Sonochemical Reactions Chemical changes/reactions induced by ultrasound No direct interaction of ultrasound field with molecules (in contrast to photochemistry,...) •Liquid phase reactions - chemical reactions driven by cavitation effects • Solid state reactions - introduction of defects = speeding up diffusion Sound Sound = pressure waves = periodic compression/expansion cycles traveling through a medium possessing elastic properties (gas, liqud, solid) Liquids and gases - longitudinal pressure waves - compression/rarefaction Solids - longitudinal and transverse waves The energy is propagated as deformations (tensile/compressive stress) in the media The molecules oscillate about their original positions and are not propagated The propagation of a sound wave = the transfer of vibrations from one molecule to another Longitudinal Pressure Waves T Sound In a typical liquid, the speed of sound decreases as the temperature increases, at all temperatures. The speed of sound in water is almost five times greater than that in air (340 m s1) Substance Speed of sound, u [m s-1] Air 343 Helium 965 Water 1482 Lead 1960 Steel 5960 Granite 6000 Speed of Sound The speed of sound (u) „2 = 1/Kp= [9P/dp]s~l/(<(fV)2>) ks = adiabatic compressibility p = density P = pressure 1600 tit £1500 Cfl 1400 «1300 —#- (/) 1200* 50 100 150 Temperature, ° C 200 Sound Intensity Sound Intensity = Power / area = Watts/m2 Source of Sound Intensity (W/m. 2) Sou Jet Airplane 30 m away 102 140 Air-raid Siren, nearby 1 120 Threshold of Pain 101 120 Concert -101 115 Riveter 103 100 Busy Traffic 105 70 Normal Conversations 106 60 Whisper 10-io 20 Threshold of Hearing 1012 0 0 dB (10 12 W/m2) 10 dB = 10 as intense 20 dB = 102 as intense 30 dB = 103 as intense 120 dB = 1012 as intense Pa = PA sin 2ti ft Pa acoustic pressure PA pressure amplitude f sound frequency c = A,f (for 20 kHz, X = 7.5 cm) p = p _|_ p r total ra rh Ph hydrostatic pressure Acoustic Pressure TT JU mAW compression compression displacement (x) graph Acoustic Pressure i i i compression compression displacement (jí) graph Compression and rarefaction (expansion) regions PA = driving pressure amplitude [Pa] I = irradiation intensity fW m~2] (500 W system - 1.3 105 W m2) p = liquid density fkg m~3] c = sound velocity in liquid fm s_1] -r (Water 1482 m s1) PA = 620 700 Pa = 6.2 bar Ultrasound Utrasound frequencies from 20 kHz to 50 MHz Generation of Ultrasound Transducer - a device converting one type of energy into another gas driven liquid driven electromechanical whistle (F. Galton), liquid atomizer siren liquid whistle homogeniser, a jet of liquid passed through an orifice on a thin metal blade, vibrations, cavitation, mixing of immiscible liquids, ketchup, mayonnaise magnetostrictive, Ni, Co/Fe, Al/Fe, Tb/Dy/Fe alloys shrink when placed in mg. field, solenoid, pulses, upper limit 100 kHz, cooling piezoelectric, oposite charges applied on crystal sides, contraction/expansion, quartz, Pb(Zr/Ti)03 ceramics (PZT), up to MHz Generation of Ultrasound casing containing transducer element upper fixed horn (booster) detachable horn replaceable tip generator screw fitting at null point Sonochemical Reactor Piezoelectric transducer Piezoelectric Ultrasound Generator Ultrasound Processor VCX 500 W Reaction vessel Sonochemical Reactor Ultrasound Processor VCX 500 W Frequency 20 kHz 0 to 40 °C Argon (flow rate 62 cm3 min-1) TIME of ultrasound treatment PULSE irradiation and a dwell time 2:2 TEMP maximum temperature 50 °C AMPL amplitude 50 % Sonochemical Reactor Ti alloy horn, minimum lenght is a half-wavelength of sound in a material, 26 cm for 20 kHz in Ti, multiples of 13 cm vibration amplitude 5-50 [im no gain in amplitude amplitude gain D/d amplitude gain D/d stepped nodal point amplitude gain (D/d)' Sonochemical Reactor PZT wafers MM L Front Mass I i I J i __ 10-20 jrm Sandwich transducer operating at 1-200 kHz Hydrodynamic Cavitation the passage of liquid through an orifice plate the kinetic energy/velocity of the liquid increases at the expense of the pressure throttling causes the pressure to fall (Bernoulli) below the threshold pressure for cavitation (vapor pressure) cavities are generated the liquid jet expands, the pressure recovers energetic collapse of the cavities Hydrodynamic Cavitation Lord Rayleigh for the British Admiralty 1895 cavitation erosion of propeller blades ■■ R ■ 2 1 ŕ? 9rr RR+-R =-[p -P-P(t)]-4v-- a 2 pFs ° R SHEET CAVITATION LEADING EDGE DETACHMENT The University of Texas at Austin @ 1996 S.A. Kinnas FACE SHEET CAVITATION / TIP VORTEX CAVITATION (developed) CLOUD CAVITATION BUBBLE CAVITATION HUB VORTEX CAVITATIO N TIP VO RTEX CAVITATIO N (inception, desinence) Snapping Shrimp snaps a claw shut to create a water jet - speed of 30 m/s, or 100 km/h a drop of the pressure to below the vapor pressure of water - cavitation bubbles acoustic pressures of up to 80 kPa at a distance of 4 cm The pressure wave is strong enough to kill small fish M. Versluis, B. Schmitz, A. von der Heydt, D. Lohse, How Snapping Shrimp Snap: Through Cavitating Bubbles. Science 289, 2114-2117 (2000) E4 S ».H d 'I PC S-3 QQ ■ ■ ■ -1.0 -0,5 00 TlMEíms) Snapping Shrimp 4 3 2 g 1 "o (2 0 30 -i in- S 0.20- PC H 0.10- Pi 1=3 0.00 -o.io d ■o Z ~ c„ £ 0.30' —l ^ :•■ S 0.20- a," 0.10" 5a 0.00 g-0.10 Pu D. Lohse, B. Schmitz, M.Versluis, Nature 413, 477-478 (2001) -1.00 -0.75 -0.50 -0.25 -0.00 TIME ŕmst -LOO -0.75 -0.50 -0.25 -0.00 TIMEínt&> Snapping Shrimp D. Lohse, B. Schmitz, M. Versi u is, Nature 413, 477-478 (2001) intense flash of light + 0.21 ms Acoustic Cavitation Cavitation effects = creation, growth, and implosive collapse of bubbles (1-2 jus) in a liquid = implosion HOT SPOT (1 ns) TRANSIENT CAVITATION: ■ THE ORIGIN OF SONOCHEMISTRY Compression II Vwwwww Expansion ^ú«i E — 1Q(M ' ■ IMPLOSION SHOCKWAVE FORMATION ------r- ^ÜU ■300 .100 RAR D QUENCHING —I------ ■ stable cavitation - bubbles oscillate for many cycles transient cavitation - transient cavities expand rapidly collapse violently Acoustic Cavitation Cavitation effects = creation, growth, and implosive collapse of bubbles in a liquid Bubble formation = breakage of liquid during expansion, overcoming tensile strength (pure water 1500 bar, only 6.2 bar available) Weak spots needed = dissolved gas molecules, solid particles, trapped gases Bubble growth (300 jus), energy absorption, size oscillations critical size (170-300 urn) = most efficient energy absorption, rapid growth, inefficient energy absorption, collapse Acoustic Cavitation Standing wave Low pressure Bubble expansion Bubble collapse Light emisssion III Acoustic Cavitation Bubbles collapse = spherically symmetrical implosion, shear forces, adiabatic compression, life time 1-2 jus Hot spot = end of the collapse temperature of the gas inside bubble 5 000 - 20 000 °C (for 1 ns) surrounding liquid layer 2000 °C pressure 500 - 1500 bar Extreme cooling rates 1010 K s-1 red hot steel poured into water 2500 K s-1 Homogeneous Sonochemistry Two-Site Mechanism Cavity interior Filled with gases and vapors temperatures 5 000 - 20 000 °C pressure 500 - 1500 bar Surrounding liquid layer temperatures 2000 °C Bulk liquid Shock waves, shear forces How to Measure the Temperature inside a Bubble ? Sonoluminescence - Light generated during the implosive collapse of bubbles in liquids irradiated with ultrasound Kenneth S. Suslick University of Illinois 95% H2S04(aq.) under Ar 20 kHz (14 W/cm2) Ti horn directly immersed T = 298 K Apparent blackbody temperature Ar emission SO and 02+ emission A 14Wrcma 22 WJcma 30 WJcm2 ^^■•^^ JĽ inrri & 7 num fi.7 mri B 35 c Jí 8 000 - 15 000 K 660 ■UWattsfcm2 22 Wattsfcm1 30 Watts/cm' 730 7&0 32u Wavelength (nm) eso Fate of Bubbles under Ultrasonic Irradiation Ultrasound Bubble nuclei Dissolution Fragmentation +■ Coalescence Rectified diffusion Buoyancy "Inactive bubbles Resonance size Collapse VV SL Rectified diffusion - during expansion phase the bubble has larger surface area - more gas diffuses inside than during compression gets out Single Bubble Sonoluminescence SBSL D. F. Gaitan, L. A. Crum, 1990 a method to trap a single sonoluminescing bubble within an acoustic standing wave field Standing acoustic wave field One bubble trapped The bubble oscillates for many cycles Bubble sonoluminescence Single Bubble Sonoluminescence SBSL D. F. Gaitan, L. A. Crum, 1990 Standing acoustic wave field 1 bar One bubble levitates in the acustic field The bubble oscillates for many cycles Bubble sonoluminescence Bjerknes force sound pressure p(x,t) A 1=0 location t=T72i .,,--'' bubble ceatthetimet=Q: volume V(t) \ -*Q en- force at tlie time t=T/2 ->-;-<- t ime - aver age d f or ce: C. A. and V. Bjerknes The force on an object in a liquid depends on its volume and the pressure gradient, the time averaged force drives the bubble towards the antinode of sound pressure and keeps it there. Single Bubble Sonoluminescence SBSL Proper conditions for a single sonoluminescing bubble within an acoustic standing wave field SBSL intensity Single Bubble Sonoluminescence SBSL Sonoluminescence Pulses 50 ps IOC- SD- in 3 3 o- Driving oressure ' ?avn P* -0.1 *' M^»ťi ^ p»# top M *^H» ^ T □ SL - 00 -I-------------------1-------------------1— 40 eo 120 TIME (microseconds! ..i 3 Q I- O h- :•■ 160 20D Single Bubble Sonoluminescence SBSL Red - MBSL in dodecane Blue - MBSL in water, 16 kHz Green - SBSL in water, 43 kHz Black - blackbody curve for 16200 K Single Bubble Sonoluminescence SBSL Red - bubble radius Green - bubble temperature Blue - acoustic pressure 1.3 bar/25 kHz 2560 2570 2580 TIME (microseconds) 2590 -6960 * ULI CC 2581.5 2581.6 25817 TIME (microseconds) ■4640 -2320 ^290 < LU c_ LU Multi Bubble Sonoluminescence MBSL Multi-bubble sonoluminescence Spatial and temporal average 250 bar Sonoluminescence Light generated during the implosive collapse of bubbles in liquids irradiated with ultrasound 85% 1-1,30, under Xe 85% H2S04 under Ar Apparent blackbody temperature (all 4 spectra) 12500 ±1500 K Sonoluminescence 95% H2S04(aq.) blackbody temperature a id-" •» i "i IQ-" 10-iů; i ■^ ' • :■:■ 10-" 2QQ 300 4ÜD 500 6ŮQ 7DD EGO Wavälôníjn (-im) Ar emission an optically opaque plasma core Sonoluminescence 95% H2S04(aq.) 160 5 Q. 120 1 ^ eo co 40 11 12 1314=ť" I I I I I I I I I I ť"=4 5 6 7 8 9 1011 121314 SO 250 300 350 Wavelength (nm} SO and 02+ emission with vibronic progression 1580 ±110 K at 3.3 bar 2470 ± 170 K at 4.2 bar 3480 ±240 K at 5.1 bar 200 250 300 Wavelength (nm) Sonofusion Fraud D - D -► 3 He (0.52MeK) - n (2. 45MeF) D-D ->T(L01MeV)-n(3.02MeV) Compression Neutron burst from PN LS Time SD, lis m -3 +3 t. [IS PMT Microphone PNG Neutron-Induced \ Luminescence oluminescence 27 *t, us Shock Wave from Bubble , reaches Wall of Test Section 54 "ŕ, us PNG Microphone Chamber with test fluid Slave Wave Form Generator Power Measurement in Sonochemistry Calorimetry P = power, W P el = input power to generator P hf = high-freq. power output Power Measurement in Sonochemistry Calorimetry P = power, W T = temperature, K t = time, s Cp = heat capacity, J g1 K1 m = mass, g Volume 50 cm3 Argon atmosphere Error 5% heat capacity, J g1 K -i v-i 54 -í O' 3 Water Tetraglyme 4.2 2.08 19 Calorimetric measurement for water 75% amplitude y = 0,2284x + 20,76 20 40 60 80 Time (s) 100 120 140 Power Measurement in Sonochemistry Chemical dosimetry The Weissler reaction Volume 50 cm3 KI 0.1 M CC14 0.2 cm3 Time 30 min CCI4 + H20 2 KI + Cl2 I2 + 2 S2Q 2- X„„„ = 355 nm max s = 26303 dm3 mol"1 cm1 Cl2 + CO + 2 HCl I2 + 2 KCl 21+ S406 Weissler Reaction ci2 + co + 2 HCl I2 + 2 KCl 2 1+ S406 020^ i -g 0.10. Q.OO.t 20 40 60 C al o ri metrically determined ultrasonic power (W) 80 Power Measurement in Sonochemistry Chemical dosimetry The Fricke reaction Volume 50 cm3 (NH4) Fe(S04)2.6H20 0.001 M H2S04 0.4 M NaCl 0.001 M Time 30 min Fe3+ ^max = 304 nm s = 2197 dm3 moľ1 cm1 Fricke Reaction H,0-----•►H +OH .2+ FeZT + OH-----^ FeJT + OH 10 1.0x10"* -(a) i i i i i i i i I i i i i i i i l - ^r- e.OxlO"5 II £ II crj M -§ 6.0X10"5 II - ^__ 1 1 o E ■■—■■ £ 4.0x10"5 - S m 4) - Ll_ <-> -5 2.0x10"5 i n o ■ i ■ ...... i , 1 ..... 100 Frequency (kHz) 1000 Power Measurement in Sonochemistry Chemical dosimetry Porphyrin decomposition ratio TPPS 3.3 106 M Volume 50 cm3 TPPS ^max = 412 nm s = 500000 dm3 moľ1 cm1 Porphyrin Decomposition 0.10 1 I 1 1 I 1 1 1 I (c) £ 0.05- CO ĽL «ŕ í ŕ o ..... ■ ■ 10 100 Frequency (kHz) 1000 Power Measurement in Sonochemistry Reactor Optimization cavitating bubbles in the optimised cell (water, 20 kHz, Pus = 10 W) and simulated intensity distribution for the same geometry Heterogeneous Sonochemistry Solid surfaces = implosion, microjets, shock waves 200 urn minimum particle size at 20 kHz for microjets surface erosion removal of unreactive coatings (oxides, nitrides, carbonaceous) fragmentation of brittle materials, increased surface area Heterogeneous Sonochemistry LARGE PARTICLES SMALL PARTICLES © O (ß> surface cavitation due to defects leading to fragmentation collision can lead to surface erosion or fusion Heterogeneous Sonochemistry Solid particles in liquid = shock waves high speed interparticle collisions (500 km/s) surface smoothing, surface coating removal Ni catalytic activity in hydrogenation increased 105 fold by NiO removal localized melting of metal particles at the impact point fragmentation, increased surface area intercalation rates enhanced 200 fold in layered oxides and sulfides (V205, Mo03, MoS2, ZrS2, TaS2) Heterogeneous Sonochemistry Metal powders Cr (mp 2130 K) and Mo (mp 2890 K) agglomerate W (mp 3683 K) does not temperature at the point of impact ~ 3000 °C • ■ * Before ultrasound 30 min. ultrasound Cavitational Corrosion of the Tip Control of Sonochemical Reactions sound intensity - minimum for cavitation threshold, depends on frequency, optimum intensity for given reaction conditions, at high powers great number of bubbles hinder sound transmission, decoupling of a liquid from the source, breakdown of transducer material, 10 - 100 W cm2 sound frequency - 20 - 100 kHz, the higher the frequency, the higher power needed to actuate cavitation, stronger cavitation effects, rarefaction phase shortens at high frequency sound attenuation - proportional to the frequency, more power needed at high frequencies Effect of Frequency on Cavitation in Water to5 -. io4 g 103 £ 102 if I 10 * 1.0 ^— 0.1 — 1 i f i i t u ) 102 IQ3 104 105 106 107 Frequency (Hz) The frequency dependence of the intensity required to produce cavitation for degassed water at room temperature. The intensity required to produce vaporous cavitation above the frequency of 100 kHz rises rapidly. Control of Sonochemical Reactions volatile reactants - primary reaction site inside the bubbles, diameter 200 urn, 5000 °C, easy bubble formation, more reactant vapors inside bubbles, but the cavitation is cushioned Fe(CO)5 Fe(acac)3 FeS04 nonvolatile reactants - reaction in the thin layer (200 nm) surrounding the bubble, 2000 °C, less cushioning, more energetic cavitation (collapse) high boiling solvents - high vapor pressure inside the bubble cushions the implosion, nonvolatile solvents give less cushioning, more energetic cavitation less cavitation in viscous liquids, viscosity resists shear forces low surface tension facilitates cavitation, in water add surfactants Control of Sonochemical Reactions temperature - higher temperature increases vapor pressure of a medium, lowers viscosity and surface tension, many bubbles formed at temperatures close to solvent boiling point, a barrier to sound transmission, reaction rates decrease with increasing temperature, more vapors in bubbles ambient gas energy developed on bubble collapse: monoatomic (Ar) > diatomic (N2) > triatomic (C02) Xe: low thermal conductivity, heat of the collapsing cavity retained He: high thermal conductivity, heat of the collapsing cavity dissipitated, no reaction external pressure - higher pressure suppresses bubble formation but makes cavitation more energetic, optimum pressure for a given frequency Effect of Temperature on Cavitation in Water 10 20 40 50 60 70 Temperature {ÜQ The effect of temperature on cavitation and its associated hysteresis effect for tap water. The increase in intensity as the temperature is increased can be observed before it falls away at the boiling point. When the temperature is allowed to fall an increase in intensity is found in the region of 50-60 °C. This is quite a significant effect and appears to occur in all liquids. Sonochemical Reactions Solid surfaces = implosion, microjets, shock waves 200 jum minimum particle size at 20 kHz for microjets surface erosion removal of unreactive coatings (oxides, nitrides, carbonaceous) fragmentation of brittle materials, increased surface area Li, Mg, Zn, Al, Cu react at room temperature MC15 + Na + CO -> M(CO)5 (M = V, Nb, Ta) Mo + 6 CO -> Mo(CO)6 r. t, 1 bar, normally needs 300 bar, 300 °C R2SiCl2 + Li -> [-SiR2-SiR2-]n + LiCl monomodal MW distribution Homogeneous Sonochemical Reactions Liquids = heating/cooling by cavity implosions H20 -+ H + OH -+ H2 + H202 precursor decomposition: metals Fe(CO)5 -^ Fe + 5 CO oxides Ga3+ + H20 -> Ga(0)(OH), diaspóre nitrides, carbides, sulfides alkane cracking polymer degradation, lower MW, surface modification emulsification of immiscible liquids (oil-water, Hg-organics, polymer-inorganics) M(acac)n as Precursors « Well studied class of compounds Many elements form acac complexes M(acac) • Metal complexes - precursors in CVD, Me sol-gel, thermolysis routes to oxides • Easily chemically modified • Volatile, organics soluble Nontoxic Chemistry of M(acac)n Precursors Thermal decompositon pathway Ismail, H. M. J. Anal. Appl. Pyrolysis 1991, 21, 315-326. Ligand Removal by Water Pinkas, J.; Huffman, J. C; Baxter, D. V.; Chisholm, M. H.; Caulton, K. G. Chem. Mater. 1995, 7, 1589-1596. Sonochemical Synthesis of Iron Oxide Nanoparticles Cao, X.; Prozorov, R.; Koltypin, Y.; Kataby, G.; Feiner, I.; Gedanken, A. J. Mater. Res. 1997, 12, 402-406. Cao, X.; Koltypin, Yu.; Prozorov, R.; Katabya, G.; Gedanken, A. J. Mater. Chem. 1997, 7, 2447-2451. »t» Fe(acac)3 hexadecane Amorphous product, by heating to 700 C converted to a-Fe2 INikitenko, S. I.; Moisy, Ph.; Seliverstov, A. F.; Blanc, P.; Madic, C. Ultrasonics Sonochem. 2003, 10, 95-102. Sonochemical Synthesis of Iron Oxide Nanoparticles Amorphous sono-Fe203 Fe(acac)3 ))))) TG Fe203 maghemite 340 °C w dynam/isothermal T Composite particles (20-30 nm) Amorphous Fe203 particles (2 to 3 nm) Embedded in organic matrix (acetate) Fe203 hematite J. Pinkas, V. Reichlova, R. Zboril, Z. Moravec, P. Bezdicka, J. Matějkova: Sonochemical synthesis of amorphous nanoscopic iron(lll) oxide from Fe(acac): Ultrasonic Sonochem. 2008, 15, 256-264 Defect SDinel SEM of Nanoscopic Fe203 0.6 E CD _: o : CO __________: ■e 0.5 = O : .Q < 0.4 0.3 0.2 0.1 0.0 : IR Spectrum of Sono-Fe203 as-synthesized Fe203 (red) after calcination to 500 °C (blue) 4000 30 00 2000 1000 Wave numbe r (cm-11 IR Spectrum of Sono-Fe203 Acetate stretching rrrtiw Diketonate vibr. absent ^asV^^^/ 1566 cur1 0.65 = 0.60 = 0.55 = 0.50 = 0.45 = E 0.401 CO 8 0T35| \< ___ 0.30 = 0.25 = 0.201 0.15 = 0.101 0.051 0.001 A = vas(COO) - vs(COO) = 134 cm1 vs(COO) 1432 cm1 -----1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------1-------r 4000 3000 2000 Wavenumber (cm-1) i-------1-------1-------r "1-------1-------1-------1-------1-------1-------r- 1000 Decomposition of Acac Ligands Speculation about the nature of residual organic groups HoO H3C h3c^ ^ch3 Acetone c DRY H3C------C^C------H Binding modes of acetate groups Deacon-Phillips Rules A = vas(COO) - vs(COO) A CH3COO- = 164 cm1 A larger than ionic form = unidentate A smaller than ionic form = bidentate A comparable to ionic form = bridging CH3 0 Fe O CH3 V V CH3 O O \/ F Fe Fe rS\^ "S N" O' -o Fe Deacon, G. B.; Phillips, R. J. Coord. Chem. Rev. 1980, 3, 227-250. TEM proves amorphous character ofsono-Fe203 Electron diffraction Crystallization of Amorphous Fe203 under TEM Beam Electron diffraction Maghemite or Magnetite Time under TEM beam 5 nm Crystallization induced by heating (300 °C) HR-TEM Fe203 calcined at 300 °C ■ W EM öipmorphous Fe203 20 nm Smaller particle size on calcination - why? 20 nm TEM Fe203 calcined at 300 °C Specific Surface Area Surface area 48 to 260 m2 g"1 (BET) depending on H20 content BET surface area of the Fe203 heated to different temperatures during 12h outgassing periods The oxide surface area increases as the acetate groups are removed, then the particle size increases because of sintering 220 200 ♦ o cm 180 E ♦ < 160 CO 140 _♦♦ ♦ 120 ( • ■ i i i i i ) 50 100 150 200 250 300 350 400 Temperature, °C Composite Particles of Sono-Fe203 R-TEM (5 nm bar) rEM (20 nm bar) fmSfift refill ffi? SM Bebest •■■■■' ti*-" riaK¥si: '-' -v^řiiSáSfe ■^S'ŕ^vKSS 5 nm Composite Particles of Fe203 10 nm XRD of amorphous Fe203 heated dynamically in air up to 250, 300, and 360 °C Maghemite Y ■ Fe203 20 40 60 80 100 29 [deg] TEM of Fe203 Calcined at 600 °C Iron oxide particle size 10 to 20 nm 50 nm HT-XRD of Sono-Fe203 280 - 390 °C 10000 9000 8000 7000 Ě 6000 < 3000 2000 1000 Hematite n^^-^^^ Calcination to 1000 °C Pseudo-isothermal 390 °C 360 °C 340 °C 330 °C 320 °C 310 °C 300 °C 290 °C 280 °C 20.0 ^^^^^^ (pseudo-isothermal heating) provides ***»»*w*^^ - a different polymorph - Hematite 30.0 70.0 2Theta Ramp 1 °C min-1, 1 min equilb., 30 min data collect., 10 °C steps Hematite Particle Size coherence length D(nm) Jllu • D (nm) m 29,0 • • 27,0 • • • 25,0 • • 23,0 • # • • 21,0 • • 19,0 • 17,0 • 15.0 -I 330 380 430 480 T,°C Dependence of the coherence length, D (nm) of a-Fe203 on the crystallization temperature under dynamic-isothermal conditions of the HT-XRD measurement