Some Examples

2. Some Examples

3. Manganese zinc ferrite

5. Liquid Phase Synthesis Che5700 陶瓷粉末處理 • Very common; simple; cheap; (will generate waste water) • Easy to get multi-component product, high uniformity, dispersion in atomic scale; • Often more steps; complex inter-relationship; often need calcination to get final useful product • Classification: (the way to remove solvent) • Solvent evaporation: spray drying, spray decomposition, evaporative decomposition of solutions EDS; emulsion drying, freeze drying • Precipitation-filtration: ordinary process; homogeneous precipitation • Solvent extraction: salting out; sol-gel (?)

6. Process Introduction Che5700 陶瓷粉末處理 • Precursor in solvent (aqueous or organic) one or several precursors  chemical reaction (additive, temp., etc.)  separation from solvent  post-processing (washing, drying, etc.)  product powder • Precipitation method: co-precipitation, homogeneous precipitation, emulsion precipitation, hydrothermal precipitation, hydrolytic precipitation (referring to sol-gel, alkoxide was hydrolyzed) • Important parameters: pH, temperature, time, precipitation agent, quantity, rate of addition, method of addition, type of cation, type of solvent and quantity, reactor size and shape, other additives, stirring, atmosphere and pressure (e.g. in autoclave)  VERY COMPLEX; often rely on experimental design

7. UO2 nuclear fuel rod material; Reaction: UO2F2 + (NH4)2CO3 (NH4)4UO2(CO3)3 + 2 NH4F Complex steps  experimental design to find optimal condition quickly, e.g. Taguchi method, Plackett – Burman etc.

8. Top figure:a,b,c (in sequence)– particle size distribution after precipitation, washing/drying and calcination, agglomeration during washing and drying is obvious • Bottom figure: relation between average size (after calcination) and sintered density; only qualitative in nature.

9. reaction * Taken from JS Reed; precipitation occurs when two chemical reacting with each other, formation of particles – described by the theory of nucleation and growth

10. Expression of supersaturation Che5700 陶瓷粉末處理 • supersaturation: C = C – C or m, x • Supersaturation ratio:  = C/C • Relative supersaturation: C = C/C; x + 1 = x/x • Dimensionless growth affinity:  = /RT • For Activity & activity coefficient of ions: thermodynamic equations such as Debye-Huckel equation

11. Electrolytic Solutions Che5700 陶瓷粉末處理 • Behavior of ions: non-ideal solution; due to strong interaction between ions • electrical neutrality: z+ NA + z- NB = 0 (Aν+Bν- = ν+ A z++ν- Bz-; ν+ z+ +ν- z- = 0;) • mean ionic activity coefficient: γ±ν = (γA□) ν+(γB□) ν-where ν=ν+ +ν- • mean ionic molality: M±ν=MA ν+MB ν- • Debye-Huckel limiting law: ln γ±= - α∣z+ z-∣√I; where I = ionic strength = ½ Σ zi2 Mi (over all ions); α: parameter of system = f(T, solvent) (find it out in handbooks for common solvents)

12. =RT ln;  = (i/Ksp) 1/;  = i Ksp: ionic product at equilibrium; i = current ionic product; ratio of these two values ~ supersaturation

13. Solubility  Thermodynamic data: mainly affected by temperature, and solution environment (e.g. other ions, pH,…)

14. Solubility (2) Temp. & pH effect:DCP = dicalcium phosphate; HAP = hydroxyapatite; System of: Ca(OH)2-H3PO4 – KOH – HNO3 – CO2 – H2O; Ca/P = 1

15. ΔT: also used as a measure of supersaturation (as shown in figure); • Solubility often increase with temperature; (there are also contrary cases, e.g. CaCO3 solubility in water decrease with temperature; the reason we get “scales”)

16. Nucleation Che5700 陶瓷粉末處理 • Several cases: homogeneous nucleation, heterogeneous nucleation, secondary nucleation • For homogeneous nucleation: for its rate, we have thermodynamic model or kinetic model • Thermodynamic model: changes between surface energy and bulk energy, energy of formation of new crystals  =  Ac – ( - ) Mc [Ac: crystal surface area; Mc: crystal mass)  when nucleus size reach some critical value  d  /d(d) = 0  to get critical nucleus size d* = 4 Vm /(RT ln) •  Finally to derive the rate equation: • Bo = C exp(- */kT) & * = 32 b 3 Vm2/(RT ln)2

18. S = 

19. Kinetic Expression of Nucleation Che5700 陶瓷粉末處理 • Kinetic viewpoint: A1 + A1 = A2 + A1 = A3 …. A i+1 +.. • A1 = monomer  Then the following kinetic equations • Ci = condensation rate; Ei = evaporation rate • Under steady state d fi/dt = 0, and B.C. f1 = n1 = constant; fG = 0 or constant (G: some critical size, e.g. critical nucleus size) Zeldovich factor

20. Solute Clustering & Nucleation Che5700 陶瓷粉末處理 • Taken from JCG, 89, 202-208, 1988. • Main viewpoint: solute molecules aggregate to form clusters (precursor to nuclei), surface energy of cluster may differ from large particles (different structure). • At 0oC, for water, 76% exist as clusters • One method to study cluster size and conc. : let supersaturated solution stand for very long time  develop spatial distribution of clusters of different size, measurement by density or opacity difference. • Indirectly, width for metastable zone, provide information on cluster (narrow: cluster already exist, easy to nucleation) • Typical cluster size: 4-10nm, ~ 103 molecules

21. Heterogeneous Nucleation Che5700 陶瓷粉末處理 • Reasons to heterogeneous nucleation: larger complex size; impurity; wall of container; liquid/air interface • Due to lowering of surface energy, (lowering barrier to nucleation) • In a sense, co-precipitation: similar effect • Epitaxial growth: similar structure between nuclei and impurity surface, therefore growth of nuclei on this impurity surface • Used to make core-shell particles, core as seed to shell particles

22. Complex ions can increase size of cluster, closer to critical nucleus size, helpful to nucleation; Impurity also influence structure (phase) of product

23. More on Nucleation Che5700 陶瓷粉末處理 Taken from TA Ring, 1996; data for BaSO4

24. Secondary Nucleation Che5700 陶瓷粉末處理 • Under-saturated condition, existing nuclei induce new nucleation – secondary nucleation • Reasons include: Initial breeding; Needle breeding Contact breeding; Fluid shear etc. • parameters: degree of supersaturation, stirring, collision between suspending particles (frequency, energy, material of container etc) • Empirical relation: secondary nucleation rateBo ~ (S-1)b MTj (rpm)h; where MT = quantity of suspending particles

25. A Model on Secondary Nucleation • Taken from Botsaris, et. al. Chem. Eng. Sci., 52(20), 3429-3440, 1996; • Their concept: in supersaturated solution, existing embryos (may be viewed as a result of coagulation between clusters), they aggregate (due to van der Waals forces attractive forces), if also seed, embryos move to seed, in the neighbor of seed: high embryo concentration, they will aggregate to form new nuclei, swept by fluid to become secondary nuclei, some may aggregate with seed to make it bigger • Theory of rapid coagulation: - dn/dt = 8D r n2 = (4kT/3) n2 (by Smoluchowski) (particle movement by Brownian motion; n: particle conc.r particle radius; D diffusion coefficient)

26. Botsaris: estimate secondary nucleation rate near a seed; curve 7: assume cluster g = 622; At = seed surface area = 1.67 cm2/cm3; system: KCl-H2O; curve 6 first half: contact nucleation; second half: similar to Botsaris’ theory

27. LH left-hand左旋光結構 To demonstrate relation between seed and nuclei: use chiral compound; low supersaturation: some effect, middle: significant; high supersaturation: homogeneous nucleation

28. This impurity show inhibiting effect

29. Induction Times Che5700 陶瓷粉末處理 • From start of generation of supersaturation until observation of crystals, - induction time • Techniques to observe crystals: turbidity, visual observation, conductivity, or properties related to concentration • It include three parts: • ti = tr + tn + tg • ti : induction time; • tr: time required for attainment of stationary embryo distribution (relaxation time) • tn: time for the formation of nucleus • tg: time for nucleus to grow into detectable crystals * One possible barrier to nucleation: dehydration reaction of ions

30. More on Induction Times Che5700 陶瓷粉末處理 • If tn: major part, nucleation dominate, tn ~ 1/Bo  then ln(tn) or ln(ti) vs ln() -2 should be linear • If tg: major, ti often becomes very long, its growth may be limited by surface nucleation ln(ti) vs ln() -1 will be linear sometimes, embryo structure differs from crystal, phase change may become barrier

31. Crystal Growth Che5700 陶瓷粉末處理 • Crystal growth: mass transfer, heat transfer can not be neglected; species entering structure, may also the rate determining step • Relation between size and solubility:Ostwald-Freundlich law, similar to Kelvin equation; small size (L small) high solubility • surface nucleation mechanism  birth and spread • screw dislocation mechanism • Impurity effect: often inhibit growth by adsorption on specific site (surface), often change morphology

32. Growth steps: • Diffusion to surface; Adsorption; Desolvation; (dehydration); Surface diffusion; Integration at kink site • terminology: ledge, step and kink

33. F = surface energy xL/ xeq = a measure of super-saturation It shows small size, large solubility; for low surface energy, size effect less significant (see Kelvin equation)

34. Growth Rates Che5700 陶瓷粉末處理 • Different mechanism, different equations to show relation between growth rate and supersaturation: e.g.  Birth & Spread mechanism (2D nucleation model):  growth rate ~ (step height) x (step velocity) 2/3 x (#critical nuclei formed/area-time) 1/3  G = A i 5/6 exp(-B/i) • General empirical equation: G = k n • Note:  can be supersaturation with respect to bulk, or to surface

35. Can be classified as: linear, parabolic, and exponential law (growth rate and supersaturation)

36. More on Growth Rates Che5700 陶瓷粉末處理 • Growth rate may depend upon size, I.e. G = f(L) • Growth rate dispersion: due to different residence time, or due to surface structure & perfection • Too fast growth rate, easy to trap mother liquid (inclusion) • Heat production: interface temperature may affect solubility near interface i.e. super-saturation, or growth rate • In general: linear growth rate = mass transfer or adsorption effect • parabolic rate = spiral steps • exponential rate = polynuclear surface control

38. Growth rate proportional to density of defects (screw dislocation)

39. Accumulation of supersaturation  nucleation  supersaturation decrease  nucleation stops  growth continue  end

40. Summary on Particle Formation • Reaction  formation of some “species” (reaction kinetics)  supersaturation  (induction times) • Nucleation (home-, hetero- ..) (critical nucleus size, nucleation rate) • growth (growth rate, crystal habit, …) • agglomeration (rate of adsorption of dispersing agent) • final particle size distribution and morphology

41. Veiled: 蓋面紗的, 遮蔽的

42. Crystal Habit • Equilibrium shape versus growth shape • Former: surface energy of each surface • Latter: relative growth of each surface, depending on growth environment • Equilibrium shape: (Wulff theorem: following equation)  large surface energy, small surface area, I.e. easy to disappear

43. equilibrium shape; Elimination of high energy surface via growth

44. Different morphology: obtained under different supersaturation (AgBr);

46. From octahedron (only 111 surface), gradually change to tetradecahedron (showing 100 surface), finally to cubic (with only 100 surfaces)

47. Taken from TA Ring, 1996; by adsorbing impurity species to control morphology

48. Ostwald Ripening Che5700 陶瓷粉末處理 • An aging process, often cause coarsening of large particles at the expense of small ones • Driving force: difference between solubility between sizes (thermodynamically-driven); Gibbs-Thompson equation; also influenced by mass transfer and growth kinetics

49. (from Wikipedia) * Ostwald ripening (often water-in-oil system) vs flocculation (oil-in-water system) * Diffusion is often rate controlling process Oil droplet in pastis mixed with water grow by Ostwald ripening

50. Taken from 游佩青博士論文稿 (成大資源工程系; p.16; 2008) * Maximum growth rate size ~ 2 x average size (where growth rate = zero) a3 – ao3 = [6 D co γM/(ρ2RT)] (t – to) where a = average size, D = diffusion coefficient; co = solubility at interface; γ=interfacial energy;