AIP Conf. Proc. 1136, 370-374(2009).
Ab Initio Calculation Of Vibrational Frequencies In AsxS1-x Glass And The Raman Spectra Ahmad Nazrul Rosli*, Hasan Abu Kassim, and Keshav N. Shrivastava Department of Physics, University of Malaya, Kuala Lumpur, 50603 Malaysia *Email of corresponding author:
[email protected] Abstract. We have made many different models for the understanding of the structure of AsS glass. In particular, we made the models of AsS3 (triangular), AsS3 (pyramid), AsS4 (3S on one side, one on the other side of As, S3-As-S), AsS4 (pyramid), AsS4 (tetrahedral), AsS7, As2S6 (dumb bell), As2S3 (bipyramid), As2S3 (zig-zag), As3S2 (bipyramid), As3S2 (linear), As4S4 (cubic), As4S4 (ring), As4S (tetrahedral), As4S (pyramid), As4S3 (linear) and As6S2 (dumb bell) by using the density functional theory which solves the Schrödinger equation for the given number of atoms in a cluster in the local density approximation. The models are optimized for the minimum energy which determines the structures, bond lengths and angles. For the optimized clusters, we calculated the vibrational frequencies in each case by calculating the gradients of the first principles potential. We compare the experimentally observed Raman frequencies with those calculated so that we can identify whether the cluster is present in the glass. In this way we find that AsS4 (S3-As-S), As4S4 (ring), As2S3 (bipyramid), As4S4 (cubic), As4S3 (linear), As2S3 (zig-zag), AsS4 (Td), As2S6 (dumb bell), AsS3 (triangle) and AsS3 (pyramid) structures are present in the actual glass. Keywords: AsS, vibrational frequency, density functional theory, glass PACS:
INTRODUCTION In recent years, there has been considerable progress in the understanding of glass phase of a solid. The glass phase is often composed of molecules or clusters of atoms. In the formation of a molecule only a single valency is present, for example in AsS arsenic is divalent. If we disturb the relative concentration of As and S by mixing more or less of As than S in AsxS1-x, there is a phase transition at a particular value of x from the single crystal to a glass. AsS is called realgar. It is sensitive to light which changes the valency of As from 2 to 3. In the compound As2S3 arsenic is trivalent. In this state As2S3 is called orpiment. Actually several other forms are also well known, e.g., As4S (duranusite), As4S3 (dimorphite) and As4S5 (uzonite). The Raman spectra
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are poorly resolved so that there is hope to identify new molecular compositions. There has been considerable effort to resolve the Raman spectra in AsS glass [1]. The fractional valency of As is also found, 1.5 in As4S3 and 2.5 in As4S5 which indicates that there is a strong sharing of orbits between As and S atoms. Yang et. al. [2] have calculated the force constants in both AsS as well as As2S3 from which they determine that As-S bond is much stronger than the As-As bond. Ohsaka and Ihara [3] have analysed the low frequency region where the phonon frequency is determined by the size of the grains in the sample, =v/2d, where v is the velocity of sound, d is the diameter of the particle and is the phonon frequency. The Raman spectra of As2S3 have been reported by Kawazoe et. al. [4]. There is a strong peak at 340 cm-1 and comparatively weaker peaks at 230 and 490 cm-1. There is a poorly resolved band at 700-800 cm-1. Tanaka [5] has also discussed the Raman peak at 350 cm-1 and humps at 230 and 500 cm-1. In recent years, we have successfully performed the density functional theory calculations which predict the vibrational frequency in reasonable agreement with the experimental values [6-10]. The detailed theory of relaxation with stretched exponential has been given by Phillips [11] and Thorpe [12] has introduced the concept of soft modes in glasses. Wang et. al. [13] have found that there is a phase transition in glasses as a function of concentration in which rigidity is the order parameter. Since our calculations of vibrational frequencies in the glasses [9,10], GePI and GePS, are in reasonable agreement with those measured by the Raman spectra, we extend our calculations to AsS. In this paper, we report our calculations of vibrational frequencies in clusters of arsenic sulphide and compare them with those found in the Raman spectra.
CLUSTERS OF ATOMS We make the clusters of atoms to obtain their vibrational spectra. The Schrödinger equation for a given cluster of atoms is solved in the local density approximation of the density functional theory [14-16]. The force constants are obtained from the derivative of the potential without any adjustable parameters. In some cases the same molecule occurs in three dimensions as well as in a plane showing the collapse of one of the dimensions. In some cases we exchange one ion for another so that we can see the effect of ion exchange. In the density functional theory, the nuclear motion equation separates out from that of the electron. In the following material, 11 different clusters are reported.
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( i ) AsS3 (triangle): In this cluster, three atoms of S are on the corners of a triangle and As is in the centre. The S-As-S angle is strictly 120o so that only one distance is sufficient to define this cluster. The optimized As-S distance is found to be 2.165 Ǻ. ( ii ) AsS3 (pyramid): As we have seen above AsS 3 stabilizes in a plane. However, it is also possible to find the stable configuration in a pyramidal form. In this case the S-S bond distance is found to be 2.359 Ǻ while the As-S distance is 3.000 Ǻ. (iii) AsS4 (S3-As-S, 3-1 model): This cluster has three S atoms on one side of As and one S on the other, which we call 3-1 model. The S atoms on one side form a triangle with S-S distance 3.080 Ǻ, with As-S distance of 2.241Ǻ, then there is one S atom on the other side with As-S distance of 2.120 Ǻ. (iv) AsS4 (Td): It is possible to put the 4 sulphur atoms on a tetrahedron with As in the centre. This is a stable configuration. When DN wave function is used, the As-S distance is found to be 2.241Ǻ. A strong vibration at 358.3 cm-1 is clearly visible. (v) As2S6(dumb bell): In this model the two As atoms are far apart. The distance between two As atoms is 3.474 Ǻ and then three S atoms are attached to each As atom. The AsS atoms are 2.169 Ǻ apart. (vi) As2S3(bipyramid): This is a bipyramidal cluster. The S3 form a triangle with one As is on top position while another As atom is on the bottom. The As-S distance is 3.388 Ǻ and S-S distance is 2.441 Ǻ. (vii) As2S3 (zig-zag): The atoms are arranged in a straight line as S-As-S-As-S. Then optimization makes the zig-zag. The As-S distance is 2.390 Ǻ and S-S distance is 2.131 Ǻ. (viii) As4S4 (cubic): The S4 atoms are on the tetrahedron sites. The cubic sites left vacant by S are occupied by As atoms. The cell size is 2.529 Ǻ so that a single distance determines the structure. (ix) As4S4 (ring): A circular cluster is formed with alternate As and S atoms with AsS distance 2.208 Ǻ. The circumference of the circle is thus 8 times this distance, i.e., 17.664 Ǻ. The diameter of this molecule is about 5.62 Ǻ. (x) As4S (Td): There are four As atoms on the tetrahedral sites and one S atom in the centre. The As-S bond distance is 2.298 Ǻ. (xi) As4S3 (linear): This molecule is genuinely linear. The bond length at the end of the molecule is 2.529 Ǻ. As one approaches from the end towards the centre, the bond becomes smaller and the values change to 2.2999 Ǻ and then near the centre to 2.152 Ǻ.
EXPERIMENTAL RAMAN SPECTRA The Raman spectra of As2S3 given by Tanaka [5] are poorly resolved. There is a peak at 20 cm-1 due to scattering from the particle size, which means that the particle size is equal to the wave length of radiation, v/2d. Here v is the velocity of sound
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and d is the diameter of the grain. Let us take = 20 cm-1 as an exercise. This is equivalent to 20c in c.p.s. units. The diameter of the particle which scatters this radiation is d=v/2, where v3×105 cm/s is the velocity of sound. Substituting v and in the expression for d, we find, d=25 Ǻ which is 250 nm. This is just the size of the particles present in the glass. Therefore, the 20 cm-1 radiation is caused by the particle size. This particle is a boson which is not related to the electronic structure of the atoms. It is also not related to the force constants. There are weak lines at 230 cm1 and 500 cm-1 along with a strong and broad line at 350 cm-1. Georgiev et. al. [1] have made efforts to resolve the broad line into components. In the glass As xS1-x (x=0.38) there is a broad line but at x=0.44 some resolution becomes apparent and lines at 185 and 220 cm-1 look like peaks on a broad back ground.
COMPARISON BETWEEN THEORY AND EXPERIMENTS In Table 1, we show the experimental as well as the values we obtained from the first principle’s calculations. All of the experimentally found frequencies agree with those calculated for the clusters. This means that the glass consists of random self organized arrangements of clusters. The existence of As4S3 (linear) shows the linear growth which gives strength to the glass by working like a “back bone”. Besides the “back bone”, there are clusters which resemble rings, pyramids, bipyramids and triangles. The clusters relax with time and reorganize their orientations. This type of self-organization gives long relaxation times to the glass. TABLE 1: Comparison of experimentally observed values of frequencies with those calculated for the given clusters.
S. No. Experimental cm-1 1. 187 2. 3. 4. 5. 6. 7. 8. 9.
218 272 308 330 342 362 378 397
Calculated (cm-1) & clusters 183 As4S4(ring), 177 As2S3(bipyramid), 173 AsS4(3-1 model) 211.9 As4S4(cubic), 210 AsS4(3-1 model) 270 AsS4(3-1 model), 279.3 As4S4(cubic) 309.6 AsS3(pyramid) 330.6 As2S3(bipyramid) 343 As4S3(linear), 344.0 As2S3(zig-zag) 358.3 AsS4(Td) 385.5 As2S6(dumb bell), 387.3 AsS3(triangular) 399.6 AsS3(pyramid)
CONCLUSION
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We find that arsenic sulphide consists of several different compositions mixed together. Although the minerals realgar (AsS) and orpiment (As2S3) are well known, we find that other molecules, such as, AsS3 (triangular), AsS3 (pyramid), AsS4 (3-1 model), AsS4 (Td), As4S4 (ring), As2S3 (bipyramid), As4S4 (cubic), As2S3 (zig-zag), As4S3 (linear), As2S6 (dumb bell) are predicted on the basis of quantum mechanical first principle calculations. This prediction is in accord with the experimentally observed Raman spectra. The usefulness of quantum mechanics for the study of glass structures is therefore well demonstrated. Hence, we predict that there exists a class of “quantum glasses” for which the vibrational frequencies are predictable by quantum mechanics. The calculations may help in decoding local structures of clusters that are produced by atomic beams. The molecular clusters are also populated in nanoscale phase separated molecular glasses.
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