organic compounds\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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ISSN: 2056-9890

2-[(6-Nitro-1,3-benzodioxol-5-yl)methyl­­idene]malono­nitrile

aDepartment of Physics, RKM Vivekananda College (Autonomous), Chennai 600 004, India, and bDepartment of Organic Chemistry, University of Madras, Maraimalai Campus, Chennai 600 025, India
*Correspondence e-mail: ksethusankar@yahoo.co.in

(Received 2 November 2011; accepted 21 November 2011; online 30 November 2011)

In the title compound, C11H5N3O4, the nitro group is rotated by 29.91 (16)° out of the plane of the adjacent aryl ring. The 1,3-benzodioxole ring is nearly planar, with a maximium deviation of 0.0562 (10) Å. The dioxolene ring adopts an envelope conformation on the O—C—O C atom. In the crystal, mol­ecules are linked via C—H⋯O inter­actions, resulting in R22(6) and R22(12) graph-set motifs.

Related literature

For applications of malononitrile derivatives, see: Brimblecombe et al. (1972[Brimblecombe, R. W., Green, D. M. & Muir, A. W. (1972). Br. J. Pharmacol. 44, 561-576.]). For related structure, see: Loghmani–Khouzani et al. (2009[Loghmani-Khouzani, H., Abdul Rahman, N., Robinson, W. T., Yaeghoobi, M. & Kia, R. (2009). Acta Cryst. E65, o2545.]). For comparison of mol­ecular dimensions, see: Allen et al. (1987[Allen, F. H., Kennard, O., Watson, D. G., Brammer, L., Orpen, A. G. & Taylor, R. (1987). J. Chem. Soc. Perkin Trans. 2, pp. S1-19.]). For puckering parameters, see: Cremer & Pople (1975[Cremer, D. & Pople, J. A. (1975). J. Am. Chem. Soc. 97, 1354-1358.]). For graph–set motif notations, see: Bernstein et al. (1995[Bernstein, J., Davis, R. E., Shimoni, L. & Chang, N.-L. (1995). Angew. Chem. Int. Ed. Engl. 34, 1555-1573.]).

[Scheme 1]

Experimental

Crystal data
  • C11H5N3O4

  • Mr = 243.18

  • Triclinic, [P \overline 1]

  • a = 7.0953 (2) Å

  • b = 8.8847 (3) Å

  • c = 9.2212 (3) Å

  • α = 84.470 (2)°

  • β = 67.634 (2)°

  • γ = 78.874 (2)°

  • V = 527.30 (3) Å3

  • Z = 2

  • Mo Kα radiation

  • μ = 0.12 mm−1

  • T = 295 K

  • 0.30 × 0.28 × 0.25 mm

Data collection
  • Bruker Kappa APEXII CCD diffractometer

  • 13806 measured reflections

  • 3494 independent reflections

  • 2700 reflections with I > 2σ(I)

  • Rint = 0.025

Refinement
  • R[F2 > 2σ(F2)] = 0.048

  • wR(F2) = 0.142

  • S = 1.03

  • 3494 reflections

  • 163 parameters

  • H-atom parameters constrained

  • Δρmax = 0.28 e Å−3

  • Δρmin = −0.30 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
C1—H1B⋯O1i 0.97 2.53 3.2692 (16) 133
C8—H8⋯O4ii 0.93 2.52 3.3640 (17) 152
Symmetry codes: (i) -x, -y+1, -z+2; (ii) -x-1, -y+2, -z+1.

Data collection: APEX2 (Bruker, 2008[Bruker (2008). APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 2008[Bruker (2008). APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); molecular graphics: ORTEP-3 (Farrugia, 1997[Farrugia, L. J. (1997). J. Appl. Cryst. 30, 565.]) and Mercury (Macrae et al. 2008[Macrae, C. F., Bruno, I. J., Chisholm, J. A., Edgington, P. R., McCabe, P., Pidcock, E., Rodriguez-Monge, L., Taylor, R., van de Streek, J. & Wood, P. A. (2008). J. Appl. Cryst. 41, 466-470.]); software used to prepare material for publication: SHELXL97 and PLATON (Spek, 2009[Spek, A. L. (2009). Acta Cryst. D65, 148-155.]).

Supporting information


Comment top

The malononitrile derivative is used to investigate a variety of possible pharmacological effects when administered by various routes to whole animals and when applied to isolated organs and tissues (Brimblecombe et al., 1972). Also, it is a component of "tear gas" commonly reffered as CS gas, which is used as a riot control agent.

In the title compound C11H5N3O4, the benzodioxole ring is nearly planar with a maximum deviation 0.0562Å for the atom O2. The ONO angle is much larger than the ideal tetrahedral or trigonal values, respectively, doubtless as a consequence of the substantial negative charge on the paired O atoms. The bond lengths C9—C10 = 1.4388 (16)Å and C9—C11 = 1.4342 (16)Å is significantly shorter than the expected value for a C—C single bond because of conjugation effects.

In the dioxole ring C1/O2/C2/C7/O1, the deviation of atom C1 is -0.0724 (16)Å. The dioxole ring adopts a envelope conformation on C1 with puckering parameters (Cremer & Pople, 1975): Q2 = 0.1145 (13)Å and φ2 = 36.7 (6)°. The malononitrile group (C9—C10N2) and (C9—C11N3) is almost linear, with the angle around central carbon atoms C10 and C11 being 179.14 (15)° and 179.09 (15)° respectively.

The values of the torsion angles C5–C4–C8–C9 = -154.85 (11)° and C4–C5–N1–O4 = -151.10 (12)° indicates that the conformation of molecule is (-)anti–periplanar. The nitro group is not co–planar to the benzodioxole ring to which it is attached, making a dihedral angle of 29.76 (4)°. The benzodioxole unit is oriented at a dihedral angle of 36.90 (4)° with respect to the malononitrile group. The triple bond distances C10N2 and C11N3 are in agreement with the literature values (1.138 (7)Å; Allen et al., 1987). The title compound exhibits structural similarities with the already reported related structures (Loghmani–Khouzani et al., 2009).

The crystal packing is stabilized by non–classical intermolecular C—H···O interactions. The molecules are linked into centrosymmetric dimers. Atom C1 acts as a donor to dioxole O1i, so forming an R22(6) graph–set motif and atom C8 acts as a donor to nitro group O4ii at forming an R22(12) graph–set motif (Bernstein, et al., 1995). Symmetry codes: (i) -x, 1-y, 2-z; (ii) -1-x, 2-y, 1-z).

Related literature top

For applications of malononitrile derivatives, see: Brimblecombe et al. (1972). For related structure, see: Loghmani–Khouzani et al. (2009). For comparison of molecular dimensions, see: Allen et al. (1987). For puckering parameters, see: Cremer & Pople (1975). For graph–set motif notations, see: Bernstein et al. (1995).

Experimental top

To a solution of malononitrile (0.082 g, 1.24 mmol) in dichloromethane (5 ml), pyrrolidine (0.073 g, 1.03 mmol) was added and stirred well for 10 minutes. To this solution 6–nitrobenzo[d][1,3]dioxole–5–carbaldehyde (0.2 g, 1.03 mmol) was added and stirring was continued for 12 h. After the completion of the reaction as evidenced by TLC, the reaction mixture was poured into 2 N HCl solution (10 ml) and extracted using 25 ml of dichloromethane. The organic layer thus obtained was concentrated under reduced pressure. Column purification (silica gel, mesh size: 60–120) of the crude mixture using 15% ethyl acetate in hexanes successfully provided the desired 2–((6–nitrobenzo[d][1,3]dioxol–5–yl)methylene)malononitrile in 90% yield (0.23 g).

Refinement top

The hydrogen atoms were placed in calculated positions with C—H = 0.93Å to 0.97Å and refined in the riding model with fixed isotropic displacement parameters: Uiso(H) = 1.2Ueq(C) for aromatic and methylene groups.

Structure description top

The malononitrile derivative is used to investigate a variety of possible pharmacological effects when administered by various routes to whole animals and when applied to isolated organs and tissues (Brimblecombe et al., 1972). Also, it is a component of "tear gas" commonly reffered as CS gas, which is used as a riot control agent.

In the title compound C11H5N3O4, the benzodioxole ring is nearly planar with a maximum deviation 0.0562Å for the atom O2. The ONO angle is much larger than the ideal tetrahedral or trigonal values, respectively, doubtless as a consequence of the substantial negative charge on the paired O atoms. The bond lengths C9—C10 = 1.4388 (16)Å and C9—C11 = 1.4342 (16)Å is significantly shorter than the expected value for a C—C single bond because of conjugation effects.

In the dioxole ring C1/O2/C2/C7/O1, the deviation of atom C1 is -0.0724 (16)Å. The dioxole ring adopts a envelope conformation on C1 with puckering parameters (Cremer & Pople, 1975): Q2 = 0.1145 (13)Å and φ2 = 36.7 (6)°. The malononitrile group (C9—C10N2) and (C9—C11N3) is almost linear, with the angle around central carbon atoms C10 and C11 being 179.14 (15)° and 179.09 (15)° respectively.

The values of the torsion angles C5–C4–C8–C9 = -154.85 (11)° and C4–C5–N1–O4 = -151.10 (12)° indicates that the conformation of molecule is (-)anti–periplanar. The nitro group is not co–planar to the benzodioxole ring to which it is attached, making a dihedral angle of 29.76 (4)°. The benzodioxole unit is oriented at a dihedral angle of 36.90 (4)° with respect to the malononitrile group. The triple bond distances C10N2 and C11N3 are in agreement with the literature values (1.138 (7)Å; Allen et al., 1987). The title compound exhibits structural similarities with the already reported related structures (Loghmani–Khouzani et al., 2009).

The crystal packing is stabilized by non–classical intermolecular C—H···O interactions. The molecules are linked into centrosymmetric dimers. Atom C1 acts as a donor to dioxole O1i, so forming an R22(6) graph–set motif and atom C8 acts as a donor to nitro group O4ii at forming an R22(12) graph–set motif (Bernstein, et al., 1995). Symmetry codes: (i) -x, 1-y, 2-z; (ii) -1-x, 2-y, 1-z).

For applications of malononitrile derivatives, see: Brimblecombe et al. (1972). For related structure, see: Loghmani–Khouzani et al. (2009). For comparison of molecular dimensions, see: Allen et al. (1987). For puckering parameters, see: Cremer & Pople (1975). For graph–set motif notations, see: Bernstein et al. (1995).

Computing details top

Data collection: APEX2 (Bruker, 2008); cell refinement: SAINT (Bruker, 2008); data reduction: SAINT (Bruker, 2008); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 (Farrugia, 1997) and Mercury (Macrae et al. 2008); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008) and PLATON (Spek, 2009).

Figures top
[Figure 1] Fig. 1. The molecular structure of the title compound with the atom numbering scheme, displacement ellipsoids are drawn at 30% probability level. H atoms are present as small spheres of arbitary radius.
[Figure 2] Fig. 2. The packing arrangement of the title compound viewed down a axis. The dashed lines indicate C—H···O intermolecular interactions, which forms R22(6) and R22(12) centrosymmetric dimers. The symmetry codes: (i) -x, 1-y, 2-z; (ii) -1-x, 2-y, 1-z.
2-[(6-Nitro-1,3-benzodioxol-5-yl)methylidene]malononitrile top
Crystal data top
C11H5N3O4Z = 2
Mr = 243.18F(000) = 248
Triclinic, P1Dx = 1.532 Mg m3
Hall symbol: -P 1Mo Kα radiation, λ = 0.71073 Å
a = 7.0953 (2) ÅCell parameters from 3494 reflections
b = 8.8847 (3) Åθ = 1.0–31.6°
c = 9.2212 (3) ŵ = 0.12 mm1
α = 84.470 (2)°T = 295 K
β = 67.634 (2)°Block, yellow
γ = 78.874 (2)°0.30 × 0.28 × 0.25 mm
V = 527.30 (3) Å3
Data collection top
Bruker Kappa APEXII CCD
diffractometer
2700 reflections with I > 2σ(I)
Radiation source: fine–focus sealed tubeRint = 0.025
Graphite monochromatorθmax = 31.6°, θmin = 2.3°
ω scansh = 1010
13806 measured reflectionsk = 1212
3494 independent reflectionsl = 1313
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.048Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.142H-atom parameters constrained
S = 1.03 w = 1/[σ2(Fo2) + (0.0779P)2 + 0.0833P]
where P = (Fo2 + 2Fc2)/3
3494 reflections(Δ/σ)max < 0.001
163 parametersΔρmax = 0.28 e Å3
0 restraintsΔρmin = 0.30 e Å3
Crystal data top
C11H5N3O4γ = 78.874 (2)°
Mr = 243.18V = 527.30 (3) Å3
Triclinic, P1Z = 2
a = 7.0953 (2) ÅMo Kα radiation
b = 8.8847 (3) ŵ = 0.12 mm1
c = 9.2212 (3) ÅT = 295 K
α = 84.470 (2)°0.30 × 0.28 × 0.25 mm
β = 67.634 (2)°
Data collection top
Bruker Kappa APEXII CCD
diffractometer
2700 reflections with I > 2σ(I)
13806 measured reflectionsRint = 0.025
3494 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0480 restraints
wR(F2) = 0.142H-atom parameters constrained
S = 1.03Δρmax = 0.28 e Å3
3494 reflectionsΔρmin = 0.30 e Å3
163 parameters
Special details top

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R–factor wR and goodness of fit S are based on F2, conventional R–factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R–factors(gt) etc. and is not relevant to the choice of reflections for refinement. R–factors based on F2 are statistically about twice as large as those based on F, and R–factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
C10.1956 (2)0.45131 (18)0.79855 (15)0.0499 (3)
H1A0.25530.34330.79690.060*
H1B0.21820.49950.87920.060*
C20.13009 (16)0.60560 (13)0.61230 (12)0.0335 (2)
C30.13982 (17)0.70725 (13)0.48999 (12)0.0345 (2)
H30.26630.72860.41900.041*
C40.04642 (16)0.77900 (12)0.47404 (12)0.0309 (2)
C50.23081 (16)0.74097 (12)0.58573 (13)0.0331 (2)
C60.24088 (17)0.63890 (13)0.71134 (13)0.0373 (2)
H60.36600.61710.78420.045*
C70.05588 (18)0.57270 (13)0.72113 (12)0.0351 (2)
C80.04545 (17)0.90159 (12)0.35650 (13)0.0347 (2)
H80.16120.97860.38180.042*
C90.10476 (19)0.91503 (13)0.21576 (14)0.0386 (2)
C100.0900 (2)1.05218 (15)0.12130 (16)0.0478 (3)
C110.2814 (2)0.79907 (17)0.14691 (15)0.0491 (3)
N10.42888 (15)0.80802 (11)0.57275 (13)0.0417 (2)
N20.0804 (3)1.16093 (16)0.04706 (18)0.0707 (4)
N30.4220 (2)0.7081 (2)0.09043 (17)0.0760 (5)
O10.02108 (14)0.46924 (11)0.82958 (10)0.0483 (2)
O20.28869 (13)0.52328 (11)0.64860 (10)0.0457 (2)
O30.43369 (15)0.84163 (11)0.44228 (12)0.0507 (3)
O40.58153 (15)0.82535 (14)0.69255 (14)0.0674 (4)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
C10.0424 (7)0.0658 (8)0.0332 (6)0.0027 (6)0.0132 (5)0.0108 (5)
C20.0307 (5)0.0392 (5)0.0288 (5)0.0007 (4)0.0115 (4)0.0001 (4)
C30.0298 (5)0.0412 (5)0.0304 (5)0.0058 (4)0.0101 (4)0.0036 (4)
C40.0308 (5)0.0307 (5)0.0304 (5)0.0039 (4)0.0114 (4)0.0004 (4)
C50.0279 (5)0.0323 (5)0.0367 (5)0.0011 (4)0.0111 (4)0.0009 (4)
C60.0306 (5)0.0396 (6)0.0343 (5)0.0040 (4)0.0056 (4)0.0033 (4)
C70.0364 (5)0.0372 (5)0.0272 (5)0.0026 (4)0.0094 (4)0.0024 (4)
C80.0349 (5)0.0324 (5)0.0388 (5)0.0057 (4)0.0167 (4)0.0030 (4)
C90.0410 (6)0.0401 (6)0.0386 (6)0.0114 (5)0.0190 (5)0.0086 (4)
C100.0602 (8)0.0460 (7)0.0449 (7)0.0211 (6)0.0253 (6)0.0122 (5)
C110.0415 (7)0.0632 (8)0.0361 (6)0.0077 (6)0.0108 (5)0.0109 (5)
N10.0309 (5)0.0360 (5)0.0550 (6)0.0031 (4)0.0153 (4)0.0051 (4)
N20.1052 (13)0.0544 (7)0.0656 (9)0.0313 (8)0.0436 (9)0.0243 (6)
N30.0539 (8)0.0989 (12)0.0516 (8)0.0105 (8)0.0062 (6)0.0049 (8)
O10.0414 (5)0.0590 (6)0.0362 (4)0.0034 (4)0.0116 (4)0.0164 (4)
O20.0336 (4)0.0603 (6)0.0375 (4)0.0003 (4)0.0141 (3)0.0121 (4)
O30.0472 (5)0.0499 (5)0.0639 (6)0.0064 (4)0.0329 (5)0.0056 (4)
O40.0323 (5)0.0746 (7)0.0705 (7)0.0072 (5)0.0034 (5)0.0157 (6)
Geometric parameters (Å, º) top
C1—O11.4319 (17)C5—N11.4614 (14)
C1—O21.4334 (15)C6—C71.3635 (15)
C1—H1A0.9700C6—H60.9300
C1—H1B0.9700C7—O11.3525 (13)
C2—O21.3547 (13)C8—C91.3420 (16)
C2—C31.3641 (15)C8—H80.9300
C2—C71.3850 (16)C9—C111.4342 (19)
C3—C41.4068 (14)C9—C101.4388 (16)
C3—H30.9300C10—N21.1355 (18)
C4—C51.4016 (15)C11—N31.138 (2)
C4—C81.4597 (14)N1—O41.2145 (15)
C5—C61.3887 (15)N1—O31.2230 (14)
O1—C1—O2107.04 (9)C7—C6—H6122.1
O1—C1—H1A110.3C5—C6—H6122.1
O2—C1—H1A110.3O1—C7—C6128.09 (10)
O1—C1—H1B110.3O1—C7—C2110.03 (10)
O2—C1—H1B110.3C6—C7—C2121.87 (10)
H1A—C1—H1B108.6C9—C8—C4126.91 (10)
O2—C2—C3128.07 (10)C9—C8—H8116.5
O2—C2—C7109.65 (9)C4—C8—H8116.5
C3—C2—C7122.28 (10)C8—C9—C11124.80 (11)
C2—C3—C4118.30 (10)C8—C9—C10119.43 (12)
C2—C3—H3120.9C11—C9—C10115.74 (11)
C4—C3—H3120.9N2—C10—C9179.14 (15)
C5—C4—C3117.50 (9)N3—C11—C9179.09 (15)
C5—C4—C8121.96 (9)O4—N1—O3123.24 (11)
C3—C4—C8120.12 (9)O4—N1—C5118.09 (11)
C6—C5—C4124.20 (10)O3—N1—C5118.67 (10)
C6—C5—N1115.70 (10)C7—O1—C1105.81 (9)
C4—C5—N1120.10 (10)C2—O2—C1105.89 (9)
C7—C6—C5115.83 (10)
O2—C2—C3—C4179.32 (11)C3—C2—C7—C60.79 (18)
C7—C2—C3—C40.78 (17)C5—C4—C8—C9154.85 (11)
C2—C3—C4—C50.01 (16)C3—C4—C8—C932.75 (16)
C2—C3—C4—C8172.74 (10)C4—C8—C9—C118.72 (19)
C3—C4—C5—C60.80 (17)C4—C8—C9—C10173.31 (10)
C8—C4—C5—C6171.78 (10)C6—C5—N1—O429.91 (16)
C3—C4—C5—N1178.10 (9)C4—C5—N1—O4151.10 (12)
C8—C4—C5—N19.32 (16)C6—C5—N1—O3148.95 (11)
C4—C5—C6—C70.81 (17)C4—C5—N1—O330.04 (15)
N1—C5—C6—C7178.14 (10)C6—C7—O1—C1173.03 (12)
C5—C6—C7—O1179.34 (11)C2—C7—O1—C17.55 (14)
C5—C6—C7—C20.01 (17)O2—C1—O1—C712.15 (14)
O2—C2—C7—O10.17 (14)C3—C2—O2—C1172.11 (12)
C3—C2—C7—O1179.75 (10)C7—C2—O2—C17.80 (14)
O2—C2—C7—C6179.29 (10)O1—C1—O2—C212.26 (14)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C1—H1B···O1i0.972.533.2692 (16)133
C8—H8···O4ii0.932.523.3640 (17)152
Symmetry codes: (i) x, y+1, z+2; (ii) x1, y+2, z+1.

Experimental details

Crystal data
Chemical formulaC11H5N3O4
Mr243.18
Crystal system, space groupTriclinic, P1
Temperature (K)295
a, b, c (Å)7.0953 (2), 8.8847 (3), 9.2212 (3)
α, β, γ (°)84.470 (2), 67.634 (2), 78.874 (2)
V3)527.30 (3)
Z2
Radiation typeMo Kα
µ (mm1)0.12
Crystal size (mm)0.30 × 0.28 × 0.25
Data collection
DiffractometerBruker Kappa APEXII CCD
Absorption correction
No. of measured, independent and
observed [I > 2σ(I)] reflections
13806, 3494, 2700
Rint0.025
(sin θ/λ)max1)0.737
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.048, 0.142, 1.03
No. of reflections3494
No. of parameters163
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.28, 0.30

Computer programs: APEX2 (Bruker, 2008), SAINT (Bruker, 2008), SHELXS97 (Sheldrick, 2008), ORTEP-3 (Farrugia, 1997) and Mercury (Macrae et al. 2008), SHELXL97 (Sheldrick, 2008) and PLATON (Spek, 2009).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C1—H1B···O1i0.972.533.2692 (16)133
C8—H8···O4ii0.932.523.3640 (17)152
Symmetry codes: (i) x, y+1, z+2; (ii) x1, y+2, z+1.
 

Acknowledgements

SK and KS thank Dr Babu Varghese, Senior Scientific Officer, SAIF, IIT, Chennai, India, for the X-ray intensity data collection and Dr V. Murugan, Head of the Department of Physics, RKM Vivekananda College, for providing facilities in the department for carrying out this work.

References

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