Jack Knoll
email: knolljs@vt.edu

Mina Shawky
email: mshawky@vt.edu

Sheng-Hung Yen
email: yshenghung19@vt.edu

Ibrahim Eshera
email: ieshera@vt.edu

Christina Dimarino
email: dimaricm@vt.edu

Reza Ghandi
email: ghandi@ge.com

Stacey Kennerly
email: stacey.kennerly@ge.com

Cyril Buttay
email: cyril.buttay@insa-lyon.fr

Characterization of 4 kV Charge-Balanced SiC MOSFETs

Keywords: Charge-balanced MOSFET, SiC, characterization, capacitance steps, voltage tail

This work demonstrates a novel charge-balanced (CB) silicon carbide (SiC) MOSFET that boasts a specific onresistance of 10 mΩ•cm 2 at 4 kV breakdown voltage, surpassing the 1-D SiC unipolar limit. This is achieved through buried pdoped regions inside the drift layers, which are more easily scalable to higher voltages compared to the p-doped pillars used in super-junction (SJ) devices. Medium-voltage CB SiC MOSFETs with different p-doped bus widths and pitches have been fabricated and characterized in this work. The unique microstructure of these devices causes interesting macro-scale characteristics, such as distinctive steps in the capacitancevoltage curves and a turn-on voltage tail that reduces with increased temperature. The switching energy of the CB MOSFET is 92% lower than that of an IGBT at 150 °C. This paper presents and interprets these intriguing static and dynamic characteristics.

I. INTRODUCTION

Silicon (Si) IGBTs are widely used in medium-voltage (MV) systems due to their low on-state losses at higher voltages; however, their bipolar structure causes slower switching speeds, resulting in high switching losses, and limited switching frequency [1]. At low frequencies, the volume and weight of passive components, such as filters and transformers, limit design flexibility and increase fabrication and installation costs for MV systems. Unipolar Si devices (e.g., MOSFET) have faster switching speeds than their bipolar Si counterparts, but their high conduction losses make them less suitable for MV applications than Si IGBTs [START_REF] Kawahara | Impact of embedding schottky barrier diodes into 3.3 kV and 6.5 kV SiC MOSFETs[END_REF][START_REF] Powell | 3300V SiC DMOSFETs fabricated in high-volume 150 mm CMOS fab[END_REF][START_REF] Fursin | Development of a high-performance 3,300V silicon carbide MOSFET[END_REF].

Unipolar silicon carbide (SiC) devices can achieve lower on-resistance at higher voltages than unipolar Si devices thanks to the higher breakdown electric field strength and wider bandgap of the material. However, at MV (greater than 3.3 kV), it is still difficult for SiC unipolar devices (e.g., MOSFET) to compete with the low conduction losses of Si bipolar devices (e.g., IGBT) [START_REF] Kawahara | Impact of embedding schottky barrier diodes into 3.3 kV and 6.5 kV SiC MOSFETs[END_REF][START_REF] Powell | 3300V SiC DMOSFETs fabricated in high-volume 150 mm CMOS fab[END_REF][START_REF] Fursin | Development of a high-performance 3,300V silicon carbide MOSFET[END_REF]. Accordingly, researchers have explored super-junction (SJ) structures to break this 1-D SiC limit (Fig. 1) [START_REF] Zhou | Performance limits of vertical 4H-SiC and 2H-GaN superjunction devices[END_REF][START_REF] Tanaka | First demonstration of dynamic characteristics for SiC superjunction MOSFET realized using multi-epitaxial growth method[END_REF][START_REF] Kosugi | Breaking the Theoretical Limit of 6.5 kV-Class 4H-SiC Super-Junction (SJ) MOSFETs by Trench-Filling Epitaxial Growth[END_REF][START_REF] Palmour | Silicon carbide power MOSFETs: Breakthrough performance from 900 V up to 15 kV[END_REF]. However, applying the SJ structure to SiC requires complex fabrication processes, which become more challenging as the drift layer thickness increases, thereby limiting the voltage scaling. The charge-balanced (CB) structure addresses this issue by using buried p-doped regions in the drift layer (Fig. 2), which simplifies the fabrication and enables scaling to thicker drift layers and hence higher voltages [START_REF] Ghandi | 3kV SiC Charge-Balanced Diodes Breaking Unipolar Limit[END_REF][START_REF] Ghandi | 4.5kV SiC Charge-Balanced MOSFETs with Ultra-Low On-Resistance[END_REF]. To avoid floating CB-regions inside the drift layer, intermittent vertical p-type pillars (p-bus) were used throughout the active area to provide a conductive path for holes during turn on. In this work, four types of CB SiC MOSFETs with greater than 3.5 kV breakdown voltage were fabricated and characterized to assess the influence of the pbus width and pitch on the device performance (Fig. 3).

II. STATIC CHARACTERIZATION

A Keysight B1505A curve tracer was used to characterize the CB SiC MOSFETs. A power resistor and a ceramic isolating plate were clamped to the CB MOSFETs (Fig. 4) to heat them to the desired temperature during static characterization. A thermocouple was placed between the ceramic isolating plate and the device under test to get an approximate measurement of the junction temperature.

A. On-Resistance, Breakdown Voltage, Leakage Current, and Threshold Voltages Fig. 5 shows the on-resistance vs. drain current at 25 °C and 175 °C for each device type. The devices with the wide and large pitch bus design (WL) have the lowest on-resistance, while the devices with the wide and small pitch bus design (WS) have the highest on-resistance. The p-type material added to the drift-layer decreases the available active area responsible for creating a conductive path when the CB MOSFETs are on; therefore, increasing the amount of p-type material in the drift layer -either by increasing the width of the bus or decreasing the pitch -will result in an increase in on-resistance. voltages. The devices with a narrow bus (NS and NL) show lower leakage current than their wide bus counterparts (WS and WL) with the same pitch. The high energy implantation process used to create the p-bus can damage the crystallographic structure of the drift layer, leading to higher leakage in wide bus devices.

The threshold voltages for each device type at room temperature and 175 °C are listed in Table I. They were extracted from the transfer characteristic curves using the constant current method by setting the gate-to-source voltage equal to the drain-to-source voltage to guarantee the device is operating in the saturation regime and measuring the gate voltage at a drain current of 1 mA [START_REF] Ortiz-Conde | A review of recent MOSFET threshold voltage extraction methods[END_REF].

B. Input, Output, and Miller Capacitances

The input, output, and Miller capacitances across drain to source voltage for all device types are plotted in Fig. 7. At 2 kV, the input, output, and Miller capacitances are 275 pF, 6.4 pF, and 1.4 pF, respectively. The output and Miller capacitances' relationships with drain to source voltage (Fig. 7) are of particular interest due to the unique steps seen in their waveforms. The cause of a similar singular step seen in the output capacitance of SJ MOSFETs has been identified [START_REF] Srikanth | On the Charge Sheet Superjunction (CSSJ) MOSFET[END_REF] and its contribution to harmonic generation has also been studied [START_REF] Pattanayak | Large-signal and small-signal output capacitances of super junction MOSFETs[END_REF]. The output and Miller capacitance steps in CB MOSFETs are caused by a rapid increase in depletion width as the individual depletion boundaries in the n-epi surrounding a single JFET or CB region meet. The steps occur at different voltages and have different heights because the contribution of the p-bus to the depletion of the n-epi varies with the distance from the source. The lowest voltage step is caused by the JFET region (Fig. 3), while the second, third, and fourth lowest voltage steps are caused by the CB region closest, second closest, and farthest from the source (Fig. 3), respectively (Fig. 8). The width and pitch of the p-bus is proportional to its contribution to the depletion of the n-epi. This causes the capacitance steps of wider and smaller pitch bus designs to occur at lower voltages (Fig. 8).

III. DYNAMIC CHARACTERIZATION A double-pulse inductive switching test (DPT) was used to evaluate the dynamic performance of the CB SiC MOSFETs up to 3 kV (Fig. 9). Two 3.3 kV SiC Schottky diodes were used in series to freewheel the current for the 10 mH inductive load. The gate driving voltages were +20 V in the on-state and -5 V in the off-state. A low-inductance current shunt was used to measure the MOSFET drain current, a low-voltage passive probe was used to measure the gate-source voltage, and a high-voltage differential probe with up to 100 MHz bandwidth was used to measure the drain-source voltage (Fig. 9). Fig. 10a and Fig. 10b show the DPT waveforms for the two device types with the highest and lowest voltage tails at 3 kV, 2 A and at temperatures of 25 °C, 100 °C, and 175 °C. The NL device has a voltage tail longer than 3.5 µs at 175 °C (Fig. 10a). The NS and WL devices (waveforms not included here) saw a reduction in their voltage tails from greater than 3.5 µs at room temperature to less than 1 µs at 175 °C. The WS device had the shortest voltage tail at room temperature and has negligible tail length at 175 °C (Fig. 10b). Fig. 10c shows the DPT waveforms for all four of the CB SiC MOSFET device types at 3 kV, 2 A, and 175 °C. The NL device experiences a small rise in the drain-source voltage during the first on pulse, and a voltage tail at the second turnon transient that exceeds 3 µs. The NS, WL, and WS devices had no measurable drain-source voltage rise during the first on pulse, and a shorter voltage tail (less than 1 µs) at the second turn-on transient. The voltage fall times decrease with a wider bus or a smaller pitch, indicating that an increase in total p-bus improves the dynamic performance.

The bump in the drain-source voltage seen during the first on period, and the drain-source voltage tail seen during the second on period (Fig. 10a) have the same physical explanation. The resistivity of SiC doped heavily with Al is at its highest point at low temperatures and begins to decrease as temperature increases [START_REF] Asada | Analytical formula for temperature dependence of resistivity in p-type 4H-SiC with wide-range doping concentrations[END_REF]. The Al-doped p-bus pillars and ptype CB layers, therefore, have a higher resistance at lower temperatures. The higher the resistance of the p-bus pillars and CB layers, the longer it takes for a sufficient number of holes to reach the CB layers to eliminate the depletion region after turn on. The slow reduction of the depletion region in the ntype portion of the drift layer surrounding the CB layers creates a p-bus structure-, temperature-, blocking voltage-, and time-dependent variable on-resistance contribution from these regions. Since the current is still ramping up during the first on period, the induced on-state drain to source voltage caused by the high on-resistance is less obvious than during the second period. The on-resistance contribution of the depletion regions is not accounted for by the static on-resistance measurement (Fig. 5) because the devices were not subjected to a high blocking voltage that would have generated a depletion region prior to measurement. Differences in the drain-source voltage waveforms of the four device types during the on periods are also related to this principle. The device types with a narrower pitch and/or a wider bus have a larger conduction path for holes to reach the CB layers and, therefore, have a lower drain to source voltage tail. The effect of this is that, despite having a higher static onresistance, the effective on-resistance of the devices with a narrower pitch and/or a wider bus is lower.

The drain to source voltage tails and switching energies for a WS device at room temperature, a drain to source voltage of 1 kV, and a 0.7 A, 1 A, and 2 A drain current are plotted in Fig. 11a and Fig. 11b, respectively. The linear increase in switching energy with drain current (Fig. 11b) indicates that the drain current does not induce a change in the variable on- resistance, but simply induces a larger voltage drop across the existing variable on-resistance. A similar relationship is found in the drain to source voltage tails and switching energies for a WS device at 175 °C, a drain to source voltage of 1 kV, and a 0.7 A, 1 A, and 2 A drain current plotted in Fig. 11c and Fig. 11d, respectively. The consistency across temperature reinforces the conclusion that the drain current does not induce a change in the variable on-resistance.

The drain to source voltage tails and switching energies for a WS device at room temperature, a drain current of 2 A, and a 1 kV, 2 kV, and 3 kV drain to source voltage are plotted in Fig. 12a and Fig. 12b, respectively. The nonlinear increase in switching energy with blocking voltage (Fig. 12b) indicates that the blocking voltage contributes to the variable onresistance non-linearly. The n-epi directly surrounding each individual CB layer depletes at less than 2 kV (as indicated by the output capacitance curves in Fig. 7b), contributing a higher variable on resistance at turn on than the n-epi farther from the CB layers that depletes at higher voltages. Although depleted n-epi has the same resistivity no matter where it is, the n-epi directly surrounding each individual CB layer has a lower cross-sectional area, causing the variable resistance contribution to be higher. The nonlinear relationship between blocking voltage and switching energy at room temperature erodes at higher temperatures (Fig. 12c and Fig. 12d). At higher temperatures, holes are transported more quickly to the CB layers, causing the n-epi to become un-depleted fast enough that the uneven contribution to the variable onresistance can no longer be detected.

Fig. 1 .

 1 Fig. 1. Specific on-resistance vs. breakdown voltage limits for 1-D SiC unipolar devices (black curve and blue markers), SiC SJ devices (grey curves), and the experimental achievements from this work (red marker).

Fig. 6 Fig. 3 .

 63 Fig. 6 shows the breakdown voltages and leakage currents for each device type at room temperature. The breakdown voltage of all device types is greater than 3.3 kV. The type NL and WL devices have a different edge termination than the type NS and WS devices, which may affect their breakdown

Fig. 4 .Fig. 5 .

 45 Fig. 4. Power resistor and ceramic isolating plate setup used to heat the CB MOSFETs.

Fig. 6 .

 6 Fig. 6. Breakdown voltage and leakage current (inset) for all device types.

Fig. 8 .Fig. 7 .

 87 Fig. 8. Output capacitance steps associated with the JFET and CB regions.

Fig. 9 . 10 .

 910 Fig. 9. Double-pulse test setup.

  . (a) Drain to source voltages and (b) switching losses of a WS CB MOSFET at room temperature, 1 kV blocking voltage, 20 Ω gate resistance, and drain currents of 0.7 A, 1 A, and 2A. (c) Drain to source voltages and (d) switching losses of a WS CB MOSFET at 175 °C, 1 kV blocking voltage, 20 Ω gate resistance, and drain currents of 0.7 A, 1 A, and 2A. . (a) Drain to source voltages and (b) switching losses of a WS CB MOSFET at room temperature, 2 A drain current, 20 Ω gate resistance, and blocking voltages of 1 kV, 2 kV, and 3 kV. (c) Drain to source voltages and (d) switching losses of a WS CB MOSFET at 175 °C, 2 A drain current, 20 Ω gate resistance, and blocking voltages of 1 kV, 2 kV, and 3 kV.

Fig. 13a shows

  Fig. 13a shows the DPT waveforms for a 4.5 kV Si IGBT (IXYX40N450HV) and a WS CB MOSFET at 3 kV, 2 A, and 150 °C. The switching losses versus temperature for the Si IGBT and the WS CB MOSFET are shown in Fig. 13b. The CB SiC MOSFET has 44% lower switching losses at 25 °C, and 92% lower losses at 150 °C, than the Si IGBT.

TABLE I .

 I THRESHOLD VOLTAGES FOR EACH DEVICE TYPE AT 25 °C

AND 175 °C


Tanguy Simon
email: tanguy.simon@insa-lyon.fr

Jean-Franc ¸ois Trégouët

Hervé Morel

Xuefang Lin-Shi

Modelling and Control of a Power Flow Controller for DC Microgrids

Keywords: Power flow control, Microgrid, Modelling, Robust control, Converter control

This paper presents a state feedback control method for a power flow controller for meshed DC microgrids. A modular generic dynamic model of the system is proposed. This model is augmented with integrators and linearised, and a state feedback control law is proposed to define the duty cycles for the PWM switching of the IGBTs. The power in each line and the voltage of a reservoir capacitor in the converter are directly controlled. The validity of the proposed model and control law are assessed on an experimental setup.

Introduction

Micro-grids are currently being studied as a solution to meet the challenge of reducing the environmental impact of our energy systems. Among the considered applications are buildings and districts, factories and residential or rural areas. One of their global advantages is their ability to increase the penetration of small renewable energy generators [START_REF] Kumar | DC Microgrid Technology: System Architectures, AC Grid Interfaces, Grounding Schemes, Power Quality, Communication Networks, Applications, and Standardizations Aspects[END_REF]. For rural and residential applications, the development of micro-grids increase the independence and empowerment of (energy) communities [START_REF]Solar Powered Health Clinics in Peru Strengthen Community Resilience[END_REF], raise awareness about ones energy consumption and greatly help the transition towards a more energy-frugal lifestyle. The experience of "off-griders" shows that the implication of consumers in their energy production leads to their adaptation in lifestyle and demand to meet the intermittency of renewable sources [START_REF] Vannini | Off the grid: re-assembling domestic life, en, ser. Innovative ethnographies[END_REF]. Similar behaviour can then be expected from "micro-griders", thereby decreasing the need for storage and oversizing of the power generation capacity.

The use of direct current (DC) in micro-grids brings various advantages: It removes the problem of reactive power and skin effects. If a voltage standard is chosen appropriately [START_REF] Anand | Optimal voltage level for DC microgrids[END_REF], it can reduce the number of power converters needed because most AC generators and loads already have a DC link (wind turbines equipped with a maximum power point tracker (MPPT), AC or DC motors drives, Photovoltaics) [START_REF] Elsayed | DC microgrids and distribution systems: An overview[END_REF]- [START_REF] Ammous | LVDC: An Efficient Energy Solution for On-Grid Photovoltaic Applications[END_REF]. Moreover, the resistive loads such as electric heaters, ovens or water heaters are able to function equally on DC or AC.

Meshed micro-grids are another line of research proposed to enhance the flexibility of the design and reduce the amount of copper needed for the wiring because the current can be split between different paths. It is especially meaningful when generation units and loads are distributed and enables a fast reconfiguration of the network. More detail about meshed structures, the use of DC and other micro-grid aspects can be found in [START_REF] Mackay | Toward the Universal DC Distribution System[END_REF].

In this context, the Power Flow Controller (PFC) must be introduced. This multi-terminal DC/DC converter is required in meshed grids to control the power flow at some strategic nodes (Fig. 1a) or at every node of the micro-grid. It is a useful actuator for a grid control algorithm when some of the other converters or dipoles cannot be remotely driven, as is often the case. The resulting micro-grid is then much more flexible and modular. This type of converter has been widely studied for high voltage grids (HVDC) [START_REF] Balasubramaniam | Series Current Flow Controllers for DC Grids[END_REF], but very little for low-voltage systems (LVDC). In the former, PFCs are usually only connected to the positive terminals of the different lines (floating) because withstanding the full line voltage would require a very expensive and inefficient converter topology [START_REF] Balasubramaniam | Series Current Flow Controllers for DC Grids[END_REF]. This problem disappears with LVDC grids, so that a single PFC can not only regulate line voltages but also act as a DC circuit breaker or even as an MPPT [START_REF] Fregosi | A comparative study of DC and AC microgrids in commercial buildings across different climates and operating profiles[END_REF].

The authors of [START_REF] Barara | Control Strategy Scheme for Consistent Power Flow Control in Meshed DC Micro-grids[END_REF] propose the use of two split-pi converters to achieve power flow control on a 3terminal node. However, the proposed control method only focuses on one of the two converters, failing to control the full node. Moreover, it does not achieve power flow control but rather voltage control with a limited current output. [START_REF] Takahashi | A multi-terminal power flow control method for nextgeneration DC power network[END_REF] propose another topology consisting of a modified split-pi with m half-bridge legs connected to the same reservoir (or link) capacitor instead of two (Fig. 1b). In addition to being simpler, this enables power flow control on a multi-terminal node. Although the topology is promising, no dynamic model of the converter is proposed and the study is limited to a two-terminal version, which does not constitute a node. Moreover, the proposed control approach is open-loop and is therefore expected to be fragile with respect to the uncertainty of the grid. Finally, the reservoir voltage has to be maintained by an additional branch that compensates the transient power imbalance. In [START_REF] Natori | A Novel Control Approach to Multi-Terminal Power Flow Controller for Next-Generation DC Power Network[END_REF], a new control law is proposed to improve the power flow control during fluctuations of the reservoir voltage. Unfortunately, the controller regulates the current rather than the power, and the computation of the current reference requires the knowledge of non local information, that is the voltage at the ending of the line. For these reasons, a fluctuation in the loads or generation units of the grid would lead to a steady-state error of the power. Furthermore, the reservoir voltage remains uncontrolled and there is therefore no guarantee that it will remain within the physical boundaries. Finally, the proposed dynamic model is a single variable transfer function that fails to capture the non-linearities of the system and does not take into account its parametric uncertainty.

The first contribution of this work is to propose a modular state-space multi-variable dynamic model of an m-terminal PFC, along with a generic grid model. It highlights the parametric uncertainties of the system, as well as its non-linearities. Based on this model, the second contribution is to establish a first multi-variable control law. It achieves simultaneous direct balancing control of the power in each line and voltage control of the reservoir capacitor. No additional hardware is required. Local properties of asymptotic stability and robustness of the resulting closed-loop are assessed on a tenth scale experimental setup.

The rest of this paper is outlined as follows. In the second section, the control problem is stated, the dynamical equations of the system are provided adopting a state-space formulation. The third section is devoted to the design of the control law. An integral action is first added. Then, the bilinear dynamics are analytically linearised to compute the control gain matrices through eigenvalue assignment. The fourth section focuses on experimental results, before giving concluding remarks in the last section.

Notations. The symbol I m stands for the identity matrix of size m × m. The null matrix of size m × n is denoted by 0 m×n while 0 m denotes a column vector. Dimensions are omitted when it is obvious from the context. The operator "diag {}" builds a diagonal matrix from entries of the input vector argument. Finally, given vector a, the notation a k refers to the k-th element of a, with 1 being the index of first element.

Problem statement and modelling

Problem statement and control objectives

The objective of this study is to achieve power control in the line connected to each terminal of the PFC while maintaining the reservoir voltage to a fixed value, despite the uncertainty of the grid. This reservoir voltage is constant if and only if the sum of powers in each line equals zero. Consequently, if the lines numbered k from one to m -1 are regulated to their corresponding constant line power reference P r k and the reservoir capacitor is regulated to its constant reservoir voltage reference v r R , the power in the unregulated line (here, line m) will naturally converge to the overall power balance (P m → -∑ m-1 k=1 P r k ). To maintain flexibility and modularity, the control law should be designed for a set of possible microgrids. Limited knowledge should be assumed on their model, so that the dynamics of each branch is partially unknown from the PFC viewpoint.

The problem tackled in this paper is the following: Given line power references P r k , (k ∈ {1, . . . , m -1}) and a reservoir voltage reference v r R , design a feedback controller delivering the gate voltages of IGBTs such that the power flowing though the k-th line and the reservoir voltage asymptotically converge respectively to P r k and v r R , despite uncertainties on each line. This study does not tackle the problem of defining P r k and v r R . They are assumed to be given and reachable.

System dynamic model

In this section, a dynamic model for an m-terminal PFC is proposed.

The grid as seen by the k-th terminal is modelled as the series connection of an inductance, a resistor and a constant voltage source. In this case, the electrical model related to the k-th branch of the PFC and the proposed grid model as seen by this terminal are depicted on Fig. 2. Let us emphasize that different L Gk , R Gk and V Gk can be considered for each terminal.

Some parameters in the model are considered unknown or uncertain to take into account the high variability of the grid: V Gk , R Gk and L Gk (k ∈ {1, . . . , m}). They are, however, considered bounded between a known max and min values. The other parameters (L, C and C R ) depend on the design of the converter and are therefore known.

An averaged model over a switching period is introduced. The PWM duty cycle (ratio) of the k-th branch is noted d k . The averaged voltages and currents are noted on Fig. 2. The dynamic equations read, with k ∈ {1, . . . , m}:

dv R dt = 1 C R m ∑ k=1 i k d k , ( 1a
) di k dt = 1 L (v k -v R d k ), (1b)
dv k dt = 1 C (i Gk -i k ), ( 1c
) di Gk dt = 1 L Gk (V Gk -R Gk i Gk -v k ) (1d)
P k = i Gk v k . ( 1e
)
Remark 1. In the case where another PFC is connected at the end of the line, it is assumed it controls the voltage instead of the power, and can therefore be modelled as a voltage source: take R Gk as the line resistance and V Gk as the nominal line voltage.

C R v R S Hk S Lk L i k C v k k L Gk i Gk R Gk V Gk PFC Grid k

State-space model

To account for the coupling between the dynamics of the branches induced by C R , a multivariable viewpoint is adopted. Recall that the vector notation of any element a k is a = [a 1 , a 2 , . . . ] . The input vector is then made of the duty cycles u = d, the state vector gathers the voltage across all capacitors and the current in all inductors

x = [v R , i , v , i G ] = [v R , i 1 , . . . , i m , v 1 , . . . ,
θ = [L G , R G ,V G ] = [L G1 , . . . , L Gm , R G1 , . . . , R Gm ,V G1 , . . . ,V Gm ] .
This allows to rewrite (1) under the state-space form:

ẋ(t) = f (x(t), u(t)) = A(θ)x(t) + N(x(t))u(t) + q(θ) y(t) = h(x(t)) , (2a)
with

J(θ) = diag {C R , L, . . . , L,C, . . . ,C, L G1 , . . . , L Gm } , (2b)
A(θ) = J(θ) -1     0 0 m 0 m 0 m 0 m 0 I m 0 0 m -I m 0 I m 0 m 0 -I m diag {-R G }     , (2c)
N(x) = J(θ) -1   i -v R I m 0 2m×m   , (2d)
q(θ) = J(θ) -1 [0 2m+1 ,V G ] , h(x) = [i G1 v 1 , . . . , i Gm-1 v m-1 , v R ] . ( 2e
)
This system is bilinear and uncertain with a non-linear (quadratic) output, making the control design very challenging.

Proposed control method

For simplicity, the design of the control law is presented here for a 3-terminal PFC, i.e. m = 3.

Multi-variable PI controller

Since there are uncertain parameters in the model, the equilibrium point to reach is also uncertain. This means that a simple state feedback control would lead to steady-state errors in the event of a change in the grid model. To cancel this deviation, an integral action is added to make sure the control objectives are asymptotically reached. Thus, a multi-variable proportional integral control law is proposed:

ż(t) = h(x(t)) -r, (3a) u(t) = K p x(t) + K i z(t) + u f f , (3b)
where r = [P r 1 P r 2 v r R ] is the vector of reference values and u f f is a constant feed-forward term. Recall that h(x(t)) = [P 1 (t) P 2 (t) v R (t)] . The rest of this section is devoted to the computation of the controller

parameters K p ∈ R m×(3m+1) , K i ∈ R m×m and u f f ∈ R m .

Linearised (small-signal) augmented model

Let us append the states z (integrator of (3a)) to x, creating an augmented state vector x a = [x , z ] . The augmented dynamics ẋa = f a (x a , u) read:

f a x z , u = f (x, u) h(x) -r . (4)
Define (x a , u ) as a constant pair zeroing the derivative of x a , i.e. f a (x a , u ) = 0. The entries of (x a , u ) are identified via the superscript . From ( 1) and (3a), one gets the following equilibrium:

v R = v r R , (5a)
u k = V Gk + V 2 Gk -4P r k R Gk 2v r R , (5b)
v k = u k v r R , (5c)
i Gk = P r k v k , (5d)
i k = i Gk , (5e)
with k ∈ {1, . . . , m} and P r 3 := -P r 1 -P r 2 . Let us select z = 0 since this vector can be defined arbitrarily. Observe that u and, in turn x a , depend on the unknown model parameters V Gk and R Gk (the entries of θ), and also on the reference values P r k and v r R (the entries of r). Let us now linearise the augmented model ( 4) at the equilibrium (x a , u ). One gets

ẋa = A a (θ, r) xa + B a (θ, r) ũ, (6a)
where xa = x ax a and ũ = uu are respectively the state and input in relative coordinates, and Indeed the discrepancy between P 3,meas and P 3,sim is the power lost in the PFC. This large value (40 W) can be explained by the fact that the setup is currently used at 5% of its rated power. These losses will be modelled in future studies for a final validation of the control process, but the simplicity of the proposed model is necessary for the design of control methods. The next paragraph shows that the proposed controller can fully cope with these inaccuracies.

J a (θ) = diag {J(θ), I 3 } , B a (θ, r) = J a (θ) -1   i -v r R I 3 0 9×3   , (6b)
A a (θ, r) = J a (θ) -1           0 u 0 3 0 3 0 3 -u 0 I 3 0 0 0 3 -I 3 0 I 3 0 0 3 0 -I 3 diag {-R G } 0   0 0 1   0 diag {i G1 , i G2 , 0} diag {v 1 , v 2 , 0} 0           . ( 6c
)
The proposed control law is tested experimentally at a tenth scale through different phases. During the first one, the references and operating point are initially at their nominal values, before being modified according to Table III and using the values from Table I. The change in θ corresponds to a step from 2 V to 10 V on the electronic load. The resulting reservoir voltage and line powers are displayed in Fig. 7, while the state variables and duty cycles are displayed in Fig. 8.

Observe on Fig. 7 that the change in power references for lines 1 and 2 leads to a spike on the reservoir voltage. Furthermore, observe on Fig. 8 that the control action is soft enough to prevent the saturation of the duty cycles. By speeding up the controller (choosing larger eigenvalues), one can reduce the voltage spike while decreasing the convergence time, although this will be done at a cost in robustness and may lead to the saturation of the duty cycles. On the bottom right figure, P r 3 is given as the theoretical value P 3 should reach in a lossless system, which explains the observed discrepancy. Although the change occurring at t = 0.67 s only is on line 3, it should be noted that it has a repercussion on all the other lines and on the reservoir voltage. This is due to the coupling of the lines, induced by the reservoir capacitor. Indeed, C R has relatively small magnitude, 60 µF.

Conclusion

In this paper, a dynamic model of an m-terminal PFC is proposed by adopting a multi-variable viewpoint to account for the coupling in the dynamics. The uncertain nature of a micro-grid is also explicitly taken into account, so that the unknown parameters appear in the model. Fig. 8: Inductor currents, line voltages and duty cycle measurements on the experimental setup in closedloop with the proposed controller, for a step in line power references followed by a step on the load voltage Moreover, a feedback control law has been proposed, in the case of a three terminal PFC. Robust asymptotic properties have been achieved, locally in the state space and locally in the parametric space. Simultaneous control of the power in each line and of the reservoir voltage of the converter is achieved. Those results have been successfully validated on a tenth scale experimental setup, for different references and operating points.

Further studies will mainly follow two different paths. First, increase the robustness of the control law by taking uncertainties into account beforehand, that is at the controller gains computation step. Second, achieve global or regional stability by enlarging as much as possible the basin of attraction of the closedloop system.

Fig. 1 :

 1 Fig. 1: Studied converter in its context

Fig. 2 :

 2 Fig. 2: Detail of k-th branch of the PFC (left) and the proposed grid model as seen by this terminal (right)

PFCFig. 4 : 5 :

 45 Fig. 4: Drawing of the experimental setup Fig. 5: Picture of the experimental setup

Fig. 6 :Fig. 7 :

 67 Fig. 6: Open-loop step response of the proposed model compared to the experimental setup (unfiltered measurements). The applied duty cycles are, for each phase, [0.7, 0.7, 0.6] , [0.7, 0.7, 0.5] , [0.8, 0.6, 0.5] .

  v m , i G1 , . . . , i Gm ] and the output vector corresponds to the following controlled variables y = [P 1 , . . . , P m-1 , v R ] . All the uncertain parameters are gathered in a vector

Table II :

 II Converter parameters

	Parameter Value Parameter Value
	L	760 µH	r L	1 Ω
	C	20 µF	r C	4.3 mΩ
	C R	60 µF	r C R	10 mΩ
	F SW	15 kHz t dead-time	0.3 µs
	T f	1 ms
	Table III: Experimental scenario
	t	0.17 s	0.67 s
	θ	θ n	θ n	θ 1
	r	r n	r 1	r 1

Computation of the controller parameters

The linearised system (6a) at the nominal operating point θ n and r n (see Table I for numerical values) can then be stabilized using the control law ũ = K x. The eigenvalues of A a (θ n , r n ) + B(θ n , r n )K are assigned by choosing the appropriate gain K through pole placement. The target poles are here chosen as the spectrum of A a (θ n , r n ) except for the three eigenvalues at zero (due to the integral action) that are shifted on the left hand side of the complex plane. Such a strategy leads to a controller ensuring local asymptotic stability under nominal reference and operating point, i.e. for r = r n and θ = θ n . A continuity argument can be invoked to prove that such a property remains valid in a neighbourhood of (θ n , r n ), i.e. the stability is preserved if the references and the uncertainties on the grid are slightly modified.

To estimate the degree of robustness of the closed-loop, the parameter domain in which θ and r belong to is sampled by successive increments on the different parameters (L Gk , R Gk or V Gk ). For each parameter, one sample is taken above the nominal value, and one is taken below, symmetrically. This results in three samples per parameter (nominal, higher and lower), and therefore in 3 9 = 19683 tested parameter combinations. For each combination (θ s , r s ), the location of the eigenvalues of A a (θ s , r s ) + B a (θ s , r s )K is depicted on Fig. 3. It comes out that every eigenvalue is located in the left hand side of the complex plane, which suggests that K has good robustness properties and justifies the experimental scenario proposed in the next section. Now that the gain K has been found, the real input u (the duty cycles) can be defined by the following equation:

which is equivalent to (3b), with K p being the ten first columns of K and K i the three last ones, and

Experimental results

The experimental setup is presented in Fig. 4 and5. A dSPACE MicroLabBox (µLB) rapid prototyping system (a) is used to control the PFC (b). The first terminal of the PFC is connected to a voltagecontrolled electronic load (EL) in series with a resistor (R) in (f), through 30 m of standard U1000 RV2 cable (Line k ) in (d). The second terminal is similarly connected to a resistor (e), and the third terminal to a power supply (PS) in (c). The switching devices used in the PFC are NGTB30N120LWG IGBTs. The numerical values of the components are listed in Table II. It includes the inductance and capacitance values as well as the parasitic resistances (series inductor resistance and parallel capacitor resistance), and the switching frequency and dead time of the PWM. The feedback state measurements are synchronised with the PWM and filtered with first-order filters of time constants T f .


Published in IAEE Energy Forum vol. 30, pp 30-31, 2021 Q4

On technology transfer and utility-scale power storage

Dr Minh Ha-Duong Directeur de recherche au CIRED/CNRS, France. < haduong@centre-cired.fr >

2021-09-14

Vietnam's recent energy transition experience shows that grid congestion issues limit how fast a country can turn to solar PV and wind power. Utility-scale battery storage could alleviate problems by time-shifting the variable electricity production, deferring the urgency to upgrade the transmission network. However, the technology is hardly bankable now in lowand middle-income countries. We propose that forming a collective of transmission network operators may accelerate access to this technology.

Historical experience with the energy transition shows that installing lots of solar and wind generation capacity often leads to a curtailment problem. This problem is worse in developing countries, who find it difficult to expand their transmission network as fast as would be required. Constrained by the prospect of wasting much of the clean electricity produced during the windiest and sunniest hours, renewable energy policies are less ambitious. The grid expansion speed is a factor limiting a fast energy transition.

For example, Vietnam was able to install over 16.5 GW of PV capacity between 2018 and 2020. That saturated the transmission network in the southern provinces. In the first four months of 2021, the network operator had to curtail 13.3 % of solar (447.5GWh) and 4.8 % of wind production (19.7GWh) [START_REF] Nguyen | Những thách thức của nhà đầu tư gió và đề xuất chính sách phát triển cho Việt Nam | Tạp chí Năng lượng Việt Nam (Défis des investisseurs éoliens et recommandations de politique de développement pour le Vietnam)[END_REF] . The practical answer has been that the next five years power development plan focuses on LNG [START_REF] Ha-Duong | Decentralized renewable energy broke Vietnam's power planning logic -Viet SE. 18[END_REF] .

Access to utility-scale electricity storage alleviates the curtailment issue. Storage de-couples the problem of installing solar and wind generation capacity from expanding the transmission network. Building hybrid solar + storage projects is not only a popular replacement option for diesel and gas turbine power generators in off-grid systems. More and more investors are starting to build hybrid solar + storage generation projects for the grid. For example, the 2.2 GW Huanghe Hydropower Development farm, completed in September 2020, includes 202.8 MW/MWh of storage capacity [START_REF] Bellini | World's largest solar plant goes online in China -2[END_REF] .

The market for battery storage is developing fast. Fortune Business Insights 4 found that « The global battery energy storage market size stood at USD 7.06 billion in 2019 and is anticipated to attain USD 19.74 billion by 2027, exhibiting a CAGR of 20.4% during the forecast period. » According to IEA Sustainable Development Scenario 5 , the annual average energy investment in Battery Storage should increase by 855 % in ten years: from 3.235 billion dollars (2019) per year over 2015-2020 to 27.669 billion dollars per year (2019) over 2025-2030. However, lower-middleincome countries are only starting to integrate battery storage technology in their energy policy plans. In Vietnam, for example, the government briefly considered giving a preferential FIT to hybrid solar PV projects integrating 2 hours of storage at 25 % of capacity before dropping the idea (Draft decision 11 update, issued 25-02-2019 by MOIT).

Battery storage technology started to deploy at the top-end of the market because the less developed countries did not offer conditions to realize the value proposition of storage projects. Financing storage by arbitrage between the low and high prices periods requires a power market with spot pricing. Financing storage by fast-response ancillary services requires an ancillary services and frequency control market. Financing storage by time-shifting around curtailment hours requires a high electricity price and low battery costs.

Admittedly, the organization of the wholesale electricity market is not a simple function of a country's wealth. However, more complex power market structures require more capacity from the regulating agencies, which is more likely to be found in advanced economies. Vasigliasindi et Besant-Jones [START_REF] Vagliasindi | Power market structure: revisiting policy options[END_REF] found that « a dichotomy emerges between high income countries characterized by a large system size for which unbundling and other reforms are significantly linked to better performance and low income countries characterized by small system power size for which there is no strong evidence that unbundling and other reforms delivered improvements in performance. »

The value of time-shifting batteries to answer curtailment is driven by the value of electricity otherwise wasted. It depends on price and the severity of curtailment: how many days per year, for how many years. Consider a typical 50 MWp early solar power project in Vietnam from 2019. It receives a feed-in tariff of 9.35 of UScent/kWh for 20 years. As the Vietnam standard power purchase agreement stipulates, it does not receive payment when curtailed. There is no ancillary services market or congestion hours pricing, so battery storage at the PV farm can be motivated only by time-shifting or obligation.

The government considered the two hours of storage / 25 % capacity clause, which meant a 12.5MW/25 MWh system for a project like the one above. Typical storage modules pack two to four MWh in a twenty-foot container, so 25MWh amounts to less than a dozen modules. In 2019, systems this size were at the technology frontier and not ready for mass deployment in Vietnam, and the government dropped the clause.

One 25 MWh battery cycle at 9.35 of UScent/kWh would be worth 2 337 USD. According to the Vietnam Technology Catalogue 7 , the capital cost for a 2-hour Lithium-Ion battery energy storage system will be around 0.7 MUSD 2019 /MW in 2022. For a 12.5 MW size battery, it amounts to 8.75 MUSD 2019 . Assuming O&M costs 1 USD/kWh ( 7 quotes a range of 0.3 -5 USD/kWh), they amount to 25 kUSD per year for the example system. There is a need to cycle the battery 3744 times, or once every day for 10.56 years, to cover the capital costs. The investment is not bankable, especially since curtailment will not happen every day for ten years.

As the cost of battery storage declines, fossil-fuel-based generation is less and less competitive with variable renewable + storage. At some point in time, this will happen even in countries where a weak power transmission infrastructure hinders the competitiveness of renewable energy. The Vietnam Technology Catalogue finds that storage costs may drop in 2050 to 0.20 MUSD 2019 /MW. In our example, the investment return period would be three years, interesting for a private investor. However, the switch point may be more than ten years away. The Technology Catalogue forecasts storage costs to be 0.40 MUSD 2019 /MW in 2030, which makes the return on investment duration larger than six years under our example, with best-case assumptions.

Utility-scale power storage is a crucial energy transition technology for low-and middle-income countries. We have shown that it remains expensive. The urgency to limit climate change requires asking how to accelerate the diffusion of this technology.

The Climate Convention has recognized the need for technology transfer measures to support countries from the South in the energy transition. To the best of our knowledge, the UNFCCC Technology Mechanism 8 has yet to support energy storage. In the case of Vietnam, the Climate Investor One fund, supported by the European Union, the Green Climate Fund, USAID, the Nordic Development Fund, and other donors, has invested in two wind power projects without storage. The projects may be profitable, but the impact is small because private investors finance 142 other similar projects.

Multilateral development, climate diplomacy and climate finance offer many possibilities to organize an accelerated uptake of utility-scale power storage in countries from the South. To start further discussions on this subject, what follows proposes a vision of an organizational arrangement in that direction.

The organization could be an alliance between transmission network operators (TNO) in receiving countries. A climate impact financial institutions collective could sponsor the alliance, which would form within an existing regional TNOs network. The intervention logic would be to capture the storage value from generation and transmission investment deferral or reduction [START_REF] Mallapragada | Long-run system value of battery energy storage in future grids with increasing wind and solar generation[END_REF] . The estimates above show that the economics are not there yet for private project investors. For infrastructure, however, long payback periods are more acceptable.

The organization could lease its members storage-as-a-service solutions to facilitate the learning curve for new adopters. Storage is a modular technology; it can be installed or removed in a few months. For TNOs, the decision to conduct a short term reversible trial is easier to take than committing to buying a new kind of asset. The organization would also provide vendor-neutral technical advice.

Collective action would make access to storage cheaper. Size gives bargaining power to negotiate quantitative discounts with hardware providers. When a member TNO does not need the assets anymore, the organization could move the batteries to another place. Reversibility reduces the risk that solving curtailment creates stranded assets. Finally, the organization would have access to capital at favourable rates by having rapid measurable emission mitigation benefits, in addition to facilitating long-term energy transition policies.

In conclusion, grid congestion headaches will continue to limit the speed of the transition to variable renewable energy sources, at least for ten more years in developing countries. However, unless wind and solar become the backbone of all countries' energy systems within the next ten years, the world is condemned to dangerous levels of climate change. The Paris Agreement requires to accelerate the access of all countries to utility-scale power storage technology.


M L Bella

M Hamidouche

Laurent Gremillard

Preparation of mullite-alumina composite by reaction sintering between Algerian kaolin and amorphous aluminum hydroxide

Keywords: Kaolin, Mullite, Aluminum hydroxide, Mullite-alumina composite

Preparation of mullite-alumina composite by reaction sintering between Algerian kaolin and amorphous aluminum hydroxide

M.L. Bella, M. Hamidouche,

Introduction

Kaolin is an abundant clay belonging to the group of phyllosilicates, kaolinite (Al2Si2O5) dominates its mineralogical composition. Kaolin is in the form of platelets, which generally have a pseudohexagonal crystal shape [START_REF] Paul | Géologie des Argiles, altérations, sédimentologie, géochimie[END_REF], Kaolin is ''1:1″ clay minerals, their layered structure is formed by a single tetrahedral Si sheet linked by covalently bonded to a single octahedral Al sheet [START_REF] Mikowski | Mechanical properties of kaolinite 'macro-crystals[END_REF]. When kaolin is sintered at a temperature above 1000 °C, it transforms into mullite (3Al2O3•2SiO2) and cristobalite (SiO2) [START_REF] Pask | Formation of mullite from sol-gel mixtures and kaolinite[END_REF]. Then, cristobalite transforms into amorphous phase at temperatures above 1400 °C [START_REF] Chen | Microstructural evolution of mullite during the sintering of kaolin powder compacts[END_REF]. According to Chen [START_REF] Chen | The processing of kaolin powder compact[END_REF], the mechanical properties of sintered kaolin depend on the firing temperature, ie according to its microstructure. Liquid phase sintering is the dominant mechanism during densification of kaolin bodies. The maximums of mechanical strength (180 MPa) and toughness (2 MPa m 1/2 ) are obtained for samples sintered between 1300 °C and 1500 °C. The presence of a large amount of vitreous phase appears to be the cause. Mullite is only the stable crystalline compound in the Al2O3/SiO2 phase diagram under normal atmospheric pressure from room temperature to its melting temperature at 1810 °C [START_REF] Li | A study of processing parameters in thermal-sprayed alumina and zircon mixtures[END_REF]. It has interesting properties such as good resistance to thermal shock, high refractory property, low thermal expansion, good creep resistance and good mechanical resistance at high temperatures [ [START_REF] Torrecillas | Thermomechanical behavior of mullite[END_REF], [START_REF] Mah | Mechanical properties of mullite[END_REF], [START_REF] Schneider | Structure and properties of mullite -a review[END_REF]]. Torrecillas et al. [START_REF] Torrecillas | Thermomechanical behavior of mullite[END_REF] have investigated the mechanical properties of dense crystalline mullite with their relationship with microstructural features. They found toughness of the order of 2.5 MPa m 1/2 and mechanical resistances exceeding 250 MPa. For thermal shock resistance, mullite presents a critical temperature difference ΔTc of about 750 °C in the case of soft cooling thermal shock with: Biot number β = 0.3, heat transfer coefficient h = 600 W/m 2 °C and specimen size of (40 × 6 × 4) mm 3 [START_REF] Hamidouche | Thermal shock behaviour of mullite ceramic[END_REF]. Also, it is characterized by good chemical stability, and good resistance to wear and friction [START_REF] Senda | Sliding wear of oxide ceramics at elevated temperatures[END_REF]. For these excellent properties, mullite is widely used as structural and functional ceramic in various applications such as components for electronics, furnace resistance supports, substrates, ball bearings, cylinders and piston rings in automotive engines, …. Researchers have made considerable efforts to synthesize mullite powder and to prepare dense sintered components [START_REF] Sacks | A Review of Powder Preparation Methods and Densification Procedures for Fabricating High Density Mullite[END_REF][START_REF] Amutharani | Low temperature pressure less sintering of sol-gel derived mullite[END_REF]. These processes involve very expensive precursors that can make them unsuitable for industrial production [START_REF] Lee | Ceramic Microstructures, Property Control by Processing[END_REF]. Synthetic methods using natural clay raw materials, which contain kaolinite, sillimanite, alumina, gibbsite or boehmite are good and cheaper alternatives which have been the subject of much research [START_REF] Pask | Formation of mullite from sol-gel mixtures and kaolinite[END_REF][START_REF] Kolli | Elaboration and characterization of a refractory based on Algerian kaolin[END_REF][START_REF] Belhouchet | Kinetics of mullite formation in zircon and boehmite mixture[END_REF]. However, mullite formed from natural clays most often contains a high amount of glass phase. A combination between kaolin clay and alumina may be the right solution in this case. Indeed excess alumina can react with the amorphous phase to form additional mullite. The addition of adequate amount of alumina (Al2O3) can therefore suppress the amorphous phase and thus increase the amount of mullite in the final material. The decrease of the amount of glassy phase has a positive effect on the mechanical properties of mullite, especially at high temperature. In this work, three Algerian kaolin are used as source materials to process mullite, referenced respectively as DD1, DD2 and DD3. They are extracted from Djebbel Debbagh, located in the northeast of Algeria. They are considered as a kaolinite clay rich in alumina (41 wt %). This makes it very suitable for the manufacture of structural ceramics based on aluminosilicate compounds. The formation of mullite prepared by reactive sintering between the three kaolin and an amorphous aluminum hydroxide are studied. In particular, the kinetics of formation of mullite are assessed, as well as, the microstructure development and the Vickers hardness, with respect to the different compositions and sintering conditions.

Experimental procedure

Experimental techniques

The chemical compositions of the raw materials (kaolin and amorphous aluminum hydroxide) were assessed by X-ray fluorescence spectroscopy (Rigaku ZSX Primus IV, Japan). X-ray diffraction (BRUKER D8 Advance with Cu Kα radiation) was used to detect and identify the different phases: 2θ between 5° and 80°, 0.05° step size, exposure 0.08 s per step. XRD was also used to measure the theoretical density of each sample as follows: First, a calibration curve linking the Si/Al molar ratio in mullite and its lattice parameter a was established from PDF files [17]. Then Rietveld refinement of XRD-diagrams enabled the determination of both the lattice parameter a and the Al2O3/mullite ratio for each material. These two properties were then used to calculate the Si/Al molar ratio in the crystalline phase of each material. On the other hand, the chemical composition of the starting kaolin (Table 2) and the Kaolin/Al(OH)3 ratio of each mixture enabled the calculation of nominal Si/Al molar ratios. Assuming a complete conservation of the aluminum and silicon during processing, it was thus postulated that the missing Si formed an amorphous phase of overall composition SiO2 and density 2.2 g cm -3 , which enabled calculating the absolute density of the obtained materials. Comparison with the observed density allowed to access the relative density and porosity.

The particle size distribution of the starting powders were measured by a laser granulometer (Malvern Mastersizer 2000). The chemical bonds of the phases formed during the firing of amorphous aluminum hydroxide -kaolin mixtures at different temperatures were studied by Fourier transform infrared (FTIR) spectroscopy (JASCO FT/IR-4200 spectrometer), with a smart endurance single bounce diamond, attenuated total reflection (ATR) cell. Spectra in the 4000-600 cm -1 range were have obtained by the co-addition of 40 scans with a resolution of 4 cm -1 . Differential thermal and thermogravimetric analyzes (DTA and TGA) were carried out in air between ambient and 1400 °C with a heating rate of 10 °C/min using a TA instrument SDT Q 600 V20.9 Build 20 apparatus.

The density of the sintered samples was measured by the Archimedes method using ionized water as the immersion medium.

Vickers hardness (HV) was assessed under ambient conditions using the Vickers indentation method instrumented with a Zwick -Roell ZHU 2.5 device, with a maximum load (F) of 9 N and a 15 s holding time at maximum load. The diagonal of the indents (2a) were measured by optical microscopy (microscope Zeiss Axiovert 40 MAT) and HV was then calculated according to the following relation:

𝐻 𝑣 = 1.8544×𝐹 2𝑎 2 (1)
The polished samples have been thermally etched, according to the following sintering cycle:

-Rapid rise in temperature (20 °C/min).

-Hold for 30 min at 150 °C below the temperature of sintering.

-Rapid temperature drop (20 °C/min). The microstructures were examined by scanning electron microscopy (SEM, SUPRA 55VP, Zeiss, Germany).

Materials

Amorphous aluminum hydroxide Al(OH)3, commercialized by sigma-Aldrich company, was used as a starting powder. Table 1 gives its chemical composition. It has a density of 2.23 g/cm 3 and it has a narrow, monomodal particle size distribution by volume centered on an average grain size of 6 μm (Fig. 1). The three kaolin used in this study are extracted from the mountains of Djebel Debbagh (northeast of Algeria). They are referenced respectively as DD1 of whitish color, the light pinkish color of kaolin referenced DD2 is caused by the presence of alunite [START_REF] Karakaya | Mineralogical and geochemical properties and genesis of kaolin and alunite deposits SE of Aksaray (Central Turkey)[END_REF][START_REF] Mutlu | Geochemistry and origin of the Şaphane alunite deposit, Western Anatolia, Turkey[END_REF] and DD3 of grayish color because of its content of manganese oxide (MnO). The three types of Kaolin contain in mass, approximately 42% of alumina and 48% of silica. Table 2 gives the average chemical composition of the three Kaolin. For preparation of the mullite samples by reactive sintering, the three kaolin were ground to a particle size less than 63 μm. Then for each kaolin (DD1, DD2 and DD3) two mixtures with alumina trihydrate were prepared, denoted M1 and M2 according to the compositions mentioned in Table 3.

Table 3 : Compositions for both studied subsystems (Kaolin + aluminum hydroxide) in (% wt).

Mixture composition M1 M2

Kaolin (%)

50

Al(OH)3 (%) 61.5 According to the stoichiometric equation: adding aluminium tri-hydroxide to kaolinite will lead to the formation of mullite: Al2Si2O5(OH)4 + 4Al(OH)3 → 3Al2O3•2SiO2 + 8H2O Calculation showed that the mass of the amorphous aluminum hydroxide needed to be add to the kaolin, to have a stoichiometric reaction, is 54.72% by mass. We opted for two additions of Al(OH)3.

-The M1 composition, with 61.5% added Al(OH)3, will give a mullite-alumina composite above the stoichiometry. This will allow all the excess of silica in the kaolin to be consumed. -The M2 composition, with 50% addition of Al(OH)3, will lead to obtaining a mullitealumina composite with an excess of silica, ie a composition below the stoichiometry. This will allow a small amount of glassy phase to be in the resulting composite. The two prepared mixtures were dispersed in ionized water according to the following ratio: 50% of powder mixture/50% of water (in mass).The suspension was ground for 48 h using an attrition grinding mill with alumina balls (∅ ≈ 1.5-2.5 mm). The quantity of balls used was 3 times the mass of the ground powder. The particle size was controlled during grinding until obtaining an average size of 2.5 μm (Fig. 2). Then the suspensions were dried at 110 °C to guarantee their complete drying. Then, the powders were de-agglomerated in a mortar and then sieved to obtain agglomerates of less than 63 μm.

Figure 2 : Particles size distribution of (DDx + aluminum hydroxide) mixtures compositions milled during up to 48 h (the mixtures with the 3 Kaolin and compositions M1 and M2 exhibited identical particle size distributions).

The samples were pressed uniaxially under a pressure of 100 MPa, to cylindrical pellets with a diameter of 25 mm and a thickness of 7.5 mm. To avoid cracking of the pellets, all samples were pre-sintered for 1 h at 600 °C with a low heating rate (1 °C/min). Finally, the pellets were sintered in air for 5 h at different temperatures (1400 °C, 1500 °C and 1600 °C) using 5 °C/min heating and cooling rates.

The flat faces of the sintered samples were polished using a BUEHLER automet 250 polisher. The polishing was carried out in two stages, the first one is a pre-polishing of the sample with four discs (Φ 250 mm) with diamond suspensions according to the fractions P120 (125 μm) (until the flatness), P220 (68 μm), P600 (30 μm) and P1200 (15 μm) for 3 min for each case. The applied force is 30 N with a rotational speed of the plate of 150 rpm with an opposite direction of rotation (disc relative to the sample) and lubrication with water. In the second step, diamond abrasive suspensions of 6 μm, 3 μm and 1 μm has been used with the same conditions in the first step except for the applied force which is this time 20 N, in addition to the use of appropriate discs. The samples were cleaned in ultrasonic tank with ethanol, after each operation.

Results and discussion

Characterization of starting materials

Amorphous aluminum hydroxide

The DTA-TGA curves of the aluminum hydroxide powder (Fig. 3) show the thermal and thermogravimetric behavior of the amorphous aluminum tri-hydroxide powder. The TGA curve for aluminum tri-hydroxide shows a total mass loss of about 35.8%, a rate very close to 34.6% (theoretical value). This loss takes place in two stages according to the following phenomena:

The first mass loss takes place between room temperature and 120 °C. It corresponds to the release of moisture adsorbed on the surface of the powder [START_REF] Xu | Thermal study of boehmite nanofibers with controlled particle size[END_REF]. The fineness of the amorphous powder explains this behavior, with a large specific surface area, which allowed it to adsorb moisture before use. The second mass loss is due to zeolite and structural water due to the transformation of amorphous alumina trihydrate into aluminum oxy-hydroxide. This is explained by the large endothermic peak between 100 °C and 500 °C observed on the DTA curve. According to the study of Li et al. [START_REF] Li | The influence of Al (III) supersaturation and NaOH concentration on the rate of crystallization of Al(OH)3 precursor particles from sodium aluminate solutions[END_REF], amorphous aluminum hydroxide generally undergoes slow dehydration as in our case up to 700 °C. Between 800 °C and 900 °C, the mass loss of 3.8% corresponds to the final de-hydroxylation of aluminum oxy-hydroxide to form γ-Al2O3 transition alumina. This transformation is evidenced by the exothermic peak centered around 860 °C, also observed by other authors [START_REF] Tiffo | Physical and mechanical properties of unheated and heated kaolin based-geopolymers with partial replacement of aluminum hydroxide[END_REF]. Transition γ-alumina then transforms into θ-Al2O3 transition alumina and then into crystalline alumina (α-Al2O3) around 1200 °C. Fig. 4a andb shows the X-ray diffraction diagrams of aluminum hydroxide fired at different temperatures from ambient to 1600 °C. Aluminum tri-hydroxide is completely amorphous between room temperature and 800 °C. This type of aluminum hydroxide has been produced by grinding during for long periods [START_REF] Tsuchida | Mechanochemical phenomena of gibbsite, bayerite and boehmite by grinding[END_REF]. Characteristic peaks of γ-alumina transition phase are observed between 800 °C and 900 °C. Between 1000 °C and 1100 °C, γ-alumina transforms into another transition alumina (θ phase) and α-Al2O3 phase starts to form [START_REF] Sato | Thermal decomposition of aluminum hydroxides to alumina[END_REF]. Above 1200 °C, only the stable α-Al2O3 phase is observed. This sequence of transformations is coherent with the work of Sato et al. [START_REF] Sato | The thermal transformation of gelatinous aluminium hydroxide[END_REF], who have shown that amorphous aluminum hydroxide transforms with temperatures increasing from ambient to above 1200 °C, as follows:

Amorphous Al(OH)3 → amorphous AlOOH → γ-Al2O3 → θ-Al2O3 → α-Al2O3 Fig. 5 presents the infrared spectra of the different kaolin DD1, DD2 and DD3. A first zone in the spectra corresponds to the high frequency bands located between 3750 cm -1 and 3550 cm -1 . It is mainly related to the vibrations of O-H hydroxyls, and particularly to the valence vibrations of the OH groups, which result in the presence of two absorption bands centered on 3694 cm -1 (external OH) and 3621 cm -1 (internal OH vibration band). A second zone, from 1200 cm -1 to 600 cm -1 , corresponds to the lower frequencies and relates to the Al-OH, Si-O, Si-O-Si and Si-O-Al bonds.

In that zone, the band at 1117 cm -1 is attributable to the elongation of the Si-O bond. The asymmetric stretch bond of Si-O -Si and the deformation of the Al-O -H bonds, respectively [ [START_REF] Frost | Raman spectroscopy of potassium acetate-intercalated kaolinites at liquid nitrogen temperature[END_REF], [START_REF] Frost | Birdwood kaolinite: a highly ordered kaolinite that is difficult to intercalate an XRD, SEM and Raman spectroscopic study[END_REF], [START_REF] Cases | Etude des propriétés cristallochimiques de kaolinites désordonnées[END_REF]] caused the bands observed at 1033 cm -1 and 910 cm -1 . The bands at 790 cm -1 and at 750 cm -1 , reduced to an inflection, are typically related to OH translation, which may be due to the presence of halloysite (2SiO2•Al2O3•4H2O) [START_REF] Frost | Raman spectroscopy of potassium acetate-intercalated kaolinites at liquid nitrogen temperature[END_REF]. A low intensity band centered at 2930 cm -1 is also observed, attributed to the presence of organic materials.

SEM observation of the three kaolin (Fig. 6) shows that the grains are agglomerates of elongated disordered plates and in form of rolled leaf-shaped grains. The absolute densities measured with a helium pycnometer for the kaolin DD1, DD2, DD3 are respectively 2.56 g/cm 3 , 2.56 g/cm 3 and 2.57 g/cm 3 .

The DTA curves of the three kaolin (Fig. 7) show the presence of two endothermic peaks. The first peak, located between 47 °C and 65 °C depending on the kaolin, is linked to the removal of water from residual humidity (surface water). This generates a mass loss between 2.5% and 5% for the 3 kaolin. The second endothermic peak is very intense; it appears at a temperature order of 501 °C for DD1, with a mass loss of 14%. In the case of DD2, it is observed at 492 °C, accompanied by a mass loss of 15% and it occurs at 487 °C for kaolin DD3 with a mass loss of 13.7%. This endothermic peak is associated with the release of kaolin structural water to form metakaolinite. In addition to these two endothermic peaks, an endothermic peak is observed, only in the kaolin referenced DD2, at a temperature of 732 °C and associated to a low mass loss of 0.63%.This thermal event is caused by the decomposition of the sulfate present in this type of kaolin [START_REF] Lei | Potassium fixation and the separation from sodium through the formation of K-alunite using activated aluminum hydroxide[END_REF][START_REF] Frost | A thermogravimetric study of the alunites of sodium, potassium and ammonium[END_REF]. The DTA curves show an exothermic peak, without mass loss, between 992.7 °C and 994.6 °C for the 3 kaolin. This peak corresponds to the crystallization of the mullite phase, formed from the transformation of kaolinite.

X-ray diffraction analyses (Fig. 8) show that the different phases present in the kaolin at room temperature are essentially kaolinite (Al2Si2O5(OH)4) and halloysite (Al2Si2O5(OH)4-2H2O) as major phases and alunite (K(Al3(SO4)2(OH)6) as minor phase. Alunite is present only in the DD2 clay, due to the presence of larger quantities of K2O and SO3 in this kaolin (Table 2). In the three kaolin, the two major phases, namely kaolinite and halloysite, transform between 600 °C and 950 °C into amorphous phases, then above 1200 °C into mullite and cristobalite. According to literature [START_REF] Gonon | Etude de la transformation de trois nuances de kaolin en fonction de la température[END_REF][START_REF] Chargui | Mullite fabrication from natural kaolin and aluminum slag[END_REF], cristobalite transforms into an amorphous phase at very high temperature (Fig. 8 shows it to happen above 1500 °C), and mullite remains as the only crystalline phase. Fig. 9 shows the thermal behavior of compositions mixtures M1 and M2 during a differential thermal analysis (DTA) from room temperature to 1500 °C, conducted in air with a heating rate of 5 °C/min. The DTA curves of figure (9 A and B) show two endothermic peaks for the two mixtures M1 and M2. The first peak is centered around 120 °C for the two mixtures M1 and M2 and corresponds to the departure of surface water from the two powders mixes (kaolin + tri-hydrated amorphous alumina) and zeolitic water located between the sheets of kaolinite of the three kaolin.

Phase evolutions of the mixtures with temperature

The second, very intense, endothermic peak is observed at 500 °C for the M1 mixtures and from at 520 °C for the M2 mixtures, and corresponds to the de-hydroxylation of kaolinite [START_REF] Sahnoune | Algerian kaolinite used for mullite formation[END_REF]. This second endothermic peak is caused by the elimination of structural water by a diffusion mechanism, which results in the formation of amorphous metakaolin, which only crystallizes at higher temperatures. Two exothermic peaks are also observed for the two compositions. The first peak lays between 940 °C and 990 °C, depending on the mixture and on the kaolin nature. This peak, associated to the formation of mullite from metakaolin, appears at temperatures below to those when kaolin is alone (992 °C). The presence of the transition alumina phases (gamma and theta) facilitates the nucleation of the mullite crystals. The second exothermic peak, between 1150 °C and 1300 °C, is observed for the six mixtures + alumina trihydrate). It corresponds to the formation of a secondary mullite phase from the reaction between θ-alumina, formed from amorphous aluminum hydroxide and excess silica from kaolin. This result agrees with those found by other authors [START_REF] Chargui | Mullite fabrication from natural kaolin and aluminum slag[END_REF][START_REF] Viswabaskaran | Effect of MgO, Y2O3and boehmite additives on the sintering behavior of mullite formed from kaolinite-reactive alumina[END_REF][START_REF] Djanganga | Sintering behavior of porous ceramic kaolin-corundum composites: phase evolution and densification[END_REF]. Fig. 10 shows the shrinkage curves as a function of firing temperature, for the six mixtures, from room temperature up to 1600 °C with a heating rate of 5 °C/min. The first shrinkage takes place between 120 °C and 220 °C, where aluminum hydroxide and kaolin release surface water. Between 500 °C and 600 °C, kaolinite undergoes de-hydroxylation and transforms into metakaolin, which causes the second shrinkage. To this effect, the hydroxyl groups are removed from the intermediate layer between the layers of Si-O and Al-O in the kaolinite crystals [START_REF] Chen | Microstructural evolution of mullite during the sintering of kaolin powder compacts[END_REF]. The third shrinkage, observed between 850 °C and 1000 °C, corresponds to the transformation of metakaolinite into so-called primary mullite [START_REF] Brindley | Kaolinite-mullite reaction series: I-III[END_REF]. A fourth significant shrinkage extends from 1020 °C to 1220 °C, and is caused by the transformations of transition alumina into α-alumina, the most stable alumina, which has the highest density. In this temperature range, the excess of silica originating from the initial kaolin is still present. The fifth and final shrinkage begins beyond 1200 °C until the end of the heating cycle. This shrinkage is associated with the reaction of the silica phase with the θ-alumina present in the mixtures up to 1300 °C. This second mullite was nucleated in the transitional vitreous liquid phase by dissolution of the alumina. The grains of the secondary mullite present a different structure (acicular) and grains size smaller than those of the primary mullite formed by kaolin transformation [START_REF] Chargui | Mullite fabrication from natural kaolin and aluminum slag[END_REF].

Sintered materials

Shrinkage kinetics

The samples shrinkage observed above 1400 °C is due to the sintering start of the composite material formed.

Microstructure and phase analysis

Table 4 groups the results of the apparent density for the different compositions, as a function of the sintering temperature. The values of the composition M1 are greater than those of composition M2, because the first composition contains more alumina. The densification-taking place at temperatures below 1600 °C is due to the small particle size of the mixture of starting powders because it is ground for 48 h. This large specific surface area reduces the diffusion distances, which increases the driving force of the sintering as found by other authors [START_REF] Sahnoune | Algerian kaolinite used for mullite formation[END_REF]. The low density observed for the mixtures based on DD1 kaolin sintered at 1400 °C. is due to the presence of the compounds before the reaction (silica, alumina). At this temperature, the cristobalite, with the impurities of the kaolin, transforms into a liquid phase. This proves the non-completion of the silica-alumina reaction but also prevents the diffusion to accelerate the sintering. These results confirms those obtained by Chantale Njiomou Djangang et al. [START_REF] Djangang | Reaction sintering and microstructural evolution in metakaolin-metastable alumina composites[END_REF].

The density increases with increasing of sintering temperature for the two compositions, due to porosity closure. In all cases, the density is lower than the absolute density of the mullite (3.17 g•cm -3 ), hinting to remaining porosity, all the more that the presence of alumina dispersoids should increase the density.

Fig. 11 shows the relative density and apparent porosity of the alumina mullite composite sintered at different temperatures. It is observed that composition M1 samples achieved relative densities of 93 %-97.8% in the specimens sintered at 1600 °C, and 96 %-98% in composition M2, in the specimens sintered at 1500 °C, on the other hand, relative densities decrease to 95 %-96% in samples sintered at 1600 °C in composition M2. In composition M1, the maximum value of the relative density is measured for the compound DD2 + Al (OH)3 (~97.8%). In the composition M2 the maximum value is found for both compounds DD1 + Al (OH)3 and DD2 + Al(OH)3 (~98%). This is due to the significant mullitization rate recorded for these two compounds. On the other hand, the compounds containing kaolin referenced DD3 systematically present the lowest relative density in the six. Indeed, DD3 contains much more volatile material and impurity compared to the other two kaolin, which creates residual porosity that may not be completely removed during the sintering process. The apparent porosity in compound M1 decreases with the increase in the sintering temperature. On the other hand, in the composition M2, it is observed that there is a slight increase in porosity and decrease in relative densities between 1500 °C and 1600 °C caused by the presence of much more of the amorphous phase around the grain boundaries compared to composition M1 that contains more excess alumina and less kaolin than composition M2.

The XRD diagrams of the mixtures M1 and M2 for the three types of kaolin, sintered for 5 h at 1400 °C, 1500 °C and 1600 °C, are gathered in Fig. 12. Mullite is the predominant main phase, and no cristobalite is detected (at these temperatures, cristobalite became amorphous and then reacted with alumina to form secondary mullite). Primary mullite results from the transformation of kaolinite while secondary mullite results from the reaction between alumina and the excess of silica in kaolin. The later one is formed by a mechanism of dissolution precipitation through the vitreous phase as mentioned also by other authors [START_REF] Liu | Mullite formation in kaoliniteαalumina[END_REF]. In the case of the sample referenced M2-DD1, no trace of Al2O3 nor any another phase is detected apart from the mullite. All other mixtures contain α-Al2O3 up to 1600 °C, due to the excess of Al2O3 added and which could not react once the amorphous phase was entirely consumed in the reaction. For the different compositions, increasing the sintering temperature accelerates the formation of secondary mullite. Indeed, from 1500 °C, the reaction between alumina-vitreous silica of kaolin seems to be complete. The fine size of the alumina grains combined with the presence of impurities in the starting kaolin, promotes the reduction of the viscosity of the glassy phase at these temperatures. This promotes the reaction of alumina with the glassy phase to form more secondary mullite, resulting in total crystallization of the compound.

Fig. 13 displays the results of the quantification of the secondary mullite formation in M1 and M2 mixtures during thermal treatment, measured by the Rietveld refinement quantitative phase analysis. In M1 composition, about 40% of the mullite formation takes place from 1400 °C. On the other hand, at the same temperature the formed mullite reaches a little more than 80% in M2 composition. At this temperature the amorphous phase has not fully reacted with the excess alumina. It's noted that from 1500 °C, the formation of mullite increases slowly. It is observed that the formation of mullite in the M1 composition reaches a little more than 99% of mullite in the compound DD2 + Al(OH)3. The M2 composition has recorded a total mullitization of the compound DD1 + Al(OH)3 at a temperature of 1600 °C for 5 h of sintering. At high temperature, the present alumina has been completely dissolved in the amorphous phase for the benefit of the formation of secondary mullite. it is noted that there is a difference in the mullite quantity formed for the three kaolins DD1, DD2 and DD3 in composition M1, compared to composition M2. The impurities present differently in each kaolin facilitate the formation of the liquid vitreous phase from the silica amount of each kaolin. In the composition M1, the alumina amount is in excess, so its dissolution in the liquid phase will be more difficult. Therefore, the precipitation of the mullite will be less.

Fig. 14, Fig. 15 show the microstructures, obtained by SEM, of mixtures (kaolins -alumina) sintered respectively at 1500 °C and 1600 °C for 5 h. The morphology of the microstructures does not present significant differences between the two mixtures M1 and M2. A high porosity is observed for all sintered mixtures at different temperatures.

In the structures, three distinct phases are observed, namely: -A matrix of secondary mullite grains with acicular form and small grain size (<1 μm), resulting from the reaction of kaolin silica and alumina. They are around 100 nm-200 nm in the case of mixtures M1 and M2 combined with DD1 and DD2. The reaction between alumina and the vitreous phase generally takes place by a dissolution-diffusion-precipitation mechanism. Kaolins containing more K2O and MnO will accelerate the transformation of cristobalite into the liquid phase and reduce its viscosity. It will lower the temperature of the dissolution and diffusion mechanism and allow the secondary mullite to precipitate at temperatures below. it is observed in the XRD diagrams (Fig. 12) that the cristobalite has not even had time to form since. Malou et al. [START_REF] Malou | Thermal shock resistance of Mullite obtained from Kaolin and tri-hydrated alumina[END_REF] have shown that the dissolution of alumina in the vitreous phase increases until the nucleation of the mullite then its crystallization. The rapid formation of mullite traps alumina particles and pores which inhibits densification of the composite. The equiaxial form of secondary mullite is caused by the presence of a large amount of alumina. -Large primary mullite crystals of very elongated shape formed from the final crystallization of kaolinite. They are randomly oriented and uniformly dispersed in the matrix of secondary mullite grains. M.A. Sainz et al. [START_REF] Sainz | XRD microstructural analysis of mullites obtained from kaolinite-alumina mixtures[END_REF] found that the compositions of the primary and secondary mullites vary significantly according to the Al2O3-SiO2 diagram. Secondary mullite is richer in alumina (74.1%) than primary mullite (71.7%). -Isotropic Alumina grains of a few micrometers dispersed in the mullitic matrix. This alumina phase comes from the excess of the alumina addition, which did not react with the kaolin silica. For the two mixtures M1 and M2 combined with DD1 and DD2, the compositions are not stoichiometric. This finding is confirmed by the spectra of analysis by X-ray diffraction. The structure of the M1 mixtures of kaolin DD3 led to a larger grain size. This growth of the crystallites could be caused by the incorporation into the mullite of Mn4+ cations, present as significant impurity in the kaolin DD3, by substitution for Al3+ and Si4+ [START_REF] Bouzidi | Influence des impuretés des kaolins sur les propriétés des produits de cuisson[END_REF]. Mullitization occurs from the alumina -silica phase by nucleation and growth due to a reaction between alumina from aluminum hydroxide and amorphous silica from kaolin. The growth rate is controlled by the dissolution of Al2O3 in SiO2. At high temperatures, nucleated mullite will grow at the interface between Al2O3 and SiO2 particles by diffusion of Al 3+ and Si 4+ via a crystal lattice. Rapid dissolution of alumina in the amorphous siliceous phase promotes homogeneous nucleation and growth of mullite within the residual vitreous phase [START_REF] Kleebe | Conversion of Al 2 O 3 -SiO 2 powder mixtures to 3:2 mullite following the stable or metastable phase diagram[END_REF]. The mixture M1 combined with DD3 (with an excess of alumina) confirms this mechanism. Indeed, some intragranular alumina grains remained trapped in clusters of formed secondary mullite.

The presence of 2.34% MnO promotes sintering in the liquid phase (small amount) in the case of the M2 mixture (less alumina) made from DD3 and sintered at 1600 °C for 5 h.

Vickers hardness

The average values of the measured hardness of M1 and M2 compositions shown in Table 5, indicate that the hardness values increase with increasing sintering temperature. The studied mullitealumina composites have higher hardness in comparison with mullite ceramics, which is about 11.3 GPa [START_REF] Raghdi | Mullite-zirconia composites prepared from halloysite reaction sintered with boehmite and zirconia[END_REF], the presence of the alumina phase increases hardness. These values are in the same order as those found by P.G. De la Iglesia et al. [START_REF] De La Iglesia | Microstructural development and mechanical performance of mullitealumina and hibonite-alumina ceramics with controlled addition of a glass phase[END_REF].

A sintering temperature of 1400 °C allows the complete reaction between the alumina and the excess silica kaolin. Beyond 1400 °C temperature, sample densification begins to take place. The Compounds sintered at 1600 °C lead to better densification with anisotropic grain growth which

Figure 1 :

 1 Figure 1 : Particle size distribution by volume of aluminum hydroxide powder used.

Figure 3 .

 3 Figure 3. DTA/TGA curves of the aluminum hydroxide raw powder.

Figure 4 .Figure 5 .

 45 Figure 4. X-ray diffraction pattern of aluminum hydroxide: (A): fired between 600 °C and 1000 °C; (B): fired at different temperatures.

Figure 6 :

 6 Figure 6 : Microstructure of Algerian kaolin referenced (A) DD1, (B) DD2 and (C) DD3.

Figure 7 :

 7 Figure 7 : TDA/TG curves of Algerian kaolin heated up to 1200°Cwith rate of 10 °C/min: (A) DD1, (B) DD2, (C) DD3.

Figure 8 :

 8 Figure 8 : XRD pattern of the three Algerian kaolin treated at different temperatures (A) DD1,(B) DD2 and (C) DD3.

Figure 9 .

 9 Figure 9. Thermal differential analysis (DTA) of the studied composition mixtures: (A) M1 and (B) M2.

Figure 10 :

 10 Figure 10 : Shrinkage curves of the green compact for compositions: (A) M1 and (B) M2.

  .05 3.10±0.01 3.05±0.05 3.07±0.02 3.00±0.02 DD3 + Al(OH)3 3.06±0.04 3.10±0.01 3.06±0.02 3.03±0.03 3.02±0.01 2.98±0.01

Figure 11 :

 11 Figure 11 : Relative density and apparent porosity of compositions: (A) M1 and (B) M2.

Figure 12 :

 12 Figure 12 : (A) XRD pattern of composition M1 sintered at different temperature, (B) XRD pattern of composition M2 sintered at different temperature.

Figure 13 :

 13 Figure 13 : Mullite formation of composition: (A) M1 and (B) M2 during thermal treatments.

Figure 14 :

 14 Figure 14 : SEM micrographs samples of the M1 and M2 compositions sintered at 1500 °C during 5 h.

Figure 15 :

 15 Figure 15 : SEM micrographs samples sintered at 1600 °C during 5 h.

Table 1 :

 1 Chemical composition of starting alumina tri-hydroxide (wt %).

		Al2O3	SiO2 Na2O MgO P2O5 SO3	Cl	K2O CaO Fe2O3	Fire loss (%)
	Al(OH)3	72.9	1.15	1.2	1.32	0.01	0.5	0.03 0.04 0.45	0.04	22.36

Table 2 :

 2 Chemical composition of starting materials (wt %).

		DD1 DD2 DD3
	Al2O3	41.9 41.6 40.6
	SiO2	48.8 48.3 46.8
	Na2O	0.05 0.06 0.04
	MgO	0.01	/	0.03
	P2O5	0.01 0.02 0.02
	SO3	0.13 1.33 0.34
	Cl	/	0.03 0.04
	K2O	0.01 0.27 0.07
	CaO	0.21	0.2	0.37
	MnO	/	0.01 2.34
	Fe2O3	0.04 0.05 0.07
	NiO	0.02 0.01 0.11
	ZnO	0.01 0.01 0.09
	As2O3	0.05 0.06 0.06
	SrO	/	0.02	/
	Fire loss (%) 8.76 8.03 9.02

Table 4 :

 4 Apparent density of all materials.

Acknowledgements

The authors would like to thank Innovation Fund, Denmark for the financial support of this study under the framework of SYNFUEL (sustainable synthetic fuels from biomass gasification and electrolysis) project (File No. 4106-00006B).

increases the hardness of the composite (alumina-mullite) [START_REF] Naga | Preparation and characterization of porous fibrous mullite bodies doped with TiO 2[END_REF]. The high content of alumina in M1 compositions leads to higher hardness than in M2 composition. At 1500 °C, the densification improves much better, but needle shaped mullite nucleated at this temperature and it grew and crystallized very well at 1600 °C. After formation of mullite by the reactions of alumina and amorphous silica, the excess alumina recrystallized as corundum crystals.

The disadvantage is its relatively low density and consequently low strength. Fully dense mullite specimens are thus difficult to prepare by using the process employed in the present study. On the other hand, the advantage of this process is its economic feasibility, the pellet of mullite developed in the present study will be highly suitable for manufacturing ceramic disks for faucet cartridges.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.