Ralf,

You might consider the possibility of collective effects. Mie theory assumes the distribution of particles is less than one per wavelength. If the density of particles is greater, then collective effects would need to be considered. An appropriate gradient in the density and size distribution of particles could eliminated the sharp discontinuity between the dielectric boundary of the irradiated material and free space, causing reflections and scattering to disappear.

Paul

yes big dependence on particle size... have a look at standard books:

Light scattering by small particles H.C. van de Hulst

Absorption and scattering of light by small particles , Bohren and Huffman

If particles are approx spherical there should be a ripple structure in the absorption efficiency as particle size increases.

Complex time dependent problem though... good luck!

In accordance with the Mie theory small partials are absorbing greater than the great particles are. The latter are scattering (Born&Wolf). Thus, melting of the particles should lead to coalescence and formation of greater particles, which results in decrease of joule dissipation. Can you control the size distribution before and after the illumination?

Both scattering and absorption efficiencies exhibit size dependence. The maxima that are observed for scattering and absorption efficiencies are usually found near the wavelength of the light source. It is, presumably, the absorption that results in heating of the particles. As the absorption index is strongly wavelength dependent, one may ask what it is at 1064 nm. If the absorption cross section is very small compared to the scattering cross section, then most of the light would be dissipated as a result of scattering not absorption

Dear Ralf,

more information about the process (particle material, layer thickness, cw or pulsed laser, dependence on laser parameters, etc. ) would be nice, but I do not think that the problem is necessarilly related to the small size of the particles.

Usually in laser sintering you have a layer of powder which in your case would appear to the laser in terms of absorption, scattering initially in much the same way as a unstructured soild surface with a surface roughness of a few micron. The initial absorption, reflection, scattering (before melting) should therefore be dominated by the bulk properties of the material.

So, I would suspect that the problem is related to either the potentially complex dynamics of the melting process or stability of the sintering (laser) setup.

Regarding literature: I know that for example for metal powders there is a large body of literature on the topic, but without more specific information it is hard to recommend specific papers, especially since I am not an expert myself. Maybe check yourself (if you haven't done so yet), for example with Google Scholar.

Cheers!

Tobias

The avalanche effect seems a good explaination, but may be, there is no need to involve variation of cross section. Larger particles could reach higher temperature because the absorbtion is proportional to the volume of the particle while the dissipation of heat is proportional to its surface area.

Thank you all for your answers! To make the problem a bit more clear, the sintered material is ZnO, which is applied as a powder bed. A Yb-glas laser (SPI G3 20W/SM-series) is used in both cw- and pulsed mode, while the former is the normal approach to sintering and the latter has been recently developed as a modification to improve the quality of the sintered lines (Exner et al, Virtual and Physical Prototyping, Vol. 3, pg 3–11, 2008).

As posted by Vinogradov the Mie theory would foretell a decreased absorbance and preferential scattering by bigger particles, which would would give the inverse effect. Even though effects like better heat dissipation of smaller particles might play a role, this might not be significant enough to ignite an avalanche effect.

So considering your answers, the observed run-away effect might also be caused by different factors like an increase in the absorbance coefficient due to rising temperature or the change in phase. I will try to find data to underpin this effect, if you have literature which might help me, please let me know!

Apreciado Ralph:

Evidentemente la teoría de la dispersión de Mie (tambien la de Raleigh) explica este comportamiento. Sucede que en los procesos agregativos el tamaño de las partículas va creciendo y cambia la condición de dispersion por lo tanto es muy importante ir sintonizando la longitud de onda de la luz con la cual se explora el medio de dispersión en correspondencia con el tamaño que van adquiriendo estas partículas.

Disculpe mi mensaje en español, mi ingles es aun un poco pobre y prefiero que una buena traducíon le ayude más que un intento mio de responderle en ingles.

Best regards

J. J. LL.

Dear Ralf,

as far as I know, there is only a dependency of particle size and light scattering (wavelength vs. particle size like the blue sky effect).

Martin

Juan Jose got it right. It is Mie Scattering phenomena. The equations are simple to solve and modeling the effects of any given particle size distribution, mean size and standard deviation, is possible.

Ralf,

You might consider the possibility of collective effects. Mie theory assumes the distribution of particles is less than one per wavelength. If the density of particles is greater, then collective effects would need to be considered. An appropriate gradient in the density and size distribution of particles could eliminated the sharp discontinuity between the dielectric boundary of the irradiated material and free space, causing reflections and scattering to disappear.

Paul

http://www.sciencedirect.com/science/article/pii/S2211285512001176

Surely it depends on the diameter of the particle. See the article in the link we recently published on size dependent light absorption in nanowires. I agree with the others, can be solved by Mie theory but not sure if you can analytically describe your system in it !

you will find answers to your question in the book by Welch and van Gemert (Optical-Thermal responses of laser irradiated tissue). In particular in the chapter on treatment of port wine stains (chapter 23 in the old version of the book)

If you are talking about light absorption by particles and their size dependence, I would like to address the problem differently. I would welcome comments.

We have to understand why light is absorbed? Classically, it is the imaginary part of the dielectric constant which is responsible or the absorption occours due to electron band structure.

It is therefore possible that if the dimensions become too small, the dielctric constant as well as the band gaps alter and resulting in the observed behaviour.

However, for absorption, the size comparable to wavelength should not have impact. Yes when size is comparable to wavelength, diffraction and interference effects can play dominant role.

I concur with Vijay Jindal that the imaginary part of the dielectric constant determines the absorption strength of the material. It is the real part of the dielectric constant that determines the reflection and scattering when there is a boundary of about a wavelength or more in extent. For sub wavelength particle sizes the distribution of particles can blur the boundary to reduce reflections and cause absorption to approach a maximum as determined by the imaginary part of the of the dielectric constant.

Thank you again for all the answers, especially the last two! It is indeed that the absorption exhibits a strong increase when radiating the material with longer wavelengths. By using a 10.6 µm CO2 laser the absorption increases by a factor of ~50x compared to the 1.064 µm fiber laser, as investigated in the following paper:

Tolochko, N. K., Khlopkov, Y. V., Mozzharov, S. E., Michail, B., Laoui, T., Titov, V. I., & Ignatiev, M. B. (2000). Absorptance of powder materials suitable for laser sintering Article information : Absorptance of powder materials suitable for laser sintering. Rapid Prototyping Journal, 6(3), 155 – 160.

By using a CO2 laser I could considerably enhance the response of the material, in a way that it can be gradually heated to any desired temperature without the sudden launch of an avalanche effect. In addition to the empirical observations, your answers provided a theoretical explanation of the phenomenon.

Many thanks,

Ralf