 Professor Ernesto Mareen will present for the thermal digital locking shadow rafting techniques for material thermal characterization and after that, after coffee break, we will have the first lecture of thermal lens spectroscopy by Professor Marcano from Derawar. I think we will have 30 minutes in advance today the coffee break and in the afternoon, in the afternoon we have the experimental session. We have some change today, I will announce now. Group one, two and three in Adriatico with Professor Angel Cifuentes we will have processing, data processing about shadow rafting method. Group four, five and six in M lab, we have there three, four experiments. Today, please be ten minutes before two here in the lobby. Well, there, Professor Mareen, you can start. Thank you, Humberto for the presentation. In my second lecture, I will tell you about one recently developed method for thermal characterization of materials. You know something about this technique because yesterday Angel talked about that in the lab. I will divide my presentation in three main points. In the first one, I will remember some concepts from the yesterday lecture. The second one, I want to speak about the photo thermal beam deflection technique. In the last point, I will talk to you about the photo thermal shadow graph method, in particular about the basic theory behind the method and some experimental details and results. What are the photo thermal techniques? We have a sample and we have an amplitude modulated light beam. Part of the energy of the incident light can be absorbed by the sample and part of the absorbed energy can be transformed into heat by means of non-radiative recombination or desiccitation processes so that heat is developed because the incident radiation is periodically modulated. You obtain temperature oscillations that are called thermal waves. You can measure these thermal waves directly using appropriated thermometers but you can also measure them indirectly measuring the changes that the thermal waves produce in other materials properties and in properties of the medium surrounding the sample. For example, you can generate acoustic waves. This is the basis of the photoagoustic method. You can measure the infrared radiation emitted by the heat sample. You can also make the changes in the optical reflectivity of the sample produced by heating or the superficial expansion of the sample but for the thermal beam deflation and related techniques such as the shadow graph method what we measured is the changes in the refractive index of the sample of the surrounding medium due to the heating. In the next lecture Professor Marcano will speak about the photothermal lens spectroscopy method and next with Professor Franco will speak about the photothermal lens microscopy method. Today we will deal with the photothermal beam deflection technique or also called mirroring technique. There are three main mechanisms involved in the generation of the photothermal signal. The first one is the optical absorption. Optical absorption is related with optical of the material. For example, the optical absorption coefficient, the optical reflectivity, transmittance and so on so that you can design one experiment to do a spectroscopy using the photothermal techniques. This is because the optical properties are wavelength dependent properties. In the second place you have a process of light absorb light energy into heat conversion and this process can depend on different properties of the sample and also of the kind of sample but in general you can define a quantum efficiency for the energy conversion process as the quotient of the generated heat and the absorber optical energy. In this way you can also design an experiment to measure these parameters and all the related properties. Then you generate heat and the heat will diffuse through the sample. In a process that depends on the thermal properties of the sample we will see later what are the thermal properties involved in the process of heat diffusion. And you can have also other processes for example generation of acoustic waves as in the photagoustic technique etc. These mechanisms are the motivation to use the photothermal effect for material characterization. For example, for measurement of the thermal properties of materials. Which are the thermal properties involved in heat transfer processes? The most known thermal property is perhaps the thermal conductivity of the material. The thermal conductivity is the proportionality factor between the heat flux density flowing across a sample due to a gradient of temperature. This relationship is given by the law of Fourier of heat conduction. This law describes an stationary process. There is not any time derivative in the Fourier law. Then the thermal conductivity is related to the thermal diffusivity through this equation. The thermal diffusivity is the equation between the thermal conductivity and the product of mass density and specific heat. The specific heat is defined by the first law of thermodynamic through an static relationship. This relationship is the generated energy in a sample of mass m due to an increase in its temperature. This is a static equation because there is no time or spatial derivative of time or position involved. The product of the density and the specific heat gives us the volumetric heat capacity of a sample. I told you yesterday that the specific heat capacity has an almost constant value for any sample. This is because its definition. It is defined as the product of density and specific heat. Specific heat is a measurement of the energy developed in a sample so that if the density of the sample increases then the specific heat capacity becomes lower and when the density of the material is lower then the specific heat, the capacity of the sample to store energy will be higher so that the product remains almost constant. This is also, as I talked yesterday, a consequence of the long amplitude law for the molar heat capacity of solids at ordinary temperatures. Epsilon is the thermal diffusivity. It is given by the square root of the product of a specific heat capacity and thermal conductivity of the materials. This parameter plays a role when we have heat transfer phenomena in the presence of periodical harmonic heat sources and the thermal diffusivity is responsible for what happens at the surface of the heat sample or at interfaces between regions with different thermal properties. The thermal diffusivity is the main parameter involved in the non-stationary homogeneous heat diffusion equation. This equation, this is the Laplacian of the temperature field, the second spatial derivative and this is the first time derivative of the temperature field. So this is a non-stationary equation. Therefore, the importance of alpha is that it is the parameter that appears when we are in the presence of non-stationary heat transfer processes. These are two tables showing the values of thermal properties for different materials. We must take care that these are values that are multiplied by 10 to the sixth. In this graph we can see that the thermal diffusivity values of matter span approximately five orders of magnitude from 10 to the, approximately 10 to the minus one for liquid samples to thousands of one millimetres per second for very good heat conductors such as diamonds that is here. The thermal conductivity chose a linear relationship with the thermal diffusivity and this is due to the constancy of the same value about which I have talked before. You can have material, for example, gas samples with very small values of the thermal conductivity but the thermal diffusivity of gases can be similar to the thermal conductivity of solids. Both thermal conductivity and thermal diffusivity are properties that depend strongly on the structure of the materials, on doping, etc., so that you can use these properties to characterize the consequence of doping material treatment, etc., on the samples. The same linear relationship can be found if we plot the quarat of the thermal diffusivity as a function of the thermal conductivity because also here the proportionality factor is the specific heat capacity of the materials. Materials with high values of the thermal conductivity have also very high values of the thermal diffusivity. How can we describe the thermal waves and what are the main properties of these waves? Suppose that we have a semi-infinite sample and that intensity-modulated radiation is absorbed at the surface of the sample. Suppose that we have only a superficial head source in the material. You can solve the heat diffusion equation with the properly boundary conditions. In this case, the continuity of the energy flux at the surface of the sample. And so you obtain this kind of solution for this equation. In this equation for the temperature field, E0 is the intensity of the incident light. I have also supposed a conversion efficiency equal to 1 for this process. Epsilon is the thermal diffusivity, omega is the angular light modulation frequency, and mu is the so-called thermal diffusion length given by the square root of the quotient of 2 times the thermal diffusivity and the angular modulation frequency. This equation is similar to the equation that describes all kinds of waves. You can define this equation in amplitude, given by this factor enclosed into the ellipse, and we can define a phase length given by this equation. Both the amplitude and the phase of the thermal wave equation depend on the thermal diffusion length, and the thermal diffusion length can be varied by changing the light modulation frequency. This is a graphical representation of the amplitude of the thermal wave as a function of the distance, also for one-dimensional heat transport. And we can see that the thermal diffusion length is the length at which the surface amplitude of the thermal wave decreases in times. So that the thermal wave is highly attenuated wave, which goes to zero in approximately one thermal wave length that is proportional to the thermal diffusion length. Using the thermal diffusion length concept, we can define what is a thermally thick and a thermally thick sample. A thermally thick sample, or a sample that is opaque to thermal waves propagating through it, is a sample for which its thickness is much greater than the thermal diffusion length. This kind of sample can be approximately the same infinite sample. A thermally thick sample is that for which the thickness is much lower than the thermal diffusion length. This is similar to a sample that is transferred in for thermal waves. The thermal wave equation is the basic for the method for thermal characterization of materials using the Schrodinger's slope method. I have evaluated here the thermal wave equation at a given distance from the head source, namely L. In this equation we can see that the plot of the logarithm of the amplitude times the square root of the modulation frequency as a function of the square root of the modulation frequency or a plot of the phase as a function of the square root of the modulation frequency become a stretch line. The slope of these stretch lines has this value and is related with the thermal diffusivity of the sample but if we know the distance from the head source at which the measurement is performed, then we can obtain from this slope the value of the thermal diffusivity. Not always the temperature can be measured directly. Sometimes what is measured is something that is proportional to the temperature value so that we have a proportionality factor or instrumental factor that can be frequency dependent. In this case we cannot use this method as it is for thermal characterization. We need to use some procedures to account for the frequency dependent instrumental factor. A method that becomes independent of this instrumental factor is that in which instead of the measurement of the temperature as a function of the line modulation frequency what is changing is the distance from the head source. If we plot the amplitude as a function of the distance in a semi logarithm scale then we become a stretch line whose slope is given by this equation and if we plot the phase lag as a function of L we also obtain a stretch line with the same slope so that if the line modulation frequency is known then we can obtain the thermal diffusivity from this kind of plot. And I repeat this is the basis of several methods for measurement of thermal diffusivity using photothermal methods and one of these techniques is the mirage technique or photothermal beam deflection technique. This technique is based in the mirage effect that is illustrated here. When you hit a solid surface then the medium surrounding the sample will also hit it and the refractive index changes so that an incident light beam will... the intensity of an incident light beam can change and you'll see effects such as that. This is the basis of the wind deflection technique. You have a sample, you have a light beam, an intensity modulated light beam that is focused onto the sample and part of the energy of this light beam is absorbed and hits the sample locally. Then the head generated in the sample will diffuse into the surrounding medium and hit this medium and as a consequence the refractive index of this medium will be also changed because there is a linear relationship between the changes in the refractive index and the temperature changes of the medium. The medium is here denoted by gamma and this coefficient is the photothermal parameter giving the amount of change in the refractive index for a given temperature variation and this is a parameter that is characteristic for different solids. For air this parameter is very small when compared with that corresponding to liquid samples so that in order to amplify the wind deflection effect generally the sample is immersed in a medium with a high photothermal parameter. For example ethanol and other solvents. Then you have here a gradient of the refractive index and if we change another laser beam parallel to the sample surface this light beam will be deflected due to the periodical changes in the refractive index and the deflection can take place in both directions in the normal direction, the direction perpendicular to the sample surface but also in the transversal direction. And measuring this displacement of the beam or the magnitude of the deflection of the beams will be proportional to the temperature, to the created temperature field in the samples around the medium so that measuring these changes, this displacement we can obtain the thermal parameters of the sample using the slope method. Here we have a puntual head source, not a uniform head source as I have described before. For this configuration we can also solve the heat diffusion equations and we obtain for the temperature distribution in the medium surrounding the sample the following equation. Here P0 is the density of the incident light energy, the sub-index S denotes the sample and gamma denotes the surrounding medium K is the thermal conductivity, J0 is the vessel function of first order, delta is the integration parameter, beta is a parameter given by this expression and here is the inverse of the thermal diffusion length, this parameter here, alpha is the thermal diffusivity, omega is the angular light modulation frequency and using this equation we can also calculate the magnitude of the deflation, the transversal and the perpendicular deflation that are given by these equations. Here appears the coefficient, the photothermal parameter given by this equation and the refractive index of the medium. This equation will be only valid if the thermal conductivity and of course the thermal diffusivity of the sample are greater than the thermal parameters of the medium surrounding the sample. If we plot the phase of the transversal component of the beam deviation as a function of the pump laser to probe laser offset the distance, for example here is the excitation, the head source and the probe beam pass at different distances from this point and we can measure the phase of the signal at different distances of the excitation point. If we plot this phase as a function of the distance we become a stretch line whose slope is related to the thermal diffusivity of the sample as explained before. We can also measure the perpendicular component but this component is more influenced by the thermal properties of the surrounding fluid. Normally we work with the transversal diffusion. This technique, like all techniques, has some limitations. For example, a flat sample surface is highly desired. The alignment is very difficult to do and the procedure can be lengthy because we must repeat the measurement at different distances from the heating point and if we want to have many points for that data processing then the procedure can be very, very lengthy. This can be overcome using several probe beams. For example, using a diffraction rating we can produce several light beams from the probe beam and then we can measure the displacement of all these beams simultaneously. For example, we have done an experiment in which we project the multiple beams onto a screen and with a web camera we film how the beams are deviated due to the heating and we have done that using a Logitech webcam. This is a very inexpensive webcam with these characteristics. This is a video of water source. The blue spot is a reflection of the probe beam. It's only a reflection to see that the beam is intensity periodically modulated and each of these points correspond to the different probes. We see that the deviation is at the center. Here is the heating point and then the crest when we go away from this point. This video can be processed digitally to obtain the phase of the signal and we can plot the phase of the signal as a function of the distance. To do that, we must use the locking amplifier method. I have talked yesterday about this method. The locking method allows to recover the useful signal from a very noisily signal in essence. This is an example of such a measurement. This is a measurement performed in a bulk sample of cadmium telluride, a semiconductor sample and this is the plot of the phase as a function of the distance. Here the heating point is at zero and we will become also a stretch line if we measure it in this direction. This is a symmetrical curve. From the slope and knowing the line modulation frequency we can obtain the thermal diffusivity values. These are preliminary results in different materials and the report values showing a very good agreement. This work was presented in the International Conference of Intransfer Fluid Mechanics and Thermodynamics in the past year. The multibin deflection method overcome this limitation of the photocermal bin deflection but we have still other limitations with this method. The alignment of the probe bins with the sample is still difficult and we need the flat sample surface among others. I will talk now about the shadow graph method with which we try to overcome these remaining limitations. A shadow graph technique is not new. It is a photographic technique that is widely used for example in fluid mechanics, aerodynamic studies of heat convention effects among others. The goal of our work was to demonstrate that the shadow graph method can be useful to detect the refractive induced perturbations produced in a sample in experiments like the photocermal bin deflection method. What are the equations behind the shadow graph method? The principal scene is also the dependence of the refractive index from the temperature. For a given temperature change we become a change in the refractive index given by this equation and the NDT is the photothermal coefficient. Suppose that we have a sample, the sample is heated and we project and expand the light bin so that we can project an image of the sample onto a shadow located behind the sample. The governing equation for this effect is this one. Here E0 is the intensity of the incident light. E is the intensity of the light bin at the shadow. L is the distance between the sample and the screen. There is a dimensional parameter, I will not enter into details about this parameter here and N is the refractive index because the refractive index depends on the temperature. We can use the dependence of the refractive index from the temperature to obtain how the shadow graph pattern will be modified due to the periodical temperature changes induced in the sample. This is a basic configuration, the experimental setup for this technique. Here this is the sample, this is the excitation light bin, a PUM bin. This is an intensity modulated light bin that is focused into the sample. Here we have the probe bin that passes through the sample and the shadow of the sample is projected onto the screen and can be filmed using a camera. These are computational simulations of this effect. This is the behavior of the phase of the shadow graph signal as a function of the distance from the hitting point. This simulation has been performed for a sample with this value of the thermal diffusivity, 10 to the minus 5 square meter per second. It is performed here for a thermally thin sample and here for a thermally thick sample. From these images we take the values closest to the sample surface and we plot the phase of the signal as a function of the distance for different modulation frequencies. Then we do a less square linear feed to these curves to compare the obtained value of the thermal diffusivity and compare them with the values used in these simulations in order to obtain the estimation error by comparing these values. We obtain several results. One of them is that for very low modulation frequencies the error becomes greater. The selection of the right modulation frequency is a very important step in these kind of experiments. The higher value of the modulation frequency that can be used will depend on the free rate of the camera used for the detection. These are the results obtained by the simulations. This is a scheme of the experiment. This is the sample, this is the pump bin. These circuits represent the gradient of the refractive index changes produced by the hitting. Here is the probe bin set of collimating lenses and here is projected a shadow of the sample and this shadow will be disturbed due to the refractive index changes. We have done two kinds of experiments. One of them using a thermographic camera working in the rare infrared ratio of the electromagnetic spectrum around one micrometer. This is a free camera. It's a very expensive camera. I don't know in Europe but in Mexico this is the cost given by the vendors of this kind of camera. This is in Mexican pesos, three millions of Mexican pesos. For this experiment, of course the probe laser must be also in the infrared region and we use a 905 nanometer wavelength diode laser. In another experiment we use a very inexpensive web cam, a computer web cam, working in the visible part of the spectrum because it's an order of magnitude below. And here the probe laser was a visible diode laser, 630 nanometer wavelength. The PUM laser in both cases was a visible laser, 445 nanometer wavelength and 250 milliwatts nominal power. The value of the light power that reaches the sample is not important for the calculation of the thermal properties. The sample is placed within a cubic centimeter glass cell and is immersed in acetone-intrin, a solvent with high photo-thermal parameter. And the experimental setup is similar as that described before. And this is the experimental results obtained using the linear infrared camera, the thermographic camera. Here are the results of the theoretical simulation for comparison. You can see that the experimental results are very similar to that predicted by the theory. This is the phase of the signal that is obtained in the case of the linear infrared camera. This camera has integrated locking capabilities so that in the measurement we obtain directly the amplitude and the phase of the signal. This is the phase of the signal. Here in the center is the heating point. And you see that the behavior is symmetrical, similar both sides of the heating point. And here are results measured only at one size to obtain a great quantity of points for different samples. Copper, lead-cellenite and zinc. From the slope of these curves, we calculate the thermal diffusivity values and they are shown in this table together with literature values for comparison. The agreement is also very well. And these are results obtained with the inexpensive webcam for a platinum filament. Here the sample was a filament of platinum. The heating point is here at zero. This is the phase image. In this case, the camera has not locking possibilities incorporated. But we have done data processing. Angel Cifuentes will talk today in the afternoon about the way to process this kind of images. And from the phase images, we obtain a curve of the phase as a function of the distance and from the slope we obtain the thermal diffusivity value of the sample. As the conclusion, the photothermal locking shadow graph method is a recently proposed method implemented to overcome some limitation of the conventional photothermal beam deflection technique. The photothermal beam deflection technique is an ancient technique that was developed approximately 20 years before. One important thing is that the technique can be implemented using very simple experimental apparatus. A simple webcam is necessary, inexpensive, diode lasers can be used to do this experiment and also highly specialized licensed hardware is not required. For example, such as that incorporated in the thermographic camera to work with this testing. And because that, the testing can be very useful for teaching thermal wave physics. For example, at universities, high schools, etc. Thank you very much. Thanks to Professor Marin for the presentation. As we will have today also an experimental session about this technique and also processing, for sure you will have a lot of questions and comments. And we have time for this. Please. Thank you very much for a very interesting and nice lecture. I have, let's say, one question or more complex. Your samples were solid, liquid but with huge homogeneity. What is going on when you have some inhomogeneities inside? For example, medium as we saw in posters with particles which are simple particles or they are a kind of core shell because they have a small layer. And it is possible to detect as I know very, very small dimension in nanometers or less than range how these properties are reflected in this case and if it is possible to be detected. What we measure in these techniques are effective values of the thermal properties of the sample. If we have a composite sample, a composite material or a non-homogeneous sample we measure the effective thermal diffusivity of the sample. Then to recover the thermal properties of each component of the sample you will use a theoretical formula that relates the effective thermal properties with the properties of the individual components. In some case that can be not possible. For example, if one component is in a very, very low amount maybe it doesn't affect the effective property. But the methodology is this, you obtain the effective parameter and then you try to obtain the properties of the different phases using some models. Thank you for the very nice presentation sir. Regarding the multi-beam deflection technique or the single beam deflection technique I wanted to ask what would be the size of the spot that we could talk about because perhaps we might have a sample which is quite flat but it's got different thermal diffusivity on different parts of the sample. So we could scan over it and for example measure these thermal diffusivity on different parts of the sample. So what would be the spot, the finest spot that we can measure that thermal diffusivity for that? For example, we can say that thermal diffusivity over a one millimeter circle two millimeter or down to microns. The model describing the photothermal beam deflection technique is a model for a point head source. So that you must try to reproduce in the experiment the condition described in the theoretical model so that we must focus the laser so much as possible. One meter a meter for example. If you have a sample that is not homogeneous in the scan direction then the method doesn't work. So you can have an homogeneity in the perpendicular direction but in this direction this is the limitation of the method of course because you will obtain a different behavior of the probe beam for the different distance. Thank you sir. Question please, comments. Thank you so much for your presentation. I have one question. If I'm correct when we have a solid object then we see the shadow graph. In this method if we have for example liquid or gas again we see the shadow graph and this technique works or not? The studied sample must be a solid sample in this method. This is a method for characterizing solid samples. But the sample must be immersed in a liquid. You can perform the experiment in air of course but the photothermal parameter of air is very small than the photothermal parameter for liquids. So that if you immerse the sample into a liquid what we do is an amplification of the photothermal effect. But what you characterize is a solid sample. Maybe you can use the same model. If you know the thermal parameters of the solid sample you can also do the same experiment to characterize the liquid. But what is useful is the use of this method for solid sample characterization. Actually measure the thermal properties of the solid object in liquid or for example gas media. Ok, thanks.