Modeling and first-principles calculation of low-frequency quasi-localized vibrations of soft and rigid As–S nanoclusters

  • Roman HolombEmail author
  • Paul Ihnatolia
  • Oleksandr Mitsa
  • Volodimyr Mitsa
  • László Himics
  • Miklós Veres
Original Article


Experimental and theoretical studies were performed on Boson peak of binary AsxS100−x glasses and As–S polycrystalline composites (mixtures of glass with polycrystallites) of different compositions. Low-frequency Raman spectra of six different compositions ranging from As6S94 to As60S40, including the stoichiometric As40S60 composition, were measured in the region of 5–100 cm−1. The Fourier-transform Raman spectra of the As–S samples in the range of 50–600 cm−1 were also measured to reveal the structure of the materials at nanoscale. In addition, density functional theory calculations were performed on different As–S nanoclusters for determination of their low-frequency vibrational modes. The effect of the structural interconnection of the clusters on their vibrational mode frequencies was modeled by attaching different numbers of heavy dummy hydrogen atoms to the dangling bonds of branchy—As2+4/3S5 and 12-membered ring-like As6S6+6/2 nanoclusters. It was found that the vibrational mode frequencies have a U-shaped dependence on the level of interconnection, which correlates with experimental findings on compositional dependence of the Boson peak position in AsxS100−x glasses. The composition dependence of spectral behavior and very low-frequency features detected at low-energy side of the Boson peak in the Raman spectra of As–S samples were also analyzed and their structural origin is discussed.


Chalcogenides Boson peak Nanoclusters Low-frequency vibrations Interconnection 



R. Holomb and V. Mitsa gratefully acknowledge the support from the Hungarian Academy of Sciences within the Domus Hungarica Scientiarum et Artium. The work was carried out within the framework of the DB-884 Project of the Ministry of Education and Science of Ukraine. The publication contains the results of research conducted with the grant support of the State Fund for Fundamental Research under the Competitive Project 0117U006384. This work was supported by the VEKOP-2.3.2-16-2016-00011 grant, which is co-financed by the European Union and European Social Fund.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. Achibat T, Boukenter A, Duval E (1993) Correlation effects on Raman scattering from low-energy vibrational modes in glasses. II. Experimental results. J Chem Phys 99:2046–2051. CrossRefGoogle Scholar
  2. Andrikopoulos KS, Christofilos D, Kourouklis GA, Yannopoulos SN (2006) Pressure dependence of the Boson peak in glassy As2S3 studied by Raman scattering. J Non Cryst Solids 352:4594–4600. CrossRefGoogle Scholar
  3. Angell CA (1995) Formation of glasses from liquids and biopolymers. Science 267:1924–1935. CrossRefGoogle Scholar
  4. Angell CA (2004) Boson peaks and floppy modes: some relations between constraint and excitation phenomenology, and interpretation, of glasses and the glass transition. J Phys Condens Matter 16:S5153–S5164. CrossRefGoogle Scholar
  5. Arsova D, Boulmetis YC, Raptis C. Pamukchieva V, Skordeva E (2005) The Boson peak in Raman spectra of AsxS1−x glasses. Semiconductors 39:960–962. CrossRefGoogle Scholar
  6. Becke AD (1997) Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals. J Chem Phys 107:8554–8560. CrossRefGoogle Scholar
  7. Beltukov YM, Fusco C, Parshin DA, Tanguy A (2016) Boson peak and Ioffe-Regel criterion in amorphous siliconlike materials: the effect of bond directionality. Phys. Rev. E 93:023006. (1–18) CrossRefGoogle Scholar
  8. Benassi P, Fontana A, Frizzera W, Montagna M, Mazzacurati V, Signorelli G (1995) Disorder-induced light scattering in solids: the origin of the Boson peak in glasses. Phil Mag 71:761–769. CrossRefGoogle Scholar
  9. Born M, Huang K (1954) Dynamical theory of crystal lattices. Clarendon, OxfordGoogle Scholar
  10. Brink T, Koch L, Albe K (2016) Structural origins of the boson peak in metals: from high-entropy alloys to metallic glasses. Phys Rev B 94:224203. (1–9) CrossRefGoogle Scholar
  11. Buchenau U, Nücker N, Dianoux AJ (1984) Neutron scattering study of the lowfrequency vibrations in vitreous silica. Phys Rev Lett 53:2316–2319. CrossRefGoogle Scholar
  12. Buchenau U, Prager M, Nücker N, Dianoux AJ, Ahmad N, Phillips WA (1986) Low-frequency modes in vitreous silica. Phys Rev B 34:5665–5673. CrossRefGoogle Scholar
  13. Buchenau U, Zhou HM, Nucker N, Gilroy KS, Phillips WA (1988) Structural relaxation in vitreous silica. Phys Rev Lett 60:1318–1321. CrossRefGoogle Scholar
  14. Buchenau U, Galperin YM, Gurevich VL, Schober HR (1991) Anharmonic potentials and vibrational localization in glasses. Phys Rev B 43:5039–5045. CrossRefGoogle Scholar
  15. Buchenau U, Galperin YuM, Gurevich VL, Parshin DA, Ramos MA, Schober HR (1992) Interaction of soft modes and sound waves in glasses. Phys Rev B 46:2798–2808. CrossRefGoogle Scholar
  16. Chumakov AI, Monaco G, Fontana A, Bosak A, Hermann RP, Bessas D, Wehinger B, Crichton WA, Krisch M, Rüffer R, Baldi G, Carini G Jr, Carini G, D’Angelo G, Gilioli E, Tripodo G, Zanatta M, Winkler B, Milman V, Refson K, Dove MT, Dubrovinskaia N, Dubrovinsky L, Keding R, Yue YZ (2014) Role of disorder in the thermodynamics and atomic dynamics of glasses. Phys Rev Lett 112:025502. (1–6) CrossRefGoogle Scholar
  17. Crupi V, Fontana A, Giarola M, Longeville S, Majolino D, Mariotto G, Mele A, Paciaroni A, Rossi B, Trotta F, Venuti V (2014) Vibrational density of states and elastic properties of cross-linked polymers: combining inelastic light and neutron scattering. J Phys Chem B 118:624–633. CrossRefGoogle Scholar
  18. Curtiss LA, McGrath MP, Blandeau J-P, Davis NE, Binning RC, Radom JrL (1995) Extension of Gaussian-2 theory to molecules containing third-row atoms Ga–Kr. J Chem Phys 103:6104–6113. CrossRefGoogle Scholar
  19. Duval E, Boukenter A, Champagnon B (1986) Vibration eigenmodes and size of microcrystallites in glass: observation by very-low-frequency Raman scattering. Phys Rev Lett 56:2052–2055. CrossRefGoogle Scholar
  20. Eggleton BJ, Luther-Davies B, Richardson K (2011) Chalcogenide photonics. Nat Photonics 5:141–148. CrossRefGoogle Scholar
  21. Elliott SR (1992) A unified model for the low-energy vibrational behaviour of amorphous solids. Europhys Lett 19:201–206.; Elliott SR (1992) Erratum. Europhys Europhys Lett 19:660.
  22. Feher A, Yurkin IM, Deich LI, Orenda M, Turyanitsa ID (1994) The comparative analysis of some low-frequency vibrational state density models of the amorphous materials—applied to the As2S3 glass. Phys B Condens Matter 194:395–396. CrossRefGoogle Scholar
  23. Ferrari M, Champagnon B, Barland M (1992) Width of the excitonic absorption peak and size of CdSxSe1−x semiconductor nanocrystallites. J Non Cryst Solids 151:95–101. CrossRefGoogle Scholar
  24. Frick B, Richter D (1995) The microscopic basis of the glass transition in polymers from neutron scattering studies. Science 267:1939–1945. CrossRefGoogle Scholar
  25. Frisch MJ, Trucks GW, Schlege HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Petersson GA, Nakatsuji H et al (2016) Gaussian 09, revision A.02. Gaussian, Inc., WallingfordGoogle Scholar
  26. Gurevich VL, Parshin DA, Pelous J, Schober HR (1993) Theory of low-energy Raman scattering in glasses. Phys Rev B 48:16318–16331. CrossRefGoogle Scholar
  27. Gurevich VL, Parshin DA, Schober HR (2003) Anharmonicity, vibrational instability, and the Boson peak in glasses. Phys Rev B 67:094203. (1–10) CrossRefGoogle Scholar
  28. Gurevich VL, Parshin DA, Schober HR (2005) Pressure dependence of the Boson peak in glasses. Phys Rev B 71:014209. CrossRefGoogle Scholar
  29. Hassan AK, Börjesson L, Torell LM (1994) The Boson peak in glass formers of increasing fragility. Non Cryst Solids 172–174:154–160. CrossRefGoogle Scholar
  30. Holomb R, Mitsa V (2004a) Boson peak of AsxS1−x glasses and theoretical calculations of low frequencies clusters vibrations. Solid State Commun 129:655–659. CrossRefGoogle Scholar
  31. Holomb RM, Mitsa VM (2004b) Simulation of Raman spectra of AsxS100−x glasses by the results of ab initio calculations of AsnSm clusters vibrations. J Optoelectron Adv Mater 6:1177–1184Google Scholar
  32. Holomb R, Mateleshko N, Mitsa V, Johansson P, Matic A, Veres M (2006) New evidence of light-induced structural changes detected in As–S glasses by photon energy dependent Raman spectroscopy. J Non Cryst Solids 352:1607–1611. CrossRefGoogle Scholar
  33. Holomb R, Veres M, Mitsa V (2009) Ring-, branchy-, and cage-like AsnSm nanoclusters in the structure of amorphous semiconductors: ab initio and Raman study. J Optoelectron Adv Mater 11:917–923Google Scholar
  34. Holomb R, Mitsa V, Johansson P, Veres M (2010) Boson peak in low-frequency Raman spectra of AsxS100−x glasses: nanocluster contribution. Phys Status Solidi C 7:885–888. Google Scholar
  35. Holomb R, Mitsa V, Petrachenkov O, Veres M, Stronski A, Vlček M (2011) Comparison of structural transformations in bulk and as-evaporated optical media under action of polychromatic or photon-energy dependent monochromatic illumination. Phys Status Solidi C 8:2705–2708. CrossRefGoogle Scholar
  36. Ivanda M, Babocsi K, Dem C, Schmitt M, Montagna M, Kiefer W (2003) Low-wave-number Raman scattering from CdSxSe1−x quantum dots embedded in a glass matrix. Phys Rev B 67:235329. (1–8) CrossRefGoogle Scholar
  37. Jakse N, Nassour A, Pasturel A (2012) Structural and dynamic origin of the boson peak in a Cu-Zr metallic glass. Phys Rev B 85:174201. (1–6) CrossRefGoogle Scholar
  38. Khodadadi S, Malkovskiy A, Kisliuk A, Sokolov A (2010) A broad glass transition in hydrated proteins. Biochim Biophys Acta 1804:15–19. CrossRefGoogle Scholar
  39. Klinger MI (2001) Separation of soft-mode and acoustic dynamics in the Boson peak of glasses: vast difference in high-pressure effects. J Non Cryst Solids 293–295:345–347. CrossRefGoogle Scholar
  40. Kobliska RJ, Solin SA (1973) Temperature dependence of the Raman spectrum and the depolarization spectrum of amorphous As2S3. Phys Rev B 8:756–768. CrossRefGoogle Scholar
  41. Kondrat O, Holomb R, Popovich N, Mitsa V, Veres M, Csik A, Feher A, Tsud N, Vondráček M, Matolín V, Prince KC (2015) In situ investigations of laser and thermally modified As2S3 nanolayers: synchrotron radiation photoelectron spectroscopy and density functional theory calculations. J Appl Phys 118:225307. (1–7) CrossRefGoogle Scholar
  42. Kondrat O, Holomb R, Csik A, Takáts V, Veres M, Mitsa V (2017) Coherent light photo-modification, mass transport effect, and surface relief formation in AsxS100−x nanolayers: absorption edge, XPS, and Raman spectroscopy combined with profilometry study. Nanoscale Res Lett 12:149(1–149(10. CrossRefGoogle Scholar
  43. Krishnan R, Binkley JS, Seeger R, Pople JA (1980) Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. J Chem Phys 72:650–654. CrossRefGoogle Scholar
  44. Laib JP, Nickel DV, Mittleman DM (2010) Terahertz vibrational modes induced by heterogeneous nucleation in n-alkanes. Chem Phys Lett 493:279–282. CrossRefGoogle Scholar
  45. Laird BB, Schober HR (1991) Localized low-frequency vibrational modes in a simple model glass. Phys Rev Lett 66:636–639. CrossRefGoogle Scholar
  46. Lima TA, Ishikawa MS, Martinho HS (2014) Boson peak as a probe of quantum effects in a glassy state of biomolecules: the case of l-cysteine. Phys Rev E 89:022715. (1–5) CrossRefGoogle Scholar
  47. Lucovsky G, Martin RM (1972) A molecular model for the vibrational modes in chalcogenide glasses. J Non Cryst Solids 8–10:185–190. CrossRefGoogle Scholar
  48. Luo P, Li YZ, Bai HY, Wen P, Wang WH (2016) Memory effect manifested by a boson peak in metallic glass. Phys Rev Lett 116:175901. (1–5)CrossRefGoogle Scholar
  49. Malinovsky VK, Sokolov AP (1986) The nature of Boson peak in Raman scattering in glasses. Solid State Commun 57:757–761. CrossRefGoogle Scholar
  50. Malinovsky VK, Novikov VN, Sokolov AP, Dodonov VG (1988) Low-frequency Raman scattering on surface vibrational modes of microcrystals. Solid State Commun 67:725–729. CrossRefGoogle Scholar
  51. Malinovsky VK, Novikov VN, Parshin PP, Sokolov AP, Zemlyanov MG (1990) Universal form of the low-energy (2 to 10 meV) vibrational spectrum of glasses. Europhys Lett 11:43–47. CrossRefGoogle Scholar
  52. Marruzzo A, Schirmacher W, Fratalocchi A, Ruocco G (2013) Heterogeneous shear elasticity of glasses: the origin of the Boson peak. Sci Rep 3:1407. (1–7) CrossRefGoogle Scholar
  53. Martin AJ, Brenig W (1974) Model for Brillouin scattering in amorphous solids. Phys Status Solidi B 64:163–172. CrossRefGoogle Scholar
  54. Mateleshko N, Mitsa V, Kikineshi A (1999) Vibrational spectra and structural studies of Hg-As-S glasses. Fizika A 8:17–24Google Scholar
  55. Naumis GG (2015) Low-frequency vibrational modes anomalies and rigidity: a key to understanding the glass and the electronic properties of flexible materials from a topological perspective. Front Mater 2:44. CrossRefGoogle Scholar
  56. Nemanich RJ (1977) Low-frequency inelastic light scattering from chalcogenide glasses and alloys. Phys Rev B 16:1655–1674. CrossRefGoogle Scholar
  57. O’Hern CS, Silbert LE, Liu AJ, Nagel SR (2003) Jamming at zero temperature and zero applied stress: the epitome of disorder. Phys Rev E 68:011306. (1–19) CrossRefGoogle Scholar
  58. Parshin DA, Schober HR, Gurevich VL (2007) Vibrational instability, two-level systems, and the boson peak in glasses. Phys Rev B 76:064206. (1–16) CrossRefGoogle Scholar
  59. Phillips WA (ed.) (1981) Amorphous solids: low-temperature properties. Springer, New YorkCrossRefGoogle Scholar
  60. Rufflé B, Ayrinhac S, Courtens E, Vacher R, Foret M, Wischnewski A, Buchenau U (2010) Scaling the temperature-dependent Boson peak of vitreous silica with the high-frequency bulk modulus derived from Brillouin scattering data. Phys Rev Lett 104:067402(1–067402(4. CrossRefGoogle Scholar
  61. Schmider HL, Becke AD (1998) Optimized density functionals from the extended G2 test set. J Chem Phys 108:9624–9631. CrossRefGoogle Scholar
  62. Scott DW, McCullough JP, Kruse FH (1964) Vibrational assignment and force constants of S8 from a normal-coordinate treatment. J Mol Spectrosc 13:313–320. CrossRefGoogle Scholar
  63. Shintani H, Tanaka H (2008) Universal link between the boson peak and transverse phonons in glass. Nat Mater 7:870–877. CrossRefGoogle Scholar
  64. Shuker R, Gammon RW (1970) Raman-scattering selection-rule breaking and the density of states in amorphous materials. Phys Rev Lett 25:222–225. CrossRefGoogle Scholar
  65. Silbert LE, Liu AJ, Nagel SR (2005) Vibrations and diverging length scales near the unjamming transition. Phys Rev Lett 95:098301. (1–4) CrossRefGoogle Scholar
  66. Sokolov AP, Kisliuk A, Quitmann D, Duval E (1993) Evaluation of density of vibrational states of glasses from low-frequency Raman spectra. Phys Rev B 48:7692–7695. CrossRefGoogle Scholar
  67. Tan P, Xu N, Schofield AB, Xu L (2012) Understanding the low-frequency quasilocalized modes in disordered colloidal systems. Phys Rev Lett 108:1176–1177. Google Scholar
  68. Taraskin SN, Loh YL, Natarajan G, Elliott SR (2001) Origin of the Boson peak in systems with lattice disorder. Phys Rev Lett 86:1255–1258. CrossRefGoogle Scholar
  69. Tikhomirov VK, Santos LF, Almeida RM, Jha A, Kobelke J, Scheffler M (2001) On the origin of the Boson peak in the Raman scattering spectrum of As2S3 glass. J Non Cryst Solids 284:198–202. CrossRefGoogle Scholar
  70. Winterling G (1975) Very-low-frequency Raman scattering in vitreous silica. Phys Rev B 12:2432–2440. CrossRefGoogle Scholar
  71. Wischnewski A, Buchenau U, Dianoux AJ, Kamitakahara WA, Zarestky JL (1998) Sound-wave scattering in silica. Phys Rev B 57:2663–2666. CrossRefGoogle Scholar
  72. Zargar R, DeGiuli E, Bonn D (2016) Scaling for hard-sphere colloidal glasses near jamming. Europhys Lett 116:68004. (p1–p5) CrossRefGoogle Scholar
  73. Zeller RC, Pohl RO (1971) Thermal conductivity and specific heat of noncrystalline solids. Phys Rev B 4:2029–2041. CrossRefGoogle Scholar
  74. Zorn R, Yin H, Lohstroh W, Harrison W, Budd PM, Pauw BR, Böhning M, Schönhals A (2018) Anomalies in the low frequency vibrational density of states for a polymer with intrinsic microporosity—the Boson peak of PIM-1. Phys Chem Chem Phys 20:1355–1363. CrossRefGoogle Scholar

Copyright information

© King Abdulaziz City for Science and Technology 2019

Authors and Affiliations

  • Roman Holomb
    • 1
    • 2
    Email author
  • Paul Ihnatolia
    • 1
  • Oleksandr Mitsa
    • 1
  • Volodimyr Mitsa
    • 1
  • László Himics
    • 2
  • Miklós Veres
    • 2
  1. 1.Uzhhorod National UniversityUzhgorodUkraine
  2. 2.Wigner Research Centre for PhysicsHungarian Academy of SciencesBudapestHungary

Personalised recommendations