Nanofocus diamond X-ray windows: Thermal modeling of nano-sized heat source systems

Abstract

a b s t r a c tAn analytical thermal model is proposed to study heat transfers occurring at high power density in X-ray tubes with micron to submicron sized source. The use of a simple analytical approach instead of a complex numerical simulation allows readily modeling of more and more challenging systems such as multi-source X-ray tubes. By significantly reducing the computing time, it enables a wider parameter range evaluation for engineering phase. We focused our work on tubes integrating a transmission window that is mainly edge-cooled. Our approach can be generally used in cylindrical lateral heat spreaders with distributed small sized source systems. The model enables an efficient estimation of temperature distributions for a large range of parameters and source designs and is, for instance, wellsuited to described nanosized heat source systems. It is developed from an electrostatic analogy with the point charge particle model and uses of a series of virtual sources. A multiscale resolution of the heat equation is proposed, hence providing the temperature distribution at any point within the whole system. Moreover, the non-linearity of equations caused by temperature-dependent thermal conductivities is solved by using Kirchhoff's transformation, giving a more realistic approach of heat conduction in diamond X-ray windows, where temperature in excess of 1000°C can be encountered. The influence of convective and radiative transfers has been discussed and the physical accuracy of the predicted temperature is controlled by adjusting the number of virtual sources of the model.

Design and optimization of thin‐film tungsten (W)‐diamond target for multi‐pixel X‐ray sources

“…With the highest thermal conductivity among all known materials, diamond has been utilized in several high brilliance X-ray sources. [11][12][13][14][15][16] The tungsten-diamond (W-diamond) thinfilm target usually is made of a thin layer of tungsten deposited on a diamond substrate. Although the radiative and thermal characteristics of thick X-ray reflection targets have been studied thoroughly, the properties of thin-film targets are very different and have not been studied thoroughly.…”

“…Improving the thermal conductivity of the target material is a viable approach to increase the focal spot power density of distributed X‐ray sources without a major modification of the tube design. With the highest thermal conductivity among all known materials, diamond has been utilized in several high brilliance X‐ray sources 11–16 . The tungsten–diamond (W‐diamond) thin‐film target usually is made of a thin layer of tungsten deposited on a diamond substrate.…”

Production and Heat Properties of an X-ray Reflective Anode Based on a Diamond Heat Buffer Layer

“…Figure 1 shows the composition of the diamond composite anode, which was produced through the following steps and methods. Based on the high thermal conductivity (TC = 1500-2000 W/m K) [12][13][14] of diamond, materials containing diamond are widely used in high-power microelectronic devices as a heat dissipator [15,16]. In order to improve the thermal conductivity of composite materials, a method for mixing diamond particles with a metal, and a method for plating a diamond film were proposed [17,18].…”

Transmission-type Window of HFCVD Diamond Film for Microfocus X-ray Tube

“…In this case, beryllium exhibits limitations in dealing with such heat densities. On the contrary, diamond is a good candidate for such applications as it is composed only of carbon (low Z material with high X-ray transparency) and it has the highest known thermal conductivity of all bulk materials (up to 2000 W·m ) for single crystal diamond at room temperature (Delfaure C, 2015, Ying X, 2000. Diamond has Low thermal expansion resulting in low thermomechanical stress and no health risk.…”

“…According to the previous report, the grain boundary scattering mechanisms are dominant only at low temperature (Klokov A, 2008, Verhoeven H, 1997, and weaken when temperature increases. So it is believed that grain boundary can be negligible when phonons propagate parallel to the horizontal axis of diamond film above 400 K, and thus an isotropic thermal conductivity is used in the simulation model (Delfaure C, 2015).…”