T Kavetskyy, O Shpotyuk, V Boyko - On the origin of nanovoids in binary chalcogenide glasses studied by fsdp-related xrd pals and monte-carlo simulation - страница 1



Серія фізична. 2007. Вип.40. С.153-158

VISNYKLVIV UNIV. Ser.Physic. 2007. N40. P. 153-158

УДК 539.216.2

PACS number(s): 61.10.Nz, 61.18.-j, 61.43.Fs



T. Kavetskyy1, O. Shpotyuk1, V. Boyko2, J. Filipecki3, M. Popescu4

Scientific Research Company "Carat", Stryjska Str., 202, 79031 Lviv, Ukraine 2Lviv Polytechnic National University, 12, Bandera Str., 79013 Lviv, Ukraine 3Institute of Physics, Jan Dlugosz University in Czestochowa, Al. Armii Krajowej 13/15, 42201 Czestochowa, Poland

4National Institute of Materials Physics, P.O. BoxMG.7, 76900 Bucharest - Magurele, Romania

In the present work the origin of nanovoids in typical binary As2Se3 and As2S3 glasses has firstly been analyzed using combination of experimental methods, such as X-ray diffraction modified in respect to the first sharp diffraction peak (FSDP-related XRD) and positron annihilation lifetime spectroscopy (PALS), along with theoretical modelling based on Monte-Carlo procedure. It has been established a good agreement between experimental and theoretical results obtained. It is supposed that the approach proposed to characterize nano-scale void species structure in the investigated binary glass compositions can also be used for ternary network glasses within As2S(Se)3-based sub-systems.

Key words: Chalcogenide glasses, X-ray diffraction, Positron annihilation lifetime spectroscopy, Monte-Carlo simulation.

Although chalcogenide glasses (ChG) are widely used in modern optoelectronics, their structural features need still more understanding. The atomic-species structure is typically taken as the main determinant for ChG' properties, while the void-species one is so far not investigated.

The idea to study nanovoids in glasses has firstly been proposed during computer modeling of glass network within Monte-Carlo procedure [1], but it was not accepted entirely owing to absence of corresponding experimental confirmations.

Further, S.R. Elliott [2,3], interpreting the nature of the first sharp diffraction peak (FSDP) in AX2-type glasses, has assumed the importance of knowledge about nanovoids for glass structure to be understood.

At the same time, for As2Se3 glass, K.O. Jensen et al. [4] have demonstrated that positron annihilation lifetime spectroscopy (PALS) can also be used as experimental tool to study void-species structure of ChG, but the origin of voids for glass has been accepted in full similarity to respective crystal.

© Kavetskyy T., Shpotyuk O., Boyko V. et al., 2007

Thus, this work is focused to study the origin of nanovoids in typical binary As2Se3 and As2S3 glasses using combination of experimental methods, such as FSDP-related XRD and PALS, along with theoretical modelling based on Monte-Carlo procedure.

The investigated samples were prepared by a standard melt-quenching procedure [5]. Ampoules synthesized were quenched in water. Before experimental measurements samples were polished to the -1,5 mm thickness disks of optical quality and annealed near 20-30 K below glass transition temperature Tg.

FSDP-related XRD patterns were obtained by HZG-4a powder diffractometer with Cu Ka-radiation in the range of 10<26<40° with a step of 0,05° and an integration time of 70 sec per point. The sample was measured in the regime of "rotation" with speed of 2 rotations per sec. The 26 error in determining the FSDP position was ± 0,01°. The program CSD (Crystal Structure Determination) „Full profile powder data reduction" V.5.11 was used for data processing. The FSDP parameters such as the interlayer separation, quasi-periodic in nature with an effective periodicity, R, and correlation length, L, over which quasi-periodic real-space density fluctuations take place, were calculated within model [16]:

where the magnitude of the scattering vector Q1 (= 4nsin6 /X) corresponds to the position of the FSDP and AQ1 is the full width at half maximum (FWHM) of the FSDP.

The PALS experiment was performed using an ORTEC spectrometer with 22Na source described in details in [6]. The PALS data were mathematically processed with LT computer program [7]. The best PALS results within two-state positron trapping model [8] were corresponded to two-component fitting procedure, giving гь т2, I1 and I2 values (where т1 - reduced bulk lifetime, т2 - defect-related lifetime, associated with nanovoid volume, I1 and I2 - corresponding lifetime intensities (I1 + I2 = 1, and I2 values testify about concentration of nanovoids in glass matrix).

In order to obtain nanovoid radius distribution in the based glass forming network of the investigated ChG, the Monte-Carlo procedure possibilities were used previously reported in [1].

FSDP-related XRD. Fig. 1 shows the XRD pattern for g-As2Se3 and Table 1

demonstrates the CSD program treatment of the obtained XRD data and calculated FSDP parameters. The FSDP for g-As2Se3 is around 26=17,67° corresponding to the scattering vector Q^1,252 A-1. The magnitude of FWHM of the FSDP is equal to 4,88° or AQ1 =0,347 A1. The interlayer separation with an effective periodicity, R (the atom-void distance in terms of Elliott's void-based model [2]), and correlation length, L, calculated according to Eqs. (1-2), are found nearby 5.016 A and 18.1 A, respectively. It means that periodicity of R=5,016 A is necessary to give the FSDP at the observed value of Q1=1,252 A1 and this real-space quasi-periodicity takes place along the correlation length of L=18,1 A.

Fig. 2 shows the XRD pattern for g-As2S3 and Table 2 demonstrates the CSD program treatment of the obtained XRD data and calculated FSDP parameters. The FSDP for g-As2S3 is around 26 =17,84°, Q^1,264 A1 that is a good agreement

with literature data. The magnitude of FWHM of the FSDP is equal to 3,88°

or AQ1 =0,276 A1. The interlayer separation with an effective periodicity or repetitive distance, R and structural correlation length, L are obtained to be equal 4,968 A and

22,8 A.

R и 2n / Q1, Lи2n/AQb

(1) (2)











Table 1. The FSDP parameters for g-As2Se3

20 30 (degrees)


Fig. 1. X-ray diffraction pattern (Cu Ka-radiation) for g-As2Se3

26 (°)

±26 (°)




FWHM (°)

± FWHM (°)




Q1 (A-1)

AQ1 (A-1)




R (A)

L (A)



Table 2. The FSDP parameters for g-As2S3

26 (°)

±26 (°)




FWHM (°)

± FWHM (°)




Q1 (A-1)

AQ1 (A-1)




R (A)

L (A)



Fig. 2. X-ray diffraction pattern (Cu Ka-radiation) for


Т. Kavetskyy, O. Shpotyuk, V. Boyko et al.

Recently [9,10], it has been shown that the analytical equation between the FSDP position, Q1, and nanovoid diameter, D, for layer-like As2Se3-type ChG can be presented in the form of expression:

Q1 = 2,3xti/D. (3) In this way, the nanovoid volume, V, in the spherical approximation, calculated using Eq. (3), is found to be equal 100,5 A3 for g-As2Se3 and 97,4 A3 for g-As2S3.

PALS. By using two-state positron trapping model [8], the most real PALS characteristics with the optimal FIT range are obtained to be equal x1«0,20 ns, X2«0,37 ns, І2«0,60 for g-As2Se3 and Т1«0,19 ns, Т2«0,37 ns, І2«0,615 for g-As2S3.

According to K.O. Jensen with co-workers [4], the defect related positron lifetime т (in ns) and vacancy volume V (in A3) are interconnected in the terms of expression:

т = 0,240 + 0,0013 xV. (4) So, the nanovoid volume, V, calculated using Eq. (4), is found to be equal 100 A3 for the both g-As2Se3 and g-As2S3.

Monte-Carlo simulation. The nanovoid distribution results obtained within theoretical modelling by Monte-Carlo simulation procedure [1] are presented in Figs. 3 and 4 for As2Se3 and As2S3 based glass forming, respectively.


О с




Fig. 3. Nanovoid distribution for layer-biased l46-atoms structural model of g-As2Se3



146 atoms



2.3 A   2.9 A



1 І

і ilium


1 1 ■J III

1.0 1.5

2.0    2.5 3.0

Nano-void radiusr„ A

800 atoms

0,5  1.0   1.5  2.0 2.5 Nano-void radiusr, A

Fig. 4. Nanovoid distribution for layer-biased 800-atoms structural model of g-As2S3

It has been found that nanovoid structure of g-As2Se3 includes at least three types of free-volume nanovoids centered near r1«1,5, r2 «2,3 and r3 «2,9 A (Fig. 3). The numerical value of the greatest nanovoids centred near r3 « 2,9 A (Fig. 3) is in full agreement with the experimental results obtained using Eq. (2) for long-lived lifetime component т2«0,37 ns, associated with the nanovoids of V«100 or r«2,88 A. From this reason another two types of nanovoids centered near r1«1,5 and r2«2,3 A make contribution into short-lived lifetime component т«0,20 ns. The nanovoids centred near 2,9 A can be found for g-As2S3 too (Fig. 4).

Finally, we have obtained a good agreement between the results obtained by FSDP-related XRD, PALS and Monte-Carlo simulation (Table 3).

Table 3

The size of nanovoids obtained by FSDP-related XRD, PALS and Monte-Carlo

simulation methods


FSDP-related XRD


Monte-Carlo simulation


r (A)

V (A3)

r (A)

V (A3)

r (A)

V (A3)















In conclusion, for the first time, the origin of nanovoids in typical binary As2Se3 and As2S3 glasses has been analyzed using combination of experimental and theoretical methods such as FSDP-related XRD, PALS and Monte-Carlo simulation. The results obtained by such independent techniques are agreed well. It means that approach proposed to study of nanovoid topology in network binary ChG is quite applicable and one should be used in the case of more structurally complicated ternary ChG compositions.

The present work is partially carried out within bilateral Ukrainian-Romanian cooperation on Science and Technology between SRC "Carat" (Lviv, Ukraine) and NIMP (Bucharest-Magurele, Romania). We would like also to thank Dr. A. Kozdras (Opole Technical University, Poland) for his assistance with LT computer treatment of PALS data and interpretation of PALS results.

1. Popescu M.A. Hole structure of computer models of non-crystalline materials // J. Non-Cryst. Solids. 1980. Vol. 35-36. P. 549-554.

2. Elliott S.R. Origin of the first sharp diffraction peak in the structure factor of covalent glasses // Phys. Rev. Lett. 1991. Vol. 67. N 6. P. 711-714.

3. Elliott S.R. Extended-range order, interstitial voids and first sharp diffraction peak of network glasses // J. Non-Cryst. Solids. 1995. Vol. 182. P. 40-48.

4. Jensen K.O., Salmon P.S., Penfold I.T., Coleman P.G. Microvoids in chalcogenide glasses studied by positron annihilation // J. Non-Cryst. Solids.1994. Vol. 170.


5. Savova E., Pamukchieva V.Calorimetric measurements on Ge-Sb-S glasses // Semicond. Sci. Tchnol. 1997. Vol. 12. P. 185-188.

6. Kozdras A., Filipecki J., Hyla M., Shpotyuk O., Kovalskiy A. and Szymura S. Nanovolume positron traps in glassy-like As2Se3 // J. Non-Cryst. Solids. 2005. Vol. 351. P. 1077-1081.

7. Kansy J. Microcomputer program for analysis of positron annihilation lifetime spectra // Nucl. Instr. Meth. Phys. Res. A. 1996. Vol. 374. P. 235-244.

8. Puska M.J. Theory of positron annihilation and trapping in semiconductors // Materials Sci. Forum. 1992. Vol. 105-110. P. 419-430.

9. Kavetskyy T.S., Shpotyuk O.I. Nanostructural voids in glassy-like As2Se3 studied with FSDP-related XRD and PALS techniques // J. Optoelectron. Adv. Mater. 2005.

Vol. 7. N 5. P. 2267-2273.

10. Shpotyuk O., Kozdras A., Kavetskyy T., Filipecki J. On the correlation between void-species structure of vitreous arsenic selenide studied with X-ray diffraction and positron annihilation techniques // J. Non-Cryst. Solids. 2006. Vol. 352. P. 700-703.


T. Кавецький1, O. Шпотюк1, В. Бойко2, Я. Філіпецкі3, M. Попеску4

'Науково-виробниче підприємство "Карат ", вул. Стрийська, 202, 7903' Львів, Україна 2Національний університет "Львівська політехніка ",

вул. Бандери., 79013 Львів, Україна 3Інститут фізики, Університет імені Яна Длугоша, вул. Армії Крайової '3/'5, 4220' Честохова, Польща

4Національний університет фізики матеріалів, P.O. BoxMG.7, 76900 Бухарест - Магуреле, Румунія

У статті вперше проаналізовано природу нанопустот в типових бінарних стеклах As2Se3 та As2S3, з використанням комбінації методів рентгенівської дифракції із застосуванням до першого різкого дифракційного піку позитронної анігіляції та Монте-Карло моделювання. Визначено добру узгоджуваність між отриманими експериментальними та теоретичними результатами. Припускається, що запропонований підхід до характеризації нанорозмірної атомно-дефіцитної структури в досліджуваних бінарних стеклах може бути також використаний для потрійних сіткових стекол на основі As2S(Se)3 підсистем.

Ключові слова: халькогенідні стекла, рентгенівська дифракція, позитронна анігіляція, Монте-Карло моделювання.

Стаття надійшла до редколегії 29.05.2006 Прийнята до друку 26.02.2007


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