The Goal: It is desirable to combine solar photovoltaic and solar thermal applications in order to extract the maximum benefit from the sun's energy, creating both electricity and useful heat. To maximize output, high solar absorbtance, and low thermal emissivity are required.

A non selective coating (like black paint) has a high thermal emittance (gives off thermal radiation (heat) to the environment) and a high absorbtance of solar radiation.

Selective coatings can allow us to manipulate the ratio of absorbtance to emittance. Some selective coatings are strong absorbers of solar radiation, but are transparent to thermal radiation, in that case, thermal emittance is determined by the properties of what the coating is applied to.

## Things To Keep In Mind

Emittance: Ability of a surface to emit heat by radiation. Emissivity is the ratio of emission of a surface to that of a black body at the same temperature. The duller the material, the higher the emissivity, the more reflective the material, the lower the emissivity. Think of comparing a bright white surface and a dull black surface in the middle of summer. The black surface, is much hotter to touch. Emissivity is a surface property, so surface roughness, temperature and wavelength all have an influence on it.

Reflectance: The percentage of incoming energy reflected off a surface at a given wavelength.

Absorbtance: The fraction of light absorbed by a sample at a given wavelength.

Transmittance: The fraction of light at a given wavelength that passes through a sample.

## Fundamentals of Semiconductors/PV

${\displaystyle e=mc^{2}}$

The following equations came from Solar Cells by Martin E. Green

pg 41 Reflection ${\displaystyle R={\frac {({\hat {n}}-1)^{2}+{\hat {k}}^{2}}{({\hat {n}}+1)^{2}+{\hat {k}}^{2}}}}$

Where:

• ${\displaystyle {\hat {n}}}$ is the real part of the index of refraction
• ${\displaystyle {\hat {k}}}$ is the imaginary part of the index of refraction
• Index of Refraction ${\displaystyle {\hat {n_{c}}}={\hat {n}}-i{\hat {k}}}$

Note: Transmission is T = 1 - R

Absorption of Light

Absorbed light at a distance into the semiconductor

Intensity of light = I

${\displaystyle I=I(x_{o})exp(-\alpha (x-x_{o}))}$

• ${\displaystyle \alpha ={\frac {4\pi f{\hat {k}}}{c}}}$

Note:

• ${\displaystyle \lambda ={\frac {c}{f}}}$

Math Equation Help in Wiki

Other Wiki Basics

Direct Band Gap Semiconductor

${\displaystyle hf=E_{f}-E_{i}}$

${\displaystyle \alpha (hf)=A(hf-E_{g})^{1/2}}$

Where

• ${\displaystyle E_{f}}$ Final energy state
• ${\displaystyle E_{i}}$ Initial energy state
• ${\displaystyle E_{g}}$ Band Gap Energy
• A is a constant with a value of 2E4 when alpha is expressed in ${\displaystyle cm^{(}-1)}$ and hf and ${\displaystyle E_{g}}$ is in eV.

Indirect Band Gap Semiconductor

${\displaystyle hf=E_{g}-E_{p}}$

${\displaystyle \alpha (hf,T)=\sum _{m=1,2n=1,2}A_{ij}({\frac {(hf-E_{gn}(T)+E_{pm})^{2}}{exp(E_{pm}/kT)-1}}+{\frac {(hf-E_{gn}(T)-E_{pm})^{2}}{1-exp(-E_{pm}/kT)}})+A_{d}(hf-E_{gd}(T))^{1/2}}$

Where

• ${\displaystyle E_{p}}$ is energy of an absorbed phonon with the required momentum

The values can be found in Table 3.1 page 49 for Silicon

## Applicable ASTM Standards

Please note, although these standards will be useful in future work, they provide little new insight for the work that is currently being conducted. I still thought it worthwhile to keep them around.

### E 408-71 (Reapproved 2008): Standard Test Methods for Total Normal Emittance of Surfaces Using inspection-Meter Techniques

Provides equation for total normal emittance (the ratio of the normal radiance of a specimen to that of a blackbody at the same temperature; dependent on wavelength and temperature. The rest of the standard goes on how to measure the emittance of large surfaces, in a non-destructive manner using portable devices, neither of which are neither an integrating sphere nor a spectrophotomer. This standard is included here when the time comes to test full-scale spectrally selective panels.

### E-1980-01: Standard Practice for Calculating Solar Reflectance Index of Horizontal and Low-Sloped Opaque Surfaces

Calculation of the Solar Reflectance Index (SRI) of horizontal and low-sloped opaque surfaces at standard conditions (emissivity /0.1). References E 903, Test Method for Solar Absorption, Reflectance and Transmittance of Materials Using Intergrating Spheres (this standard is not accessible through Queen's resources, it is possible that it has been superseded by something else). Standard definition of thermal emissivity as: the ratio of radiant flux emitted by a surface at a given temperature to that emitted by a blackbody radiator at the same temperature (for temps below 150ºC).

• Gives equation for steady state surface temp of a material exposed to the sun (define solar absorptance as 1-solar reflectance)

### C 1549-04: Standard Test Method for Determination of Solar Reflectance Near Ambient Temperature Using a Portable Solar Reflectometer

Technique for determining the solar reflectance of a flat opaque material in a laboratory or field setting using portable solar reflectometer to evaluate temperatures and heat flows across surfaces exposed to solar radiation. This references E 903 again. It would be great to get that one. Measurements are made when a sample is heated by a tungsten lamp for 2 seconds out of a 10 second measurement cycle. 4 detectors measure the reflection at 20º from the sample surface. Solar energy that is absorbed is defined as Energy absorbed=area*solar flux*(1-solar reflectance), where solar reflectance is a dimensionless quantity. Describes how to perform the measurement, again, not using an integrating sphere.

### E 1175-87 (Re-approved 2009): Standard Test Method for Determining Solar or Photopic Reflectance, Transmittance, and Absorptance of Materials Using a Large Diameter Integrating Sphere

Accurate optical property measurements of spatially nonuniform materials is covered in this standard. For large specimens with specular and diffuse optical properties. Suggests that transmittance is measured by placing sample on top of port, but reflectance is measured by placing sample inside the sphere, this is not what PIKE recommends we do. Large sphere is used to average the disparities in the material (the sample size is large and so is the beam of light hitting it). States again that absorption can be calculated as 1-total solar reflectance in opaque materials. A large sphere is defined as one with a minimum radius of 1 m. Our sphere is definitely not large. Unfortunately, this also isn't very useful.

## Testing Papers

The following papers are to help create a procedure for measuring emmisivity ect.

### The challenge of high-performance selective emitters for thermophotovoltaic applications

A. Licciulli, D Diso, G Torsello, S Tundo, A Maffeszzoli, M Lomascolo, and M Mazzer. Semiconductor Science and Technology. 18 (2003) S174-S183

This is a review article on what's been done in materials science for high temperature application of thermophotovoltaics. Selective emitter is denied as a class of materials equilibrium thermal-radiation emission occurs in a narrower spectral region compared to a black body at the same temperature. This isn't quite the same kind of selective surface we have been looking for, but it's a neat article none the less. Operating temperatures for devices in question is 100-1500ºC. Says that detailed microscopic analysis and the basic theory of the mechanisms ruling high temp emission is required.

• Equation for spectral radiance of at black body in terms of wavelength and temp that might be useful
• Equation for emissivity of a surface as a function of temperature
• Suggest measuring temp of samples using a thermocouple, but cautions that conduction will occur and remove heat from that area of the sample more quickly, non invasive temperature measurement techniques may include IR radiation thermometers, one study referenced knew the emissivity based on the power of the furnace they assumed the sample to be in equilibrium with.

### Reflectance, Solar Absorptivity and Thermal Emissivity of SiO2 -Coated Aluminum

G. Hass, J.B. Ramsey, J.B. Heaney, and J.J. Trilo. Applied Optics. Volume 8, Issue 2. February 1969. pp275-282

This is an old article, but I thought it might be helpful because we're working with aluminum too. Confirms what we already know that aluminum can be coated with surface films to produce a surface that is non absorbing in the visible region, but strongly absorbing in the IR region. Describe the effects of varying the size of an electron beam used in SiO2 deposition has on absorptance in UV region (wide beam = no absorption in far UV to near IR). They used highly polished samples to measure reflectance, this isn't possible for us since it seems to mess up the integrating sphere even more, and we want to test the aluminum in the condition we're going to use it in. Solar reflectance was measured using a modified Beckman DU instrument with a Perkin-Elmer model 350 double beam spectrophotometer. (reflectance measurements were absolute). Absorption and emission were evaluated graphically from charts with distorted λ scales and integration by means of planimeter.

• Used a thermocouple (copper-constantan) to measure the temperature of the sample. Equation to calculate emissivity as sample cools:ϵ=WCP3σAt(τ2-τ1)1T23-1T13, corrected because of heat losses from attached thermocouples
• Some reflectance and emissivity graphs, might be helpful to see if ours are anything close to right.

### Spectral selectivity of high-temperature solar absorbers

D.M. Trotter, Jr., and A. J. Sievers. Applied Optics. Vol. 19, No. 5. March 1980 pp 711-728

The first paragraph in this is really helpful. There should be a cutoff wavelength in spectral selective materials at which point the spectral absorptance abruptly drops to zero. This position is weakly a function of operating temperature (verifying that we should be checking this) and the solar flux concentration (this value is fixed by the sun, but in our experiments we should try to use the same) They suggest the cut off frequency should be less than or equal to 2x3.14xc/2.

• equations for thermal emittance and solar absorption in terms of area, operating temperature, energy flux, the solar spectrum and Plancks law spectral distribution
• Use models consisting of models with selectively absorbing coatings
• Values of emissivity determined by the overlap between the blackbody absorptivity and what the material produces at a given temp
• lots of math in this paper, I don't think its exactly what we want, deals a lot with material thickness
• Graph of a thermally broadened and blackbody emissivity appears to show aluminum having the same emissivity with temperature as an aluminum black body?
• emissivity is also strongly correlated to incidence angle

### Integrating Sphere for Mid- and Near-infrared Reflection Spectroscopy

Leonard M. Hanssen, and Keith A. Snail. Handbook of Vibrational Spectroscopy. John Wiley & Sons Ltd. 2002

This is a literature review article on integrating spheres, it does an excellent job summarizing what's been done in the past and some of the nuances associated with operating spheres. Here are some highlights…Integrating spheres are the primary analysis tool for quantitative characterization of reflectance and absorptance for materials that are highly scattering.

• reflectance is defined as the ratio of flux reflected from a surface to that incident on the same surface
• integrating sphere throughput is the efficiency of the integrating sphere system related to the incident flux of the detector over the input flux
• First recording spectrophotomer made in 1928 at MIT, 1916 Taylor and Rosa develop a technique for measuring absolute reflectance using an integrating sphere
• National Institute of Standards and Technology is developing a standard for the integrating sphere using roughened gold, another is used by the National Physics Laboratory (UK) based on flame-sprayed aluminum.
• Key aspects of sphere design are shape and Lambertian inner coating that allows light to be reflected off all surfaces equally in all directions – the detector should receive a flux directly proportional to the light on the sphere. If the sphere isn't perfect, the high surface reflectance ensures that the light bounces around several times before it hits the detector
• Several methods for solving for sphere efficiency (throughput), conservation of energy, integral equation of sphere irradiance, solving a matrix equation determined by the number of distinct regions in the sphere (all methods are consistant)
• Absolute reflectance sphere are used to calibrate standards for reflectance instruments
• Describe some spheres where the sample goes on the inside of the sphere, and others where it goes on top. For some methods of collection (which we obviously wont use) the sample has to be the same material as the sphere
• Relative reflectance measurements are fine for the vast majority of applications
• We have a substitution type sphere (the reference and the sample can't be on the detector at the same time). This is the simplest design and doesn't require any moving parts which would suggest we should be keeping our mirror in the sample position when making measurements
• Some losses because our sample is flat, may not direct light everywhere

### Inverse estimation of temperature dependent emissivity of solid metals

J. Zueco and F. Alhama. Journal of quantitative spectroscopy & radiative transfer [0022-4073] Zueco yr.2006 vol.101 iss.1 pg.73-86 [1]

Super mathy review. They figure out what temp the sample was at without actually measuring it. They say that total emissivity depends on temperature, but experimental methods (2 referenced) are complicated and time consuming – their approach lets you measure for a smaller amount of time, figure out and equation that governs temp. Check references from this paper, they might have something more useful

### Temperature-dependent emissivity of silicon-related materials and structures

Ravindra, N.M.; Abedrabbo, S.; Wei Chen; Tong, F.M.; Nanda, A.K.; Speranza, A.C.;Semiconductor Manufacturing, IEEE Transactions on Volume 11, Issue 1, Feb. 1998 Page(s):30 – 39 [2]

Might be able to use this paper for the math in it, but they used very specific equipment that allowed them to measure everything over a huge temperature range. Emissivity is an important parameter in radiation thermometry.It is defined as the ratio of the radiance of a given object to that of a blackbody at the same temperature and for the same spectral and directional conditions. It is a function of wavelength and temperature. In this experiment transmittance and reflectance were measured and equations are provided that link the observed to the true values. A spectral emissometer (one of three in the USA) allowed measurement of radiance, reflectance, transmittance, and temperature simultaneously. They got % emittance, % transmittance, and % reflectance as a function of temperature across wave lengths.

### Optical Characterization of Industrially Sputtered Nickel-Nickel Oxide Solar Selective Surface

M Adsten, R. Joerger, K. Jarrendahl, E. Wackelgard. Solar Energy Volume 68. No.4 pp 325-328. Year 2000. [3]

Their goal was to see if the optical constants of the materials and manipulated materials they were testing were close to the ideal ones. They measured absolute spectral specular reflectance and transmittance using a non-standard spectrophotometer with a small (4mm) integrating sphere as a detector. Their sample didn't go on the sphere, but on a different surface and they spun the sphere all over the place because they were concerned about angles. Also used Co Variable Angles of incidence Spectroscopic ellipsometry (VASE). No temperature series.

### Mathematical Framework for Predicting Solar Thermal Build-up of Spectrally Selective Coatings at the Earth's Surface

N.P. Lavery, Applied Mathematical Modelling 31 (2007) 1635-1651 [4]

This article talks about the different colour paints and their ability to absorb the spectrum of light. Temperature was also observed and found the black gets the hot while lighter colours remain cooler. It has some interesting graphs to show this. 5mjmp 20:16, 22 September 2009 (UTC)

### Stainless steel/tin/glass coating as spectrally selective material for passive radiative cooling applications

T. Mouhib, A. Mouhsen, E.M. Oualim, M. Harmouchi, J.P. Vigneron, P. Defrance. Optical Materials 31 (2009) 673–677[5]

The authors are studying spectrally selective surfaces in a radiative cooling application. They assume that heat transfer occurs only by radiation and ignore the effects of conduction and convection. They state that at equilibrium the energy emitted is balanced by the energy that is absorbed.Absorptance is defined as 1-(Rsol+Tsol), where are Rsol is the solar reflectance (estimated as the average spectral reflectance over the entire solar spectrum). Measured reflectance, transmittance and absorptance using a spectroradiometer and a monochromator. Have graphs of Reflectance vs wavelength

### Spectral selectivity of composite enamel coatings on 321 stainless steel

H. J. Brown-Shaklee, W. Carty and D. D. Edwards. Solar Energy Materials & Solar Cells 93(2009)1404–1410[6] This article examines porcelain enamel coatings on stainless steel that do not normally exhibit spectrally selective properties unless coated with a low emissivity coating. If they did work though, they'd be ideal for high temp, harsh environments. Shows lots of %A graphs at different temperatures

• Measured refractive index using Becke line method
• solar absorptance and thermal emittance found from total reflectance measurements assuming that Kirchoff's law applies
• 200-2,500nm diffuse reflectance using UV-vis-NIR spectrometer
• 2,500-25,000 FT-IR spectrometer with a cold coated integrating sphere with a mercury-cadmium-telluride detector
• Thermal emittance determined using a weighted integration over the Planck distribution for a specific temperature

### Structure and optical properties of pulsed sputter deposited CrxOy/Cr/Cr2O3 solar selective coatings

H. C. Barshilia, N. Selvakumar and K.S. Rajam. Journal of Applied Physics 103, 023507 (2008)[ [7]

• Black chrome coatings used for domestic hot water applications. This study designed a dielectric/metalic/dielectric coating of Cr2O3 resulting in high absorptance in the visible region and low emittance in the IR region. 3 layers deposited on copper substrate by chemical vapour deposition.
• Notes that info on thermal stability, microstructure and optical properties are lacking
• Used XRD, x-ray photo-electron spectroscopy (XPS), atomic force microscopy (AFM), micro-Raman spectroscopy, solar spectrum relectometer and emissometer and a phase modulated spectroscopic ellispometry
• Operating temperature of solar thermal collector listed between 80 and 85ºC, tested thermal stability between 200ºC and 400ºC
• Report average from emissivity and absorption measurements made at four different positions
• Heated emissometer to desired temperature so that sample wouldn't have to be heated (we probably can't do this because our integrating sphere need to be cooled)

### Models for the Angle-Depenedent Optical Properties of Coated Glazing Materials

M. Rubin, R. Powles and K. Von Rottkay. Solar Energy Vol. 66, No. 4, pp. 267–276, (1999) [8]

Not terribly useful for thermal dependence of coatings, however might be good to keep around when trying to model the angle-dependent optics. They used a Perkin-Elmer Lambda 19 Spectrophotometer to measure the transmittance and reflectance. This paper really focuses on transmittance at different angles

### Optical Characterization of Industrially sputtered nickel-nickel oxide solar selective surface

M. Adsten, R. Joerger, K. Jarrendahl and E. Wackelgard. Solar Energy Vol. 68, No. 4, pp. 325–328, (2000) [9]

Their goal was to find if the optical constants of their materials were close to the ideal ones, and learn enough about the materials to improve them if they weren't. Commercial absorber in question had a solar absorptance of 0.94-0.96, and a thermal emittance of 0.13-0.15. Tools employed:

• Rutherford backscattering to determine atomic composition
• Xray photo electron spectroscopy for surface composition
• Non-standard spectrophotometer with an integrating sphere to measure absolute reflectance and transmittance (in this case sample is loaded on a ring and sphere 4mm large acts as the detector and is rotated all around the sample

Although graphs in paper show different temperatures (0ºC and 55ºC) measurements for reflectance, no mention is made of how they did this in the paper

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