A. Salazar

THERMAL DIFFUSIVITY MEASUREMENTS IN SOLIDS BY THE MIRAGE TECHNIQUE : EXPERIMENTAL RESULTS

This work provides the experimental confirmation of a generalized theory for thermal diffusivity measurements of solid samples using the ‘‘mirage’’ technique presented by the authors in a previous paper [A. Salazar, A. Sanchez‐Lavega, and J. Fernandez, J. Appl. Phys. 65, 4150 (1989)]. Moreover the influence of different effects on such determinations has been analyzed, and the limits of validity of the method have been established. The most important influence relies on the finite nature of two parameters: the height of the probe beam above the sample surface h and the radius of the exciting beam a. Such effects in all solids are discussed in detail according to their bulk thermo‐optical properties and for two ways of measuring: ‘‘bouncing’’ (probe beam sent to the sample surface at a small angle) and ‘‘skimming’’ (probe beam parallel and grazing the surface). The first way of measuring gives reliable results while the second one must be managed with care. In any case, significant shifts in the thermal di...

Theory of thermal diffusivity determination by the ‘‘mirage’’ technique in solids

A complete theoretical treatment of the ‘‘mirage’’ (optical beam deflection) technique has been performed for thermal diffusivity measurements in solids. Numerical calculations of the transverse deflection show there is a linear relation between the first noncentral zeros of the real part of this function and the inverse root frequency. The slope of this straight line is related to the thermal diffusivity through a factor (γ) which depends on the thermal and optical properties of the sample. We found γ=1 for transparent materials as well as for opaque thermally thin materials, whereas γ=1.44 for opaque thermally thick samples. We study further the experimental limits which make a sample to be considered as an opaque or transparent and as thermally thick or thin, and present a complete classification of solids according to their optical and thermal properties. The different behaviors observed may be related to the different geometry of thermal waves propagating through the media.

Thermal diffusivity measurements in opaque solids by the mirage technique in the temperature range from 300 to 1000 K

A method to measure the thermal diffusivity of solid samples as a function of temperature is presented. The measurement technique is based on the mirage effect and in its linear zero‐crossing relation for the transverse deflection, whose slope directly gives the diffusivity of the material. A 3D theoretical model has been developed in order to include both the effects of the radiative and convective heat transfers between the sample and its surroundings, and the temperature dependence of the refractive index and thermal diffusivity of the gas. The model also incorporates the effects introduced by the mirage parameters (sizes of the pump and probe beams, and probe beam height). The samples studied are opaque and thermally thick, and the applicability of the method is restricted to materials with diffusivity ≳1 mm2/s. Two experimental mirage setups are presented, one with the sample being heated in an open environment, and the other with the sample heated within a furnace. In the first case the range of measurable temperatures goes from ambient to ∼500 K, whereas in the second the upper limit is ∼1000 K. A comparison of the experimental results obtained with this method with those from the literature on calibrated samples of pure nickel, pure cobalt, and an AISI‐302 alloy of low thermal diffusivity, confirm the validity of the model and method proposed.

EFFECTIVE THERMAL DIFFUSIVITY OF LAYERED MATERIALS MEASURED BY MODULATED PHOTOTHERMAL TECHNIQUES

Modulated photothermal techniques provide useful methods based on linear relations to measure the thermal diffusivity of homogeneous materials. We have analyzed theoretically the applicability of such linear relations to two particular cases of layered composites, i.e., two-layer materials and superlattices. In order to measure the through-thickness and in-plane thermal diffusivities of these anisotropic materials, planar and pointlike excitations have been studied. The main result of this article is that the linear relations encountered for homogeneous materials still hold for layered composites, although their slopes do not always give the effective thermal diffusivities of the sample parallel and perpendicular to the layers, as derived from the in-parallel and in-series thermal resistors models, respectively. However, an “apparent” thermal diffusivity is obtained from which the thermal parameters of each layer can be retrieved.

Energy propagation of thermal waves

Although waves are ubiquitous in nature it is difficult to give a precise and unambiguous definition of what a wave is. Actually the distinction between wave-like and non-wave-like behaviour can be fuzzy, as it is the case of a solid sample excited by a periodic heat source. The resulting temperature oscillations inside the sample have the same mathematical expression as highly damped waves, the so-called thermal waves. The aim of this paper is to stress the energy propagation as the key to affirm whether there is wave motion. In this way it is demonstrated that there is no wave nature in these improperly called thermal waves by showing that they do not transport energy. This result has been obtained not only in the frame of the parabolic heat conduction equation that evidences the diffusive nature of the heat conduction process, but also in the frame of the hyperbolic heat conduction equation, that is a wave equation.

Thermal diffusivity measurements using linear relations from photothermal wave experiments

We present a methodology to retrieve the thermal diffusivity of bulk homogeneous samples based on a set of simple linear relations that exist between two measurable magnitudes in modulated photothermal experiments. The influence of the photothermal parameters involved (exciting beam radius and height and radius of the probe beam) is evaluated to assert the validity of the linear relations. Specifically, we discuss the thermoreflectance and mirage techniques and their more convenient use and method, depending on the kind of sample to analyze (solid, liquid, gas), to obtain the thermal diffusivity.

Thermal diffusivity measurements on solids using collinear mirage detection

A report on the adequacy of the collinear mirage technique for thermal diffusivity measurements on bulk homogeneous solids is presented. A 3D theoretical model for collinear deflection has been developed from which two simple linear relations between measurable parameters and the thermal diffusivity have been obtained. Two methods, the so‐called zero‐crossing and phase methods, are discussed in detail. The second one seems to be a promising tool for thermal diffusivity determination. It has been validated by means of experimental measurements on a set of samples with known thermal diffusivities. The technique is restricted to semitransparent solids but is also valid for materials with either high or low thermal diffusivities, being specially useful for this last group.

On the influence of the coupling fluid in photopyroelectric measurements

In this work, the influence of the coupling fluid in the measurement of the thermal properties of solid samples using a photopyroelectric (PPE) setup in the standard back configuration is analyzed. It is demonstrated theoretically and experimentally that due to the coupling fluid, the thermal diffusivity of the sample is underestimated. However, its influence disappears when performing relative measurements as a function of the temperature. That is the reason why the PPE technique is very appropriate for the thermal characterization of phase transitions.

Simultaneous measurement of thermal diffusivity and optical absorption coefficient using photothermal radiometry. II Multilayered solids

coefficient using photothermal radiometry. II Multilayered solids Agustı́n Salazar, Raquel Fuente, Estibaliz Apiñaniz, Arantza Mendioroz, and R. Celorrio Departamento de Fı́sica Aplicada I, Escuela Técnica Superior de Ingenierı́a, Universidad del Paı́s Vasco, Alameda Urquijo s/n, Bilbao 48013, Spain Departamento de Matemática Aplicada, EINA/IUMA, Universidad de Zaragoza, Campus Rı́o Ebro, Edificio Torres Quevedo, Zaragoza 50018, Spain

Thermal diffusivity of anisotropic materials by photothermal methods

In this paper we analyze the possibility of extending the photothermal methods developed for thermal diffusivity measurements of isotropic materials [A. Salazar and A. Sanchez‐Lavega, Rev. Sci. Instrum. 65, 2896 (1994)] to the case of anisotropic specimens. A full theoretical treatment of the photothermal signal generation for the case of an anisotropic sample with its principal axes aligned with the sample surface is presented. Three photothermal detection schemes have been studied: infrared radiometry, photothermal reflectance, and optical beam deflection (mirage effect). The fundamental result we have obtained is that when using infrared radiometry, photothermal reflectance and collinear mirage setups, the thermal magnitude retrieved is the resistivity to heat diffusion (a tensor defined as the inverse of the thermal diffusivity tensor). Only the perpendicular mirage experiment allows one to directly retrieve the thermal diffusivity along any direction of the material. Experimental measurements perform...