Thermal Conductivity Resources

Renaissance Man – Towards the Unattainable Perfection

So! What is next?

Following the guidance provided in the previous Blog, a decision has been made on the choice of a method and apparatus either “home-developed” or commercially available, for measurement of the thermal conductance or conductivity of the specimen. A series of measurements have been undertaken over the required temperature on our new material. Now comes the final decision regarding the need to justify and compare the accuracy and precision levels for the measured values that have been claimed for the specific method and test conditions.

This is customary not only for one’s needs of satisfaction in attaining good measurement performance but also now that national and international trade has expanded so much there is the necessity for a “leveling of the playing field” National and international regulation has been introduced requiring accreditation and certification as additional factors particularly in areas related to energy conservation. Thus, for many materials precision and reproducibility of the measured performance values has become an important, often a controlling factor. At this point, the importance of the use of REFERENCE MATERIALS enters the equation.

World,Map,And,Network,Connection

However, before addressing the subject in detail it becomes necessary first to illustrate the difference, possible confusion, that often exists between accuracy and precision of a measured value, especially as each method is claimed to have such values for its total operational range. This can be illustrated by the example of taking a specific number of throws of a dart at a dartboard that is a series of concentric circles of regular increase of radius (area) around the central bull. 

Take a selected number of shots of the dart and measure the position and distance of each hole to the centre of the bull. Assuming the individual hole is spread randomly across the bull and outer areas, the average of the distances will provide the accuracy level for the thrower (and dart). A X% level can be declared where the concentration is in the area of bullseye. Where the holes are concentrated in a group within another area or at the same distance or position from the centre this average distance will now provide a value for the precision levels. An indication of bias will be shown if the concentration occurs at a specific position in an area while a single hole outside that of the concentrations can then be classed as an outlier.

If the area of the bull now represents a Reference Material of known levels of accuracy and precision the analogy to thermal property measurements becomes obvious. A single set of measured values at one distance from the bull, provides the accuracy and limits for a measurement. The accuracy and precision levels for the method are now represented by the average of all the results obtained at different distances or with different apparatus and users.

To answer the question of what is a Reference Material? Factually it is an artefact that is required not only to verify and quantify the precision and bias of standard methods of measurements but also validate other, particularly new, techniques, calibrate comparative methods, reference points in inter-laboratory studies, and act as a referee in questions particularly of competitive performance claims. To stress its importance the International Standards Organization (ISO) has taken steps to clarify the issue by developing two Standards plus a Guide to define both the term and the necessary support information for when and how it is applied.

In the field of measurement of thermal transport properties three types of reference material exist:

  1. Certified or Standard Material (CRM or SRM): a single specimen or artefact obtained from a well characterized stable, reproducible, preferably homogeneous, stock of a material having known provenance and certified thermal property values. These values are based on extensive testing, using absolute (primary) measurement techniques, including direct measurement of all necessary quantity parameters carried out by or under the auspices of a national measurements laboratory (NML) or equivalent organization,’
  2. Transfer Standard (TS): a single specimen having unique property values obtained using an absolute (primary) method by an NML or equivalent body,
  3. Reference Material (RM) a commercially available material of known provenance having accepted values based on extensive evaluation by several equivalent reputable sources using one or more standard test method(s).

Currently, it is not possible to assign a definite precision limits as the accuracy range for existing references existing does vary from 1% to 6%, depending on the material, both the range of property and temperature range, and the analysis statistics used for the verification. Since a TS is based on the unique measured value its precision is that of the proven apparatus used by the measurement organization.

However, before addressing the subject further it is necessary to dispel a recent suggestion that has arisen due to a total misconception of this artefact. This concerns a claim that it is now allowable? to develop a personal consensus (accepted) reference material (standard) with an assigned thermal property value of thermal conductivity at room temperature. This can be achieved first by selecting a material and undertaking a review of all published data that one can find for specimens having the same or similar name, descriptive details, and use for a specific temperature range.

Following a statistical analysis of the claimed accuracy of each, if such information has been included, an assigned thermal conductivity value at room temperature value with derived accuracy and precision can be developed. The claim is further magnified by the ridiculous suggestion that values at higher and lower temperatures can be developed from comparisons with the behaviour of a similar “known material”. However, any such values totally neglect consideration of the lack of provenance for each specimen and that each measured value is solely that for the measured specimen and not the material.

In an earlier Blog I mentioned that Mother Nature has a habit of playing “dirty tricks” on us, for example by providing asbestos as a valuable material for many applications as a thermal insulation but which is also a killer. However, this is dwarfed by the situation she has forced upon us by making the ranges of thermal conductivity and temperature of application some seven and four orders of magnitude respectively for all materials. This is reinforced further when the factors of the added effects of environmental and mechanical pressure are introduced. But to crown it all most materials and systems are not ideally homogeneous and isotropic in the sense of the term being applied to dense solids.

Thus, the selection of a suitable reference material often requires a compromise between what is considered ideal for the purpose and what is available. Once the choice is made, the need becomes that of undertaking the extensive lengthy programs of measurements of the various physical and thermal property values required both to establish the provenance of the material and the evidence to support the final declared thermal property values.

Due to the real needs caused by this factor of broad ranges of property of materials, there is a continuing call by the many users and consumer workers in industry, government, and academia for more CRMs. Unfortunately, it is sad to report that the response has been extremely limited such that the cupboard is somewhat bare but luckily not empty. At the outset, the contents relate primarily to different types and forms of solids, but it is emphasized that the present situation relates also to fluids and molten materials. My personal estimate is that the total number is between thirty and forty. However. it is unfortunate that most of these have certified values either at “a room temperature” range or for a specific, often limited range of temperature.

The apparent poor response to demands is due principally to both the high costs and long times involved in undertaking all of the required experimental measurements to establish provenance and especially the steady-state methods rather than the faster transient techniques. to provide the property values. However, a most time-consuming effort is that of the statistical analysis of all of the individual and combined results that is necessary to produce the certified values. As an example, I include a summary of the extensive European Union funded program in the late nineties carried out on the glassy ceramic material Pyroceram 9606. This material was chosen by a group of experienced workers as the best one to satisfy all the requirements of stability and reproducibility required for a high temperature CRM for thermal conductivity and thermal diffusivity to 1200k.

The subsequent extensive program involved a total of twelve organizations, six characterizing and verifying the stability and reproducibility and a further different group of six directly measuring both properties. Thermal conductivity was measured on multi-sets of specimens by the steady-state guarded hot plate method and single and parallel wire versions of the transient hot-wire line source method, thermal diffusivity by the flash, electron bombardment, and hot-wire methods. Specific heat by DSC and hot-wire methods and linear expansion by dilatometry were included to enable subsequent derivation of conductivity from the measured diffusivity to verify internal consistency. Analysis of results by a further evaluation group from the Institute of Reference Materials and Measurement in Belgium produced the certified reference for each property for the BCR 724 resulting reference. The complete study took two years to complete at a multi-six figure (dollar or euro) cost.

One important conclusion from this study was the essential need for measurements of other properties including thermal expansion, and specific heat to complete the circle that ensures internal consistency. The thermal expansion measurements are undertaken over a broad temperature range to enable the provision of adjusted thermal property values that allow for changes of dimension.

Thus, the dominant factor required in the provision of the reference values becomes the establishment of the accuracy of the absolute methods selected for the chosen material. For high thermal conductivity materials such as metals, alloys and other electrical conducting materials (k>5 W/m.k) the axial rod and radial flow methods have indicated that accuracy levels of +/-3% and higher can be obtained over a broad temperature range of 100 to above 1200k especially when supported by electrical resistivity measurements.

 However, for all other materials (k>5W/m.k) where the most suitable absolute method available is the guarded hot plate the picture is more complex since at present the accuracy and precision levels can vary between a definite 1% and higher to approximately 6% and lower. The ranges are highly dependent on numerous factors including the temperature range, the apparatus size and the design the experimental procedure, and finally the type of material that can range from a homogeneous solid ceramic or polymer to a heterogeneous, sometimes anisotropic variable density fibrous. cellular and layered types.

In a previous blog, I mentioned the successful development and use of the heat flow meter method in the thermal insulation industry. This method is totally dependent on the availability of one or more reference materials. Based essentially on the cooperative development work carried out at the national standards laboratories first in the USA followed by the UK, Canada, and France there are now three reference materials, two are different density and types of glass fibre and one a cellular plastic. These have certified thermal resistance values of 1% accuracy over the approximate temperature range 250k to 350k of 1%.

Naturally, there were great expectations that other reference materials could be developed but much disappointment that this was not to be. The major stumbling block was that this high level of accuracy of the method at room temperature could not be attained and certainly not maintained at elevated temperatures. As an example, based on several interlaboratory studies carried out in the nineteen fifties, eighties, and early 2000s the percentage deviations in the accuracy level at 800k were over 20, 17, and 6, respectively. The significant improvement in the last set was due to recommendations resulting from a detailed review of the ISO standard by a European group of experts from national and commercial organizations.

Essentially changes were made to improve the basic hot plate apparatus configuration coupled with additional revision in the experimental and analysis procedures. Results of a recent European inter-comparison carried out as part of a programme to develop a high temperature thermal insulation reference material confirmed that this order of accuracy can be attained up to 800k. However further analysis is required before the proposed candidate material can be certified material.

Thus we are left with the current disturbing situation that although very high measurement accuracy of 1% is possible at temperatures close to room ambient on thermal insulation products it has not been possible to maintain that level for the much greater number of materials and systems in the approximate property range 0.03-5 W/m.k or for any extended ranges of temperature. The only reference materials in the property range having certified values over a broad temperature range of application are polymethyl methacrylate a plastic, Pyrex7740 a glass and, Pyroceram 9606 a ceramic having values of approximately 0,2, 1.2, and 6 W/m.k and corresponding accuracy levels of approximately 1.5%, 3%, and 6% respectively. Clearly, additional artefacts are necessary due to the numbers and types of materials and systems that are now in constant use.

There are several claimed reference materials, especially as transfer standards that have accepted reference values for thermal diffusivity. Although the extensively used flash method is not an absolute method and requires relatively small specimens it has proved to be most suitable for several national measurement laboratories to develop new experimental versions with and improved data analyses of results. These have indicated that accuracies of the order of 5% can be attained over a broad temperature range for homogeneous solids only including polymers ceramics and metals.  

Initially, verification was undertaken using existing homogeneous CRMs and RMs, for example, Armco iron, 304 stainless steel, Pyroceram 9606 and, polymethyl methacrylate. The reference thermal conductivity values were compared to those derived from the measurement values using measured density and selected literature values for specific heat. However, due to uncertainties that often existed in the latter property, improvements in accuracy were obtained once the separately measured specific heat of the specimen was used and this is a necessity for reference material purposes.

This use of thermal diffusivity is of some value in providing reference values for many materials having a thermal conductivity in the lower range. However, it must be stressed that this can use of the property applies ONLY to homogeneous isotropic materials and is not suitable for consideration when the material is other than so described. 

It is my intention to provide further details on particular materials the property range and sources in a separate blog.

Renaissance Man.

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