Modeling of Heat Transfer in an
Aluminum X-Ray Anode Employing
a Chemical Vapor Deposited
Diamond Heat Spreader
David J. Stupple1
Torr Scientific Ltd.,
Unit 11, Pebsham Rural Business Center,
Pebsham Lane,
Bexhill-on-Sea,
East Sussex TN40 2RZ, UK
e-mail: d.stupple@torrscientific.co.uk
Victor Kemp
Mecway Ltd.,
1 Goring Street,
Thorndon,
Wellington 6011, New Zealand
e-mail: victor@mecway.com
Matthew J. Oldfield
Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: m.oldfield@surrey.ac.uk
John F. Watts
Professor
Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: j.watts@surrey.ac.uk
Mark A. Baker
Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: m.baker@surrey.ac.uk
X-ray sources are used for both scientific instrumentation and
inspection applications. In X-ray photoelectron spectroscopy
(XPS), aluminum Ka X-rays are generated through electron beam
irradiation of a copper-based X-ray anode incorporating a thin
surface layer of aluminum. The maximum power operation of the
X-ray anode is limited by the relatively low melting point of
the aluminum. Hence, optimization of the materials and design of
the X-ray anode to transfer heat away from the aluminum thin film
is key to maximizing performance. Finite element analysis (FEA)
has been employed to model the heat transfer of a water-cooled
copper-based X-ray anode with and without the use of a chemical
vapor deposited (CVD) diamond heat spreader. The modeling
approach was to construct a representative baseline model, and
then to vary different parameters systematically, solving for a
steady-state thermal condition, and observing the effect on the
maximum temperature attained. The model indicates that a CVD
diamond heat spreader (with isotropic thermal properties) brazed
1
Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL
OF HEAT TRANSFER. Manuscript received June 7, 2018; final manuscript received June
26, 2018; published online August 28, 2018. Assoc. Editor: Milind A. Jog.
Journal of Heat Transfer
into the copper body reduces the maximum temperature in the 4
lm aluminum layer from 613 C to 301 C. Introducing realistic
anisotropy and inhomogeneity in the thermal conductivity (TC) of
the CVD diamond has no significant effect on heat transfer if the
aluminum film is on the CVD diamond growth face (with the highest TC). However, if the aluminum layer is on the CVD diamond
nucleation face (with the lowest TC), the maximum temperature is
575 C. Implications for anode design are discussed.
[DOI: 10.1115/1.4040953]
Introduction
X-rays are used as an excitation source in analytical techniques
such as X-ray photoelectron spectroscopy (XPS) and X-ray diffraction, and in X-ray inspection and imaging. X-rays are produced by accelerating high-energy electrons to strike a metallic
anode where the electrons cause the emission of X-ray photons
through anode atomic core-level excitation. This conversion is
inefficient, with 99% of the electron energy converted into heat
within the anode assembly. It is advantageous to maximize X-ray
flux to increase signal-to-noise ratio and minimize analysis time,
but preventing damage to the anode from excessive heating is
usually the limiting factor. In XPS, a common anode material is
aluminum, producing characteristic aluminum Ka X-rays. A thin
coating of aluminum is applied to the tip of a hollow copper anode
body with the internal surfaces cooled by pumped water. Often, a
smaller beam spot on the anode is desirable, providing a smaller
focused X-ray spot on the sample and hence finer spatial resolution of the analysis. If high X-ray flux is demanded from a small
spot, the power density at the anode can be very high. Some anodes employ a chemical vapor deposited (CVD) diamond heat
spreader, brazed flush into the copper body beneath the aluminum
film (Fig. 1). This technical brief reports the findings of finite element analysis (FEA) of the thermal performance of a watercooled anode both with and without a diamond heat spreader, and
the effects of material and geometry variations.
Generating a high X-ray flux may be desirable, so efficient
removal of heat from the anode film to the cooling system is
important. CVD diamond has excellent thermal conductivity
(TC), a typical quoted value being 1800 W m 1 K 1 at room temperature.2 Single crystal gemstone diamonds have a TC of approximately 2200 W m 1 K 1 at room temperature [1]. In reality,
polycrystalline CVD diamond can have substantially anisotropic
and inhomogeneous TC, varying from one face to another by a
factor of 4 [1,2].
Numerical methods have previously been used to model the
spread of surface heat through a cylindrical diamond heat
Fig. 1 (a) The beveled tip of a typical X-ray anode as used in a
commercial XPS system, with (b) a cutaway view showing the
recessed diamond heat spreader, one of several cooling fins
and internal water cooling
2
http://www.hediamond.cn/en/product/24.html
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Table 1 Thermal conductivity values for the baseline model
materials
Material
Aluminum
Chromium
CVD diamond
Braze
Copper
Thermal
conductivity/W m
1
K
189.6
93.7
2082.4 at 20.9 C
100.0
404.0
1
Temperature
dependence
None
None
Yes
None
None
Fig. 2 An overview of the mesh used as the basis of the analysis. (Color variations within components (e.g., within aluminum) are visual aids to facilitate the modeling process.
spreader, with isotropic and temperature-independent TC, on a
copper substrate, demonstrating that performance was sensitive to
the radius of the heat spreader [3]. Finite element analysis has
been used to analyze stress in a revolving X-ray anode during
heating and cooling, again with heat applied at the surface [4].
Monte Carlo analysis was used to simulate subsurface heat
delivery by electron emission in field effect devices, informing
subsequent numerical analysis of the heat flow [5]. FEA of heat
sinks on laser diodes has shown the superior performance of CVD
diamond over aluminum nitride heat spreaders [6], again with the
TC of the diamond assumed isotropic and temperatureindependent. Here, we use FEA in conjunction with Monte Carlo
analysis to model the use of a CVD diamond heat spreader in a
generic XPS X-ray anode. The effects of different thermal conductivities and of anode design variations are examined. Identification of those parameters which have the greatest effect on the
thermal performance will allow design choices to be made that
cost-effectively optimize anode cooling. No previous analysis
includes subsurface heat delivery and temperature-dependent, anisotropic, and inhomogeneous TC of diamond.
Fig. 3 A previously published temperature-dependent TC profile of CVD diamond used in the baseline FEA model [11,12].
The curve has been extrapolated to higher temperatures (above
270 C).
Finite Element Analysis Modeling Approach
The commercial FEA package Mecway3 was used for pre and
postprocessing. Mecway’s internal solver was used for the
sensitivity analysis of thermal properties and dimension changes.
Calculix Crunchix (CCX) is a free structural FEA solver [7]. CCX
was used where both temperature dependence and anisotropy of
TC was needed.
A baseline model was created, and then parameters were varied
systematically, solving for a steady-state thermal condition, and
comparing the maximum temperature attained. Rather than a circular body with a beveled tip (Fig. 1), the anode was modeled as a
square tube with a flat tip, with the mesh representing one quarter
of the whole. The model comprises a copper tube, an inset CVD
diamond, a braze layer between diamond and copper, an aluminum anode layer, and a chromium adhesion layer between aluminum and diamond (Fig. 2).
The 20 W electron beam was modeled with a Gaussian profile
[8]. Most previous studies have assumed surface heating, while
here a software package for Monte Carlo simulation, CASINO
V2.42 [9], was used to model the vertical delivery of heat by
10 keV electrons into the aluminum film.
The thermal conductivities of the materials in the baseline
model are listed in Table 1.
3
https://mecway.com/
124501-2 / Vol. 140, DECEMBER 2018
Fig. 4 Baseline model modified to have direct cooling of the
diamond underside
The density of the sputtered aluminum film was assumed to be
80% of bulk aluminum and the TC adjusted accordingly. This is a
reasonable assumption for a sputtered film [10]. The temperaturedependent TC values of the CVD diamond material were
extracted from published measurements [11,12], with extrapolation to higher temperatures (Fig. 3).
To model the effect of direct cooling on the underside of the
diamond, the cooling fins and a region of the copper and braze
were removed to expose the diamond. The convection condition
was applied to all newly exposed surfaces (Fig. 4).
Results and Discussion
Heat Spreader. The model without the heat spreader reported
a maximum aluminum temperature of 613 C, greater by 312 C
than the model with a diamond heat spreader (Fig. 5).
Thermal Properties. The TC of both the diamond heat
spreader and the aluminum anode material has a large effect on
the aluminum temperature (Fig. 6). The aluminum temperature is
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Fig. 5 The copper-bodied model (right) has a maximum steady-state temperature 613 C, whereas the baseline model with
the diamond heat spreader (left, same temperature scale) has maximum 301 C
Fig. 6 Effect of varying TCs of components, and the convection coefficient of
the cooling water. The steep curves indicate those thermal properties that have
the greatest effect on the aluminum temperature.
relatively insensitive to the thermal conductivities of most other
components. This suggests that while the quality of diamond is of
great importance, the material choice for the anode body is more
flexible. A material with more suitable engineering properties
than copper might be feasible with minimal effect on the aluminum temperature.
diamond heat spreader allows it to maintain a comparable temperature gradient to that of the copper model despite the considerably
lower maximum temperature (Fig. 8). This gradient drives the
heat flux. With the anode film on the nucleation face, where TC
Dimensions. The aluminum temperature of the model is highly
sensitive to the thickness of the aluminum (Fig. 7). The temperature is moderately increased by reduction of the diamond thickness, but with little improvement from a thicker diamond. Unlike
earlier numerical modeling [3], the width of the diamond here had
little effect. Changes to other dimensions also had little effect,
though making the copper tip thinner caused a slightly increased
temperature.
Anisotropy and Inhomogeneity. Introducing anisotropic and
inhomogeneous thermal properties of CVD diamond [1,2] shows
that the orientation of the diamond is important. In the CVD process, the nucleation face of the diamond is next to the substrate,
and the growth face is furthest from the substrate. With the
aluminum anode on the growth face, temperatures are similar to
the isotropic model; with the anode on the nucleation face—
where the TC is lower [2]—the maximum temperature is 273 C
higher at 575 C.
The primary role of the diamond is to facilitate the vertical flow
of heat away from the hot spot at the center. The high TC of the
Journal of Heat Transfer
Fig. 7 The peak temperature of the aluminum for different
dimensions in the model. The aluminum temperature of the
baseline model is highly sensitive to the thickness of the aluminum layer (steep curve).
DECEMBER 2018, Vol. 140 / 124501-3
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There is no benefit to be gained from having a hole in the metal
body such that the diamond is directly cooled by water. The lateral flow of heat should not be impaired by having the metal body
too thin or in poor thermal contact with the side walls.
The contribution of the side walls to heat removal is important. The return route of the cooling water should be fully
exploited by passing the water over as much internal surface as
possible.
The TC of the anode body does not seem to be a critical factor.
It might be beneficial to choose a metal with more suitable
mechanical properties than copper, without necessarily affecting
the anode cooling, especially if the material is one that resists
fouling by the cooling fluid.
Conclusions
Fig. 8 A comparison of vertical and horizontal temperature
profiles in models with and without a diamond heat spreader.
The profiles are taken from the top/center of each model. While
the temperatures are higher without a heat spreader, the temperature gradients are quite similar.
may be lower by a factor of 4 [2], the removal of heat from the
hot spot is impaired.
Away from the center, both the diamond and the copper body
serve to channel the heat mainly horizontally to the side walls
(Fig. 9). In both models, approximately 65% of the heat is
removed via the side walls, so that most of the heat flux in the tip
is horizontal, rather than vertically toward the nearest cooled surface, as might be expected. Any restriction of the heat flow to the
walls will raise the maximum temperature reached in the aluminum. This is why making the copper wall of the anode tip thinner
caused a slight increase in temperature.
Likewise, removing a part of the metal body so that the diamond
is directly cooled by the water (Fig. 4) had no beneficial effect.
With the diamond cooled directly, the aluminum reached 310 C. A
model with no through-hole in the copper reached 307 C. Removing copper material restricts the heat flow to the side walls.
Design Implications
This model suggests that the TC of the diamond heat spreader
should be as high as possible and that the aluminum coating
should be applied to the growth surface of the diamond to minimize the effect of anisotropic microstructure in the CVD diamond
material. The diamond should not be made too thin, in this model
no thinner than 100 lm. The TC of the aluminum thin film should
be enhanced by ensuring that the film is as dense and pure as possible. The film should be as thin as the application will allow.
The analysis confirms that a high-quality CVD diamond heat
spreader can drastically reduce the steady-state temperature of the
anode, here by 312 C, but the diamond must have its growth face
outermost because of the effects of anisotropic microstructure.
Fitting the diamond with the nucleation face outermost increases
the model temperature by 273 C.
Even with a greatly reduced maximum temperature, heat flow
both within the aluminum film and in adjacent components is
maintained when the heat spreader is present. The high TC of diamond allows it to efficiently remove heat at the base of the anode
film. This maintains a temperature gradient within the aluminum
that is similar in magnitude to the copper-bodied anode and that
drives the heat flow.
Around 65% of the heat is removed by the coolant via the side
walls. Measures that might be expected to assist cooling, such as
thinning the wall at the tip, or having direct cooling of the diamond, actually throttle heat flow to the walls, giving higher
temperatures.
The main implications for anode design are as follows:
(i) reduce the aluminum layer thickness as much as practically allowable;
(ii) fabricate the aluminum layer to be dense and thermally
conductive;
(iii) fit the CVD diamond heat spreader with the growth face
outermost;
(iv) do not impede the flow of heat to the side walls by thinning the anode walls.
More broadly, anode designs might incorporate a metal that is
easier to braze to and less prone to fouling than copper. The route
of the coolant must be optimized to fully exploit the cooling
opportunities both at and away from the anode tip; anode designs
where the return path from the tip is via a narrow channel may be
far from optimum.
Fig. 9 A schematic diagram of the heat flux through a central section of the anode tip, with
the anode tip center at top left. For clarity, the heat flux magnitude range of 0–1.5 MW m22 is
chosen, such that the highest fluxes near the center of the tip (top left) are not shown. The
section shown is from the heat spreader model; the model with no heat spreader shows a similar pattern. The flux magnitude is proportional to arrow length.
124501-4 / Vol. 140, DECEMBER 2018
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Appendix: Conversions of values in the text to U.S. customary
units
C
270
273
301
307
310
312
575
613
Wm
1
93.7
100
189.6
404
2082.4
K
1
F
lm
Millipoints
mm
Points
518
523
574
585
590
594
1067
1135
1
2
3
4
5
8
90
100
150
420
450
980
2.8
5.7
8.5
11.3
14.2
22.7
255
283
425
1191
1276
2778
1
1.8
2
5.6
2.8
5.0
5.7
15.7
nm
millipoints
20
200
0.06
0.57
Btu/(h F ft)
54.1
57.8
109.5
233.4
1203.2
MW m
2
Btu/(h in2)
1.5
3302
W
Btu/h
20
68
Funding Data
Engineering and Physical Sciences Research Council
(EPSRC Grant No. EP/G037388/1) via the MiNMaT Centre
for Doctoral Training at the University of Surrey, in collaboration with Torr Scientific Ltd.
Journal of Heat Transfer
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