Mechanical relaxation of some tellurovanadate glasses
Yasser B. Saddeek
a,1
, R. El-Mallawany
b,
⁎, H. Afifi
c
a
Physics Department, Faculty of Science, Al-Azhar University, P.O. 71452, Assiut, Egypt
b
Physics Department, Faculty of Science, Menofia University, Egypt
c
Ultrasonic Laboratory, National Institute for Standards, Tersa St., Giza, P.O. 136, Egypt
abstract article info
Article history:
Received 9 January 2015
Received in revised form 13 February 2015
Accepted 7 March 2015
Available online xxxx
Keywords:
Tellurite glasses;
Elastic properties;
Ultrasonic relaxation;
Two-well systems
The ultrasonic relaxation process of ZnO–TeO
2
–V
2
O
5
and CeO
2
–TeO
2
–V
2
O
5
glasses was investigated in terms of
the central force model of acoustically active two-well systems. The theoretical treatment of the vibrations of
two-well systems revealed that, the equilibrium interatomic separation, the number of loss centers and the acti-
vation energy are affected with the mutual potential energy of the studied glasses. The number of loss centers is
related to the compositional dependence of the elastic moduli and the average ring diameter. The results showed
that degree of elongation or contraction of the two-well system depends on the concentration of CeO
2
or ZnO.
The theoretically determined longitudinal and transverse deformation potentials due to the acoustic loss pro-
duced by two-well systems decrease with the increase of ZnO/CeO
2
content.
© 2015 Elsevier B.V. All rights reserved.
1. Introduction
In materials engineering design prediction and understanding over
the physical properties are essential to develop new class of functional-
ized materials. The modification of properties induced by the addition of
transition metal oxides (TMO) or rare earth oxides (REO) into host glass
matrix like tellurite glasses has attracted a lot of attention due to their
physical properties and applications [1–17].
The present study will be carried out to analyze quantitatively the ul-
trasonic relaxation at low temperature of 70TeO
2
–xZnO–(30 - x)V
2
O
5
(TZV) and 70TeO
2
–xCeO
2
–(30 - x)V
2
O
5
(TCV) glasses in terms of the
central force model [18–23]. This model presents the magnitude of the
two-well barrier heights (in longitudinal and transverse modes) and de-
formation potential occurring in the phenomenological theory. The longi-
tudinal and transverse deformation potentials of two-well potential will
be determined theoretically via the correlation to the elastic moduli [24].
2. Theoretical analysis
The central force model computed the magnitude of the two well
barrier heights and deformation potential (D) occurring in the phenom-
enological theory [18–23]. The model predicts that all anions move in
identical symmetric interatomic wells. The wells have a single central
minimum corresponding to the equilibrium positions of the anions,
and are harmonic for sufficiently small O vibrations, though at larger
amplitudes anharmonic effects will appear as the wells become flat bot-
tomed. The behavior of ultrasonic attenuation at low temperatures was
explained on the basis that the thermal equilibrium of the two-well po-
tential systems is disturbed and the relaxation occurs via thermally ac-
tivated jumps of the moving particles such as oxygen atoms over the
potential barrier E as shown in Fig. 1.
When the O atom is longitudinally displaced, the variation of the
mutual potential energy U of the system with the position r of the oxy-
gen atom in the two well systems will be given by
U ¼ -a
1
r
þ
1
2er
0
-r ð Þ
þ b
1
r
m
þ
1
2er
0
-r ð Þ
m
ð1Þ
where e is the elongation factor and equals to R/2r
0
, i.e. the A–A separa-
tion divided by the equilibrium separation 2r
0
, a and b are constants for
a given molecular type, which can be obtained as b =(ar
0
m - 1
)/ m, and
6 b m b 12. The quantity U/2 may be regarded as the mutual potential
energy of half the O atom plus one of the A atoms and is taken as the po-
tential in which the O atom vibrates, each A atom being considered in-
finitely heavy. The equilibrium bond energy (mutual potential
energy), U
0
, can be estimated according to the model [18–23]. Also,
when the O atom is transversely displaced by an amount d, the potential
energy will be given by,
U¼
-2a
e
2
r
2
0
þ d
2
1=2
þ
2b
e
2
r
2
0
þ d
2
m=2
ð2Þ
where a, b, and m have the same values as those values taken in the case
of longitudinal vibrations. It was noted that for e N 1 (elongation) a sin-
gle minimum only in the two well-potential by the vibrating oxygen
Journal of Non-Crystalline Solids 417–418 (2015) 28–33
⁎ Corresponding author.
E-mail address: raoufelmallawany@yahoo.com (R. El-Mallawany).
1
Physics Department, Faculty of Science, Majmaa University, Zulfi, Saudi Arabia.
http://dx.doi.org/10.1016/j.jnoncrysol.2015.03.003
0022-3093/© 2015 Elsevier B.V. All rights reserved.
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journal homepage: www.elsevier.com/ locate/ jnoncrysol