High Pressure Study of Lithium Azide from Density-Functional Calculations
K. Ramesh Babu, Ch. Bheema Lingam, Surya P. Tewari, G. Vaitheeswaran
aa r X i v : . [ c ond - m a t . m t r l - s c i ] N ov High Pressure Study of Lithium Azide from Density-FunctionalCalculations
K. Ramesh Babu a , Ch. Bheema Lingam b , Surya P. Tewari a,b and G. Vaitheeswaran a, ∗ a Advanced Centre of Research in High Energy Materials (ACRHEM),University of Hyderabad, Prof. C. R. Rao Road,Gachibowli, Andhra Pradesh, Hyderabad- 500 046, India b School of Physics, University of Hyderabad,Prof. C. R. Rao Road, Gachibowli,Andhra Pradesh, Hyderabad - 500 046, India (Dated: 17 March 2011)
Abstract
The structural, electronic, optical and vibrational properties of LiN under high pressure have been studied using plane wavepseudopotentials within the generalized gradient approximation for the exchange and correlation functional. The calculatedlattice parameters agree quite well with experiments. The calculated bulk modulus value is found to be 23.23 GPa whichis in good agreement with the experimental value of 20.5 GPa. Our calculations reproduce well the trends in high pressurebehavior of the structural parameters. The present results show that the compressibility of LiN crystal is anisotropic andthe crystallographic b-axis is more compressible when compared to a- and c-axis which is also consistent with the experiment.Elastic constants are predicted which still awaits experimental confirmation. The computed elastic constants clearly shows thatLiN is a mechanically stable system and the calculated elastic constants follows the order C > C > C implies that theLiN lattice is stiffer along c-axis and relatively weaker along b-axis. Under the application of pressure the magnitude of theelectronic band gap value decreases, indicating that the system has the tendency to become semi conductor at high pressures.The optical properties such as refractive index, absorption spectra and photo conductivity along the three crystallographicdirections have been calculated at ambient as well as at high pressures. The calculated refractive index shows that the systemis optically anisotropic and the anisotropy increases with increase in pressure. The observed peaks in the absorption andphoto conductivity spectra are found to shift towards the higher energy region as pressure increases which imply that in LiN decomposition is favored under pressure with the action of light. The vibrational frequencies for the internal and lattice modesof LiN at ambient conditions as well as at high pressures are calculated from which we predict that the response of the latticemodes towards pressure is relatively high when compared to the internal modes of the azide ion. . INTRODUCTION Alkali metal azides are an interesting class of compounds which find wide range of ap-plications as explosives and photographic materials. These are model systems for studyingthe fast reactions in solids with complex chemical bonding . Under the action of heat,light these metal azides become unstable and decompose into metal and nitrogen. Since thedecomposition of metal azides involves the electron-transfer mechanism it would be neces-sary to understand the electronic band structure of these systems . A number of studies atthe level of Hartree-Fock (HF) and density functional theory (DFT) has been performed tounderstand the electronic band structure and decomposition mechanism . Moreover, thehigh pressure behavior of metal azides is an important aspect because of the formation ofpolymeric nitrogen, a high energy density material . Previously the high pressure studyon sodium azide, NaN , revealed that a new structure is formed with nitrogen atoms con-nected by single covalent bonds, which was considered to be an amorphous like structure .Since NaN and LiN are isostructural at ambient conditions, it would be of interest to studythe pressure effect on LiN with the motive of formation of polymeric nitrogen. RecentlyMedvedev et al reported the behavior of LiN under high pressures. Their study revealedthat the system is stable up to the pressure of 60 GPa, which is in contrast to that of sodiumazide that undergoes a set of phase transitions below the pressures of 50 GPa . With thismotivation we aim to study theoretically the pressure effect on LiN crystal system. In orderto understand the behavior of LiN under high pressure, it is essential to study the physicaland chemical properties of the system under high pressure. To the best of our knowledgethe structural, electronic, vibrational and optical properties of LiN at high pressures havenot been explored theoretically. Moreover, these properties under pressure are important ina better understanding of the stability of LiN . In this paper, we present a first-principlesstudy of solid monoclinic LiN under hydrostatic pressure of up to 60 GPa using densityfunctional theory. The structural parameters, bulk modulus, energy band gap, density ofstates, optical and vibrational properties of LiN under pressure are reported. The remain-der of the paper is organized as follows: A brief description of our computational methodis given in section 2. The results and discussion are presented in section 3. Finally we endwith a brief summary of our conclusions in section 4.2 IG. 1: (Colour online) crystal structure of LiN II. COMPUTATIONAL DETAILS
The first-principles density functional theory calculations were performed with the Cam-bridge Sequential Total Energy package program , using Vanderbilt-type ultrasoft pseudopotentials and a plane wave expansion of the wave functions. The electronic wave func-tions were obtained using density mixing scheme and the structures were relaxed usingthe Broyden, Fletcher, Goldfarb, and Shannon (BFGS) method . The exchange-correlationpotential of Ceperley and Alder parameterized by Perdew and Zunger in the local den-sity approximation (LDA) and also the generalized gradient approximation (GGA) withthe Perdew-Burke-Ernzerhof (PBE) parameterization was used to describe the exchange-correlation potential. The pseudo atomic calculations were performed for Li 2 s , N 2 s p .The Monkhorst-Pack scheme k-point sampling was used for integration over the Brillouinzone . The convergence criteria for structure optimization and energy calculation were setto ultra fine quality. It is well known that the cut-off energy and k-point mesh influencesthe convergence of calculations, we tested the dependence of energy cut-off and k-point gridand found that for 520 eV plane wave cut-off energy and 5x8x5 k-point mesh, the changein total energy is less than 1meV. So we chose these plane wave cut-off energy and k-pointmesh for all the calculations. 3e performed the calculation by adopting the experimental crystal structure ,a=5.627˚ A , b=3.319˚ A , c=4.979˚ A , and β =107.4 as the initial structure and it is relaxedto allow the ionic configurations, cell shape, and volume to change at ambient pressure. Ourcalculations were conducted on one unit cell with two molecules. Starting from the opti-mized crystal structure of lithium azide at ambient pressure, we applied hydrostatic pressureup to 60 GPa. The external pressure was gradually increased by an increment of 1 GPain each time. Under a given pressure, the internal co-ordinates and unit cell parametersof the lithium azide crystal were determined by minimizing the Hellmann-Feynmann forceon the atoms and the stress on the unit cell simultaneously. In the geometry relaxation,the self-consistent convergence on the total energy is 5x10 − eV/atom and the maximumforce on the atom is found to be 10 − eV/˚ A . Based on the equilibrium structures, theelectronic, optical and vibrational properties have been calculated. The vibrational frequen-cies have been calculated from the response to small atomic displacements . The elasticconstants are calculated for the optimized crystal structure at ambient conditions by usingvolume-conserving strain technique as implemented in CASTEP code. We have relaxedthe internal co-ordinates of the strained unit cell to arrive at the elastic constants. III. RESULTS AND DISCUSSIONA. Crystal structure and properties at ambient pressure
At ambient pressure, LiN crystallizes in the monoclinic structure with the C2/m spacegroup and contains two molecules per unit cell. Each azide ion is surrounded by six cationsand vice versa. The structure is iso-structural to low temperature phase of sodium azide ( α NaN ). In order to determine the theoretical equilibrium crystal structure for lithium azide,we performed a full geometry optimization of both the lattice constants and the internalatomic co-ordinates within LDA and GGA. The crystal structure of LiN from our geometryoptimization in GGA is shown in Fig 1. In Table I, we compare the lattice constants andunit cell volume with experimental data and previous theoretical results . Compared tothe experimentally measured lattice constants of LiN , our LDA calculations underestimatea, b, and c by 5.3%, 3.6%, and 5.1% whereas GGA calculations overestimate a, b, and c by2.3%, 1.7%, and 2.3%, respectively. This discrepancy between theory and experiment can4 ABLE I: The calculated ground state properties of monoclinic LiN at ambient pressurePresent work Other calculations Experiment c Lattice parameter LDA GGAa (˚A) 5.328 5.761 5.696 a , 5.626 b a , 3.317 b a , 5.035 b β a , 106.7 b Li (0, 0, 0) (0, 0, 0) (0, 0, 0) b N (0.1244, 0.5, 0.7456) (0.1005, 0.5, 0.7490) (0.1040, 0.5, 0.7376) b (0.1048, 0.5, 0.7397)N (0, 0.5, 0.5) (0, 0.5, 0.5) (0, 0.5, 0.5) b (0, 0.5, 0.5)B (GPa) 42.27 23.23 – 20.5 da Ref (26), b Ref (8), c Ref (22), d Ref (12) be expected for a molecular crystal like LiN where the Vanderwaals forces are importantwhich could not dealt with the LDA and GGA in the DFT calculations . However, ourcalculated volume of LiN using GGA is closer (less error) to the experimental volume whencompared to LDA and therefore for further calculations we adopted GGA. B. Structural and electronic properties under pressure
Starting from the zero-pressure equilibrium lattice structure, we applied hydrostatic com-pression to the LiN unit cell in the pressure range from 0 to 60 GPa. This was done throughCASTEP using variable cell optimization under the constraint of a diagonal stress tensorwith fixed values of diagonal matrix elements equal to a desirable pressure. The obtainedpressure-volume relation of LiN is shown in Fig 2(a), together with the results of experimentby Medvedev et al . Our calculations show that the volume decreases monotonically withpressure and at 60 GPa the volume compression is V/V = 57%. Qualitatively our calcula-tions reproduce the trend of pressure - induced reduction of volume by experiment (wherethe volume compression at 62 GPa is V/V = 58%). From the calculated P-V relation wecan also observe that at a given pressure, the theoretical unit cell volume is greater thanthat of the experiment, which is also due to the inherent limitation of DFT-GGA function-5ls. However, as pressure increases, the computed cell volume approaches the experimentalvalues. For example, if we observe keenly, the discrepancy between theoretical and experi-mental volumes decreases from 5.8% at 0 GPa to 2.68% at 60 GPa. This result implies thatour abinitio -GGA calculations performed under high pressure might be more reliable.The dependence of lattice constants of LiN on pressure is shown in Fig 2(b), where ourtheoretical results are compared with the experimental data . The experimental trend forthe lattice constants upon compression is well reproduced by our GGA calculations. Amongthe three axes, we find the better agreement between our GGA calculations and experimentsfor reduction of lattice constant for b-axis, whereas the reduction of lattice constant for aand c - axes is overestimated by our calculation. The possible reason for this behavior isthe theoretical values of initial zero-pressure lattice constants a and c are 2.3% larger thanthe experimental values (see Table 1). In Fig 2(c), we have shown the trends in the ratiosof a/a , b/b , and c/c of LiN as function of pressure along with the experimental data .It can be observed that the b-axis is the most compressible which is also consistent withexperimental result. The anisotropy ratios c/a and c/b with increasing pressure are shownin Fig 2(d). The c/a ratio increases from 0.884 at 0 GPa to 0.909 at 60 GPa, whereasthe c/b ratio increases from 1.508 at 0 GPa to 1.566 at 60 GPa, which indicates that thecompressibility of LiN is anisotropic. This is in good agreement with the experiment .The pressure dependence of the monoclinic angle of LiN is shown in Fig 2(e) where it isalso compared with experiment . The change in monoclinic angle is more below 20 GPawhereas above this pressure it is only of 2 , this implies that the shear of layers is morebelow 20 GPa whereas it is less pronounced at high pressures (at 60 GPa). Due to the affectof the shear of the structure the azide ions become closer to each other and therefore theinteraction will be more.The electronic structure of solids can be characterized by means of electronic band gap.bThe electronic band structure of LiN at 0 GPa and at 60 GPa are shown in Figs 3(a) and3(b) respectively. The band structure at 0 GPa clearly shows that the top of the valence bandand the bottom of the conduction band occurs at Z-point in the Brillouin zone indicatingthat the material is a direct band gap material with a separation of 3.32 eV, the valueslightly lower than the previous theoretical value of 3.46 eV at the PWGGA-DZP level and 3.7 eV in Ref 6. Unfortunately, as far as we know, there is no experimental value of theband gap available for LiN to compare our theoretical band gap result. Ofcourse, we could6xpect that our band gap value might be lower than the experimental band gap, because itis well known that first-principles calculation of the electronic structure of semiconductorsand insulators using GGA give an underestimation of the band gap values compared toexperiments . This underestimation of the gap is mainly due to the fact that GGAsuffers from artificial electron self-interaction and also lack the derivative discontinuities ofthe exchange-correlation potential with respect to occupation number. One way to solvethe band gap problem is to apply a perturbative correction to the energy levels, as in theGW approximation . However the band gap at 60 GPa is observed to be indirect with amagnitude of 2.26 eV as it is occurred between the Z and A points. Based on the equilibriumcrystal structures obtained at different pressures, we calculated the band gap and examinedits change under hydrostatic compression. The calculated band gaps as functions of pressureare shown in Fig 2(f). It can be seen that the band gap reduces smoothly under compressionwith out any significant discontinuity. But in different pressure ranges the average decreaseof the band gap is different (upto 20 GPa 0.065 eV/GPa and 0.1 eV/GPa from 20 to 60).The decrease in the band gap with pressure indicates that the electrical conductivity ofLiN increases meaning that at high pressures LiN might changes from insulator to semiconductor.The nature of bonding and the electronic band gap under pressure can be studiedby the total and partial DOS. Moreover, lithium azide is photosensitive and undergoesdecomposition under the action of suitable wave length of light and the essential step in thephoto chemical decomposition involves the promotion of a valence electron from the valanceband to the conduction band, therefore it would be necessary to know the information aboutthe type of states that are present in both valence and conduction bands. For LiN , thetotal and partial DOS at ambient and at 60 GPa pressure are shown in Figs 4(a) and 4(b)respectively. Overall the distribution of states is same at both pressures, and there is nohybridization between the Li states and N states at ambient as well as at 60 GPa, indicatingthat ionic bond is more favored in LiN . This is also observed by using the charge densitydistribution plots shown in Figs 5(a) and 5(b). The p states of azide ion are dominatingat the Fermi level and as pressure increases the delocalization of the azide ion states isobserved, see Fig 4(b). This is also clearly observed by the charge density distribution plotsshown in Figs 5(c) and 5(d). We have also shown the charge density plots of the states atthe minimum of the conduction band which are also derived mostly from the p type azide7tates and a very little contribution from the s states of Li and azide ion both at 0 GPa and60 GPa in Figs 5(e) and 5(f) respectively. Expt V o l u m e ( ¯ / f o r m u l a un i t) Pressure (GPa)
Theory (a) c (E)c (T) b (E)b (T) a (E) L a tt i ce p a r a m e t er ( ¯ ) Pressure (GPa)a (T) (b) a/a (T) a/a (E) b/b (T) b/b (E) c/c (T) c/c (E) a / a0 , b / b , c / c Pressure (GPa) (c) c/b A n i s o t r o p y r a t i o Pressure (GPa)c/a (d)
Theory Expt M o n o c li n i c a n g l e ( d e g ree s ) Pressure (GPa) (e) B a nd ga p ( e V ) Pressure (GPa) (f)
FIG. 2: (Colour online) a) Volume variation of LiN with pressure, b) Variation of lattice parame-ters of LiN with pressure, c) Variation of normalized lattice parameters of LiN with pressure, d)Variation of c/a amd c/b of LiN with pressure, e) Variation of monoclinic angle β of LiN withpressure, f) Band gap variation of LiN with pressure. CEDBAY E n er gy ( e V ) Z (a) -10-50510 E CDBAY E n er gy ( e V ) Z (b) FIG. 3: (Colour online) Band structure of LiN at 0 and 60 GPa C. Bulk modulus and elastic constants
In order to know about the crystal stiffness and the mechanical stability at ambientconditions, we calculated the bulk modulus and elastic constants of LiN . The calculated9
10 -8 -6 -4 -2 0 2 4 6 8 10 D O S ( s t a t e s / e V ) s psum N3Energy (eV)
LiN3 (a) -10 -8 -6 -4 -2 0 2 4 6 8 10 LiN Energy (eV) s p sum D O S ( s t a t e s / e V ) N3 (b) FIG. 4: (Colour online) Total and partial DOS of LiN at 0 and 60 GPa values are listed in Table II (bulk modulus value is shown in Table I). Our calculated bulkmodulus value within GGA is 23.23 GPa and it is slightly over estimated by that of thereported value of 20.5 by Medvedev et al , but it still comparable with that of alkali halidecrystal NaCl for which B = 23.84 GPa. We have also given the calculated LDA bulkmodulus value for comparison. One should note here that our LDA bulk modulus value isoverestimated by that of GGA value and the experiment. This might be due to the fact10 a) (b)(c) (d)(e) (f) FIG. 5: (Colour online) Charge density distribution of LiN at 0 and 60 GPa (a) and (b) are at0 GPa and 60 GPa, (c) and (d) are of the states near by Fermi level, (e) and (f) are of minimumof the conduction band. that LDA overbinds the system as the volume is largely underestimated which is a commonfeature in DFT-LDA calculations and therefore one would expect large bulk modulus. Since11 ABLE II: Single-crystal elastic constants (C ij in GPa)) of LiN calculated at the theoreticalequilibrium volumeParameter C C C C C C C C C C C C C the bulk modulus values are different in LDA and GGA therefore the choice of exchange-correlation functional also very important for this system. Our GGA bulk modulus valueis in good agreement with that of experiment this once again shows that GGA functionalis the good exchange-correlation functional for this system. As expected for ionic solids,lithium azide is a soft material because of its low bulk modulus value. For a monocliniccrystal there are 13 independent elastic constants namely, C , C , C , C , C , C ,C , C , C , C , C , C , and C . The mechanical stability of the crystal requires thewhole set of elastic constants satisfies the Born-Huang criterion . For the case of LiN , itis found that the calculated elastic constants obey this stability criteria and therefore themonoclinic Lithium azide is mechanically a stable compound. Furthermore for a molecularcrystal like LiN one can correlate the elastic constant values with the structural propertiesof the crystal. Since LiN is a monoclinic system, the elastic constants C , C , and C can be directly relate to the crystallographic a, b, and c-axes respectively. The calculatedvalues of these three constants follows the order C > C > C , which implies that theelastic constant C is the weakest for LiN . This reveals the fact that a relative weakness oflattice interactions is present along the crystallographic ‘b’ axis. For the relative magnitudeof the elastic constants C and C the analysis of crystal structure of LiN shows that thelargest number of close-contact (less than 2.3 ˚A) inter molecular interactions to be situatedalong the crystallographic c-axis. Therefore the increased number of interactions along thec-axis would stiffen the lattice in this direction which is consistent with the value of C . Thelowest number of interactions is along the b-axis which is further supported by the lowestvalue of C . 12 . Optical properties under high pressure Lithium azide becomes unstable and undergoes decomposition by the action of light. Thephoto chemical decomposition of lithium azide can be understood by the optical transitionsfrom the valance band to the conduction band. From the total and partial DOS the stateslying near the Fermi level are the p states of azide ion, therefore the decomposition of thelithium azide can be initiated by the formation of azide radicals in the following way. N − + hυ → N ∗ (1) N ∗ + E → N + e − (2)where E is the thermal energy required to dissociate the azide radical N ∗ . The combinationof two positive holes will give nitrogen gas with the liberation of energy Q and the electrontrapped to the metal atom sites and thereby form the metal atom2 N → N + Q (3) Li + + e − → Li (4)Therefore in order to understand the photochemical decomposition phenomena at ambientas well as at high pressures it would be necessary to understand its optical properties thatare resulting from the interband transitions. In general the optical properties of mattercan be described by means of the complex dielectric function ǫ ( ω ) = ǫ ( ω ) + iǫ ( ω ), where ǫ ( ω ) and ǫ ( ω ) describes the dispersive and absorptive parts of the dielectric function.Normally there are two contributions to ǫ ( ω ) namely intraband and interband transitions.The contribution from intraband transitions is important only for the case of metals. Theinterband transitions can further be split in to direct and indirect transitions. The indirectinterband transitions involve scattering of phonons. But the indirect transitions give onlya small contribution to ǫ ( ω ) in comparison to the direct transitions, so we neglected themin our calculations. The direct interband contribution to the absorptive or imaginary part ǫ ( ω ) of the dielectric function ǫ ( ω ) in the random phase approximation without allowancefor local field effects can be calculated by summing all the possible transitions from theoccupied and unoccupied states with fixed k-vector over the Brillouin zone and is given as ǫ ( ω ) = V e π ¯ hm ω Z d k X |h ψ C | p | ψ V i| δ ( E C − E V − ¯ hω ) (5)13ere ψ C and ψ V are the wave functions in the conduction and valence bands, p is themomentum operator, ω is the photon frequency, and ¯ h is the Planck’s constant. The realpart ǫ ( ω ) of the dielectric function can be evaluated from ǫ ( ω ) using the KramerKroningrelations. ǫ ( ω ) = 1 + 2 π P Z ∞ ǫ ( ω ′ ) ω ′ dω ′ ( ω ′ ) − ( ω ) (6)where ‘P’ is the principle value of the integral.The knowledge of both the real and imaginaryparts of the dielectric function allows the calculation of the important optical properties suchas refractive index, absorption, and photo conductivity .In this present study, we investigated the static dielectric constant, refractive index,absorption spectrum and photo conductivity of lithium azide along the three crystal direc-tions at ambient pressure as well as at the high pressures. The static dielectric constant ǫ (0) as a function of pressure is shown in Fig 6(a). Clearly ǫ (0) increases with pressurealong all the three directions. The static refractive index (n= √ ǫ (0)) of the system in threedirections is given by n = 1.73, n = 1.34, and n = 2.61. Clearly, n = n = n therefore we conclude that the lithium azide is an anisotropic crystal with bi-axial crystalproperties. At ambient pressure, our calculated values of ǫ (0) and n(0) along [100] directionare in good agreement with that of previous calculations . The calculated refractive indexincreases with increase in pressure as shown in Fig 6(b), implies that the crystal bindingwill be more under the application of pressure. In Fig 6(c), we have shown the calculatedabsorption spectra and photo conductivity spectra of LiN along [100], [010], and [001] di-rections at 0 GPa. Our calculated results indicates that there is anisotropy in the calculatedoptical spectra. Our calculated absorption spectra along [100] direction is in good agree-ment with that of the reported absorption spectra in Ref [8]. The peaks in the absorptionspectra are due to the interband transitions from the occupied to unoccupied states. Theabsorption starts from the energy of 3.32 eV, which is the energy gap between the valanceand conduction bands. The first absorption peak in all the three directions is observed at(5.98 eV) but the absorption coefficient is found to be different and it is around 1.9x10 m − in [100] and [010] directions whereas it is 4.5x10 m − along [001] direction. From thisresult the decomposition of lithium azide takes place under the action of ultra violet lightthat starts from the absorption edge of 3.32 eV.Photo conductivity is due to the increase in number of free carriers when photons areabsorbed. The calculated photo conductivity shows that LiN is photo sensitive and display14 wide photo current response in the absorption region of 3.3 to 20 eV. The calculatedabsorption and photo conductivity spectra at pressures of 20 GPa, 40 GPa, 60 GPa areshown in Fig 6(d), 6(e), and 6(f) respectively. It can be clearly observe that the fundamentalabsorbtion energy region and also the absorption coefficient along the three crystallographicdirections increases with pressure. At 0 GPa, the fundamental absorption was found tobe between 3.3 to 20 eV and at 20 GPa, it increases to 23 eV and it further increasesto 25 and 28 eV at 40 and 60 GPa. And also the absorption coefficient along the threedirections increases with pressure over the entire absorption energy region. This means thatas pressure increases the response of the electrons to the incident photon energy increases.This can be understood by the increase in photo conductivity, which shows a broad photocurrent response in the absorption region as pressure increases. Overall, lithium azide showsa strong absorption (absorption coefficient of the order of 10 m − ) as a function of pressureover a broad energy range. Therefore from the study of optical properties of Lithium azideunder pressure we came to a conclusion that, although LiN is stable up to 60 GPa it maybecome unstable or decompose under the action of light which is equal to the absorptionenergy range of LiN (ultra violet light). In the above case LiN becomes more unstableand decomposes easily into metal and nitrogen under pressure by the influence of ultravioletlight. E. Vibrational properties
Vibrational properties are obtained by the use of linear response method within thedensity functional perturbation theory (DFPT) . In this method the force constants matrixcan be obtained by differentiating the Hellmann-Feynman forces on atoms with respect tothe ionic co-ordinates. This means that the force constant matrix depends on the groundstate electron charge density and on its linear response to a distortion of atomic positions.By variational principle the second order change in energy depends on the first order changein the electron density and this can be obtained by minimizing the second order perturbationin energy which gives the first order changes in the density, wave functions, and potential.In the present study the dynamical matrix elements are calculated on the 5x8x5 grid of k-points using the linear response approach. The calculated total and partial phonon densityof states of LiN at 0 GPa and 60 GPa are shown in Fig 7 and Fig 8. From the partial15honon density of states it can be observed that at 0 GPa, the frequency modes below 300cm − are due to the both lithium and azide ion, whereas above this frequency the states areentirely dominated by the the azide ion. At 60 GPa, the modes are shifting towards highfrequency region.The vibrational frequencies at gamma point are shown in Table III. The group sym-metry decomposition into irreducible representations of the C2/m point group yields a sumof A u +2B u for three acoustic modes and 4A g +2B g +5A u +10B u for the 21 optical modes.The modes from M1 to M13 involves the vibrations from the lattice (including both metalatom and azide ion) whereas modes from M14 to M21 are entirely due to the azide ion. TheM14 mode, which is due to the N symmetric bending along b-axis, has frequency 640.02cm − is in good agreement with that of the experimental value of 635 cm − . The M15mode, located at 645.45 cm − originates from the asymmetric bending of azide ion alongb-axis. The M16 and M17 modes having frequencies 645.45 cm − and 645.62 cm − are dueto the symmetric and asymmetric bending of azide ion along a-axis. The modes from M18to M21 are the stretching modes of azide ion. Our calculated value of 1262.51 cm − forthe symmetric stretching of azide ion is in good agreement with that of the experimentalvalue − . The asymmetric stretching frequency of azide ion is found to be 2006.51cm − , the value lower than that of experimental value 2092 cm − . This discrepancy maybe due to the overestimation of the crystal volume because of GGA exchange-correlationfunctionals. In order to understand the intramolecular and intermolecular interactions undercompression, we calculated the vibrational frequencies for the optimized crystal structuresup to the pressure of 60 GPa at a pressure step of 5 GPa and are shown in Fig 9. It can beclearly observe that as pressure increases all the vibrational frequencies of all modes fromM1 to M21 increases with increase in pressure, except the bending modes of azide ion fromM14 to M17 which decreases and have minima at about 30 GPa for M14 and M15 modes,at about 10 GPa for M16 mode and at 5 GPa for M17 mode. This clearly shows that theintramolecular interaction enhances under the application of pressure. In Table III we haveshown the coefficients for the pressure-induced shifts of the vibrational frequencies of allvibrational modes of LiN from M1 to M21. These values are obtained by a linear fit ofthe vibrational frequencies with respect to pressure. From the calculated values it is clearthat different vibrational modes show distinctly different pressure dependent behavior. Thepressure-coefficients for lattices modes are found to be higher than that of internal modes,16ndicating that the lattice modes show most significant shift over internal modes. The latticemode M13 has high pressure coefficient of 8.1 cm − /GPa and among the internal modes,the asymmetric stretching modes of azide ion M20 and M21 have high pressure coefficientof 3.3 cm − /GPa. Over all the behavior of vibrational modes under compression indicatesthat the intermolecular and intramolecular interactions increases. The observed frequencyshifts are more for lattice modes compared to the internal modes under compression. Thisimplies that intermolecular interaction is affected more significantly than the intramolecularinteraction under compression.The knowledge of the volume dependencies of the vibrational modes allows to calcu-late the Gr¨uneisen parameters ( γ i ) associated with them. The Gr¨uneisen parameter of i th vibrational mode can be defined as γ i = − ∂ ( lnν i ) ∂ ( lnV ) (7)The calculated Gr¨uneisen parameters ( γ i ) of LiN resulting from a linear fit of the ln ν as afunction of ln V are listed in Table III. It can be observed from Table III that the calculated γ is high for lattice modes and the values are low for internal modes which are entirely dueto the azide ion vibrations. This also implies that the change in lattice parameters andthereby the volume with pressure has large affect on vibrational modes especially latticemodes whereas the vibrational frequencies of azide ion has less influence by the pressure. IV. CONCLUSIONS
In summary, the structural, electronic, optical and vibrational properties of lithium azideunder hydrostatic compression up to 60 GPa have been studied using density functionaltheory within generalized gradient approximation. The calculated structural parameters areoverestimated compared to the experiment, which is due to the GGA exchange-correlationfunctionals. It is also observed that Lithium azide remains in the monoclinic structure inthe studied pressure range of 60 GPa as observed in experiment. From the calculation oftotal and partial DOS it is found that lithium azide is an ionic solid with a band gap of3.32 eV and the gap decreases as pressure increases indicates its ability to become semi-conductor at high pressures. The single crystal elastic constants at ambient pressure havebeen calculated and found that the system is mechanically stable. The calculation of refrac-17
10 20 30 40 50 6023456789 ( ) Pressure (GPa) (a) n Pressure (GPa) (b) m - ) f s - ) Photon energy (eV) (c) m - )
20 GPa f s - ) Photon energy (eV) (d) m - )
40 GPa f s - ) Photon energy (eV) (e) m - )
60 GPa f s - ) Photon energy (eV) (f)
FIG. 6: (Colour online) (a) The calculated static dielectric constant as a function of pressure. (b)The calculated refractive index of LiN as a function of pressure. (c) The calculated absorptionand photo conductivity of LiN at the pressure of 0 GPa (d) at 20 GPa (e) at 40 GPa and (f) at60 GPa. . tive index suggests that the LiN is anisotropic material and the anisotropy increases withpressure. The absorption spectra and photo conductivity spectra at various pressures have18 .0000.0040.0080.0120.00000.00070.00140.00210 400 800 1200 1600 2000 24000.0000.0020.0040.006 LiN30 GPa P h o n o n D O S ( / c m - ) Li Frequency ( cm-1 ) N3 FIG. 7: (Colour online) Total and partial Phonon density of states (PhDOS) of LiN at 0 GPa LiN360 GPa P h o n o n D O S ( / c m - ) Li Frequency ( cm-1 ) N3 FIG. 8: (Colour online) Total and partial Phonon density of states (PhDOS) of LiN at 60 GPa been calculated and found that the absorption peaks are shifting towards the high energyregion and photo current increases as pressure increases. Therefore we conclude that thedecomposition of lithium azide is more favorable by the action of light (ultra violet) underpressure. The vibrational frequencies at ambient and high pressures have been calculated.19 M14 M15 M16 M17 M18 M19 M20 M21 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10
M11
M12
M13
Pressure (GPa)
M14 M15 M16 M17 F re qu e n c y ( c m - ) Pressure (GPa) F re qu e n c y ( c m - ) FIG. 9: (Colour online) Pressure-induced shifts of vibrational frequencies of LiN . The inset figureshows the enlarged case of pressure dependence of M14 to M17 modes. At ambient pressure the calculated vibrational frequencies are in good agreement with theexperiment values. The calculated vibrational frequencies at high pressures together withpressure coefficients and Gr¨uneisen parameters show that the intermolecular interactions arehighly affected by the applied pressure. 20 . ACKNOWLEDGMENTS
K R B would like to thank DRDO through ACRHEM for financial support. All theauthors acknowledge CMSD, University of Hyderabad for computational facilities.*Author for Correspondence, E-mail: [email protected] Fair, H. D.; Walker, R. F. Energetic Materilas; vol 1, Plenum Press; New York, 1977. Bowden, F. P.; Yoffe, A. D. Fast Reactions in Solids; Butterworth Scientific Publications,London, UK, 1958. Evans, B.L.; Yoffe, A. D.; Gray, P. Chem. Rev. 1959, 59, 515. Seel, M.; Kunz, A.B. Int. J. Quantum. Chem. 1991, 39, 149. Gordienko, A. B.; and Zhuravlev, Y. N.; and Poplavnoi, A. S. Phys. Status. Solidi B 1996, 198,707. Gordienko, A. B.; Poplavnoi, A. S. Phys. Status. Solidi B 1997, 202, 941. Younk, E. H.; Kunz, A. B. Int. J. Quantum Chem. 1997, 63, 615. Zhu, W.; Xiao, J.; Xiao, H. Chem. Phys. Lett. 2006, 422, 117. Eremets, M. I.; Gavriliuk, A. G.; Trojan, I. A.; Dzivenko, D. A.; Boehler, R. Nat. Mater. 2004,3, 558. Eremets, M. I.; Hemley, R. J.; Mao, H. K.; Gregoryanz, E. Nature 2001, 411, 170. Eremets, M. I.; Popov, M. Yu.; Trojan, I. A.; Denisov, V. N.; Boehler, R.; Hemley, R. J. J.Chem. Phys. 2004, 120, 10618. Medvedev, S. A.; Trojan, I. A.; Eremets, M. I.; Palasyuk, T.; Klap¨otke, T. M.; Evers, J. J.Phys.: Condens. Matter, 2009, 21, 195404. Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannopoulos, J. D. Rev. Mod. Phys.1992, 64, 1045. Segall, M.; Lindan, P.; Probert, M.; Pickard, C.; Hasnip. P.; Clark, S.; Payne, M. J. Phys.:Condens. Matter, 2002, 14, 271. Vanderbilt, D. Phys. Rev. B 1990, 41, 7892. Kresse, G.; Furthmuller, J. Phys. Rev. B 1996, 54, 11169. Fischer, T. H.; Almolf, J. J. Phys. Chem. 1992, 96, 9768. Ceperley, D.M.; Alder, B. J. Phys. Rev. Lett. 1980, 45, 566. Perdew, J. P.; Zunger, A. Phys. Rev. B 1981, 23, 5048. Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. Monkhorst, H. J.; Pack, J. Phys. Rev. B 1976, 13, 5188. Pringle, G. E.; Noakers, D. E. Acta Crystallogr. B 1968, 24, 262. Gonze, X. Phys. Rev. B 1997, 55, 10337. Refson, Keith.; Tulip, Paul R.; Clark, S. J. Phys. Rev. B 2006, 73, 155114. Mehl, M.J.; Osburn, J.E.; Papaconstantopoulus, D.A.; Klein, B.M. Phys. Rev. B 1990, 41,10311. Perger, W. F. Int. J. Quant. Chem. 2010, 110, 1916. Perdew, John. P.; Chevary, J. A.; Vosko, S. H.; Jackson,Koblar A.; Pederson, Mark R.; Singh,D. J.; Fiolhais, C. Phys. Rev. B 1992, 46, 6671. Perdew, John P.; Levy, Mel. Phys. Rev. Lett. 1983, 51, 1884-1887. Jones, R. O.; Gunnarsson, O. Rev. Mod. Phys. 1989, 61, 689-746. Manjon, F.J.; Errandonea, D.; Segura, A.; Munoz, V.; Tobias, G.; Ordejon, P.; and Canadell,E. Phys. Rev. B 2001, 63, 125330. Kanchana, V.; Vaitheeswaran, G.; Souvatzis, P.; Eriksson, O.; and Leb`egue, S. J. Phys.: Con-dens. Matter, 2010, 22, 445402. Bheema Lingam, Ch.; Ramesh Babu, K.; Tewari, Surya P.; Vaitheeswaran, G.; and Leb`egue, S.Phys. Status. Solidi RRL 5, No:1, 2010, 10. Born, M.; Huang, K. Dynamical Theory of Crystal Lattices; Oxford University Press: Oxford,1998. Sinha, Sonali.; Sinha, T. P.; Mookerjee, A. Phys. Rev. B 2000, 62, 13, 8828. ABLE III: The calculated vibrational frequencies of monoclinic LiN at ambient pressure, Pres-sure coefficients (cm − /GPa) and Gr¨uneisen parameters ( γ ) of the vibrational frequencies of allvibrational modes of monoclinic LiN from the linear fit of the present GGA results. Values inparenthesis are from experimentMode Symmetry Frequency (cm − ) Pressure coefficient(cm − /GPa) Gruneisen Parameter ( γ )M1 B u
138 2.1 1.26M2 A u u u u u g u u g u u g u a u u u g g a u u a a Ref (3).
10 20 30 40 50 60
M14 M15 M16 M17 M18 M19 M20 M21
Pressure (GPa) Pressure (GPa) M1 M2 M3 M4 M5 M6 M7 M8 M9 M10
M11
M12
M13