Journal of Non-Crystalline Solids 306 (2002) 209–226
www.elsevier.com/locate/jnoncrysol
On the structure of phosphosilicate glasses
V.G. Plotnichenko *, V.O. Sokolov, V.V. Koltashev, E.M. Dianov
Fiber Optics Research Center, General Physics Institute, Russian Academy of Sciences, 38 Vavilov Street, Moscow 119991, Russia
Received 21 June 2001; received in revised form 8 February 2002
Abstract
Vibrational spectra of phosphosilicate glasses with P2 O5 concentrations up to 15 mol% are investigated by the
methods of Raman spectroscopy and quantum-chemical modeling. We have found that the Raman band at 1320 cm1
characteristic for such glasses is not simple and may be decomposed into two components with frequencies at 1317
and 1330 cm1 caused in our opinion by single phosphorus centers (O@PO3 tetrahedra surrounded by SiO4 ones) and
by double phosphorus centers (pairs of O@PO3 tetrahedra bonded by a common oxygen atom). In the investigated
phosphosilicate glasses manufactured by MCVD and SPCVD methods the ratio of concentrations of single and double
centers varies from 1:5 to 1:2. A novel interpretation of the Raman bands distinct from the traditional one is suggested.
The approach to the Raman spectra analysis developed in this article can be applied for control and optimization of
manufacturing process of phosphosilicate and similar glasses as well as optical fibers.
2002 Elsevier Science B.V. All rights reserved.
PACS: 61.43.Fs; 63.50.þx; 78.20.Bh; 78.30.j
1. Introduction
Phosphorus is one of the main dopants in highpurity silica glass (v-SiO2 ) used in fiber optics
technology to form an optimal refractive index
profile in a fiber and to modify the viscosity of
its core and cladding [1]. Phosphosilicate glasses
(P2 O5 )x (SiO2 )1x with P2 O5 concentration x K 15
mol% are used in developing stimulated Raman
fiber lasers and amplifiers [2,3]. Phosphosilicate
glasses are also sensitive to UV radiation near
190 nm [4] which allows one to form the refractive
*
Corresponding author. Tel.: +7-095 135 8093; fax: +7-095
135 8139.
E-mail address: [email protected] (V.G. Plotnichenko).
index gratings in phosphosilicate-core fibers [2].
Finally, phosphosilicate glasses doped with rareearth elements are considered to be a potential material for optical amplifiers, converters and
sources of visible and near IR radiation [5,6]. However, despite of wide applications of phosphosilicate glasses, their structure and optical properties
are yet to be investigated sufficiently.
Phosphosilicate glass is thought currently to
consist of silicon–oxygen, SiO4 , and phosphorus–
oxygen, O@PO3 , tetrahedra bonded randomly in
a three-dimensional network where each silicon
atom is bonded with four silicon or phosphorus
atoms by oxygen linkages, and each phosphorus
atom has only three such bridging bonds. In the
fourth vertex of the O@PO3 tetrahedron there is a
non-bridging oxygen atom bound with the central
0022-3093/02/$ - see front matter 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 1 7 2 - 9
210
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
phosphorus atom with a double bond, O@P.
Owing to a high polarizability of the double bond
an intensive band with a maximum at 1320 cm1
caused by the stretching vibrations of the O@P
bonds arises in the Raman spectra [7–9]. Similar
band with a frequency at 1390 cm1 [10,11] is characteristic as well for vitreous P2 O5 (v-P2 O5 ) where
the atomic network is formed by O@PO3 tetrahedra [12].
Our analysis of the Raman spectra of phosphosilicate glass samples manufactured by modified
chemical vapor deposition (MCVD) and surface
plasma chemical vapor deposition (SPCVD) methods in different laboratories has shown that the
intensity of the O@P band grows with molar
concentration of P2 O5 in (P2 O5 )x (SiO2 )1x glass [9].
The frequency of maximum and shape of the band
do not depend on P2 O5 concentration in glasses
with x K 15 mol% manufactured under the same
conditions. We have found as well that this band is
composite and may be represented by two components with frequencies at about 1317 and 1330
cm1 , whose intensity ratio is determined by the
features of the production process, and, probably,
by the subsequent thermal history of the samples.
We assume that the low-frequency component
corresponds to O@PO3 tetrahedra bonded only
with the SiO4 tetrahedra (single phosphorus centers) and the high-frequency one is caused by pairs
of the O@PO3 tetrahedra bound together by
PAOAP linkages (double phosphorus centers).
The random structure of the phosphosilicate
glass network is insufficient to explain such an
interpretation, since for low P2 O5 concentration
( K 15 mol%) in absence of correlations in arrangement of phosphorus atoms, mainly single
(bonded with silicon atoms only) O@PO3 tetrahedra occur in the glass and the number of any
groups of O@PO3 tetrahedra should not exceed
5% of the total amount of phosphorus tetrahedra. Thus the intensity of the low-frequency
component should be at least 20 times as high
as the intensity of the high-frequency component.
However, we observe in the Raman spectra just an
inverse relation: the intensity of the low-frequency
component is 5–10 times lower than that of the
high-frequency component. This may be explained
by predominant formation of double phosphorus
centers in the investigated glasses. Since in manufacturing phosphosilicate glasses by chemical vapor
deposition (CVD) methods, being most frequently
used in fiber optics, the oxidation of phosphorus
oxychloride occurs, and molecules of the most
stable phosphorus oxide, P2 O5 , arise, the formation of double phosphorus centers seems to be
quite natural.
The main goal of this work was to verify this
hypothesis both theoretically and experimentally and to interpret the vibrational spectrum
of phosphosilicate glass and its dependence on
phosphorus concentration. For this purpose the
quantum-chemical modeling of the structure and
vibrational properties (vibrational frequencies, IR
absorption and Raman scattering intensities) of
phosphorus centers in phosphosilicate glass was
performed and Raman spectra of phosphosilicatecore optical fibers made in different laboratories by
MCVD and SPCVD methods were measured and
analyzed.
2. Quantum-chemical calculations
All calculations were performed with the help of
the GAMESS (US) program [13] in Hartree–Fock
approximation using basis sets and effective core
potentials (ECP) developed in Ref. [14] for oxygen
and fluorine and in Ref. [15] for phosphorus, silicon, chlorine, bromine and iodine. One extra
d-type polarization function was included in ECP
basis for each atom (f ¼ 0:80, 0.55, 0.80, 0.395,
0.75, 0.389, 0.266 for O, P, F, Si, Cl, Br and I
atoms, respectively). 3-21G standard basis set
was used for hydrogen. As shown in Ref. [16,17],
such a choice of the basis provided a good description of properties of the systems under consideration.
To verify our approach we have calculated
several molecules of phosphorus oxihalogenides,
O@PA3x Bx , for A, B ¼ H, F, Cl, Br and I. Results
for some molecules are collected in Table 1. In this
table and everywhere in what follows the IR ab2 ,
sorption intensities are given in Debye2 /amu/A
4
and the Raman intensities in A /amu.
The comparison of the calculated geometrical
parameters with the experimental data available
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
211
Table 1
Results of the quantum-chemical calculations of phosphorus oxihalogenides molecules, O@PA3x Bx
Molecule
)
O@P bond length (A
)
PAX bond length (A
O@PAX angle (deg)
XAPAX angles (deg)
O@P vibration frequency (cm1 )
Corrected frequency
Experimental frequency [18]
2 )
IR absorption (Debye2 /amu/A
4 /amu)
Raman intensity (A
O@PH3
O@PF3
O@PCl3
O@PBr3
O@PI3
1.467
1.395
116.808
101.238
1376.33
1273
–
8.0
7.8
1.428
1.520
117.135
100.834
1512.68
1400
1416.8
7.7
4.7
1.440
1.985
114.614
103.873
1429.16
1322
1321.5
6.0
10.5
1.445
2.191
114.024
104.559
1400.22
1295
1277
5.4
13.5
1.451
2.430
113.110
105.600
1371.19
1268
–
5.0
16.2
[18] confirms the conclusion made in Ref. [16,17]
about the basis set choice. The Hartree–Fock approximation is known to overestimate systematically the vibrational frequencies. Comparing the
calculated and experimental [18] frequencies of the
stretching vibration of O@P bonds in O@PA3x Bx
molecules we have found that the scaling factor
for this vibration in these molecules is 0.925 and
the estimated average accuracy of calculated frequency of this vibration is 15 cm1 (better than
2%). All calculated vibrational frequencies are
given further with the appropriate scaling factors
taken into account.
One of the crystalline polymorphs of P2 O5
(hexagonal [19,20]) is formed by P4 O10 molecules.
According to certain models such molecules may
occur both in v-P2 O5 and in (ultra) phosphate
glasses. Therefore we have calculated the P4 O10
molecule using our approach. The results of calculations are as follows (the experimental values
from the review [20] are given in brackets): O@P
(1:40 0:03 A
); OAP
bond lengths – 1.423 A
bond lengths – 1.600 A (1:60 0:01 A); O@PAO
angles – 117.57 (117); OAPAO angles – 100.29
(101); PAOAP angles – 125.67 (124.5); frequencies of the stretching O@P bond vibrations –
1434 (A1 ) and 1401 (F2 ) cm1 (1430 and 1405
cm1 , respectively); IR absorption intensities – 0.0
and 13.0, Raman intensities – 15.5 and 7.7, respectively.
The calculations of molecules prove sufficient
reliability of our approach for quantum-chemical
modeling of the vibrational properties of silica
glass, phosphorus centers in phosphosilicate glass
and v-P2 O5 , which has been performed in a molecular cluster model. The main results of the
modeling are given in Table 2.
2.1. Silica glass
Vibrational properties of the silica glass network were simulated by the cluster ðH3 SiAOÞ3 B
SiAOASiBðOASiH3 Þ3 containing two SiO4 tetrahedra bonded together by common bridging O
atom and each connected to three Si atoms with
dangling bonds saturated by H atoms. According
to calculations, in the equilibrium configuration
the SiAO bond lengths were equal to 1.612 and
for central SiAOASi linkage and to 1.608
1.610 A
for other linkages (there are two short
and 1.607 A
and two long SiAO bonds in each SiO4 tetrahedron). The SiAOASi angles were equal to 144.2
both in the central linkage SiAOASi and in other
linkages, and all the OASiAO angles in SiO4 tetrahedra were 109.4. Hence the calculation reproduces the mean geometrical parameters of
silica glass [21].
Our approach also allows one to describe well
the most typical vibrational properties of the silica
glass network. For further consideration the antisymmetric stretching vibrations of the OASi
bonds in the SiAOASi linkages are of the most
interest. There are two types of such vibrations
with frequencies 1194 and 1091 cm1 . According to Ref. [22], the first-type vibrations corresponds to LO phonons, and the second-type ones
to TO phonons. IR absorption intensities for these
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V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
Table 2
Results of the quantum-chemical modeling
Model
Geometry
Silica glass
SiAO bond lengths
Single phosphorus center
Double phosphorus center
P2 O5 glass
Vibrations
Frequency
IR
Raman
SiAOASi angles
OASiAO angles
1.612
1.610
144.2
109.4
SiAO bonds
antisymmetric stretching in
the SiAOASi linkages
1194
1091
8.8
16.1
0.1
0.1
O@P bond length
PAO bond lengths
SiAO bond lengths
O@PAO angles
OAPAO angles
PAOASi angles
1.458
1.563
1.669
114.7
103.8
134.4
O@P bond stretching
O@P bond lengths
PAO bond lengths in
the PAOAP linkage
PAO bond lengths in
the PAOASi linkages
SiAO bond lengths in
the PAOASi linkages
O@PAO angle in the
PAOAP linkage
O@PAO angles in the
PAOASi linkages
OAPAO angle in the
PAOAP linkage
OAPAO angles in the
PAOASi linkages
PAOASi angles
1.455
1.601
138.0
O@P bond length
PAO bond lengths
O@PAO angles
OAPAO angles
PAOAP angles
1.449
1.571
112.3
103.0
130.9
1316
6.2
1.9
PAO and SiAO bonds
antisymmetric stretching
in the PAOASi linkages
1068
1067
24.5
0.6
1.550
O@P bond stretching
1331
8.8
2.1
1.660
PAO bonds antisymmetric
stretching in the PAOAP
linkage
1120
6.5
0.3
PAO and SiAO bonds antisymmetric stretching in the
PAOASi linkages
1102
24.5
0.7
1100
23.7
0.3
1391
1386
7.8
8.0
1.9
2.5
1020
25.4
1.7
111.8
116.4
103.2
104.0
O@P bond stretching
PAO bonds antisymmetric
stretching in the PAOAP
linkages
, angles in degrees, frequencies in cm1 , IR absorption intensities in Debye2 /amu/A
2 , Raman intensities A
4 /amu.
Bond lengths in A
vibrations are 8.8 and 16.1, respectively, and the
Raman intensities are 0.1 for the vibrations of the
both types. Notice that to compare the results of
the calculations directly with the experiment, in
which the polarizations of the incident and scattered light are not fixed, the calculated Raman
intensities are given hereafter averaged over the
polarization.
2.2. Single phosphorus center
Single phosphorus center in phosphosilicate
glass designated as O@PðOASiÞ3 was simulated
by O@PðAOASiH3 Þ3 cluster containing a single
O@PO3 tetrahedron bonded with three Si atoms,
the dangling bonds of those saturated by H atoms.
Calculated configuration of the single phosphorus
center is shown in Fig. 1. The O@P double bond
, PAO bond lengths were 1.563
length was 1.458 A
, SiAO bond lengths were 1.659 A
, O@PAO
A
angles were 114.7, OAPAO angles were 103.8,
PAOASi angles were 134.4.
Calculated vibrational properties of the O@
PðOASiÞ3 center were as follows: frequency of
the O@P bond stretching vibration was 1316 cm1 ,
IR absorption and Raman intensities were 6.2
and 1.9, respectively; frequencies of antisymmetric
stretching vibrations of the OAP and OASi bonds
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
213
Fig. 1. Calculated configuration of the single phosphorus center.
Fig. 2. Calculated configuration of the double phosphorus
center.
in the PAOASi linkages were 1068 and 1067 cm1 ,
for both vibrations IR absorption and Raman
intensities being 24.5 and 0.6, respectively.
2.3. Double phosphorus center
The calculated frequency of the double bond
vibration in the single phosphorus center appears
to be somewhat lower than the value 1320 cm1
experimentally observed for the maximum of the
corresponding Raman band in phosphosilicate
glasses. This suggests that there are relatively few
such centers in phosphosilicate glasses, i.e. single
phosphorus atoms surrounded by SiO2 network,
since phosphorus mainly forms centers with more
complex structure. For low P2 O5 concentration
these centers are primarily two-atom ones with
two O@PO3 tetrahedra bonded together by common bridging oxygen atom. In what follows these
centers are designated as O@PAOAP@O.
The double phosphorus center in phosphosilicate glass was simulated by the cluster containing
two O@PO3 tetrahedra bonded to each other by
common bridging O atom. Each of the tetrahedra
was bonded to two Si atoms with dangling bonds
saturated by H atoms. Calculated configuration of
the double phosphorus center is shown in Fig. 2.
According to the calculations, length of the O@P
, lengths of PAO bonds
double bonds was 1.455 A
, lengths of
in the PAOAP linkage was 1.601 A
PAO and SiAO bonds in the PAOASi linkages
, respectively, O@PAO
were 1.55 and 1.66 A
angles were 111.8 in the PAOAP linkage and
116.4 in the PAOASi linkages, OAPAO angles
between PAOAP and PAOASi linkages and
between two PAOASi linkages were 103.2
and 104.0, respectively, PAOASi angles were
138.0.
In general, the stretching vibrations of the O@P
double bonds in the O@PAOAP@O double center
interact with each other. As a result, two combined
vibrational modes, co-phase and opposite-phase,
arise. However, this interaction turns out to be
weak and the frequencies of these combined modes
differ slightly (less than by 2 cm1 ). Calculated
frequencies of these stretching vibrations are 1331
cm1 , IR absorption and Raman intensities for
each O@P bond in the double center are 8.8 and 2.1,
respectively. Frequency of antisymmetric stretching vibration of the OAP bonds in the PAOAP
linkage is 1120 cm1 , IR absorption and Raman
intensities are 6.5 and 0.3, respectively. Frequencies
of antisymmetric stretching vibrations of the OAP
and OASi bonds in the PAOASi linkage are 1102
and 1100 cm1 , IR absorption intensities are 20.1
and 23.7, Raman intensities are 0.7 and 0.3, respectively.
214
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
2.4. Vitreous P2 O5
The vibrational properties of v-P2 O5 network
were simulated by calculating clusters of two types
similar to the clusters used for single and double
phosphorus centers in phosphosilicate glass. The
first cluster, O@PðAOAH2 P@OÞ3 , contains one
O@PO3 tetrahedron bonded with three O@P
groups with dangling bonds of the P atom saturated by H atoms. The second cluster, ðO@PH2 A
OÞ2 @ðO@PÞAOAðP@OÞ@ðOAH2 P@OÞ2 , contains
two O@PO3 tetrahedra bonded to each other by
common bridging O atom, each tetrahedron bonded with two O@P groups with dangling bonds of
the P atom saturated by H atoms.
In the calculated equilibrium configuration of
the first cluster the O@P double bond length was
, the PAO bond lengths were 1.574 A
,
1.446 A
O@PAO angles were 115.7, OAPAO angles were
102.6, PAOAP angles were 130.8. In the calculated equilibrium configuration of the second
cluster the O@P double bond lengths were 1.449
, the PAO bond lengths were 1.571 A
, O@PAO
A
angles were 112.3, OAPAO angles were 103.0,
PAOAP angles were 130.9. So the calculation
reproduces the mean geometrical parameters of
v-P2 O5 and II and III orthorhombic crystalline
polymorphs of P2 O5 [12,19].
The calculation resulted in the following vibrational properties of the first cluster: the O@P
bond stretching vibration frequency was 1357
cm1 , IR absorption and Raman intensities were
6.1 and 2.1, respectively, antisymmetric stretching
vibration frequency of OAP bonds in the PAOAP
linkage was 1024 cm1 , IR absorption and Raman
intensities were 25.5 and 1.2, respectively. In the
second cluster, similar to the O@PAOAP@O
double center, the O@P double bond stretching
vibrations interact with each other giving rise to
co-phase and opposite-phase combined vibrational
modes. This interaction is considerably stronger
than that in the O@PAOAP@O double center, the
calculated frequencies of these modes being 1391
and 1386 cm1 , respectively. IR absorption intensities are 7.8 and 8.0, and Raman intensities are
1.9 and 2.5, respectively. Frequency of antisymmetric stretching vibration of OAP bonds in
the PAOAP linkage is 1020 cm1 , IR absorption
and Raman intensities are 25.4 and 1.7, respectively.
Thus, the calculations suggest that there is a
general trend of change of vibrational frequencies
and Raman intensities in the process of association
of O@PO3 tetrahedra: frequency of the O@P bond
stretching vibrations and the corresponding
Raman intensity increase achieving their maxima
in v-P2 O5 , the frequency of antisymmetric
stretching vibrations of OAP bonds in the PAOAP
linkages practically does not change, the corresponding Raman intensity increasing. These
changes of frequencies and intensities are most
pronounced for the association of two single
O@PO3 tetrahedra and become considerably lower
with the number of the tetrahedra increasing.
3. Experiment
We have measured the Raman spectra of two
sets of fibers with a core made of phosphosilicate
glass, (P2 O5 )x (SiO2 )1x , manufactured by MCVD
method in different laboratories [9,23]. According
to measurements of the refractive index profile in
the fiber preforms, the maximal P2 O5 concentration in the fiber cores was 4.6, 8.5, 14.2, 15.0 mol%
in the set 1 and 6.6, 8.8, 11.0, 13.2, 14.7 mol% in
the set 2 [9,23]. 1 Besides, we have also measured
the Raman spectrum of a phosphosilicate-core
fiber manufactured using the SPCVD method [24].
And finally, the Raman spectra of a fiber with
9 mol% of P2 O5 in the core manufactured in the
same laboratory and by the same technology, as
the set 1 fibers, were measured before and after the
244 nm UV irradiation by KrF laser with the dose
density of about 1 kJ cm2 (see Ref. [25]).
The Stokes–Raman scattering spectra excited
by the 514.5 nm light of an Ar laser 2 were measured using a triple spectrograph 3 with a spectral
resolution of about 1 cm1 . The spectra were
measured without regard for the polarization of
1
The refractive index measurements are described in Ref.
[23].
2
3
Spectra Physics Stabilite 2000.
Jobin Yvon T64000.
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
215
both incident and scattered light. The laser beam
was focused by a microscope 4 upon a spot of 1–3
lm in diameter into the core at the input end of the
fiber under investigation. The core diameter of the
fibers was about 7 lm. The length of the fibers was
about 5 m. A backward geometry was used for
collecting of the laser light scattered from the fiber
core. The experimental approach is described in
Ref. [26] as well.
To analyze the vibrational properties and to
compare them with the results of quantum-chemical calculations, it is convenient to use the reduced
Raman spectra defined as follows [27]:
Ire ðxÞ ¼ I e ðxÞ
x
4
ðX0 xÞ ðnðxÞ þ 1Þ
ð1Þ
where Ire ðxÞ is the reduced Raman intensity, I e ðxÞ
is the measured Raman intensity, x is the Stokes
shift, X0 is the frequency of the incident light, nðxÞ
is the Bose distribution function.
The reduced experimental Raman spectra for
the fibers sets 1 and 2 are given in Figs. 3 and 4,
respectively. Fig. 5 shows the influence of UV irradiation on the reduced spectrum of the phosphosilicate-core fiber.
Fig. 3. Reduced Raman spectra of the set 1 fibers with the
maximal P2 O5 concentration in the core: (a) 4.6 mol%, (b) 8.5
mol%, (c) 14.2 mol%, (d) 15.0 mol%.
3.1. Decomposition of experimental Raman spectra
For our purposes the points of the greatest interest are the Raman band with the frequency
of the maximum at about 1320 cm1 caused by
stretching vibrations of O@P double bonds and
an adjacent frequency range J 860 cm1 with the
Raman bands caused by antisymmetric stretching vibrations of the SiAO and PAO bonds in
SiAOASi, PAOASi and PAOAP linkages (bridging O atoms moving parallel to the SiASi or SiAP
lines) [8,25]. This spectral range is separated from
the lower-frequency part and hence can be analyzed separately.
To interpret Raman bands and to understand
their relation to the glass structure we have decomposed the reduced spectra in the 860–1460
cm1 frequency range in components described by
4
Olympus BH2-UMA.
Fig. 4. Reduced Raman spectra of the set 2 fibers with the
maximal P2 O5 concentration in the core: (a) 6.6 mol%, (b) 8.8
mol%, (c) 11.0 mol%, (d) 13.2 mol%, (e) 14.7 mol%.
Voigt functions. Various decompositions of each
spectrum were analyzed using the v2 criterion. We
216
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
Fig. 5. Reduced Raman spectra of the fiber with 9 mol% of
P2 O5 in the core: (a) before UV irradiation, (b) after UV irradiation (KrF laser at 244 nm, dose density about 1 kJ cm2 ).
have found that no more than five components can
be determined uniquely from each of the experimental spectra to ensure both the required accuracy of decomposition relevant to experimental
accuracy of the measured spectra and unambiguity
of the decomposition. According to the quantumchemical calculations cited above, two components
describe the O@P vibrational band (1320 cm1 )
and other three components describe the bands of
SiAOASi, PAOASi and PAOAP linkage vibrations. For greater number of components either
the errors of the Voigt function parameters turned
out to be unsuitably high or the decomposition
became ambiguous, in other words, there were at
least two different sets of components providing
similar (in the sense of the v2 criterion) approximation of the experimental spectrum. The main
results of the decomposition are given in Tables 3
and 4. As an example of the decomposition, Fig. 6
shows the experimental spectrum and the fitting
curves for one of the set 2 fibers (13.2 mol% of
P2 O5 in the core). Relative intensities of the decomposition components are shown in Figs. 7 and
8 versus P2 O5 concentration in glass for the fibers
of the sets 1 and 2. Notice that for each fiber the
intensities of all the components are normalized to
the intensity of the 1330 cm1 component (O@P
stretching bonds in the double phosphorus center).
To interpret the decompositions obtained and,
in particular, to study the concentration dependencies (relative) Raman intensities of vibrational
modes in phosphosilicate glass network are required. We shall use the Raman intensities obtained in the above-described quantum-chemical
modeling.
4. Discussion
The frequencies of two decomposition components of the experimental Raman band at 1320
cm1 given in Tables 3 and 4 agree well with the
calculated frequencies of the O@P bond stretching
vibrations in the single and double phosphorus
centers, respectively. Therefore it is reasonable
to suppose that the components of this band
are mainly caused just by the single and double
Table 3
Results of decomposition of Raman spectra of the set 1 fibers in the 880–1460 cm1 frequency range
4.6 mol%
8.5 mol%
14.2 mol%
15.0 mol%
Frequency
Raman
intensity
Frequency
Raman
intensity
Frequency
Raman
intensity
Frequency
Raman
intensity
1
2
3
4
5
1327.8 1.4
1314.2 1.1
1179.5 9.2
1137.6 2.3
1027.7 2.6
1.00 0.03
0.15 0.04
0.48 0.15
0.13 0.09
0.16 0.01
1331.5 1.2
1317.3 1.1
1179.1 3.8
1145.7 2.2
1022.3 1.3
1.00 0.01
0.15 0.02
0.39 0.02
0.06 0.01
0.16 0.01
1329.7 1.2
1313.7 1.1
1188.0 4.4
1149.3 2.3
1017.4 1.4
1.00 0.01
0.15 0.02
0.30 0.02
0.10 0.02
0.15 0.03
1330.5 1.2
1314.9 1.1
1192.0 8.9
1149.0 2.3
1018.8 1.7
1.00 0.02
0.15 0.01
0.29 0.05
0.12 0.03
0.14 0.05
v2
0:20 103
1
0:30 103
Frequencies in cm , Raman intensities are normalized to the 1330 cm
1:50 103
1
component for each fiber.
2:00 103
0:35 104
1331.5 1.1
1317.4 1.1
1180.5 2.0
1147.7 1.3
1020.4 1.3
1.00 0.01
0.12 0.01
0.27 0.01
0.18 0.02
0.14 0.01
217
0:65 104
0:40 104
v2
Frequencies in cm1 , Raman intensities are normalized to the 1330 cm1 component for each fiber.
1:10 104
0:92 104
1329.6 1.1
1315.4 1.1
1188.4 3.0
1144.9 1.2
1018.1 1.5
1.00 0.01
0.13 0.01
0.39 0.01
0.11 0.01
0.16 0.01
1.00 0.01
0.12 0.02
0.50 0.01
0.07 0.01
0.17 0.01
1330.0 1.1
1316.8 1.1
1171.4 1.5
1142.0 1.1
1019.5 1.3
1
2
3
4
5
1330.6 1.1
1316.2 1.1
1183.1 1.9
1144.8 1.1
1017.8 1.3
1.00 0.01
0.12 0.01
0.44 0.01
0.10 0.01
0.16 0.01
1328.2 1.1
1314.5 1.1
1180.0 1.9
1141.5 1.1
1016.8 1.3
1.00 0.01
0.12 0.01
0.31 0.02
0.15 0.01
0.14 0.01
Frequency
Frequency
13.2 mol%
Raman
intensity
11.0 mol%
Frequency
Frequency
Raman
intensity
8.8 mol%
Raman
intensity
6.6 mol%
Table 4
Results of decomposition of Raman spectra of the set 2 fibers in the 880–1460 cm1 frequency range
Frequency
Raman
intensity
14.7 mol%
Raman
intensity
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
Fig. 6. Decomposition of the reduced Raman spectrum of the
set 2 fiber with 13.2 mol% of P2 O5 in the core. Open circles are
the experimental points, thin lines are the components of the
decomposition, thick line is the result of the fitting.
phosphorus centers. Using the intensities of the
decomposition components of this band and the
calculated Raman intensities for the O@P bond
stretching vibrations in the single and double
phosphorus centers, one may estimate roughly the
ratio of concentrations of such centers. It turns
out that in the investigated phosphosilicate glasses
there are more double centers than single ones. On
the average, the approximate ratios between the
concentration of the double centers and that of the
single ones are 3 in the set 1 fibers, 4 in the set 2
fibers, and 2 in the SPCVD-manufactured fiber.
More precise estimations are given in what follows.
On the strength of the results of our calculations and the analysis of concentration dependencies of the intensities we have attributed other
components of the experimental Raman spectra
(Figs. 3–5) to SiAOASi linkages (1185 cm1 ),
PAOASi and SiAOASi linkages (1025 cm1 ),
and PAOAP linkages (1150 cm1 ), as shown in
Fig. 9. Our interpretation differs from the only
original interpretation of the Raman spectra of
phosphosilicate glasses [8] we know. In Ref. [8] the
bands with the maxima at frequencies about 1200
218
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
Fig. 7. Experimental dependence of relative intensities of the
decomposition components on P2 O5 concentration in the set 1
fibers cores (for each concentration the intensities of all the
components are normalized to the intensity of the 1330 cm1
component): (j) 1330 cm1 component; ( ) 1317 cm1 component; (N) 1185 cm1 component; (.) 1150 cm1 component;
(r) 1025 cm1 component.
Fig. 8. Experimental dependence of relative intensities of the
decomposition components on P2 O5 concentration in the set 2
fibers cores (for each concentration the intensities of all the
components are normalized to the intensity of the 1330 cm1
component): (j) 1330 cm1 component; ( ) 1317 cm1 component; (N) 1185 cm1 component; (.) 1150 cm1 component;
(r) 1025 cm1 component.
and 1020 cm1 are attributed to PAOAP linkages,
the band at 1145 cm1 ––to PAOASi linkages, and
nothing is said about the SiAOASi linkages at all.
Most likely, the interpretation given in Ref. [8] is
based on the data for (ultra) phosphate glasses
and v-P2 O5 (notice that our calculations give for
the frequency of antisymmetric stretching of OAP
bonds in PAOAP linkages in v-P2 O5 just 1020
cm1 ). However, as is shown below, the assignments made in Ref. [8] contradict to the dependencies of the Raman band intensities on P2 O5
concentration in glass.
In general, using all the data on the intensities
of decomposition components of the experimental
Raman spectra and the calculated Raman intensities for the phosphorus centers and v-SiO2 one is
able to estimate not only the ratio between concentrations of the single and double phosphorus
centers but also the relative concentrations of O@P
bonds and of SiAOASi, PAOASi and PAOAP
linkages, and even the P2 O5 molar concentration
in phosphosilicate glass, and hence, the absolute
Fig. 9. An interpretation of the components of the experimental Raman spectrum of a phosphosilicate-core fiber (shown
as measured, i.e. not reduced).
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
concentrations of all these bonds and linkages.
However, this is possible only on the basis of certain additional assumptions concerning the structure of the glass network.
4.1. Model of phosphosilicate glass network
A model of phosphosilicate glass network based
on the assumption of a complete absence of correlations in arrangement of phosphorus atoms is
developed in Ref. [7,28]. The model allows one to
find relative concentrations of O@P bonds and of
SiAOASi, PAOASi and PAOAP linkages in this
glass. We have extended this model to the case
when there are no other phosphorus centers in
glass except for double and single centers (both the
single and the double centers may either be isolated or form any groups).
In this model the structure of phosphosilicate
glasses expressed by the formula (P2 O5 )x (SiO2 )1x
is conveniently presented as ððIÞn ðIIÞ1n Þx (SiO2 )1x
where (I) and (II) are single and double phosphorus centers, respectively, and n is a parameter
of relative concentration of these centers. The
above-mentioned ratios between double and single
phosphorus centers allow one to estimate roughly
the n parameter to be 0.25 and 0.20 on the average for set 1 and set 2 fibers, respectively, and
0.30 for the SPCVD-manufactured fiber.
In phosphosilicate glass (with P2 O5 molar concentration equal to x) described by such model, the
relative concentrations, fi , of single (I) and double
(II) phosphorus centers, O@P double bonds and
SiAOASi, PAOASi and PAOAP linkages in respect to total number, N, of bridging linkages in
glass are as follows:
fðIÞ ¼ 12nxð1 xÞN 1 ;
i
h
fðIIÞ ¼ 8ð1 nÞxð1 xÞ þ ð2 þ nÞ2 x2 N 1 ;
fO@P ¼ ½8ð1 nÞxð1 xÞ þ 2ð2 þ nÞxð2 þ nxÞN 1 ;
fSiAOASi ¼ 4ð1 xÞ2 N 1 ;
fPAOASi ¼ 4ð2 þ nÞxð1 xÞN 1 ;
i
h
fPAOAP ¼ 8ð1 nÞxð1 xÞ þ 2ð2 þ nÞ2 x2 N 1 ;
ð2Þ
219
where N ¼ 4ð1 xÞ2 þ 4ð2 þ nÞxð1 xÞ þ 8ð1 nÞ
xð1 xÞ þ 2ð2 þ nÞ2 x2 .
These expressions for relative concentrations,
fi , are derived without considering obvious dependence of phosphosilicate glass density on P2 O5
content. In our model this dependence should
be derived from experimental data and it may be
readily taken into account. Unfortunately no such
data have come to our notice. However, since the
density of v-P2 O5 [20] is not too different from that
of v-SiO2 , one would expect that the phosphosilicate glass density depends only slightly on P2 O5
content, at least for P2 O5 concentrations up to 15
mol%.
The relative concentrations, fi (2), and corresponding Raman intensities derived using fi and
the quantum-chemically calculated intensities for
each phosphorus center and linkage (see Table 2)
are shown versus molar P2 O5 concentration in
Figs. 10 and 11, respectively, for the parameter of
relative concentration of single and double phosphorus centers, n, equal to 0.2. To make it possible
to compare the calculated and experimental results, the relative concentrations are normalized to
the concentration of O@P bonds in the double
centers, and the relative intensities, similar to the
experimental Raman spectra, are normalized to
the total intensity of O@P bond stretching vibrations in the double center. To illustrate the behavior of the relative concentrations, fi , they are
shown for the complete range of P2 O5 molar
concentration, from 0 to 100%, while corresponding Raman intensities are given for the range from
1 to 15 mol% actual for our measurements.
The comparison of Figs. 10 and 11 with the
results of decomposition of experimental Raman
spectra proves qualitatively the validity of assignments of the components in the 860–1200 cm1
range to antisymmetric stretching vibrations of
certain linkages, made in foregoing calculations,
since the intensities of the components do depend
on P2 O5 molar concentration in accordance with
our model. On the contrary, the assignments made
in Ref. [8] contradict this model since the intensity
of the component attributed in Ref. [8] to the
PAOAP linkages decreases with growth of P2 O5
concentration.
220
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
Fig. 10. The relative concentrations in the phosphosilicate glass
model for the parameter of relative concentration of the single
and double phosphorus centers n ¼ 0:2: (a) O@P bonds in the
single phosphorus centers (fðIÞ ), (b) O@P bonds in the double
phosphorus centers (2fðIIÞ ), (c) total concentration of O@P
bonds (fðIÞ þ 2fðIIÞ ), (d) SiAOASi linkages (fSiAOASi ), (e)
PAOASi linkages (fPAOASi ), (f) PAOAP linkages (fPAOAP ).
Fig. 11. Calculated Raman intensities in the phosphosilicate
glass model for the parameter of relative concentration of the
single and double phosphorus centers n ¼ 0:2: (a) O@P bonds
in the single phosphorus centers, (b) O@P bonds in the double
phosphorus centers, (c) total intensity of Raman scattering on
O@P bonds, (d) SiAOASi linkages (LO-type vibrations), (e)
PAOASi linkages and SiAOASi linkages (TO-type vibrations
of the latters), (f) PAOAP linkages.
4.2. Estimations of concentrations
Now we are to estimate the relation between the
single and double phosphorus centers as well as
P2 O5 molar concentration from our Raman measurements. The model considered in the previous
section together with the calculated Raman intensities for each phosphorus center and linkage
makes it possible to obtain the dependencies between the n parameter and P2 O5 molar concentration for experimental relative Raman intensities
of O@P bond stretching vibrations in single phosphorus centers and of antisymmetric stretching
vibrations of SiAO bonds in SiAO linkages. These
dependencies make it possible to find both the
relative concentration parameter of the single and
double phosphorus centers, n, and P2 O5 molar
concentration by solving a system of two nonlinear equations.
Such dependencies are shown in the Figs. 12
and 13 for MCVD-manufactured fibers of the set 1
and 2, respectively, and in Fig. 14 for the SPCVD-
manufactured fiber. These figures illustrate graphically the solution: the points where the respective
lines cross give the P2 O5 molar concentration and
the n parameter for each fiber (look for further
explanations in the figures captions). Notice that
only the close vicinity of the cross point are shown
in the figures.
For the set 1 fibers with the P2 O5 molar concentration in the core, according to the refractive
index measurements, being 4.6, 8.5, 14.2 and 15.0
mol% we have obtained the following estimations
of P2 O5 molar concentration: 6:1 3:0, 7:7 0:5,
10:1 0:7 and 10:5 2:5 mol%, respectively. For
the set 2 fibers with P2 O5 molar concentration in
the core, according to the refractive index measurements, being 6.6, 8.8, 11.0, 13.2 and 14.7 mol%,
the estimations 5:6 0:3, 6:5 0:4, 7:3 0:4,
9:3 0:6 and 10:7 0:7 mol%, respectively, are
obtained. For the SPCVD-manufactured fiber, the
P2 O5 concentration is estimated to be 1:9 0:7
mol%.
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
221
Fig. 12. Determining P2 O5 molar concentration and the relative concentration parameter of the single and double phosphorus centers, n, in the set 1 fibers on the basis of experimental
data on the relative Raman intensities of the O@P bonds
stretching vibrations in the single phosphorus centers (nearly
vertical lines) and the relative Raman intensities of the antisymmetric stretching vibrations of the SiAO bonds in the
SiAOASi linkages (nearly horizontal lines). Bold lines are the
mean values, thin lines are the confidence intervals for the fibers
with assumed P2 O5 molar concentrations: solid lines – 4.6%,
dash line – 8.5%, dot lines – 14.2%, dash dot lines – 15.0%. The
point of respective lines crossing give P2 O5 concentration and
the n parameter for each fiber.
Fig. 13. Determining P2 O5 molar concentration and the relative concentration parameter of the single and double phosphorus centers, n, in the set 2 fibers on the basis of experimental
data on the relative Raman intensities of the O@P bonds
stretching vibrations in the single phosphorus centers (nearly
vertical lines) and the relative Raman intensities of the antisymmetric stretching vibrations of the SiAO bonds in the
SiAOASi linkages (nearly horizontal lines). Bold lines are the
mean values, thin lines are the confidence intervals for the fibers
with assumed P2 O5 molar concentrations: solid lines – 6.6%,
dash line – 8.8%, dot lines – 11.0%, dash dot lines – 13.2%, dash
double dot lines – 14.7%. The point of respective lines crossing
give P2 O5 concentration and the n parameter for each fiber.
Within the limits of the accuracy of our analysis, the n parameter turn out to be one and the
same for all the set 1 fibers (0:20 0:03) and for all
the set 2 fibers (0:16 0:02). Notice that these
values are close enough to each other (again within
our accuracy). For the SPCVD-manufactured
fiber the n parameter is 0:28 0:07. So it seems
reasonably safe to suggest that the relation between the single and double phosphorus centers is
determined mainly by the manufacturing process
and does not depend practically on the P2 O5
concentration.
Evidently the values of P2 O5 molar concentration in the fiber cores obtained on the basis of our
approach turn out to be systematically lower than
the results based on the refractive index measurements. This is explained by a non-uniform radial
distribution of P2 O5 in the fiber cores [23]. The
measurements of the Raman spectra in fibers
provide the Raman intensity averaged over the
core. It is reasonable to suggest that for homogeneous samples the approach based on the Raman
spectra analysis and other methods of measurement of P2 O5 concentration should give close results.
4.3. Influence of UV irradiation
In our previous article [25] the experimental
frequencies were obtained for the most intensive Raman bands in phosphosilicate glass caused
by phosphorus centers with the O@P double
bond, intensities of those decreasing considerably after UV irradiation. In the frequency range
222
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
are connected to fourfold-coordinated phosphorus
atoms, and hence, in decrease of the Raman intensity at about 1150 cm1 , since the frequencies
and Raman intensities for vibrations of PAOAP
and PAOASi linkages connected to fivefold-coordinated phosphorus atoms are lower than those of
the same linkages connected to fourfold-coordinated atoms [25].
The analysis of experimental Raman spectra of
the fibers before and after UV irradiation allows us
to conclude that
Fig. 14. Determining P2 O5 molar concentration and the relative concentration parameter of the single and double phosphorus centers, n, in the SPCVD-manufactured fiber on the
basis of experimental data on the relative Raman intensities of
the O@P bonds stretching vibrations in the single phosphorus
centers (nearly vertical lines) and the relative Raman intensities
of the antisymmetric stretching vibrations of the SiAO bonds in
the SiAOASi linkages (nearly horizontal lines). Bold lines are
the mean values, thin lines are the confidence intervals. The
point of respective lines crossing give P2 O5 concentration and
the n parameter.
860–1460 cm1 there are two of these bands, 1320
and 1150 cm1 . From the aforesaid it follows that
the first band is caused by the stretching vibrations
of O@P double bonds of different types while the
second one is mainly contributed by an antisymmetric stretching vibration of PAO bonds in the
PAOAP linkages and, to a lesser degree, by the
same vibrations of PAO and SiAO bonds in
the PAOASi linkages.
According to Ref. [25], the reduction of the
1320 cm1 band intensity after UV irradiation is
caused by a decrease in the O@P double bond
concentration owing to the transition of a part of
phosphorus atoms from the fourfold-coordinated
form (O@PO3 ) into the fivefold-coordinated form
(PO5 ) in a photoinduced reaction of non-bridging
oxygen atoms with SiAOASi linkages. Clearly,
such changes result in decrease of concentration
of those PAOAP and PAOASi linkages, which
• Raman intensity of the 1320 cm1 band, and
hence the total concentration of O@P double
bonds decreases by three times after UV irradiation;
• the ratio between intensities of the 1320 cm1
band components changes considerably: the
low-frequency component intensity decreases
only slightly, and practically all the reduction
of the Raman band total intensity is caused by
a decrease in the high-frequency component intensity;
• the frequencies of the Raman band components
do not change.
It is reasonable to assume that under UV irradiation the O@P double bonds disappear both in
single phosphorus centers and in double ones. In
the double phosphorus center either one O@P bond
or both bonds may disappear. In the first case a new
phosphorus center arises, with one O@P double
bond and a PAOAP linkage between fourfold- and
fivefold-coordinated phosphorus atoms. Our calculation shows that in this center the frequency and
the Raman scattering intensity of the O@P bond
stretching vibration are close to those in the single
phosphorus center and the frequency of the Raman
scattering intensity of the antisymmetric stretching
vibrations of PAO bonds in the PAOAP linkage
are close to those in the double phosphorus center.
Hence the new phosphorus centers do contribute to
the low-frequency component of the 1320 cm1
band. So reactions of three types may occur under
UV irradiation, with the O@P double bonds disappearing in each of them.
Unfortunately, basing only on the decomposition of the 1320 cm1 band before and after irra-
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
diation, it is impossible to estimate the fractions of
the phosphorus centers participating in these reactions. However one can find the limiting fractions of the phosphorus centers participating in
reactions of disappearing of one and two O@P
bonds. If all the single centers disappear under UV
irradiation then one double bond turns out to
disappear in 50% of the double centers and both
double bonds turn out to disappear in 6% of the
centers. If no single centers disappear at all under
UV irradiation then one double bond disappears
in 35% of the double centers and both double
bonds disappear in 25% of them. To estimate the
fraction of the single centers disappearing in the
real situation one should use the data on changes
in intensities of components of the Raman spectrum in the range 860–1200 cm1 caused by the
linkages of different types. However the PAOAP
and PAOASi linkages connected with both fourfold-coordinated and fivefold-coordinated phosphorus atoms must be taken into account to
decompose the Raman spectra in this range in the
UV-irradiates glasses. In other words, at least two
extra components must be taken into account. The
experimental accuracy available gives no way to
perform such a decomposition.
Nevertheless, the decrease of Raman scattering
near 1150 cm1 due mainly to a reduction of
concentration of the PAOAP linkages connected
at least with one fourfold-coordinated phosphorus
atom suggests the second limiting case to be more
close to the reality.
4.4. On the estimations of Raman cross section in
phosphosilicate glass
Analyzing the operation of a stimulated Raman
laser based on phosphosilicate-core fiber the authors of Ref. [3] make three assumptions being of
interest for our discussion, namely
1. the laser generation occurs independently on
P2 O5 and SiO2 fiber core glass constituents;
2. the Raman gain coefficient for the 1320 cm1
band is proportional to P2 O5 molar concentration and that for the 440 cm1 band––to SiO2
molar concentration;
223
3. the maximum value of the Raman gain coefficient for the 1320 cm1 band corresponds to
the value measured for v-P2 O5 in Ref. [10].
Under these assumptions Raman gain coefficients were estimated for the wavelengths 1.24 and
1.31 lm and the conclusion was made that the
Raman cross section ratio for the 1320 cm1 band
in v-P2 O5 and for the 440 cm1 band in v-SiO2 was
considerably higher than that obtained in Ref.
[10].
The assumptions made in Ref. [3] seem to be
incorrect. Firstly, the laser generation cannot occur
independently on P2 O5 and SiO2 glass constituents.
The matter is that, besides the vibrational modes,
which actually are classified as vibrations of P2 O5
and SiO2 constituents, there are the combined
modes caused by interaction of vibrations of the
glass constituents. The simplest of them are the
vibrations of PAOASi linkages with frequency
varying approximately in the limits 440–480 cm1
with P2 O5 concentration growth [25]. The corresponding Raman band overlaps with the 440 cm1
band of the v-SiO2 network caused mainly by
vibrations of SiAOASi linkages. Secondly, as follows from the foregoing, the Raman gain coefficient for the 1320 cm1 band is not proportional to
P2 O5 molar concentration in the glass since the
gain is determined by the concentration of O@P
bonds at least of two types causing this band. And
finally, strictly speaking, it is not correct to use the
Raman cross section for v-P2 O5 since, as it follows
from the results of above quantum-chemical
modeling, the Raman cross section on a O@P
bond increases with associating O@PO3 tetrahedra
together: the Raman intensity is minimum in single
phosphorus center of phosphosilicate glass and
it is maximum for v-P2 O5 (see Table 2).
Since the fiber used in Ref. [3] was made in the
same laboratory and by the same technology as the
set 2 fibers, it is safe to assume that n 0:2 for this
fiber. For P2 O5 concentration x 13 mol% [3] the
relative concentrations of various bonds in the
fiber core turn out to be fI 0:06, fII 0:16,
fSiAOASi 0:62 and fPAOASi 0:20. Using the calculated ratio 2.3 between Raman intensities for
O@P bonds in double and single phosphorus centers and assuming the Raman intensity for the
224
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
O@P bond in v-P2 O5 to be equal to the corresponding intensity for the double phosphorus
center, we conclude that the ratio between complete Raman cross sections for the O@P bond
stretching vibrations in phosphosilicate glass under
investigation and in v-P2 O5 is 2.8. It is somewhat
higher than the value 2.6 found in Ref. [3]. This
seems natural since the Raman intensity for the
O@P bond in v-P2 O5 is higher than in the double
phosphorus center. So, as a matter of fact, there
is no contradictions with the results of Ref. [10].
On the other hand, the relative amount of
SiAOASi linkages is well below the unity (0.62)
so it seems too low to explain the Raman gain in
the 440 cm1 band observed in Ref. [3] (the experimental value of the Raman gain coefficient
corresponds to the concentration fSiAOASi 0:95).
This implies that more than 30% of the gain in this
band is caused by other contributions, namely, as
follows from aforesaid, by PAOASi linkages.
Unfortunately, the clusters used for the quantumchemical modeling are insufficiently large to
calculate exactly the ratio between the Raman
intensities for PAOASi and SiAOASi linkage vibrations contributing to this band. Nevertheless
the calculations allow us to estimate roughly the
ratio between these intensities as 1.5–3. With
fSiAOASi and fPAOASi taken into account this just
results in the contribution of PAOASi linkages
of the order of 30%.
5. Summary
In this work the vibrational properties of
phosphosilicate glasses with P2 O5 concentration
up to 15 mol% manufactured by the MCVD and
SPCVD methods were investigated using the
Raman spectroscopy and quantum-chemical modeling. The main results and conclusions consist in
the following:
• the experimental Raman spectra can be decomposed in the frequency range 860–1460 cm1 in
five components;
• the Raman band at 1320 cm1 typical for phosphosilicate glasses is not simple but contains at
least two components, their frequencies being
1317 and 1330 cm1 in the investigated glasses
and the relative intensity ratio depending on
manufacturing techniques;
• the low-frequency component of this Raman
band is caused by single phosphorus centers
(O@PO3 tetrahedra) and the high-frequency
one––by double phosphorus centers (pairs of
O@PO3 tetrahedra bonded together by common oxygen atom). The investigated phosphosilicate glasses contain 2–4 times as much
double centers as single ones. Other three components of the Raman spectra are caused by
Si–O–Si (1185 cm1 ), PAOASi and SiAOASi
(1025 cm1 ) and PAOAP (1150 cm1 ) linkages;
• up to 60% of the double phosphorus centers are
destroyed under 244 nm UV irradiation.
In this work we have proposed a model of the
network of phosphosilicate glass allowing one to
calculate the concentrations of phosphorus and
silicon sites, O@P double bonds and SiAOASi,
PAOASi and PAOAP linkages for any P2 O5
concentration in the glass. We have shown that
using this model together with the results of decomposition of experimental Raman spectra allows one to find both the P2 O5 content and the
concentration of all these species in the glass.
The main object of research in this work has
been the optical fibers drawn from preforms manufactured by CVD methods for which, as is noted
above, the formation of double phosphorus centers
seems natural. In the framework of our approach
the analysis of the Raman spectra of phosphosilicate glasses manufactured by other methods is of
obvious interest. In our opinion, such approach to
the analysis of Raman spectra may be used to optimize and control any process of manufacturing
either phosphosilicate glasses, or other similar
glasses and optical fibers on their basis.
Acknowledgements
The authors are grateful to M.M. Bubnov,
K.M. Golant, A.N. Guryanov, G.A. Ivanov and
V.F. Khopin for the phosphosilicate-core fibers
and for valuable discussions.
V.G. Plotnichenko et al. / Journal of Non-Crystalline Solids 306 (2002) 209–226
Appendix A. Model of phosphosilicate glass network
A model of phosphosilicate glass network developed in Refs. [7,28] allows one to find relative
concentrations of O@P bonds and of SiAOASi,
PAOASi and PAOAP linkages in such glass. The
model is based on the assumption of a complete
absence of correlations in arrangement of phosphorus atoms in the glass network.
The main assumption of the present work is
that there are two types of phosphorus centers in
the phosphosilicate glass, single phosphorus centers (O@PO3 tetrahedra bonded only with the SiO4
tetrahedra) and double phosphorus centers (pairs
of the O@PO3 tetrahedra bound together by
PAOAP linkages). We have extended the model of
Refs. [7,28] to such a case.
The main points of our model are as follows.
(1) There are no other phosphorus centers in glass
except for double and single centers. The structure of phosphosilicate glass with composition
(P2 O5 )x (SiO2 )1x is presented as ððIÞn ðIIÞ1n Þx (SiO2 )1x where (I) and (II) are single and double phosphorus centers, respectively, and n is a
parameter of relative concentration of these
centers.
(2) Both the single and the double centers may either be isolated or form any groups. Two single centers are joined together by a PAOAP
linkage forms a double center. A single center
joined by a PAOAP linkage with a double one
forms a pair of double centers, and so on. So
there are three structural units in the phosphosilicate glass:
(a) SiO2 unit with four SiAO bonds;
(b) P2 O5 single-center unit with six ðIÞAO
bonds;
(c) P2 O5 double-center unit with four ðIIÞAO
bonds.
Probabilities of formation of these bonds are denoted as p0 , p1 , and p2 , respectively.
(3) There are six types of oxygen linkages in the
glass:
(a) SiAOASi,
(b) SiAOAðIÞ,
(c) SiAOAðIIÞ,
225
(d) ðIÞAOAðIÞ,
(e) ðIÞAOAðIIÞ,
(f) ðIIÞAOAðIIÞ.
Probabilities of formation of these linkages are
denoted as p1 , p2 , p3 , p4 , p5 , and p6 , respectively.
The probabilities pi and pi are related by obvious formulae: p1 ¼ p20 N 1 , p2 ¼ 2p0 p1 N 1 , p3 ¼
2p0 p2 N 1 , p4 ¼ p21 N 1 , p5 ¼ 2p1 p2 N 1 , p6 ¼ p22 N 1 .
The normalizing factor, N 1 , is nothing but a
complete number of bridging linkages of any type
in phosphosilicate glass.
In phosphosilicate glass with composition ((I)n (II)1n )x (SiO2 )1x the bond formation probabilities
are readily shown to be
p0 ¼
2ð 1 x Þ
2 þ nx
p1 ¼
3nx
2 þ nx
p2 ¼
2ð1 nÞx
:
2 þ nx
The relative concentrations, fi , of single (I) and
double (II) phosphorus centers, O@P double
bonds and SiAOASi, PAOASi and PAOAP linkages in respect to total number, N, of bridging
linkages in the phosphosilicate glass are expressed
in terms of the pi probabilities as follows:
fðIÞ ¼ p2
fðIIÞ ¼ p3 þ p4 þ p5 þ p6
fO@P ¼ p2 þ 2ðp3 þ p4 þ p5 þ p6 ÞfSiAOASi ¼ p1
fPAOASi ¼ p2 þ p3
fPAOAP ¼ p3 þ 2ðp4 þ p5 þ p6 Þ
and the total number of linkages
N ¼ p1 þ p2 þ 2ðp3 þ p4 þ p5 þ p6 Þ:
The explicit formulae for the relative concentrations, fi , of single (I) and double (II) phosphorus centers, O@P double bonds and SiAOASi,
PAOASi and PAOAP linkages and the total
number, N, of bridging linkages in the phosphosilicate glass derived from these expressions are
given in Section 4 (see (2) and what follows).
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