Giant Discharge Current in Thermally Poled Silicate Glasses - The

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Giant Discharge Current in Thermally Poled Silicate Glasses A. A. Lipovskii,†,‡ A. I. Morozova,‡ and D. K. Tagantsev*,‡,§ †

St. Petersburg Academic University, St. Petersburg 194021, Russia Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia § Research and Technological Institute of Optical Materials Science, St. Petersburg 192171, Russia ‡

ABSTRACT: Giant thermally stimulated depolarization currents (TSDCs) in poled silicate glasses have been observed above the glass transition temperatures, Tg, with such giant currents exceeding by 5−6 orders of magnitude ones observed up to now below Tg. In accordance with the given interpretation, these depolarization currents are conditioned by the relaxation (discharge) of the “frozen” volume charge, formed in glasses by poling, via the ion drift under the electric field as well as “frozen” in the poled glass. It is shown that the main portion of the “frozen” volume charge in poled glasses relaxes just via the ion drift mechanism. The closeness of the activation energy of this process and the activation energy of the viscous flow of the glass is revealed.

1. INTRODUCTION Thermally stimulated discharge or, the same, thermally stimulated depolarization current (TSDC) technique is in wide use to characterize charge accumulation and transport in dielectrics. The technique is based on measuring the thermal dependence of relaxation current in a polarized medium, which allows deducing activation energy and relaxation time of corresponding discharge/depolarization processes, and it was effectively applied to study different electrets, mainly polymers1,2 and crystals, including ferroelectrics3,4 and various composite materials.5,6 Generally, the TSDC approach is capable of sensing such polarization-related phenomena as the orientation of dipoles and ferroelectric domains, separation of charge carriers, and their trapping by defects and interfaces of a material. In all these cases, the first step of the TSDC study is the polarization of a medium by dc voltage applied at elevated temperature, while the second step supposes secondary heating of the medium, which allows activating medium depolarization and measuring corresponding current. Although being developed mainly for organic polymers, during the last three decades TSDC analysis is used to distinguish mobile cations in inorganic glasses and to find their activation energies.7,8 After the demonstration of “noncentralsymmetric” properties of thermally poled glasses, such as the second harmonic generation and the linear electrooptic sensitivity,9,10 many efforts were made to study the phenomenon of thermal poling, and this included TSDC studies, e.g., refs 8 and 11−13. These studies were mainly aimed at the deduction of the activation energies characterizing the behavior of cations in studied glasses. Specific features of most studies, except the work by A. Obata and coauthors,14 are (1) the pico- or nanoampere scale of the discharge currents corresponding to accordingly low electric currents returned by the poled glasses and (2) the range of temperatures lying essentially below the © 2016 American Chemical Society

glass transition temperature, Tg. At the same time the electric currents of glass poling fall in the range of hundreds of microamperes per square centimeter.15 This shows an incomplete depolarization of poled glasses in all earlier performed TSDC measurements except that reported in ref 14. Additionally, TSDC studies of polymers have shown the importance of the experiments at temperatures in the Tg region.16,17 In this paper we report extremely high depolarization currents observed in poled silicate glasses above Tg (550−800 °C). The measured currents were found to be 5−6 orders of magnitude higher than the ones reported in the aforementioned TSDC studies of similar glasses below Tg (200−500 °C). It appears that the complete depolarization of poled glasses takes place at temperatures above Tg only. Generally, this should open new insights into the interpretation of the origin of second harmonic generation phenomena in poled multicomponent glasses. In this connection, it is worth recollecting that the TSDC technique implies that the depolarization current is the result of a spontaneous release of the trapped charge carriers (or dipoles) in the polarized media. This release (charge relaxation, in other terms) is considered to obey the first-order kinetics, that is ⎛ t⎞ Q (t ) = Q 0 exp⎜ − ⎟ ⎝ τ⎠

(1)

where Q(t) is the rest of the trapped charge; Q0 is the charge trapped just after the polarization procedure (at t = 0); and τ is the relaxation time which is Arrhenius’ function of temperature: Received: July 18, 2016 Revised: August 24, 2016 Published: September 15, 2016 23129

DOI: 10.1021/acs.jpcc.6b07144 J. Phys. Chem. C 2016, 120, 23129−23135

Article

The Journal of Physical Chemistry C

capable of migrating under applied electric field; it was univalent ions of sodium (Na+). Another glass (Menzel microscope slides25) was a silicate glass, but it contained two types of ions capable of migration: univalent sodium and potassium ions (Na+ and K+) and bivalent ions of calcium and magnesium (Ca2+ and Mg2+). Compositions of the selected glasses are presented in Table 1.

τ(T) = τ0 exp(W/kT), where W is the activation energy, k the Boltzmann constant, T the absolute temperature, 1/τ = ω the relaxation frequency, and 1/τ0 the phonon frequency ω0 (ω0 = 1/τ0). The ratio t/τ in eq 1 can be presented as ωt (t/τ = ωt), and it is the number of the relaxation acts (releases of one charge carrier) having taken place by time t. Thus, in the case of nonisothermal conditions, when T = T(t) and therefore τ(t) = τ(T(t)), eq 1 takes the form ⎛ Q (t ) = Q 0 exp⎜ − ⎝

∫0

t

Table 1. Composition of the Used Glasses in Molar % of Oxides

⎞ 1 dt ⎟ τ (t ) ⎠

(2)

Respectively, the depolarization current, I, is I = dQ/dt. In the case of a linear temperature increase, differentiating eq 2 by time results in the dependence of the depolarization current on temperature in the following form ⎛ W Q 1 − I(T ) = 0 exp⎜ − τ0 uτ0 ⎝ kT

∫0

T

⎛W ⎞ ⎞ exp⎜ ⎟dT ⎟ ⎝ kT ⎠ ⎠

SA7 Menzel

1 uI(T )

∫T

(3)

∞

I(T )dT

Al2O3

B2O3

Na2O

K2O

MgO

CaO

others

12.5 72.2

35 1.2

17.5 -

35 14.3

1.2

4.3

6.4

0.33

In accordance with the performed viscosity measurements, the glass transition temperatures Tg of these glasses were 550 and 565 °C for SA7 and Menzel glasses, correspondingly. These temperatures are the ones at which glass viscosity is equal to 1012 Pa·s. Samples for dc polarization were 1 mm thick and 30 mm long and wide (area 900 mm2). Anodic and cathodic electrodes were made of carbon of high density (MPG7 in Russian nomenclature), and anode and cathode surfaces were polished. Anode and cathode areas were about 15 × 15 mm2 and 40 × 40 mm2, correspondingly. The temperature of glass polarization was 275 °C, and the applied voltage was 2 kV. The polarization was performed in ambient atmosphere up to the moment when the polarization current ceased to change. Examples of the time dependence of polarization currents in glasses SA7 and Menzel are presented in Figure 1. We attributed the currents observed after 100−120 min (in Figure 1) to the surface conductivity. After poling, the samples were cooled to room temperature under applied voltage. Then the voltage was off, and the samples were being heated with a constant heating rate. When heating, the depolarization current was measured. Accuracy of the current measurements was ±1 μA, so that we could not measure currents typical (nA and pA) for almost all TSDC studies of poled glasses performed by other researchers below Tg (below 500 °C). In our experiments, measurable currents appeared in the vicinity and above Tg only. The results of two depolarization experiments for both glasses are presented in Figure 2. One can see that the reproducibility of these experiments is not good enough, but a set of the specific features of the TSDC curves for each glass do not differ. First, one can see that the number of bands in the TSDC spectra of SA7 and Menzel glasses differs. Definitely, there are two bands in both TSDC spectra of glass Menzel and only one for glass SA7. The bands do not have shapes which could be approximated by the function predicted by the theory, that is, by eq 3. We believe that it is due to the problem of electrode contacts. Indeed, used electrodes are made of carbon. Above 600 °C carbon is known to undergo oxidation, and this (and other reasons) leads just to the instability in electrode contacts. We would not like to discuss the contact problem here. Moreover, we did not try to solve this problem; instead, we have performed several similar experiments resulting in the TSDC spectra which were found not to differ in the following (see Figure 2, where blue and red symbols belong to two similar experiments): (1) the rise of depolarization currents starts at the same temperature, (2) the maxima of the TSDC bands are observed at the same temperatures, and (3) the depolarization currents vanish at the same temperatures.

where u is the heating rate dT/dt. Here we used that τ(T) = τ0 exp(W/kT) and dt = dT/u. Equation 3 was first reported in ref 18. This dependence looks like a spectral band, and it can be used for calculating a tabulated dependence τ(T) by the area method14 as follows τ (T ) =

SiO2

(4)

Because τ(T) = τ0 exp(W/kT), being plotted in coordinates (ln τ, 1/kT), this tabulated dependence τ(T) (actually, the tangent of the slope of this dependence) gives the value of the activation energy W, that is, the depth of the potential wall for trapped charge carriers (ions). It should be noted that the area method additionally gives values of ω0 = 1/τ0 which, in general, should be seen as spectral bands in infrared spectra. In the case of poled glasses, depolarization currents observed during a linear heating are related to the relaxation of volume charge which, in accordance with ref 19, is “frozen” in the subsurface anodic layers of poled glasses. We consider the observed depolarization currents in poled glasses being related to the redistribution of the “frozen” ions that results in bringing the system to the thermodynamically equilibrium state. In accordance with TSDC studies performed below Tg, the revealed values of W are typical for ion diffusivity in glasses; for the relaxation of univalent ions they fall between 0.7 × 10−19 and 1.3 × 10−19 J.16,20,21 These temperatures coincide with ones at which relaxation bands in the spectra of internal friction in glasses appear, which are identified with the losses related to the migration of univalent ions through a diffusion or hopping mechanism.22−24 In this view, the observation of depolarization currents in TSDC experiments above Tg does not fall in the ideology of the TSDC technique because the relaxation of “frozen” volume charge going with activation energies equal to about (1 ± 0.3) × 10−19 J must be completed before achieving temperatures close to Tg. Below we report our experiments in which we have observed high TSDC peaks above Tg and give our interpretation of the mechanisms of relaxation of “frozen” volume charge in poled glasses in the mentioned temperature region.

2. EXPERIMENTAL AND RESULTS Two glasses were used in our experiments. One glass (lab glass SA7) was a borosilicate glass containing only one type of ion 23130

DOI: 10.1021/acs.jpcc.6b07144 J. Phys. Chem. C 2016, 120, 23129−23135

Article

The Journal of Physical Chemistry C

Figure 1. Dependence of polarization current in SA7 (left) and Menzel (right) glasses on time.

Figure 2. Thermally simulated depolarization currents in poled Menzel (left) and SA7 (right) glasses at fixed heating rates. The heating rates are indicated in the graphs.

Generally speaking, the electrode processes supposedly related to the reaction of carbon oxidation could result in the appearance of additional electric currents which could decorate the currents related to the studied depolarization processes. However, additional TSDC experiments with nonpoled glasses showed that these decorating currents do not exceed 20 μA (for SA7) and, therefore, are negligibly small compared to the total currents (up to 800 μA in SA7 glass). In spite of these general conclusions, one can see that it is difficult to determine the shapes of the components (TSDC bands) comprising the two-headed depolarization current function for glass Menzel depicted in Figure 2. The shape of such function for SA7 glass, which has one maximum only, is more obvious. We drew by eye a curve averaging the experimental curves obtained in two experiments (see the dashed curve for SA7 glass in Figure 2) and exploited it for calculating the temperature dependence of the volume charge relaxation time, using eq 4. Relaxation times were calculated for four temperatures, and the resultant dependence τ(T) is presented in Figure 3. One can see that this dependence in coordinates (ln τ, 1/T) is a linear one, and therefore, it can be used for calculating the activation energy of the relaxation process, W, which in the case of SA7 glass was assumed to be related to the migration of sodium ions: W = k × d(ln τ)/d(1/T). The calculated value of the activation energy proved to be equal to 3.2 × 10−19 J. This value casts doubt upon this assumption because typical activation energies of the migration of sodium ions in oxide glasses are equal to about 1 × 10−19 J.

Figure 3. Temperature dependence of the relaxation time of depolarization process in poled SA7 glass.

Finally, it should be emphasized that: (1) unlike the studies performed before this research all TSDC bands are observed above Tg, (2) the depolarization currents in both studied glasses exceed by 5−6 orders of magnitude the ones measured in the very similar glasses at temperatures below Tg by other researchers, and (3) the maximal depolarization current in SA7 glass exceeds the one in Menzel glass, while the total areas under the depolarization current bands in these glasses are about the same. The latter correlates with total concentrations 23131

DOI: 10.1021/acs.jpcc.6b07144 J. Phys. Chem. C 2016, 120, 23129−23135

Article

The Journal of Physical Chemistry C

∇[μ(x,y,z) + U(x,y,z)] = 0), where μ is the chemical potential of the ions, U the potential of any other field (it could be gravity, or for charged particles, it could be the electric field). The polarization procedure results in a disturbance of thermodynamic equilibrium; moreover, it is known to be accompanied by the appearance of the “frozen” electric field.19,30−32 This disturbance provokes a particle flux, j, which returns the system to the equilibrium state. The driving forces of this process are the gradients of μ and U, where U is the potential of the “frozen” electric field. In the linear approximation, this flux in one-dimensional form can be expressed via the following relation: j = −γ∇[μ(x) + U(x)] = −γ∇μ(x) − γ∇U(x), where γ is the constant related to the glass properties. The flux can be presented as the sum of two contributions: j = jμ + jU = nvμ + nvU, where n is the particle concentration and vμ and vU are the particle velocities, related to the chemical and electric driving forces, so that

of ions capable of migration under applied voltagein SA7 glass they are ions of sodium only, and in Menzel glass they are ions of sodium and potassium, as well as calcium and magnesium. In Menzel glass the total concentration (in molar %) of all oxides of movable elements (glass modifiers) multiplied by their valences is 36.5, while in SA7 glass this is 35; that is, the amount of movable charges related to modifying ions in these glasses is about the same.

3. DISCUSSION In our study we have determined the activation energy of the relaxation time of “frozen” violume charge only for poled SA7 glass, which proved to be equal to 3.2 × 10−19 J. The two TSDC bands observed in Menzel glass lie about at the same temperatures, and therefore, the activation energies of charge relaxation in Menzel glass should have about the same values as was found for SA7 glass. Unlike the activation energies typical for ion hopping (diffusion) mechanism (about 1 × 10−19 J), the found activation energies in the glasses under study are typical for the process of viscous flow in oxide glasses (including silicate ones) where the kinetic units are bridging (and nonbridging) oxygen atoms, and the elementary kinetic act is considered the switching of such oxygen atoms.26 This fact makes us assume that the viscous flow of the glass matrix should be involved in the process of “frozen” charge relaxation. Moreover, comparing the absolute values of depolarization currents measured below Tg (200−500 °C) and above Tg (550−800 °C) makes us conclude that most of the “frozen” volume charge relaxes just above Tg. The study on the annealing of poled glasses below Tg27 is in favor of this conclusion because the annealing did not result in ion concentration leveling. At the same time, in refs 27 and 28 one finds that after annealing quite below Tg or even after the exposition at room temperature the second harmonic generation (SHG) signal from the poled multicomponent glasses essentially decreases which is not in consonance with the absence of ion concentration leveling.27 This indicates that there could be other mechanisms of forming optical nonlinearity during glass poling, which could be responsible for SHG and its relaxation at low temperatures. It appears to be a challenge to be resolved in a separate research. It appears essential to mention that (in accordance with thermodynamics) in the depolarization process the charged particles (ions) should move back to the material space (subsurface anodic layers) where they resided before the polarization, but this space dramatically differs from the one in which these particles moved in the polarization process. In particular, the subsurface anodic layers are known19 to be depleted of the host movable ions (ion modifiers) of the initial glass. In addition, it is also known that the polarization process results in the decrease of the glass volume29 and, therefore, in the decrease in the free volume necessary for the realization of the ion-exchange diffusion (or hopping) mechanism. At the same time, the presence of the “frozen” electric field in poled glasses switches on the drift mechanism of the charged particle motion. Given the aforementioned speculations, the process of volume charge relaxation in poled glasses can be described as follows. First, let the glass contain only one type of charged particles (ions) capable of migrating. In the initial (unpoled) glass there is a thermodynamic equilibrium to which corresponds the condition: μ(x,y,z) + U(x,y,z) = const (or

jμ = nvμ = −γ ∇μ(x) = −γ where D = γ

dμ dn dn = −D , dn dx dx

dμ dn

and jU = nvU = −γ ∇U (x) = −γF = −γqzE

where ∇U = F = qzE is the force acting on the charged particle (ion); q is the electron charge; z is the valence of the ion; and E is the “frozen” electric field. One can see that vU = −ζF, where the value ζ = γ/n is the constant of proportionality between particle velocity and acting force. By definition, such a constant is called the mobility. It should be noted that, allowing for the relation between chemical potential and concentration (μ ∼ kT ln n) and combining the obtained expressions for D = γdμ/ dn and ζ = γ/n, we get the well-known Einstein relation, that is, ζ = D/kT. At the same time, for the steady process we can accept that the force, acting on a particle, F (or qzE), is equal to the friction force, which for spherical particles of radius r, following Stokes,33 is equal to 6πrηv, where η is the viscosity of the medium through which a spherical particle moves with velocity v. Thus, in our case, we can write qzE = 6πrηvU and, therefore, vU = (qzE)/(6πrη), so that jU = nvU = nζqzE, where ζ proves to be equal to 1/6πrη. Finally, we come to the expression for the total particle flux in the following form: qzE dn j = jμ + jU = −D dx + n 6πrη . If there are i types of charged (+ and − ) particles34 taking part in the relaxation of the volume charge in poled glasses, the total flux, J, is J=

∑ ji i

= −∑ Di i

dni 1 qE + dx η 6π

∑ i

zini ri

(5)

Here E and ni are functions of x. At the same time, both E and ni are not independent values; their interrelation is controlled by the Poisson’s equation (div εE = ρ(x)) which in the oneq dE dimensional case has the form dx = ε ∑i zini(x), where we assume that the distribution of volume charge ρ is defined by the expression ρ(x) = q ∑i zini(x) (ε is the permittivity). After integration, the Poisson’s equation takes the form x q E(x) = ε ∑i ∫ zini dx . Finally, after substitution of E in eq 5 0 with this expression for E(x) we have 23132

DOI: 10.1021/acs.jpcc.6b07144 J. Phys. Chem. C 2016, 120, 23129−23135

Article

The Journal of Physical Chemistry C J(x) = −∑ Di i

2 dni 1 q + (∑ dx η 6πε i

∫0

x

⎛ zn ⎞ zini dx)⎜⎜∑ i i ⎟⎟ ⎝ i ri ⎠

depolarization currents related to the diffusion mechanism and the areas under the TSDC bands (observed below 500 °C) are several orders of magnitude less than the ones observed in our research above Tg (550−800 °C), it is reasonable to assume that the main part of the “frozen” volume charge, resulting from the polarization procedure, relaxes through the drift mechanism which works above Tg only. Rather low depolarization currents conditioned by the first term in eq 6 (at T < Tg) are supposed to be related to the fact that the migration of charged particles (that is, diffusion of trapped ions) in glasses goes through an ion-exchange diffusion mechanism, but the polarized subsurface layers contain very small amounts of the ions capable of exchanging, so that the majority of the trapped ions, forming the volume “frozen” charge, relaxes through the drift mechanism which, in accordance with eq 6, works only above Tg. In this connection, there is a reason to introduce a value characterizing relative cross sections of the two relaxation channels (mechanisms). Let it be α, with 0 < α < 1. We introduce this value in eq 6 as follows

(6)

where only ni are functions of x. Here we have neglected that η can be a function of x as well. Because we consider all the particles being charged, J(x) is a function describing the space distribution of the total charge flux (internal electric current) in the depleted anode layer. Discharge of the “frozen” volume charge takes place when anode and cathode surfaces of a poled glass are in short-circuit mode, and the observed depolarization currents characterize just this process. Kinetics of the charge redistribution is controlled by the condition of the total charge conservation, in other words, by the equation of continuity d dt

∑ qzini + div J(x) = 0 i

(7)

This equation should be supplemented by boundary conditions and initial condition for each n, that is, by functions nt=0 = f(x). Actually, the set of the functions f(x) describes the space distribution of all charged particle concentrations in the poled glass, and the solution of eq 7 at x = 0 gives the time dependence of the depolarization current in the poled glass at constant temperature. However, not solving eq 7, the structure of eq 6 allows us to make several general inferences which can help one to understand the mechanisms of relaxation of “frozen” volume charge in poled glasses and interpret TSDC spectra in the whole temperature range, from T < Tg to T > Tg. Equation 6 comprises two terms. The first term is related to the diffusion flux controlled by the gradients of chemical potentials of the particles involved in the glass polarization process. It is the term that is just responsible for the appearance of the TSDC bands described by eq 3. The second term is related to the drift of charged particles under the action of the “frozen” electric field. Both terms are functions of temperature: temperature dependence of the first term is defined by the set of temperature dependences of the diffusivities Di and the one of the second term by the temperature dependence of the glass viscosity η. In eq 6, coefficients Di and 1/η are the Arrhenius functions of temperature, that is, ∼exp(−W/kT), where W are the activation energies of the corresponding processes (WDi for diffusion and Wη for viscous flow). In silicate glasses, the typical activation energy of viscous flow exceeds the one of ion diffusion by 2−3 times, so that, in linear heating, the same values of the coefficients Di and 1/η are achieved at different times (temperatures). In accordance with this deduction, in TSDC spectra the bands of the depolarization current related to the diffusion mechanism (to the first term of eq 6) appear at lower temperatures, while the bands related to the electric-fieldstimulated drift mechanism (to the second term of eq 6) appear at higher temperatures. It is easy to show that if typical activation energies WDi and Wη differ by 2−3 times and maxima of TSDC bands related to the diffusion mechanism appear at 200−400 °C (T < Tg), the maxima of bands related to the drift mechanism should be seen at 500−800 °C (just at T > Tg). To the best of our knowledge, all TSDC studies of poled glasses (maybe, except ref 14) were restricted by the upper limit of heating equal to 500 °C. Thus, in those studies, the TSDC bands related to the diffusion mechanism could be observed only. Taking into consideration that both the typical

J(x) = −α ∑ Di i

2 dni 1−α q + (∑ dx η 6πε i

∫0

x

zini dx)×

⎛ zn ⎞ ⎜⎜∑ i i ⎟⎟ ⎝ i ri ⎠

In accordance with the above-mentioned speculations, value α should be equal to the typical ratio between the total areas under the low-temperature TSDC bands and the ones of the high-temperature bands, that is, α = 10−5−10−6. It is worth to note that the charge redistribution process kills the electric field, so that the drift mechanism ceases to work. This deduction causes one to assume that α should be a function of time. In addition, radii of ions Na+, K+, Ca2+, and Mg2+, which are contained in glasses under our study, are 0.98, 1.33, 1.04, and 0.74 Å, correspondingly;35 that is, their radii do not differ more than ±30%. Therefore, the drift velocities of these ions are mainly conditioned by their charges (valence), in other words, by the values zi in the second term of eq 6. Note that the charge of ions Na+ and K+ is twice less than the one of Ca2+ and Mg2+. In such a case, the low-temperature (at 580 °C) band of the TSDC spectrum of glass Menzel (Figure 2), which contains all mentioned ions, should be attributed to the drift of the bivalent ions of calcium and magnesium and the high-temperature band (at 670 °C) to the drift of sodium and potassium ions. This inference contradicts data on TSDC studies performed at temperatures not exceeding T g , where volume charge relaxation, in accordance with our conclusions, should be related to the hopping (diffusion) mechanism. In case the only diffusion mechanism works (this corresponds to the TSDC spectra measured in the temperature range below Tg), the TSDC bands conditioned by the relaxation of the volume charge related to the migration of univalent ions should appear first, that is, at lower temperatures as compared to the temperatures at which diffusion of bivalent ions takes place. Verification of this conclusion needs additional study.

4. CONCLUSIONS Two silicate glasses were poled and then studied by the TSDC technique above their glass transition temperatures, Tg. One glass (SA7) contained only univalent ions capable of migrating (Na+), while another glass (Menzel) contained two types of 23133

DOI: 10.1021/acs.jpcc.6b07144 J. Phys. Chem. C 2016, 120, 23129−23135

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The Journal of Physical Chemistry C capable of migrating ions, namely; in addition to univalent Na+ and K+, it contained bivalent ions Ca2+ and Mg2+. It was found that the depolarization currents observed in the present study (above Tg) exceed by 105−6 times ones observed below Tg by other researchers and that glass SA7 demonstrates only one band (peak) in the TSDC curve and glass Menzeltwo. Such giant depolarization currents above Tg compared to the ones observed below Tg evidence that the main portion of the “frozen” volume charge in poled glasses relaxes just above Tg. It was shown that the number of high-temperature bands in TSDC curves of studied glasses is conditioned by the number of movable ions, which differ in their charges (valences), rather than simply the number of ions capable of migrating. In accordance with the proposed interpretation, the giant depolarization currents observed above Tg and related to the relaxation of the “frozen” volume charge formed during the glass polarization procedure are conditioned by the ion drift under the action of the “frozen” electric field. The activation energy of this process is close to the activation energy of the viscous flow of silicate glasses. Volume charge relaxation below Tg via this mechanism cannot take place because of too high viscosity of silicate glasses at these temperatures. In our opinion, presented results should open new insights into the interpretation of the origin of second harmonic generation phenomena in poled multicomponent glasses.

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(10) Long, X.-C.; Myers, R. A.; Brueck, S. R. J. Measurement of the linear electro-optic coefficient in poled amorphous silica. Opt. Lett. 1994, 19 (22), 1819−1821. (11) Topic, M.; Music, S.; Ristic, M. The use of windowing polarization for the study of multi-component glass. Mater. Chem. Phys. 2004, 87, 311−317. (12) Mariappan, C. R.; Roling, B. Investigation of bioglass-electrode interfaces after thermal poling. Solid State Ionics 2008, 179, 671−678. (13) Mariappan, C. R.; Yunos, D. M.; Baccaccini, A. R.; Roling, B. Bioactivity of electro-thermally poled bioactive silicate glass. Acta Biomater. 2009, 5, 1274−1283. (14) Obata, A.; Nakamura, S.; Yamashita, K. Interpretation of electrical polarization and depolarization mechanisms of bioactive glasses in relation to ionic migration. Biomaterials 2004, 25, 5163− 5169. (15) Redkov, A. V.; Melehin, V. G.; Lipovskii, A. A. How does thermal poling produce interstitial molecular oxygen in silicate glasses? J. Phys. Chem. C 2015, 119 (30), 17298−17307. (16) Shimizu, H.; Nakayama, K. Relaxation phenomena in the vicinity of the glass transition of poly-(p-phenylene sulfide). J. Appl. Phys. 1993, 74 (3), 1597−1605. (17) Henn, F.; Giuntini, J.-C.; Bisquet, J.; Garcia-Belmonte, G. An explanation of the peculiar behavior of TSDC peaks at Tg: a simple model of entropy relaxation. IEEE Trans. Dielectr. Electr. Insul. 2006, 13 (5), 1042−1048. (18) Bucci, C.; Fieschi, R. Ionic thermoconductivity. Method for the investigation of polarization in insulators. Phys. Rev. Lett. 1964, 12, 16. (19) Lepienski, C. M.; Giacometti, J. A.; Leal Ferreira, G. F.; Freire, F. L., Jr.; Achete, C. A. Electric field distribution and near-surface modifications in soda-lime glass submitted to a DC potential. J. NonCryst. Solids 1993, 159 (3), 204−212. (20) Suszynska, M.; Krajczyk, L.; Capelletti, R.; Baraldi, A.; Berg, K.-J. Microstructure and silver nanoparticles in ion-exchanged and deformed soda-lime silicate glasses. J. Non-Cryst. Solids 2003, 315, 114−123. (21) Graca, M. P. F.; Ferreira da Silva, M. G.; Valente, M. A. NaNbO3 crystals dispersed in a B2O3 glass matrix - Structural characteristics versus electrical and dielectrical properties. Solid State Sci. 2009, 11, 570−577. (22) Nemilov, S. V. Ageing kinetics and internal friction of oxide glasses. Glass Sci. Technol. 2006, 78 (6), 269−278. (23) Mazurin, O. V.; Strel’tsina, M. V.; Shvaiko-Shvaikovskaja, T. P. Properties of glasses and glass-forming melts, Handbook; Science (Nauka): Leningrad, 1977. (24) Zdaniewski, W. A.; Rionone, G. E.; Day, D. E. The internal friction of glasses. J. Mater. Sci. 1979, 14 (4), 763−775. (25) www.menzel.de (accessed July 18, 2016). (26) Nemilov, S. V. Thermodynamic and Kinetic Aspects of the Vitreous State; CRC: Boca Raton, FL, 1995. (27) An, H.; Fleming, S. Second-order optical nonlinearity and accompanying near-surface structural modifications in thermally poled soda-lime silicate glasses. J. Opt. Soc. Am. B 2006, 23 (11), 2303−2309. (28) Qiu, M.; Pi, F.; Orriols, G.; Bibiche, M. Signal damping of second-harmonic generation in poled soda-lime silicate glass. J. Opt. Soc. Am. B 1998, 15 (4), 1362−1365. (29) Redkov, A. V.; Melehin, V. G.; Statcenko, V. V.; Lipovskii, A. A. Nanoprofiling of alkali-silicate glasses by thermal poling. J. Non-Cryst. Solids 2015, 409, 166−169. (30) Doremus, R. H. Mechanism of electrical polarization of silica glass. Appl. Phys. Lett. 2005, 87, 232904. (31) An, H.; Fleming, S. Second-order optical nonlinearity in thermally poled Pyrex borosilicate glass. Opt. Commun. 2008, 281, 1263−1267. (32) Dussauze, M.; Rodriguez, V.; Lipovskii, A.; Petrov, M.; Smith, C.; Richardson, K.; Cardinal, T.; Fargin, E.; Kamitsos, E. I. How does thermal poling affect the structure of soda-lime glass? J. Phys. Chem. C 2010, 114, 12754−12759. (33) Batchelor, G. K. An introduction to fluid dynamics; Cambridge University Press: 1967.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research was supported by Russian Scientific Foundation, grant #16-12-10044.

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REFERENCES

(1) van Turnhout, J. Thermally Stimulated Dischage Of Electrets. In Electrets; Sessler, G. M., Ed.; Springer-Verlag: Berlin-Heidelberg-New York, 1980. (2) Menczel, J. D.; Prime, R. B. Thermal Analysis of Polymers: Fundamentals and Applications; John Wiley & Sons: 2014. (3) Xu, Y. Ferroelectric Materials and Their Applications; Elsevier: 2013. (4) Borstel, G.; Krumins, A.; Millers, D. Defects and Surface-Induced Effects in Advanced Perovskites; Springer Science & Business Media: 2012. (5) Zhang, X.; Yue, Z.; Peng, B.; Xie, Z.; Yuan, L.; Zhang, J.; Li, L. Polarization response and thermally stimulated depolarization current of BaTiO3-based Y5V ceramic multilayer capacitors. J. Am. Ceram. Soc. 2014, 97, 2921−2927. (6) Rathore, B. S.; Gaur, M. S.; Singh, K. S. Investigation of optical and thermally stimulated properties of SiO2 nanoparticles-filled polycarbonate. J. Appl. Polym. Sci. 2012, 126, 960−968. (7) Bhuiyan, A. H.; Ahmed, S. hermally stimulated depolarization current in sodium-potassium borosilicate glass. J. Non-Cryst. Solids 1981, 43 (3), 353−363. (8) Dash, P.; Furman, E.; Pantano, C. G.; Lanagan, M. T. Activation energy for alkaline-earth ion transport in low alkali aluminoborosilicate glasses. Appl. Phys. Lett. 2013, 102, 082904. (9) Okada, A.; Ishii, K.; Mito, K.; Sasaki, K. Phase-matched secondharmonic generation in novel corona poled glass waveguides. Appl. Phys. Lett. 1992, 60 (23), 2853−2855. 23134

DOI: 10.1021/acs.jpcc.6b07144 J. Phys. Chem. C 2016, 120, 23129−23135

Article

The Journal of Physical Chemistry C (34) If glass poling takes place in ambient atmosphere, they could be not only host cations of the glass but also negative charged nonbridging oxygen [D. E. Carlson, K. W. Hang, G. F. Stockdale, J. Am. Ceram. Soc. 1972, 55, 337−341] or hydronium coming to the glass from atmosphere also [R. H. Doremus, Appl. Phys. Lett. 2005, 87, 232904]. (35) Bugaenko, L. T.; Ryabykh, S. M.; Bugaenko, A. L. A nearly complete system of average crystallographic ionic radii and its use for determining ionization potentials. Moscow Univ. Chem. Bull. 2008, 63 (6), 303−317.

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DOI: 10.1021/acs.jpcc.6b07144 J. Phys. Chem. C 2016, 120, 23129−23135