncertainty in the pressure determination is less than

1%. The complete apparatus for infrared experiments, in-

cluding the optical beam condenser and the cryogenic sys-

tem, has been extensively described in a previous report.22

Both infrared and Raman setup were the same employed in a

previous experiment on nitrogen.4 The instrumental resolu-

tion was better than 0.1 and 0.3 cm1 in infrared and Raman

experiments respectively, while the frequency accuracy was

0.1 cm1 in Raman and much higher 0.005 cm1 in infra-

red measurements. The temperature of the sample is mea-

sured by a Si-diode placed in the copper ring where the dia-

mond is mounted, the resulting uncertainty on the sample

temperature is estimated in 2 K.

In all the experiments the sample was prepared starting

from the disordered phase 2 to 3 GPa, the - phase

transition was slowly crossed at room temperature, the

sample annealed at about 300 K for not less than 21 hours

below 5 GPa. All the cooling cycles were performed at con-

stant pressure at the rate of 2 to 3 K per hour.

III. RESULTS

The phase diagram of solid nitrogen was carefully

probed between 25 K and room temperature along several

isobars up to 40 GPa in Raman and 30 GPa in infrared ex-

periments. Also isothermal scans were performed up to the

same final pressures values at 25, 100, and 300 K. For the

sake of clarity we will present the Raman and the infrared

results in two distinct subsections.

A. Raman

Room temperature spectra in the loc and phases see

Fig. 2 relative to the intramolecular vibration region showtwo symmetric peaks, assigned to the 1 and 2 modes, up to

about 17 GPa. Above this pressure the 2 peak starts to be

asymmetric on the high-frequency side, and a weaker band is

clearly detectable at 21 GPa. The two bands are fully re-

solved only above 30 GPa. This splitting of the 2 mode was

already observed in previous Raman experiments at about 20

GPa and ascribed to the formation of a new crystal structure

different from the phase.7,9 This doublet instead repre-

sents the A 1g and Eg components of the 2 mode in the

phase. X-ray experiments at 300 K report indeed, above the

phase and up to 50 GPa, only the phase transition at 16.3

GPa leading to the phase.8,10 As to the lattice region, the

FIG. 1. Phase diagram of nitrogen. The boundary between the and the

phases is a result of this study and will be discussed in the last section. Stars

represent data from Ref. 4; empty circles and full squares derive, respec-

tively, from infrared and Raman results of the present study.

FIG. 2. Room temperature Raman spectra of solid nitrogen, in the loc and

phases, showing the 2 and 1 bands. The splitting of the 2 band is

observable above 17 GPa.

8523J. Chem. Phys., Vol. 112, No. 19, 15 May 2000 High-pressure phases of solid nitrogen


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spectra collected in this work are in good agreement with

those reported by Schneider et al.,7 and the broadness of all

the bands does not allow to improve their analysis.

Isobaric coolingwarming cycles were performed be-

tween 5 and 41 GPa every 2 to 3 GPa. In these measure-

ments pressure was varied, between one cycle and the other,

only at room temperature. A more careful sampling 1

GPa, was carried out in the pressure region 1725 GPa

where the transition to the phase was observed at lowtemperature.19 In the cooling cycles between 5 and 10 GPa

the loc and loc phase transitions are identified, re-

spectively, by a cusp and by a discontinuity in the frequency

evolution with temperature of the 1 mode, as already re-

ported by Scheerboom and Schouten5,6 Above 10 and up to

17 GPa only the discontinuity in the frequency of the 1mode is observed, clearly indicating that only the loc

phase transition occurs. Between 17 and 23 GPa we did not

observe any particular change in the internal spectrum on

cooling apart from a progressive better resolution of the 2doublet decreasing temperature. In the 23 GPa cycle a dis-

tortion of the main peak of the 2 doublet, consisting in a

pronounced asymmetry in the low frequency side, is ob-

served at about 30 K. In the higher-pressure cycles such

distortion is observed at progressively higher temperatures,

being followed by a rapid intensification of the new low-

frequency band, and by a decrease of the intensity of the

main peak of the 2 doublet in the phase. The complete

transformation can be followed in Fig. 3a, where the iso-

baric cooling at 30 GPa is reported. For comparison we re-

port in Fig. 3b the isothermal evolution with pressure of the

same modes at 30 K. The clear resemblance of the spectral

sequences reported in the two figures indicates that an iden-

tical succession of crystal structures is probed in the two

isobaric and isothermal experiments.Identical conclusions are also extracted by the spectra

measured in the lattice phonons region. In Fig. 4 we report

the spectra measured along the same isobar at 30 GPa. The

broad bands observed at room temperature are progressively

better resolved as the temperature is lowered. At 116 K eight

bands can be identified, six as main peaks and two as shoul-

ders. This spectrum is very similar, apart from the width of

the bands, to those measured at 30 K up to 20 GPa. Below 90

K the spectrum shows some changes at about 200 and 320

cm1. The doublet at about 200 cm1 transforms into a trip-

let where the band at lower frequency seems to be the new

one. More complex is the evolution of the spectral feature at

320 cm

1: At 73 K the doublet is transformed into a struc-ture which can be decomposed in four different peaks. The

new peaks are the lowest and the highest in frequency. On

further cooling the weaker peak of the original doublet pro-

gressively weakens and completely disappears at low tem-

perature. In total, ten different clear peaks are identified at 30

K. This spectral structure is stable above 30 GPa in perfect

agreement with the information obtained from the internal

vibron region.

Isobaric cycles have been performed starting from room

temperature states reached also releasing pressure and the

resulting spectra are completely equivalent to those recorded

in the compression cycles. It is worth to mention the absolute

lack of hysteresis observed following this procedure, because

a strong hysteresis is on the contrary observed releasing pres-

sure at low temperature. With this procedure, in fact, the

high-pressure spectral features, observed above 23 GPa per-

sist down to 10 GPa in low-temperature decompression

cycles indicating a strong metastability affecting the nitrogen

crystal at low temperature. The metastability region is indi-

cated by a gray-shaded area in Fig. 1.

B. Infrared

Room temperature compression experiments showed the

appearance of a weak peak in the 2 region, at about 2355

cm1, when the pressure was raised above 11 GPa. The in-

tensity of this peak rapidly increases rising pressure up to 20

GPa, then it remains almost constant. The frequency evolu-

tion of the infrared 2 component with pressure is reported in

FIG. 3. a Raman spectra collected cooling along the 30 GPa isobar, show-ing the transition at about 90 K. b Spectra collected each one at the

lowest temperature 30 K of different isobars showing the same phase

transition at about 23 GPa.

8524 J. Chem. Phys., Vol. 112, No. 19, 15 May 2000 Bini et al.


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Fig. 5. This is fitted with two straight lines, whose intercept

and slope are reported in Table I, among the other param-

eters fitting the pressure evolution of the band frequencies

measured in this study. A clear discontinuity is observed at

17.3 GPa where the frequency of this peak suddenly de-

creases of 1.5 cm1. The appearance of the peak at about 11

GPa and the discontinuity in the frequency perfectly fit the

pressure values of the two phase transitions loc and

loc reported by x-ray diffraction experiments below 20

GPa.

8,10,13

Isobaric cooling cycles at 11 to 12 GPa and 19 GPa were

carried on starting with room temperature samples in the loc

and in the phases, respectively. In both runs a single band

is always observed in the 2 region. The cycles at 11 to 12

GPa reveal a discontinuity in the frequency of the peak at

about 200 K very similar to those reported at lower pressures

in Ref. 4 and interpreted as due to the loc phase transi-

tion.

Several different samples in the phase were isother-

mally compressed at 3040 K. In Fig. 6 some spectra mea-

sured in the 2 region during compression cycles at 30 K are

reported. The single band of the phase splits into two peaks

above 18 GPa and a significant increase of the absorption is

observed. No further changes are detected when the pressure

is further raised to 30 GPa. Releasing pressure the intensity

of the doublet progressively decreases but the two peaks per-

sist down to about 10 GPa showing, therefore, the same

metastability already observed in the Raman experiment.

The frequency data relative to the low-temperature compres-sion full symbols and decompression empty symbols

cycles are reported in Fig. 7.

FIG. 5. Pressure shift of the infrared frequency of the 2 mode measured at

room temperature. The frequency jump allows to precisely determine the

phase transition between loc and the phase. The parameters of the straight

lines are given in Table I.

FIG. 4. Raman spectra of the lattice modes collected as a function of tem-perature at 30 GPa.

TABLE I. Parameters of the parabolic fit to the pressure evolution of the frequencies of the internal modes 1 and 2 and Raman lattice modes P 1 to P8 ,

and PAPB in the phase. The values are the zeroth-, first-, and second-order coefficient, respectively, when pressure is measured in GPa and frequency in

cm1. The fit reproduces the experimental values in the pressure range where they have been measured.

Mode

loc phase

295 K

phase

30 K

phase

295 K

phase

30 K

1(R) 2336.63 2.94 2332.70 4.08 0.045 2333.72 3.60 0.029 2343.85 3.10 0.022

2a(R) 2334.11 1.90 2327.87 2.68 0.025 2330.41 2.48 0.018 2332.92 2.45 0.028

2330.12 2.65 0.029

2b(

R)

2328.04 2.75

0.027 2329.55 2.51

0.021 2320.18 3.06

0.0202308.18 3.81 0.033

2(IR ) 2327.18 2.75 0.026 2329.54 2.20 0.006 2333.22 2.02 0.009 2325.95 2.69 0.022

2330.21 1.88 0.011

P 1 152.55 16.78 0.268 195.52 11.00 0.094 217.82 9.71 0.074

PA 181.46 7.01 0.037

P2 117.23 11.20 0.132 137.72 9.80 0.091

P 3 107.01 11.88 0.171 120.74 8.98 0.082 85.13 11.33 0.107

PB 114.95 9.46 0.100

P4 83.32 9.24 0.127 154.46 3.42 83.30 8.04 0.070

P 5 70.75 7.74 0.110 80.39 4.89 0.031 52.77 7.36 0.057

P 6 59.73 7.08 0.086 71.22 5.17 0.028

P C 104.90 2.65

P7 63.50 4.04 0.080 48.74 2.65 0.005

P 8 39.79 3.10 0.059 36.56 3.03 0.031 2.53 3.86 0.016



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Finally, once the 2 doublet was obtained, we raised the

temperature isobarically at 27 GPa. The decrease of the dou-

blet intensity was distinguished, as also observed in the iso-

thermal decompressions at 3040 K, by a much faster reduc-

tion of the higher-frequency peak. The doublet structure is

observed up to 120 K, where it is replaced by a single

weak band which lasts up to room temperature.

IV. DISCUSSION

A. Phase diagram

The combination of infrared and Raman studies in

simple molecular crystals gives a full vibrational information

which has been demonstrated to be extremely powerful to

provide structural information. This approach has been re-

cently applied to CH4, N2, and O2 crystals.4,2325 There are

several open questions, especially at low temperature, about

the number, the structures and the boundaries of the high-

pressure crystal phases of solid nitrogen. Our attention willbe first devoted to the identification of the different phase

transitions resulting from the present studies, then an inter-

pretation of the structural properties of the high-pressure and

low-temperature phases will be attempted.

At room temperature the appearance of a 2 infrared

component indicates a first phase transition at about 11 GPa.

This observation agrees nicely with the x-ray data of Han-

fland et al.,13 and with the value 10.5 GPa reported by

Scheerboom et al.6 on the basis of Raman experiments. This

transition is straightforwardly assigned to the -loc second-

order phase transition. We have studied this transformation

in a previous report between 5 and 10 GPa below 270 K

establishing the blockage dynamics of the disklike molecules

of the phase in lower symmetry sites leading to the forma-

tion of the two site structure of the loc phase.4 Increasing

further the pressure at room temperature, the discontinuity in

the frequency evolution of the 2 infrared component, re-

ported in Fig. 5, reveals another phase transition at 17.3 GPa(loc ). Again the agreement with the x-ray data

8,10,13 is

excellent. The transition reported in previous Raman analysis

at about 20 GPa phase7 but not observed in the x-ray

measurements is now easily resolved. In fact, the only evi-

dence of that phase transition was the splitting of the 2mode7,9 which we demonstrated to be present already at 17

GPa. No other phase transitions were detected at room tem-

perature up to 41 GPa.

In the isobaric cooling and warming cycles above 10

GPa two types of transition were observed. The first, de-

tected below 16 GPa and assigned to the loc transition, is

characterized by the splitting of the 2 Raman band and by

the discontinuity in the frequency dependence on tempera-ture of the 2 infrared component. The second, observed

above 22 GPa in all the isobaric cycles, is characterized, in

Raman, by the disappearance of the most intense component

of the 2 doublet of the phase, by the rapid intensification

of the other component and by the appearance of a lower

frequency peaksee Fig. 3a and, in infrared, by the forma-

tion of a doublet, which replaces the single 2 infrared com-

ponent of the phase see Fig. 6. The changes in the Raman

spectrum closely recall the ones measured by Schiferl et al.19

at 15 K and interpreted as the transition between the and

the phases. All our data concerning the loc , the loc ,

and the phase transitions, derived both from infrared and

Raman experiments are reported in Fig. 1, where according

to these results, we propose the new phase diagram of nitro-

gen up to 40 GPa and below room temperature. The full line

indicating the loc phase boundary is drawn according to

the linear relation extracted by the Raman data reported in

Ref. 5. A linear fit has been used also to reproduce our data

concerning the phase boundary, which accordingly is

described by the relation PGPa0.115TK18.270. As

to the loc transition, we used our infrared data from the

present experiment circles and those reported in a previous

report stars4 to redraw the phase boundary. The best linear

relation is given by: PGPa0.0695TK1.838.

In the low-temperature part of the phase diagram Fig. 1a shaded area indicates the P-T region where we found

metastability especially in the decompression cycles. The

scarce reversibility of the phase transition was put in

evidence by a reproducible behavior in recovering the spec-

tral signatures characteristic of the phase releasing pres-

sure. We explain this metastability as due to the close resem-

blance of the structures of the and phases.

B. The loc phase

In order to get a better insight into the structural proper-

ties of these high-pressure phases, we have tried to identify,

FIG. 6. Low-temperature infrared absorption spectra in the region of the 2mode as a function of pressure.

FIG. 7. Pressure evolution of the frequency of the 2 infrared mode mea-

sured at 30 K. Full and empty symbols refer, respectively, to pressure in-

crease and release experiments.



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according to group theoretical arguments, the crystal struc-

tures which account for the observed vibrational spectral pat-

tern. In the loc phase, one single Raman peak for the 1mode and one infrared and two Raman bands for the 2mode have been detected. This observation, made in a pre-

vious report up to 10 GPa as a function of temperature,4 is

confirmed by the present results collected up to 17 GPa and

higher temperatures. Moreover, the sharpness of the bands,

the practically Lorentzian line shape, especially for the infra-red mode,4 and the excellent signal to noise ratio indicate a

good crystal quality and do not allow to speculate about the

presence of other weak or partially hidden peaks. According

to these considerations the three-site tetragonal structure

( P42 /ncm;D 4h16 ) proposed by Hanfland et al. for the loc

phase,13 on the basis of room temperature x-ray diffraction

experiment, poorly agrees with the observed spectroscopic

vibrational pattern. In this structure four molecules, corre-

sponding to the spherelike molecules of the phase 1mode, have C2h symmetry and should originate three Ra-

man components while only one is observed experimentally.

The disklike molecules of the phase sit now on two differ-

ent sites: four have C2v and eight C2 symmetry. From thefour C2v molecules two Raman and one infrared peaks are

expected while three Raman and one infrared peaks should

be obtained by the C2 molecules. Consequently, according to

the proposed tetragonal structure,13 a much higher number of

peaks, in infrared as well as in Raman, should be observed in

both 1 and 2 regions. Also taking into account other te-

tragonal structures having a two-site structure in a 3:1 ratio

between 2 and 1 type molecules, we always get from sym-

metry considerations a larger number of peaks than that ex-

perimentally observed. In a previous report4 we assumed that

also the loc phase was cubic since the second-order transi-

tion between the and the loc phases indicates a continuity

of the structural properties.5,6 A local molecular rearrange-

ment inducing a site symmetry reduction suffices to account

for the vibrational changes during the transformation. On the

basis of group theory arguments we found three crystal struc-

tures (Fm3,F132,Fm3m) that fit perfectly both infrared and

Raman experimental spectra of the loc phase.

C. The and phases

There are several aspects which must be considered in

the interpretation of the phase transition and, conse-

quently, of the phase. The observed number of lattice Ra-

man bands changes from eight to ten see Fig. 4.Only the peak at about 330 cm1, represented by the shoul-

der of the most intense band in the low-pressure phase,

clearly disappears at the transition, while three new modes

appear in the high-pressure phase. All other bands of the

phase show only a slope change. The evolution of the Raman

phonon frequencies with pressure is shown in Fig. 8, and the

fitting parameters are listed in Table I. In the 1 region there

are no changes in the spectral pattern, either in infrared and

in Raman see Figs. 2 and 3, and the evolution with pressure

of the Raman peak is continuous also across the transition.

On the contrary, larger changes during the transition are ob-

served in the 2 region. In infrared, a strong intensification of

the spectrum as a whole is detected and a new component

rises on the low-frequency side of the 2 band. The Raman

spectrum changes drastically at the formation of the phase,

where it is composed by two strong and two weak bands. In

Fig. 9 the frequency evolution with pressure of the four Ra-

man and two infrared bands of the phase at 30 K is re-

ported. The infrared values, limited to 27 GPa and including

also the data collected releasing pressure, have been fitted

according to a linear law and compared with the Raman data.

Only in one case the infrared and Raman frequencies coin-

cide, namely the high-frequency infrared band and the most

intense high-frequency Raman peak. However, the differencein frequency among the other bands 25 cm1 is much

larger than the uncertainty on the peak position 0.1 cm1,

ensuring that different Davydov components are observed.

This conclusion contrasts with the R3c structure proposed,

by pure qualitative arguments, in Ref. 19. In fact, being this

structure is non-centrosymmetric, all the crystal components,

one for the 1 and three for the 2 mode, should be infrared

FIG. 8. Low-temperature pressure evolution of the Raman active lattice

modes through the phase transition. The parameters of the quadratic fits

are listed in Table I.

FIG. 9. Low-temperature evolution with pressure of 1 and 2 Raman com-

ponents. In the inset the frequencies of the infrared 2 bands full dots,

measured up to 27 GPa, are extrapolated to higher pressure and compared

with the corresponding Raman components empty squares.



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and Raman active. A centrosymmetric structure seems to be

more consistent with our data, in which case the coincidence

of one infrared and one Raman 2 components should be

considered accidental.

The simplest approach to the phase transition con-

sists in the conservation across the transition of the R 3c

structure with a site symmetry lowering. In this case it is not

possible, either preserving or ignoring the 3:1 ratio between

the 2 and 1 type molecules, to reproduce the observedspectral pattern. In order to account for the smooth changes

between the and phases the next step is, in our opinion, to

consider the nonisomorphic R 3c sub- and supergroups.26 No

one, among the maximal nonisomorphic subgroups, can

originate a number of internal components comparable to the

experimental results, either considering a two-site in ratio of

3:1 structure, or a combination of three different sites with

the 2 molecules split on two different sites. Among the

minimal nonisomorphic supergroups, the five cubic phases,

due to the high symmetry of the factor group ( O h), satisfy

the spectroscopic observations also considering only two site

structures in a 3:1 ratio. The exact number of infrared andRaman components, detected in the 2 region, are repro-

duced only in one case. This result is obtained for the Pm3n

structure (O h3), the same of the phase, with 24 molecules

on sites Cs and eight on sites D 3 . According to the correla-

tion diagram among molecular, site and factor group symme-

tries, four Raman and two infrared components are expected

in the 2 region, while two Raman bands should be active in

the 1 region. On the other hand the number of the lattice

bands predicted according to this structure is 10 in infrared

and 20 in Raman, while only 10 Raman peaks have been

clearly identified.

Finally, we considered those structures which, according

to different theoretical approaches, were found to be stable inthe P-T ranges that we have assigned to the phase. Most of

the theoretical effort was devoted to the low temperature and

pressure range characteristic of the phase. The trigonal

R 3c structure, suggested by Schiferl et al. in Ref. 19, was

confirmed first by LeSar,27 and then by Etters et al.28 This

conclusion was later re-discussed by these authors29 and a

lower symmetry structure, R3c , found first by Nose and

Klein,30 was favored. To complete the calculation scenario it

is worth mentioning also another constant pressure and tem-

perature MD molecular dynamics calculation performed by

Nose and Klein31 where, using a different potential with re-

spect to that of Ref. 30, a stable tetragonal structure wasfound below 100 K at 7 GPa. Specific calculations along the

300 K isotherm were performed in Ref. 29 and for pressures

higher than 20 GPa the Pm3n structure of the phase is

replaced by a tetragonal structure with 32 molecules per unit

cell. This structure was indicated as a minor variant of the

phase where the molecules are frozen in sites of lower sym-

metry. From this analysis it results that, independently of the

calculation, tetragonal structures are quite often found to dis-

tinguish high-pressure phases of solid nitrogen. For this rea-

son we extended our analysis, based on group theory argu-

ments, taking into account a tetragonal structure for the

phase. Two-site structures never provide a vibrational pattern

similar to the experimental spectra: while, on the contrary,several solutions are offered by considering three site struc-

tures. In particular six crystal structures, two having C4h and

four D 4h symmetry, allow to obtain the exact number of

observed infrared and Raman components of the internal

modes.

D. Vibrational coupling

The accuracy of our Raman and infrared frequencies de-

termination allows us to draw important conclusions about

the size and the effect of the vibrational coupling in the ,

loc , and nitrogen phases. This problem has been discussed

extensively in the literature, and also recently it has been thesubject of a spectroscopic study on isotopic substituted

samples.32 On the basis of molecular dynamics computations

it has been argued that this effect should be very small in

solid N2, giving a splitting between the Eg and A 1g compo-

nents of the 2 mode of 0.2 cm1 at maximum.28 Conse-

quently, when a larger splitting was observed first,7 it was

rather attributed to the occurrence of a phase transition. With

the present knowledge of the phase diagram we can now

readdress the question, comparing not only the frequencies

of the A 1g and Eg Raman modes, but also that of the infrared

component Eu , measured in this study.

At room temperature, where the range of existence of the

, loc and phases is wider, such an analysis allows thedetermination of the influence of the different molecular ori-

entations on the vibrational coupling. Concerning the Raman

data, the two A 1g and Eg components are split only above the

loc transition, and are essentially degenerate below it, in

the and loc phase. The separation is 1.0 cm1 at the tran-

sition, and grows almost linearly with pressure, up to 40

GPa. This difference is represented in Fig. 10 solid squares.

The frequency of the Eu infrared component is, in the

phase, lower than the two Raman ones, and the difference

between this and the lowest Raman component empty

squares amounts to about 1.5 cm1. We can, therefore,

state that the coupling affects the modes much more than

FIG. 10. Vibrational coupling splitting among the A1g , Eg , and Eu com-

ponents of the 2 mode in the , loc , and phases. Plotted it is the differ-

ence of the weaker Raman band full symbols and of the infrared band

empty symbols with respect to the stronger Raman band. In the delta phase

no active infrared band exists, and the Raman band does not show any

detectable splitting.



8/8

predicted theoretically.28 A quantitative analysis, as done re-

cently for oxygen,25 is complicated because of the different

relative orientations of neighboring molecules in the phase,

and is beyond the scope of the present work. The presence of

an infrared peak at lower pressure allows to extend this

analysis to the loc phase, where the A 1g and Eg Raman

bands are almost degenerate at room temperature. In this

pressure range we notice that the infrared and Raman fre-

quency coincide, in the limit of the present accuracy. Sincethe density change at the loc transition is only 5%,

20 the

jump of the frequency difference should be ascribed to the

complete freezing of the rotation of the molecules in the

phase. These results demonstrate that the vibrational cou-

pling between nitrogen molecules is strongly dependent on

the molecular orientation, and greater than the average for

the particular orientation occurring in the phase.

V. CONCLUSIONS

The analysis as a function of temperature of the internal

and external vibrational modes of solid nitrogen between 5

and 41 GPa provides a definitive evidence of the phase tran-

sition between the and the phases. Several isobaric cool-

ing cycles allowed to monitor this continuous and reversible

phase-transition and to draw the relative phase-boundary for

temperatures lower than 300 K. The comparison between

isobaric and isothermal cycles put in evidence a metastability

range of the order of 10 GPa at low temperature. In fact,

when the pressure is changed below 100 K, either in com-

pression or decompression cycles, the coexistence of the two

phases is always observed preventing any conclusion on the

structural evolution. At room temperature our vibrational

data are in perfect agreement with the structural x-ray stud-

ies, as concerns the numbers and the position of phase tran-

sitions, and the existence of an intermediate phase be-tween the and phases can be ruled out. The analysis of the

Raman and infrared activity in the fundamental vibration re-

gion, discussed on the basis of group theory arguments, do

not agree with the tetragonal structure proposed for the locphase on the basis of x-ray data and a cubic structure, closer

to that of the phase, is favored. For the phase our data are

consistent with a centrosymmetric structure but a precise

definition of the factor group symmetry is not possible. If a

two-site structure is retained in the phase, as in the and

phases, we found that a cubic structure factor group O hsymmetry is the only one compatible with our results.

Three-site structures offer, on the contrary, several solutions

either considering cubic and tetragonal unit cells. Finally, theprecise knowledge of the frequencies of Raman and infrared

components of the 2 mode increasing pressure across dif-

ferent crystal structures provided an excellent basis to dis-

cuss the vibrational coupling among neighboring molecules.

The coupling is negligible in the and loc phases while it

starts to be appreciable in the phase, pointing out the im-

portance of the freezing of the relative orientation.

ACKNOWLEDGMENT

This work has been supported by the European Union

under Contract ERB FMGE CT 950017.

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Roberto Bini et al- High-pressure phases of solid nitrogen by Raman and infrared spectroscopy