M Hyla, V Boyko, O Shpotyuk - Two-cation corner- and edge-sharing interlinked clusters in asge-s glasses - страница 1

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ВІСНИК ЛЬВІВ. УН-ТУ

Серія фіз. 2009. Bun. 43. С. 118-125

VISNYKLVIV UNIV. Ser. Physics. 2009. Is. 43. P. 118-125

PACS number(s): 61.43.Fs, 31.15.A

TWO-CATION CORNER- AND EDGE-SHARING INTERLINKED CLUSTERS IN As/Ge-S GLASSES

M. Hyla1, V. Boyko2, O. Shpotyuk2, J. Filipecki1

institute of Physics, Jan Dlugosz University Al. Armii Krajowej 13/15, 42 201 Czestochowa, POLAND e-mail: m.hyla@ajd.czest.pl 2Institute of Materials, Scientific Research Company "Carat" Stryjska Str., 202, 79031 Lviv, UKRAINE

Quantum mechanical ab initio calculations of corner- and edge-sharing cluster interlinking in binary As/Ge-S glass formers were performed using HyperChem Realise 7,5 program. The average formation energies (AFE) of clusters with respect to single pyramid-like AsS3/2 and tetragon-like GeS4/2 building blocks were calculated. It was shown that AFE associated with the number of Lagrangian constraints per atom would explain the adaptability of chalcogenide glass-forming backbone to structural self organization.

Key words: Chalcogenide glasses, ab initio calculations.

The chalcogenide glasses (ChG) derive their name from chalcogen (Ch) elements S, Se or Te but not O as a main component in their chemical composition. They are important materials both for fundamental investigation of particularities in the disordered state and for different applications. Two common chalcogenide systems consist of V-VI elements, i.e. compounds with pnictogen (P) atoms from V group (e.g. As, Sb), where the glass-forming regions are mostly centered around stoichiometric P2Ch3 composition, and compounds with group IV elements, i.e. Si, Ge (denoted tetragens, T, in view of the prevalent tetrahedral coordination), where binary glass-forming IV-VI compositions are centered around stoichiometric TCh2 composition. The atoms in ChG form extended three dimensional networks, they maintaining short-range order by keeping the number of covalent bonds to nearest neighbours in strong dependence on the valence of constituent atoms. Hence group IV elements are four-fold, group V elements are three­fold and group VI elements are two-fold coordinated.

Amorphous chalcogenides of arsenic and germanium are the most characteristic materials. It is well know that at stoichiometricAs2S3 and GeS2 compositions (i.e. at the compositions where only heteropolar chemical bonds exist) one As atom is linked to three S atoms and each S atom is linked to two As atoms in As-S glass or each Ge atom is linked to four S atoms and each S atom is linked to two Ge atoms in Ge-S. Experimental data suggest the presence of following structural units in a glass-forming network - pyramidal As(S1/2)3 with As atom raised above the plane defined by three S atoms and tetrahedral Ge(Se1/2)4 being a tetrahedron centred on Ge atoms [1].

In dependence on chemical composition the ChG change the number of Lagrangian

© Hyla M., Boyko V., Shpotyuk O. et al., 2009

constraints per atom nc forming under- (nc<3), over- (nc>3) or optimally-constrained (nc=3) atomic networks with fully saturated covalent bonding. It was assumed by Phillips [2] that optimal mechanical stability of the network can be achieved when nc=3, this network being called self-organized phase. The underconstrained (floppy) network with nc<3 is easily deformed, but in the overconstrained (rigid) networks with nc>3 any deformation requires stretching or bending bonds. The bonds are not distributed randomly and the network can adapt itself to lower the stress due to overconstrained regions. In general, the nc number can be calculated according to the known mean-field constraints theory [3, 4]:

= - + (2Z-2 V

■3) + —-

N

(1)

where: Z is coordination number of glass network constructed by nr atoms

having r bonds Zrnr = N ; n and nring- corrections on dangling bonds and rings, respectively.

In this work, we have used new cation-interlinking network cluster approach (CINCA) to built the simplest molecular-like species with fully-saturated covalent bonding within binary As/Ge-S systems: pyramid-like AsS3/2 building blocks having 3 shared S atoms and tetragon-like GeS4/2 building blocks having 4 shared S atoms. These basic structural units having 2 cations (As or Ge) create the whole ChG network. They can be interconnected into two ways, especially as atom-shared clusters (ASC) with shared S atom or as bond-shared clusters (BSC) with shared S-S bond. Figure 1 shows ASC (a) and BSC (b) for two pyramidal units. The ending chalcogen atoms belong to basic unit in the case of BSC cluster, while we should consider only half-part contribution of each terminal chalcogen atom in the case of ASC (because the next half takes part in another unit).

ASC

BSC

a b Fig. 1. ASC cluster interlinked with S atom (a) and BSC cluster interlinked with S-S bond (b) for two pyramidal As(S1/2)3 units (the black color is for S atoms and grey one for As atoms)

The calculations only for ASC structural units were performed. We have studied the formation energy of different type of interconnections between building structural units: corner-sharing CS, edge-sharing ES or face-sharing FC, either pyramidal or

M. Hyla, V. Boyko, О. Shpotyuk et al.

tetrahedral basic units. As a point of reference, energies of single As(S1/2)3 building blocks having 3 shared chalcogen atoms (Z = 2,40) and Ge(S1/2)4 building blocks having 4 shared chalcogen atoms (Z = 2,67). All clusters are shown in fig. 2 and 3.

c d

Fig. 2. Schematic view of geometrically optimized single (a), corner- (b), edge- (c) and face-shared (d) As(S1/2)3 units (the black color is for S atoms and grey one for As atoms)

Recently, the first-principles methods have been very successful to calculate structural properties of materials. In order to study the optimal geometries and calculate formation energy of clusters ab initio method based on the Hartree-Fock approximation was used. A few ab initio calculations of clusters energy were carried out by R.M. Holomb and co-workers [5-7]. Although the calculations do not allow to drive a conclusion about preferences in connection suitable building units. Then, a new energetic parameter, an average formation energy (AFE), which is defined as formation energy per atom in a cluster, was introduced in our calculations. We have made our conclusions on the base of this parameter. In addition, our analysis was supplemented by mean-field constraints theory.

Quantum mechanical calculations were performed using HyperChem Realise 7,5 PC program [8]. The RHF ab initio level was taken as a ground for mathematical calculating procedure, either geometry optimization or single point energy, the 6-311G* basis set, being employed. All ending S atoms within clusters were additionally terminated by H atoms to be two-fold coordinated in full respect to their saturated covalent bonding. As a result of single point energy calculations, the total energy Et for each molecule was obtained. Since all clusters were of ASC type, the V energy of S atom along with energy of H atoms and bonds between them were subtracted from total energy Et. The ASC energy was calculated as half of total energy of H-S-H molecule giving EASC = -125091,0876 kcal/mol. The energy of single As, Ge and S atoms was accepted to be EAs = -1401900,133 kcal/mol, EGe = -1302219,833 kcal/mol and ES = -249381,9706 kcal/mol, respectively. The overall energy of atoms within cluster Eat was equal to:

where nAs, nGe and nS are the number of As, Ge and S atoms, respectively. The cluster formation energy, Ef, was calculated as:

Ef = Ec - Eal, (3) where Ec was total energy of the cluster, Eat was overall energy of atoms forming the cluster.

To estimate the glass-forming tendency within cation-interlinked clusters, the average formation energy AFE defined as cluster formation energy per atom was introduced:

Ea/ = Ef / N, (4) where Ef was cluster formation energy in respect to (3), N was total number of atoms in the cluster (N = nAs + nGe + nS).

The structures of clusters studied displayed in fig. 2 and 3 (the terminated H atoms are not shown).

The optimized bond distances and bond angles for all clusters are given in table 1 and 2. These values are quite close to known experimental data proper to crystalline As2S3 and GeS2. We calculated the number of Lagrangian constraints per atom, nc, too. The results of both constraints and energetic calculations for both binary systems (As-S and Ge-S) are presented in Table 3 and 4, respectively.

Table 1

Geometric parameters of optimized As(S1/2)3-based clusters

 

Bond distance

Bond angle

Type

[10-4 nm]

[deg]

 

As-S

S-As-S

As-S-As

 

2251,5

101,94

 

As(Si/2)3-single

2254,0

102,94

-

 

2256,1

92,67

 

 

2248,6

102,62

98,9

 

2252,3

103,17

 

As(S1/2)3-CS

2263,5 2264,3

92,35 96,98

 

 

2252,4

99,57

 

 

2253,1

97,14

 

 

2252,2

101,00

91,18

 

2266,7

101,60

91,16

As(Si/2)3-ES

2266,3 2267,4

88,83 101,46

 

 

2267,0

100,89

 

 

2250,6

88,80

 

 

2284,8

86,99

74,74

 

2284,9

86,98

74,74

As(Si/2)3-FS

2284,6

86,99

74,74

 

2284,8

86,99

 

 

2284,8

86,98

 

 

2284,7

86,99

 

Table 2

Geometric parameters of optimized Ge(S1/2)4-based clusters

 

Bond distance

Bond angle

Type

[10-4 nm]

[deg]

 

Ge-S

S-Ge-S

Ge-S-Ge

 

2224,9

112,67

 

 

2236,6

109,62

 

Ge(S1/2)4-single

2236,6 2215,1

109,42 102,80

-

 

 

112,67

 

 

 

109,42

 

 

2238,5

108,56

98,42

 

2238,7

107,88

 

 

2238,5

110,67

 

 

2242,7

108,28

 

 

2238,5

109,53

 

Ge(S1/2)4-CS

2238,6 2238,5

111,82 110,67

 

 

2242,8

111,83

 

 

 

108,55

 

 

 

107,88

 

 

 

109,53

 

 

 

108,28

 

 

2224,0

111,88

83,79

 

2223,9

113,88

84,30

 

2231,5

110,06

 

 

2242,4

110,05

 

 

2224,0

113,88

 

Ge(S1/2)4-ES

2223,9 2242,4

95,96 110,05

 

 

2231,4

113,88

 

 

 

111,88

 

 

 

110,05

 

 

 

113,88

 

 

 

95,96

 

 

2194,9

124,80

67,62

 

2274,9

124,80

67,62

 

2274,9

121,89

67,81

 

2269,7

91,76

 

 

2194,9

92,13

 

Ge(S1/2)4-FS

2275,6 2275,6

92,13 124,91

 

 

2269,7

124,91

 

 

 

121,71

 

 

 

92,11

 

 

 

92,11

 

 

 

91,72

 

Table 3

Results of calculated the number of Lagrangian constraints per atom, nc,.and energetic calculations

for both binary system As-S; Z=2,40

Cluster characterization

Energetic parameters

Type

N

nc

AsnSmHp

total energy, Et

AsnSm

cluster

energy, Ec

Forma­tion energy,

Ef = Ec -

AFE

average formation

energy,

Efav-Ef/N

 

 

 

kcal/mol

kcal/mol

kcal/mol

kcal/mol

As(S1/2)3 -single

2,5

3,00

-2151444,860

-1776171,598

-198,509

-79,404

As(S1/2)3 -CS

5

3,00

-4052707,566

-3552343,215

-397,038

-79,408

As(S1/2)3 -ES

5

2,60

-3802519,623

-3552337,448

-391,271

-78,254

As(S1/2)3 -FS

5

2,20

-3552319,113

-3552319,113

-372,936

-74,587

Table 4

Results of calculated the number of Lagrangian constraints per atom, nc,.and energetic calculations

for both binary system Ge-S; Z=2,67

Cluster characterization

Energetic parameters

Type

N

nc

GenSmHp

total energy,

Et

GenSm

cluster

energy, Ec

Forma­tion energy,

Ef = Ec -

Eat

AFE average formation

energy,

Efav-Ef/N

 

 

 

kcal/mol

kcal/mol

kcal/mol

kcal/mol

Ge(S1/2)4

-single

3

3,67

-2301637,257

-1801272,907

-289,133

-96,378

Ge(S1/2)4

-CS

6

3,67

-4353080,104

-3602533,578

-566,029

-94,338

Ge(S1/2)4

-ES

6

3,00

-4102907,744

-3602543,394

-575,845

-95,974

Ge(S1/2)4

-FS

6

3,00

-3852684,078

-3602501,903

-534,354

-89,059

In the case of pyramidal As(S1/2)3-based clusters, the highest AFE value (-74,587 kcal/mol) is achieved for face-sharing interlinking (table 3). It means that these structural units are unprofitable in ChG from energetic point of view. The AFE either of single As(S1/2)3 pyramid or two corner-sharing As(S1/2)3 pyramids are the lowest ones being as high as -79,404 kcal/mol and -79,408 kcal/mol, respectively. Hence the structure of binary As-S system prefers units built of corner-sharing As(S1/2)3 pyramids.

These corner-sharing pyramids form the optimally-constrained atomic network (nc=3), while the edge-sharing pyramids form only under-constrained glassy network (nc<3).

Therefore, on the basis of our calculations, we can expect the corner-sharing pyramidal-like interlinking in stoichiometric As2S3 ChG in full respect to known structural model given by Zachariasen yet in the 1930-s [9].

In the case tetrahedral Ge(S1/2)4-based clusters, the highest AFE value (-89,059 kcal/mol) is achieved for face-sharing interlinking too (see table 4). So these structural units apparently do not occur in the real glass-forming networks. The lowest AFE value (-96,378 kcal/mol) is character for single Ge(S1/2)4 cluster and two-cation interlinking edge-sharing cluster (-95,974 kcal/mol), while the corner-sharing tetrahons

have AFE=-94,338 kcal/mol.

Therefore, the edge-sharing tetrahedral-like units form the optimally-constrained glassy network (nc=3), while the corner-sharing units form the over-constrained one (nc>3). In general, this conclusion appears to be consistent with outrigger raft model proposed by Phillips [10].

On the basis of calculations performed with HyperChem Realise 7,5 program, it is shown that corner-shared As(S1/2)3 pyramids form the optimally-constrained atomic network (nc=3) with the lowest AFE value, while the edge-sharing interlinking of Ge(S1/2)4 tetragons is the most preferential one for optimally-constrained Ge-S glassy network.

1. Feltz A. Amorphous inorganic materials and glasses. Weinheim; Basel; Cambridge; New York, NY; VCH, 1993.

2. Phillips J.C. Topology of covalent non-crystalline solids // J. Non-Cryst. Sol. 1979. Vol. 34. P. 153-181.

3. Thorpe M.F. Continous deformations in random networks // J. Non-Cryst. Sol.

1983. Vol. 57. P. 355-370.

4. Thorpe M.F. Bulk and surface floppy modes // J. Non-Cryst. Sol. 1995. Vol. 182. P. 135-142.

5. Holomb R.M. The frequencies spectrum by quantum-chemical calculations of GenSm clusters (n=2, m=3, 5-7; n=4, m=3) // Phys. and Chem. Sol. State. 2003. Vol. 4. N 4. P. 711-715.

6. Holomb R.M., Mitsa V.M. Simulation of Raman spectra of AsxS100-x glasses by the results of ab initio calculations of AsnSm clusters vibrations // J. Opt. Adv. Mat. 2004. Vol. 6. N 4. P. 1177-1184.

7. Holomb R.M., Mitsa V.M. Mateleshko N.I. Low-frequencies (LF) Raman spectrums of AsxS1-x glasses, vibrational spectrums of AsnSm clusters calculated by "ab initio" method and the distribution of clusters length // Nauk. Visnyk Uzhgorod. Univ. Ser. Physic. 2002. N 11. P. 136-140.

8. HyperChem Professional 7.5, Hypercube Inc., http://www.hyper.com

9. Zachariasen W.H. The atomic arrangement in glass // J. Am. Chem. Soc. 1932. Vol. 54. P. 3841-3851.

10. Phillips J.C., Beevers C.A. and Gould S.E.B. Molecular structure of As2Se3 glass // Phys. Rev. B. 1980. Vol. 21. N 12. P. 5724-5732.

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M Hyla, V Boyko, O Shpotyuk - Two-cation corner- and edge-sharing interlinked clusters in asge-s glasses