# thermal diffusivity definition by a dynamic method

The procedure in which bottom the periodic heating of one surface of the sample lays, has been offered for the first time A.Dzh. An angstrom unit in 1863 as it is featured in operation [180]. S.Lang [181] modified a method, having offered the upper surface of the explored material located on the pyroelectric detector to shine is sinusoidal the modulated thermal stream.

The thermal wave, transiting through explored the sample, is spread in the detector. Change of temperature in a pyroelectric crystal of the detector causes polarisation change that leads to course of a pyroelectric current in an external circuit. C the help of the synchronous amplifier (Lock-In amplifier) registers amplitude of the pyroelectric current going from the detector, and a difference in phase between a thermal stream impinging on the explored sample and pirotokom. C use of methods of mathematical modelling, yields calculation of the frequency dependence pirotoka and differences in phase between impinging onThe sample it is sinusoidal the modulated thermal wave and pirootklikom. Coefficient of thermal diffusion of the explored sample select so that the calculated curve of the frequency dependence of a difference in phase coincided with observational [181]. Authors [183,184] it was offered to use for coefficient definition temperaturopovodnosti a method of a rectangular thermal wave (TSWM - Thermal Square Wave Method at single-frequency) when the surface of the sample heats up prjamougolgno the modulated thermal stream. The given method [184-188] initially has been developed for the analysis of a lateral view of polarisation volume segnetoaktivnyh materials alternatively LIMM to a method (The Laser Intensity Modulation Method - LIMM) [189-193], allowing to explore only thin-film materials. In comparison with LIMM a method, TSWM has more simple mathematical apparatus. Co-ordinate dependences (lateral view) of polarisation on a thickness of the ferroelectric sample in it pay off on a time dependence pirotoka, registered with use of the analogue-digital transformer (ATSP). Further it has been shown, that TSW the method allows to analyze not only a polarisation state in volume materials and thin films [187, 194], but also in schistose structures [195], and also to spend an estimate of coefficient of thermal diffusion (temperaturoprovodnosti) not ferroelectric materials,

Located on a ferroelectric crystal [183, 184, 196].

At the heart of a method measurings of the pyroelectric current induced in a ferroelectric crystal on which not ferroelectric material is placed, with the help prjamougolno the modulated thermal stream (lay i.e. at an alternation of temperature of the sample) (fig. 2.10). In experiment in quality segnetoelektrieskogo a crystal authors [184] use

Ferroelectric crystal tantalata lithium (TL). The given select is caused by that the given material has stable, homogeneous on

To thickness spontaneous polarisation which cannot be changed action of an external field or a temperature lapse rate.

Drawing 2.10. The recording plan pirootklika at measuring of thermal diffusivity TSM by a method

At use in pyroelectric examinations prjamougolno the modulated thermal stream, pirootklik homogeneously polarised segnetoaktivnogo a material iterates its shape, if the depth of penetration of a temperature wave in the sample (/) is less than one third of thickness of the sample (), the so-called "sheet" response [197] otherwise is observed.

Authors [198] score, that pirootklik iterates the shape of thermal impulses, when frequency of modulation of a thermal stream (ω = 2πf) much more than return time of a thermal relaxation (τ_{r}) [199]: where and - coefficient of thermal diffusion. In a context of the formula (2.20), a depth of penetration of a temperature wave in the substance, equal according to [200]

It can be interpreted as length of a thermal relaxation.

The shape pirotoka, i.e. a time dependence, for one continuance of modulation of a thermal stream, pays off under the formula [201]

66

Where γ - pirokoeffitsient a ferroelectric material, h - its thickness, S - the area of electrodes, - allocation of temperature which is from

Solutions of the equation of a thermal conduction for a case of structural system C different thermal performances of stratums, l - co-ordinate (in a direction, perpendicular surfaces which the thermal stream influences).

Comparison of the observational shapes pirootkpika with settlement, allows to estimate quantity of a thermal diffusivity and a material thermal conduction through which there transits a temperature wave.

Authors [184] analyse a case when on a ferroelectric material not ferroelectric material is placed. For calculation pirootklika a ferroelectric material the formula for calculation pirootklika in a requirement is used, that the depth of penetration of a temperature wave in a ferroelectric material is less than 1/3 its thickness [187]:

Here h - a thickness of a ferroelectric material, d - a thickness of not ferroelectric material, I_{tl} - a pyroelectric current of a ferroelectric material, S' - the area of a shined surface (м^{2}), β_{0} - an absorption constant of impinging radiation by a surface of the sample, W_{0} - a power density of a thermal stream (Вт/м^{2}), γ - pyroelectric coefficient of a ferroelectric material (Кл/м^{2}К), r - its density (kg/m^{3}), with - a specific heat capacity (Dzh/kg), τ - duration of a light gap of an impulse (), ⅛ / and ∣y coefficients of thermal diffusion of the dielectric material and a ferroelectric material, according to (m/s^{2}), k_{l}и к_{2} - thermal conductivities of the dielectric film and a ferroelectric substrate, accordingly

- Characterises radiation losses, σ -

Quantity of the "blockage" appearing in the beginning of an impulse pirootklika (fig. 2.11), is spotted by thickness nesegentoelektricheskogo a stratum and coefficient of thermal diffusion of an explored material [184].

Authors [184] it is offered to use TSW a method for definition of a thermal diffusivity of thin-film materials, and in operation [196] it is shown, that it can be applied and to the analysis of massive materials.

Authors [196] carry out the shape and quantity analysis pirootklika TL depending on values of thermal conductivities and thermal diffusion of a material through which there transits a temperature wave (fig. 2.12) and it is scored, that use of [184] procedures featured in operation allows to vary at calculation of two parametres, namely - values of thermal conductivities and thermal diffusion. This results from the fact that, (5) value calculated under the formula pirootklika (with other things being equal) that more than is less value of a thermal conductivity (fig. 2.12,). At reduction of value of coefficient of thermal diffusion inverse relationship takes place - quantity pirootklika also decreases (fig. 2.12,). During too time if change of value of a thermal conductivity changes only quantity pirootklika reduction of coefficient of thermal diffusion conducts and to change of its shape - (the "blockage" observed in the beginning of the response is incremented by fig. 2.12 it is scored by a dotted line).

When the thickness of an explored material is much less than thickness of a ferroelectric material, frequency of modulation of the thermal stream used in experiment, can be spotted from a requirement l≤h∕3. At the analysis of massive samples with a thickness () bolshej thickness of the sample, requirement performance ∕> h i.e. that the length of a thermal relaxation of a temperature wave was more thickness of an explored material is necessary. C 68

Other leg, as well as for a case of thin-film materials, the formula (5) is applicable only when I

## More on topic thermal diffusivity definition by a dynamic method:

- definition of a thermal diffusivity by means of Linseis XFA 500
- measuring of a thermal diffusivity by means of the analyzer temperaturoprovodnosti and thermal conductions Linseis XFA 500
**CHAPTER 3. APPLICATION PYROELECTRIC TSW THE METHOD FOR DEFINITION OF THERMAL PERFORMANCES OF MATERIALS**- 2.1 Equations of material and thermal balances for deriving of dynamic model of process of drying.
- definition of concentration of a suspended matter gravimetricheskim (weight) method and definition of dimensional composition of corpuscles by a mesh analysis method
- a method of dynamic light scattering
- Kalugina Olga Nikolaevna. EXAMINATION of THERMAL PERFORMANCES of the DIELECTRIC MATERIALS by the METHOD of the THERMAL WAVE. The dissertation on competition of a scientific degree of the candidate of physical and mathematical sciences. Tver - 2016, 2016
- a method of thermal noise
- examination of thermal performances of germanium TSW by a method
- 2.3.1 Installation on pyroelectric effect measuring by a dynamic method
- definition of coefficient of thermal diffusion of not ferroelectric materials
- definition of coefficient of thermal diffusion of ferroelectric sheet materials on the basis of ceramics TSTS
- 1.2 Methods of definition of coefficient of thermal diffusion
- measurement of sizes of corpuscles by means of a method of dynamic dispersion of light
- Definition of a rational operating mode of an experimental dynamic separator with dezagregirujushchim the device