We present a new mounting design for thin crystal optics with cryogenic cooling compatibility. We design a crystal geometry with two symmetric strain-relief cuts to mitigate the distortion from mounting. We propose to sputter gold onto the crystal and the holder to ensure excellent thermal contact and sufficient mechanical bonding. The system is analyzed and verified by finite element analysis to have an acceptable level of strain due to mounting. The thermal performance of this mounting scheme is validated in an example cryogenic cooling system and the results indicate a tolerance of power density up to ∼1 kW/mm2.

The brightness of x-ray sources has been dramatically improved since the first dedicated synchrotron radiation sources in 1970s.1 Recently, with the successful demonstration and operation of x-ray free-electron lasers (XFELs),2–5 the brightness of the x-ray photon beam is further improved by orders of magnitude. With this high brightness and other unique properties such as short pulse duration, the XFELs enable new frontier research across many areas of science.6–9 However, the unprecedentedly high peak power density has been challenging the design and operation of the x-ray optics. During operation, such x-ray sources deposit intense and localized heat load to the optics elements. This leads to distortion and performance degradation if no appropriate action is taken.10,11

To mitigate heat load, active cooling has been employed and integrated into the optics system for synchrotron radiation applications.12 In general, two combinations of cooling techniques and material selections are most popular: the liquid nitrogen (LN2) cooled silicon and the water cooled diamond. The LN2 cooled silicon optics, mostly monochromators, has been successfully commissioned in synchrotron radiation facilities across the world.13–17 This solution is very attractive because the thermal dissipation properties of silicon are greatly improved at a low temperature. In addition, the coefficient of thermal expansion (CTE) of silicon has a zero point near 125 K. In other words, the distortion induced by thermal load could be nearly eliminated if the temperature is well controlled at a steady state. On the other hand, diamond crystal with water cooling is an alternative combination18–22 since the thermal properties of diamond (specifically the ratio between thermal conductivity and CTE) at room temperature are close to those of silicon at cryogenic temperature. In addition, diamond crystals have low power absorption and high x-ray transparency. With the development of the crystal growth techniques,23 the quality of synthesized diamond can be almost as high as silicon,24–26 indicating the feasibility to develop diamond counterparts of the silicon optics with better resistance to thermal load.27,28 In facilities running at relatively low beam repetition rates, diamond optics has been demonstrated as successful as the silicon ones; it can even provide unique features such as hard x-ray self-seeding.29,30 However, for facilities running at high beam repetition rates, such as EuXFEL31 and LCLS-II-HE, the increasing power density by XFELs is again challenging the cooling of the optics, even though the total average power is not extremely high. This high power density pushes the limit to where cryogenic cooling and diamond have to be combined. Even for thin crystal based applications, such as hard x-ray self-seeding29,30,32 and beam splitting,28 the thermal load is intense enough to undermine the optics performance.33 Intuitively, one would extend the cryogenic cooling solution to these applications, but several technical difficulties hinder an easy adaptation from the conventional cooling solution.

One major challenge is the conflicting requirements between clamping strain minimization and heat dissipation. Working at the Bragg condition, the thin crystal is very vulnerable to external clamping force from the holder: a very small amount of force could cause the deviation of the Bragg condition.34,35 Therefore, a soft with minimal contact area is essential. However, a hard with maximal contact area is necessary to ensure efficient heat dissipation from the crystal to the cooler. This conflict disables the direct application of the cryogenic cooling techniques, which were initially developed for thick bulk crystals. Moreover, the CTE mismatch between system components of different materials would introduce additional distortion of the crystal, if the system is assembled at a temperature different from the operational temperature. Takiya et al.22 developed a mounting method for a 0.5-mm-thick diamond crystal with water cooling. They successfully mitigated distortion due to CTE mismatch by introducing another diamond platelet as a buffer between the diamond crystal and the copper holder. However, such a mounting method is not optimal for a thin crystal with a thickness of ∼0.1 mm. At present, there is hardly any report on cooling design for thin crystals, especially at cryogenic temperature.

To provide the cryogenic cooling applicability on thin crystals, in this paper, we report a new mounting design for thin crystals under extremely high power density. To enable an excellent thermal contact conductance, we propose to sputter gold onto both the thin diamond crystal and copper holder with titanium as an under-layer, followed by a thermal press to enhance the thermal and mechanical bonding. To minimize the residual strain due to the bonding, two strain-relief cuts are introduced symmetrically on the crystal. The system is analyzed and verified by finite element analysis (FEA) using the ANSYS Mechanical module to have an acceptable level of strain due to CTE mismatch. The thermal performance of this mounting scheme is analyzed in an example cryogenic cooling system and the results indicate a tolerance of power density up to ∼1 kW/mm2.

To simultaneously achieve low clamping strain and high thermal contact conductance (TCC), the mounting mechanism consists of two major parts: the crystal geometry design and the thermal bonding design. These two parts cooperatively contribute to the compatibility of this method with cryogenic cooling. Here, we first note that all dimensions in this work are selected for demonstration purpose only. For certain application, one would optimize the dimensions of the system according to the specific requirements from the operating conditions.

FIG. 1.

Thin crystal dimensions (numbers in mm) with two symmetric strain-relief cuts. The beam footprint shown at the tip is 500 μm (full width at half maximum, FWHM). The bonding area is marked as light gold.

FIG. 1.

Thin crystal dimensions (numbers in mm) with two symmetric strain-relief cuts. The beam footprint shown at the tip is 500 μm (full width at half maximum, FWHM). The bonding area is marked as light gold.

Close modal

The conceptual geometry of the crystal is shown in Fig. 1. The thickness of the diamond crystal is set to 150 μm as an example. Here, the crystal is designed to have two symmetric strain-relief cuts near the two bonding areas where thermal bonding will be created to attach the crystal to the holder in a thermally efficient manner. The strain-relief cuts provide effective buffering to prevent the propagation of the strain due to tight bonding. The symmetric configuration allows us to maximize the heat dissipation from the beam footprint on the strain-free tip. Meanwhile, this symmetric configuration also helps in minimizing the tilting distortion by balancing the external force from both sides (up and down sides in Fig. 1). Furthermore, this configuration also allows us to keep the material from other growth sectors outside the working area as heat sink, and the usage of the material is maximized.

FIG. 2.

Thin diamond crystal attached to the holder by thermal bonding. The left figure view is from the front side, and the right one is from the back side. Certain clearance is opened on the holder for the photon beam to enable the operation in both reflection and transmission configurations.

FIG. 2.

Thin diamond crystal attached to the holder by thermal bonding. The left figure view is from the front side, and the right one is from the back side. Certain clearance is opened on the holder for the photon beam to enable the operation in both reflection and transmission configurations.

Close modal

The thermal bonding between the crystal and the oxygen-free high thermal conductivity (OFHC) copper holder is constructed by metal deposition and thermocompression.36 To yield a good bonding from both thermal and mechanical perspectives, gold is selected due to its softness, high thermal conductivity, and its adhesion properties under thermocompression. It is an important component as it provides multiple functionalities: (1) excellent TCC, (2) reasonably good mechanical bonding, and (3) a soft buffer to mitigate the distortion due to CTE mismatch. We list out the technological process as follows:

  • Step 1. Adhesion layer sputtering: A very thin (a few nanometer) titanium undercoat layer is sputtered onto the bonding area of the crystal with other parts covered by Kapton. This thin titanium undercoat layer would adhere strongly to diamond presumably due to the lattice parameter similarity.36 On the other side of the copper holder, which is polished to a mirror finish, the same process should be carried.

  • Step 2. Gold layer attaching: While the sputtering of titanium is fading out, that of the gold should start to ensure a mixed phase for better TCC and mechanical bonding. Gold by electron-beam evaporation should then be conducted until the thickness of the gold layer reaches about 25–50 μm to create a soft finish and similarly for the holder side.

  • Step 3. Thermocompression: After deposition, the components are ultrasonically cleaned and the Kapton is removed. The crystal and holder are thermocompressed together in a jig at 240 kPa, 750 K for about 10 min.

The geometry of the holder near the thermal bonding area is illustrated in Fig. 2. The overall shape and dimension should be determined according to specific situations. In this general presentation, the strain-free tip of the crystal is the optical working area. Near this area, a beam clearance cutoff is made to increase the angular acceptance of the beam so that the setup would be compatible with both reflection and transmission operation. The removal of the material near the bonding area also reduces the local stiffness so that the distortion stress due to CTE mismatch is reduced as well.

Since the purpose of this mounting mechanism is its compatibility with cryogenic cooling, the desired operational temperature would be ∼60–100 K. For either diamond or silicon, there is no benefit to go for even lower temperature: for diamond, its thermal conductivity reaches its maximum within this range;37 for silicon, its thermal expansion coefficient passes zero near 125 K.38 

When thermocompressed at 750 K, a presumably rigid bonding is created between the crystal and the holder. Later, when the system is cooled down to 60 K, the different CTEs of diamond, gold, and copper result in different thermal expansion behavior among the components. As a consequence, the crystal will be distorted. The distortion of the crystal leads to an inhomogeneous surface slope, defined as the deviation of the local surface normal n̂ from the original normal ẑ, δθ=arccosn̂ẑ/n̂ẑ. The inhomogeneous surface slope disturbs the Bragg angle at different locations and causes the broadening of the reflected beam spectrum. Such an effect is particularly detrimental in the monochromator as the reflected beam will not be fully transported by the following crystals. Overall, the transmittance of the monochromator is reduced, or the intensity of the output beam is degraded. One distortion mitigation mechanism is designed by Takiya et al.22 In the design, they utilized another thick diamond platelet as a buffer to resist the distortion from the copper base and to maintain rigid connections for improved heat transfer. In our design, both the strain-relief cuts and the relatively thick gold bonding layer work as buffers for mitigating the mounting strain due to CTE mismatch.

To evaluate the surface slope, finite element analysis (FEA) by the ANSYS Mechanical module is conducted. Only a local relevant part of the system (shown in Fig. 2) is simulated to reduce computational cost. In FEA, the static elastic equation with thermal stress is solved,

σ+F=0,
(1)

where σ is the stress tensor and F is an external force. The stress tensor can be written according to the generalized Hook’s law as

σij=2μεij+λeαTTrefδiji,j=1,2,3,
(2)

where ɛ is the strain tensor, λ and μ are Lamé elastic constants, e = εkk = ε11 + ε22 + ε33 is the dilatation, α is secant CTE, and δij is Kronecker’s symbol. The strain tensor is a superposition of both thermal strain and elastic strain, where the latter is related to the displacement field by Cauchy strain tensor,

ε=12uT+u.
(3)

The temperature T is solved by the steady state heat conduction equation

κT+q̇=0,
(4)

where κ is the thermal conductivity and q̇ is a volumetric heating source. More details can be found in Refs. 39 and 40 and ANSYS Mechanical manual. The simulation is carried out with all faces stress-free (σn = 0) and all contact connections bonded (u1 = u2 = for all contact pairs with two faces). A thermal condition (temperature for all bodies) is set to be 60 K to mimic the cooled situation, while the reference temperature for thermal expansion is set as 750 K to approximate the thermocompression condition. The material properties of diamond,37 gold,41,42 and OFHC copper43 are all temperature dependent.

The surface slope contour near the beam footprint by FEA results is shown in Fig. 3. The footprint size is assumed to be 500 μm in FWHM. In this regime, the surface displacement field was simulated by FEA and the results were exported to an in-house MATLAB code to calculate the surface slope. Within the spot, the typical surface slope is only ∼1 μrad. A standard deviation of 0.4 μrad was obtained, which is a small value compared to, for example, the Darwin width of 8 μrad for the C (0 0 4) rocking curve at 9.5 keV. The results indicate that the distortion due to mounting and CTE mismatch is effectively suppressed, especially considering the low stiffness of the thin crystals .

FIG. 3.

The surface slope contour in the beam footprint (the light red circular area) due to mounting distortion from 750 to 60 K. Across the whole regime, the surface slope is ∼1 μrad with a standard deviation of 0.4 μrad.

FIG. 3.

The surface slope contour in the beam footprint (the light red circular area) due to mounting distortion from 750 to 60 K. Across the whole regime, the surface slope is ∼1 μrad with a standard deviation of 0.4 μrad.

Close modal

To evaluate the cooling performance of the mounting mechanism, an example of cryogenic cooling system is presented for demonstration purpose, as shown in Fig. 4. The system consists of the crystal and the mounting design, a copper holder, a bunch of flexible copper thermal braids, a cryogenic cooler head, and PEEK insulation spacers. The key design principle of the system is to introduce minimal heat leakage from the rotation stage, which works at room temperature, through heat conduction. It should be emphasized that the conduction heat leakage could severely degrade the cryogenic cooling performance even if the temperature is not as low as liquid helium temperature. PEEK spacers are therefore employed between the tightening bolts and the mounting disk as thermal isolation. The heat leakage through thermal radiation is not as serious as the conduction in this temperature range; however, thermal radiation shield is still needed to reject this additional burden for the cryogenic cooler. Therefore, the flexible thermal braids, the cryogenic cooler, and the mounting disk should be wrapped by shielding materials such as Mylar or aluminum foils. The flexible copper thermal braids are installed to allow the motion of the holder with a fixed cryogenic cooler.

Based on this system, relatively extreme heating condition is simulated with FEA to evaluate the cooling performance of the design. The cryogenic cooler temperature is set as 77 K (LN2 temperature, also the reference temperature for thermal expansion), indicating a constant temperature boundary condition on the end face of the thermal braids at 77 K. The peak spacers and the tip of the stainless steel bolts are in direct contact with the rotation stage and therefore set at a fixed temperature of 300 K. All surfaces are assumed to receive thermal radiation from the 300 K environment with an effective emissivity of 0.02 evaluated from two layers of Mylar thermal shield. The TCC at the bonding area is set as 1.54 × 106 W m−2 K−1 according to the experimental measurement by Hudson.36 To simulate an extreme heating, a total power as high as 15 W is deposited into a 47 μm (FWHM) footprint at the center. Such a high power corresponds to a power density of 1.33 kW/mm2, assuming that all power is deposited into a circular footprint of 60 μm (3σ range) radius.

The temperature distribution of the system and crystal are displayed in Fig. 5. At the spot center, the maximal temperature is 141.9 K, which is 28.65 K higher than the temperature at the bonding area. This indicates that the heat dissipation performance of such geometry is very efficient, even though the crystal is very thin and the heat conduction cross section is very small. Compared to a single sided bonding design, the symmetric design utilizes both sides, effectively shortening the thermal path between the hotspot and the heat sink. The heat transport across the bonding area is also very efficient due to the excellent thermal contact created by the sputtered gold layer and thermocompression. A significant temperature drop can be observed on the flexible copper thermal braids as a trade-off for the motion capability. However, the heat transfer is still sufficient to maintain a relative low base temperature, as indicated by Fig. 5. The heat conduction leakage to the system from the motion controller is calculated as 1.85 W, and the thermal radiation leakage to the system is obtained as 0.4 W. Compared to 15 W of heat load from the photon beam, the thermal insulation is sufficient for this case. However, the thermal insulation can be further improved according to specific requirements from certain applications.

FIG. 4.

Two views of the example system. The crystal is mounted on the holder (1) by metal deposition. The holder (1) is mounted on the rotation stage (4) with PEEK spacers to minimize the heat leakage through conduction. The holder is connected to the cryogenic cooler (3) through flexible copper thermal braids (2).

FIG. 4.

Two views of the example system. The crystal is mounted on the holder (1) by metal deposition. The holder (1) is mounted on the rotation stage (4) with PEEK spacers to minimize the heat leakage through conduction. The holder is connected to the cryogenic cooler (3) through flexible copper thermal braids (2).

Close modal
FIG. 5.

Temperature distribution of the whole system (upper figure) and the crystal (lower figure).

FIG. 5.

Temperature distribution of the whole system (upper figure) and the crystal (lower figure).

Close modal
FIG. 6.

The surface slope contour in the beam footprint the colored circular area due to thermal load. Across the whole regime, the surface slope is ∼3 μrad with a standard deviation of 0.4 μrad.

FIG. 6.

The surface slope contour in the beam footprint the colored circular area due to thermal load. Across the whole regime, the surface slope is ∼3 μrad with a standard deviation of 0.4 μrad.

Close modal

In addition to the temperature, the surface slope near the beam footprint is also calculated to illustrate the effectiveness of the cryogenic cooling as shown in Fig. 6. Overall, the surface slope is maintained at a low level of ∼3 μrad with a standard deviation of 0.4 μrad. Near the edge of the footprint, some large surface slope can be observed due to the temperature gradient. Meanwhile, near the center of the footprint, a peak-valley pattern slope can be identified. This pattern corresponds to a thermal bump due to very small beam footprint size. One would expect an even smaller surface slope near the center if a larger size beam is incident. Assuming that the maximal surface slope allowance is about half of the Darwin width at 9.5 keV for C (0 0 4), the maximal absorbed power density for the system is 1.33 kW/mm2. As a comparison, the time average absorbed power for LCLS-II-HE hard x-ray self-seeding crystal is ∼3 W at the repetition rate of 300 kHz and 9.5 keV, and the corresponding average power density is 0.303 kW/mm2. Another reference high power density is the hard x-ray self-seeding crystal at European XFEL, which is ∼0.0846 W and ∼0.0104 kW/mm2 with 400 pulses in a pulse train at 10 Hz, assuming that the absorbed pulse energy is 6.16 μJ from XFEL at 7.5 keV and 15 μJ from spontaneous radiation at 250 pC electron pulse charge.

Based on the analysis results, an experimental testing is scheduled to verify the design performance. However, one should keep in mind that the thermal conductivity of thin diamond may not be the same as that of bulk diamond44 since the heat carrier mean free path is suppressed by the small thickness dimension. For example, the bulk diamond thermal conductivity reaches its maximum at 70 K, but the thin film diamond thermal conductivity peaks at 250 K.45 Therefore, designing the system to operate at 70 K would yield inefficient heat conduction in crystal as the thermal conductivity is not optimal. This may indicate that a cooling system operating at the temperature corresponding to the peak of bulk diamond thermal conductivity does not necessarily deliver the most efficient cooling performance in reality.

In this paper, we present a new design of the mounting mechanism for thin crystals with cryogenic cooling. By finite element analysis, we show that the symmetric geometric design of the crystal with two strain-relief cuts can effectively mitigate the distortion due to CTE mismatch. We also evaluate the thermal performance of the system to illustrate that extremely high power density can be handled. With more and more needs for cryogenically cooled thin crystals, we believe that our design would benefit the development of the field and community.

Funding for this research was provided by the U.S. Department of Energy (DOE) (Contract No. DE-AC02-76SF00515) and the U.S. DOE Office of Science (Award No. FWP-2013-SLAC-100164 to Juhao Wu).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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