High temperature heat exchangers, with operating temperatures above 650°C, are important for industrial processes and waste heat recovery [1, 2] . Specifically, the next generation of high pressure closed-cycle solar thermal receivers, used to heat working fluids via concentrated solar radiation, could benefit from the use of compact heat exchange technology with high temperature mechanical performance [3] . Typical materials with sufficient strength and creep resistance at these operating temperatures are nickel-based superalloys [4] , with material costs approaching 20 times that of stainless steel.
Conventional printed circuit heat exchanger (PCHE) technology has been explored to enable microchannel solar receivers (MSR) capable of handling thermal fluxes well over 100 W/cm 2 [5] . PCHE technology uses photochemical machining (PCM) to etch fluid passages in sheet metal, followed by the diffusion bonding (DB) of stacks these etched sheets into microchannel arrays [6] . This produces joints with near parent material strength [3, 7, 8] . The main disadvantage of applying PCHE technology to MSRs is that isotropic PCM limits the depth-to-width aspect ratios to less than 1:2 [2] , leading to increased pressure drop, shorter flow paths, more headers on the backside of the receiver, resulting in higher mass and cost. Greater channel depth-to-width aspect ratios have the potential to reduce pressure drops across the device leading to fewer headers, less mass and lower cost.
Prior efforts to shape the MSR flow geometry have included the use of wire electro discharge machining (EDM) to increase the depth-to-width aspect ratio of the flow
High temperature heat exchangers, with operating temperatures above 650°C, are important for industrial processes and waste heat recovery [1, 2] . Specifically, the next generation of high pressure closed-cycle solar thermal receivers, used to heat working fluids via concentrated solar radiation, could benefit from the use of compact heat exchange technology with high temperature mechanical performance [3] . Typical materials with sufficient strength and creep resistance at these operating temperatures are nickel-based superalloys [4] , with material costs approaching 20 times that of stainless steel.
Conventional printed circuit heat exchanger (PCHE) technology has been explored to enable microchannel solar receivers (MSR) capable of handling thermal fluxes well over 100 W/cm 2 [5] . PCHE technology uses photochemical machining (PCM) to etch fluid passages in sheet metal, followed by the diffusion bonding (DB) of stacks these etched sheets into microchannel arrays [6] . This produces joints with near parent material strength [3, 7, 8] . The main disadvantage of applying PCHE technology to MSRs is that isotropic PCM limits the depth-to-width aspect ratios to less than 1:2 [2] , leading to increased pressure drop, shorter flow paths, more headers on the backside of the receiver, resulting in higher mass and cost. Greater channel depth-to-width aspect ratios have the potential to reduce pressure drops across the device leading to fewer headers, less mass and lower cost.
Prior efforts to shape the MSR flow geometry have included the use of wire electro discharge machining (EDM) to increase the depth-to-width aspect ratio of the flow 
High temperature heat exchangers, with operating temperatures above 650°C, are important for industrial processes and waste heat recovery [1, 2] . Specifically, the next generation of high pressure closed-cycle solar thermal receivers, used to heat working fluids via concentrated solar radiation, could benefit from the use of compact heat exchange technology with high temperature mechanical performance [3] . Typical materials with sufficient strength and creep resistance at these operating temperatures are nickel-based superalloys [4] , with material costs approaching 20 times that of stainless steel.
Conventional printed circuit heat exchanger (PCHE) technology has been explored to enable microchannel solar receivers (MSR) capable of handling thermal fluxes well over 100 W/cm 2 [5] . PCHE technology uses photochemical machining (PCM) to etch fluid passages in sheet metal, followed by the diffusion bonding (DB) of stacks these etched sheets into microchannel arrays [6] . This produces joints with near parent material strength [3, 7, 8] . The main disadvantage of applying PCHE technology to MSRs is that isotropic PCM limits the depth-to-width aspect ratios to less than 1:2 [2] , leading to increased pressure drop, shorter flow paths, more headers on the backside of the receiver, resulting in higher mass and cost. Greater channel depth-to-width aspect ratios have the potential to reduce pressure drops across the device leading to fewer headers, less mass and lower cost.
Prior efforts to shape the MSR flow geometry have included the use of wire electro discharge machining (EDM) to increase the depth-to-width aspect ratio of the flow
High temperature heat exchangers, with operating temperatures above 650°C, are important for industrial processes and waste heat recovery [1, 2] . Specifically, the next generation of high pressure closed-cycle solar thermal receivers, used to heat working fluids via concentrated solar radiation, could benefit from the use of compact heat exchange technology with high temperature mechanical performance [3] . Typical materials with sufficient strength and creep resistance at these operating temperatures are nickel-based superalloys [4] , with material costs approaching 20 times that of stainless steel.
Conventional printed circuit heat exchanger (PCHE) technology has been explored to enable microchannel solar receivers (MSR) capable of handling thermal fluxes well over 100 W/cm 2 [5] . PCHE technology uses photochemical machining (PCM) to etch fluid passages in sheet metal, followed by the diffusion bonding (DB) of stacks these etched sheets into microchannel arrays [6] . This produces joints with near parent material strength [3, 7, 8] . The main disadvantage of applying PCHE technology to MSRs is that isotropic PCM limits the depth-to-width aspect ratios to less than 1:2 [2] , leading to increased pressure drop, shorter flow paths, more headers on the backside of the receiver, resulting in higher mass and cost. Greater channel depth-to-width aspect ratios have the potential to reduce pressure drops across the device leading to fewer headers, less mass and lower cost.
Prior efforts to shape the MSR flow geometry have included the use of wire electro discharge machining (EDM) to increase the depth-to-width aspect ratio of the flow 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to channels [9, 10] . However, wire EDM limits the design of the patterned microchannel plate to a single repeating geometry across the entire array ( Figure 1 ). Subsequent work on the MSR has shown the need to use post geometries with varying shapes within the flow region of the device. Metal forming processes provide one possible means to handle posts with varying shapes as well as to increase the depth-to-width aspect ratio of microchannels. Electrically assisted (EA) forming has advantages compared to conventional embossing with a furnace due to its fast temperature ramp and additional reduction in flow stress known as the electroplastic effect [11] . As H230 is a high temperature material, reduction in flow stress is required to make the MSR viable for forming. Also reduced time at temperature could reduce surface scale, which would be detrimental to the diffusion bonding process. Chan et al. (2012) demonstrated the EA microstamping of microchannels into copper, showing that larger grains resulted in higher surface roughness and greater thickness variation [12] . Further, Xu (2015) EA embossed microchannel arrays into ultrafine grain aluminum, determining that die filling was improved when the grain size was small compared to feature size [13] . However, in both cases, top-facing faying surfaces adjacent to the microchannels showed poor flatness, making downstream diffusion bonding difficult. Using 316L stainless steel, Fu showed that increased embossing pressure, as a means to improve die fill and flatten faying surfaces, led to tearing of posts from the base material during demolding [14] . To date, no one has demonstrated the means to produce a microchannel/micropost array that can be diffusion bonded using embossing processes. In this paper, electrically-assisted (EA) embossing is investigated as one means for producing high aspect ratio arrays while being capable of handling a wide variety of post shapes. In the next section, a MPD is developed and evaluated by the use of a unit cost model, to determine the impact of EA embossing on the cost of a MSR. Next, methods used to validate the cost model are described followed by preliminary micro experimental results and discussion.
A MPD based on EA embossing, was developed for a 1 Megawatt MSR produced out of Haynes 230 using the lamina design as shown in Figure 1 . To meet cost targets set by the U.S. Department of Energy, each panel was required to cost $25,000 at a production quantity of 1,000 units/year, permitting a cost of $25 per kilowatt beyond all other costs associated with constructing a MSR power plant. Subsequently, the MPD was evaluated by determining the cost of the MSR using cost models previously described elsewhere [15] .
Pressure drop across the array of microchannels in parallel can be defined as:
where ∇ is the pressure drop, is the density, v is the mean velocity, L is the channel length and DH is the hydraulic diameter [16] . The hydraulic diameter for a non-circular cross section is defined as:
where H is the channel height and W is the channel width. By doubling the channel depth-to-width aspect ratio from 1:2 to 1:1 and assuming a square channel of 0.3 mm, decreases in the pressure drop allow for increases in the flow path between inlet and outlet headers (L) leading to the need to increase mass flow rate to achieve the same outlet temperature of the working fluid [5, 17] . Considering all of these factors, the resulting header spacing reduces the number of headers for an EA-embossed design from 30 to 15 [17] . Figure 2 shows the process flow diagram and design of an EA-embossed MSR. The microchannel plate was formed by first embossing the post array and second, flattening the tops of the posts to enable diffusion bonding. Inlet and outlet through features produced by wire EDM, were needed in the microchannel plate to enable fluid from the headers on the backside of the MSR to pass into the microchannel array. As previously reported [9, 10] , efforts were made to design the headers to be sand cast. The microchannel plate and top plate were joined using diffusion bonding. Figure 3 shows the cost of goods sold (COGS) graph and its breakdown into the seven cost categories. Capital tooling costs, consumables and raw material costs were determined based on vendor estimates, and all other cost categories (facility, labor, maintenance, and utilities) used assumptions summarized in Table 1 . As a result of the increased microchannel depth leading to fewer headers, the overall mass of the device was reduced by 24% over the previous PCM design. The cost model found that the total cost of the MSR @ 1,000 units per year for the EA embossing design was estimated to be $22,254 ( Figure 4 ). In support of this cost model, forming force was estimated using material properties supplied by the material vendor [18] . A simple force calculation for producing a 300 µm deep channel within a 5 mm thick plate was determined to be 60 MPa at 650°C. Multiplying by the size of the MSR patterned area (90 cm x 90 cm) resulted in a total force requirement of 5,000 tons. A budgetary quote for a 5,000-ton four post hydraulic press was found to be approximately $850,000. The equipment cost used for the EA embossing steps was produced by multiply $850,000 by two to account for modifications to the press such as, integration of a power supply, improved parallelism and strengthening of the embossing platens. Capacity was determined by the opening and closing time of the tool. The embossing die was estimated to cost approximately $500,000 with a life of 1,000 stamps, which is a conservative estimate for die life. 
In order for EA embossing to be an effective shaping process for the microchannel array, it must satisfy both performance and process requirements. Based on prior work, it was expected that the channel variation across the array needed to be below 5% [19] . Further, the faying surface for diffusion bonding required adequate roughness (Ra = 0.5 µm) and flatness (5 µm) of the bonding surface to enable fit up with the top plate.
To validate that EA embossing can obtain all required bonding and patterning requirements, an EA embossing tool was designed, fabricated, and placed into a Instron universal tester equipped with a 50kN load cell (Figure 4) . Insulating quartz platens were utilized to insulate the Instron from both thermal and electrical loads during testing. The tool also included retraction springs and electrical platens that allowed for the die and workpiece to be connected to a power supply capable of applying 1000 amps through the embossed workpiece. Current was directed to flow through the die touch tool and into the workpiece as a means of guaranteeing proper current density. To avoid electrical shorts or poor connections, preloads of approximately 5kN were applied before current was turned on. The voltage across the system was varied to keep a constant current density. The power supply was programed to increase total current as a function of time linked to the extension rate of the press. This is to account for changes in the surface area of the die in contact with the workpiece as its pressed deeper into the H230. Parallelism of the die to the workpiece was accounted for with two spherical bearings that allowed for the pressure bearing columns to adjust to maintain good contact. Pressure was applied before embossing to allow these bearings to comply ensure good contact. 
Die inserts made of CPM T15 alloy, having excellent hot hardness, were purchased from Sun Microstamping of Clearwater, FL. The room temperature hardness for CPM T15 is 68 HRC [20] compared to nine HRC for H230 [18] . The alloy composition is listed in Table 2 . Post features were machined using wire EDM as through holes with a 3°draft angle to facilitate die removal from the workpiece after embossing. The die consisted of the inverse of an array of 16 microposts separated by 280 µm channels at the bottom of the posts ( Figure 5 and Table 3 ). These die inserts were attached to the EA embossing tool by fastening screws, ensuring a good electrical connection. 
A second die was fabricated from commercially pure tungsten in round bar form. The tungsten raw material was formed by powder processing using hot isostatic pressing, then warm formed into a round of 38.1 mm in diameter, and ground to tolerance. Next, it was cut into 25.4 mm thick disks by wire EDM and channel features were machined by wire EDM (Figure 6 ). Table 3 .4 summarizes the nominal sizes of the tungsten die features. 
Embossing of the microchannel array was performed using an open die with a current density of 18 A/mm 2 [21] , and was kept constant throughout the embossing process. The final embossing temperature reached was 607 ± 8°C as measured with a thermocouple in contact with the workpiece directly outside of the forming area. This temperature is lower than what was achieved during tensile tests on the same current density [21] . Although higher temperatures were likely obtained at the die-workpiece interface, the lower temperatures were attributed to heat conduction into the embossing tool. After pressing, the electrical current was disengaged, and the die was removed from the workpiece by retraction springs on the embossing die.
For this investigation, one mm thick Haynes 230 was solutionized and cut to size prior to EA embossing. Conditions for the embossing test articles are listed in Table 5 . For the third test article (TA3), increased embossing force was applied in an attempt to further the depth of the channels, which led to die failure. Higher currents were not attempted due to concerns over the high temperature mechanical properties of the CMP T15 die. For the samples that were successfully embossed, a second embossing step was performed to flatten the post array to enable diffusion bonding to the tops of the post array (Figure 7) . Flattening was performed using a flat tungsten carbide die without the application of current. 
A Haynes 230 bonding recipe developed by Kapoor, M., et al [22] was modified for this test article to eliminate the need for a Ni-based interlayer. Diffusion bonding conditions for H230 were determined through analysis and testing [23] . Diffusion bonding was performed in a vacuum of 10 -5 torr with a bonding pressure of 12.7 MPa and a bonding temperature of 1150°C, to limit creep during bonding to 2% as determined by [23] .
After bonding, samples were cross sectioned using wire EDM, ground flat with increasing grit sandpaper and then polished with 5 nm alumina polish. Samples were then optically investigated to determine feature dimensions and electron backscatter diffraction (EBSD) was utilized to investigate the microstructure of the formed posts. Prior to cross sectioning, the top and bottom surfaces of the test articles were imaged using a white light interferometric microscope (Zygo Zescope) to evaluate the planarity of theses surfaces. Bond line characterization was performed by optical micrograph where the pores were summed up and divided by the total bonding length, determining the percent area bonded at the top of the posts and the perimeter of the microchannel post array. Percent bonded area was calculated via equation 5:
Test article 1 (TA1) achieved a depth-to-width aspect ratio of 0.93:1 after the first strike with an average depth of 282 ±4.9 µm and an average channel width of 304 ±58.7 µm. The channel width variability is due to the far outside channels, which showed much larger widths (382 µm on average), compared to the inside channels (274 µm on average). This was not due to die dimensions, rather it was attributed to the unconstrained nature of open die embossing, where the outside of the test article was able to strain laterally to the stamping direction. Similarly, the use of a die with through hole post features lead to "mushrooming" of the post tops, due to die-workpiece friction. This phenomenon was more pronounced on the inside of the die where the material was more constrained (Figure 7) .
After embossing, the backside of TA1 was imaged showing a large out-of-plane deformation of 48 µm in the center of the test article (Figure 8 ). This suggested that the lower platen of A2 tool steel had plastically deformed under the embossing load. This led to the replacing of the tool steel platen with a tungsten carbide platen for TA2. Using the new platen, TA2 showed significantly lower channel depth with an average depth of 162 ±6.5 µm. This was attributed to the stiffer backside platen which consumed more strain energy. TA2 showed a channel width variation of 305 ±38.1 µm, similar to TA1, with more consistent channel widths in the middle of the array (265 µm on average) and larger widths along the perimeter (326 µm on average). The backside of TA2 also showed less plastic deformation than TA1 with a maximum out-of-plane deformation of 9.2 µm, an 81% decrease from TA1 ( Figure  10 ). This is in contrast to the 43% reduction in channel depth between the first and second embossing operations. In an attempt to increase the channel depth further, TA3 was subjected to greater embossing force, which resulted in die fracture. The effect on the test article was that channel regions under the smaller part of the fractured die were made deeper as that piece of the die was less constrained than the remainder of the die (Figure 11 ). As a result, TA3 had an average depth of 179 ±34.5 µm, with increased variability due to the greater depth under the fractured part of the die. A summary of width and depth characterization for the three test articles is presented in Table 6 . 
A second strike of TA1 was made to flatten the diffusion bonding faying surface at the top of the posts. The flattening step was found to decrease channel depth (251 ±16.3 µm). This decrease in channel depth was attributed to two phenomena. First, the plastic deformation on the backside of the test article was reduced by approximately 20 µm ( Figure 13) . Second, the middle posts of the array showed a larger height reduction as they were initially taller than the posts on the outside. After flattening, the tops of the posts showed flatness of 4 µm, sufficient for diffusion bonding (Figure 14) . The final average channel depth-to-width aspect ratio was found to be 0.87:1 which was near the goal of 1:1.
Similar results were found in TA2 and TA3. TA2 showed a decrease in backside deformation ( Figure 15 ) by 5.5 µm, leading to an increase in the variability of the channel Figure 14 . Backside of test article two after second strike, with a reduction of 5.5 µm at maximum height.
Diffusion bonding was performed on all three test articles, using the recipe discussed above. After bonding all test articles were characterized via a scanning white light interferometric profilometer. Figure 16 shows the top surface of TA2 after bonding showing a 4 µm depression over the micrpost array. Because the formed posts experience more stress than the unformed base material around it, it is expected that this is the result of creep within the microposts during diffusion bonding. Due to failure of a control thermocouple, TA1 overshot the bonding temperature and experienced excessive creep during bonding. Consequently, only TA2 and TA3 were characterized by metallography after bonding. Figure 17 shows a cross-section of TA2 with significant deformation of the posts and severe changes to microchannel dimensions. Average channel depths of TA2 and TA3 were found to be 87 ±6.2 µm and 101 ±13.3 µm, respectively (Table 8) . These 
To better understand the creep phenomenon of the microposts, electron backscatter diffraction (EBSD) was performed on a new set of microposts after EA embossing but, prior to diffusion bonding. Figure 18 shows an EBSD image with elongated grains in the direction of the embossing force (i.e. along the post height) as well as a summary of the orientation angle of these grains. More than 35% of the grains show a low angle orientation (< 15°), which is consistent with subgrain formation during high strain. These elongated subgrains have high grain-boundary area-to-volume ratios, which is known to reduce creep resistance of materials at high temperatures [24] . Figure 19 shows the area fraction of grains as a function of the log of their size. The grain size in the deformed posts have a maximum of approximately 40 µm with smaller grains having lower are fractions. In prior work, the creep resistance of H230 has been shown to decrease by seven times at 760°C due to prior thermomechanical processing [25] . In that case, the material was cold rolled and intermediate solution treated four times to reduce grain size by 33% from 57 µm on average to 37 µm on average. This reduction in creep resistance was attributed in part to the reduced grain size [25] . Reduced grain size increases grain boundary density providing for increased grain boundary sliding and faster diffusion rates [26] . Further, H230 is capable of forming tungsten-rich and molybdenum-rich carbides at the EA embossing temperature, which would remove solution strengthening elements out of the matrix that can also reduce strength and ductility [27] . These results suggest that a post-forming solutionizing heat treatment to 1.) restore strengthening elements to the matrix; and 2.) increase grain size, would improve the creep properties of the material after forming, allowing the laminae to be diffusion bonded. 
Failure of the CPM T15 occurred when applying a flow stress of 1.9 GPa. Failure was of a brittle nature, fracturing the die into two pieces. CPM T15 is a precipitation hardened material. Investigation into the properties of this material, determined that forming temperatures were near the aging temperature of the die, leading to over aging and loss of strength. Die wear was not observed, indicating that the material was extremely hard compared to H230.
As a result of this failure, a tungsten die was machined, as described earlier, in an attempt to choose a material that was harder than H230, but still malleable enough so that facture could be avoided without significant increases in die wear. Wrought alpha tungsten was chosen for the second set of dies and was believed to have adequate hardness (106 Rockwell B at RT) and yield strength (700 MPa) at [18] . Upon testing this material at the embossing temperature, it was found to deform rapidly and only gave 85 µm deep imprints into the H230 samples at greatest depth. Subsequent hardness testing of the alpha tungsten used for tooling showed a RT value of 88 Rockwell B which is below what was expected. In addition, it has been shown that properties of recrystallized alpha tungsten drops significantly with increasing temperature compared to wrought [29] . Contacting the vendor, the process history of the received raw material was found to be: 1. hot isostatic pressing of powder; 2. hot working into a round; 3. grinding to tolerance; and 4. stress relief anneal. A previous report from NASA showed that the yield strength of tungsten which had been subjected to a stress relief anneal, was under 92 MPa @ 400°C in compression [30] while the yield strength of H230 in tension at the same temperature is over 300 MPa [18] . These findings suggest that the tungsten needs to be sufficiently cold worked to work as an embossing die for H230. For hot working of Haynes 230, Haynes International suggested using Haynes 25, a solid-solution-strengthened cobalt-based superalloy, or Haynes 282, a precipitationhardened nickel-based superalloy.
Channel size variability was found to be greater than desired. Variability of the channel height and channel width are both important as they both have an effect on the hydraulic diameter. The open die embossing setup can account for significant discrepancies in the channel width. This result has been reported in other works using EA embossing approaches to the formation of microchannels [31, 32] . Reduced channel depth in the center of the array has also been observed and attributed to uneven pressure distribution between the die and the workpiece surface [33] .
Suggested improvements to advance this work includes constraining the lateral motion of deformation, chamfering the edges of the workpiece and increasing the material thickness. Constraining the lateral motion of the workpiece will limit outward motion of the deformation at the expense of increased forming load. By adding chamfered edges to the workpiece, you can allow some of the deformation to move outward increasing bulk deformation, while still resulting in improved feature consistency along the edge of the sample. This approach has the added benefit of reducing the force required as a function of part consistency [33] .
The use of EA embossing and diffusion bonding of Haynes 230 shows promise for producing economically viable micropost arrays for application within microchannel solar receivers. Channel-depth-to-width aspect ratios of 0.93:1 and 0.87:1 were obtained after embossing and flattening, respectively. Efforts to increase this aspect ratio will require the use of different tool materials as described above. Further, the relative standard deviation for channel depth across the micropost array was found to be 1.8% and 6.9% after embossing and flattening, respectively, while channel width was found to be 19.2% and 26.7% after embossing and flattening, respectively. Future strategies for managing these dimensions include constraining the lateral motion of the workpiece within a closed die, although as the size of the micropost array approaches one meter in scale, the effect of lateral strain may be insignificant. Diffusion bonding of the micropost arrays in this work resulted in considerable creep and loss of channel dimensional integrity. A solutionizing heat treatment of the Haynes 230 micropost array prior to diffusion bonding is needed to restore the high temperature mechanical properties of the posts, preventing accelerated creep during diffusion bonding.