CC BY
6
DOI: 10.21122/2220-9506-2023-14-3-173-178
Application of the Thermal Diffusivity Standard for the Heat Transfer Parameter Control in Absorbing Materials
E.V. Ivakin
Belarusian State University, Nezavisimosti Ave., 4, Minsk 220030, Belarus
Received 27.03.2023
Accepted for publication 12.09.2023
Abstract
Metrological support creation and use of heat transfer etalons are important stages in the development of modern materials science. This is especially concerned to the emergence of new materials in the world with previously unattainable thermophysical parameters. The purpose of this work was to develop and experimentally verify the idea of joint application of the transient gratings method which is well-known in nonlinear optics and the single thermal diffusivity etalon of conventional type for the heat transfer metrological control in materials of a wide values range. The method proposed is based on thermal diffusivity etalon application as a source of calibrated optical signals that are excited in it by short laser pulses. Their lifetime is formed by the etalon thermal diffusivity and on the transient grating spatial period. The etalon linear graph of gratings lifetimes as a function of the gratings periods squared and grating lifetime of the material under study are used for the thermal diffusivity calculation. Thermal diffusivity of thin sub-surface layers of the samples under study - duraluminium, monocrystalline silicon and thermoelectric lead telluride film was measured. The results obtained are in close agreement with the reference values.
Keywords: transient gratings, etalon of thermal diffusivity, metrological control, sub-surface layers
Адрес для переписки:
Ивакин Е.В.
Белорусский государственный университет, пр. Независимости, 4, г. Минск 220030, Беларусь e-mail: [email protected]
Для цитирования:
E.V. Ivakin.
Application of the Thermal Diffusivity Standard for the Heat Transfer
Parameter Control in Absorbing Materials.
Приборы и методы измерений.
2023. - Т. 14, № 3. - С. 173-178.
DOI: 10.21122/2220-9506-2023-14-3-173-178
Address for correspondence: Ivakin E.V.
Belarusian State University, Nezavisimosti Ave., 4, Minsk 220030, Belarus e-mail: [email protected]
For citation: E.V. Ivakin.
Application of the Thermal Diffusivity Standard for the Heat Transfer
Parameter Control in Absorbing Materials.
Devices and Methods of Measurements.
2023, vol. 14, no. 3, pp. 173-178.
DOI: 10.21122/2220-9506-2023-14-3-173-178
Б01: 10.21122/2220-9506-2023-14-3-173-178
Применение эталона температуропроводности
для контроля параметра теплопереноса в поглощающих
материалах
Е.В. Ивакин
Беларуский государственный университет пр-т Независимости, 4, г. Минск 220030, Беларусь
Поступила 27.03.2023 Принята к печати 12.09.2023
Создание, контроль и постоянное использование эталонов теплопереноса являются важнейшими факторами в развитии современного материаловедения. Это в особенности актуально в связи с появлением новых материалов с недостижимыми ранее теплофизическими параметрами. Целью работы являлась разработка и экспериментальное апробирование идеи совместного применения известного в нелинейной оптике метода динамических решёток и одного эталона температуропроводности стандартного типа для метрологического контроля параметров теплопереноса в материалах с широким диапазоном значений. Предложенный метод основан на использовании стандартного эталона температуропроводности как источника калиброванных оптических сигналов, возбуждаемых в нём короткими лазерными импульсами. Их длительность определяется коэффициентом температуропроводности эталона и периодом динамической решётки. Последний легко контролируется средствами современной оптики. Построенный с помощью эталона линейный график зависимости времени жизни множества динамических решёток от квадрата их периодов в сочетании с измеренным временем жизни решётки в исследуемом материале позволяют вычислить коэффициент температуропроводности. В приповерхностных слоях микронной толщины в трёх образцах -дюралюминий, монокристаллический кремний и термоэлектрик теллурид свинца - проведены измерения искомых параметров. Результаты тестирования близко соответствуют справочным значениям.
Ключевые слова: динамические решётки, эталон температуропроводности, метрологический контроль, поверхностный слой
Адрес для переписки:
Ивакин Е.В.
Белорусский государственный университет, пр. Независимости, 4, г. Минск 220030, Беларусь e-mail: [email protected]
Для цитирования:
E.V. Ivakin.
Application of the Thermal Diffusivity Standard for the Heat Transfer
Parameter Control in Absorbing Materials.
Приборы и методы измерений.
2023. - Т. 14, № 3. - С. 173-178.
DOI: 10.21122/2220-9506-2023-14-3-173-178
Address for correspondence:
Ivakin E.V.
Belarusian State University, Nezavisimosti Ave., 4, Minsk 220030, Belarus e-mail: [email protected]
For citation: E.V. Ivakin.
Application of the Thermal Diffusivity Standard for the Heat Transfer
Parameter Control in Absorbing Materials.
Devices and Methods of Measurements.
2023, vol. 14, no. 3, pp. 173-178.
DOI: 10.21122/2220-9506-2023-14-3-173-178
Introduction
The heat transfer standards reproduction and storage are currently based on the comprehensively studied materials application [1]. Metrological value is supported by using a set of several measures and its implementation at a given temperature can be carried out only at a separate points of the mastered metrological range. The need to expand the range of measures, insufficiency of the existing set of measures and nonuniform of their distribution over the range of thermal diffusivity are problems that are relevant and have been discussed for a long period of time [24]. However, their solution by traditional means is a very long and expensive procedure. The substance used as a reference measure must have chemical inertness, physical homogeneity, non-hygroscopicity, absence of phase transitions, stability of properties over time, low cost, etc.
In [5] an attempt is made to create a new class of metrological control devices - a multivalued etalon of thermal conductivity. The essence of the proposed approach is to create a standard with controlled internal heat sources, which, depending on their power and distribution in space, form a specific thermo-physical parameter, and it is then used for metrologi-cal control of materials. However, for a number of objective reasons of a fundamental nature, this idea have received a negative assessment by the experienced specialists (see, for example, [6]).
The aim of this work was to develop a method for multi-valued metrological thermal diffusivity control of a material in an extended range of values by using a standard unambiguous standard in combination with the transient grating method application. The method was tested by samples application with well-known thermal parameters.
Transient grating application
for the metrological problem of heat transfer
solving
Patent [7] proposes the idea of solving one of the metrological problems on the basis of the transient gratings method application, which is now widely used in the scientific world [8-10]. According to the method, two interfering beams from a pulsed laser light up the sample at an angle 0 to each other. In this case, an interference pattern is formed in the form of light and dark rectilinear equidistant bands following the period Л, depending on the angle between the beams Л = ^/2sin(0/2). Due to the absorption of light,
spatially periodical heating of the sample occurs on the surface or in volume, which leads to a phase diffraction grating formation with the same period Л. The third light beam from the continuous wave laser is directed to the sample and the light beam undergoes diffraction with the formation of diffraction orders of plus and minus the first orders. A diagram of a laser device for determining the thermal diffusivity of materials is shown in Figure 1. In different embodiments, it is given in numerous works concerning the transient gratings recording or application (see, for example, [11]).
Figure 1 - Diagram of a laser-based device for the thermal diffusivity of materials measurement: 1 - source of pulsed laser radiation; 2, 3 - interfering light beams; 4 - sample under test; 5 - continuous wave laser; 6 - special diffraction beam splitter; 7 - detector for the diffracted signal kinetics recording; 8, 9, 10 - diffracted beams of zero and of the ±1-orders; 11 - digital system for the diffraction signal recording and processing; 12, 13 - optical elements for light beams bringing to the sample under study
According to the early developed theory [12] for three-dimensional transient gratings, in the approximation, which is obviously performed when making measurements, the intensity of the signal of the first order of diffraction varies according to the exponential law:
I(t) = I(0){exp(-t/T)}:
(1)
where the diffraction signal decay т is inversely proportional to the thermal diffusivity x of the sample under study in the direction of the grating vector:
T = Л2/8П2Х.
(2)
If the heating of the sample is essentially of surface nature and therefore the thermal gradient is formed simultaneously in two directions - along the sample surface (due to spatially periodic heating) and along the normal to it, the diffracted signal decay is recorded through an complementary error function [12]:
I(t) = 1(0) {erfc(t/x)05}2 ; T = л2/4п2х .
(3)
(4)
Figure 2 - Calibration graph Xetalon(Aetalon)2
Then, transient grating with an arbitrarily selected period Ax is excited in the sample under study and lifetime of the transient grating tx is determined by standard interpolation.
With the help of the graph in Figure 2, it is found to which period of the thermal grating Aetalon the equality Tetalon = tx is valid. The desired value
of thermal diffusivity xx is calculated using the formula below:
From the above relations it follows that in order to measure x by the transient grating method, it is necessary to experimentally determine two values: grating period and its lifetime. The grating period can be measured for example, by using a standard microscope equipped with an eyepiece-micrometer. The time constant t is determined by standard comparison of the experimental kinetics of diffraction signals recorded with the theory in accordance with the relations (1) or (3) depending on the type of grating (volume or surface).
Metrological support of the thermal diffusiv-ity measurements begins with the calibration of the measuring setup, shown in Figure 1. For this purpose a stainless steel etalon of thermal diffusivity No. MTO 01.01.005-30/062, manufactured and officially certified at the Research Institute of Metrology named after D.I. Mendeleev, St. Petersburg, is used. According to the passport attached to the etalon, its thermal diffusivity is xetalon = 0 04 cm2/sec. Further, using the etalon as the sample under study, and the transient grating recording of different grating periods, a linear calibration graph Tetalon(Aetalon)2 should be constructed, as shown in Figure 2. The scale along the x axis from x = 0 to the maximum value x = (Aetalon)2 is selected depending on the range of measured parameters expected.
(
X x Xetalon
Л
x
л2
Л1
etalon
(5)
It is convenient to determine the value of the
Aetalon using the ^talon^etalon^ stored directly in the rather popular program OriginPro8. In this case, it is also advisable to use the Screen Reader option within this program. Using the manual movement of the crosshair, we find the point on the line graph that gives Y = tx. At the same time, we find the value of A2etalon and calculate the thermal diffusivity of the sample under study using the ratio (5).
Results of control measurements
It is worth to note that since all the necessary information when performing measurements is taken from optical radiation, the surface and volume of the sample under study should be of high optical quality with minimal losses caused by light scattering.
Control measurements of thermal diffusivity were performed for duraluminium and silicon samples. The specimens are made in the form of plates 30x30 mm and 2 mm thick, one surface of which is polished to optical quality. The heat transfer in the semiconductor film of the currently popular narrowbandgap thermoelectric PbTe with a thickness of 2.3 pm on a glass substrate was also studied. In all samples excited by laser beam at wavelength 0.532 pm, the surface heating is realized.
Duraluminium grade D16T
Figure 3 - Kinetics of the diffracted signal decay at surface excitation of duraluminium. Grating period is Ax = 25 pm. Its lifetime according to comparison with theory (3), is 0.31 ps
At Л. = 25 pm by using the pl°t Tetalon (Ле1а1сп)
and the OriginPro8 program, the value of Ле1а1сп. is determined. By using the ratio (5), thermal diffusivity of sample was found to be xx = 0.496 cm2/s. From the reference data [13] it follows that the thermal diffusivity of duralumin grade D16T, as the result of dividing its thermal conductivity by the bulk heat capacity, lies in the range of 0.48-0.51 cm2/s.
Monocrystalline silicon
With this semiconductor, all the same actions are performed as with duralumin. At the grating period Лх = 25 pm, diffraction kinetics with a decay time of 0.21 ps was registered. It was found that in this case Л2бЫт = 30.7 pm2. As a result, we determine the value of thermal diffusivity:
Xx = 0.04^3627) = 0.83 cm2/s.
The reference value of monocrystalline silicon thermal diffusivity is 0.9 cm
Lead telluride thermoelectric film
When studying thin film on a substrate, it is important, first of all, to use radiation at a wavelength that provides high surface absorption to excite the thermal grating, so that the initial depth of heating of the film is significantly less than its thickness. and secondly, to choose the grating period so small that during the relaxation of the DR the heat does not reach the surface of the substrate. The latter requirement is met when satisfying the inequality Л < nd, where d is the film thickness [12]. Otherwise, the measurement result will refer to the effective thermal diffusivity of the film-plus-substrate system.
Figure 4 - Diffraction signal during excitation of a thermal transient grating in a 1.3 pm thick PbTe film on glass. The period 1x and the lifetime tx of the lattice are 5 pm and 0.37 ps, respectively. The white line is the theoretical curve (ratio (3))
By using the graph in Figure 2, the OriginPro8 program, as well as ratio (5), the required value of is determined to be 0.018 cm2/s. This value of thermal diffusivity well corresponds to the result of measurement obtained in [15].
Conclusion
A method is proposed that allows metrological support measurements of the thermal diffusivity %x of solid-state materials in a wide range of %x values by using a single etalon with a certified thermal diffusivity value Xetalon. The basis of the measurements is a line graph xetalon^etalon)2 constructed, which, due to the method application, can be considered as a multi-valued graphic material for metrological support of thermal measurements.
It has been experimentally shown that a thermal diffusivity etalon with a passport value %etak>n = 0.04 cm2/sec can be used for metrological support of measurements of samples with thermal diffusivity in different ranges compared to xetalon: %x = 0.496; 0.830 and 0.018 cm2/s. This possibility is realized as well through the use of an easily controlled parameter - the transient grating period Л.
References
1. GOST 8.140-82. GSI. State primary standard and state verification scheme for measuring the thermal conductivity of solids from 0.1 to 5 W/(mK) in the temperature range of 90-500 K and from 5 to 20 W/(mK) - in the temperature range of 300-1100 K.
2. Kirillov VI. Metrological support of technical systems. Minsk: New knowledge Publishing; 2017. 424 p.
3. Artemyev BG. Metrology and metrological support. Minsk: FSUE "STANDARTINFORM" Publishing; 2010. 568 p.
4. Shishkin IF. Theoretical metrology. Part 2. Ensuring the uniformity of measurements: 4th ed. St. Petersburg, 2012. 240 p.
5. Sokolov NA, Sokolov AN. Multivalued measures of thermal conductivity for the range of 20-500 W/(m.K). Measuring Techniques. 2009;52(7): 751-754. DOI: 10.1007/s11018-009-9349-5
6. Zarichnyak YP, Khodunkov VP. On the feasibility of multivalued measures of thermal quantities in metrology. Izv. universities. Instrument Engineering. 2020;63: 257-263.
7. Ivakin EV, Kisialiou IG. A method for determining the thermal diffusion of solids and the device for its implementation. Euroasian patent No. 017906. The date of patent grant is April 30, 2013.
8. Sawada T, Harata A. Transient reflection grating for sub-surface analysis: GHz ultrasonic, thermal spectroscopy and imaging. Appl. Phys. A. 1995;61:263-268. DOI: 10.1007/BF01538191
9. Ivakin EV. Laser diffraction relaxmeter for the kinetics photoexcitation and study in condensed matter. Optical Journal. 2000;67:27-31.
10. Scaev P, Gudelis V, Jarasiunas K, Ivakin E, Ki-sialiou I, Nesladek M, Haenen K. Carrier recombination and diffusivity in monocrystalline CVD-grown and single-crystalline HPHT diamonds. Phys. Status Sol. 2012; A209.9:1744-1749.
DOI: 10.1002/pssa.201200052
11. Maznev AA, Nelson KA, Rogers JA. Optical heterodyne detection of laser-induced gratings. Optics
Letters. 1998;23(16):1319-1321. DOI: 10.1364/OL.23.001319
12. Kading O, Skurk H, Maznev A, Matthias E. Transient thermal gratings at surfaces for thermal characterization of bulk materials and thin films. Appl. Phys. A. 1995;61:253-261. DOI: 10.1007/BF01538190
13. Beletskii VM, Krivov GA. Aluminium alloys -composition, properties, technology, application. Reference book. KOMINTEKH Publishing, 2005.
14. Smith R. Semiconductors. Translation from English. Mir Publishing; 1982. 560 p.
15. Paraschuk T, Dashevsky Z, Woiciechowski K. Feasibility of a high stable PbTe: In semiconductor for thermoelectric energy applications. J. Appl. Phys. 2019; 125:245103. DOI: 10.1063/1.5106422
