www bzfxw com BRITISH STANDARD BS EN 821 2 1997 Advanced technical ceramics — Monolithic ceramics — Thermo physical properties — Part 2 Determination of thermal diffusivity by the laser flash (or heat[.]
BRITISH STANDARD Advanced technical ceramics — Monolithic ceramics — Thermo-physical properties — Part 2: Determination of thermal diffusivity by the laser flash (or heat pulse) method The European Standard EN 821-2:1997 has the status of a British Standard ICS 81.060.99 BS EN 821-2:1997 BS EN 821-2:1997 National foreword This British Standard is the English language version of EN 821-2:1997 It supersedes BS 7134-4.2:1990 The UK participation in its preparation was entrusted to Technical Committee RPI/13, Advanced technical ceramics, which has the responsibility to: — aid enquirers to understand the text; — present to the responsible European committee any enquiries on the interpretation, or proposals for change, and keep the UK interests informed; — monitor related international and European developments and promulgate them in the UK A list of organizations represented on this committee can be obtained on request to its secretary Cross-references The British Standards which implement international or European publications referred to in this document may be found in the BSI Standards Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Find” facility of the BSI Standards Electronic Catalogue A British Standard does not purport to include all the necessary provisions of a contract Users of British Standards are responsible for their correct application Compliance with a British Standard does not of itself confer immunity from legal obligations Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, the EN title page, pages to 15 and a back cover This standard has been updated (see copyright date) and may have had amendments incorporated This will be indicated in the amendment table on the inside front cover This British Standard, having been prepared under the direction of the Sector Board for Materials and Chemicals, was published under the authority of the Standards Board and comes into effect on 15 November 1997 © BSI 04-2000 ISBN 580 28389 Amendments issued since publication Amd No Date Comments BS EN 821-2:1997 Contents National foreword Foreword Text of EN 821-2 © BSI 04-2000 Page Inside front cover i ii blank EUROPEAN STANDARD EN 821-2 NORME EUROPÉENNE June 1997 EUROPÄISCHE NORM ICS 81.060.99 Descriptors: Ceramics, powdery materials, thermodynamic properties, tests, determination, diffusion, thermal conductivity English version Advanced technical ceramics — Monolithic ceramics — Thermo-physical properties Part 2: Determination of thermal diffusivity by the laser flash (or heat pulse) method Céramiques techniques avancées — Céramiques monolithiques — Propriétés thermo-physiques — Partie 2: Détermination de la diffusivité thermique par la méthode Flash laser (ou impulsion de chaleur) Hochleistungskeramik — Monolithischer Keramik — Thermophysikalische Eigenschaften — Teil 2: Messung der Temperaturleitfähigkeit mit dem Laserflash- (oder Wärmeimpuls-) Verfahren ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ This European Standard was approved by CEN on 1997-05-24 CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the Central Secretariat or to any CEN member This European Standard exists in three official versions (English, French, German) A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official versions CEN members are the national standards bodies of Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom CEN European Committee for Standardization Comité Européen de Normalisation Europäisches Komitee für Normung Central Secretariat: rue de Stassart 36, B-1050 Brussels © 1997 CEN — All rights of exploitation in any form and by any means reserved worldwide for CEN national Members Ref No EN 821-2:1997 E EN 821-2:1997 Foreword This European Standard has been prepared by Technical Committee CEN/TC 184, Advanced technical ceramics, the secretariat of which is held by BSI This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by December 1997, and conflicting national standards shall be withdrawn at the latest by December 1997 EN 821 consists of three Parts: — Part 1: Determination of thermal expansion; — Part 2: Determination of thermal diffusivit; — Part 3: Determination of specific heat capacity (ENV) According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom Contents Foreword Scope Normative references Definitions Principle Apparatus Test pieces Calibration Test procedure Results 10 Test report Annex A (informative) Fundamental equations for calculation Annex B (informative) Deviations from ideal behaviour Annex C (informative) Bibliography Figure — Schematic representation of transient at rear face of test piece Figure — Schematic diagram of thermal diffusivity apparatus Figure — Schematic diagram of a typical ambient and low temperature test piece holder Figure — Heat loss correction curves Table — Values of constant Wx for a range of transient times Table B.1 — Coefficients for the decay time heat loss correction Table B.2 — Finite pulse time correction constants Page 3 3 9 10 11 12 12 14 ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ 11 10 13 14 © BSI 04-2000 EN 821-2:1997 Scope This Part of EN 821 specifies a method for the determination of thermal diffusivity of advanced monolithic technical ceramics, to an accuracy of approximately ± % It is suitable for the measurement of thermal diffusivity values in the range 0,1 mm2/s to 000 mm2/s at temperatures greater than – 180 °C Annex A gives the mathematical derivation of the calculations, and Annex B contains instruction on actions necessary when the calculations cannot be made in the usual way NOTE It is not advisable to exceed the temperature at which the test piece was manufactured NOTE This method involves the use of a high powered pulsed laser system or high energy photoflash equipment as well as high vacuum and high temperature furnace capability Such equipment therefore should be operated within established safety procedures (See EN 60825) Normative references This European Standard incorporates, by dated or undated reference, provisions from other publications These normative references are cited at the appropriate places in the text and the publications are listed hereafter For dated references, subsequent amendments to or revisions of any of these publications apply to this European Standard only when incorporated in it by amendment or revision For undated references the latest edition of the publication referred to applies EN 45001, General criteria for the operation of testing laboratories EN 60584-1, Thermocouples — Part 1: Reference tables EN 60584-2, Thermocouples — Part 2: Tolerances 3.4 transient half time the time required for the temperature to rise to half of its peak or maximum Principle Thermal diffusivity is a measure of the heat flow in a material under non-steady state conditions It can also be related to thermal conductivity via the specific heat of the material using the relationship: (1) where a Ỉ Ơ cp is the thermal diffusivity in is the thermal conductivity in is the density in is the specific heat in m2/s Wm–1K–1 kg/m3 J/(kg·K) Thermal diffusivity is measured by applying a high intensity short duration heat pulse to one face of a parallel sided homogeneous test piece, monitoring the temperature rise at the opposite face as a function of time, and determining the transient half time (t0,5) The transient temperature rise (see Annex A) is shown schematically in Figure The signal from the temperature detector is recorded with an appropriate data acquisition system The experimental data are subject to both systematic and random errors e.g those associated with a) test piece thickness determination; b) time measurement on transient curve; c) response time of detectors; d) response time of recording and analysis equipment; e) trigger delays; f) non-uniform heating of the test piece ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ Definitions For the purposes of this Part of EN 821, the following definitions apply 3.1 thermal diffusivity thermal conductivity divided by heat capacity per unit volume NOTE Improvement in the accuracy can be obtained by increasing the sophistication of the data collection and analysis systems 3.2 thermal conductivity density of heat flow rate divided by temperature gradient under steady state conditions 3.3 specific heat the heat capacity per unit mass © BSI 04-2000 EN 821-2:1997 ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ © BSI 04-2000 Figure — Schematic representation of transient at rear face of test piece © BSI 04-2000 ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ EN 821-2:1997 Figure — Schematic diagram of thermal diffusivity apparatus EN 821-2:1997 Apparatus NOTE The essential features of the apparatus are shown in Figure 5.1 Heat pulse source The heat pulse source may be a pulsed laser, a flash tube or an electron beam The pulse energy shall be uniform over the face of the test piece NOTE This is reasonably simple to achieve in the case of the flash lamp, which should be housed in a totally reflecting box with a hole, and a light guide of approximately 25 mm diameter abutting the sample NOTE Significant errors in derived data can arise if the temperature rise exceeds K, especially in materials where the thermal diffusivity is strongly temperature dependent The pulse source shall produce a rise in temperature not exceeding 10 K (preferably not exceeding K) on the rear face of the test piece For measurement at high temperature, the use of a laser is recommended; flash tubes are usually restricted to a maximum of 400 °C NOTE Where a laser is used, it is recommended that a neodymium-glass laser system is utilized because of its excellent beam uniformity over the whole diameter “Footprint” paper or photographic film can be used to monitor this uniformity and also to align the beam centrally on the sample front face 5.2 Environmental control chamber 5.2.1 General The environmental control chamber shall be either a furnace (see 5.2.2), a cryostat (see 5.2.3), or a draught-proof enclosure (for ambient temperature measurements) 5.2.2 Furnace, capable of operation within the temperature range required, and of sufficient size to contain the specimen holder (see 5.6) The heating elements for the furnace may be constructed from either: a) nickel-chrome alloy, for temperatures up to 000 °C; or b) platinum or silicon carbide, for temperatures up to 500 °C; or c) graphite, tantalum or tungsten, for temperatures above 500 °C In steady state conditions the drift in temperature shall be less than 0,01 K/s The temperature of the test piece shall be monitored either by a thermocouple in accordance with EN 60584-1 or by an optical pyrometer (preferably two-colour) An appropriate inert atmosphere or vacuum shall be used when necessary to protect furnace parts and test piece holder (see 5.6) from oxidation, and to protect the test piece and its coating (see 6.3) from structure/phase changes, stoichiometric changes and compatibility problems NOTE Care should be taken to avoid decomposition of materials at high temperatures and under reducing conditions At high temperatures some types of ceramics may vaporize (e.g nitrides and silicates) or otherwise react with the environment or the applied coating The furnace shall either be fitted with a window, transparent to the incident heat pulse radiation, or else the heat pulse source may be placed inside the furnace, for example at temperatures where a flash lamp may be employed The furnace shall also be fitted with a window, transparent to the emitted thermal radiation opposite the rear face of the test piece, for measurement of temperature using a pyrometer and for transmission of the transient pulse to a remote detector 5.2.3 Cryostat, capable of temperature control to 0,01 K NOTE Various liquids can be used (in a vacuum flask) to provide the low temperature environment e.g liquid nitrogen, liquid oxygen, solid carbon dioxide-acetone mixture, iced water etc., or a slow flow of boiled and pre-heated liquid nitrogen 5.3 Transient detector 5.3.1 General The transient detector shall be either an infra-red detector (see 5.3.2) or a thermocouple (see 5.3.3) It shall be capable of detecting changes of < % of the total rear face temperature rise of the test piece with a rapid linear time response, which shall discriminate to % of the half rise time of the transient (t0,5) 5.3.2 Infra-red detector, of type appropriate to the minimum test piece temperature required e.g a liquid nitrogen cooled indium antimonide (InSb) cell (for test piece temperatures down to 40 °C) or a lead sulphide (PbS) cell (for test piece temperatures down to 250 °C) The detector shall be kept at some distance from the test piece (remote from the high temperature environment) and hence a lens shall be used to focus the radiation from the centre of the rear face on to the detector Therefore all viewing windows and lenses shall transmit radiation in the appropriate wavelength band The sensor shall always be protected against damage or saturation from the direct laser beam energy 5.3.3 Thermocouple, of appropriate type for the required temperature range, manufactured in accordance with the tolerances given in EN 60584-2, allowing use of the reference tables given in EN 60584-1 The wire diameter shall be 0,15 mm ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ NOTE The thermocouple may serve a secondary purpose of monitoring the test piece temperature by switching into a digital thermometer © BSI 04-2000 EN 821-2:1997 The wire ends of the thermocouple shall be prepared to minimize heat losses from the test piece into the wires, and are pressed against the test piece by using fine (1 mm to mm diameter) twin bore alumina tube and springs NOTE Figure shows an example of a test piece and thermocouple holder suitable for use at ambient temperature and below Non-conducting test pieces shall be coated on the rear face (see 6.3) in order to effect the thermocouple junction, where the wires are open ended and separated by approximately mm The extra thickness of the high conductivity coating shall not increase the transient at t0,5 by more than % and this shall be checked by calculation NOTE The use of a number of thermocouple junctions in differential mode may be used to increase the sensitivity of measurement of the transient 5.4 Signal amplifiers Signal amplifiers, including spike protections, analogue-digital converters, high temperature bias circuitry They shall have low noise and fast response so as not to introduce errors into the transient measurements None of the electronic components shall become saturated or the signals distorted The integration time shall be less than 0,3 ms Brass screw Thermocouple wires Spring Pin-vice chuck Insulating plastic Alumina twin bore tube Polished nickel reflector Transparent plastic Test piece Figure — Schematic diagram of a typical ambient and low temperature test piece holder © BSI 04-2000 EN 821-2:1997 5.5 Data acquisition system Test pieces The system for acquiring and storing data may be either a computer data processor (preferred) or a storage oscilloscope The system shall be equipped with an accurate means of recording the energy pulse to initiate the recording system, for example a triggering photocell 6.1 Sampling NOTE The computer data processor is able to analyse several thousands of data points from the transient, and can be programmed to drive the laser and trigger systems, collect data, analyse for heat losses etc., print out results and produce plots of thermal diffusivity against temperature The oscilloscope is not very accurate and does require a means to photograph the trace for manual analysis It is important in both cases to verify the accuracy of time bases and response times 5.6 Test piece holder For tests at near ambient temperature or below, the test piece holder may be constructed from a material of poor thermal conductivity (e.g a plastics material) An example is shown in Figure At higher temperatures, where plastics materials become unsuitable, the test piece holder shall be constructed of suitably refractory materials (metals, graphite, etc.) in such a manner as to minimize heat transfer between it and the test piece, e.g by allowing the test piece to be clamped at only three points on or near its periphery For use at temperatures below room temperature, the test piece holder shall be constructed in such a way that it can be inserted into an evacuated stainless steel vessel which can be placed inside the cryostat (see 5.2.3) When a thermocouple is employed as the transient detector, the test piece holder shall incorporate a device which pushes the two thermocouple leads into contact with the conducting rear surface of the test piece using a spring arrangement (e.g as shown in Figure 3) The test piece holder shall also be of such design as to minimize the amount of incident energy arriving on the sides of the test piece, either directly or scattered to the transient detector, especially when an infra-red detector is employed When using a laser energy source, the specimen holder shall be equipped with apertures to the front and rear of the test piece, the diameters of which are not more than 0,5 mm and not less than 0,2 mm smaller than the diameter of the test pieces, such that only the front face of the test piece receives the energy pulse When using a flash-lamp energy source and a thermocouple as a transient detector, the use of apertures is advisable to avoid spurious detector level changes immediately after the heat pulse has been fired (see clause 8) Test pieces or components should be sampled according to the guidance given in ENV 1006 Whenever possible, six test pieces should be cut (see 6.2) from the same bulk material to obtain a level of the material variability Where measurements are required over a large temperature range then the minimum number of test pieces shall be prepared in each of two thicknesses, one for high temperature and one for low temperature measurement, with an overlap of at least two measurement points (for comparison) A separate test report (see clause 10) is issued for each test piece 6.2 Size The test piece shall be of sufficient size to enable a circular disc or a square plate of between mm and 15 mm diameter or side to be exposed to the laser beam The bulk material shall be as far as possible homogeneous, and consist of a single rigid layer with grain and pore sizes of less than a few hundred microns, with the exception of single crystals NOTE The microstructure of the ceramic can influence the results, especially if the material has a high level of porosity, or a texture on the scale of the thickness of the test piece Test pieces for use on the laser system (see 5.1) shall have a diameter less than the laser rod diameter, or if a beam expander is used, the expanded spot diameter, or sides short enough to allow coverage of the test piece by the laser pulse The test piece thickness shall be chosen to be as follows: a) representative of the bulk material; b) thick enough so that the t0,5 value [see equation (3)] is > 50 times the heat pulse width, thus reducing the finite pulse time effect, and so that the transient half time is within the range 0,025 s to 0,2 s; NOTE If experimental conditions not fall within these limits, then corrections for finite pulse time and/or heat losses (see Annex B, B.3 and B.2 respectively) should be used c) thin enough to minimize the heat loss from the test piece surface, taking account of b) above NOTE Heat losses may also occur through the sample holder and this can be reduced by holding the sample at three points only NOTE Normally the thickness of a test piece should be > 10 times the scale of any heterogeneities © BSI 04-2000 EN 821-2:1997 NOTE The optimum test piece thickness within the range depends on the magnitude of the estimated thermal diffusivity Many ceramics possess a large negative temperature dependence of thermal diffusivity and as measurement temperatures increase, t0,5 values increase Therefore in order to enable accurate measurement of the rear face temperature rise, with little or no correction, a second test piece should be used (see 6.1) with reduced thickness as measurement temperatures increase, whilst observing the thickness and homogeneity criteria above The thickness shall be measured, using a transducer, to an accuracy of 0,5 %, and be uniform within ± 1,0 % across a diameter or side of square NOTE The diameter or side of square is not critical as the aperture stop will adjust for any irregularities However, the outer diameter should not be in contact with more of the test piece holder than necessary to give good support, and preferably at only three points or studs, to minimize the heat loss to the holder 6.3 Coating Test pieces with a highly polished surface shall be initially roughened by abrasion where the scale of the surface irregularities is < 0,1 % of the thickness NOTE This gives better coating adhesion and more diffuse absorption Test pieces which are transparent or translucent shall be coated on the front face with a thin layer designed to absorb the laser beam The coating shall be opaque and non-reflective and shall adhere to, and not react with, the test piece over the temperature range to be measured It shall also not melt or vaporize over this temperature range All surfaces shall be degreased before coating NOTE Coatings such as platinum, nickel, copper, gold and colloidal graphite are appropriate Test pieces shall also be coated on the rear face If an infra-red detector (see 5.3.2) is used, the coating shall be of high emissivity If a thermocouple (see 5.3.3) is used as a transient detector, the coating shall be electrically conducting In such a case, these coatings shall be either vacuum sputtered metal (aluminium and copper are suitable), colloidal silver, or other appropriate highly conducting material When used with a thermocouple, the thickness of the coatings shall be greater than 4m Calibration 7.1 Calibration of apparatus All of the instruments used in the method or in the analysis shall be calibrated against traceable standards The test piece thickness (L) and transient half time (t0,5) are required in equations (2) and (3) Hence it is required that the calibration of the thickness measurement transducer (see 6.2) and of the response times (see clause 5) be known accurately © BSI 04-2000 7.2 Calibration of measurement The measurement of thermal diffusivity by this method is absolute and calibration of the method itself is not essential NOTE There are no recognized standard reference materials for thermal diffusivity measurements although several materials are used as such The use of such standards is recommended to check the operation of the equipment Only alumina has been used to identify a ceramic standard, but there are recognized ceramic thermal conductivity standards and these could be used as reference materials if the specific heat of the material is accurately known in equation (1) Care should be taken in the use of these references or standards to ensure that the transient half time and diffusivity values match closely that of the unknown materials and that the transient half times are established in identical ways Test procedure Prepare the test piece in accordance with clause Measure its thickness to the nearest 0,01 mm with a micrometer Place the test piece in the test piece holder (see 5.6), which is appropriately constructed for the temperature conditions of measurement Assemble the apparatus in an appropriate manner, ensuring that the trigger photocell can receive incident radiation, that the temperature measurement thermocouple is correctly positioned to record the test piece temperature, and that if appropriate, the thermocouple used as a rear-face transient detector is making good electrical contact through the test piece or its coating Allow the test piece to heat or cool to the required measurement temperature and maintain this temperature for at least 10 min, or until the temperature drift recorded is less than 0,01 K/s, whichever takes the greater time Record the test piece temperature Adjust the amplification of the transient detector circuit, and offset any detector voltage to zero such that a transient with low noise covers at least 75 % of the monitor screen Energize the heat pulse source, set all trigger circuits and arm the data acquisition system When the test piece temperature is stable, fire the heat pulse source and collect data for up to 10 times the recorded half rise time value, including % pre-flash and 95 % post-flash information NOTE If a significant change in detector voltage occurs between the pre-flash and immediate post-flash levels, the assembly of the systems is examined for evidence of heat pulse energy directly affecting the detector, e.g if the test piece has cracked due to thermal damage Perform at least three determinations at each test piece temperature EN 821-2:1997 Results 9.1 Principle of calculation In theory, any point on the rise curve can be analysed to yield the thermal diffusivity, a This will be given by equation (2) as follows: (2) where L tx x Wx is the test piece thickness in millimetres; is the time for the test piece rear face to reach a fraction of the maximum temperature, in seconds (see Table 1); is the percentage of the maximum rise in temperature; is a constant relating a to L and tx in the absence of radiation loss and finite pulse corrections Table gives a few of the Wx values with corresponding tx values for an ideal curve (i.e no corrections) Table — Values of constant Wx for a range of transient times x Wx (equation 2) tx 10 0,653 t0,1 20 0,832 t0,2 30 0,999 t0,3 40 1,174 t0,4 50 1,370 t0,5 60 1,601 t0,6 70 1,894 t0,7 80 2,302 t0,8 90 2,996 t0,9 To evaluate the thermal diffusivity, a, proceed using the calculation methods given in 9.2 or 9.3 NOTE It is recommended that more than one evaluation technique is used to ensure the reproducibility of the result t0,5 is the time from the initiation of the pulse until the rear face of the piece reaches one half of its maximum temperature, in seconds Check the thermal diffusivity values at fractional temperature rises other than t0,5 If the values at t0,3, t0,5 and t0,7 calculated using the relevant values of Wx in Table are all within ± % then it can be assumed that no corrections apply and the accuracy of the measurements lie within the range ± % If the spread of thermal diffusivity values so calculated is greater than ± %, analyse the response curve for radiation heat loss, finite pulse time effects, or non-uniform heating effects NOTE Examples of such analyses are given in Annex B, and references to further methods are given in Annex C Use two different methods to analyse the rising and declining parts of the thermal transient If results from two different methods differ by more than % the original data are suspect, and the experimental set-up shall be re-examined to check for the electronic drift or for heat reaching the test piece through the test piece holder If it is not possible to adjust the sample thickness to achieve t0,5 greater than 50 times the heat pulse width [see b) of 6.2], then apply a finite pulse time correction NOTE Annex B gives an example of such a correction method Make regular inspection procedures of the energy beam profile and any system optics, since non-uniform heating effects can seriously distort the curve At temperatures differing considerably from room temperature, consideration shall be given as to whether a correction is applicable to the thickness L because of thermal expansion changes with temperature For example, a material with a linear thermal expansion coefficient of 10 × 10–6 K–1 will increase L by % at 000 °C and the true value will be % larger than the measured or calculated value to which a correction is not applied 9.3 Alternative methods of calculation Methods of calculation other than that given in 9.2 and corrections other than those in Annex B are Calculate the thermal diffusivity, a, from equation permitted If such alternative methods are used, these shall be mentioned in the test report (3) [see 10 l)] giving full details and/or references 9.2 Calculation based on t0,5 NOTE References citing some alternative methods are given in Annex C where: L 10 is the test piece thickness, in millimetres; © BSI 04-2000 EN 821-2:1997 10 Test report The test report shall include the following information: a) the name and address of the testing establishment; b) the date of the test; unique identification of report and each page, customer name and address and signatory; c) a reference to this standard, i.e “Determined in accordance with EN 821-2”; d) the description of the test material; (material type, manufacturing code, batch number, date of receipt); e) method of production of test pieces from supplied material; f) test piece thicknesses, and thickness and type of coatings; g) measurement temperature(s); h) heat pulse source and pulse width; i) transient detector employed; j) environmental conditions, i.e vacuum, inert gas, etc.; k) measured values of transient half time t0,5, in seconds; l) the method of calculation employed, giving full details if not that in 9.2; m) the thermal diffusivity value(s) in m2/s; n) calculated values of heat loss corrections, if any, giving full details if not the methods given in Annex B; o) calculated value of finite pulse time correction, if any, giving full details if not the methods given in Annex B; p) a statement regarding the thermal expansion of the test piece and whether or not a correction to the thickness was applied; q) a statement regarding the use or otherwise of a reference material for checking purposes; r) discussion of errors and correction procedures; s) comments about the test or test results Figure — Heat loss correction curves © BSI 04-2000 11 EN 821-2:1997 Annex A (informative) Fundamental equations for calculation Following Parker’s method (reference 1, Annex C) and using an assumption of no heat losses, the general heat transmission equation for linear flow of heat between two parallel planes is given by: It can be shown that the temperature rise %T at the rear face of a parallel sided test piece of thickness L subjected to a heat pulse of short duration absorbed in a finite element of the front surface is given by: and: At any time t, the rear surface will rise to a fraction of Tmax: When V = 0,5: hence: [equation (3), in 9.2] where t0,5 is the time, in seconds, taken for the sample rear face to reach one half of its maximum temperature Hence for unidirectional heat flow, uniform irradiation of the sample front surface and no corrections for heat losses and finite pulse time effects, the thermal diffusivity a of a material is calculated from equation (3) However, any point on the transient curve can be measured, e.g t0,1 to t0,9, and the more general equation (2) can be used: [equation (2), in 9.1] where Wx is a function of tx Table shows the values of Wx applicable to values of tx when no heat losses or other corrections apply When corrections are applied, these alter the value of Wx in equation (2) (see Annex B) Annex B (informative) Deviations from ideal behaviour B.1 General The calculation of thermal diffusivity using equations (2) or (3) is modified if heat is lost from the sample or if the pulse transit time is less than 25 times the duration of the heat pulse Example modifications applying to the calculation method given in 9.2 are described in B.2 to B.3 12 © BSI 04-2000 EN 821-2:1997 B.2 Heat loss correction B.2.1 General The mathematical derivation given in Annex A assumes that no heat is lost from the test piece during the time taken for the heat pulse to pass through it For good conductors at temperatures close to ambient, this is a reasonable approximation, but for poor conductors and for most samples at high temperatures, corrections for heat losses will almost certainly be applicable Provided that use of a suitable holder design has minimized heat lost from the test piece by conduction and that the duration of the transient is short enough for heat lost by convection to be neglected (there are no convective losses if the measurement is performed in vacuum), the main source of heat loss is by radiation from the test piece surfaces The best way to analyse heat loss is to compare the entire experimental curve with one or more of the many theoretical models available Examples of analytical methods are given in the references in Annex C Two suitable techniques that modify the W0,5/;2 parameter in the thermal diffusivity evaluation in equation (3) are described below B.2.2 Example procedure Two heat loss correction techniques are used, one based on the rising portion of the temperature/time curve, and one based on the decaying portion Data capture of the rear surface temperature/time transient can continue out to 5t0,5 or 10t0,5 (see Figure 1) This choice will depend on the type of recording equipment used The use of 10t0,5 will provide the most reliable heat loss correction and is best suited to a computer data acquisition system The use of 5t0,5 is best suited for use with an oscilloscope where the amount of data recorded is limited NOTE The original sources of these methods are given in Annex C a) Rise time correction (Clark and Taylor’s method; reference in Annex C) From the data recorded, calculate the ratio t0,75/t0,25 (see Figure 1), then a value for W0,5/;2 for use in equation (3) can be calculated: W0,5/;2 = – 0,3461467 + 0,361578(t0,75/t0,25) – 0,06520543(t0,75/t0,25)2 (B.1) Corrections based on other ratios (e.g t0,7/t0,3 or t0,8/t0,2) are possible, but should be stated in the report b) Decay time correction (Cowan’s method; reference in Annex C) From the data recorded, calculate the ratio %T(10t0,5)/%T(t0,5) or %T(5t0,5)/%T(t0,5), where %T(10t0,5) and %T(5t0,5) are the rises in rear surface temperature at times of 10t0,5and 5t0,5respectively, and %T(t0,5) is the temperature rise at t0,5 The new value of W0,5/;2 (allowing for heat loss) is then read from the graph in Figure and can be used in equation (3) to calculate the thermal diffusivity at t0,5 Alternatively, it can be found from the following polynomial equation: W0,5/;2 = A + BỴ + CỴ2 + DỴ3 + + FỴ5 + GỴ6 + HỴ7 (B.2) where Ỵ = %T(10t0,5)/%T(t0,5) or %T(5t0,5)/%T(t0,5), and the coefficients A to H are given in Table B.1 These data in Table B.1 were prepared by reference 10 in Annex C by digitising the curves in the original reference in Annex C (see Figure 4) Table B.1 — Coefficients for the decay time heat loss correction Coefficient Ỵ = %T(5t0,5)/%T(t0,5) Ỵ = %T(10t0,5)/%T(t0,5) A 1,37197 B – 6,60729 – 0,225519 C 13,4875 0,608794 D – 14,2789 1,09003 E 8,33319 – 1,14911 F – 2,54624 G 0,318889 H © BSI 04-2000 0,0512553 0,694679 – 0,222146 0,0291019 13 EN 821-2:1997 B.3 Finite pulse time effect (reference 13 in Annex C) When t0,5 is less than 50 times the heat pulse duration, the shape of the heat pulse influences the shape of the temperature transient at the rear surface of the test piece The shape of the heat pulse from a neodymium-glass laser and a flash-lamp can be approximated by a triangular pulse of duration Ù with a maximum occurring at ¶.Ù where ¶ is a fraction between zero and one To apply the finite pulse correction it is necessary to know Ù and ¶ for the equipment being used This is most easily achieved by using a fast response photodiode (as used in several laser calorimeters) or by measuring the change in resistance of a thin (approximately 25 4m) tantalum foil strip when subjected to the heat pulse The parameters Ù and ¶ usually change with the heat pulse power and so should be determined at the power to be used Once Ù and ¶ are known, the thermal diffusivity a is given by the equation: (B.3) where the constants C1 and C2 are given in Table B.2 for values of ¶ (see also reference in Annex C) Table B.2 — Finite pulse time correction constants ¶ C1 C2 0,15 0,34844 2,5106 0,28 0,31550 2,2730 0,29 0,31110 2,2454 0,30 0,30648 2,2375 0,50 0,27057 1,9496 The finite pulse time correction given in equation (B.3) should not be used for t0,5 less than 10Ù: thicker samples should be used or the pulse width reduced Annex C (informative) Bibliography General references and calculation methods Parker, W J, Jenkins, R J, Butler, C P, Abbot, G L, Flash method for determination of thermal diffusivity, heat capacity and thermal conductivity, J Appl Phys., 32, 1679-84, 1961 Taylor, R, An investigation of the heat pulse method for measuring thermal diffusivity, Brit J Appl Phys, 16, 509-15, 1965 Beedham, K, Dalrymple P, The measurement of thermal diffusivity by the flash method An investigation into errors arising from the boundary conditions, Rev Hautes Temp Refr 7, 278-83, 1970 Righini, F, Cesairliyan, A, Pulse method of thermal diffusivity measurements (a review), High temps High Press 5, 481–501, 1973 Degiovanni, A, Diffusivité et méthode flash Conférence de la SFT (1976), Rev Génerale de Thermique, 1977 Degiovanni, A, Identification de la diffusivite thermique pour l’utilisation des moments temporals partiels, High Temperature — High Pressure, 17, 683-9, 1985 Takahashi, Y, Yamamoto, K, Ohsato, T, Advantages of logarithmic method — a new method for determining thermal diffusivity in the laser flash technique, Netsu Sokutei 15, 103-9, 1988 (In Japanese) Radiation losses Clark, L M III, and Taylor, R E, Radiation loss in the flash method for thermal diffusivity, J Appl Phys 34, 714-9, 1963 Cowan, R D, Pulse method of measuring thermal diffusivity at high temperatures, J Appl Phys 34, 926-7, 1963 10 Preston, S D, AEA Technology Ltd, Risley, UK, 1993 14 © BSI 04-2000 EN 821-2:1997 Finite pulse time effects 11 Cape, J A, Lehmann, G W, Temperature and finite pulse time effects in the flash method for measuring thermal diffusivity, J Appl Phys 34, 1909-13, 1963 12 Heckman, R C, Finite pulse time and heat loss effects in pulse thermal diffusivity measurement, J Appl Phys 44, 1455-60, 1973 13 Taylor, R E, Clark III, L M, Finite pulse time effects in flash diffusivity method, High Temperatures — High Pressures, 6, 65–72, 1974 14 Larsen, K B, Koyama, K, Correction for finite pulse time effects in very thin samples using the flash method of measuring thermal diffusivity, J Appl Phys 39, 4408-16, 1968 Non-uniform heating effects 15 Mackay, J A Schriempf, P, Corrections for non-uniform surface heating errors in flash-method thermal-diffusivity measurements, J Appl Phys 47, 1668-71, 1976 European Standards and Prestandards 16 EN 60825 Safety of laser products — Equipment classification, requirements and user’s guide 17 ENV 1006 Advanced technical ceramics — Methods of testing monolithic ceramics — Guidance on the sampling and selection of test pieces © BSI 04-2000 15 BS EN 821-2:1997 BSI — British Standards Institution BSI is the independent national body responsible for preparing British Standards It presents the UK view on standards in Europe and at the international level It is incorporated by Royal Charter Revisions British Standards are updated by amendment or revision Users of British Standards should make sure that they possess the latest amendments or editions It is the constant aim of BSI to improve the quality of our products and services We would be grateful if anyone finding an inaccuracy or ambiguity while using this British Standard would inform the Secretary of the technical committee responsible, the identity of which can be found on the inside front cover Tel: 020 8996 9000 Fax: 020 8996 7400 BSI offers members an individual updating service called PLUS which ensures that subscribers automatically receive the latest editions of standards Buying standards Orders for all BSI, international and foreign standards publications should be addressed to Customer Services Tel: 020 8996 9001 Fax: 020 8996 7001 In response to orders for international standards, it is BSI policy to supply the BSI implementation of those that have been published as British Standards, unless otherwise requested Information on standards BSI provides a wide range of information on national, European and international standards through its Library and its Technical Help to Exporters Service Various BSI electronic information services are also available which give details on all its products and services Contact the Information Centre Tel: 020 8996 7111 Fax: 020 8996 7048 Subscribing members of BSI are kept up to date with standards developments and receive substantial discounts on the purchase price of standards For details of these and other benefits contact Membership Administration Tel: 020 8996 7002 Fax: 020 8996 7001 Copyright Copyright subsists in all BSI publications BSI also holds the copyright, in the UK, of the publications of the international standardization bodies Except as permitted under the Copyright, Designs and Patents Act 1988 no extract may be reproduced, stored in a retrieval system or transmitted in any form or by any means – electronic, photocopying, recording or otherwise – without prior written permission from BSI This does not preclude the free use, in the course of implementing the standard, of necessary details such as symbols, and size, type or grade designations If these details are to be used for any other purpose than implementation then the prior written permission of BSI must be obtained BSI 389 Chiswick High Road London W4 4AL If permission is granted, the terms may include royalty payments or a licensing agreement Details and advice can be obtained from the Copyright Manager Tel: 020 8996 7070