Romanian Reports in Physics, Vol. 53, Nos. 3–8, P. 469–476, 2001
STUDY OF THE COMPOSITIONAL DEPENDENCE OF THE
REFRACTIVE INDEX IN THE xNa2O ⋅ (1-x) P2O5 SYSTEM
ANA IOANID, MIRELA IORDACHE
Faculty of Physics, University of Bucharest, PO Box, MG-11, Bucharest-Magurele, Romania
(Received October 22, 2001)
Abstract: The study of the compositional dependence of the refractive index via the molar
refractivity and molar volume using te Lorentz-Lorenz relation has been performed. The oxygen ionic
refractivity and the oxygen electronic polarizability have been evaluated in connection with the group
basicity of oxygen in Qn-type phosphate tetrahedra provided by depolymerization reaction as x
increases.
Key words: refractive index, molar refractivity, optical basicity.
1. INTRODUCTION
Phosphate glasses are technologically important materials because they
generally have higher thermal expansion characteristics and lower transition
temperatures than silicate or borate glasses. These glasses also have a very
interesting molecular structure. While metaphosphate glass (1:1) can be composed
of phosphate tetrahedra chains with theoretically infinite lengths, the structure of
other binary sodium phosphate glasses with the nominal Na/P ratios ranging from
0.33 to 1.27, is significantly different [1]. The addition of a monovalent alkali
oxide disrupts the phosphate chains by breaking bridging oxygen bonds to form
non-bridging oxygen to acommodate the alkali cation and additional oxygen. Thus,
an understanding of how the composition affects the structure of phosphate glasses
is critical to the design of glasses with specific properties.
The refractive index is important for optical applications. The mass density
can be an important factor in the biological and organic agrochemical applications.
But, while density may be achieved by incorporating cations of appropriate mass,
the attainment of a specified refractive index is less strainghtforward and we examine
the problem in this study in terms of molar refractivity and molar volume [2],
which are analysed in relation to the separate contributions by the cations and
phosphate oxyanions, in the 25-65 mol% Na2O range. The ionic refractivity of the
oxyanion units can be evaluated in correlation with the group basicity that is modified
whenever more than one type of oxide is present in an oxyanion group [3].
470
Ana Ioanid, Mirela Iordache
2
2. STRUCTURAL PROPERTIES OF SODIUM PHOSPHATE GLASSES
Simple phosphate glasses are composed of PO4 tetrahedra which form long
chains or rings of PO4 tetrahedra sharing corners. In P2O5, the phosphate tetraedron
PO4 has the structure depicted in Fig.1. In terms of Qn-site, in which n represents
the number of bridging oxygens per phosphate tetrahedron, this group is Q3-site,
with three bridging oxygens P-O (BO) and one non-bridging oxygen P=O (NBO).
Fig. 1 – Structure of PO4 tetrahedron in P2O5.
The evolution of the simple phosphate glass structure by addition of a
monovalent oxide modifier may be presented in the frame of the reorganization
theory [4]. In this theory, the addition of the alkali oxide modifier Na2O to P2O5
disrupts its structure consisting of all Q3-phosphate tetraedra, by breaking bridging
oxygen bonds to form non-bridging oxygen to accommodate the alkali cation Na+
and the additional oxygen.
This structural depolymerization reaction can be represented by
and in terms of Qn-site,
2Q3 + Na 2O → 2Q 2
(1)
Depolymerization continues up to the metaphosphate composition (50 mol%
Na2O, 50 mol % P2O5 ) at which the structure consists of infinitely long chains of
Q2-tetrahedra. Adding Na2O in excess of 50 mol %, the structure depolymerizes
according to reaction
3
Compositional dependence of the refractive index in xNa2O⋅(1-x)P2O5 system
471
and in terms of Qn-site,
2Q 2 + Na 2O → 2Q1
(2)
The relative site populations q1, q2, q3 of Q1, Q2, Q3 tetrahedra, respectively,
have been evaluated by the chemical shift of the 31P and 23Na RMN spectra,
depending on the [Na ] ratio [1]. For the considered system, [Na ] = y = x , so
[P]
[P]
1− x
n
that the Q -site distribution has a direct compositional dependence.
3. MOLAR REFRACTIVITY
Molar refractivity is a separable quantity such that assigned values can be
attributed to constituent atoms or ions and with the operation of good additivity. On
the other hand, the ionic refractivity is a measure of individual ion. For an isotropic
material, the molar refractivity is related to the refractive index n by the LorentzLorenz expression
R mol = Vmol
n2 −1
n2 + 2
(3)
where Vmol is the molar volume and molar refractivity have expression
R mol =
4π
Ν A α molec
3
(4)
where NA is Avogadro’s number and α molec = α cations + α anions is the electronic
polarizability of the molecule evaluated as the sum of the cation and anion
polarizabilities. In the following evaluations we will use the Lorentz-Lorenz
expression with molecular quantities Vmolec and R molec .
Taking into account the above considerations we can write the molecular
refractivity of the xNa2O.(1-x) P2O5 system
R molec ( x ) = 2 xR Na + + 2(1 − x ) R P 5 + + (5 − 4 x ) R O 2 −
(5)
In the considered system the oxygen ions are constituents of the stable
oxyanions of phosphate tetrahedra. The ionic refractivity R O 2 − is evaluated in
correlation with the group basicity λ [3]. It is known that the group basicity is a
very important parameter of a glass and which defines the microscopic basicity of
an individual oxygen in a mixed oxyanion, i.e. after that the negative charge of the
all oxygens has been neutralised by the P5+ cation. Thus the group basicity will
have to be modified whenever more than one type of oxygen (BO and NBO) is
present in the oxyanion group. In Table 1 are given the group basicity values for
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Ana Ioanid, Mirela Iordache
4
the Qn-site tetrahedra in the considered system evaluated with the formula
z r
1
5+
λ = 1 − P P (1 − ) in which z P is the oxidation number of the P cation, rP is his
γP
2
ionic ratio with respect to the total number of oxygen in phosphate group and γ P is
the basicity moderating power of the P5+ cation.
Table 1
n
Group basicities of the Q -site oxyanions in the xNa2O⋅(1-x) P2O5 system
n
Q -site oxyanion
group basicity
λ
Q4
0.25
Q3
0.40
Q2
0.50
Q1
0.57
Q0
0.63
Ionic refractivity R O 2 − . For a given glass it is possible to obtain the values of
the ideal optical basicity Λ
Λ = 1− ∑
i
zi ri
1
zr
(1 − ) ≅ ∑ i i
2
γi
i 2γ i
(6)
which is the average of all the oxygens from glass. In this formula z i is the
oxidation number of the i cation, ri is his ionic ratio with respect to the total
number of oxygen in glass and γ i is the basicity moderating power of the i cation.
The ionic refractivity values of the oxygen may be evaluated using the relation
Λ = (R O 2 − − 1.5) / 4.25
(7)
established from experimental data. These R O 2 − values are average of all the
oxygens from the glass.
4. RESULTS
In this study we propose to evaluate the ionic refractivity R O 2 − and the ideal
optical basicity Λ using an averaging formula which takes into account the relative
site populations q k ( x ) , so that
R O 2 − ( x ) = ∑ q k ( x )R Ok 2 −
(8)
Λ ( x ) = ∑ q k ( x )λ k
(9)
k
and
k
5
Compositional dependence of the refractive index in xNa2O⋅(1-x)P2O5 system
473
k
where R O
group and λ k is the
2 − is the ionic refractivity of the oxygen in k-type
group basicity for the same k-type group. Then it follows that
λ k = ( R Ok 2 − − 1.5) / 4.25
(10)
Using the values of λ k from Table 1, we obtain R1O 2 − = 3.922 , R O2 2 − = 3.625 ,
R 3O 2 − = 3.200 . In Fig. 2 is plotted the Λ ( x ) dependence whose values have been
obtained with (9) using values of q k ( x ) by extrapolation of the experimental data
of q k ( x ) from [1].
0.56
0.54
0.52
Λ
0.50
0.48
0.46
0.44
0.42
0.2
0.3
0.4
0.5
0.6
x Na2O
Fig. 2 – Dependence of the optical basicity Λ on composition
in the xNa2O⋅(1-x)P2O5 system.
Ionic refractivity R P 5 + . The experimental value of the refractive index
n = 1.365 for the metaphosphate glass (x = 0.50) is known [5]. On the other hand,
for x = 0.50, q1 (0.50) = q 3 (0.50) = 0 and q 2 (0.50) = 1 [1]. The molecule volume
Vmolec has been evaluated as the sum of all the ionic volumes appreciated with the
ionic
radius.
From
the
Lorentz-Lorenz
relation,
we
obtain
R molec (0.50) = R Na + + R O 2 − + R P 5 + . The ionic refractivity R Na + is tabelated [6]. We
obtain the ionic refractivity of P5+ in a phosphate tetrahedra, R P 5 + =5.574. In Fig. 3
are plotted the dependences R O 2 − ( x ) evaluated with (8) and R molec ( x ) evaluated
with (5).
474
Ana Ioanid, Mirela Iordache
6
14
13
24
3
10 xR[cm ]
12
11
Rmolec
10
RO2-
9
8
7
6
5
4
3
0
10
20
30
40
50
x Na2O
Fig. 3 – Dependence of the oxygen ionic refractivity R 2 − and the molecular refractivity
O
R molec on composition in the xNa2O⋅(1-x)P2O5 system.
In Fig.4 is plotted the dependence of the predicted values for the refractive
index on composition.
This study provides an interesting result that consists in the dependence of
the electronic polarizability of the oxygen α O 2 − in the considered phosphate glasses
on the ideal optical basicity Λ . In Fig. 5 are plotted, for comparison, the
dependences R O 2 − ( Λ ) and α O 2 − ( Λ ) . In the (0.40 ÷ 0.60) range values of the ideal
optic basicity, the oxygen electronic polarizability α O < 1 for the considered
2−
phosphate glasses, while 1 < α O < 2 for some barium silicates [3] and α O 2 − > 2
2−
for free oxygen ion (the polarizability values are in 10−24 cm3 ). These less values of
the α O in the phosphate glasses then in silicate glasses agree with the general
2−
tendency of tightening of the electron clouds of oxygen in the M-O bond (M = P5+,
Si4+) with increasing the valency of the cation (P5+ facing Si4+) and with decreasing
the ionic radius of the cation (r =0.34 for P5+ facing r =0.41 for Si4+) [7].
On the other hand, it is known that the polarization of the ion originates from
the transitions of the outermost electron in a level to other levels in which the
variation of the angular momentum of the atomic orbitals under consideration is
∆A = 1 . Thus, the increase of the α O as x Na2O increases, can be attributed to the
2−
delocalization of 2p electrons of the oxygen in optical transitions to 3s levels of
cations with high ionicity as Na+ ions.
7
Compositional dependence of the refractive index in xNa2O⋅(1-x)P2O5 system
475
1.42
1.40
n
1.38
1.36
1.34
1.32
0.2
0.3
0.4
0.5
0.6
x Na2O
Fig. 4 – Dependence of the predicted refractive index on composition
in the xNa2O⋅(1-x)P2O5 system.
4.00
24
3
αO2-[A ]
3
10 xRO2-[cm ]
0.930
3.75
0.868
3.50
0.806
3.25
0.744
3.00
0.42
0.44
0.46
0.48
0.50
0.52
0.54
0.56
Λ
Fig. 5 – Dependence of the oxygen ionic refractivity R 2 − and the oxygen electronic
O
polarizability α 2 − on composition in the xNa2O⋅(1-x)P2O5 system.
O
5. CONCLUSIONS
The mains results of this study refer to the variation of the refractive index and
of the oxygen electronic polarizability with the composition of the xNa2O.(1-x)P2O5
phosphate glasses system.
476
Ana Ioanid, Mirela Iordache
8
The refractive index decreases from 1.42 to 1.30 when x increases from 0.25
to 0.65, i.e., a decrease of ca 5%, while for all the ranges of the optical applications
the refractive index varies between 1.5 and 1.1, i.e., 15%.
The ordering radius decreases as x increases via the depolymerization
reaction.
The electronic polarizability of the oxygen increases as x increases by the
delocalization of 2p electrons of the oxygen in optical transitions to 3s levels of the
high ionicity alkali cations.
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