Download presentation

Presentation is loading. Please wait.

Published byMeghan Hudman Modified over 3 years ago

1
1 Particle Packing Forming: strongly related to particle packing (science and technology) Results from packing: packing density and porosity Factors: particle size and distribution, particle shape, resistance of particles to pressure (deformation; binder effect), flow resistance (friction between particles) For uniform spheres: five different packing arrangements – cubic, orthorhombic, tetragonal, pyramidal, tetrahedral etc. Different packing density: higher coordination number to higher packing density, theoretical maximum: 74%. Che5700 陶瓷粉末處理

2
2 In theory, we can obtain ordered packing of mono-disperse particles; in reality, it is often to get packing as shown above (small range of ordering)

3
3 Packing Density and Pore Size Che5700 陶瓷粉末處理

4
4 Packing Characteristics Tortuosity o : for cubic packing o = 1.0; tetrahedral packing o = 1.3 Number of particle contact Nc = 3 (PF) (CN)/( a 3 ) PF = packing fraction; CN = coordination number for nonregular packing Nc = 3 (1- )/( a 3 ); since CN ~ / (usually between 6 – 10) Container wall effect (on packing): insignificant when container dia./particle dia. > 10 Use two particle sizes, small one can fill into interstice, thus increase packing density Che5700 陶瓷粉末處理

5
5 Furnas Model In theory, if three kinds particle in packing: PF max = PFc + (1- PF c ) PF m + (1- PF c )(1- PF m ) PF f f i, w = W i /W total W c = PF c c ; medium and fine the same The small particle size have to be small enough, size ratio > 7, to effectively increase packing density In industry, often mix two or more particles to get high density packing, to reach densification at lower sintering temperature Che5700 陶瓷粉末處理

6
6 圖中直線代表粒子粒徑比 值無限大的理論值 ; Highest density occurs when small particle fill completely porosity from large particles (volume fraction for fines ~ 26% or porosity from large particles ~26%) In reality, since the size ratio will not be too large, the highest point of packing density usually moves toward the middle point.

7
7

8
8 Packing of Continuous Distribution E.g. log normal distribution: theoretical calculation shows that, under random packing, larger geometric standard deviation, denser packing (spheres) Andreasen cumulative distribution (1): usually n = 0.33 – 0.5; experience: 1/n increase, packing density increase Zheng modified distribution (2): one more parameter, a min Che5700 陶瓷粉末處理

9
9 Taken from JS Reed, 1995; often packing density 60-69%; In reality, particles not very spherical, will affect packing density

10
10 Results from real particle size distributions, sample: calcined Bayer alumina; it is not very easy to rationalize

11
11 Hindered Packing Including external and internal factors: Bridging of particles and agglomerates with rough surface of walls (mechanical vibration [– tap density], lubrication, large force causing particle fracture may improve somewhat;) Coagulation, adhesion between particles also retard particle motion and hence packing into dense structure High aspect ratio often produce high porosity Adsorbed binder molecule also hinder particle movement Che5700 陶瓷粉末處理

12
12 Ordered Structure in Suspension For monodisperse particle systems: particle interaction + gravity force ordered structure (so called order- disorder phase transition question: a thermodynamic and mechanical equilibrium problem) Defects : point defect (vacancy), line defect (dislocations), planar defects (grain boundary), volume defects (cracks) Point defect: can be estimated from thermodynamics; other defects: related to processing Measurement of ordered domain size: Scherer equation (peak broadening) = FWHM = k /(L cos ) = full width at half height; k = constant ~ 0.9 Che5700 陶瓷粉末處理

13
13 本圖取自 TA Ring, 1996; Measurement of ordered array structure: light diffraction (iridescence) n = 2 d sin can estimate size of structure from diffraction peaks (d)

14
14 Sinterbility of Agglomerated Powders Source: J. Am. Cer. Soc., 67(2), 83-89, 1984 (by FF Lange) A new concept: Pore coordination number; thermodynamic analysis: pore will disappear only when its coordination number is less than a critical value; Real system: irregular particle size and shapes & irregular arrangement (packing) Agglomerates: hard (partially sintered); soft (held by van der Waals forces)

15
15 General experiences: soft agglomerates produce better sintering results than hard agglomerates This author thinks: “particle arrangement” is important A pore: has its volume, shape and coordination number R>Rc: pore surface convex; R

16
16 Theoretical calculation: equal-sized spheres, random packing, pore volume always 0.37 ~ 0.41 (or density: 059 ~ 0.63); for real powder: tap density rarely over 30% of true density Theoretical calculation: different sized sphere can produce bulk density up to 95%; Consolidation force to increase bulk density: depend on resistance of particle packing unit to deformation (via particle rearrangement) ; as shear stress increase, agglomerate first to shear apart into their smaller domains, next domain deformation, finally, particle deform or fracture; Grain growth: a method to reduce pore coordination number; grain growth from mass transport (temperature effect) If pore growth faster, we may get pores with higher coordination number

17
17 Transparent Alumina Grain size ≦ 500 nm; residual porosity: negligible (e.g. 0.03%) Possible methods: (a) Use high sintering temperature (grain growth problem); or (b) through special particle coordination and low temperature sintering (shaping technique or particle size distribution – key: homogeneity; e.g. no agglomerates) Following data from: J. Am. Cer. Soc. 89(6), 1986-1992, 2006. Raw material: Al 2 O 3, 99.99% pure, 150-200 nm;

18
18 Shaping methods: (a) dry pressing (uniaxial pressing at 200 MPa; cold isostatic pressing CIP at 700MPa (pre-shaped at 30-50 MPa); (b) gel- casting (4-5 wt% monomer); (c) slip casting into porous alumina mold Binder burnout: 800 o C, very small shrinkage (< 0.2%), develop neck, provide strength for Hg intrusion analysis Mercury porosimetry better than SEM to measure pore size distribution No large pores (>75 nm): an indication of homogeneity

19
19 Gel-casting versus uniaxial pressing

20
20 Pore size distribution: do not change much from green state to intermediate sintering stage; Homogeneity: poor for uniaxial pressing Pore size ~ 50 nm ~ 1/3 of particle size

21
21 Slip casting provides the best particle coordination: pore size ~ 35 nm ~ 1/5 particle size Observation: Smaller and larger pore are eliminated at similar rates

22
22 Density – grain size trajectory of different processing

23
23 (a) slip casting without binder, presintered at 1200 o C, then HIP 1170 o C, ave. grain size = 0.44 μm (b) gelcasting, presintered at 1240 o C, HIP 1200 o C, ave. grain size = 0.53 μm (both densities > 99.9%) All above data taken from J. Am. Cer. Soc. 89(6), 1985-1992, 2006.

Similar presentations

OK

INTRODUCTION The ultimate goal of a manufacturing engineer is to produce steel/metal components with required geometrical shape and structurally optimized.

INTRODUCTION The ultimate goal of a manufacturing engineer is to produce steel/metal components with required geometrical shape and structurally optimized.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on moles concept Ppt on networking related topics for peace Ppt on grease lubrication intervals Ppt on union budget 2012-13 Ppt on save environment posters Free ppt on mobile number portability delhi Ppt on self awareness quotes Ppt on cd/dvd rental Ppt on swine flu Ppt on satellites launched by india