Evolution of electrical resistance of graphite foils during spark plasma sintering.

doi:10.21203/rs.3.rs-4012340/v1

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Evolution of electrical resistance of graphite foils during spark plasma sintering.

https://doi.org/10.21203/rs.3.rs-4012340/v1

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The progression of the electrical resistance of graphite foils during spark plasma sintering process (SPS) was investigated at constant temperature and pressure. The study applied various set-ups of the SPS device, and the electrical data used for the evaluation of electrical resistance (heating power and current) was obtained from the SPS apparatus in real-time. The contact resistance and resistance due to graphite foil/s was evaluated by subtracting the resistance of the single punch set-up from the set-up of two punches in direct contact and the set-ups with various graphite foils. The results showed that during the initial stages of sintering, set-up resistance increases with time and that, overall, set-up resistance increases with number of graphite foils. Both contact resistance and resistance due to graphite foils was found to decrease with sintering time. In contrast to previous conceptions, the electrical resistance of graphite foils changes in response to sintering conditions during the SPS process.

Spark plasma sintering

Electrical resistance

Graphite foil

Set-up resistance

Spark plasma sintering (SPS) is a Field assisted sintering technology (FAST) in which a low voltage and high intensity pulsed direct current are applied alongside uniaxial pressure during sintering. Compared to traditional sintering processes such as hot pressing (HP) and hot isostatic process (HIP), the SPS process has the advantages of high heating rates (up to 1000°C /min), short sintering time (3 to 5 mins) and the ability to minimize grain grown [1–4]. Most advantages of SPS are associated with the fact that heating takes place internally through Joule heating when the electric current flows through the graphite tooling and the sample, if conductive. During sintering, it’s a widespread practice to insert a graphite foil horizontally in between the punch and the sample so as to prevent direct contact between the two. Additionally, graphite foil/s also enhances physical, electrical, and thermal contact between the surfaces and also facilitates the removal of the sample at the end of the sintering process [5, 6]. The flow of current in SPS is perpendicular to the surface of the horizontal graphite foil/s. According to Matsubara et al., [7], electrical resistance of a graphite foil in the out-of-plane direction (perpendicular to the flow of current) is much higher compared to the in-plane direction (parallel to the flow of electrical current). This means that the, when a graphite foil is inserted in the SPS device horizontally, it contributes its maximum electrical resistance. Hence, in addition to the aforementioned advantages, graphite foil/s may also contribute substantially to the overall electrical resistance of a given SPS set-up [2].

Various authors have reported ways in which graphite foil/s influences the SPS process. Minier et al., [8] reported that the graphite foil enhances current and thermal dissipation into the die when inserted in between the die and the sample. In Vanmeensel et al., [6], the authors observed that the difference in the temperatures measured by a pyrometer focused on the surface of the die and that focused inside the punch is dependent on the presence of the vertical graphite foil. In the study by Chawake et al., [1], it was noted that the combined electrical resistance of the punch and the graphite foil becomes dominant after a critical value of the relative density of the sample. Thus far, different values of electrical resistance of the graphite foil/s have been reported. For the out-of-plane direction, Vanmeensel et al., [6], presented a value of between \(3\times {10}^{-3}-4\times {10}^{-3}{\Omega }\) for a temperature range of 25°C – 1750°C while in Chawake et al., [1], the authors reported a value of \(1.6\times {10}^{-3}\varOmega\). In both cases, the thickness of the graphite foil was 0.2 mm and 20 mm in diameter. Recognizing the fact changes in SPS parameters such as temperature and pressure may affect the electrical resistance of graphite foils, this study was aimed at investigating the evolution of the electrical resistance of graphite foil/s and at constant temperature and pressure.

This study was conducted by applying various setups of the tooling-sample assembly of the SPS device. The SPS apparatus used for the study was the HDP 25 manufactured by FCT Systeme GmbH which comes with a PC unit for online tracking of process parameters such as heating power, voltage, and current. Experiments for the study were conducted at the Institute of Materials Science at TUBAF- Germany. The tooling for the SPS device consisted of a graphite die with an outer and inner diameter of 40 mm and 20 mm respectively, while two of the three punches used had a diameter of 20 mm and a height of 40 mm. The length and diameter of the third punch was 80 mm and 20 mm, respectively. The starting material consisted of a 0.2 mm thick graphite foil sheet supplied by the SGL group (SIGRAFLEX®) from which 20 mm diameter samples were prepared.

To establish the resistance of the SPS column, we used a single punch set-up (see Fig. 1a). In the second set-up, two punches (upper and lower) were placed into direct contact as shown in Fig. 1b. The aim of this set up was to establish the behavior of contact resistance when sintering at a fixed temperature and pressure. In the third set-up, we inserted a graphite foil in between the two punches (Fig. 1c). In the 4th, 5th, and 6th set-ups, the number of graphite foils increased from one to two, four, and eight, respectively. In all the setups used, a non-conducting corundum foil \({(\text{A}\text{l}}_{2}{\text{O}}_{3})\) with electrical resistivity of \(2.0\times {10}^{6} {\Omega }\text{c}\text{m}\)was inserted in between the punch and the inner walls of the die. The purpose here was to ensure that all the current was flowing through the punches (see Fig. 1) and the graphite foil/s. The outer surface of the die was also covered with graphite felt to reduce heat loss from radiation. An average load of 5 kN corresponding to a pressure of 15 MPa was also applied. Annealing was conducted in a vacuum at 1000°C for a period ranging between 2 and 4 hrs. Temperature monitoring was achieved through a pyrometer that was focused on the base of the upper punch. The average heating rate was 200°C/min and current density was \(197\text{A}/{\text{c}\text{m}}^{2}\). At the end of each annealing cycle, rapid cooling was by water circulating through the electrodes. The electrical resistance for each set-up was evaluated using the expression \(\text{R}=\text{P}/{\text{I}}^{2}\) in which P (Watts) is heating power, R (Ohms) is electrical resistance and \(\text{I}\) (Ampere) is the electric current. Scatter data was smoothened and fitted using Origin software.

3.1 Set-up resistance

Figure 2 (a-b) shows the electrical resistance of the set-ups for single punch and two punches with zero graphite foils for an annealing time of 2 and 4 hrs., while Fig. 2c shows the electrical resistance for the set-ups of the two punches with one, two and eight graphite foils for an annealing time of 2 hrs. Figure 2d shows the electrical resistance of two punches with four graphite foils for an annealing time of 4 hrs. The trend observed in Fig. 2 is that at the initial stages of annealing, electrical resistance increases linearly with time after which it either becomes constant or starts decreasing. For short annealing times such as 2 hrs., the increase in resistance is linear (see Fig. 2a and b). Considering the resistance values, the set-up for the single punch (Fig. 2a) has the lowest electrical resistance with a peak value of about \(7.5 \times {10}^{-3}\varOmega\) while the set-up for two punches with eight graphite foils (Fig. 2c) depicts the highest resistance peak value of about \(8.95\times {10}^{-3}\varOmega\). In Fig. 2b, the resistance values at the start of the annealing process are different for the 2 and 4 hrs. Apart from thermal expansion and mechanical pressure, annealing time cannot affect the electrical resistance of a set-up hence the variations in resistance observed between the 2 and 4 hrs. are mere statistical deviations.

The observed increase in electrical resistance with annealing time (Fig. 2) may be attributed to a range of factors. Firstly, the non-conductive corundum foil ensures that the punches are in a series arrangement with the graphite foil/s. For a series circuit, the same quantity of current flows through each resistor and the total resistance is the sum of the individual resistors in the circuit [9]. The total set-up resistance, therefore, is the sum of resistances of the upper and lower punches, the graphite foil/s, as well as contact resistance. Thus, as the current flows through the upper to the lower electrodes, the resistance increases cumulatively. Furthermore, at the initial stages of annealing, the electric current has to develop flow paths through the various resistive materials in the setup i.e., the upper punch, the various layers of the graphite foil/s, and the lower punch. Also, at the interface between the punch and the graphite foil, the abrupt change in materials (punch/foil) cause an increase in electrical resistance at the start of the sintering process [1, 10, 11].

Additionally, it has been reported in various texts [5, 12] that at the end of a sintering cycle, flakes of graphite foil are found stuck on contact surfaces of the sample. This means that under the combined action of heat and pressure during sintering, the physical properties of the graphite foil changes. It’s possible that such changes could also affect the electrical resistivity of the graphite foil. The aforementioned factors may thus explain the observed increase in set-up resistance at the initial stage of annealing shown in Fig. 2. The increase in resistance with the number of graphite foils (Fig. 2c) also reveals the additive nature of graphite foils on the set-up resistance during SPS process.

3.2 SPS electrical parameters

The key operating parameters of the SPS include the voltage, current, heating power, and the sintering/annealing temperature. From Fig. 3a and b, both the annealing temperature and voltage were constant. The proportional-integral-derivative controller (PID) coordinates the operations of the SPS process. According to Minier et al., [8] and Maniere et al., [13], the PID adjusts the used voltage as a variable function of the overall resistivity of a given SPS set-up and controls the current for heating. This means that the observed increase in set-up resistance shown in Fig. 3 is not as a result of process adjustments by the PID controller but is rather due to either the series arrangement of the SPS tooling, the intrinsic behavior of the electrical resistivity of the materials in the set-up, the response of the tooling materials to the annealing process or a combination of the three factors. Comparing the various set-ups, however, the voltage is higher for set-ups in which resistance was low. For instance, in Fig. 3, the single punch set-up depicts the highest voltage, but in Fig. 2, the same set-up depicts the lowest set-up resistance. The reverse is true for the set-up of two punches with eight graphite foils. According to Ohms law, an increase in electrical resistance at constant voltage will cause a decrease in current [9]. Therefore, the increase in set-up resistance observed in Fig. 2 and the constant voltage shown in Fig. 3a results in a decrease in electric current flowing through the set-up (see Fig. 3c). Since heating in SPS is by the Joule heating, the decrease in electric current will translate into a decrease in the heating power as shown in Fig. 3d.

3.3 Resistance of graphite foils

To obtain the resistance of the graphite foils, the resistance of the single punch set-up was subtracted from the resistance of the two punches with one, two, four, and eight graphite foils, respectively. Figure 4a-b shows the change in resistance with time for one, two, four, and eight graphite foils for annealing time ranging between 2 and 4 hrs. In Fig. 4a, the electrical resistance of one graphite foil appears to be increasing with time. Such unexpected observation may been due to the clouding of the resistance of the graphite foil by contact resistance from the punches. However, the resistance of two, four, and eight graphite foils decreases gradually with annealing time. Graphite foils have a negative temperature coefficient of resistivity [14–18] hence, its electrical resistance decreases with an increase in temperature (i.e., its conductivity increases with an increase in temperature). Over the annealing period, the temperature increased from room temperature to 1000°C, which was the dwell-time temperature. Furthermore, In SPS, the temperature measured by the pyrometer does not represent the actual annealing temperature. Various investigations have shown that the actual sintering temperature could be higher than the pyro temperature by about 250°C [6, 19–23]. Additionally, application of pressure during SPS annealing is also known to compact the various layers of the foil causing a reduction in thickness which in turn leads to a decrease in electrical resistance of the graphite foils [24, 25]. Hence, the observed decrease in the electrical resistance of graphite foils may be associated with the combined effect of positive local fluctuations in temperature and pressure. As expected, the resistance of eight graphite foils annealed for 2 hrs. is higher than the resistance of four graphite foils annealed for 4 hrs. (see Fig. 4b). This means that annealing time does not have an effect on the evolution of the electrical resistance of graphite foils during the SPS process.

After expressing the resistance of the graphite foil/s as a percentage of the set-up resistance, the contribution of graphite foil/s to the set-up resistance was found to decrease with time but increase with number of graphite foils as well. At the initial stage, the contribution of one and two graphite foils was slightly more than 6.0% and 8.0%, respectively. For the two graphite foils, however, it dropped from 8.0% to about 6.5%. We observed a similar trend for the four and eight graphite foils where the percentage contribution dropped from 13.5% to about 8.0% and from 17.0–16.0%, respectively. This confirms that graphite foils account for a substantial amount of set-up resistance.

3.4 Contact resistance

The set-up of two punches with zero graphite foils (see Fig. 1b) was used to establish the behavior of contact resistance at constant temperature and pressure during SPS. It was evaluated by subtracting the resistance of the single-punch set-up from that of two punches with zero graphite foils. In Fig. 5, the contact resistance decreases with annealing time. From the curve, contact resistance reduced from \(9.0\times {10}^{-4} \varOmega\) to about \(7.0 \times {10}^{-4}\varOmega\) for an annealing time of 4 hrs. The drop in resistance may be associated with applied pressure during the SPS process. Mechanical pressure has the effect of flattening asperities on contact surfaces hence alleviating constriction effects. Additionally, pressure causes deformation of particle-to-particle contacts leading to the rapture of surface film [24] hence increasing conduction spots. Pressure also causes the formation of new conduction contacts which ultimately increases the spatial density of current paths leading to a more uniform current transmission [24]. Thus, to a significant extent, pressure may have influenced the drop in the contact resistance. Indeed, in earlier texts [3, 26], contact resistance was reported to decrease with both temperature and pressure. Figure 5 also compares the contact resistance to the resistance due to two, four, and eight graphite foils. Compared to contact resistance, the resistance due to two graphite foils is lower while that of four and eight graphite foils is higher. Therefore, from Fig. 5, it may be deduced that when two graphite foils are inserted in between the two punches, contact resistance decreases. This may be due to the scaling down of contact resistance by the smooth surfaces of the graphite foil [27].

Assuming that the contact resistance between the punches and the graphite foils is too low to be of any significant effect, the observed resistance for two graphite foils may be a result of the intrinsic resistivity of the two graphite foils only. A similar deduction may be made for the case of four and eight graphite foils but with the understanding that the combined resistance of the four and eight graphite foils is much higher hence the two curves are higher than that of contact resistance.^

The study was aimed at establishing the evolution of the electrical resistance of graphite foils in SPS at constant temperature and pressure. The investigation was conducted by using different setups of the SPS apparatus. The findings show that at the initial stages, electrical resistance increases linearly with time, especially for a series arrangement of the punches and the graphite foils. This happens as the electric current develops flow paths through the SPS tooling materials. Furthermore, during the SPS process, the resistance of the graphite foil/s changes with time. This observation was attributed to the response of the graphite foil to the heat and pressure applied during the SPS process. On the other hand, graphite foils tend to reduce the contact resistance between the two contacting surfaces. In SPS, part of the endeavors is to maximize heat generation (through the Joule heating effect) for densification process. Thus, the percentage contribution of the graphite foils to the set-up resistance affirms the importance of graphite foils to the enhancement of the Joule heating effect in SPS even though its volume may be small.

Competing interests

The authors declare that they have no relevant financial or non-financial interest to disclose.

Funding

The authors declare that there was no funding, grants or any other support received during the preparation of this manuscript.

Author contribution

All authors were involved at every stages of this work and they have read, edited, and approved the manuscript.

Acknowledgment

The support of the DUT Internal M and D Grants scheme and that of CEMEREM Kenya-Germany are highly acknowledged. One of the authors would like to appreciate the technical support provided by Prof. Rafaja and Dr. Solomon of the Institute of Materials Science at TUBAF, Germany.

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Editorial decision: Minor Revisions Needed
15 Jun, 2024
Reviewers agreed at journal
24 Apr, 2024
Reviewers invited by journal
06 Mar, 2024
Editor assigned by journal
05 Mar, 2024
First submitted to journal
04 Mar, 2024

You are reading this latest preprint version

Evolution of electrical resistance of graphite foils during spark plasma sintering.

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Version 1

Abstract

Figures

1. Introduction

2. Materials and Methods

3. Results and Discussion

3.1 Set-up resistance

3.2 SPS electrical parameters

3.3 Resistance of graphite foils

3.4 Contact resistance

4. Conclusions

Declarations

Competing interests

Funding

Author contribution

Acknowledgment

References

Status:

Version 1