1. Mihai Oane1 , Rareş Victor Medianu1, Ovidiu Păcală2
The thermal field in laser or electron beam – double Nano-particles-layered interaction
Mihai Oane1 , Rareş Victor Medianu1, Ovidiu Păcală2
1NATIONAL INSTITUTE FOR LASER, PLASMA AND RADIATION PHYSICS, STR. ATOMISTILOR 409, ,MAGURELE, ROMANIA
2 NATIONAL INSTITUTE FOR ATOMIC PHYSICS , STR. ATOMISTILOR 407, , MAGURELE, ROMANIA
ABSTRACT
In the present work we want to figure out the difference between thermal fields in double (one nano size and another variable size: from nano to bulk size) layered interaction. We choose the same materials for bulk and nano-particles media (ZnO for the nano size layer and Au for the material with variable size), the only reason for the temperatures differences being the scale of the irradiated samples. From mathematical point of view we will use the Green function method. We suppose that the incident beam is a laser TEM 00, with w=1mm. A parallel with electron heating of solids is also made
THE ANALYTICAL MODEL
For solving the heat equation we will use the Green function method. We introduce the effective thermal conductivity for this multilayer medium as [1,2]:
(1)
Where: l is the total thickness of this medium structure. Similarly, the effective thermal conductivity for the heat that flows in a parallel direction is:
(2)
Where: A is the area of the near and far faces.
Since for most cases of interest, the heat flux is unidirectional due to the temperature gradient, the heat equation in equilibrium can be written as:
(3)
Where K : are thermal conductivities along the x, y, z directions and A: is the heat source of the equation. Because we are considering, in this chapter, a solid without melting, we can neglect the blackbody radiation of the sample. We introduce then the linear temperature by the expression:
(4)
Where in the above equation is the linearized temperature.
It can be observed that the variation of the linear temperature is equal to the variation of the usual temperature when K is independent of T. The linear temperature obtained now for the heat equation is [1, 2]:
(5)
Where: P is the normalized incident power, is the surface reflectivity when the incident beam is perpendicular to the layer structure of the substrate and T is the original substrate temperature before the laser irradiation. A function is defined by ( ) :
(6)
With: , and , which are the normalized coordinates of the system. Here w represents the waist of the laser beam.
We know from literature that for [3,4] ZnO at 20 nm we have: K=1Wm-1K-1, and for Au bulk solid K=300 Wm-1K-1, at 500nm ; also: K=350 Wm-1K-1, at 100 nm and: K=200 Wm-1K-1 At 50 nm we have: K=100 Wm-1K-1.We choose for Au bulk the geometry of a cube with l=4mm. One can easily calculate:
If we are working in arbitrary units, we have: and in consequence:
The schematic representation of the studied system.
Fig. 1.
CONCLUSIONS
The conclusion is obviously: in the range 500 nm – 20 nm of Au thin film, the smaller is the thermal conductivity the greater is the temperature variation.
This is an important conclusion because open up the possibilities to construct thermal shields using nano-materials. We can construct sandwiches of nano-materials with cooling agent between them.
For the electron beams with medium incident power the situation is the same, due to the fact that the absorption properties are almost the same like in the case of laser beams of medium power
(hundreds of W) [5].
REFERENCES
[1] Y.-F. Lu , “Laser-induced temperature distribution in substrates with periodic multilayer structures”, J. Appl. Phys., 1993; 74(9), ;
[2] M. Oane ,F. Scarlat, S. – L. Tsao, I. N. Mihăilescu , "Thermal fields in laser-multi-layer structures interaction" ,Optics & Laser Technology, 2007, 39, ;
[3] H. Morkoc and U. Ozgur, “Fundamentals Materials and Device Technology”, Zinc Oxide, 2009 WILEY-VCH, Verlang GmbH& Co, ISBN: ;
[4] P.E.Hopkins and J. C. Duda, “Heat Transfer-Mathematical Modeling, Numerical Methods, and Information Technology”, 2011, InTech ISBN: , Cap.13 “Introduction to Nanoscale Thermal Conduction;
[5] M. Oane, R. V. Medianu and A. Bucă, “Radiation Effects in Materials”, , 2016, In Tech, ISBN: , Cap.16”A Parallel between Laser Irradiation and Relativistic Electrons Irradiation of Solids”.
Acknowledgments: the authors acknowledge with thanks for the financial support of this work by contract NUCLEU/2016