Structural, Electronic and Optical Properties of Well-Known Primary

Home , Fulminate

arXiv:1603.00216v1 [cond-mat.mtrl-sci] 1 Mar 2016 xenlsiuib rdcn O N CO, producing by stimuli blasting external metal in dynamite detonator. initiate to ignition cap used safe is a it guarantees which hence initiator and as when MF possible of only use was the dynamite of application wide The togsokt h eodr xlsv hc ed to leads which explosive secondary the detonation. to an shock by sufficiently initiated strong a output transmits is which high which explosive, a primary initiation, a adjacent of to with sensitivity consists explosive low explosive secondary but typical of pri- A charge namely main secondary. categories two and high into the mary charge, classified electric are or explosives friction, impact, shock, heat, o eodr xlsvsadaeioeetoi ihthe with cyanamides. iso-electronic and cyanates are azides, and corresponding initiators explosives as secondary applications find for they explosives, primary of ,000k e eri h einn f20 of beginning the about in was year Germany per in seen kg only clearly be 1,00,000 production can annual this its and from years many over service able u oisecletpiigpwr ihperformance, high detonated. power, easily be priming can explosive excellent it primary and its as used to been long due and widely first, the opsto rdcs Hg(CNO) products: composition ih.M sdtntdb prsadflames sun- and and sparks friction by impact, detonated is shock, MF to light. sensitive very is MF ae pnsniiiyt h xenlsiuisc as such stimuli external the to sensitivity upon Based tutrl lcrncadotclpoete fwell-kno of properties optical and electronic Structural, 1 h elkonpiayepoie ivrFliae(F,si (SF), Fulminate (b Silver compressibility explosives m anisotropic primary bulk known equilibrium well obtained teste the The methods compound. correction investigated non-local the i Waals the der Among van weak MF. the energetic capture di to op employed its been and However have of electronic methods years elastic, years. 300 structural, dependent many after pressure recently over determined service are invaluable structures rendered has it adgpisltr.As Oculn sfudt emr pron more be to found is coupling SO sho Also MF and insulators. SF gap B of band structures modified electronic Tran-Blaha TB-mBJ f developed calculated using The recently within interactions Electroni method (SO) wave t axis. spin-orbit (similar that including c-axis along along calculated interactions detonate to non-bonded sensitive Hg...O more is MF that eraei h olwn re:C order: following the in decrease a lobe tde n on ob infiatfrbt S a (SF both for significant SO numbers: be of PACS to effect bo The found Ag-C MF. and than studied unstable bonding. been more chemical also be of has to SF nature st makes the of which density describe bond Partial to respectively. MF, used and were SF of atoms Hg and nrai umntscm ne h class the under come fulminates Inorganic 4,5 ecr umnt M)i n ftewl-nw rmr expl primary well-known the of one is (MF) Fulminate Mercury .INTRODUCTION I. Fdtnt fe h ntainwith initiation the after detonate MF dacdCnr fRsac nHg nryMtras(ACRHE Materials Energy High in Research of Centre Advanced 3 Fhsrnee invalu- rendered has MF 2 ahbwi yeaa-504,Tlnaa India. Telangana, 500046, Hyderabad- Gachibowli, nvriyo yeaa,Po.C .RoRoad, Rao R. C. Prof. Hyderabad, of University → 2 n ga h de- the as Hg and , .YdknauadG Vaitheeswaran G. and Yedukondalu N. g+2O+N + 2CO + Hg > a > 3 )udrpesr,cneunl h orsodn elastic corresponding the consequently pressure, under c) 22 th ecr Fulminate Mercury n loit also and > Dtd coe ,2018) 2, October (Dated: 2 century. C Fwas MF 11 > C 2 33 . 6 4 h tutrladmcaia rprissuggest properties mechanical and structural The . gCO h oeua tutr si otatt the to contrast in prediction is theoretical structure previous molecular The Hg-CNO. al ei tutr fM slna ngsphase gas in linear is and molecular MF the of that structure proved they Lewis and MF of structure o Fad254NmfrL)adt aebet- have to and LA) for 210 300 m ignition above of N and MF (temperature 2.5-4 stability and (1-2 thermal sensitivity MF ter impact for less LA), m for N km/s km/s 5.3 4.25 and found velocity MF was (detonation for LA reliably Since more water. detonate of to addition by desensitized is elcdb LA. by replaced Fa 3Y ee n hypeitdbn CNO-Hg- bent structure. predicted of molecular they molecule of single and units a level ONC B3LYP for at out MF carried been cal- have (DFT) culations Theory com- Functional energetic Density Moreover, this of pound. structure crystal correct the ported single using MF of structure made crystal been crystal the have until investigations determine debate several determina- extensive to 1931 an the is Since but symmetry time 2007. crystal long its a of for tion ethanol explosive and primary acid a nitric accepted. mercury, widely from was the MF for interpretation of Howard’s formation them, among MF, thesis etcytlsrcueo F eety eke al et Beck Recently, MF. cor- of determine to structure unsuccessful crystal were rect attempts these but 3 eea ehd eepooe nteltrtr osyn- to literature the in proposed were methods Several aeadtie hoeia netgto nmolecular on investigation theoretical detailed a made ia rpriso F o-oa correction Non-local MF. of properties tical l oeta ierzdagetdplane augmented linearized potential ull cvr.I h rsn td,w report we study, present the In scovery. 2,13,14 tutr n pia rpriswere properties optical and structure c vraieadla zd.M exhibits MF azide. lead and azide lver D)det ihcmrsiiiyof compressibility high to due RDX) o ,ot8-d ehdwrswl for well works method optB88-vdW d, tsadeeto hredniymaps density charge electron and ates dlsrvasta Fi otrthan softer is MF that reveals odulus htteecmonsaeindirect are compounds these that w h orc oeua n crystal and molecular correct the , trcin nlyrdadmolecular and layered in nteractions ceJhsn(BmJ potential. (TB-mBJ) ecke-Johnson dM)o h compounds. the of MF) nd ucdfr4 for ounced di oedrcinlta Hg-C than directional more is nd n odrXrydffato methods diffraction X-ray powder and svssne17 since osives 7–9 opigo pia properties optical on coupling ∗ o o A n ec Fwslargely was MF hence and LA) for C npiayexplosive: primary wn 10–12 d n 5 and oee,M a enue as used been has MF However, M), th 18 d sae fAg of -states etr and century u ti ngo accord good in is it but 18 neaanBc et Beck again Once moduli i.e. o ONC- 17 for C 15,16 re- 2

17 with their recent X-ray diffraction study. In addition Enl = 1 dr n(r)φ(r,r′)n(r′) dr′ the authors also proposed that Hg-C-N angle is 180 o in c 2 Z Z o isolated molecule whereas it is 169 in the crystalline where n(r) is the electron density and the kernel φ(r,r′) solid form which is due to intermolecular interactions ′ ′ 3 is a function of n(r) and n(r ), their gradients, and r-r . and packing effects. However, except the crystal struc- However, this method requires massive computation to ture most of the fundamental physical properties are un- evaluate the double integral in the above equation using known for the investigated compound at electronic level. the fast-Fourier transform grid points, especially for large With this motivation, we performed a detailed study of cells.25 structural and mechanical properties under pressure up It is well known fact that the standard DFT func- to 5 GPa using advanced dispersion corrected methods tionals severely underestimate the band gap by 30- and electronic structure, optical properties by including 40% for semiconductors and insulators.26 In contrast to SO interactions at ambient pressure by means of first LDA/GGA functionals, recently developed Tran-Blaha principles calculations within the frame work of density modified Becke Johnson (TB-mBJ)27 potential shows re- functional theory (DFT). The rest of the article is orga- markable success in predicting the energy band gaps for nized as, in section II, we briefly describe methodology diverse materials28–31 and competing with the compu- of our calculation. In section III, the structural, elastic, tationally expensive methods such as GW approxima- electronic structure and optical properties of MF are dis- tion and hybrid functionals. Therefore, in the present cussed. Finally, in section IV, we summarize the results, work, TB-mBJ potential has been used to get reliable which concludes our paper. energy band gap thereby calculation of electronic structure and optical properties of SF and MF. This semi-local potential is implemented through WIEN2K package.32 II. COMPUTATIONAL DETAILS To achieve the required convergence of energy eigenval- ues, the wave functions in the interstitial region were ex- First principles calculations were performed using the panded using plane waves with a cut-off Kmax = 7/RMT Vienna ab-initio Simulation Package (VASP)19 based on while the charge density was Fourier expanded up to DFT with the all-electron projected augmented wave Gmax = 14, where Radius of Muffin Tin (RMT) is the (PAW) method. The ion-cores are described within smallest atomic sphere radius and Kmax denotes the mag- the PAW method while electron-electron interactions nitude of the largest K vector in plane wave expansion. are treated with the Perdew-Burke-Ernzerhof (PBE)20 The RMT radii are assumed to be 2.0, 1.05, 1.05 and parametrization of the generalized gradient approxima- 1.25 Bohrs for Ag/Hg, C, N and O, respectively. The tion (GGA) with plane wave cut-off energy of 1000 eV wave functions inside the spheres are expanded up to × × and a 9 9 5 k-mesh according to the Monkhorst-Pack lmax = 10. Self-consistency of total energy is obtained grid scheme.21 Quasi-Newton algorithm is used to relax by using 9×9×5 k-mesh in the Irreducible Brillouin Zone the ions and the system was fully relaxed with residual (IBZ). The frequency-dependent optical properties have forces smaller than 0.001 eV/A˚. been calculated using a denser k-mesh of 19× 19×12 in In order to treat weak dispersive interactions, there the IBZ. are two kinds of dispersion corrections; first one is pair- wise additive correction, second one is non-local correction and both of these methods have shown remarkable III. RESULTS AND DISCUSSION success recently. In the first method, vdW parameters for heavy metals (namely Cs, Ba, Hg, Tl, Pb and Bi etc.) A. Crystal structure i.e. 6th and 7th periods of the periodic table elements are not well optimized whereas the second method is used to MF is a long standing primary explosive but the molec- study the simple as well as heavy metal based systems ular geometry and crystal structure of MF has been and the results show success of this method in treating resolved more than 300 years of after its discovery.17 the van der Waals (vdW) interactions for wide range of The chemical formula of MF i.e. Hg(CNO) is analogous materials. Therefore, in the present study, we have used 2 to the corresponding Mercury Azide (MA), Hg(NNN)2. the second method so-called non-local correction method Moreover, the fulminate and/or azide single anion is lin- proposed by Dion et al22 and further modified by Klimes 23 ear and contain 16 valence electrons resulting a negative et al, in which the vdW contribution to the total en- charge. MF crystallizes in the orthorhombic centro sym- ergy is described through modifications to the correla- metric space group Cmce with lattice parameters a = tion energy functional within DFT. Specifically, the DFT 5.470A˚, b = 10.376A˚, c = 7.70A˚, V = 437.03 A˚3, and exchange-correlation functional takes the form: Z = 4.17 While MA crystallizes in non-centro symmetric GGA LDA nl space group Pca21 with lattice parameters a = 10.632A˚, Exc = Ex + Ec + Ec b = 6.264A˚, c = 6.323A˚, V = 421.10 A˚3 and Z = 4,33 con- GGA 20 LDA ∼ 17 Here Ex is the exchange energy, Ec is the local sequently MA is 4% more densely packed than MF. density approximation (LDA) correlation energy24 and As shown in figure 1, the crystal structure consists of MF nl Ec is the non-local correction which is given by molecule at each corner as well as face centre of the unit 3 cell (see figure 1a), the planar MF molecules are located section I, MF possesses perfect linear molecular structure at x = 0 and x = 0.5 along b-axis17 and the layers are in single molecular gas phase.3 While in the crystalline stacked along a and c-axes as depicted in figure 1b and solid form, the calculated angle between Hg-C and C-N 1c, respectively. Apart from this, experimental measure- bonds is 167.7o and it is deviated by 12.3o from linearity ments reveal that the arrangement of MF molecules in (180o) which is in good agreement with experimental17 b-c plane leads to two non-bonded contacts between Hg deviation of 11o. This deviation clearly indicates that and O atoms (see figure 1d) with a distance of Hg...O = slightly distorted linear molecular structure of MF in the 2.833 A˚ within the unit cell, which is less than the sum of crystalline form when compared to its molecular struc- the vdW radii 3 A˚ of Hg and O atoms (vdW radii 1.5 A˚ ture in gas phase. for Hg and O atoms) which causes weak vdW interactions in the crystalline MF.17 The intermolecular interactions play a significant role in predicting the structure and sta- B. Equation of State and Compressibility bility of the layered and molecular crystalline solids. The effect of SO coupling is of minor importance for We turned our attention to investigate the effect of structural optimization.35,37,43? Therefore, we first ob- hydrostatic pressure on crystal structure of MF. In or- tain the ground state crystal structure of MF by per- der to understand the behavior of unit-cell parameters forming full structural optimization of both lattice con- and their relative compressibilities under compression, stants and internal co-ordinates without inclusion of SO we have presented the lattice constants as a function of interactions. The obtained equilibrium volume of MF pressure. The pressure dependent lattice constants show is overestimated by ∼ 20.9% within PBE-GGA func- that a and c lattice constants decrease whereas lattice tional. This clearly represents that the standard PBE- constant ’b’ increases with pressure. Increase of lattice GGA functional is inadequate to predict the ground constant ’b’ under hydrostatic pressure is interesting in state properties of the energetic layered and molecular MF and this is similar to the case of silver azide (SA)45 solid MF. Recently, usage of non-local correction meth- in which lattice constant ’a’ increases as a function of ods become successful in describing the structural prop- pressure for ambient phase (Ibam). This clearly indi- erties of energetic molecular solids,25,38–40 nitrogen rich cates the anisotropic behavior of lattice constants under salts,41 organic-inorganic hybrid perovskite,42,43 and lay- the studied pressure range as depicted in figure 2a. Equa- ered materials.44 With this motivation, we have also used tion of state (EOS) represents the functional relationship various non-empirical dispersion corrected methods to between the thermodynamic variables (pressure, volume capture vdW interactions to reproduce the ground state and temperature) for solids. The calculated volume de- properties which are comparable with the experiment.17 crease monotonically as a function of pressure as shown in The computed ground state volume with non-local dis- figure 2b. By fitting pressure-volume data to third-order persion corrected methods for MF is overestimated by Birch-Murnaghan equation of state,46 the obtained equi- around 1.7% using vdW-DF; 5.9% using vdW-DF2 and librium bulk modulus (B0) and its pressure derivative are underestimated by around 0.4% using optB88-vdW; 1.1% found to be 12.2 GPa and 7.9 respectively using optB88- using optB86b-vdW methods. Among the examined non- vdW. However, the calculated B0 value 12.2 GPa for MF local dispersion corrected methods, optB88-vdW method is lower than that of SF (20 GPa),47 SA (39 GPa)48 and works well for the MF. The small discrepancies be- LA (26 GPa49 and 41 GPa50) which indicates the soft na- tween theoretical values at 0 K and experimental data ture of MF when compared to other well-known primary at 295 K17 were observed. The order of discrepancies explosives. about ∼0.4-5.9% are previously reported for secondary Further, to understand the compressibility of MF, nor- explosive molecular crystals with vdW-DF methods at malized lattice constants, bond lengths and bond an- 0 K.25,38,40 The calculated ground state unit cell lattice gles are plotted as a function of pressure as displayed constants, volume and density of MF using various non- in figure 3. The pressure dependent lattice constants local correction methods are compared with the exper- show anisotropic axial compressibilities of 96.2%, 102.4% imental data17 and are presented in Table I. In addi- 83.3% along a, b, and c crystallographic directions, re- tion, we have also calculated the intra-molecular inter- spectively and the order of compressibility is as follows actions for equilibrium structure obtained using optB88- b>a>c. As depicted in figure 3a, c-axis is the most com- vdW method. The calculated bond lengths Hg-C, C-N pressible for MF which is due to high compressibility of and N-O are 2.028 (2.029), 1.172 (1.143), 1.235 (1.248) A˚ non-bonded Hg...O intermolecular interactions along the and bond angles Hg-C-N, C-N-O and C-Hg-C are 167.7 c-axis as shown in figure 3b. While the intra-molecular (169.1), 179.7 (179.7) and 180 (180) o respectively, which bonds Hg-C, C-N, and N-O show very less compressible are in good agreement with the experimental17 results nature (see figure 3b) over the studied pressure range. given in parenthesis. The C≡N bond length in an iso- This clearly shows that the intermolecular interactions lated molecule is 1.160 A˚ and the calculated value for are weaker than intra-molecular interactions in the lay- MF is 1.172 A˚ which is strongly suggesting that there ered MF. The bond angle Hg-C-N shows more compress- exists a triple bond between C and N atoms as observed ible behavior whereas C-N-O and C-Hg-C exhibit less 17 in the experiment (d(C≡N) = 1.143 A˚). As discussed in compressible nature under the studied pressure range as 4 depicted in figure 3c. Overall, we observe that Hg-C, C- strain along b- and c-axis respectively while C23 couples N, and N-O bonds are stiffer whereas Hg...O non-bonded a applied normal stress along b-direction with an uniax- 54 distance is more compressible under the application of ial strain along c-axis. C23 has the largest value among hydrostatic pressure. the three transverse coupling elastic moduli and the low values of C12 and C13 would suggest that the crystal system is susceptible to shear along the crystallographic b- c C. Elastic constants and mechanical properties and -axes when normal stress is applied along crystallographic a direction. In addition, we have also calculated the elastic moduli as a function of pressure. As depicted Elasticity describes the response of a crystal under ex- in figure 4, all the elastic moduli increase (except C ), ternal strain which gives an information about the bond- 66 especially C22 grows rapidly as a function of pressure. ing characteristics for the anisotropic character of the However, we observe a softening of C elastic constant solid.51 Quantifying and understanding the elastic re- 66 with pressure which may induce shear instability in MF sponse of energetic materials is a necessary first step to- under high pressure. wards determining the mechanical and chemical mecha- When mono-crystalline samples are not available then nisms that produce this anisotropic behavior under shock it is not possible to measure the single crystal elastic loading.52 Numerous researchers focused their attention constants. Instead, the polycrystalline bulk and shear on understanding detonation initiation by mechanical moduli may be determined i.e. the average isotropic elas- shock.53 Detonation of an energetic material can be con- tic moduli can be obtained from anisotropic single crys- sidered as a collective property of the material and is tal elastic moduli.56 The Vigot, Reuss and Hill approxi- highly depends upon intermolecular interactions, molec- mations can predict the theoretical maximum, minimum ular arrangements, and molecular composition which has and average polycrystalline elastic moduli, respectively. a measurable effect on the macroscopic properties of the The obtained B value 12.2 GPa from EOS is comparable energetic solid.54 Therefore, we focused our attention to 0 with the derived B value of 14.2 GPa. Shear modulus understand the elastic behavior of energetic MF. Due to R G value 3.6 GPa is closely comparable (in magnitude) orthorhombic crystal symmetry, MF has nine indepen- R with the novel secondary explosive CL-2053 using Reuss dent elastic constants namely C , C , C , C , C , 11 22 33 44 55 approximation and the low value of shear moduli indi- C ,C ,C , andC . As presented in Table II, the cal- 66 12 13 23 cates that overall MF is more susceptible to shear forces. culated elastic constants are positive and obey the Born’s In addition, we also made an attempt to calculate the mechanical stability criteria,55 which indicate that MF sound wave velocities thereby Debye temperature of MF is mechanically stable at ambient pressure. A direction using the expressions given in Ref.36 as presented in Ta- in which intermolecular interactions are weak would re- ble II using the isotrpic elastic moduli obtained from Hill flect a higher compressibility along that direction. The approximation. Overall, the calculated polycrystalline compressibility of orthorhombic lattice constants a, b, elastic moduli, sound wave velocities and Debye temper- and c can be directly correlated with the diagonal elas- ature of MF are lower than the layered nitrogen rich alkali tic constants C , C , and C , respectively. As dis- 11 22 33 and alkaline-earth metal azide salts.57 Furthermore, the cussed in the above section, the compressibility order for stiffness of lattice and bond parameters can be clearly the investigated compound is b>a>c which reveals that understand by analyzing the nature of chemical bonding MF has the weakest interactions along the c-axis due to for the investigated compound. weak intermolecular interactions along c-axis (see figure 1d). Consequently, C33 possesses lowest value in magnitude among the three diagonal elastic moduli and they D. Electronic structure and chemical bonding decrease in the following order C22>C11>C33 as compressibility order of the lattice constants (b>a>c). Pre- viously Haycraft et al53,54 made a correlation between Silver and Mercury fulminates are iso-electronic with linear compressibility and elastic constants thereby rele- the corresponding azides, cyanates, and cynamides. Iqbal vance to shock detonation sensitivity for RDX and CL-20 et al2 accomplished a detailed study on electronic struc- single crystals. They reported that RDX and CL-20 are ture and stability of inorganic fulminates, which reveals found to be more sensitive to detonation along c and a- that nature of the bond between metal and carbon atoms axes, respectively. On the similar path, the calculated is ionic in sodium, potassium and thallous fulminates compressibility and elastic moduli disclose that MF is whereas it is covalent in silver and mercury fulminate found to be more sensitive to detonation along the c- salts and this will be further reflected in their order of axis. The other three diagonal elastic constants decrease stability. Iqbal et al58 also proposed that the heavy metal as follows: C55>C44>C66. C66 and C44 are found to be based salts are unstable than light metal salts because of relatively small compared to C55, which is an indication the asymmetric inter ionic distances. In addition, X-ray of the soft shear transformation along (001) and/or (100) electron spectroscopy study59 on inorganic azides reveals planes. On the other hand, three off-diagonal elastic con- that heavy metal azides are unstable than alkali metal stants (C12,C13, andC23); C12 and C13 couple an applied azides due to their directional bonding nature. There- normal stress component in the a-direction with uniaxial fore, the investigation of electronic structure and chem- 5 ical bonding is vital to understand the stability of the dle bands are due to s,p-states of fulminate group and energetic materials. finally the top of VB is mainly dominated by p-states of fulminate group, d-states of Ag atom and SO split- From theoretical perspective, electronic structure cal- ting is mainly due to 4d-states of Ag atom. Especially, culations for silver and mercury fulminate salts are lack- the bands along the high symmetry directions between ing in the literature. Since SO plays a significant role for U to R are split due to SO coupling for SF. While in heavy metals, in the present work, we have attempted case of MF, the lowest lying bands around -10 eV are a comparative analysis of electronic structure between due to d-states of Hg and s-states of C atoms and the SF and MF including SO interactions. In analogy to the s,p-states of fulminate group are positioned around -7.8 Zeeman effect, when an electron moves in an electric field p eV. The middle bands are derived from s,p-states of C, E, it experiences a magnetic field B ∼ E × 2 in its eff mc N, O atoms and 5d-states of Hg atom, which are split rest-frame (where m, p and c are mass, momentum of an due to SO in the energy range between -4.5 to -7.0 eV electron and speed of light, respectively)-a field that in- and the similar kind of splitting is seen for 5d-bands of duces a momentum-dependent Zeeman energy called the Hg atom in case of red-HgI .62 The bands around -2.5 eV SO coupling, Hˆ ∼ µ (E × p)σ/mc2, where σ is the 2 SO B are dominated by d, s-states of Hg atom and finally the µ × 24 vector of the Pauli spin matrices and B (= 9.27 10 top valence bands are mainly due to p-states fulminate JT−1) is the Bohr magneton. In crystals, the electric field ∇ group. From the calculated electronic band structures is given by the gradient of the crystal potential E = - V, with and without SO, it is found that inclusion of SO is which produces a SO field w(p) = -µ (∇V × p)/mc2.60 B more significant for 4d and 5d-bands of Ag and Hg atoms We first optimized the fractional co-ordinates of both SF 17,61 in the energy range -2 to -4 eV and -4.5 to -7 eV for SF and MF at the experimental lattice constants within and MF, respectively as depicted in figure 5c & f. PBE-GGA using FP-LAPW method and are presented in Table III. The calculated band gaps are found to be 2.13 Further, the intrinsic characteristics of chemical bond- and 3.64 eV for SF and MF respectively at the PBE- ing in SF and MF was investigated by examining the total GGA level. The PBE-GGA band gap value is slightly and partial density of states (PDOS). We have plotted higher than LDA value of 2.0 eV47 for SF. The obtained the PDOS of SF and MF with and without SO as de- TB-mBJ band gap values for SF and MF are found to picted in figure 6. As illustrated in figure 6, the conduc- be 3.32 and 4.92 eV respectively. When SO is included, tion band is mainly due to p-states of C, N, O and s,p,d- the TB-mBJ band gaps are found to be 3.30 and 4.82 states of metal (Ag/Hg) atoms. The lowest lying states eV for SF and MF, respectively and the corresponding positioned between -4.5 to -7.0 eV are due to hybridiza- reduction in the band gap values after inclusion of SO tion of predominantly 5d-sates of Hg which are split due are 0.02 and 0.1 eV. The small reduction in the band to SO and anionic p-sates of C, N and O atoms in MF gap values are due to occurrence of SO splitting at the whereas less contribution arises from Ag-4d states for SF lower part of the valence band (VB) for SF (between -2 in this energy range. The states at -2.5 eV below Fermi to -4 eV) and for MF (between -4.5 to -7 eV). The ob- energy are derived from 5d and 6s-states of Hg atom. The tained TB-mBJ band gap values with SO are lowered by top of the valence band is mainly dominated by fulminate 0.7 eV for SF and increased by 0.42 eV for MF when group (more contribution from 2p-states of oxygen atom) compared to the optical energy gap measurements2 of in both of the compounds SF and MF while 4d-states of 4.0 and 4.4 eV for SF and MF, respectively. However, Ag atom are predominant in case of SF but very less con- wrong space group has been used for MF (which results tribution from 5d-states of Hg atom in case of MF. This a bent molecular structure of MF, which is in contrast to implies that there exists a strong hybridization between the recent experimental measurements.17) in the optical Ag and C when compared to Hg and C atoms. This does and spectroscopic measurements.2,14 We have calculated strongly suggest that Ag-C bond has more directional band structures of both the compounds without and with bonding nature over Hg-C bond which indicates that SF SO coupling as presented in figures 5a (5d) and 5b (5e) is more unstable than MF. Moreover, we also observe s, p- for SF (MF), respectively. For clear understanding, we states of fulminate group and d-states of metal atom are have also plotted the band structures without and with dominant in the VB and strong hybridization between SO on top of each other as displayed in figures 5c & f. Ag/Hg and C, N and O atoms of anionic group which As illustrated in figure 5, SF and MF are indirect band shows the covalent nature in the studied compounds in gap insulators along S-(Γ-Z) and R-Γ directions, respec- contrast to the ionic fulminates. The N-O, C-N, Ag-C tively. To a large extent the band structures of both the and Hg-C bonds show less compressibility behavior with compounds look essentially similar with and without SO increasing pressure (see figure 3), this is due to strong hy- except for few bands in the lower part of the VB which are bridization between (Hg/Ag)-d and s, p-states of C, N, split due to the SO interactions as shown in the figures and O atoms leads to strong covalent character. Further- 5c & f. There are few energetically low lying bands, three more, this can be clearly analyzed from electronic charge for SF and five for MF (see figure 1 of the supplementary density maps which are used for accurate description of material64). In case of SF, the lowest bands in the VB chemical bonds. The calculated electron charge density region are derived from s-states of C, p-states of O atoms maps along various crystallographic planes of MF using and the bands are positioned around -10 eV. The mid- TB-mBJ potential are as shown in figure 7. It shows 6 anisotropic bonding interactions and the charge cloud is other important optical constants such as refraction, re- distributed within the CNO molecule indicating covalent flectivity, absorption and photo conductivity of the mate- character as previously reported for SF.47 Overall, the C, rials. The calculated static refractive indices with (with- N, and O atoms are covalently bonded within CNO group out) SO using the dielectric function n = ǫ(0) are given and the metal atom is also covalently bonded with CNO by n100 = 1.41 (1.53), n010 = 2.32 (2.36),p n001 = 1.62 group through C atom in both SF and MF compounds. (1.72) for SF and n100 = 1.35 (1.45), n010 = 2.26 (2.28), 2 The presence of covalent bonding in SF and MF makes n001 = 1.41 (1.50) for MF. Iqbal et al proposed that them more sensitive than the ionic fulminates. There- high values for the refractive index suggest that direc- fore, the heavy metal fulminates can find applications as tional bonding might be present in the crystal. The au- initiators for secondary explosives due to their instabil- thors also observed high refractive index value for SF ity (high sensitivity) which arises from the structure and over MF when the direction of light was parallel to a- bonding nature of the materials. axis. From the calculated refractive indices of both of the compounds, we clearly see that SF has high refractive indices along all the crystallographic directions than IV. OPTICAL PROPERTIES MF. Apart from the PDOS, the polarized refractive indices also show that SF has more covalent character when Investigation of optical properties for energetic mate- compared to MF which implies that SF is more unsta- rials is interesting because the knowledge of optical con- ble than MF. Also, the obtained refractive indices are stants is useful for determining decomposition mecha- distinct in all three crystallographic directions, which indicates the anisotropy of the SF (see figures 3 of sup- nism, laser-augmented combustion and ignition. The op- 64 tical spectra also allow an estimation of surface reflection plementary material) and for MF (see figure 9 (top)). losses and spatial distribution of radiation absorption.63 As illustrated in figure 9 (bottom), the calculated reflec- Moreover, electronic structure calculations could provide tivity spectra show that the reflectivity starts at around an information about the nature and location of inter 2 % and reaches to a maximum reflectivity of 12-14 % band transitions in crystals. In our previous work,47 along a- (at around 16 eV) and c (at around 4 eV for we made a detailed analysis of optical spectra of SF- SF and 16 eV for MF)-directions whereas it starts at polymorphs without inclusion of SO. In the present around 15 % and reaches to a maximum value of 50 % study, we mainly focused on the optical spectra of centro- at around 7 and 9 eV along b-direction for both of the symmetric orthorhombic structures of SF and MF with compounds. This implies that SF and MF has maximum and without inclusion of SO interactions. The complex reflectivity along b-direction when compared to a- and c-directions. The calculated absorption spectra is shown dielectric function ǫ(ω) = ǫ1(ω) + iǫ2(ω) can be used 64 to describe the linear response of the system to elec- in figure 4 of supplementary material for SF and figure tromagnetic radiation which is related to interaction of 10 for MF and absorption starts after the energy 3.30 photons with electrons. The imaginary part of dielec- and 4.82 eV for SF and MF, respectively which is the energy band gap between the VB maximum and Con- tric function ǫ2(ω) is obtained from the momentum ma- trix elements between the occupied and unoccupied wave duction band minimum. The absorption coefficients are ∼ 7 −1 functions within selection rules. The orthorhombic sym- found to have order of magnitude 10 m which shows metry of SF and MF allows three non-zero components that absorption of the compounds lie in the Ultra-Violet of the dielectric tensors along [100], [010] and [001] di- (UV) region. Photo conductivity is due to the increase in the number of free carriers when photons are absorbed. rections. The calculated real ǫ1(ω) and imaginary ǫ2(ω) parts of dielectric function with and without inclusion of The calculated photo conductivity shows a wide photo SO are as displayed in figure 2 of supplementary mate- current response in the absorption region of 3.30-25 eV rial for SF64 and in figure 8 for MF. The major peaks in and 4.82-25 eV as shown in figure 4 of supplementary material and figure 10 for SF and MF, respectively. Overall, ǫ2(ω) of SF are mainly arises due to optical transitions between Ag(4d) → N(2p) states.47 The prominent peaks we observe that inclusion of SO interactions has significant influence on optical properties of the heavy metal in ǫ2(ω) for MF are as follows: the peak at 5.9 eV orig- → energetic SF (see figures 2, 3 and 4 of the supplementary inates from the transition O(2p) Hg(s), the peak at 64 around 8.0 eV arises probably from the transition Hg(6s) material ) and MF salts as shown in figures 8, 9 and → N(p), the peaks in the energy range 10-16 eV are from 10. Also, SF and MF show a strong anisotropic and wide the transition Hg(5d) → N/C/O(p) and finally the peaks range of absorption. This results suggest the possible de- around 19.5 eV are due to the transition between Hg(5d) composition of SF/MF into Ag/Hg, CO and N2 under → Hg(p) states along three crystallographic directions. the action of UV light. Therefore, SF/MF decompose under the action of UV light and they may explode due The ǫ (ω) can be derived from the ǫ (ω) using the 1 2 to photochemical decomposition. Kramer-Kronig relations. The calculated real static dielectric constant along three crystallographic directions with (without) SO are found to be 2.00 (2.34), 5.39 (5.56), 2.64 (2.96) for SF and 1.83 (2.09), 5.11 (5.21), 1.99 (2.26) for MF. Using ǫ1(ω) and ǫ2(ω), one can derive 7

V. CONCLUSIONS and charge density maps. The covalent nature might be the reason for more sensitiveness to external stimuli In conclusion, ab-initio calculations have been per- of heavy metal fulminates when compared to ionic fulmi- formed to understand the pressure dependent structural nates. The effect of SO coupling on the optical properties and elastic properties of long standing primary explo- is found to be significant for both of the compounds. The sive, MF. Non-empirical van der Waals density functional most probabilistic electric-dipole transitions are found to methods vdW-DF, optB88-vdW and optB86b-vdW re- occur between Ag(4d) → N(2p) states for SF whereas produce the experimental volume within ∼ 1.7%. Among O(2p) → Hg(s), Hg(6s) → N(p) and Hg(5d) → Hg(p) the non-local correction methods tested, optB88-vdW states for MF. The calculated absorption coefficients are 7 −1 method works well for the examined compound. MF is found to be in the order of 10 m which shows that SF found to be softer than the well known primary explo- and MF are found to decompose under the irradiation of sives SF, SA and LA. The lattice constant b increases UV light. whereas lattice constants a, c are decreasing with pressure which shows anisotropic compressibility of MF. The calculated linear compressibility and elastic moduli re- VI. ACKNOWLEDGMENTS veal that MF is more sensitive to detonation along c- axis. The Hg...O non-bonded interactions are responsible Authors would like to thank Defense Research for high compressibility of MF along c-axis. The semi- and Development Organization (DRDO) through local TB-mBJ potential has been used to calculate the ACRHEM for the financial support under grant No. electronic structure and optical properties including SO DRDO/02/0201/2011/00060:ACREHM-PHASE-II, interactions. The computed electronic structures show and the CMSD, University of Hyderabad, for pro- that the investigated compounds are indirect band gap viding computational facilities. NYK would like to insulators. We also noticed that SO is more pronounced acknowledge Prof. M. C. Valsakumar, Department for 4d and 5d-states of Ag and Hg atoms of SF and of Physics, IIT Palakkad for his valuable discussions MF, respectively. The nature of chemical bonding is an- and suggestions. ∗Author for Correspondence, E-mail: alyzed through the calculated partial density of states [email protected]

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TABLE I: Calculated ground state lattice parameters (a, b, and c in, A˚), volume (V in, A˚3), density (ρ in, gr/cc) of orthorhombic MF using various non-local correction methods. Experimental data have been taken from Ref. 17 and the relative errors were given in parentheses with respect to experimental data. Here ”-” and ”+” represent under- and overestimation of calculated values when compared to the experiments. Parameter vdW-DF vdW-DF2 optB88-vdW optB86b-vdW Expt.17 a 5.518 5.559 5.451 5.447 5.470 (+0.9%) (+1.6%) (-0.3%) (-0.4%) b 10.749 10.742 10.677 10.661 10.376 (+3.6%) (+3.5%) (+2.9%) (+2.7%) c 7.497 7.748 7.478 7.445 7.700 (-2.6%) (+0.6%) (-2.9%) (-3.3%) V 444.67 462.67 435.22 432.33 437.03 (+1.7%) (+5.9%) (-0.4%) (-1.1%) ρ 4.251 4.086 4.343 4.372 4.33 (-1.8%) (-5.6%) (+0.3%) (-1.0%)

TABLE II: Calculated single elastic moduli (Cij , in GPa), polycrystalline bulk (BX , in GPa) and shear moduli (GX , in GPa) in the Voigt, Reuss, and Hill approximations (X = V, R, H, respectively), Young’s modulus (E, in GPa), the longitudinal, transverse, and average sound wave velocities (vl, vt, and vm, in km/s) and Debye temperature (θD, in K) of MF using optB88-vdW method. Elastic moduli Polycrystalline elastic moduli Sound wave velocities C11 24.7 BV 22.2 vl 2.43 C22 68.2 GV 7.3 vt 1.13 C33 17.7 BR 14.2 vm 1.27 C44 3.6 GR 3.8 θD 152 C55 8.5 BH 18.2 C66 2.5 GH 5.6 C12 8.1 E 15.1 C13 10.2 C23 26.4

TABLE III: Calculated fractional co-ordinates of SF and MF within PBE-GGA using FP-LAPW method at the experimental lattice constants a = 3.880 A˚, b = 10.752 A˚, c = 5.804 A˚ for SF61 and 5.47 A˚, 10.376 A˚, and c = 7.70 A˚ for MF.17 Compound Atom Wyckoﬀ Present Expt. SF61 Ag 4a (0.0000, 0.0000, 0.0000) (0.0000, 0.0000, 0.0000) C 4c (0.0000, 0.1444, 0.2500) (0.0000, 0.1517, 0.2500) N 4c (0.0000, 0.2549, 0.2500) (0.0000, 0.2595, 0.2500) O 4c (0.0000, 0.3700, 0.2500) (0.0000, 0.3758, 0.2500) MF17 Hg 4a (0.0000, 0.0000, 0.0000) (0.0000, 0.0000, 0.0000) C 8f (0.0000, 0.8191, 0.0937) (0.0000, 0.8180, 0.0950) N 8f (0.0000, 0.7080, 0.1208) (0.0000, 0.7110, 0.1230) O 8f (0.0000, 0.5916, 0.1496) (0.0000, 0.5930, 0.1490) 10

FIG. 1: (Color online) (a) Unit cell of MF along b-axis, (b, c) Planar layers of MF molecules stacked along a-axis with a a ˚ ˚ distance of 2 = 2.735 A, and (d) Two equivalent Hg...O = 2.833 A non-bonded interactions viewed along c-axis. Light ash, dark ash, blue and red color balls represent mercury, carbon, nitrogen and oxygen atoms, respectively.

7.6 440

7.2 optB88-vdW 6.8 c (Å) 420 B-M EOS fit 6.4 ) 10.9 3 400 10.8 b (Å) 10.7 Volume (Å 10.6 380

B0 = 12.2 GPa 5.4 ’ B 0 = 7.9 a(Å) 5.3 360

5.2 0 1 2 3 4 5 0 1 2 3 4 5 Pressure (GPa) Pressure (GPa) (a) (b)

FIG. 2: (Color online) (a) Calculated lattice constants and (b) volume of MF as a function of pressure using optB88-vdW method. 11

1.05 a) b) c) 1 1 1 Hg-C Hg-C-N 0.95 0.98 Hg...O

0 C-N-O C-N 0.98 C-Hg-C X/X 0.9 N-O a/a0 0.96 b/b 0.85 0 0.96 c/c 0 0.94 0.8 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 Pressure (GPa) Pressure (GPa) Pressure (GPa)

FIG. 3: (Color online) Calculated normalized (a) lattice constants, (b) bond lengths and (c) angles of MF as a function of pressure using optB88-vdW method. Where X0 and X represent obtained lattice parameters at ambient and as a function of pressure, respectively.

C11 C 200 C22 12 C C33 13 C C44 23 150 C55

C66

100

50 Elastic constants (GPa)

0 1 2 3 4 5 Pressure (GPa)

FIG. 4: (Color online) Calculated elastic constants of MF as a function of pressure using optB88-vdW method. 12

4 4 4

2 2 2 TB-mBJ TB-mBJ TB-mBJ+SO TB-mBJ+SO

0 0 0 Energy(eV) Energy (eV) Energy(eV)

-2 -2 -2

-4 -4 -4 Γ Z T Y S X U R Γ Z T Y S X U R Γ Z T Y S X U R (a) (b) (c)

3 3 3 TB-mBJ TB-mBJ+SO TB-mBJ+SO TB-mBJ

0 0 0 Energy (eV) Energy(eV) Energy(eV)

-3 -3 -3

-6 -6 -6

Γ Z T Y S X U R Γ Z T Y S XUR Γ Z T Y S X U R (d) (e) (f)

FIG. 5: (Color online) Calculated electronic band structures of (a, b, c) SF (top) and (c, d, e) MF (bottom) without (black dotted lines) and with (solid red lines) inclusion of SO coupling using the TB-mBJ potential at the experimental lattice constants.17,61 13

30 Total_so Total_so 20 Total 15 Total

0 0 O O s_so p_so p_so 1 p s 0.6 p

0 0 N N s_so p_so 0.5 p_so s 0.2 p p

0 C 0 s_so PDOS (States/eV) p_so s_so C 0.3 0.2 s PDOS (States/eV) p_so p s 0.1 p 0 Hg 0 d_so s_so Ag 0.6 p_so 10 d_so d s p d 5 5 0 -6 -3 0 3 Energy (eV) 0 0 -4 -2 0 2 4 -6 -3 0 3 Energy (eV) Energy (eV) (a) (b)

FIG. 6: (Color online) Calculated total and partial density of states of SF (left) and MF (right) with and without inclusion of SO interactions using the TB-mBJ potential at the experimental lattice constants.17,61

FIG. 7: (Color online) Calculated electronic charge densities of MF along crystallographic (100), (010), and (001) planes. 14

3 15 [100] [010] [001] 3 10 2 without SO 2 with SO (ω)

1 5 ε 1 1 0

0 0 15 2 2

10 (ω)

2 1 ε 1 5

0 0 0 0 9 18 27 36 0 9 18 27 36 0 9 18 27 36 Energy (eV)

FIG. 8: (Color online) Calculated real (ǫ1(ω)) and imaginary (ǫ2(ω)) parts of complex dielectric function of MF with (solid red lines) and without (dotted black lines) inclusion of SO interactions using the TB-mBJ potential at the experimental lattice constants.17

4 [100] [010] [001] 1.6 1.6 without SO 1.2 with SO ω) 2 1.2 n(

0.8 0.8

0.1 0.4 0.1 ω) R( 0.2

0 0 0 0 9 18 27 36 0 9 18 27 36 0 9 18 27 36 Energy (eV)

FIG. 9: (Color online) Calculated refraction (n(ω)) and reﬂectivity (R(ω)) spectra of MF with (solid red lines) and without (dotted black lines) inclusion of SO interactions using the TB-mBJ potential at the experimental lattice constants.17 15

150 200 150

) [100] [010] [001] -1 m 6 150

(10 100 100

100 α(ω) 50 50 50

0 0 0 4 3 )

-1 10 without SO 3 (fs with SO 2

σ(ω) 2 5 1 1

0 0 0 0 9 18 27 36 0 9 18 27 36 0 9 18 27 36 Energy (eV)

FIG. 10: (Color online) Calculated absorption (α(ω)) and photo conductivity (σ(ω)) spectra of MF with (solid red lines) and without (dotted black lines) inclusion of SO interactions using the TB-mBJ potential at the experimental lattice constants.17