Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application

The study of optical and thermophysical characteristics of the absorbing coatings (AC) for sensitive elements of pyroelectric detectors of radiation based on carbon nanotubes paste (CNTP-black) is performed in comparison with those AC formed from gold disperse layer (Au-black) and dielectric lacq...

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Дата:2009
Автори: Bravina, S.L., Morozovsky, N.V., Dovbeshko, G.I., Fesenko, O.M., Obraztsova, E.D.
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Мова:English
Опубліковано: Інститут металофізики ім. Г.В. Курдюмова НАН України 2009
Назва видання:Наносистеми, наноматеріали, нанотехнології
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Цитувати:Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application / S.L. Bravina, N.V. Morozovsky, G.I. Dovbeshko, O.M. Fesenko, E.D. Obraztsova // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2009. — Т. 7, № 1. — С. 137-145. — Бібліогр.: 22 назв. — англ.

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spelling irk-123456789-763422015-02-10T03:02:43Z Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application Bravina, S.L. Morozovsky, N.V. Dovbeshko, G.I. Fesenko, O.M. Obraztsova, E.D. The study of optical and thermophysical characteristics of the absorbing coatings (AC) for sensitive elements of pyroelectric detectors of radiation based on carbon nanotubes paste (CNTP-black) is performed in comparison with those AC formed from gold disperse layer (Au-black) and dielectric lacquer paint (DLP-black). The spectral dependences of reflectance and absorbance of CNTP-black, Au-black and DLP-black in IR-spectrum range 2.5—25 μm are presented. By photothermomodulation method, the frequency spectra of pyroelectric response amplitude and phase are obtained. The estimation of thermal diffusivity values of the investigated blacks as AC for sensitive elements of pyroelectric detectors is performed in situ. Prospects of using CNTP-black based AC for pyroelectric and other thermal detector applications are shown. Виконано порівняльні дослідження оптичних і теплофізичних характеристик вбирних покриттів (ВП) для чутливих елементів піроелектричних приймачів випромінення на основі пасти з вуглецевих нанорурок (ВНР- пасти), золотої черні (Au-черні) і діелектричної лакофарбової черні (ДЛФ-черні). Представлено спектральні залежності ІЧ-відбивання і вбирання ВНР-черні, Au-черні і ДЛФ-черні в інтервалі довжин хвиль 2,5—25 мкм. За допомогою фототермомодуляційнної методи одержано частотні спектри амплітуди і фази піроелектричного відгуку. Визначено «у місці знаходження» величини температуропровідности досліджуваних типів черні як ВП для чутливих елементів піроелектричних приймачів випромінен- ня. Показано перспективність використання ВП на основі черні з ВНР- пасти для піроелектричних й інших теплових приймачів випромінення. Проведены сравнительные исследования оптических и теплофизических характеристик поглощающих покрытий (ПП) для чувствительных элементов пироэлектрических приемников излучения на основе пасты из углеродных нанотрубок (УНТ-пасты), золотой черни (Au-черни) и диэлектрической лакокрасочной черни (ДЛК-черни). Представлены спектральные зависимости ИК-отражения и поглощения УНТ-черни, Au- черни и ДЛК-черни в интервале длин волн 2,5—25 мкм. С помощью фототермомодуляционного метода получены частотные спектры амплитуды и фазы пироэлектрического отклика. Проведено определение «в месте нахождения» величины температуропроводности исследуемых типов черни как ПП для чувствительных элементов пироэлектрических приемников излучения. Показана перспективность использования ПП на основе черни из УНТ-пасты для пироэлектрических и других тепловых приемников излучения. 2009 Article Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application / S.L. Bravina, N.V. Morozovsky, G.I. Dovbeshko, O.M. Fesenko, E.D. Obraztsova // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2009. — Т. 7, № 1. — С. 137-145. — Бібліогр.: 22 назв. — англ. 1816-5230 PACS numbers: 61.48.De, 77.70.+a, 78.20.Ci, 78.67.Ch, 81.05.ub, 81.07.De http://dspace.nbuv.gov.ua/handle/123456789/76342 en Наносистеми, наноматеріали, нанотехнології Інститут металофізики ім. Г.В. Курдюмова НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The study of optical and thermophysical characteristics of the absorbing coatings (AC) for sensitive elements of pyroelectric detectors of radiation based on carbon nanotubes paste (CNTP-black) is performed in comparison with those AC formed from gold disperse layer (Au-black) and dielectric lacquer paint (DLP-black). The spectral dependences of reflectance and absorbance of CNTP-black, Au-black and DLP-black in IR-spectrum range 2.5—25 μm are presented. By photothermomodulation method, the frequency spectra of pyroelectric response amplitude and phase are obtained. The estimation of thermal diffusivity values of the investigated blacks as AC for sensitive elements of pyroelectric detectors is performed in situ. Prospects of using CNTP-black based AC for pyroelectric and other thermal detector applications are shown.
format Article
author Bravina, S.L.
Morozovsky, N.V.
Dovbeshko, G.I.
Fesenko, O.M.
Obraztsova, E.D.
spellingShingle Bravina, S.L.
Morozovsky, N.V.
Dovbeshko, G.I.
Fesenko, O.M.
Obraztsova, E.D.
Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application
Наносистеми, наноматеріали, нанотехнології
author_facet Bravina, S.L.
Morozovsky, N.V.
Dovbeshko, G.I.
Fesenko, O.M.
Obraztsova, E.D.
author_sort Bravina, S.L.
title Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application
title_short Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application
title_full Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application
title_fullStr Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application
title_full_unstemmed Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application
title_sort carbon nanotubes based black absorbing coatings for pyroelectric and other thermal detector application
publisher Інститут металофізики ім. Г.В. Курдюмова НАН України
publishDate 2009
url http://dspace.nbuv.gov.ua/handle/123456789/76342
citation_txt Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application / S.L. Bravina, N.V. Morozovsky, G.I. Dovbeshko, O.M. Fesenko, E.D. Obraztsova // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2009. — Т. 7, № 1. — С. 137-145. — Бібліогр.: 22 назв. — англ.
series Наносистеми, наноматеріали, нанотехнології
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fulltext 137 PACS numbers: 61.48.De, 77.70.+a, 78.20.Ci, 78.67.Ch, 81.05.ub, 81.07.De Carbon Nanotubes Based Black Absorbing Coatings for Pyroelectric and Other Thermal Detector Application S. L. Bravina, N. V. Morozovsky, G. I. Dovbeshko, O. M. Fesenko, and E. D. Obraztsova* Institute of Physics, N.A.S.U., Nauky Prosp., 46, 03028 Kyyiv, Ukraine *Natural Science Centre of A. M. Prokhorov Institute of General Physics, R.A.S., Vavilov Str., 38, 119991 Moscow, Russia The study of optical and thermophysical characteristics of the absorbing coatings (AC) for sensitive elements of pyroelectric detectors of radiation based on carbon nanotubes paste (CNTP-black) is performed in comparison with those AC formed from gold disperse layer (Au-black) and dielectric lac- quer paint (DLP-black). The spectral dependences of reflectance and absorb- ance of CNTP-black, Au-black and DLP-black in IR-spectrum range 2.5—25 μm are presented. By photothermomodulation method, the frequency spectra of pyroelectric response amplitude and phase are obtained. The estimation of thermal diffusivity values of the investigated blacks as AC for sensitive ele- ments of pyroelectric detectors is performed in situ. Prospects of using CNTP-black based AC for pyroelectric and other thermal detector applica- tions are shown. Виконано порівняльні дослідження оптичних і теплофізичних характе- ристик вбирних покриттів (ВП) для чутливих елементів піроелектричних приймачів випромінення на основі пасти з вуглецевих нанорурок (ВНР- пасти), золотої черні (Au-черні) і діелектричної лакофарбової черні (ДЛФ- черні). Представлено спектральні залежності ІЧ-відбивання і вбирання ВНР-черні, Au-черні і ДЛФ-черні в інтервалі довжин хвиль 2,5—25 мкм. За допомогою фототермомодуляційнної методи одержано частотні спект- ри амплітуди і фази піроелектричного відгуку. Визначено «у місці знахо- дження» величини температуропровідности досліджуваних типів черні як ВП для чутливих елементів піроелектричних приймачів випромінен- ня. Показано перспективність використання ВП на основі черні з ВНР- пасти для піроелектричних й інших теплових приймачів випромінення. Наносистеми, наноматеріали, нанотехнології Nanosystems, Nanomaterials, Nanotechnologies 2009, т. 7, № 1, сс. 137—145 © 2009 ІМФ (Інститут металофізики ім. Г. В. Курдюмова НАН України) Надруковано в Україні. Фотокопіювання дозволено тільки відповідно до ліцензії 138 S. L. BRAVINA, N. V. MOROZOVSKY, G. I. DOVBESHKO et al. Проведены сравнительные исследования оптических и теплофизических характеристик поглощающих покрытий (ПП) для чувствительных эле- ментов пироэлектрических приемников излучения на основе пасты из углеродных нанотрубок (УНТ-пасты), золотой черни (Au-черни) и ди- электрической лакокрасочной черни (ДЛК-черни). Представлены спек- тральные зависимости ИК-отражения и поглощения УНТ-черни, Au- черни и ДЛК-черни в интервале длин волн 2,5—25 мкм. С помощью фото- термомодуляционного метода получены частотные спектры амплитуды и фазы пироэлектрического отклика. Проведено определение «в месте на- хождения» величины температуропроводности исследуемых типов черни как ПП для чувствительных элементов пироэлектрических приемников излучения. Показана перспективность использования ПП на основе чер- ни из УНТ-пасты для пироэлектрических и других тепловых приемников излучения. Key words: thermal detectors, absorbing coatings, metal black, paint black, carbon nanotubes black. (Received November 28, 2007) 1. INTRODUCTION Application field of one of the most important class of thermal detec- tors, pyroelectric detectors of radiation (PDR), includes all modern en- gineering branches from space and paramilitary equipment to household appliances, public and individual security and fire alarm systems [1—9]. The principle of operation of PDR is based on the temperature de- pendence of polarization of sensitive element (SE) material and regis- tration of electrical charge connected with polarization change in- duced by temperature variation [2, 3, 5—9]. Radiation absorption by the surface or volume of SE is the first and very important stage of ra- diation conversion into the electrical response of thermal detectors [2, 3, 5]. That is why sensitive and frequency characteristics of commonly used PDR with surface absorption are largely determined by thermo- physical parameters of absorbing coating (AC) of SE [10—14]. Well-known technologies for making up the AC of PDR use thin dis- perse layers of noble (Pt, Au and Ag) and other (Ni, Cr and Ni—Cr) met- als evaporated in the conditions of ‘imperfect’ vacuum and deposited in certain atmosphere and temperature conditions [10—13]. Thin layers of different lacquer and paints [10, 14] formed by smearing or pulveri- zation are also used as AC. These so-called metal and dielectric blacks possess sufficient spectral characteristics in the near- and middle-IR range [11, 14]. However, these blacks have relatively low thermal con- ductivity and restrict the speed of response of PDR by the time of thermal diffusion through the layer of AC [10, 12, 13] that demands the further development of AC technologies. CARBON NANOTUBES BASED BLACK ABSORBING COATINGS 139 Progress in modern technology allows enriching AC stock with blacks based on carbon nanotubes (CNT), which are mainly character- ized by the combination of high values of thermal and electrical con- ductivity [15—17] and resulted in the development of effective absorb- ing CNT-coating for pyroelectric detectors [17]. Recently, we reported about the development of AC based on thin (∼ 1 μm) layers of SiO<Cu> metal—oxide composite [18] and AC based on CNT-paint [19]. In a given paper, we present the results of the comparative study of AC thin layers based on metal disperse layer and dielectric paint blacks and also carbon nanotubes paint black as AC for sensitive elements of pyroelectric detectors and other types of thermal detectors of radiation. 2. EXPERIMENTAL 2.1. Sample preparation Metal-black AC were manufactured by evaporation of corresponding metal (gold in this experiment) and deposition of its vapours on the SE electrode surface under imperfect vacuum condition of 0.1—10 Torr in nitrogen atmosphere with a low content of oxygen at the substrate temperature of about 200 K [18]. For the manufacture of dielectric lacquer paint (DLP) black AC, the solution of industrial multi-pigment black lacquer paint was used. For the manufacture of CNT-based black AC, the carbon single wall nanotubes (SWNT) prepared by the method of arc discharge in He- atmosphere [20] were used. The characterization of these SWNT by Raman scattering and electron microscopy was performed. The length and diameter of the SWNT were of 1—2 μm and 14—15 Å, respectively. Then, suspension on the base of SWNT crumbled preliminary, organic binder and dissolvent were prepared. The DLP-black AC and CNTP-black AC were prepared by depositing a thin layer of solution of low viscosity on the SE electrode surface and subsequent evaporating solvent at heightened temperature. After dry- ing on the electrode surface were obtained the layers of 5—20 μm thick- ness close to that of Au-black AC. For manufactured CNTP-black, AC has the value of 20—50 kΩ/ surface resistance and a high degree of blackness close to that of DLP-black and Au-black AC. For the pyroelectric investigations, the SE with AC deposed directly on the main surfaces of 100—200 μm LiNbO3 plates of polar Z-cut with evaporated Cu/Cr-electrodes of 20—50 mm2 of area were formed. Such SE with various types of AC were connected by means of a ring-shape holder to the input of the FET matching stage [21] with variable from high (∼ 10 GΩ at the frequency of 20 Hz) to relatively low (∼ 100 kΩ) input impedance value. 140 S. L. BRAVINA, N. V. MOROZOVSKY, G. I. DOVBESHKO et al. 2.2. Measurements For the optical investigations, Au-black, DLP-black and CNTP-black AC were put on the electroded LiNbO3 thin plates. The measurements of reflectance of the samples were performed in the middle infrared range 2.5—25 μm with IFS 66 Bruker Instrument. The pyroelectric response measurements were performed by the modulation photopyroelectric thermowave method [22] in the fre- quency range 10 Hz ≤ fm ≤ 100 kHz of modulation of IR-radiation flux. The measuring system for thermowave probing allowed us to obtain the amplitude-to-frequency ( )mU fπ and phase-to-frequency ( )mfπφ depend- ences of pyroelectric response in two operation modes of pyroelectric current and pyroelectric voltage characteristic for PDR operation. Due to the fact that, in the pyroelectric current mode, 1 1/U U cπ π= ∝ γ , and, in the pyroelectric voltage mode, 2 1/ mU U c fπ π= ∝ γ ε , where γ is the pyroelectric coefficient, с1 is the volume heat capacity, there is pos- sibility to evaluate the dielectric permittivity ε from pyroelectric measurements [2, 21, 22] by introducing the dielectric ratio 1 2/ mD U U fπ π π π= ∝ ε . The connection of amplitude and phase of pyroelectric response with the thermal parameters of both SE of PDR and AC material in conse- quence of the fundamental frequency dependence of the length of tem- perature wave 1/2( / )T T ma fλ = π , where aT is the thermal diffusivity [18, 19, 22], allows one to estimate the value of aT for material of AC by analysing ( )mU fπ and ( )mfπφ dependences. 3. RESULTS AND DISCUSSION 3.1. Optical IR Characterization In Figure 1, the spectral dependences of reflectance R(ν) (Fig. 1, a) and absorbance (Fig. 1, b) of Au-black, DLP-black and CNTP-black in IR- spectrum range of wavenumbers 400 ≤ ν ≤ 4000 cm −1 corresponding to that of wavelengths 5 ≤ λ ≤25 μm are presented. For Au-black, R(ν) value changes in the limits 1.5—6% and corre- sponding A(λ) value changes in the limits 94—98%. For both types of the paints, R(ν) change is no more than 3%. Due to opacity of prepared paint layers, the A(λ) value is no less than 97%. It should be pointed out the different shapes of obtained spectra for Au-black, DLP-black and CNTP-black in all spectral range and particu- larly in the range of 8—20 μm. The regularity of R(ν) and A(λ) spectrum for CNTP-black is better than for DLP-black, which results in a better level of spectral non- selectivity and in a higher value of integral absorbance of CNTP-black in the investigated spectral range. The absorbance value for CNTP- CARBON NANOTUBES BASED BLACK ABSORBING COATINGS 141 black AC is higher and its spectral uniformity is better than the same for DLP-black AC. 3.2. Photopyroelectric Characterization In Figure 2, the dependences of 1,2 ( )mU fπ and 1,2 ( )mfπφ are shown for SE of PDR obtained under irradiation of the Cu-electrode without AC and the other one with AC from Au-black. Significant difference in 1,2Uπ levels for the electrodes with AC and without it at low frequencies corresponds to a good quality of Au- black. The existence of 180°-difference for 1,2 ( )mfπφ dependences obtained for Cu-electrode side and Au-black side corresponds to different signs of pyroelectric reaction at the different polar Z + and Z − surfaces. Flat frequency dependences of 1Uπ , 2 mU fπ , Dπ and 1,2πφ under irra- diation of the side of Cu-electrode (Fig. 2, left side) correspond to thermal, polar and dielectric uniformity. Then, the following types of 1( )mU fπ , 1( )mfπφ and 2( )mU fπ , 2 ( )mfπφ de- pendences are characteristic [3, 5, 18, 19, 22]: 1( ) const( )m mU f fπ = and 1( ) const( )m mf fπφ = in the pyroelectric current mode, 2( ) 1 /m mU f fπ ∝ and 2( ) const( )m mf fπφ = in the pyroelectric voltage mode. In this case, 2 ( ) const( )m m mU f f fπ = and 1 2( ) ( ) / ( ) const( )m m m m mD f U f U f f fπ π π π= ∝ ε = , and also ϕπ2 − ϕπ1 = 90° due to capacitive character of current and voltage in the circuit of pyroelectric SE. The noticeable approaching the values of 1( )mU fπ to 2( )mU fπ and 1( )mfπφ to 2( )mfπφ under fm increasing is connected with deviation from a b Fig. 1. Spectral dependences of reflectance (a) and absorbance (b) of Au- black, dielectric lacquer-paint black and CNT-paint black. 142 S. L. BRAVINA, N. V. MOROZOVSKY, G. I. DOVBESHKO et al. the conditions of pyroelectric current mode. Under that with fm in- creasing, the SE impedance 1 2 mf Cπ (C is the total capacity of SE and load circuit) becomes less than the load resistance LR and the inequal- ity 2 1m Lf R Cπ << necessary for performing pyroelectric current mode changes for the opposite 2 1m Lf R Cπ >> , characteristic for the pyroelec- tric voltage mode, which leads to the coincidence of the dependences. The weak high-frequency drop of 2( )m mU f fπ , 1( )mU fπ and increase of 2( )mfπφ noticeable at the high-frequency interval corresponds to the existence of under-electrode non-homogeneity. Taking into considera- tion the value of aT = 1.5⋅10−6 m 2/s known for LiNbO3 [5], with regard to the value of λT for fm = 40 kHz, it is possible to evaluate the thickness of this non-homogeneity as about 3 μm. Under irradiation from the side of Au-black (Fig. 2, right side), flat frequency dependences of 1Uπ , 2 mU fπ and 1,2πφ are characteristic at low frequencies which corresponds to inequality / 1T Lλ >> between the length of temperature wave and the thickness L of the AC layer. At fre- quencies higher than 1 kHz, we observed a significant decrease of re- sponse amplitude and additional positive phase shift. Such peculiarities are connected with damping action of AC, which is manifested under approaching λT to L with increasing fm value. Under further increase of fm, the inequality / 1T Lλ < is getting valid. Enhancement of this ine- quality leads to decrease of exponential in respect to 1/2 mf multiplier for fm 2 2 1 2 1 Fig. 2. Modulation frequency dependences, 2 ( )mU fπ , 2 ( )m mU f fπ and ( )mD fπ and also 1( )mfπφ and 2( )mfπφ for SE of PDR with AC from Au-black on one side. CARBON NANOTUBES BASED BLACK ABSORBING COATINGS 143 the response amplitude 1/2( ) exp( / ) exp( ( / ) )m T m TU f L L f aπΔ ∝ − λ = − π and increase of a linear in respect to 1/2 mf contribution to the phase 1/2( ) / ( / )m T m Tf L L f aπΔφ = λ = π . As a result, with increasing fm, the level of pyroelectric response under irradiation from the Au-black side becomes even lower than under irradiation from the side of the Cu- electrode (see Fig. 2, left and right sides). In Figure 3, 1,2 ( )mU fπ , 2 ( )m mU f fπ , ( )mD fπ and 1,2( )mfπφ dependences for SE of PDR with AC from DLP-black and AC from CNTP-black are shown. Under irradiation of the side with DLP-black AC (Fig. 3, a), the be- haviour of 1,2 ( )mU fπ and 1,2 ( )mfπφ dependences similar to that observed for Au-black AC (Fig. 2) is shifted to higher frequencies and the region of high-frequency drop of amplitude—frequency dependence is ob- served for fm > 5 kHz. Under irradiation of the side with CNTP-black (Fig. 3, b), the de- pendences of 1,2 ( )mU fπ as for DLP-black are less sharp than observed in the case of irradiation as Au-black AC (see Fig. 2 and Fig. 3, b). Near the same levels of 1,2Uπ for Au-black AC, DLP-black AC and CNTP- black AC at low frequencies correspond to good absorption of CNTP- black AC. The high-frequency drop of 2( )m mU f fπ and increase of 2( )mfπφ for CNTP-black AC connected with thermal damping are not so sharp and are observed at the frequencies of 1 order higher than those ones for AC from Au-black (compare Fig. 2 and Fig. 3, b). a b Fig. 3. Modulation frequency dependences 1( )mU fπ , 2 ( )mU fπ , 2( )m mU f fπ and ( )mD fπ and also 1( )mfπφ and 2( )mfπφ for similar SE of PDR with AC from dielectric lacquer-paint black (a) and AC from CNT-paint black (b). 144 S. L. BRAVINA, N. V. MOROZOVSKY, G. I. DOVBESHKO et al. The obtained 1,2( )mU fπ and 1,2( )mfπφ dependences for SE with differ- ent AC allow one to estimate the value of thermal diffusivity of each AC material. It can be done by analyzing the characteristic depend- ences of ( )mU fπ and ( )mfπφ in the frequency range where the thermal damping is significant. The estimated aT values for Au-black AC, DLP- black AC and for CNTP-black AC are presented in Table. The obtained Ta values for CNTP-paint black are at least of an order of value higher than аT values for other black AC under investigation and are comparative with aT values for massive graphite. It can be con- nected with a high contribution of relatively large regions of high con- tacted CNT-bundles interconnected through developed surrounding of small CNT-bunches. 4. CONCLUSION Combination of enhanced spectral characteristics and thermal parame- ters of CNT paint black in comparison with those inherent to Au-black and dielectric lacquer paint black with foresight of further progress in CNT-based technologies allows us to consider the CNT-based paint black as promising for absorbing coatings of thermal detectors of ra- diation. REFERENCES 1. B. J. Mates and T. A. Perls, Rev. Sci. Instr., 32, No. 3: 332 (1961). 2. L. S. Kremenchugsky, Ferroelectric Detectors of Radiation (Kiev: Naukova Dumka: 1971) (in Russian). 3. S. B. Lang, Sourcebook of Pyroelectricity (London—NewYork—Paris: Gor- don&Breach Sci. Publ.: 1974). 4. F. G. Brown, Soc. Photoopt. Instrum. Engrs, 62: 201 (1975). 5. L. S. Kremenchugsky and O. V. 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