Review of flash sintering: materials, mechanisms and modelling

Figures & data

Figure 1. Some snapshots taken from initial work linked to FS. (a) Patent front page of ‘electrical glower light’ dated 1897 taken from original document GB189719424. The lamp described in this document employed a magnesia glower (7 mm length, hollow cylinder outer diameter 1.4 mm and inner diameter 0.4 mm). The glower was first heated using a flame, when it reached a sufficient temperature an AC power source was switched on (0.23 A, 118 V) and the 27 W lamp emitted an intensity of 26 cd (candles). (b) Snapshot of document published in 1908 on electroluminescence of selected oxides [8]. In this work, when the material could not be prepared by melting is was produced by sintering pastes. (c) Drawing showing an experimental setup for FS (see top heading) developed by Hill et al. [9] in 1952. A ceramic lining allowed electrical insulation between the punches and the die, thus allowing current to entirely flow across the powder.

Figure 2. Volumetric peak power dissipation vs. electrical discharge time for different sintering ECAS techniques. The referred operating conditions are taken from typical processing parameters reported in the literature. The peak power density for Ultrafast ECAS was calculated by assuming a sample volume of 63–625 mm³ (current density of 100–1500 A mm⁻² and voltages of 3 V–30 kV). The peak power densities in FS are derived from Raj et al. [12], even higher peak dissipation can be reached during switching from voltage to current control mode. The discharge time does not account for incubation time. The peak power densities in SPS have been calculated assuming a power of 1–10 kW for a graphite moulding having diameter of 20 mm.

Figure 3. The temperature-dependence of conductivity of typical metallic, semiconductor (narrow and wide band gap) and ionic conductor, W (T_m = 3380°C) [21], Cu (T_m = 1084°C) [22], B_4.3C (T_m* = 2447°C) [23], SiC (T_m* = 2730°C, 3.1 eV) [24], YSZ (T_m ≈ 2700°C) [25], BaTiO₃ (T_m = 1618°C, 1.55 eV) [26], Al₂O₃ (T_m = 2050°C) [27]. Colour coded: metals (grey), semiconductors (green), oxygen ion conductors (blue) and insulating oxides (red). * The material might decompose before melting.

Figure 4. Schematic representation of different FS experimental setups: (a) sample is suspended in a furnace using two Pt wire electrodes (adapted from Cologna et al. [33]); (b) sample is pressed between two electrodes (adapted from Caliman et al. [34]); (c) a commercially available SPS machine is used (adapted from Grasso et al. [35]); (d) contactless mode where a plasma is used to carry current across the sample (adapted from Saunders et al. [36]); and (e) setup developed at Rutgers University (RU Tech ID#: 2014-056).

Figure 5. (a) Power density and shrinkage relationship in 3YSZ under a field of 100 V cm⁻¹ (DC). (b) Powder density and specimen temperature measured by lattice thermal expansion in situ by synchrotron during FS of 3YSZ under a field of 170 V cm⁻¹ (DC). Adapted from Raj [19] and Lebrun et al. [62].

Table 1. Sets of real-time input and output parameters that can be adjusted and recorded during FS.

Input	Output
Materials (crystallite size, purity, sample preparation etc.)	Shrinkage (Section 2.2.1)
Sample geometry (aspect ratio and surface/volume ratio)	Electrical parameters (Section 4.1.7)
Applied potential difference (current, voltage, power and frequency and waveform)	Sample temperature (Section 2.2.2) IS analysis (Figure 6b)
Pressure (externally applied uniaxial load)	Optical emission spectroscopy
Sintering time (t)	In situ XRD (Figure 8)
Sintering atmosphere
Flash configuration (Figure 4)
Electrodes (material and configuration (i.e. contactless, sliding))
Heating furnace to reach TOnset

Figure 6. (a) FS setup and dimensions of DBS green sample (adapted from Naik et al. [63]). (b) Sketch of the experimental setup for dilatometric measurements which can be coupled with impedance spectroscopy during the FS event. LVDT and Pt–Pt 10%Rh thermocouple are used to measure the linear shrinkage. Adapted from Francis et al. [49].

Table 2. Physical principle and probing position for the different temperature measurement methods used in the literature.

Method	Principle	Probing position, local or averaged, Source of error
Thermocouple	Heat transferred to an electrically insulated metals junction	Surface, Local Thermal contact and thermal insulation of the thermocouple
Pyrometer/thermo-cameras	Spectral radiation intensity of samples at given wavelengths	Surface, Local Uncertain emissivity and electroluminescence
Optical emission spectroscopy	The spectral emission from the sample	Surface, Local Blackbody radiation fitting
Impedance analysis	The relationship between impedance and temperature	Bulk, Averaged Change in sample shape/dimensions and characteristics*
Thermal expansion	The relationship between thermal expansion and XRD peak positions of Pt placed on samples	Bulk, averaged, Change in material shape (e.g. softening)

Depending on the method of measuring the temperature, there might be some significant errors in the measurements.

*Any modification in the material during FS induced by application of electric field such as electrochemical reduction, changes in composition and phase transformation etc.

Figure 7. Emission spectra collected in situ for W powder matching black body radiation and temperatures (obtained from black body radiation fitting) at different time intervals [68].

Figure 8. The arrangement for in situ XRD experiments at the Pohang Light Source II. Adapted from Terauds et al. [71].

Figure 9. Pie chart showing the number of papers published on FS, grouped by material type. The conductivity mechanism (at T_Onset) is colour coded: oxygen ion conductors (blue), insulating oxides (red), semiconductors (green), metals (grey). Some materials might show a mixed conductivity mode depending on the temperature. Some of the materials have been consolidated as composites.

Figure 10. (a) Research papers published starting from July 2010 till the May 2016. (b) Pie chart showing the nationality of first author’s institution.

Figure 11. (a) Arrhenius plot of volumetric power dissipation for several different ceramics sintered by FS using DC fields. The furnace heating rate was 10°C min⁻¹ and the currents were limited to 80 mA mm⁻². The dark grey region with a power dissipation ranging from 7 to 40 mW mm⁻³ highlights the ‘abrupt’ increase in electrical conductivity of the sample. The sample is DBS with gauge length 20 mm and cross-section 3 × 1.6 mm². (b) Linear shrinkage measured during FS of 3YSZ under various DC electric fields. (c) Multi-layered NiO–ZrO₂ anode to 8YSZ electrolyte with and without the applied field (DC) heated at a rate of 10°C min⁻¹. Adapted from Lebrun et al. [62], Cologna et al. [5], and Francis et al. [49], respectively.

Table 3. Experimental procedures for FS, including materials, conductivity mode, crystallite size of starting powder, sample size, FS condition current, voltages, relative density and grain size of the produced materials.

Ref, First author, publication year	Composition, crystallite size, purity(%), conductivity mode*	Sample size (mm) before sintering	Sintering conditions		Characterisation of sintered materials
			Field, current dens., Vol. power density, Time, TF, TS, Pressure	Waveform (AC, DC)	Relative density (%)	Average grain size (µm)
3YSZ and its composites
Cologna et al. (2010) [5]	3YSZ, I, V	DBS, L = 21, W = 3, T = 1.58	20–120 V cm^−1, 1–5 A, TF 900–1300°C	DC	…	…
Francis et al. (2012) [82]	3YSZ, P = 1,2,5 and 10 µm, I, V	DBS, L = 20, W = 3.3,T = 1.6	20–120 V cm^−1 <80 mW mm^−3, TF 920–1040°C,	DC	68–96	200–400 nm
Francis et al. (2012) [42]	3YSZ, P = 60–70 nm, I, V	D = 5, H = 10	100 V cm^−1, 0.1 A, TF 750–1050°C, 1.5–12 MPa	DC	95–98	135 ± 15 nm
Todd et al. (2015) [13]	3YSZ (T), I, V	After sintering L = 10.0, CS (L = 5.0, W = 1.5)	80–1200 V cm^−1, 0.5 A, TF 800–1200°C	DC	99	…
M'peko et al. (2013) [70]	3YSZ, I, V	DBS	55 V cm^−1 , 1 A, 900°C	DC	98.3–98.6	308–526 nm
Qin et al. (2016) [74]	3YSZ, I, V	DBS L = 21, W = 3,T = 1.58	100 V cm^−1, 50–100 mW mm^−3, 2–60 s, TF 900°C	AC and DC	…	1–100 µm
Jha et al. (2016) [83]	3YSZ, I, V	…	60–120 V cm^−1, 67 mW mm^−3, 1–5 s, TF 800°C	DC	…	…
Lebrun et al. (2016) [39]	3YSZ, P = 70 nm	DBS L = 3.5, W = 1.3,T = .65	TS 800–1600°C	DC	70–80	200–350 nm
Francis et al. (2013) [49]	3YSZ, I, V	DBS, L = 20, W = 3.1,T = 1.8	100 V cm^−1, 20–120 mA mm^−2, TF 900°C	DC	…	…
Terauds et al. (2015) [71]	3YSZ,P = 60 nm, I, V	B, L = 3.25, CS (1.3 × 0.58)	1200 V cm^−1, TS 800–1600°C,	DC	…	…
Naik et al. (2014) [84]	3YSZ–Al2O3 composite, I, V	DBS, L = 21, W = 3.3, T = 1.8	50–100 V cm^−1, 50 mA mm^−2, TF1000–1300°C	DC	80–95	690–760 nm (3 YSZ) 680–730 nm (Al2O3)
Liu et al. (2016) [85]	3YSZ SiC (10 wt-%)-	DBS, L = 20, W = 3.34, T = 1.26	100 V cm^−1, 80 mA mm^−2, 60 s, TF 1000°C	DC	97	230 nm
8YSZ and its composites
Baraki et al. (2012) [86]	8YSZ, P = 20–30 nm, 99.9%, I, V	D = 11, H = 6	40–100 V cm^−1, 65 A mm^−2, TF 1200°C	AC (50 Hz)	73–83	1.27 ± 0.55 µm
Downs et al. (2013) [38]	8YSZ, C = 20 nm, I, V	DBS, L = 21, W = 3, T = 2.25 ± 0.05	60–2250 V cm^−1, 120 mA, TF 390–960°C	DC	…	…
Muccillo et al. (2011) [75]	8YSZ, I, V	D = 5 or 7, H = 3	15 V, 10 mA mm^−2, TF 900°C	AC (1 kHz)	94	200 nm
Steil et al. (2013) [57]	8YSZ, P = 30 nm, I, V	D = 8, H = 2	500 V cm^−1, 30 mA mm^−2, TF 800–975°C	AC (1 kHz)	90–97	100 nm
Cologna et al. (2011) [66]	8YSZ, P = 0.15 µm, I, V	DBS, L = 21, W = 3.2,T = 2	30–150 V cm^−1 , 10 mW mm^−3, 750°C	DC	96	0.47–0.49 µm
Muccillo et al. (2013) [50]	8YSZ, I, V	D = 5, H = 5	100–200 mV, 100–500 mA, TF 800–1000°C	AC	…	<500 nm
Park et al. (2013) [69]	8YSZ, I, V	Cylinders with different sizes	160 V cm^−1, 800 mA, TS > 1500°C	DC	…	…
Francis et al. (2013) [49]	Multi-layered NiO–ZrO2–cubic ZrO2	DBS, L = 21, W = 3.2,T = 2.7	150 V cm^−1, 120 mA, TF 390–960°C	DC	99	…
Yttria
Yoshida et al. (2014) [47]	undoped Y2O3, e, h for T > 900°C	DBS, L = 20, W = 3.5, T = 1.0	75–1000 V cm^−1, 5–60 mA, TS ≈1550°C	DC	93–99	1000 V cm^−1 0.97 µm
Yoshida et al. (2016) [87]	1mol-% Ni^2+-doped Y2O3	DBS, L = 20, W = 3.4,T = 1.1	750 V cm^−1, 60 mA, TF 876°C	DC	96–98	1 µm
Fuel cell materials
Hao et al. (2012) [88]	Ce0.8Gd0.2O1.9, G = 0.3 µm, I,V	DBS, L = 20, W = 3.2,T = 1.24	70 V cm^−1 10 mW mm^−3, TF 545°C	DC	100	0.3 µm
Jiang et al. (2015) [76]	Ce0.8Gd0.2O1.9 Ce0.9Gd0.1O1.95, Ce0.8Sm0.2O1.9, ≥99.5%, I,V	Bar, L = 25, CS (6.5 × 1.6)	55 V cm^−1, 0.9 A, TF 554–667°C	DC	93.7–99.8	0.25–0.33 µm
Muccillo et al. (2012) [89]	BaCe0.8Gd0.2O3−δ, I,P	D = 5.0, H = 4.5	0–62 V, 2700 mA, TF 910°C	AC (1 kHz)	84	…
Gaur et al. (2015) [52]	(La0.6Sr0.4) (Co0.2Fe0.8)O3–Gd0.1Ce0.9O2 composite, I	DBS, L = 20, W = 3.5, T = 1.0	5–150 V cm^−1, <1.5 A mm^−2, TF 210–990°C	DC	99	1–2.5 µm
Lisenker et al. (2016) [59]	Li1.5Al0.5Ge1.5(PO4)3	–	300 V cm^−1, 40 mA mm^−2, TS 800°C	AC (1 MHz)	80.3	…
Alumina and its composites
Cologna et al. (2011) [33]	MgO-doped α-Al2O3, P = 100–300 nm, >999.99%	DBS, L = 21, W = 3.3, T = 1.8	1000 V cm^−1, 60 mA, TF 800–1400°C	DC	99	1.9 µm
Bichaud et al. (2015) [90]	Al2O3/TZP composite	D = 8, H = 5	100 or 200 V cm^−1,100–200 mA mm^−2	AC	…	80 nm (ZrO2) 100 nm (Al2O3)
Downs et al. (2016) [91]	Al2O3/TZP composite	D = 10, H = 3	<700 V cm^−1,100–200 mA mm^−2	DC	…	100 nm (ZrO2)
Naik et al. (2014) [63]	3YSZ–Al2O3 composite, 99.99%, I, V	Before DBS, L = 21, W = 3.3, T = 1.8	50–150 V cm^−1, 84 mA mm^−2, TF 1060–1400°C	DC	97–99.8	652 ± 122 (3 YSZ) 772 ± 150 nm (Al2O3)
Liu et al. (2015) [92]	Al2O3–Y3Al5O12–ZrO2 eutectic	Cylinder	495 V cm^−1, 0.3 A, TF 1345°C	DC	4.4 g/cm^3	0.3–3 µm
Caliman et al. (2015) [34]	β-alumina (MgNa2Al10O17), P = 300 nm	Cylinder, D = 8, H = 4	100–120 V cm^−1, 8–100 mA mm^−2, 1 kHz, TF 550°C	AC	88	…
Biesuz et al. (2016) [53]	α-Al2O3	DBS, L = 20, W = 3.3,T = 1.6	500–1500 V cm^−1, 2–7 mA mm^−2, TF 900–1400°C	DC	3.8 g/cm^3	…
Bajpai et al. (2016) [93]	Ca5(PO4)3(OH)	DBS, L = 20, W = 3.3,T = 1.6	750–1000 V cm^−1, 8–10 s, TF 1020–1060°C	DC	full density	160–320 nm
Functional dielectrics
M'Peko et al. (2014) [94]	BaTiO3, P = 70 nm, 99.98%, E	DBS, L = 20, W = 3.5,T = 1.6–2.0	500 V cm^−1, 9.3 mA mm^−2, TF 688°C	DC	94	300–400 nm
Uehashi et al. (2015) [77]	BaTiO3, 99.9%, E	Bar (2 × 10 × 30)	100 V cm^−1, 1020°C	DC	90–95	…
Shomrat et al. (2015) [78]	KNbO3, C = 1–3 µm	D = 3, H = 10	600 V cm^−1, TF 750°C	DC	95	1–3 µm
Corapcioglu et al. (2016) [83]	K0.5Na0.5NbO3	DBS, L = 20, W = 3.5,T = 1.2	100–500 V cm^−1, 7–40 mA mm^−2, 10–60 s, TF 900–1090°C	DC	95	…
Karakuscu et al. (2012) [48]	SrTiO3, P = 0.15 µm, 99.9%	DBS	150–1000 V cm^−1, 60 mA, TF 390–960°C	DC	95	1 µm
Oxides semiconductors
Jha et al. (2015) [40]	TiO2, P = 20 nm, 99.995%	L = 3.7 CS (1.33 × .55)	100 V cm^−1, 25 mA mm^−2, TF 800°C	DC	…	3–5 µm
Jha et al. (2014) [95]	TiO2 (P = 20 nm, 99.995%)-Al2O3 (P = 10 µm, 99%)	DBS, L = 19.8, W = 3.4, T = 1.1	250 V cm^−1, 18 mA mm^−2, TF 850°C	DC	90–98	…
Zhang et al. (2016) [79]	TiO2 (P = 30 nm, 99.9%)	D = 6.4, H = 1	500 V cm^−1, 20 mA mm^−2, 30 s, TF 900–1078°C	DC	86–97	0.21–1.11 µm
Muccillo et al. (2014) [58]	SnO2, SnO2–2 wt-%MnO2	D = 5, T = 5–7	80–100 V cm^−1, 1–5 A, TF 900–1300°C	AC (1 kHz)	94	722–757 nm
Schmerbauch et al. (2014) [41]	nanocrystalline ZnO, P = 16 ± 4 µm	D = 5.04, H = 5 ± 0.05	0–160 V cm^−1 (50 Hz), 140 mA mm^−2, TF 700°C	AC	94–95	970 ± 210 nm
Zhang et al. (2015) [96]	ZnO	D = 6.4, H = 1	300–1000 V cm^−1, <120°C in Ar + 5 mol-% H2, 1–4 A	DC	>97	∼1 µm
Zhang et al. (2015) [56]	Bi2O3 (P < 0.5 µm, 99.9%)-doped ZnO (P = 90–210 nm, 99.8%)	D = 6.4, H = 4	300 V cm^−1, 1 or 4 A, TF 870°C	DC	88.2–90.8	13.1–12.6 µm
Non-oxide semiconductor
Solvas et al. (2013) [80]	SiC, P = 0.45 µm, E	D = 10, H = 2.5–3	360 V,15 A, TF 1170–1670°C	DC	56–88	1–2 µm
Grasso et al. (2016) [61]	SiC, E	D = 20 or 60, H = 3 or 10	<10 V, 2 kA, 15 s TS 2300°C, ≈15 MPa	Pulsed DC	96	10–20 µm
Grasso et al. (2016) [43]	SiC, E	D = 60	Similar to above line	Pulsed DC	…	Highly textured crystal, 500 µm
Niu et al. (2016) [32]	B4C, P = 2.36 µm, E	Cylinder	1.4–2 kA, 5 s, die temp 1931°C	DC	94.3	3.5 µm
Metallic conductor
Gaur et al. (2014) [97]	MnCo2O4, P = 1.17 µm, E	DBS, L = 20, W = 1.65,T = 3	15–17.5 V cm^−1, 1.4–1.6 A mm^−2, TF 120–150°C,	DC	…	8 µm
Prette et al. (2010) [37]	MnCo2O4, P = 10 µm, E	DBS, L = 21, W = 3.27 ± 0.02, T = 1.10 ± 0.08	7.5–12.5 V cm^−1, <10 A, TF 325°C	DC	99	18.7 ± 0.2 µm
Grasso et al. (2014) [35]	ZrB2, P = 2.4 µm, E	D = 20 H = 8	25 kW,1.5 kA, TS 1452–2198°C, ≈15 MPa	DC	75.9–95	2.6–11.8 µm
Castle et al. (2016) [98]	Nd–Fe–B, 50 nm E	D = 20 H = 12	12 kW,10, TS 1080°C, ≈15 MPa	DC	≈100%	Aspect ratio 11

The reported values are indicative of the processing conditions. Some values were not given, we tried to collect most of the representative data.

*Conductivity mode under probing voltages, DBS: dog-bone shape, L: length, W: width, T: thickness, D: diameter, H: height, CS: cross-section, P: particle size, C: crystallite size, conductivity modes I: ionic E: electronic. Charge carries h: hole, V: vacancy, E: electron, P: proton.

Figure 12. SEM micrographs of (a) 3YSZ, (b) 8YSZ and (c) Y₂O₃ FSed as described in the text above using DC fields. Adapted from Baraki et al. [86], M'Peko et al. [70], and Yoshida et al. [47], respectively.

Figure 13. Effect of applied electric field (0–1000 V cm⁻¹) on the shrinkage for (a) pure Al₂O₃ and (b) MgO (0.25 wt-% MgO) doped Al₂O₃. The resulting SEM micrographs for MgO-doped Al₂O₃ obtained using (c) FS (1000 V cm⁻¹, DC) T_F = 1260°C) and (d) conventional sintering (1550°C for 1 h), the resulting grain sizes were 0.8 and 1.5 µm. In both cases the furnace heating rate was 10°C min⁻¹. Adapted from Cologna et al. [33].

Figure 14. SEM micrographs of SrTiO₃ obtained using (a) FS (150 V cm⁻¹ DC), T_F = 1200°C) and (b) conventional sintering (1400°C for 1 h). Adapted from Yoshida et al. [47].

Figure 15. (a) Microstructure of FSed BaTiO₃ at an applied voltage (DC) of 250 V cm⁻¹ and current limit of 9.3 mA mm⁻², T_F = 822°C. (b) TEM bright field image and the electron diffraction pattern of a secondary phase in flash-sintered BaTiO₃ at an applied voltage of 100 V cm⁻¹ (DC), T_F = 1020°C for 60 s. (c) Microstructure of flash-sintered KNbO₃ with applied electric field of 600 V cm⁻¹ (DC), T_F = 750°C. Adapted from M'Peko et al. [94], Uehashi et al. [77], and Shomrat et al. [78], respectively.

Figure 16. Microstructures of ZnO obtained using at 80 V cm⁻¹ (AC) stopped (a) before and (b) after FS as well as fully sintered specimens at (c) 0 V cm⁻¹ for 2 h, (d) 40 V cm⁻¹ for 1 h, (e) 80 V cm⁻¹ for 2 h and (f) 160 V cm⁻¹ 1 h, with T_F = 700°C. Current densities were between 54 and 151 mA mm⁻². Adapted from Schmerbauch et al. [41].

Figure 17. (a) SEM micrograph of FSed Co₂MnO₄ (DC). (Adapted from Prette et al. [37]). (b) The relative density and grain size vs. discharge time for FSPSed (pulsed DC) ZrB₂ sample and (c) SEM microstructure of ZrB₂ after 35 s discharge. (Adapted from Grasso et al. [35] (d) SEM micrograph of Nd–Fe–B type permanent magnetic material with aligned nanocrystalline platelike grains. Adapted from Castle et al. [98]).

Figure 18. (a) Temperature of 8YSZ samples (0.6–0.9 mm thick) under constant voltage (8–8.5 V (DC)) as function of time (no current limit). Inset: decrease in resistance (AC real component) divided by its room temperature reference value. (b) Empirical relationship between DC electric field and incubation time for FS of 3YSZ at different isotherms T_F (1000, 1200, 1275 and 1300°C). Adapted from Park and Chen [69] and Naik [106], respectively.

Figure 19. (a) Effect of particle size on the FS behaviour of 3YSZ, the shrinkage is plotted against furnace temperature with and without field (100 V cm⁻¹ (DC)) (Adapted from Francis et al. [82]). (b) Difference in conductivity for polycrystalline and single crystal 8YSZ and (c) the resulting power absorption of dense specimens while heating in flash mode. The figures were kindly provided by Professor Jian Luo from University of California, San Diego Jian Luo PDP. 2016. Private communication.

Figure 20. Shrinkage strain of 3YSZ samples under different uniaxial pressures using the setup shown in Figure 4(b) in a 100 V cm⁻¹ applied field. Adapted from Francis [54].

Figure 21. (a) Measured electric power dissipation plotted against furnace temperature and (b) measured conductivity as function of the reciprocal of the estimated T_S for FS ZnO using four different atmospheres (in a 300 V cm⁻¹ DC electric field). Adapted from Zhang and Luo [96].

Figure 22. FS attempts in β-Al₂O₃ with different electrode materials and atmospheres during isothermal at 550°C under an applied AC field of 100 V cm⁻¹ (AC). FS occurred when Ag electrodes were used instead of Pt. Adapted from Caliman et al. [34].

Table 4. Bulk effects occurring within the material as result of DC bias applied across sample during FS.

Conductivity mode	Positive electrode	Negative electrode
Electronic	No marked effect*	No marked effect*
Semiconductor (n)	Peltier effect (hot)	Peltier effect (cold)
Semiconductor (p)	Peltier effect (cold)	Peltier effect (hot)
Wide-band gap insulator	breakdown	breakdown, max heating
Ionic conductors (oxygen vacancies)	If V < Velctrochem	If V < Velctrochem
	Oxygen pumping out of sample	Oxygen pumping into sample
	If V < Velctrochem	If V > Velctrochem
	Electrochemical reduction progress toward it	Electrochemical reduction started
Ionic conductors (flow of charged species)	Ionic currents affect the reaction kinetics in diffusion couples

The asymmetric polarity induced effects depends on the materials conduction mode and current density.

*Electromigration effects requires very high current densities (order of 10⁶ A cm⁻²) [111], migration direction sign is given by effective charge of a chemical element.

Figure 23. (a) The relationship between AC conductivity measured at room temperature plotted against the amount of oxygen deficiency of 3YSZ. Adapted from Sano et al. [113]. The sample was reduced in controlled conditions using electrochemical reduction. (b) Electrical conductivity (real component) for 12YSZ measured using IS for low and high sub-stoichiometric (ZrO_2−X) samples. Adapted from Levy et al. [114].

Figure 24. SEM micrograph of fracture in 8YSZ along a cross-section parallel to the electric field (50 mA mm⁻², (DC) electric-loading time: 1440 min at T_F of 1250°C, thickness: 1.5 mm). Adapted from Kim et al. [116].

Figure 25. SEM micrographs of the fractured surfaces of FSed ZnO (300 V cm⁻¹, DC): (a) near the anode; and (b) cathode, respectively. (Adapted from Zhang et al. [56]). A schematic of the Peltier effect occurring during FS for an n-type semiconductor was added by us.

Figure 26. Images of 5L5NS during 150 V cm⁻¹ (DC) when the furnace temperature was (a) T < T_Onset and (b) T_Onset < T < T_Soft of EFIS. The anode and cathode are at the top and the bottom, respectively. (c) Photoemission spectra at the 200 V cm⁻¹ test condition ranging from 350 to 900 nm for NS and 2L8NS. Note: Intensity of 2L8NS was offset by an arbitrary amount for comparison. (Adapted from McLaren et al. [123]). (d) Emission spectra of Na and Li oxidation (added by us).

Figure 27. (a) Temperature dependence (Arrhenius-like plot) of macroscopic conductivity for the bulk and grain boundaries (gb) in 3YSZ (adapted from M’Peko et al. [70]). (b) Comparison of mechanical bending strength in 3YSZ (adapted from Francis [54]). (c) O-K edge ELNES profiles in undoped Y₂O₃ obtained using a* conventional sintering at 1600°C in air, b* at 1550°C in flowing N₂ + 5% H₂ gas, and c* FS at 1000 V cm⁻¹ (adapted from Yoshida et al. [87]). (d) PL intensity (black) and DLE to NBE ratio (blue) in ZnO specimens as function of external electrical fields (adapted from Schmerbauch et al. [41]). (e) Raman spectra of (top) FSPS (35 s) and conventional SPS (2100°C) samples (adapted from Grasso et al. [35]).

Table 5. Atomic ratios in 10 mol-% Y₂O₃-doped ZrO₂ bicrystal with a symmetric 24° [001] tilt grain boundary.

	Y/Zr	O/Zr	O/Y
Bulk	0.25 ± 0.04	2.12 ± 0.13	8.48 ± 1.45
Grain-boundary core	0.50 ± 0.07	1.65 ± 0.23	3.30 ± 0.65

These materials were processed in absence of an electric field. Future work is needed to clarify how an electric field would affect the atomic distribution at the grain boundaries.

Figure 28. (a) Blackening observed in 8YSZ after flash heating of dense samples at T_F = 800°C, the current was limited to 65 mA mm⁻² (voltage was increase at 5 V min⁻¹ (DC)). The dense material had grain size of 0.66, 3.8, 5.3, 11.5 µm from left to right. The cathodic reaction occurred at the upper side, blackening was apparent for all samples except the one with 0.6 µm. (b) Measured current plotted against electric field (4 point measurements) for 8YSZ single crystal (T_F = 600°C) heated in flash mode (voltage was increase at 5 V min⁻¹ until runaway took place), the deviation from the Ohmic behaviour at a field of 25 V cm⁻¹ and current density of 0.01 mA mm⁻² corresponded to the blackening. Both figures adapted from Downs [134].

Table 6. Summary of work carried on modelling of FS. Materials, type of modelling, results achieved and limitation/assumption of the models are listed.

Materials and Ref.	Type of modelling	Results achieved	Assumption and limitations
3YSZ [67]	FEM modelling analysis of temperature distribution during FS	Predict temperature distribution inside the sample.	The model does not account for sample shrinkage.
8YSZ [19]	Stationary heating based on black body radiation	Estimate sample surface temperature in stationary conditions	It is difficult to apply the model during transitory heating
3YSZ [13]	Analytical, modelling of Joule heating and significance of temperature dependence of electrical resistivity	Predicted the thermal runaway for NTC due to inverse Arrhenius dependence of resistivity on temperature	Effects of shrinkage are not considered. Conductivity is derived from electrical data instead of being measured on the material in equilibrium conditions
3YSZ [141]	Analytical solution, solve the energy balance equations	Predicts sample temperature distribution and conditions for thermal runaway	Applied to samples with cylindrically geometry
Several materials [142,143]	Analytical, predicts thermal runaway and relates TOnset to the applied field	Predicts a linear dependence of versus TOnset^−1	The analysis is limited to TOnset under constant voltage mode
3YSZ, BaTiO3 [144]	Bifurcation theory used to explain the onset of FS	The temperature dependent resistivity is sufficient to predict the occurrence of the flash event	Mostly applied to the initial stage of FS around TOnset
3YSZ [84]	Analytical, based on surface energy balance for nucleation under an applied field	Models incubation time as a transition from insulation to conductive state	The model does not describe in detail the nucleating phase
3YSZ [145]	Analytical, grain growth kinetics under a DC bias	Grain growth inhibition induced by vacancy segregation at the grain boundary	It does not account for polarity induced effects (Section 4.1.6)
ZnO and ZnO–Bi2O3 [56]	Predict thermal runaway based on heat generation and its dissipation	Predicts onset	It is limited to the initial stage of FS

Figure 29. FEM simulation of T_S distribution in 3YSZ for the application of 70 W electric power supply (DC) for 3 s. Sample gauge section: 120 V cm⁻¹; T_F: 850°C. Adapted from Grasso et al. [67].

Figure 30. FS data taken from literature showing the linear relation between vs. 1000/T_Onset. The linearity is applicable to semiconductors circled in green, oxygen ion conductors in blue, and insulating oxides in red. Adapted from Dong and Chen [143] references are numbered in the original work.

Figure 31. First industrial scale demonstration of FS process for continuous manufacturing of floor tiles (15 × 15 cm) fabricated using FS. (courtesy of Lucideon Ltd., UK).

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