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In this work the time resolved thermal lens method is combined with interferometric technique, the thermal relaxation calorimetry, photoluminescence and lifetime measurements to determine the thermo physical properties of Nd2O3 doped sodium zincborate glass as a function of temperature up to the glass transition region. Thermal diffusivity, thermal conductivity, fluorescence quantum efficiency, linear thermal expansion coefficient and thermal coefficient of electronic polarizability were determined. In conclusion, the results showed the ability of thermal lens and interferometric methods to perform measurements very close to the phase transition region. These techniques provide absolute values for the measured physical quantities and are advantageous when low scan rates are required.
©2008 Optical Society of America
1. Introduction
It is well recognized that the measurement of the thermophysical properties is of outmost importance for those working in the optical materials area. The interaction between lasers and matter usually results in thermal loading causing degradation and/or reduction of the material performance. The changes in properties such as thermal conductivity (K), thermal diffusivity (D), temperature coefficient of the optical path length (ds/dT) and fluorescence quantum efficiency (η) with the sample temperature rise define the figure of merit of a given material. The measurement of these properties as a function of temperature with conventional techniques is always a challenging task because it demands the construction of high cost devices and appropriate excitation regime to obtain the data, especially when performed in the temperature interval where the material is submitted to phase modifications.
In the past few years we have applied Thermal Lens Spectrometry (TLS) to evaluate the thermo-optical properties of transparent materials as a function of temperature, including optical glasses, crystals, polymers and liquid crystals [1–8]. In those experiments the use of time resolved procedure permitted us to obtain the data with optical excitations that resulted in temperature variations less than 10-2°C, allowing to study the samples during phase modification. The particular interest of this work is to apply the TLS technique combined with interferometric method, thermal relaxation calorimetry, photoluminescence and lifetime measurements to determine simultaneously the thermophysical properties of Nd2O3 doped sodium zincborate glass (SZB2) as a function of temperature, including the region where glass transitions occur. The measured properties were: thermal conductivity; thermal diffusivity; temperature coefficient of the optical path length; fluorescence quantum efficiency; linear thermal expansion coefficient; and thermal coefficient of the electronic polarizability.
2. Experimental
The composition of the zincborate glass was: 35ZnO – 30Na2CO3 – (35-x)B2O3 – xNd2O3, with x=2 mol%. The sample presents a glass transition temperature around 400°C, as measured previously by Differential Thermal Analysis (DTA) [8]. The glass sample was cut and polished, resulting in a disk of approximately 5 mm in diameter and 2 mm thick.
The extra cavity continuous wave (CW) two beam mode mismatched thermal lens (TL) method [9] is based on the determination of the nonradiative decay of the absorbed light, and is therefore complementary to purely optical procedures. The remote nature of the TL method means no contact between the sample and the detector and is a characteristic that permits measurements of a sample in a variety of environments, including the use of a furnace to modify the material temperature [1–5]. In particular, the TL sensitivity does not depend on the temperature scan rate, which allows measurements with temperature variation as low as desirable, according to the sample characteristics. The experiments were performed using the time resolved mode mismatched configuration [1–9], shown in Fig. 1, in which an Ar+ laser at 514.5 nm was the excitation beam, and a He-Ne laser at 632.8 nm was the probe beam. The excitation beam was focused by a converging lens, L1 (f=20.0 cm), and the sample was put at its focal plane. Exposure of the sample to the excitation beam was controlled by means of a shutter, what is strongly recommended when performing the measurements in the glass transition regions. Photodiode P1 was used to trigger the signal. The probe beam was focused by lens L2 (f=15 cm), arranged to have the sample positioned near to its confocal position. The angle φ<1.5° was used to deviate the probe beam to the TL detection plane (photodiode P2), positioned in the far field. The probe beam was aligned to pass through the TL to maximize the signal. In the CW time resolved experiments the oscilloscope was used to record the TL signal build up. For measurements as a function of temperature, a sample holder containing a furnace and a heat sink device was used. Thermal paste was used to improve the thermal contact between the sample and the thermal reservoir. The furnace temperature variation was performed using a LakeShore 340 temperature controller with a resolution better than 0.01°C. The experiments were carried out with a temperature variation of 3°C/min, and each consecutive excitation beam shot was done in a time interval of 20s, which was an adequate delay to obtain the complete TL relaxation between each consecutive event.
Fig. 1. A schematic diagram of the time-resolved TL experimental apparatus. Mi, Li, and Pi stand for mirrors, lenses, and photodiodes, respectively.
The data thus obtained were processed using a least-square-curve fitting to the analytical expression for the temporal evolution of the probe beam intensity derived in Ref. [10] and adapted for a solid sample in Ref. [9], as:
in which V=Z1/Zc and m=(ωp/ωe)2. Here, I(t) is the temporal dependence of the probe beam intensity at the detector; I(0) is the initial value of I(t); θ is approximately the thermally induced phase shift of the probe beam after passing through the sample; Zc is the confocal distance of the probe beam; Z1 is the distance from the probe beam waist to the sample; D is the thermal diffusivity; ωp and ωe are the probe beam and excitation beam radii at the sample position, respectively. The values of ωp, ωe, Zc and Z1 were measured as described in Ref. [11]. In this work we used ωe=49 µm, ωp=201 µm, Z1=5.3 cm, and probe beam Zc=2.1 cm. Then, m=17.2 and V=2.5.
The measured parameters resulting from the fitting of the experimental data with Eq. (1) are D and θ. The quantity θ is the probe beam phase shift induced by the thermal lens, given [1,2] as:
in which Leff=[1-exp(-Ael0)]/Ae, Ae is the optical absorption coefficient at the excitation beam wavelength; l0 is the sample thickness; P is the excitation beam power; λp is the probe beam wavelength; λe is the excitation beam wavelength; η is the fluorescence quantum efficiency; <λem> is the average emission wavelength and (ds/dT)p is the temperature coefficient of the optical path length change at the probe beam wavelength. It is important to clarify that ds/dT measured with the TL technique contains the occurrence of the sample surface bulging as a consequence of the localized beam excitation [5]. Hereafter, we will call it as (ds/dT)LT. The value of Ae was obtained by measuring the optical transmittance of the samples at 514.5 nm at the same temperature range in which the TL experiments were performed.
The interferometric technique was employed to determine the temperature dependence of the ds/dT parameter without the presence of thermal lens (with the absence of sample bulging). In this method a heater induces a slow and uniform variation of temperature in the whole sample. The moving fringes of a weak He-Ne laser with the sample temperature rise can be detected and used to calculate ds/dT (the experimental procedure is described elsewhere [12]). The principle of measurement for the determination of ds/dT is based on the interference theory [13], which results in:
in which n is the refractive index at the initial temperature and αT is the linear thermal expansion coefficient. We called it as (ds/dT)INT in order to distinguish from the value obtained from Thermal Lens experiment, which is given by [9]:
Here, ν is the Poisson’s ratio; Y is the Young’s modulus; and qll and q⊥ are the stress-optical coefficients parallel and perpendicular to the beam direction, respectively. The last term in Eq. (4) is related to the stress-optical coefficients. Usually this term is much smaller than the two previous ones and can be omitted in the calculation [9]. In this way, the relation between the value of (ds/dT)LT and (ds/dT)INT (Eqs. (3) and (4)) can be written as follows:
We reinforce that in the TL experiment there is a nonuniform heat profile, so it is sensitive to the effect of surface bulging and stress, differently from what occurs in the interferometric measurements.
3. Results and discussion
Figure 2 shows the TL transient of the SZB2 glass for three different temperatures at 30, 300 and 460 °C. The curve fittings, using Eq. (1), represented by the solid lines, give the respective values of D(T) and θ/P(T). The inversion of the transient profile from probe beam focusing to defocusing occurred around 450°C, as a consequence of the change in (ds/dT)LT signal from positive to negative.
Fig. 2. Normalized TL signal I (t)/I(0) for the SZB2 glass sample at three different temperatures: 30°C, 300°C and 460°C. Circle: experimental data; solid line: best curve fitting using Eq. (1).
Figure 3 shows the resulting temperature dependence for the measured parameters between 25°C and 470°C: (a) excitation beam power normalized θ/P(T); (b) thermal diffusivity, D(T); and (c) (ds/dT)INT(T), respectively. The error for θ/P is on the order of 2% while for D it is about 5%. As observed, there were strong variations in θ/P, D, and (ds/dT)INT when the temperature was scanned through the region where the glass transition was expected. The inset of Fig. 3(a) shows the temperature derivative of θ/P(T) together with the DTA data. The observed peaks correspond to the glass transition of the SZB2 glass that occurred at about 395°C, as indicated. These plots show the glass transition quite well. This result indicates that the TL and interferometric techniques provided information equivalent to DTA data. As previously proposed [14], the resulting signal of the TL technique would be dθ/dt=dθ/dT.dT/dt, that is proportional to dθ/dT and can provide accurate information regarding the onset of the glass transition.
Fig. 3. Temperature dependence of: (a) normalized TL signal, θ/P; (b) thermal diffusivity; (c) (ds/dT)INT measured via interferometric method. The inset in (a) shows the DTA thermogram and the θ-1 dθ/dT curve.
To obtain K(T), we have independently measured the specific heat (cp) as a function of temperature using the thermal relaxation method, described elsewhere [15]. Due to the limitation of our device it was done up to 300 °C. These parameters are related by the equation K=ρcpD, with ρ as the mass density. The volumetric thermal expansion coefficient, β, of the glass at room temperature is of the order of 10-5 K-1, with a minimal increase up to the beginning of the glass transition region. Then the variation in the samples volume in the considered temperature interval is less than 1%. Therefore, for the data up to 300 °C the mass density, ρ(T), can be considered approximately constant in our calculations.
Figure 4(a) shows the obtained values for cp(T) and K(T), using ρ=3.22 g/cm3 [8], in the temperature range between 25°C and 300°C. It can be observed that the values of cp(T), K(T) and D(T) (shown in Fig. 3(b)) rise monotonically in this temperature interval.
The 4F3/2 Nd3+ level fluorescence quantum efficiency at room temperature was calculated by means of the Judd Ofelt (JO) theory [8] and luminescence decay, using the equation η=τ rad/τ exp. The experimental lifetime (τ exp) was measured with the argon ion laser at 514.5 nm as described in Ref. [16]. Assuming those previously determined JO parameters [8], the radiative lifetime, τ rad, are then determined. The experimental and calculated (τ rad) lifetimes were 60µs and 182µs, respectively. The resulting η was found to be 0.33±0.03, which is an expected value for this class of glasses [17,18]. To determine η(T) we carried out photoluminescence measurements for different temperatures using also the pumping source at 514.5 nm. The inset in Fig. 4(b) shows the photoluminescence spectra for three different temperatures. The variation of the integrated area under the photoluminescence curve at different temperatures can be assumed as proportional to the temperature variation of η. In this way η(T) was calculated and the results are shown in Fig. 4(b). It can be observed that the value at room temperature is about 30% lower than that at 300°C.
Fig. 4. Temperature dependence of: (a) specific heat and thermal conductivity; (b) fluorescence quantum efficiency. The inset in (b) shows the luminescence spectra at different temperatures.
Having η(T), K(T) and θ/P(T), the temperature dependence of (ds/dT)TL was determined using Eq. (2), with Ael0=0.24, λp=632.8 nm, and <λem>=1061 nm [8], data not shown. As an example, at room temperature, with K=4.4×10-3W/cmK, θ/P=-1.87 W-1, and η=0.33, the value for (ds/dT)LT was found to be 3.2×10-6 K-1. Then, by using the calculated (ds/dT)TL(T) and (ds/dT)INT(T) (shown in Fig. 3(c)) in Eq. (5), the temperature dependence of the linear thermal expansion coefficient, αT(T), can be calculated. To do that we used previously measured data of n=1.64 and ν=0.25 [8]. The obtained results are shown in Fig. 4(a). One interesting fact is the high value of αT of about 17.8×10-6K-1 at room temperature and 34×10-6K-1 at 300°C. The large values of this parameter for borate glasses have been investigated before and correlated to the strong relationship between αT and the amount of alkali oxides in the glass structure [19].
Another important information is the temperature dependence of the coefficient of the electronic polarizability, Φ(T). According to Prod’homme [20], the temperature coefficient of refractive index (dn/dT) is given by:
By using dn/dT of Eq. (3) in Eq. (6), and including the temperature dependence of the related parameters, Φ(T) can be determined as follows:
Here we assumed n constant for temperatures up to 300 K, what can be done because dn/dT of this glass at room temperature is very low, -12×10-6 K-1, what would result in an error in Φ(T) of about 1%. Then, Fig. 5(b) shows the calculated Φ(T) data. Campbell et al [21] have shown that this parameter can be considered as an additive contribution from each glass component. Moreover, Izumitani et al [22], after analyzing the composition of several glasses, observed that Φ is related to the electronic polarizing power of the network forming ions, described by the field strength Z/a2, with a as the inter-ionic distance in the dipoles and Z as its total charge. The authors observed that a decrease in the ratio Z/a2 produces an increase in Φ values, indicating that Φ is mainly determined by the elongation of the inter-ionic distance, a. Therefore, the influence of temperature on Φ value may be understood as follows: the distance a is expected to increase as the temperature increases, resulting in a decrease of the field strength. As a consequence Φ(T) goes to higher values as the temperature increases, similarly to what occurs with αT(T). Taking the Φ values at room temperature reported for typical glass components such as B2O3, Na2O and ZnO as 13.9×10-6 K-1, 50.1×10-6 K-1, and 39.5×10-6K-1, respectively, we estimated Φ for the SZB2 glass as 39×10-6 K-1, which is very close to the one obtained in this work (also at room temperature), 34×10-6 K-1. Finally it is important to mention that the thermo-optical properties of SZB2 glass at high temperatures are not available in the literature. Therefore, the data presented in this work may be useful for future applications using this material.
Fig. 5. Temperature dependence of the linear thermal expansion coefficient (curve a) and thermal coefficient of the electronic polarizability (curve b).
4. Conclusion
In conclusion, this work shows that the use of time resolved thermal lens and interferometric techniques combined with conventional measurements of specific heat, radiative lifetimes and photoluminescence allows the determination of the absolute value of the thermophysical properties of SZB2 glass as a function of temperature. The results show the ability of the thermal lens and interferometric techniques to perform measurements very close to the glass transition region. We emphasize that these methods provide absolute values for the measured physical quantities and are advantageous when low scan rates are required.
Acknowledgments
The authors are thankful to the Brazilian Agencies FAPESP, CAPES, CNPq, and Fundação Araucária for the financial support of this work.
References and links
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