Reconstruction quality of a biological network when its constituting elements are partially observed

Victor Picheny, Jimmy Vandel, Matthieu Vignes and Nathalie Villa-Vialaneix (authors listed in alphabetical order) MIA-T unit, INRA Toulouse, chemin de Borderouge, 31326 Castanet-Tolosan Cedex, France Motivation Unravelling regulatory regulations between biological entities is of utmost importance to understand the functioning of living organisms. As the number of available samples is often very low (often less than one hundred), inference methods are frequently performed on a subset of variables which make sense in the mechanisms under study. Classical remedies are either data driven (e.g., differentially expressed genes) or knowledge driven (e.g., using ontology information). However, whatever the chosen solution, important variables are very likely missed by the selection process, which is the issue at stake in the present paper.

Dealing with partially available variables A Gaussian graphical framework is considered, which is specified by its concentration matrix K = Σ -1 (Σ is the covariance matrix of the Gaussian model). Because of high-dimensional issues, K (from which the underlying network can be deduced), is frequently estimated by adding an ℓ 1 -penalty to the model likelihood (the method is known under the name glasso, see [START_REF] Friedman | Sparse inverse covariance estimation with the graphical lasso[END_REF]. But, if the gene expressions are represented by the variable X = (X o , X h ), where the first p nodes X o are observed and the remaining nodes are hidden, directly applying the glasso to the observed variables leads to a spurious estimation of the network topology:

Σ -1 o,o = K o,o -K o,h K -1 h,h K h,o .
In less formal terms, this simply means that estimating the true network topology on observed nodes need to access some information on the structure of hidden nodes. [START_REF] Chandrasekaran | Latent variable graphical model seletion via convex optimization[END_REF] gives identifiability conditions for this model and proposed a consistent convex formulation of the problem which allows them to solve it (hereafter denoted by "CPW-S+L"). However, whether accounting or not for unobserved variables improves the inference quality, prediction capability and global understanding of the system remains an open question in practice.

Aim and scope

The objective of this work is twofold. Firstly, we conduct an empirical study to evalu-ate and compare the use of (blindly used) glasso and CPW-S+L for network reconstruction, as regards to: (i) the sample size n, (ii) the ratio of missing variables r, (iii) the missing node context (random or peculiar nodes), (iv) several methods for simulating the data. The overall objective is to provide some guidelines for practicioners for the choice of the methods and for the analysis of their results.

Secondly, we aim at discussing the concept of "natural graph" inherited from the complete graph. Three different possibilities to account for the reference graph (i.e., graph projections) were studied: (i) the graph whose links reflect path existence in the complete graph, (ii) the graph inherited from edges of the complete graph only, or (iii) the graph learnt from complete data. This questions whether inference algorithms purely recover actual edges or whether they reflect dependencies either direct or of higher orders. The concept of reference graph is also closely linked to the user's objective, in particular, whether inference or prediction is sought.

Preliminary results

Our first experiments show that, as expected, the overall reconstruction quality decreases as n decreases and as r increases. Moreover, the reconstructed network quality is worse when central nodes are missing than when nodes are missing at random. Also, glasso obtains worse performance than CPW-S+L but a perhaps more surprising conclusion is that predicted edges do not replace links which cannot be retrieved because intermediate nodes are missing.


Mohamed Lakdhar Sahli
email: mohamed.sahli@ens2m.fr

Jean-Claude Gelin

Thierry Barrière

J-C Gelin

T Barriere

Characterisation and replication of metallic micro-fluidic devices using three different powders processed by hot embossing

come

Characterisation and replication of metallic micro-fluidic devices using three different powders processed by hot embossing

INTRODUCTION

In recent years, the miniaturisation and manufacturing of micro-components have gained increasing attention in both industry and academia [START_REF] Gietzelt | Development of a micro annular gear pump by micro powder injection moulding[END_REF][START_REF] Fu | Replication of metal microstructures by micro powder injection moulding[END_REF][START_REF] Benito-Lopez | Spiropyran modified microfluidic chip channels as photonically controlled self-indicating system for metal ion accumulation and release[END_REF][START_REF] Heaney | Isotropic forming of porous structures via metal injection moulding[END_REF]. The microinjection moulding process is rapidly becoming one of the most promising fabrication technologies for the mass production of thermoplastic polymer micro-parts [START_REF] Zhang | Microstructure and mechanical properties of high Nb containing TiAl alloy parts fabricated by metal injection molding[END_REF][START_REF] Karatas | Investigation of mouldability for feedstocks used powder injection moulding[END_REF][START_REF] Mccormick | Microchannel electrophoretic separations of DNA in injection-molded plastic substrates[END_REF]. Most of the applications are concentrated in the fields of micro-optics, micro-fluidics and medical instruments. Hot embossing is also a manufacturing method used for the fabrication of polymer-based microcomponents. It provides several advantages, such as low-cost moulds, high replication accuracy for micro-feature generation and ease of operation [START_REF] Juang | Hot embossing in microfabrication[END_REF][START_REF] Juang | Hot embossing in microfabrication. II. Rheological characterization and process analysis[END_REF]. For these reasons, manufacturing by hot-embossing [START_REF] Martynova | Fabrication of plastic microfluid channels by imprinting methods[END_REF][START_REF] Lan | A parameter study on the micro hot-embossing process of glassy polymer for pattern replication[END_REF] rather than injection moulding is advantageous. It also introduces less residual stress into the polymer because the polymer chains must stretch and flow only a very short distance from the substrate into the patterned microstructure during hot-embossing. Additionally, the temperature variation range for the polymer is smaller than that required in injection moulding, which leads to reductions in both the shrinkage that occurs during cooling and the frictional forces that act on the micro-features during demoulding [START_REF] Jean | High fidelity hot-embossing of COC microdevices using a one-step process without pre-annealing of polymer substrate[END_REF][START_REF] Chien | Hot embossing of microfluidic platform[END_REF][START_REF] Pv. Muterlle | Microstructure and tensile properties of metal injection moulding Co-29Cr-6Mo-0.23C alloy[END_REF][START_REF] Heckele | Hot embossing -the molding technique for plastic microstructures[END_REF][START_REF] Sahli | Quality assessment of polymer replication by hot embossing and micro-injection moulding processes using Scanning Mechanical Microscopy[END_REF].

Conventionally, the mould tooling is made of either steel or aluminium and can be manufactured by Computer Numerical Control machining (CNC) and Electric discharge machining (EDM); after it is manufactured, the mould can be used to produce polymer microparts via either hot embossing or injection moulding [START_REF] Yh | Effect of machining parameters on surface textures in EDM of Fe-Mn-Al alloy[END_REF][START_REF] Recha | Influence of cutting edge radius on the wear resistance of PM-HSS milling inserts[END_REF]. The surface quality of the mould is highly dependent on the cutting conditions used during machining, which significantly influence the resulting surface roughness [START_REF] Klocke | Advanced tool edge geometry for high precision hard turning[END_REF][START_REF] Chou | Tool nose radius effects on finish hard turning[END_REF]. For example, in micro-fluidic systems, these techniques generate tools with a high surface roughness and micro-channels that generate a reduction in the overall efficiency of fluidic flow. In this study, to establish the basis of micro-pattern manufacturing of the metallic tool using the hot embossing process, an alternative method was applied to form micro-channels in the metallic moulds with a low surface roughness. The micro-fluidic chip developed here is used as an example to discuss the use of various mould insert materials by hot embossing.

Various investigations have been conducted concerning the influence of both the physical and processing parameters, such as the particle size and solid loading of the powder in the mixture, the effect of sintering temperature on the control and dimensional changes, the density, mechanical properties and roughness surfaces of the components, have received increasing attention in recent years [START_REF] Ca | The effects of tool surface quality in micro injection moulding[END_REF]. German et al. [START_REF] German | In situ dimensional change, mass loss and mechanisms for solvent debinding of powder injection moulded components[END_REF] investigated the effect of solid loading on the dimensional change that occurs during solvent debinding of the injection moulded components. Liu et al. [START_REF] Liu | Mixing and characterisation of 316L stainless steel feedstock for micro powder injection moulding[END_REF] investigated the effects of solid loading and extrusion on mixing and feedstock homogeneity for the injection moulding of micro-structured components. The results demonstrated that 316L stainless steel feedstock with a suitable solid loading (equal to 58 vol. %) can be successfully used for the forming of micro-structured parts with proper shape retention. The micro-structured parts exhibit the necessary strength for demoulding with no observable debinding defects and a final sintered microstructure characterised by shape retention.

Recently, Tay et al. [START_REF] By | Characterisation of micro gears produced by micro powder injection moulding[END_REF] have succeeded in the manufacturing of micro-gears using the micro-powder injection moulding process with 316L stainless steel powder possessing particle sizes of 2.4 m and a multi-component wax-based binder system. The analysis revealed different grain structures at the tooth (≈35 m) and hub of the micro-gear (≈5 m). Significant grain growth was also observed at the tooth. Meng et al. [START_REF] Meng | Replication and characterization of 316L stainless steel micromixer by micro powder injection moulding[END_REF] conducted an experimental analysis on the replication of a micro-fluidic system by micro-powder injection moulding using 316L stainless steel. Additionally, they also investigated the dimensional change and surface roughness of the micro-mixer. They obtained proper replication with appropriate shape retention lacking in visible defects by use of a powder injection moulding process with a 316L stainless steel feedstock. The dimensional shrinkage of the micro-mixer occurred mainly in the sintering step, whilst the dimensional change was not noticeable in the debinding step. The surface topography of the silicon mould insert was properly replicated in the stainless steel micro-mixer. Fu et al. [START_REF] Fu | Micro-hot-embossing of 316L stainless steel micro-structures[END_REF] investigated the manufacturing of a 316L stainless steel cylindrical micro-structure array using a silicon mould insert with the hot embossing process. Their results demonstrated the effects of various embossing parameters on the filling of micro-cavities in the silicon mould insert and the de-moulding of microstructures. This study was only focused on the replication of a micro-structured array with an aspect ratio of 2. It was limited to the use of 316L stainless steel with unknown solid loading and binder percentages in its feedstock. Most of the work up to date on hot embossing focused on to use this process as a flexible, low-cost micro-fabrication method for polymer microstructures over large surface areas. To date our work was focused on the use of the hot embossing process adapted to metal powders for the manufacturing of a micro-fluidic die mould with low surface roughness. An integrated rapid prototyping chain was established for rapid manufacturing of the micro-structured master in metallic powders made from elastomeric moulds by use of the hot embossing process. This rapid manufacturing chain, offers a rapid and flexible manufacturing route for fabrication of prototype micro devices from polymer solutions. This study uses the lithography technology to fabricate the silicon mould insert with nanoscale details and surface roughness at a lower cost. Due to the mechanical strength limitation, silicon material is usually not suitable to use as mould material. In this study, the silicon master was used for casting of silicone to fabricate elastomeric micro-fluidic mould. The choice to use a flexible mould was related to the demoulding facilities for the micro-structures and the increase of lifetime of the mould when used in the hot embossing process.

This paper describes the elaboration and characterisation of different feedstocks for use in metallic hot embossing and the manufacture of micro-structures with low surface roughness. In the experimental tests presented here, only the temperature and pressure were considered while analysing the manner in which the metallic die master can be archived with the highest replication accuracy. These experiments allow us to understand and qualify the influence of hot embossing processing conditions on the geometrical embossed accuracy of the replicas and the mechanical properties of the final components after solid state sintering. The sintering stage was carried out in vacuum using the metallic micro-structured samples obtained at different solid loadings. Therefore, the present work also analysed the shrinkages, densities, Vickers hardness values and roughness variations of the micro-fluidic specimens using three shades.

EXPERIMENTAL MATERIALS AND METHODS

2.1.MATERIALS

Fine powders of 316L stainless steel were used to develop the mixtures dedicated to the hot embossing process. The powder particulates had a spherical shape and an average particle size of 5 µm -80%. This shape is generally more appropriate for obtaining a feedstock with low viscosity. The powders had a density equal to 7.9 g.cm -3 and were provided by Sandvik Osprey Company. Figure 1 gives a photograph of the 316L stainless steel powder particle distribution.

The micron-size pre-alloyed powder (Fe-Ni 8 %) was composed of PA-FN08 and cobalt tungsten carbide with 19.9 % WC (Co-WC). The ME1107 powders were characterised to have an average particle size of 5 µm. The powders were provided by Eurotungstene Company ® (Eramet) with densities equal to 7.93 and 9.74 g.cm -3 , respectively. The powder morphology is given in Fig. 2. Before mixing, the powders were dried in a vacuum oven at a temperature of 120 °C for 5 h to remove any moisture.

Feedstocks of Co-WC, Fe-Ni 8% and 316L stainless steel based on 40 to 75 % solid loadings (by volume) were prepared using a twin-screw mixer. The binder system used in this study consisted of paraffin wax, polypropylene and stearic acid. The composition of the binder corresponded to the ratio of PP:PW:SA given as relative fractions 40:55:5. The characteristics of the different binder systems and the raw powders are related in Tables 1 and2.

PROCESSING STEPS

The main steps of the hot embossing process include the Lithographie, Galvanoformung, Abformung (UV-LIGA) process for the SU-8/Si mould fabrication (the master mould with a thick negative photoresist (SU-8) deposited on large silicone wafer (Si)), elastomeric inverse mould manufacturing using a casting process, the development of metal powder feedstocks for filling the mould, the hot embossing process, and the debinding and sintering stages. The processing stages have been developed for use in the rapid manufacturing of high-quality metallic replicas onto the elastomeric moulds, as illustrated in Fig. 3.

MIXING TESTS

Experiments related to the mixing of binders and feedstocks were carried out using a twinscrew Brabender ® Plastograph EC mixer with a pair of rotor blades. The maximum capacity of the mixing chamber was 55 cm 3 . The twin-screw mixer was connected with appropriate software to measure the mixing torque; the same processing conditions were used for each mixture, including a mixing temperature of 160 °C, a mixing time equal to 30 min and a mixing rotation speed of 30 rpm. The mixtures were prepared individually with different solid loadings from 40 % up to 75 % with an incremental increase of 5 % for each level.

The powders were loaded when the temperature had stabilised at the required mixing temperature to facilitate homogeneous mixing of the powder and binder components. During a mixing test, the mixture homogeneity can be evaluated through the mixing torque curves. Uniform mixing is achieved when the torque reaches a stable, steady state value. Figure 4 shows Scanning Electron Microscope images (SEM) of the different feedstock powders after the mixing stage. Finally, the feedstocks were granulated into small pellets for rheology characterisation and were used in the hot embossing process for the development of microfluidic replicas.

ELASTOMERIC MICRO-STRUCTURED MOULD

SU-8 negative photoresist was spin coated onto a clean silicon wafer and exposed by the UV LIGA method to obtain the micro-fluidic system as a micro-mould for casting, which is abbreviated as the SU-8/Si master. Figure 5 presents the SU-8/Si mould insert with the microfluidic structure. The dimensions of a typical micro-fluidic cavity are shown in Fig 6b .The elastomeric die cavity moulds were obtained by casting silicone rubber over the SU-8/Si master, enabling the development of micro-structures with very well defined and smooth sidewalls. The silicone rubber (Sylgard 184) used as the material for the elastomeric moulds was provided by Dow Corning Inc ® . The silicone base and catalyst were thoroughly mixed a ratio of 1:10. The mixture was degassed for approximately 5 min in a primary vacuum to avoid the trapping of air in the silicone. Next, the silicone mixture was poured over the SU8/Si and cured at 70°C for 4 h; after curing, the silicone was easily pealed from the SU-8/Si master. The elastomeric mould was obtained with one face that contained all of the details of the original master. The manufacturing process details for the fabrication of the SU-8/ Si and PDMS moulds is also described in [START_REF] Js | Pressure Free Fabrication of 3D Micro-components Using Al Powder[END_REF][START_REF] Imbaby | Fabrication of 316-L stainless steel micro parts by softlithography and powder metallurgy[END_REF][START_REF] Zhang | Micro-fabrication of three-dimensional, free-standing ceramic MEMS components by soft moulding[END_REF][START_REF] Zhu | A net-shape fabrication process of alumina micro-components using a soft lithography technique[END_REF]. Figs. 5a, 5b and 6a display micrographs of the SU-8/Si master and the negative replicas. Accordingly, the micro-fluidic system was produced with a model that considers subsequent shrinkage during the sintering stage (Fig 6a andb). Scanning mechanical microscopy (SMM) was used to obtain a digital fingerprint corresponding to a portion of the elastomeric die cavity mould manufactured by casting. The fingerprint allows for a description of manufacturing quality and the quantification of geometry as well as the surface, as a part of the intrinsic characteristics of the elastomeric die cavity mould. Both details of interest in the elastomeric die cavity mould developed by casting were obtained with SMM corresponding to the shapes illustrated in Figure 7.

2.2.3.HOT EMBOSSING PROCESS

The elastomeric die cavity mould was used for the hot embossing process to manufacture micro-components using feedstocks based on polypropylene, paraffin wax and stearic acid. This process involved heating a feedstock to its softening temperature (i.e., just above the melting temperature for a semi-crystalline thermoplastic polymer) and then pressing it into an elastomeric mould with applied pressure. Next, the feedstock was cooled down, and the part was demoulded at room temperature. After the cooling stage, the metallic replicas were easily peeled from the elastomeric die cavity mould. The elastomeric die cavity mould was repeatedly used with little degradation. The embossed tests were gradually established and carried out in two different cases. In the first case, the tools were heated at a temperature equal to 170 °C with a heating rate of 5 °C/s; additionally, the dwell time was 10 min, and the forming force was varied from 200 to 400 N. In the second case, the tools were heated from room temperature to a temperature in the interval from 130 to 190 °C; the heating rate was 5 °C/s, while the forming force was slowly increased to a load of 400 N. The temperatures were between the highest melting temperature T f (T f_PP =125°C) and the lowest degradation temperature T d (T d-SA =200°C) of the binder system. In both cases, the final qualities of the metallic replicas were measured with SMM to determine the dimensions and surface roughness.

2.2.4.DEBINDING AND SINTERING STAGES

The process was comprised of two sequential stages, including thermal debinding followed by solid state sintering. In the thermal debinding stage, the residual binders were converted into gas and eliminated. Then, the powders were sintered, resulting in strengthened green parts capable of yielding products without defects. First, the debinding was performed at 500 °C in a thermal oven. The defect-free embossed parts were placed on an Al 2 O 3 plate. The debinding temperature used was based on the TGA curve identified for the binder system. Because the SA and PW finish begin to degrade at approximately 330 °C, the first debinding temperature used was 350 °C. The temperature was then gradually increased to 500 °C, which corresponded to the TGA curve that leads to a significant loss of polypropylene weight and the removal of all residual binder. The debinding was performed in the temperature range between 350 and 500 °C.

In this study, the second stage of the solid state sintering process was conducted in vacuum with graphite heating element furnace offering a maximum temperature of 1900°C. The samples were maintained at this temperature for 1 h, and then the temperature was increased between 900 -1050 °C, 1000 -1285 °C, 1000 and 1360 °C a rate of 5 °C/min, 10 °C/min or 15 °C/min for Co-WC, Fe-Ni and 316L, respectively. Table 3 summarises the processes associated with the debinding and sintering stages. Additionally, the same primary vacuum was used during the sintering test.

T 1 [Stainless steel]=1000-1360°C T 1 [Co-WC]=900-1050°C T 1 [Fe-Ni]=1000-1285°C Dwelling (1 h) 2. Sintering
Cooling down (cooling rate 5°C/min)

2.3.SAMPLE CHARACTERISATION 2.3.1. RHEOLOGY CHARACTERISATION AND THE THERMAL DEGRADATION PROPERTIES (TGA)

The rheological behaviour of the feedstocks was measured using a capillary rheometer provided by Instruments Bohlin ® . A series of experiments were performed in which the samples were extruded through a die with a 1 mm diameter and measuring 16 mm in length. Three temperatures were tested, including 150, 170 and 190 °C, beyond the melting temperature of the binder. Shear rates varying from 10 2 to 10 4 s -1 were applied using the die with the measurements reported above, giving a ratio (L/D) equal to [START_REF] Sahli | Quality assessment of polymer replication by hot embossing and micro-injection moulding processes using Scanning Mechanical Microscopy[END_REF].

The degradation temperature ranges of the binder components in the powder/binder feedstocks were obtained from thermogravimetric analyses (TGA). The analysis results indicated the thermal limitations for the initial processes, including the mixing and hot embossing processes. TGA was performed using a Setaram Setsys analyser ® .

ROUGHNESS CHARACTERISATION

To assess the dimensional and geometrical qualities of the replicas, comparative 2D profile measurements and 3D contours were performed using scanning mechanical microscopy (SMM). The dimensions, the surface roughness and the surface topographies of the elastomeric mould inserts and the micro-fluidic samples were collected using a mechanical profilometer (Tencor-Alpha Step IQ) with a 5 m diamond tip radius operated a scanning speed of 5 m/s over a length of 1 mm both inside and outside the reservoir pattern (2 mm in diameter). Scans were collected on both the elastomeric mould insert and the microsystem samples (zone 1, see Fig. 6b). The shrinkage of the micro-fluidic device was determined by the dimensional changes in width and height measured for the micro-sized structures.

RESULTS AND DISCUSSION

Thermal degradation characteristics

The degradation temperature ranges, as related to the binder components in the powder/binder feedstocks, were obtained by thermogravimetric analyses (TGA), which were performed using a Setaram Setsys analyser ® . Fig. 8 shows the TGA curves of the multicomponent binder and the individual binder components. In the TG curves collected above 170, 250 and 350 °C, the stearic acid, paraffin wax and polypropylene each start to decompose, respectively. Additionally, each degradation temperature range is very broad, and the associated mass percentage loss of each of the three materials tends to 0 % (complete loss) at higher temperatures, which is the ideal case for binder removal in debinding of the Metal Injection Molded (MIM) part.

Similarly, the multi-component binder, which resulted from mixing of the individual binder components, also underwent two distinct degradation steps. Through a comparison of the TGA curves, it is reasonable that the full degradation of PW and SA occurred in the first degradation temperature range (170 -330 °C), whereas the degradation of PP took place at the higher temperatures (340 -450 °C). Above 450 °C, all of the binder components were burned off. Based on the TGA results, a multi-step debinding profile was established, demonstrating the progressive removal of each of the three binder components. The progressive debinding over a wide temperature range can help to retain the integrity of the micro-structured cavities and prevent the formation of debinding defects, such as cracking and slumping.

PREPARATION AND CHARACTERISATION OF THE FEEDSTOCKS

Several feedstocks were developed by using different powders indifferent loading ratios (see table 4). The mixing torques were measured and plotted versus times for different Fe-Ni 8 % feedstocks in Figure 9. The observed torque peaks are due to the introduction of small amounts of feedstock into the mixture. It should be noted that the mixture with a solid loading of 60 % had the lowest torque homogenisation, reaching a value of approximately 1.5 N.m. Therefore, the optimal load of Fe-Ni powder was identified to be 60 %. Beyond a load of 62 %, the feedstock did not demonstrate mixability. Instead, it reached the threshold of mixability, which leads to the formation of an inhomogeneous mixture. During the mixing tests, Co-WC, Fe-Ni and 316L powders were found to be non-mixablefor critical solid loads greater than or equal to 46, 62 and 66 %, respectively. The following table summarises the results that were obtained for the different powder mixing experiments. Figure 10 illustrates the mixing behaviour of three different feedstocks with solid loadings of 40, 60 and 60 %, which are denoted as Co-WC, Fe-Ni 8% and 316L stainless steel, respectively. The imposed mixing parameters were a rotor speed of 30 rpm, a temperature of 160 °C and 30 min of mixing time. Varying the solid loading caused variation in the torque level, indicating differences in the mixture viscosity values. The mixing torque of the Co-WC feedstock loaded at 40 % was significantly higher in comparison to the constant torque level for both feedstocks loaded at 60 %, which led to higher viscosity. This might be due to the particle size distribution and the higher density of Co-WC, which would have increased the resistance on the rotor blades. Similarly, the low solid loading appearance apparently can be deceptive.

In the case of the Co-WC powder, the solid loading range tested was measured. It was found to below in comparison to that of the stainless steel and Fe-Ni powders (see table 4). These low values appear closely related to the packing ability of the powders, the particle shapes and sizes, the particle size distributions and the tendency of the powder to agglomerate. Measurements of shear viscosity were performed on the feedstock mixtures at different temperatures with a two-channel capillary rheometer; different shear rates were considered with the same capillary die diameter Ø = 1 mm (Fig. 11). Viscosity is one of the important parameters in the evaluation of the rheological behaviour of the MIM feedstock. Figure 11 shows the apparent viscosity-shear rate curves of the extruded feedstock tested at different temperatures in the range of 150 to 190 °C. It should be noted that the 316L stainless steel feedstock was difficult to extrude at the lower temperature, corresponding to 130 °C, which is very close to the melting temperature of the PP polymer.

The feedstock viscosity decreases with shear rate and temperature, indicating pseudoplastic flow behaviour and increases with high powder volume ratios. Normally, the exhibition of pseudo-plastic flow by the feedstock during moulding eases the mould filling process and minimises jetting defects [START_REF] German | Injection molding of metals and ceramics[END_REF] and [START_REF] Kn | The influence of mixing route on the properties of ceramics injection molding blends[END_REF]. As displayed in figure 11, the viscosity is temperature sensitive, decreasing with increasing temperature. This is attributed to the reduction in solid volume content, arising from increased binder expansion and destruction of the molecular chains during heating. From figure 11, it can be observed that the feedstock shows mouldability in the hot embossing process.

Figure 12 shows the shear viscosity of the different feedstocks versus the shear rate, which were developed and mixed under the same conditions and tested at 170 °C. The results indicate that the three feedstocks possess pseudo-plastic rheological behaviour up to a shear rate of 10 4 s -1 . It was observed that the Co-WC feedstock exhibited viscosities higher than those of the other two feedstocks. This trend is the same as that observed for mixing torque.

HOT EMBOSSING TESTS 3.3.1. Influence of the embossing load

In this portion of the investigation, the soft embossing process was conducted using the process mentioned above. Figure 13 relates typical results concerning the first experimental series. The feedstocks gradually filled the elastomeric mould cavities as the forming load was increased, followed by constant temperature and even during cooling of the cavities.

Thus for a properly defined forming temperature, by increasing the forming load of the feedstock substrate, one can help facilitate filling and is able to improve the surface roughness of the metallic replicas. Hence, the surfaces of the replicated parts were found to be smooth with R a <1 µm. This result can be partially related to the increased forming load, which is favourable for decreasing the surface roughness. %, obtained by the hot embossing process at different forming loads (unit: µm).

Influence of the hot embossing temperature

In this portion of the investigation, the experimental procedure was conducted at different temperatures ranging from 130 to 190 °C, and with the loading applied only once, the embossing temperature was reached. In this second series of experiments, the hot embossing process capability for the replication of purely metallic templates was also evaluated in terms of dimensional changes and the quality of pattern transfer. In Figures 14 and15, each view corresponds to different stages in the formation of cavities and micro-channels. At 130 °C, which is close to the melting temperature of PP, the surfaces of the embossed patterns were extremely rough, caused by partial melting of the binder system. However, it was found that the filling ratio increased with increasing forming temperature, yielding an accurate replica of the original imprint.

After several tests, it was found that the temperature strongly influenced the resulting filling rate and the final surface roughness of the cavities. This trend regarding the related effects can be directly observed in Figures 14c andd. These experimental results are consistent with the results obtained from other positions of the same sample (see Figure 15c andd). This could be due to the binder fluidity during hot embossing, which can affect the flow of the feedstock into the detail regions of the die mould. Therefore, at 190 °C, the feedstocks may be pushed by the binders toward the mould details, leaving fewer defects in the final shape. The average surface roughness, R a , measured at the base of the reservoirs decreased sharply at the melting temperature; then, the R a values levelled off at higher temperatures (beyond 170 °C), see Fig. 16. Figure 17 shows the topographies of the metallic replicas fabricated with three different feedstocks. It is evident that the Co-WC feedstock replica was significantly rougher than that of the other feedstock replicas, most likely due to the feedstock viscosity. This trend is the same as that observed in the mixing torque and viscosity analyses. Hence, this result confirmed that the Co-WC feedstock with solid loadings from 42 to 44 % was not feasible for hot embossing. At a 40 % solid loading, the result is acceptable but is simply not sufficient to achieve fluid flow.

Thus far, the most uncomplicated method for decreasing the Co-WC feedstock viscosity is to lower the viscosity of the binder by increasing the forming temperature beyond 190 °C. However, this is impractical because the binder begins to degrade at this temperature. The second possible solution is to develop a new formulation, one that is particularly well suited for this specific powder. The adopted final solution was to use the Co-WC feedstock with a solid loading of 38 %. This led to reduced feedstock viscosity and improvements in the filling ability and the surface quality of the replicas. As depicted in Figure 18, the feedstock gradually filled the mould cavities while the temperature was maintained in the loading stage. However, the feedstock was not able to completely fill the gap due to its low fluidity at 130 °C (see Figure 14a and15a) at the end of hot embossing process. Additionally, the profiles of the embossed replicas at 130 °C show defects, such as ridges in the top surface. At higher temperatures, filling is a quick process, and complete filling occurs when the hot embossing temperature exceeds 160°C (see Figure 14c and15c). These results show that high replication accuracy can be achieved using the proper forming temperature in the hot embossing process without vacuum.

In Figure 18, the cast embossed replicas are compared to an elastomeric imprint. The scanning microscopy mechanical (SMM) profile relates the variation observed in these cases (the cross section shown is related to zone 1 in Figure 6b). Although a constant load was maintained until separation, and there was no apparent irregularity during the experiment, the SMM profiles indicate the presence of a distinct trace of the samples after embossing. It can be concluded that the forming load and temperature values determine the replication accuracy in terms of the width and shape and have significant influence on the accuracy of the final replication. Fig. 19 shows the photograph of the micro-fluidic samples following the embossed processing step using the different sample types. The samples were obtained under the same conditions. Good shape retention without warpage or cracking was achieved following de-moulding.

DEBINDING AND SINTERING RESULTS

As an example, the 316L stainless steel components shown in Figure 20 were obtained after debinding was started at room temperature and completed at 500 °C over the course of approximately 150 min; following this step, the temperature was maintained for 30 min. After, the components were heated to 1250 °C with a heating rate of 10 °C/min and then were held at a constant temperature for 60 min. Finally, the cooling stage was carried out a rate of 10°C/min for the components. As shown in Figure 20, the components were correctly sintered without the appearance of obvious defects or cracks near the interface. Figure 21 shows a photograph of the micro-fluidic components after undergoing different processing steps. As shown in Figure 22, the metallic replicas were approximately 10 µm shallower than designed, which is likely due to shrinkage after the sintering step. In this stage, the component undergoes a low dimensional anisotropic shrinkage in the range of 10 to 14 %, depending on the powder characteristics, the solid loading, etc. This dimensional change occurred across the sample and can be compensated in the design of the mould cavity. The dimensions of the micro-fluidic samples for three different solid loadings are given in Table 5. Compared with the silicon mould insert, the dimensional change after the sintering stage is clearly evident. The dimensional changes in the length and width of the microstructures showed similar trends. For example, in the Co-WC samples, the shrinkage values were approximately 21 and 24 %. However, the width and height of the embossed microstructures decreased gradually as the sintering temperature was increased, regardless of the powder used. Co-WC powders are usually sintered with a partial liquid phase at temperatures above 1280 °C to reduce the size of the pores, to improve the hardness and the density and to evolve the microstructure and grain size [START_REF] Sun | Characterizations of ball-milled nanocrystalline WC-Co composite powders and subsequently rapid hot pressing sintered cermets[END_REF][START_REF] Sivaprahasam | Microstructure and mechanical properties of nanocrystalline WC-12Co consolidated by spark plasma sintering[END_REF][START_REF] Sh | The effect of sintering conditions on the properties of WC-10wt%Co PIM compacts[END_REF]. In our application, the sintering temperature choice was limited to temperatures between 900 and 1050 °C, i.e., without the liquid phase. The presence of this phase causes deformation of the micro-fluidic structures; that is, they disappear with increasing temperature. The results show that the occurrence of the partial liquid phase is closely associated with the development of a deformed micro-fluidic structure.

MICROSTRUCTUREEVOLUTION

Figures 23 and 24 include the micrographs of polished sintered microstructures, collected under an optical microscope at different sintering temperatures. It can be observed that the number of pores and the pore size both decreased as the sintering temperature was increased. In Fig. 23, at the temperature of 1100 °C, a considerable amount of porosity is present, and the pore structure is irregular, indicating that the part was not appropriately sintered. Following sintering at the temperature of 1200 °C, the grain size became larger than that at the temperature of 1100 °C, while the pore size became smaller. A higher sintering temperature of 1300 °C resulted in higher densification, smoother pore structures and smaller pore sizes. At 1350 °C and above, the microstructures became denser still, and fewer tiny pores were found. Following sintering, scanning electron micrographs were collected for two micro-fluidic replicas (60 % and 64 % of 316L stainless steel) without polishing. The specimens were observed in zone 2 (see Fig. 6), and the results are related in Figures 25 and26. The grain sizes were dramatically increased following sintering. The porosity has almost entirely disappeared in the embossed specimen with a solid loading of 60 %, and the decrease in porosity in the specimen with a solid loading of 64 % is clearly revealed, as well; this occurred as a result of the elimination of pores via grain boundary and volume diffusion at high temperatures [START_REF] Rp | Micro-structural evolution of injection molded gas-and water-atomized 316L stainless steel powder during sintering[END_REF]. The sizes and dimensions of the final components were measured and compared with the geometry of the embossed die mould to qualify the linear shrinkage with the respective sintering stage (see Fig. 27). The analyses of the dimensions were carried out on the sintered specimens embossed with the three feedstocks loaded at either 60 -64 % of 316L stainless steel, 40 -44 % of Co-WC or 56 -60 % of Fe-Ni, respectively. The mean shrinkages are given in Table 6. During the thermal debinding and sintering stages, an embossed sample undergoes binder elimination and subsequent particle bonding, resulting in dimensional changes in the samples. The overall shrinkage of cavities in the die mould after the sintering stage was found to be in the range from 10 to 20 %. The same phenomenon has been encountered by other authors, including Lohand et al. [START_REF] Nh | Statistical analysis of shrinkage variation for powder injection moulding[END_REF]. In comparison with the embossed mould insert, the width (a) and length (b) of the sintered samples decreased. As shown by the results related in Table 6, the sintering cycle with the heating rate of 10 °C/min generated shrinkage in the Fe-Ni sample, totalling to 11.2 % in the y-y direction and 12.3 % in the x -x direction.

The main parameters affecting the final sample size already have been studied, and these include the metal powder morphology, the binder ingredients and proportions, the mixing conditions, the mould design, the embossing parameters, the rheological behaviour of the embossing materials, the debinding and sintering stages, the equipment and even the environmental conditions. Among these often integrally-related factors, the most sensitive are the solid loading and the mould design [START_REF] Nh | Statistical analysis of shrinkage variation for powder injection moulding[END_REF]. As shown, different degrees of shrinkage were revealed for the same directions in the micro-fluidic samples using the same solid loading. Because all of the conditions during the processing were also identical, these differences in our experimental results can be explained by the differences in the metal powder morphology between the 316L stainless and Fe-Ni powders.

Sintering of the micro-fluidic systems was studied as a function of heating rate. In regard to the three feedstocks, 316L stainless steels, Fe-Ni and Co-WC, the sintering cycle with the heating rate of 15 °C/min tended to give the maximum shrinkage values, which were recorded as 9.7 %, 10.7 % and 13.1 % in the y-y direction, respectively. It can be observed that a very high shrinkage in the y-y direction was also revealed for the low feedstock loadings. This allowed for movement of the powder particles, leading to increased distortion.

Densities of the resulting micro-fluidic specimens

Additionally, the densities of the sintered micro-fluidic specimens were measured with the water displacement method (the Archimedes method) for each of the three feedstocks, and the resulting values are reported in Figures 28 and29. The theoretical densities of the stainless steel, Fe-Ni 8 % and Co-WC powders are, respectively, 7.90, 7.93 and 9.74 g.cm -3 . The sintering temperature and solid loading both had a significant effect on the densification, i.e., the density increased significantly with increasing temperature and solid loading, as summarised in Fig. 28 and29. The influence of sintering temperature on the densification of 316L stainless steel was more pronounced in comparison with that of Fe-Ni; similarly, a significant densification change was identified when the tool steel softened at 1300 °C. All experiments for the measurement of density in Co-WC cavity die moulds were obtained with a sintering temperature of 900 to 1050 °C. The relative densities of the sintered micro-system samples were determined to be above 95 % of the theoretical density of the three materials.

Vickers hardness evolution of the micro-fluidic specimens

After sintering the metallic die replicas, the specimens were subjected to hardness tests to assess and to qualify the mechanical property evolution versus the final sintering temperature. The hardness measurements were conducted on the polished sections of the different sintered components. Each area was polished using diamond pastes with 3 µm and 0.1 µm particle diameters at 150 rpm. Finally, the samples were polished again using a diamond paste of 0.1 µm for approximately 20 s and then were observed with an optical microscope. Fig. 30 demonstrates the variations in hardness for the micro-fluidic specimen as a function of the sintered temperature, as viewed from the top surface of the specimen. When the final sintering temperature was increased, the increase in density as the porosity is removed leads to an incremental increase in hardness. For example, the Co-WC spherical fine powders present the highest hardness, attaining 1200 HV1 at 1000 °C, followed by Fe-Ni material (188 HV1 at 1250 °C) and 316L (197 HV 1 at 1360 °C). The hardness can be increased with further improvements in the material density and the proper control of grain growth.

Roughness variation of the micro-specimens

The surface roughness variations of the die mould cavities sintered a temperature in zone 2 (see Figure 6b) are shown in Fig. 31. It can be observed that an increase in the final sintering temperature caused a slight increase in the surface roughness of the materials. This roughness variation can be improved by using ultra-fine powders, which result in a significantly increased surface finish in the final die mould and also result in a more complete fill, yielding significantly finer details. Both mechanical and laser cutting are common fabricating processes used in today's manufacturing industries. Each method employs its own distinct equipment, and has its own advantages and disadvantages. As example, in milling operations, feed, cutting speed, cutting tool material, workpiece material, cutting tool geometry, vibrations and tool wear are some of the most important factors that affect the surface roughness of the mould machined [START_REF] Paris | Surface shape prediction in high speed milling[END_REF][START_REF] Houming | Dynamic characteristics of conjunction of lengthened shrink-fit holder and cutting tool in high-speed milling[END_REF]. Several authors [START_REF] Eker | The effect of alloying elements on surface roughness and cutting forces during machining of ductile iron[END_REF] and [START_REF] Ghani | Study of tool life, surface roughness and vibration in machining nodular cast iron with ceramic tool[END_REF] argue that to prevent chatter and achieve good workpiece surface quality, the frequency of the cutting edge entering the cut during each rotation of the tool (tooth passing frequency) must differ from the natural and harmonic frequencies. The main weakness of the realisation of metallic mould inserts obtained by these process is the inability to obtain 3D shape variables of size less, and low roughness than, few microns from 0.1<Ra<1µm. It was also found that these traditional processes can also cause a loss of precision when going nanostructures or microstructures with large aspect ratio.

In this study, innovative solutions have been proposed and developed for manufacturing metallic tools to routinely reproduce a micro and nano-structured surface, with a lateral resolution less than 100 nm, even near to 10 nm for feedstocks produces very low viscosity. The study feasibility and the ability to rapid manufacturing have been demonstrated, and this should be applicable in several various applications. However, it should be emphasized that, a decrease in the surface roughness may result in part from contributions to drive the flow characteristics of liquid in channels, because the surface effects are significant [START_REF] Zhao | Surface-directed liquid flow inside microchannels[END_REF].

Conclusions

In the present analysis, the feasibility of hot embossing of micro-fluidic die mould cavities has been tested as 316L stainless steel, Fe-Ni 8% and WC-Co. The findings can be summarized as follows:

1) It has been shown that feedstock with solid loading in the range 40-64 vol.%, 40-44 vol.% and 40-60 vol.%, for 316L stainless steel, WC-Co and Fe-Ni 8%, respectively, are homogeneous and moldable through the feedstock homogeneity and rheological tests. However, feedstock with solid loading of 64 , 40 and 60 vol.% were selected to be the better choice, as higher concentration of solid particles are preferred to limit shrinkage during debinding and sintering. Based on the thermogravimetric analysis and rheology measurements, the optimal mixing parameters were chosen to be a mixing temperature, mixing speed and mixing time of 160 °C, 30 rpm, and 30 min, respectively.

2) In terms of rheological characteristics, different feedstocks are shear thinning fluids as viscosity decreases with increase in shear strain rate. In this case, the viscosity decreases with increasing temperature, but viscosity of the WC-Co feedstock is less sensitive to shear strain rate and temperature compared to that of the other feedstocks.

3) Based on the thermal characterisations of the feedstock, in one hand the feasibility of the feedstock for hot embossing of micro-fluidics die moulds was investigated, and in second hand, was also used to develop a suitable thermal treatment for both stages of the binder elimination process. The analysis of the hot embossing process for micro-structured metallic replicas demonstrated that the microstructure shapes were successfully embossed with the use of suitable forming parameters. These results confirm that the increasing temperature and pressure stage can determinate the replication accuracy by depth as well as the replication accuracy of the width and shape measurements. It was found that the replication accuracy strongly depends on the processing conditions. The results show also that microstructures can be successfully obtained, without visual debinding defects and the final sintered microstructures exhibit proper shape retention.

4) The dimension accuracy of the final die mould was mainly determined by geometrical dimension precision of embossing stage. In all processing parameters, the solid loading,

Figure 1 .

 1 Figure 1. The particle size distribution for the 316L stainless steel powder (d 50 = 3.4 m).

Table 2 .Figure 2 .

 22 Figure 2. SEM micrographs of the different feedstocks, including (a) the 316L stainless steel powder, (b) FeNi 8 % and (c) Co-WC.

Figure 3 .

 3 Figure 3. A schematic manufacturing diagram of the powder components developed by rapid prototyping.

Figure 4 .

 4 Figure 4. SEM micrographs of the feedstock after mixing, including (a) Fe-Ni 8 % (the solid loading equal to 64 %), b) Co-WC (the solid loading equal to 44 %) and (c) 316L (the solid loading equal to 60 %).

Figure 5 .

 5 Figure 5. SEM micrographs of the SU-8/Si master mould showing (a) a reservoir and (b) a channel.

Figure 6 .

 6 Figure 6. a) Geometry of the patterns of the elastomeric die cavity mould and b) a description of the mould dimensions and micro-fluidic geometries (unit: mm).

Figure 7 .

 7 Figure 7. 3D topographic imprints of the elastomeric die cavity mould realised by casting.

Figure 8 .

 8 Figure 8. TGA curves of all binders and the combined binder systems (PW 55 %, PP 40 %, SA 5 %).

Figure 9 .

 9 Figure 9. Mixing torque vs. time for three different solid loadings corresponding to three different Fe-Ni 8% feedstocks, obtained from the mixing test (160°C, 30 min and 30 rpm).

Figure 10 .

 10 Figure 10. Mixing torque vs. time for three different feedstocks, carried out with a mixing test (160 °C, 30 min and 30 rpm), corresponding to a Co-WC feedstock, 316L stainless steel and a Fe-Ni feedstock and obtained at different solid loadings of 40 %, 60 % and 60 %, respectively.

Figure 11 .

 11 Figure 11. Viscosity of the 316L stainless steel feedstock with a solid loading of 60 % by vol., tested at different temperatures.

Figure 12 .

 12 Figure 12. Viscosity of the three different feedstocks tested at 170°C, corresponding to the Co-WC feedstock, 316L stainless steel and the Fe-Ni feedstock, analysed at different solid loadings of 44 %, 60 % and 60 %, respectively.

Figure 13 .

 13 Figure 13. 3D topographic imprints of the Fe-Ni 8 % feedstock replicas with a solid loading content of 62 vol.%, obtained by the hot embossing process at different forming loads (unit: µm).

Figure 14 .

 14 Figure 14. 3D topographic imprints of Co-WC replicas with a solid content of 44 vol. %, obtained by the hot embossing process at different forming temperatures (unit: µm).

Figure 15 .

 15 Figure 15. 3D topographic imprints of Co-WC replicas with a solid content of 44 vol. %, obtained by the hot embossing process at different forming temperatures (unit: µm).

Figure 16 .

 16 Figure 16. 3D topographic imprints of 316L stainless steel replicas with a solid content of 64 vol. %, obtained by the hot embossing process at different forming temperatures (unit: µm).

Figure 17 .

 17 Figure 17. A comparison of 3D topographic imprints of the different metallic replicas, each obtained by the hot embossing process at a forming load and temperature of 400 N and 130 °C, respectively (unit: µm)

Figure 18 .

 18 Figure 18. A comparison of the variations in the 2D topographical profiles of the elastomeric moulds and the Fe-Ni 8 % metallic replicas obtained by hot embossing at different temperature, along the x-x direction (zone 1).

Figure 19 .

 19 Figure 19. Photographs of the micro-fluidic samples after the embossing step using two different feedstocks for (a) Co-WC with the solid loading of 38 % vol. and (b) Fe-Ni with the solid loading of 60 % vol.

Figure 20 .

 20 Figure 20. A photograph of the micro-fluidic system replica after the sintering stage (a solid loading equal to 60 % in vol. of 316L stainless steel powders).

Figure 21 .

 21 Figure 21. Photographs of the micro-fluidic tools after (a) the embossing and (b) sintering steps, produced using 316L stainless steel feedstocks (with a solid loading of 64%).

Figure 22 .

 22 Figure 22.A comparison of variations in the 2D topographical profiles of the elastomeric moulds and the metallic replicas after the sintering stage using 316L stainless steel feedstock (60 % vol.) and obtained by the hot embossing process, sampled along the x-x direction (zone 1).

Figure 23 .

 23 Figure 23. Optical micrographs of the sintered micro-structured stainless steel samples sintered at different temperatures: (a) 1100 °C, (b) 1200 °C, (c) 1300 °C and (d) 1360 °C.

Figure 24 .

 24 Figure 24. Optical micrographs of the sintered micro-structured stainless steel samples sintered at different temperatures: (a) 1150 °C, (b) 1200 °C, (c) 1250 °C and (d) 1300 °C.

Figure 25 .

 25 Figure 25. Scanning electron micrographs of the micro-fluidic specimens (embossed with a solid loading of 60 %) before polishing.

Figure 26 .

 26 Figure 26. Scanning electron micrographs of the micro-fluidic specimens (embossed with a solid loading of 64 %) before polishing.

3. 6 . 6 . 1 .

 661 PHYSICAL PROPERTIES OF THE RESULTING MICRO-FLUIDIC REPLICAS 3.Shrinkage of the resulting micro-fluidic specimens

Figure 27 .

 27 Figure 27. The top view of a section of localised dimensional measurements in the micro-fluidic simple.

Figure 28 .

 28 Figure 28. Effect of the sintering temperature on the sintered density (dwell time 60 min, 10 °C/min).

Figure 29 .

 29 Figure 29. Effect of the solid loading on the sintered density (dwell time 60 min, 1250 °C).

Figure 30 .

 30 Figure 30. The variation in hardness as a function of the final sintering temperature.

Figure 31 .

 31 Figure 31. Surface roughness (R a ) of the elastomeric mould inserts and the Fe-Ni micro-fluidic samples at different processing steps (a solid loading of 60% vol.).

Table 1 .

 1 Characteristics of the three different powders.

	Powder

size and density Powder Particle shape d10 (µm) d50 (µm) d90 (µm) Density (g/cm 3 ) Tap density (g/cm 3 )

	Inox 316L	Spherical	1.80	3.40	6.0	7.90	4.60
	Fe-Ni 8 %	Irregular	2.40	4.40	8.0	7.93	2.90
	Co-WC	Irregular	2.90	6.10	11.9	9.74	2.17

Table 3 .

 3 A description of the debinding and sintering treatments used for the different elaborated feedstocks.

	Steps	Procedure
		Heating up to 350°C
		(heating rate 10°C/min)
	1. Thermal debinding	Dwelling (30 min) Heating up to 500°C
		(heating rate 10°C/min)
		Dwelling (30 min)
		Heating up to temperature (T 1 )
		(heating rate 5 to 15°C/min)

Table 4 .

 4 An analysis of the field mixing and the mixability limit of the feedstocks

	Feedstocks	Field mixing range tested (%)	Early not mixable (%)
	316L stainless steel	40-64	66
	Co-WC	40-44	46
	Fe-Ni 8 %	40-60	62

Table 5 .

 5 Dimensions of the elastomeric mould and micro-sized structures of the micro-fluidic samples.

	Dimensions	Si				Micro-sized structure
	[mm]	mould
		insert
			316L stainless steel		Fe-Ni 8%		Co-WC
			1250 °C-10 °C/min	1200 °C-10 °C/min	1000 °C-10 °C/min
			60 %	62 %	64 %	56 %	58 %	60 %	38 %	40 %
	Ø	2	1.60±0.01	1.66±0.01	1.72±0.01	1.56±0.01	1.64±0.01	1.68±0.01	1.52±0.1	1.56±0.1
	a	6	4.92±0.01	5.04±0.01	5.16±0.01	4.74±0.01	4.98±0.01	5.04±0.01	4.56±0.1	4.74±0.1
	b	14	11.34±0.01 11.48±0.01 11.90±0.01 10.92±0.01 11.34±0.01 11.90±0.01 10.78±0.1 11.06±0.1
	c	14	11.10±0.02 11.62±0.02 12.32±0.02 10.78±0.02 11.48±0.02 11.76±0.02 10.78±0.2 11.20±0.2
	d	4	3.24±0.01	3.36±0.01	3.48±0.01	3.12±0.01	3.28±0.01	3.40±0.01	3.04±0.1	3.16±0.1
	e	14	11.48±0.02 11.62±0.02 12.18±0.02 11.06±0.02 11.34±0.02 11.76±0.0 2 10.50±0.2 10.92±0.2

Table 6 .

 6 Linear shrinkage in the y-y direction corresponding to the micro-fluidic part (a sintering time of 60 min).

	Linear shrinkage				Solid loading
		316L stainless steels	Fe-Ni 8%	Co-WC
		60 % 62 % 64 % 56 % 58 % 60 % 38 % 40 % 42 %
	Sintering temperature		1250 °C		1200 °C	1000 °C
	Heating rate [°C/min]				Means value
	5	10.1	9.7	9.7	10.9 10.7 10.5 14.1 13.5 13.1
	10	9.9	9.6	9.8	11.2 10.7 10.6 14.3 13.7 13.2
	15	9.6	9.9	9.7	11.3 10.8 10.7 14.2 13.7 13.1

the embossing temperature and the sintering temperature have the most important effects on the dimension precision and the material properties. The high powder loading allowed obtaining sintered parts with 96% of the theoretical densities.


M Sahli

J-C Gelin

DEVELOPMENT OF A FEEDSTOCK FORMULATION BASED ON POLYPROPYLENE FOR MICRO POWDER SOFT EMBOSSING PROCESS OF 316L STAINLESS STEEL MICRO-CHANNEL PART

Keywords: Hot embossing, binder system, 316L stainless steel, rheological characteristics, homogeneity

To exploit the potential of micro-system technology, the micro-powder embossing process, a rapid manufacturing production technology of micro structured die mould, was currently being investigated. Present work focused on establishing a suitable binder system for micro-powder embossing process. Multi-component binder systems, comprising of different weight percentages of Paraffin Wax (PW), Stearic acid (SA) and Polypropylene (PP) were investigated. The compatibility between binder constituents was studied by Thermogravimetric analysis (TGA) showing a partial miscibility between both components. The feedstock comprised of 316L stainless steel powder and a wax-based thermoplastic binder was used to achieve a feedstock with 60 to 68% vol. powder loading. The degradation temperature of binders was determined by using Thermogravimetric analysis (TGA) and flow behaviour through rheometer. Homogeneity of the feedstock was verified by using Thermogravimetric analysis (TGA) and Scanning Electron Microscopy (SEM). Then, hot embossing was done and it was found that the feedstocks having solid loading up to 68 vol% were successfully embossed and components were without physical defects. The polymeric part was driven off by thermal debinding using a thermal cycle designed on the basis of a thermogravimetric study of the binder. Finally the vacuum sintering of the parts allow high quality parts to be obtained.

INTRODUCTION

Hot embossing is a significant processing method for polymer-based microfabrication. It provides several advantages such as low-cost for moulds, high replication accuracy for micro-features and simple operation [START_REF] Juang | Hot embossing in microfabrication, I. Experimental[END_REF][START_REF] Juang | Hot embossing in microfabrication. II. Rheological characterization and process analysis[END_REF]. In the last few years, hot embossing is being explored as a shaping method for the fabrication of micro-structured die mould for thermoplastic moulding applications, characterized by very low roughness (<0.01 m), such as micro-fluidic systems. In hot-embossing, both the base polymer substrate and the master die are heated above the glass transition temperature (or softening point) of the thermoplastic and a controlled force is applied. The assembly is then cooled below the glass transition temperature after which the substrate is separated from the mould/die. In recent years, many studies have been conducted to investigate the hot embossing process. As example, the pressure distributions on the surface of polymer during hot embossing process have been investigated. The results indicate that a higher embossing pressure results in more uniform shrinkage in the elastically deformed state during cooling [START_REF] Chen | Preventing non-uniform shrinkage in open-die hot embossing of PMMA microstructures[END_REF]. Becker and Heim [START_REF] Becker | Hot embossing as a method for the fabrication of polymer high aspect ratio structures[END_REF] demonstrated that the hot embossing process could enable microstructures replication with high aspect ratio (height/section) over large thermoplastic polymer areas. The metal embossing process consists of four steps. Initially, metal powders are mixed with suitable organic binders. Binder is added between metal powder particles as the flow-vehicle to get embossed micro-parts of the desired shape. The embossing mixture of binder and powder is called feedstock. During embossing, the feedstock flows into and fills a mould under heat and pressure to form a green part with the desired shape. The embossed micro-part then undergoes a debinding step where the polymer is extracted out and the powder is sintered to get full or near full density. This process enables the use of a wide range of materials such as those with high strength, hardness or other functional properties, which will broaden the applications of microcomponents. Various investigations have been conducted, concerning the influence of physical or processing parameters such as size and loading rate of the powder in the mixture, the sintering temperature on the control and dimensional changes; density; mechanical properties and roughness surfaces of components have received increasing attention in recent years [5]. Meng et al. [START_REF] Meng | Replication and characterization of 316L stainless steel micro-mixer by micro powder injection moulding[END_REF] have conducted an experimental analysis on replication of micro-fluidic system by micro powder injection moulding using 316L stainless steel. In addition, they have also investigated the dimensional change and surface roughness of the micro-mixer. They obtained in this study, the proper replication with appropriate shape retention and without visible defects by powder injection moulding using 316L stainless steel. The dimensional shrinkage of the micro-mixer took place mainly in the sintering step, whilst the dimensional change was not noticeable in the debinding step. The surface topography of the silicon mould insert was well replicated in the stainless steel micromixer. Recently, Tay et al. [START_REF] By | Characterisation of micro gears produced by micro powder injection moulding[END_REF] have succeeded in the manufacturing of micro-gears using the micro-powder injection moulding process with 316L stainless steel powder possessing particle sizes of 2.4 m and a multi-component wax-based binder system. The analysis revealed different grain structures at the tooth (≈35 m) and hub of the micro-gear (≈ 5 m). Significant grain growth was also observed at the tooth. Meng et al. [START_REF] Meng | Replication and characterization of 316L stainless steel micro-mixer by micro powder injection moulding[END_REF] conducted an experimental analysis on the replication of a micro-fluidic system by micro-powder injection moulding using 316L stainless steel. Additionally, they also investigated the dimensional change and surface roughness of the micro-mixer. They obtained proper replication with appropriate shape retention lacking in visible defects by use of a powder injection moulding process with a 316L stainless steel feedstock. The dimensional shrinkage of the micro-mixer occurred mainly in the sintering step, whilst the dimensional change was not noticeable in the debinding step. The surface topography of the silicon mould insert was properly replicated in the stainless steel micro-mixer. German et al. [9] investigated the effect of powder loading on the in situ dimensional change during solvent debinding of powder injection moulded components. Tseng [10] evaluated the influence of powder loading on the dimensional control in ceramic injection moulding using a statistical analysis. Fu et al. [START_REF] Fu | Micro-hot-embossing of 316L stainless steel micro-structures[END_REF] investigated the manufacturing of a 316L stainless steel cylindrical micro-structure array using a silicon mould insert with the hot embossing process. Their results demonstrated the effects of various embossing parameters on the filling of micro-cavities in the silicon mould insert and the de-moulding of microstructures. Meng et al. [START_REF] Moballegh | Copper injection moulding using a thermoplastic binder based on paraffin wax[END_REF] have conducted an experimental analysis on the dimensional change and surface roughness of replication of micro-fluidic system by micro powder injection moulding using 316L stainless steel. They obtained the well replication with good shape retention and without visible defects. The dimensional shrinkage took place mainly in the sintering step. The surface topography of the silicon mould insert was well replicated in the stainless steel micro-mixer.

This study uses the lithography technology to fabricate the silicon mould insert with nanoscale details and surface roughness at a lower cost. Due to the mechanical strength limitation, silicon material is usually not suitable to use as mould material. In this study, the silicon master was used for casting of silicone to fabricate elastomeric micro-fluidic mould. The choice to use a flexible mould was related to the demoulding facilities for the micro-structures and the increase of lifetime of the mould when used in the hot embossing process. In this study, the whole process is examined using 316L stainless steel, known by their good mechanical properties and corrosion resistance, behaviour suitable for a wide range of applications. The thermophysical and rheological characterisation, and feasibility of the feedstock using a multi-component binder system for micro hot embossing of a micro-fluidic system, is reported in this paper. The work covers the determination of a suitable powder loading for feedstock preparation, evaluation of the feedstock homogeneity, thermal characteristics and mechanical properties, in using properly formulated binders, as well as the morphology of the microstructures.

MATERIALS AND EXPERIMENTAL WORKS

Materials

Fine powders of 316L stainless steel were used to develop the mixtures dedicated to the hot embossing process. The powder particulates had a spherical shape and an average particle size equal to 5 µm (Fig. 1a). This shape is generally more appropriate for obtainning a feedstock with a low viscosity. The powders had a density equal to 7.9 g.cm -3 and were provided by Sandvik Osprey Company ® . Fig. 1b gives a photographs of the 316L stainless steel powder particle distribution. The binder system consists of paraffin wax (PW), stearic acid (SA) and polypropylene (PP) where the highest melting temperature of the binder system measured on a Setaram differential scanning calorimeter (DSC 92) is 160 °C. The lowest degradation start temperature of the binder system measured on a Setaram ® thermogravimetric analyser is 180 °C. The character istics of the different binder systems were related in Table 1.

Rheology characterisation and thermogravimetric analysis (TGA)

The rheological behaviour of the feedstock was measured using a capillary rheometer provided by Instruments Bohlin ® . A series of experiments were performed in which the samples were extruded through a die with a 1 mm diameter and measuring 16 mm in length. Three different temperatures 170 °C, 190 °C and 210 °C were used. Shear rates of 10 2 to 10 4 s -1 were applied using the die with the measurements reported above, giving a ratio (L/D) equal to 16.

The degradation temperature ranges of the binder components in the powder-binder feedstocks were obtained from thermogravimetric analyses (TGA) using a Setaram Setsys analyser ® . The analysis results were essential to determine the maximum embossing temperature and removal of binder in thermal debinding cycle. Thermogravimetric analysis was carried out in the temperature range 25 -500 °C at a heating rate of 10 °C/min.

Mixing tests and soft embossing process

Experiments related to the mixing of binders and feedstocks were carried out using a Brabender ® Plastograph EC mixer with a pair of rotor blades. The maximum capacity of the mixing chamber was 55 cm 3 . The mixtures were prepared with different vol.% incremental solid loadings from 20 vol.% up to 80 vol.% with an incremental increase of 5% for each level. The mixing temperature was set at 170 °C, which is within the highest melting temperature (160 °C). This allowed complete melting and prevented total binder degradation. During mixing, the binder system was fed at first followed by the addition of powder in small consecutive loadings. The embossing tests were carried out to an imposed displacement, equal to 1mm, using an universal testing machine (type 6025, Instron ® ). Soft embossing was carried out above the upper melting point of the feedstock at 170 °C in a micro -structured mould.

Fabrication of micro-fluidic system

The silicon (Si) mould master was fabricated with micro-fluidic structure by means of photolithography and Deep Reactive Ion Etched technique (DRIE) to emboss microfluidic structure on stainless steel 316L feedstocks (Fig. 2). The dies were fabricated as follows. Firstly, the wafer was cleaned in piranha solution for 2 min followed by deionized water rinse for 2min and dehydration on a hotplate at 110 °C for 5 min. A 2.5 µm thick SPR220 positive photoresist was deposited on the surface of the wafer using a spin coater using a spin speed of 1200 rpm and a spinning time of 30 s and then soft baked at 115 °C for 15 min on a hot plate , then cooled down to room temperature. The resist was exposed using an EVG ® 620 automated mask alignment with an energy of 300 mJ/cm 2 .

The DRIE was performed on Alcatel A601 machine with the Bosch process technology. Silicon structures with depth of approximately 100 µm were obtained. Finally, the dies were treated with C 4 F 8 gas under a flow of 500 sccm for 5 min to

Debinding and sintering stages

Firstly, the debinding was performed at 500 °C in a thermal oven. The embossed parts were placed on an Al 2 O 3 plae. The debinding temperature used was based on the TGA curve identified for the binder system. Because the SA and PW finish begin to degrade at approximately 330 °C, the first debin ding temperature used was 350 °C. The temperature was then gradually increased to 500 °C, which corresponding to the TGA curve that leads to a significant loss of polypropylene weight and the removal of all residual binder. Secondly, the stage of solid state sintering process was conducted in vacuum furnace with graphite heating element offering a maximum temperature of 1900 °C. The temperature were increa sed up to 1000 -1360 °C, with 0.1 °C/min to 10 °C/min for 316L stainless.

RESULTS AND DISCUSSIONS

Thermo properties

The thermal properties of the binders provide basic guidelines for subsequent replication process steps. Fig. 4a shows the differential scanning calorimetry result of the binders where three endothermic peaks, 60 °C, 7 0 °C and 170 °C, were observed during heating due to the melting of major binder components. From the differential scanning calorimetry result, the melt temperature for hot embossing process should be higher than 170 °C so as to enable complete fill ing of the micro-cavities. The degradation temperature ranges, as related to the binder components in the powder/binder feedstocks, were obtained by thermogravimetric analyses (TGA), which were performed using a Setaram Setsys analyser ® . Fig. 4b shows the TGA curves of the multi-component binder and the individual binder components. In the TG curves collected above 180, 200 and 340 °C, the stearic acid, paraffin wax and polypropylene each start to decompose, respectively. Additionally, each degradation temperature range is very broad, and the associated mass percentage loss of each of the three materials tends to 0 % (complete loss) at higher temperatures, which is the ideal case for binder removal in debinding of the Metal Injection Molded (MIM) part. Similarly, the multi-component binder, which resulted from mixing of the individual binder components, also underwent two distinct degradation steps. Through a comparison of the TGA curves, it is reasonable that the full degradation of PW and SA occurred in the first degradation temperature range (180 -330 °C), whereas the degradation of PP took place at the higher temperatures (340 -450 °C). Above 450 °C, all of the binder components were bur ned off. Based on the TGA results, a multi-step debinding profile was established, demonstrating the progressive removal of each of the three binder components. The progressive debinding over a wide temperature range can help to retain the integrity of the micro-structured cavities and prevent the formation of debinding defects, such as cracking and slumping.

The thermograms of Fig. 5 indicate a significant decrease in weight loss of the blends. The results show that the thermal stability of blends decreases with an increase in wax content. A decomposition was registered around 450 °C, except for the compound containing that the PW virgin whose decomposition finished around 330 °C and the decomposition process ended around 5 00 °C.

Mixing behaviour and powder loading

In order to study the effect of the loading rate of each component on the rheological properties of feedstock suitable for filling micro-cavities in hot embossing process, three different mixtures with two starting components were carried out. In the mixing tests, the component loading of each PW or 316L stainless powder was increased gradually from 0% to 100% by adding the PW or 316L stainless powder with an increment equal to 5% for each level. The mixing torque vs. mixing time is related in Fig. 6a. The related mix torques corresponding in the combines (PW, PP) evolves the same way with lower values then (PP, 316L stainless). We can conclude that using more paraffin wax can reduce the viscosity of the mixture and using the polypropylene gives component rigidity to the embossed. On the basis of these comments, this study will be realised using the feedstocks prepared, using two different formulations (F1 : 28wt.% PW + 2wt.% SA + 10wt.% PP; F2 : 10wt.% PW + 2wt.% SA + 28wt.% PP). Mixing tests by continuously increasing powder loading were also realised to determine the critical solid loading using the two formulations. The powder loading was increased gradually from 20% to 80% by adding the powders with an increment equal to 5% for each level. The mixing torque vs. mixing time is related in Figure 6b. Three different zones appear looking the curve in Fig. 6b. In zone 1, there is mainly binder in the mixture and the torque remains almost at the same low level. In zone 2 (F1: 50% to 65%, F2: 50% to 70%) the torque begins to slightly increase starting from powder loading equal to 50%. In zone 3, the torque increases rapidly from 70% or 80% depending on the chosen formulation, to the maximal powder loaded feedstock corresponding to 70% or 80%. So in relation with this incremental test, the critical solid volume loading was determined for F1, F2 equal to 70% and 80%, respectively. It results that the mixing torques using formulation 1 were smaller than the torques of the next test using formulation 2 for the same powder loading as shown in Fig. 6b. Fig. 7a shows the variation in the torque with time during the mixing experiments. The experiments were performed for a mixing temperature of 170 ºC (according to ATG tests) and mixer speeds values: 10, 30 and 50 rpm. For a given powder particle loading, it was observed that an increase the mixing speed results in a decrease in the mixing torque. Reducing the mixing time, below 40min, results in a high heterogeneity of feedstocks. However, in this case, steady state torque was not achieved. The proper mixing conditions were obtained from a temperature, speed and mixing time equal to 170 °C, 50 rpm and 60 min, respectively. Fig. 7b shows the torque evolution for feedstock with a different reloading powder, using formulation 2. The torque stabilizes at a steady level in a short time (60 min) indicating uniform mixing. The torque value increases as the powder loading varies from 45 vol.% to 70vol.% due to the higher powder content. It is proportional to the shear stress of the mixer, which indicates the work energy consumed to disperse and distribute the powder in the binder. The scanning electron micrographs of the feedstock were shown in Fig. 8. In the figure, stainless steel and binder system could be distinguished due to various contrast levels caused by different levels of atomic number. Stainless steel appears brighter than the binder system due to more back-scattered electrons released by virtue of its higher atomic number. For the mixed feedstock, the particles disperse homogeneously into the matrix and were surrounded by the binder. Finally, the proper parameters in the mixing tests were 170 °C f or the mixing temperature, 50 rpm as the mixing rotation speed and 60 min for mixing time, but the weight of the powders were different.

Rheological characteristics

Fig. 7a shows the results from the capillary rheometer in term of shear viscosity vs. shear rate curves of the mixed feedstock (from F1 and F2, 316L stainless steel powder, D 50 =5 m) tested at 170 °C. According to the viscosity cur ves related in Figure 9a, the formulations F1 and F2 give a similar behaviour for 316L stainless steel powder. The viscosity of the feedstock decreases with shear rate, indicating pseudo-plastic flow behaviour. Normally, feedstock exhibiting pseudo-plastic flow during embossing eases cavities filling. As shown in the figure 9b, the viscosity is also temperature sensitive, decreasing with increasing temperature.

Debinding and sintering results

To investigate the micro-replication feasibility of the feedstock for hot embossing, subsequent processing steps were conducted. For this, it is of interest to examine cylindrical samples compacted at different stages of manufacturing. The cylindrical samples (Ø 6 mm × 10 mm) were successfully compacted using two formulations, already presented previously. The samples after compaction (green bodies) were debound and sintered under the conditions imposed in the cycle and according to the TGA analysis. As example, on compacted samples with formulation 1, it was found that for a speed V 1 , from 1 to 10 °C/min, all samples underwent a slum ping, whatever the value of speed V 2 . For a speed V 1 equal to 0.1 °C/min, the sample was cracked with distortion, for V 2 equal to 2 at 10 °C/min. Decreasing the second spe ed, V 2 at 1 °C/min, was conducted, no visual defects such as cr acks, bubbles, slumping, distortion or cracking were observed (see Fig. 10). From a rheological point of view, a formulation F1 was more fluid than F2 but also more sensitive to the first level of the debinding since it contains more paraffin.

Fabrication of micro-fluidic die mould

In order to allow to investigate the influence of forming temperature on the filling stage and replication accuracy during the hot embossing process, set of experiments were performed. From 170°C to 210°C, the imposed he ating rate was 5°C/s, the hot embossing time was also 5min and an imposed displacement was set to 1mm. In this case, the final qualities of metallic replicas using two different feedstock (F1, F2), described previously, were measured with Scanning mechanical microscope (SMM) to determine dimensions and surface roughness. Fig. 11 shows the side view of the embossed reservoirs where the walls of the microstructures were successfully replicated. The down surfaces of the reservoirs and channels were flat, indicating good filling during hot embossing process. The feedstocks gradually fill the cavities of the elastomeric mould when increasing the forming temperature. The surface roughness was much lower in the replicas made from a feedstock 1 (F1) as the feedstock 2 (F2). So the surface of replicated parts were smooth with R a <0.1µm using feedstock 1. It can be related to the fact that a decreasing viscosity was favourable to decrease surface roughness. The microstructures were debound and sintered. The debound micro-fluidic systems have no visual defects such as slumping, distortion or cracking.

CONCLUSIONS

316 stainless steel feedstock using a multi-component binder system consisting of PW and PP was produced for the micro hot embossing of micro-fluidic systems. A study of the influence of feedstock fluidity on filling rate of cavities and roughness surface replicas were performed. Two kinds of formulations were used to obtain feedstocks with different solid loading contents. The findings can be summarized as follows:

1) DSC and TGA show that hot embossing of the feedstock should be carried out above 160 °C (i.e. the upper melting temperature) b ut below 250 °C as beyond which the binder components paraffin wax and stearic acid start degrading.

2) The torque measurements of mixtures of binder and 316L stainless steel reveal that the stearic acid reduces the viscosity. Besides, torque values also increase when polypropylene quantity increases indicating a higher viscosity. We can also observe that torque values were higher when powder loading increases.

3) Rheological tests show that the feedstocks exhibit pseudoplastic flow behaviour and moldability. From rheological measurements it was observed that viscosity of all the feedstocks decreases when the shear rate increase.

4) Based on the thermal and rheological characterisations of the feedstock, the feasibility of the feedstocks for hot embossing of micro-fluidic systems was investigated. The results show that micro-structures can be successfully fabricated.

The microstructures have the necessary strength for demolding, there have no visual debinding defects and the final sintered microstructures have good shape retention.

Figure 1 .

 1 Figure 1. (a) scanning electron micrograph, (b) particle size distribution for 316L stainless steel powders (d 50 =3.4 m) used in the related investigations

  create a thin layer of Teflon-like material on the sidewall surfaces to further facilitate mould release and to reduce the friction between Si die mould and elastomeric replicas during de-moulding. The silicone rubber (Sylgard 184) provided by Dow Corning Inc ® was used as the material for the elastomeric moulds. A silicone base and catalyst were thoroughly mixed with a ratio 1:1. The mixture was degassed during approximately 5 min in primary vacuum to avoid air trapped in the silicone leading to a porous matrix and defects in the resulting replicas. Next, it was poured over the Si master and cured at 70 °C during 4 h. F ig. 3a shows micrographs of patterned on silicone elastomeric substrates used in this study. Example of schematic drawing with dimensions of the micro-structures of the elastomeric mould is shown in Figure3b. The forming temperature of the proposed feedstock was tested in the range of 170 to 210 °C.

Figure 2 .

 2 Figure 2. SEM micrographs of silicon master mould: (a) reservoir and (b) channel.

Figure 3 .

 3 Figure 3. (a) Elastomeric die cavity mould, (b) definition of mould size dimension for µfluidic geometries.

Figure 4 .

 4 Figure 4. (a) Differential scanning calorimetry result of binders, (b) TGA curves of all binders and the combined binder systems (PW 55 %, PP 40 %, SA 5 %).

Figure 5 .

 5 Figure 5. TGA curves for (a) 100% PW; (b) 80/20 PW/PP blend; (c) 60/40 PW/PP blend; (d) 40/60 PW/PP blend; (e) 20/80 PW/PP blend and (f) 100% PP.

Figure 6 .

 6 Figure 6. Mixing torque vs. powder volume loading, obtained through the continuously rising powder loading technique (a) at 170 °C and mixing time 30 min, (b) feedstock formulation F1 and F2, mixing time: 60 min, mixing temperature: 170 °C.

Figure 7 .

 7 Figure 7. (a) Torque vs. mixing time profiles associated to the feedstocks with different mixing velocity, (b) mixing behaviour for six different powder loadings, Formulation 2.

Figure 8 .

 8 Figure 8. SEM photo of feedstock (powder volume loading equal 60%) after mixing stage used in the proposed investigations.

Figure 9 .

 9 Figure 9. Shear viscosity vs. shear rate corresponding to (a) feedstock formulations F1 and F2 realised at 170 °C and (b) feedstock formulations F 1 at different temperatures.

Figure 10 .

 10 Figure 10. Dedound and sintering of cylindrical samples at different conditions: (a) F1 and (b) F2.

Figure 11 .

 11 Figure 11. 3D topographies imprint of 316L stainless steel replicas realised though soft embossing process at different forming temperatures.

Table 1 .

 1 Characterisation of the different binder components

	Binders	Density Melting temperature Degradation temperature
			range
	Stearic acid (SA)	0.890	70 °C	180-280 °C
	Paraffin wax (PW)	0.910	60 °C	200-330 °C
	Polypropylene (PP)	0.900	160 °C	340-450 °C

5) Finally, from the experiments carried out, it was concluded that, binder formulations and MIM feedstocks were shown a pseudo-plastic flow behavior and suitable for hot embossing. The addition of steatite powder to the binder formulations increased the viscosity of the feedstocks.