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Elastic and anelastic properties of rare earth phosphate glasses
288
Journal of Non-Crystalline Solids 121 (1990) 288-293 North-Holland
ELASTIC AND A N E L A S T I C P R O P E R T I E S O F RARE E A R T H P H O S P H A T E G L A S S E S G. C A R I N I , M. C U T R O N I , G. D ' A N G E L O , M. F E D E R I C O , G. G A L L I and G. T R I P O D O Dipartimento Fisica, Universita' di Messina, Ctrd. Papardo salita Sperone 31, 98010 S. Agata, Messina, Italy
G.A. S A U N D E R S and W A N G Q I N G X I A N School of Physics, University of Bath, UK
The behaviour of the ultrasonic attenuation between 10 K and 400 K in Sm203-P205 glasses is characterized by the presence of very broad peaks, due to thermally activated relaxations of structural defects, typical of amorphous materials. A study of these anomalies reveals that the addition of Sm203 to P205 has little influence on the mean activation energy of the relaxation process, but does cause a decrease in the number of relaxing particles. The effect of temperature on the anomalous negative hydrostatic pressure derivatives of the elastic moduli of samarium phosphate glass is also examined experimentally. Reduction of the temperature below 300 K causes aCn/aP and aB/OP to increase steeply to more negative values: both longitudinal and shear Gruneisen parameters, which are negative, become much larger. It is suggested that application of pressure drives the samarium ion f ~ d transition and that the ion size collapse couples to the acoustic modes, strongly enhancing acoustic mode softening.
1. Introduction The acoustic attenuation behaviour below the glass transition temperature, To, of almost all dielectric [1] and metallic [2] glasses shows a welldefined peak, not present in the corresponding crystals. The peak temperature increases with increasing frequency, following an Arrhenius-like law and as a consequence is normally attributed to thermally activated relaxations of structural defects, introduced by the topological disorder. The location of the peak temperature in the same frequency range seems to depend on the nature of bonds present in the glass. In fact the glassy oxides [1,3], characterized only by strong covalent bonds, show peaks at higher temperatures than the chalcogenide glasses [4,5], in which weak Van der Waals bonds are also present. However, despite extensive experimental evidence, the microscopic origin of the relaxing particle and its possible dependence on the stoichiometry are still unknown. Many interesting microscopic explanations [3,6] have been proposed for
the vitreous oxides, but they are only phenomenological and their validity has not been proved in a general way. To gain a further understanding of the problem, we have extended the range of investigated systems. Glasses of the Sm203-P205 system were chosen because specific structural information [7] is available which can help to gain an insight into the microscopic origin of the observed acoustic anomalies. Measurements have been made between 253 K and 453 K of the hydrostatic pressure dependences of ultrasonic velocities in (Sm203)0. 2(P2Os)0.8 glass to examine in detail the unusual temperature and pressure dependences of the elastic properties of these rare-earth glasses. When the samarium phosphate glasses are subjected to hydrostatic pressure, their bulk and shear moduli decrease, probably due to pressure dependent valence fluctuation of the samarium ion [8]. The negative pressure derivative of the bulk modulus B is particularly unusual: when compressed volumetrically these glasses become easier to squeeze!
0022-3093/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
G. Carini et aL / Properties of rare earth phosphate glasses
289
2. Experimental details o
o
O°o
o
o
The preparation and characterization of (Sm203)x(P2Os)l_ x glasses, x being the molar fraction, has been described elsewhere [7]. The acoustic attenuation of 10-70 MHz longitudinal sound waves was measured between 15 and 450 K by the experimental set-up previously described [9]. The ultrasonic velocity was measured using the pulse echo overlap technique. Ultrasonic pulses at a frequency of 10 MHz were generated by X- and Y-cut quartz transducers. The hydrostatic pressure dependences of the ultrasonic wave transit times, Tp, were measured in a piston and cylinder apparatus. The hydrostatic pressure was determined by measuring the change induced in the electrical resistance of a calibrated manganin wire coil inside the pressure chamber. The lowest temperature at which the ultrasonic measurements could be made was limited by the stringent requirement of ensuring that the pressure is indeed hydrostatic and therefore that the transmitting fluid remains liquid. The upper temperature was restricted by transducer bonding difficulties. To account for pressure induced changes in sample dimensions, the 'natural velocity' IV ( = loTp, where l 0 is the path length at atmospheric pressure) technique [10] was used, the experimental data being converted to a change of natural velocity ( I V / W o - 1). The pressure dependence of the relative changes in natural velocity of longitudinal and shear waves were found to be linear up to an applied maximum pressure (1.5 x 108 Pa).
i
o
o
•
I0
~
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o
oE
°o
MHz
o70 0 0
o~
0
0 0
0
0
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•
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•
-e
I
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•
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•
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•
200
400
T (K) Fig. 1. Temperature dependence of the longitudinal waves acoustic attenuation in the (Sm203)o.25(P2Os)0.75 glass. other dissipative processes, has been subtracted from the experimental data. An increase of Sm 203 concentration gives rise to a small increase in the peak temperature and a strong decrease in the peak height. Further, the peak width is significantly reduced by increased samarium oxide concentration. The observed relaxation peaks are much broader than a Debye peak, ruling out a single ralaxation time approach. This peculiarity, typical for the sub-To relaxations observed in glasses, can be interpreted as arising from the existence of a distribution of relaxation times due to random deviations in the local arrangement of
12 I n
3. Results and discussion 3.1. A c o u s t i c a t t e n u a t i o n
The behaviour with temperature of the acoustic attenuation at various frequencies in one of the glasses examined is shown in fig. 1. A very broad attenuation peak is observed, the temperature of which increases with increasing frequency, indicating a thermally activated relaxation process. In fig. 2 the relaxation losses at the same frequency (70 MHz) for the glasses 'with two different Sm203 contents are compared: a flat background, due to
._u 4 8
<
G
I
100
200 T (K)
300
Fig. 2. Comparison between the relaxation losses in the glasses with x = 0.05 and x = 0.25. The frequency of longitudinal ultrasounds is 70 MHz. The continuous line corresponds to the theoretical fit by eq. (1).
290
G. Carini et al. / Properties of rare earth phosphate glasses
the system. Since in a thermally activated process the relaxation time is defined by an activation energy E and a characteristic time ,to, , r = , r 0 e x p ( E / k T ) , a ,r-distribution corresponds to a distribution of E and ,ro. To provide a quantitative interpretation of the relaxation losses, we assume a single value for ,to, so that the ,r-distribution can be related to an E-distribution P ( E ) , which was taken as Gaussian; in this case, a useful form for the acoustic attenuation is [1,11]
(3) the energies involved in the relaxation process are little affected by an increase of samarium oxide concentration. The peculiarities revealed encourage us to extend our study to other concentrations of the Sm203-P205 system and to other phosphate glasses with different network modifier ions, in order to identify the structural units, which are present in the P205 glassy network and are subjected to thermally activated local motions.
NB2 (P wZ'r( E ) d(E). a = 4 p o 3 k T J ( E ) 1 + w2'rZ(E)
3.2. Elastic and anharmonic properties
(1)
The pressure derivatives of the elastic stiffness moduli were obtained using Here N is the total number of relaxing 'particles', B the deformation potential, v the sound velocity, w the angular frequency, T the absolute temperature and O the density. The least squares fit of the data by a Minuit minimum search program furnishes the most probable value E m and the width E 0 of the distribution, % and the product N B 2. The values of the parameters are: E m = 90 meV, E 0 = 70 meV, z0 = 1.7 × 10 -14 S, N B 2 = 3.207 X 1020 eV 2 cm -3 for the glass with x = 0.05; E m = 99 meV, E 0 = 5 0 meV, ,r0 = 4 . 5 × 1 0 -14 s, N B 2 = 1.218 × 1020 eV 2 cm -3 for the glass with x = 0.25. Typical fits of the relaxation loss are shown by continuous lines in fig. 2; the fits of experimental data taken at different frequencies give values of the parameters which differ only by a small amount, confirming the validity of the theoretical approach. The behaviour of the parameters indicates that the increased concentration of Sm203: (1) seems to decrease the degree of distortion of the glassy network. In fact the decrease of E 0 indicates a tendency of the system towards a single relaxation time process. Such a circumstance can be connected with an increasing degree of order in the system; (2) probably decreases the total number of relaxing particles. In fact, it is unusual that the observed decrease of the product N B 2 arises from a change of the deformation potential B; other systems, such as the silver borate glasses [11], show only small deviation around a mean value and no definite dependence on the composition;
[-~C-~] e=0 = 2 c l l [ d((Wl/d--~°' - 1) ] e=0 + - -Cll 3B s ,
+ - -G4 3B ~ , "~
P=0 = 2 3Cll
dP
d(Ws/Ws0 - 1) ] -4C44
dP
~ e=0'
where W and W0 are the natural velocity and its zero pressure value, respectively, and I and s refer to the longitudinal and shear ultrasonic modes respectively. The elastic constants of the 20 mol% Sm203P205 glass are almost independent of the temperature in the explored range. The bulk modulus B does show a small decrease as the temperature is reduced, an anomalous feature but much less pronounced than that observed in a (Sm203)0.1(P205)0.9 glass [7]. The elastic behaviour under pressure is a most unusual feature of the samarium phosphate glasses. The present results (fig. 3(a)) confirm the anomalous behaviour reported before [7,8] that at room temperature ~ C l l / ~ P , 3C44/3P and O B / 3 P are all negative. An interesting new finding is that there is a pronounced effect of temperature on these pressure derivatives of the
291
G. Carini et al. / Properties of rare earth phosphate glasses
(a) ,.. -O.t, E
~-0.6 ei/%
'--0.8 P
1
I
i
i !
I
I
J
l
0.0
elastic stiffness expected for an amorphous material is that found for TeO 2 glass [14], for which OCll/OP, 0C44/0Pand OB/OPare all positive and are almost independent of temperature. The dramatic increase in the negative values of OB/aP and aCla/OPof the samarium phosphate glasses show that the longitudinal acoustic modes soften under pressure and that this softening is enhanced as the temperature is reduced. A negative OCiJaP means that application of pressure leads to a decrease of the vibrational frequencies (oi associated with long wavelength acoustic modes. This effect can be quantified by recourse to the Gruneisen mode parameters 7i = - - d In ~ i / d In V,
which express the volume (or strain) dependence of the normal mode frequency oh. For an isotropic solid there are just two such Gruneisen parameters, namely 3q and 7s for longitudinal and shear elastic waves, respectively. These can be determined from the elastic constants and their hydrostatic pressure derivatives using
-i.0 "6 O -2.0
0-_3.
l
200
I
i
300
I
t.O0
l
500
T(K) Fig. 3. (a) The long wavelength acoustic mode Gruneisen parameters of (Sm203)o.2(P2Oh)o.8 glass. (b) The temperature dependence of the hydrostatic pressure derivatives of C]a, C,~ and the bulk modulus of (Sm203)o.2(P2Oh)o. 8 glass.
elastic stiffness modufi. Above about 320 K, OB/aP shows a small positive value. Although OCll/aP does not change much with temperatures > 320 K, it remains negative with a magnitude of about unity. The pressure derivative oc44/aP, which corresponds to the shear acoustic mode, retains a fairly constant small negative value over the whole temperature range of the study. In fact a small, and sometimes negative, ac44/aP also occurs in transition metal phosphate glasses and may well be due to mode softening associated with bond-bending interactions in the phosphate network [12,13]. However, the interesting feature of the results is the steep increase towards more negative values of 0 C l l / 0 P and OB/aP as the temperature is decreased below room temperature. The more usual behaviour under pressure of the
71
6Cll Bs [ 3 - [ - ~ 1
- 3[~-1
- 4[-~1
]
7~
6C44112C44-3BS[dd~]-3Bs+3cI2] (3)
The mean long wavelength acoustic mode Gruneisen parameter 7e~ is then given by: 7el = (71 + 27s)/3. These acoustic mode Gruneisen parameters vary markedly with temperature (fig. 3(b)). These results show that the large increase of acoustic mode softening as the temperature is reduced is not restricted to the longitudinal modes: both Y] and 7s, which have negative values over the entire temperature range 250 K to 450 K, become much larger as the temperature is reduced below 300 K. In certain rare-earth elements (Ce, Sm, Eu, Tm and Yb) the occupation number of the 4f shell can take on more than one value. The variable valence leads to a rich variety of anomalies in the physical properties of compounds or alloys of these elements. The 4f states are close in energy to the 5d and 6s states which serve as the valence orbitals.
292
G. Carini et al. / Properties of rare earth phosphate glasses
Two outer shell electronic configurations occur for samarium, namely 4f65d ° and 4f 55da and produce oxidation states of + 2 and + 3, respectively. Variable valence resulting from the f--* d electronic transition can be induced by applying pressure, alloying or changing temperature. As a consequence of atomic screening, the samarium ion size depends strongly on the valence. Decrease of the 4f occupation number by one occurs on transition of the valence state from 2 to 3 and causes an abrupt contraction in the samarium ion size: Sm 2÷ (4f 6) has an almost 20% larger ionic radius than Sm 3÷ (4f5). This decrease results in a strong coupling to phonons, particularly those in longitudinal modes, which in consequence are renormalized leading to a soft bulk modulus and phonon softening. Application of hydrostatic pressure to certain crystalline bivalent compounds can induce a valence transition towards a trivalent state via an intermediate valence state, in the case of SmS causing marked decreases in the bulk and longitudinal moduli [15]. For samarium phosphate glasses ~B/aP, ~Cll/~P and a c 4 4 / ~ P are negative. However the elastic behaviour under pressure of lanthanum phosphate glasses is normal in that they stiffen; lanthanum does not have a variable valence, its ion remains fixed in the 3 + state. N o w the R a m a n spectra of samarium phosphate glasses closely resemble those of other phosphate glasses, including those with lanthanum [7,8]. Thus the basic structural features of the samarium glasses are similar to those of other phosphate glasses. Hence the anomalous elastic properties of samarium phosphate glasses must be ascribed to the variable valence of the samarium ions rather than being due to a structural feature of the phosphate network. The negative values of O B / a P and OC11/OP can be understood on the basis that the effect of pressure is to cause the samarium ions to tend to change their oxidation states from + 2 towards the much smaller ion size associated with the + 3 state. As the temperature is reduced below 300 K this tendency for applied pressure to drive the f ~ d transition of the samarium ions becomes enhanced. The collapse in ion size couples to the acoustic modes producing a strong increase of acoustic mode softening as the temperature is reduced.
4. Summary The temperature behaviour of the acoustic attenuation of two samarium phosphate glasses reveals the presence of broad anelastic relaxation peaks, which are a c o m m o n feature of the acoustic behaviour of glassy oxides and are normally attributed to thermally activated local motions of structural defects. It is found that the additions of S m 2 0 3 to P205 decrease the magnitude of the observed acoustic anomalies, giving rise to structural modifications of the network which probably reduce the number of relaxing particles. The result is that it will be possible to identify the microscopic groups, which are involved in local motions, by an appropriate extension of this study to other concentrations of this glassy system. Moreover the elastic behaviour under pressure of these glasses is unusual, because the pressure derivatives of the elastic stiffness moduli and the Gruneisen parameters are negative and strongly temperature dependent; such glasses become easier to compress as pressure is increased. This behaviour is not typical of other phosphate glasses and of the amorphous materials, in which the pressure derivatives of elastic constants are usually positive and almost independent of temperature. Since the structure of samarium glasses is similar to that of other phosphate glasses, it is concluded that the anomalous behaviour under pressure m a y arise from valence instability of the samarium ions. We are very grateful to Mr B. Bridge for specimens, to Mrs W.A. L a m b s o n for assistance with sample preparation and to Mrs G. La Camera for carefull drawings. We would also like to thank Mr H.A.A. Sidek for useful discussions. One of the authors (W.Q.) would like to thank Zhejiang Normal University of the People's Republic China for financial support.
References [1] S. Hunklinger and W. Arnold, Physical Acoustic, Vol. XII, eds. W.P. Mason and R.N. Thurston (Academic Press, New York, 1976) p. 155.
G. Carini et al. / Properties of rare earth phosphate glasses [2] M. Dutoit, Phys. Lett. 50A (1974) 221. [3] R.E. Strakna and H.T. Savage, J. Appl. Phys. 35 (1964) 1445. [4] G. Carini Jr., M. Cutroni, G. Galli and F. Wanderlingh, J. Non-Cryst. Solids 30 (1978) 61. [5] G. Carini, M. Cutroni, M. Federico and G. Galli, J. Non-Cryst. Solids 64 (1984) 29. [6] O.L. Anderson and H.E. Bommel, J. Am. Ceram. Soc. 38 (1955) 125. [7] A. Mierzejewski, G.A. Saunders, H.A.A. Sidek and B. Bridge, J. Non-Cryst. Solids 104 (1988) 323. [8] H.A.A. Sidek, G.A. Saunders, R.N. Hampton, R.C.J. Draper and B. Bridge, Philos. Mag. Lett. 57 (1988) 49. [9] G. Carini, M. Cutroni, M. Federico and G. Tripodo, Phys. Rev. B 37 (1988) 7021.
293
[10] R.N. Thurston and K. Brugger, Phys. Rev. 133 (1964) A1604. [11] G. Carini, M. Cutroni, M. Federico, G. Galli and G. Tripodo, Phys. Rev. B30 (1984) 7219. [12] M.P. Brassington, A.J. Miller and G.A. Saunders, J. NonCryst. Solids 44 (1981) 157. [13] J.D. Comins, J.E. MacDonald, E.F. Lambson, G.A. Saunders, A.J. Rousell and B. Bridge, J. Mater. Sci. 22 (1987) 2113. [14] N. Benbattouche, G.A. Saunders and H.A. Sidek, Philos Mag. B60 (1989) 643. [15] T. Hailing, G.A. Saunders and H. Bach, Phys. Rev. B29 (1984) 1848.
Journal of Non-Crystalline Solids 121 (1990) 288-293 North-Holland
ELASTIC AND A N E L A S T I C P R O P E R T I E S O F RARE E A R T H P H O S P H A T E G L A S S E S G. C A R I N I , M. C U T R O N I , G. D ' A N G E L O , M. F E D E R I C O , G. G A L L I and G. T R I P O D O Dipartimento Fisica, Universita' di Messina, Ctrd. Papardo salita Sperone 31, 98010 S. Agata, Messina, Italy
G.A. S A U N D E R S and W A N G Q I N G X I A N School of Physics, University of Bath, UK
The behaviour of the ultrasonic attenuation between 10 K and 400 K in Sm203-P205 glasses is characterized by the presence of very broad peaks, due to thermally activated relaxations of structural defects, typical of amorphous materials. A study of these anomalies reveals that the addition of Sm203 to P205 has little influence on the mean activation energy of the relaxation process, but does cause a decrease in the number of relaxing particles. The effect of temperature on the anomalous negative hydrostatic pressure derivatives of the elastic moduli of samarium phosphate glass is also examined experimentally. Reduction of the temperature below 300 K causes aCn/aP and aB/OP to increase steeply to more negative values: both longitudinal and shear Gruneisen parameters, which are negative, become much larger. It is suggested that application of pressure drives the samarium ion f ~ d transition and that the ion size collapse couples to the acoustic modes, strongly enhancing acoustic mode softening.
1. Introduction The acoustic attenuation behaviour below the glass transition temperature, To, of almost all dielectric [1] and metallic [2] glasses shows a welldefined peak, not present in the corresponding crystals. The peak temperature increases with increasing frequency, following an Arrhenius-like law and as a consequence is normally attributed to thermally activated relaxations of structural defects, introduced by the topological disorder. The location of the peak temperature in the same frequency range seems to depend on the nature of bonds present in the glass. In fact the glassy oxides [1,3], characterized only by strong covalent bonds, show peaks at higher temperatures than the chalcogenide glasses [4,5], in which weak Van der Waals bonds are also present. However, despite extensive experimental evidence, the microscopic origin of the relaxing particle and its possible dependence on the stoichiometry are still unknown. Many interesting microscopic explanations [3,6] have been proposed for
the vitreous oxides, but they are only phenomenological and their validity has not been proved in a general way. To gain a further understanding of the problem, we have extended the range of investigated systems. Glasses of the Sm203-P205 system were chosen because specific structural information [7] is available which can help to gain an insight into the microscopic origin of the observed acoustic anomalies. Measurements have been made between 253 K and 453 K of the hydrostatic pressure dependences of ultrasonic velocities in (Sm203)0. 2(P2Os)0.8 glass to examine in detail the unusual temperature and pressure dependences of the elastic properties of these rare-earth glasses. When the samarium phosphate glasses are subjected to hydrostatic pressure, their bulk and shear moduli decrease, probably due to pressure dependent valence fluctuation of the samarium ion [8]. The negative pressure derivative of the bulk modulus B is particularly unusual: when compressed volumetrically these glasses become easier to squeeze!
0022-3093/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
G. Carini et aL / Properties of rare earth phosphate glasses
289
2. Experimental details o
o
O°o
o
o
The preparation and characterization of (Sm203)x(P2Os)l_ x glasses, x being the molar fraction, has been described elsewhere [7]. The acoustic attenuation of 10-70 MHz longitudinal sound waves was measured between 15 and 450 K by the experimental set-up previously described [9]. The ultrasonic velocity was measured using the pulse echo overlap technique. Ultrasonic pulses at a frequency of 10 MHz were generated by X- and Y-cut quartz transducers. The hydrostatic pressure dependences of the ultrasonic wave transit times, Tp, were measured in a piston and cylinder apparatus. The hydrostatic pressure was determined by measuring the change induced in the electrical resistance of a calibrated manganin wire coil inside the pressure chamber. The lowest temperature at which the ultrasonic measurements could be made was limited by the stringent requirement of ensuring that the pressure is indeed hydrostatic and therefore that the transmitting fluid remains liquid. The upper temperature was restricted by transducer bonding difficulties. To account for pressure induced changes in sample dimensions, the 'natural velocity' IV ( = loTp, where l 0 is the path length at atmospheric pressure) technique [10] was used, the experimental data being converted to a change of natural velocity ( I V / W o - 1). The pressure dependence of the relative changes in natural velocity of longitudinal and shear waves were found to be linear up to an applied maximum pressure (1.5 x 108 Pa).
i
o
o
•
I0
~
30
o
oE
°o
MHz
o70 0 0
o~
0
0 0
0
0
0
•
•
,< ._o
•
-e
I
eJlea.
•
•
*e
oo
•
•
•
•
•
200
400
T (K) Fig. 1. Temperature dependence of the longitudinal waves acoustic attenuation in the (Sm203)o.25(P2Os)0.75 glass. other dissipative processes, has been subtracted from the experimental data. An increase of Sm 203 concentration gives rise to a small increase in the peak temperature and a strong decrease in the peak height. Further, the peak width is significantly reduced by increased samarium oxide concentration. The observed relaxation peaks are much broader than a Debye peak, ruling out a single ralaxation time approach. This peculiarity, typical for the sub-To relaxations observed in glasses, can be interpreted as arising from the existence of a distribution of relaxation times due to random deviations in the local arrangement of
12 I n
3. Results and discussion 3.1. A c o u s t i c a t t e n u a t i o n
The behaviour with temperature of the acoustic attenuation at various frequencies in one of the glasses examined is shown in fig. 1. A very broad attenuation peak is observed, the temperature of which increases with increasing frequency, indicating a thermally activated relaxation process. In fig. 2 the relaxation losses at the same frequency (70 MHz) for the glasses 'with two different Sm203 contents are compared: a flat background, due to
._u 4 8
<
G
I
100
200 T (K)
300
Fig. 2. Comparison between the relaxation losses in the glasses with x = 0.05 and x = 0.25. The frequency of longitudinal ultrasounds is 70 MHz. The continuous line corresponds to the theoretical fit by eq. (1).
290
G. Carini et al. / Properties of rare earth phosphate glasses
the system. Since in a thermally activated process the relaxation time is defined by an activation energy E and a characteristic time ,to, , r = , r 0 e x p ( E / k T ) , a ,r-distribution corresponds to a distribution of E and ,ro. To provide a quantitative interpretation of the relaxation losses, we assume a single value for ,to, so that the ,r-distribution can be related to an E-distribution P ( E ) , which was taken as Gaussian; in this case, a useful form for the acoustic attenuation is [1,11]
(3) the energies involved in the relaxation process are little affected by an increase of samarium oxide concentration. The peculiarities revealed encourage us to extend our study to other concentrations of the Sm203-P205 system and to other phosphate glasses with different network modifier ions, in order to identify the structural units, which are present in the P205 glassy network and are subjected to thermally activated local motions.
NB2 (P wZ'r( E ) d(E). a = 4 p o 3 k T J ( E ) 1 + w2'rZ(E)
3.2. Elastic and anharmonic properties
(1)
The pressure derivatives of the elastic stiffness moduli were obtained using Here N is the total number of relaxing 'particles', B the deformation potential, v the sound velocity, w the angular frequency, T the absolute temperature and O the density. The least squares fit of the data by a Minuit minimum search program furnishes the most probable value E m and the width E 0 of the distribution, % and the product N B 2. The values of the parameters are: E m = 90 meV, E 0 = 70 meV, z0 = 1.7 × 10 -14 S, N B 2 = 3.207 X 1020 eV 2 cm -3 for the glass with x = 0.05; E m = 99 meV, E 0 = 5 0 meV, ,r0 = 4 . 5 × 1 0 -14 s, N B 2 = 1.218 × 1020 eV 2 cm -3 for the glass with x = 0.25. Typical fits of the relaxation loss are shown by continuous lines in fig. 2; the fits of experimental data taken at different frequencies give values of the parameters which differ only by a small amount, confirming the validity of the theoretical approach. The behaviour of the parameters indicates that the increased concentration of Sm203: (1) seems to decrease the degree of distortion of the glassy network. In fact the decrease of E 0 indicates a tendency of the system towards a single relaxation time process. Such a circumstance can be connected with an increasing degree of order in the system; (2) probably decreases the total number of relaxing particles. In fact, it is unusual that the observed decrease of the product N B 2 arises from a change of the deformation potential B; other systems, such as the silver borate glasses [11], show only small deviation around a mean value and no definite dependence on the composition;
[-~C-~] e=0 = 2 c l l [ d((Wl/d--~°' - 1) ] e=0 + - -Cll 3B s ,
+ - -G4 3B ~ , "~
P=0 = 2 3Cll
dP
d(Ws/Ws0 - 1) ] -4C44
dP
~ e=0'
where W and W0 are the natural velocity and its zero pressure value, respectively, and I and s refer to the longitudinal and shear ultrasonic modes respectively. The elastic constants of the 20 mol% Sm203P205 glass are almost independent of the temperature in the explored range. The bulk modulus B does show a small decrease as the temperature is reduced, an anomalous feature but much less pronounced than that observed in a (Sm203)0.1(P205)0.9 glass [7]. The elastic behaviour under pressure is a most unusual feature of the samarium phosphate glasses. The present results (fig. 3(a)) confirm the anomalous behaviour reported before [7,8] that at room temperature ~ C l l / ~ P , 3C44/3P and O B / 3 P are all negative. An interesting new finding is that there is a pronounced effect of temperature on these pressure derivatives of the
291
G. Carini et al. / Properties of rare earth phosphate glasses
(a) ,.. -O.t, E
~-0.6 ei/%
'--0.8 P
1
I
i
i !
I
I
J
l
0.0
elastic stiffness expected for an amorphous material is that found for TeO 2 glass [14], for which OCll/OP, 0C44/0Pand OB/OPare all positive and are almost independent of temperature. The dramatic increase in the negative values of OB/aP and aCla/OPof the samarium phosphate glasses show that the longitudinal acoustic modes soften under pressure and that this softening is enhanced as the temperature is reduced. A negative OCiJaP means that application of pressure leads to a decrease of the vibrational frequencies (oi associated with long wavelength acoustic modes. This effect can be quantified by recourse to the Gruneisen mode parameters 7i = - - d In ~ i / d In V,
which express the volume (or strain) dependence of the normal mode frequency oh. For an isotropic solid there are just two such Gruneisen parameters, namely 3q and 7s for longitudinal and shear elastic waves, respectively. These can be determined from the elastic constants and their hydrostatic pressure derivatives using
-i.0 "6 O -2.0
0-_3.
l
200
I
i
300
I
t.O0
l
500
T(K) Fig. 3. (a) The long wavelength acoustic mode Gruneisen parameters of (Sm203)o.2(P2Oh)o.8 glass. (b) The temperature dependence of the hydrostatic pressure derivatives of C]a, C,~ and the bulk modulus of (Sm203)o.2(P2Oh)o. 8 glass.
elastic stiffness modufi. Above about 320 K, OB/aP shows a small positive value. Although OCll/aP does not change much with temperatures > 320 K, it remains negative with a magnitude of about unity. The pressure derivative oc44/aP, which corresponds to the shear acoustic mode, retains a fairly constant small negative value over the whole temperature range of the study. In fact a small, and sometimes negative, ac44/aP also occurs in transition metal phosphate glasses and may well be due to mode softening associated with bond-bending interactions in the phosphate network [12,13]. However, the interesting feature of the results is the steep increase towards more negative values of 0 C l l / 0 P and OB/aP as the temperature is decreased below room temperature. The more usual behaviour under pressure of the
71
6Cll Bs [ 3 - [ - ~ 1
- 3[~-1
- 4[-~1
]
7~
6C44112C44-3BS[dd~]-3Bs+3cI2] (3)
The mean long wavelength acoustic mode Gruneisen parameter 7e~ is then given by: 7el = (71 + 27s)/3. These acoustic mode Gruneisen parameters vary markedly with temperature (fig. 3(b)). These results show that the large increase of acoustic mode softening as the temperature is reduced is not restricted to the longitudinal modes: both Y] and 7s, which have negative values over the entire temperature range 250 K to 450 K, become much larger as the temperature is reduced below 300 K. In certain rare-earth elements (Ce, Sm, Eu, Tm and Yb) the occupation number of the 4f shell can take on more than one value. The variable valence leads to a rich variety of anomalies in the physical properties of compounds or alloys of these elements. The 4f states are close in energy to the 5d and 6s states which serve as the valence orbitals.
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Two outer shell electronic configurations occur for samarium, namely 4f65d ° and 4f 55da and produce oxidation states of + 2 and + 3, respectively. Variable valence resulting from the f--* d electronic transition can be induced by applying pressure, alloying or changing temperature. As a consequence of atomic screening, the samarium ion size depends strongly on the valence. Decrease of the 4f occupation number by one occurs on transition of the valence state from 2 to 3 and causes an abrupt contraction in the samarium ion size: Sm 2÷ (4f 6) has an almost 20% larger ionic radius than Sm 3÷ (4f5). This decrease results in a strong coupling to phonons, particularly those in longitudinal modes, which in consequence are renormalized leading to a soft bulk modulus and phonon softening. Application of hydrostatic pressure to certain crystalline bivalent compounds can induce a valence transition towards a trivalent state via an intermediate valence state, in the case of SmS causing marked decreases in the bulk and longitudinal moduli [15]. For samarium phosphate glasses ~B/aP, ~Cll/~P and a c 4 4 / ~ P are negative. However the elastic behaviour under pressure of lanthanum phosphate glasses is normal in that they stiffen; lanthanum does not have a variable valence, its ion remains fixed in the 3 + state. N o w the R a m a n spectra of samarium phosphate glasses closely resemble those of other phosphate glasses, including those with lanthanum [7,8]. Thus the basic structural features of the samarium glasses are similar to those of other phosphate glasses. Hence the anomalous elastic properties of samarium phosphate glasses must be ascribed to the variable valence of the samarium ions rather than being due to a structural feature of the phosphate network. The negative values of O B / a P and OC11/OP can be understood on the basis that the effect of pressure is to cause the samarium ions to tend to change their oxidation states from + 2 towards the much smaller ion size associated with the + 3 state. As the temperature is reduced below 300 K this tendency for applied pressure to drive the f ~ d transition of the samarium ions becomes enhanced. The collapse in ion size couples to the acoustic modes producing a strong increase of acoustic mode softening as the temperature is reduced.
4. Summary The temperature behaviour of the acoustic attenuation of two samarium phosphate glasses reveals the presence of broad anelastic relaxation peaks, which are a c o m m o n feature of the acoustic behaviour of glassy oxides and are normally attributed to thermally activated local motions of structural defects. It is found that the additions of S m 2 0 3 to P205 decrease the magnitude of the observed acoustic anomalies, giving rise to structural modifications of the network which probably reduce the number of relaxing particles. The result is that it will be possible to identify the microscopic groups, which are involved in local motions, by an appropriate extension of this study to other concentrations of this glassy system. Moreover the elastic behaviour under pressure of these glasses is unusual, because the pressure derivatives of the elastic stiffness moduli and the Gruneisen parameters are negative and strongly temperature dependent; such glasses become easier to compress as pressure is increased. This behaviour is not typical of other phosphate glasses and of the amorphous materials, in which the pressure derivatives of elastic constants are usually positive and almost independent of temperature. Since the structure of samarium glasses is similar to that of other phosphate glasses, it is concluded that the anomalous behaviour under pressure m a y arise from valence instability of the samarium ions. We are very grateful to Mr B. Bridge for specimens, to Mrs W.A. L a m b s o n for assistance with sample preparation and to Mrs G. La Camera for carefull drawings. We would also like to thank Mr H.A.A. Sidek for useful discussions. One of the authors (W.Q.) would like to thank Zhejiang Normal University of the People's Republic China for financial support.
References [1] S. Hunklinger and W. Arnold, Physical Acoustic, Vol. XII, eds. W.P. Mason and R.N. Thurston (Academic Press, New York, 1976) p. 155.
G. Carini et al. / Properties of rare earth phosphate glasses [2] M. Dutoit, Phys. Lett. 50A (1974) 221. [3] R.E. Strakna and H.T. Savage, J. Appl. Phys. 35 (1964) 1445. [4] G. Carini Jr., M. Cutroni, G. Galli and F. Wanderlingh, J. Non-Cryst. Solids 30 (1978) 61. [5] G. Carini, M. Cutroni, M. Federico and G. Galli, J. Non-Cryst. Solids 64 (1984) 29. [6] O.L. Anderson and H.E. Bommel, J. Am. Ceram. Soc. 38 (1955) 125. [7] A. Mierzejewski, G.A. Saunders, H.A.A. Sidek and B. Bridge, J. Non-Cryst. Solids 104 (1988) 323. [8] H.A.A. Sidek, G.A. Saunders, R.N. Hampton, R.C.J. Draper and B. Bridge, Philos. Mag. Lett. 57 (1988) 49. [9] G. Carini, M. Cutroni, M. Federico and G. Tripodo, Phys. Rev. B 37 (1988) 7021.
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[10] R.N. Thurston and K. Brugger, Phys. Rev. 133 (1964) A1604. [11] G. Carini, M. Cutroni, M. Federico, G. Galli and G. Tripodo, Phys. Rev. B30 (1984) 7219. [12] M.P. Brassington, A.J. Miller and G.A. Saunders, J. NonCryst. Solids 44 (1981) 157. [13] J.D. Comins, J.E. MacDonald, E.F. Lambson, G.A. Saunders, A.J. Rousell and B. Bridge, J. Mater. Sci. 22 (1987) 2113. [14] N. Benbattouche, G.A. Saunders and H.A. Sidek, Philos Mag. B60 (1989) 643. [15] T. Hailing, G.A. Saunders and H. Bach, Phys. Rev. B29 (1984) 1848.