1
SizeSize and and ShapeShape Characterization of Characterization of OblateOblate ParticlesParticles
W. PABST,1 E. GREGOROVÁ,1 C. BERTHOLD,2 et al.
1 Department of Glass and Ceramics, Institute of Chemical Technology, Prague, Czech Republic
2 Institut für Geowissenschaften, Universität Tübingen, Germany
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
CPPS-Lecturead Units 5-7
Introduction 1 – Sizing methodsThe most important sizing methods used routinely for
ceramic raw materials characterization are:
Laser diffraction (Mie / Fraunhofer approximation) – DL Sedimentation analysis (Stokes equation) – DS
Microscopic image analysis – DM
All these methods are based on different physical principles and thus measure different equivalent
diameters. Only for spherical particles the sizing results coincide (calibration standards).
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
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Introduction 2 – Oblate Particles
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10 µm
Kaolinit
Quarz-Aggregate
10 µm
Kaolinit
Quarz-Aggregate
kaolin
SiC platelets
boron nitride
… pyrophyllite, talc, mica, tabular alumina …2 µm
quartz aggregates
kaolinite
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Introduction 3 – Oblate particles
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Low degree of anisometry(example pyrophyllite)
High degree of anisometry(example kaolin)
Particle size distributions measured via sedimentation analysis(Micromeritics Sedigraph 5100) and laser diffraction (Fritsch Analysette 22)
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Introduction 4 – Oblate particles
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Kaolin type Kaolinite Quartz Feldspar Other clay and
mica minerals Sedlec Ia 91 ± 3 2 ± 1 − 7 ± 2 Imperial / Premier 89 ± 4 3 ± 2 − 8 ± 3 Sp-EX 84 13 1 2 KDG 77 ± 4 13 ± 3 1 ± 1 9 ± 3 KD50 69 ± 4 23 ± 3 1 ± 1 7 ± 3
Kaolin type SD50 [µm] LD50 [µm] Median LS
shape factor Sedlec Ia 1.3 5.9 48.4 Imperial / Premier 1.5 5.5 30.1 Sp-EX 2.9 8.0 17.9 KDG 2.4 5.0 10.3 KD50 7.7 11.8 5.6
Correlation of average particle shape and mineralogical phase composition in 5 commercial kaolin types from three different deposits (Czech Republic)
PABST et al.: Brit. Ceram. Trans. 100, 106 (2001)
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Introduction 5 – Oblate particles
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Different average shape and quantitative phase composition in different size fractions of kaolins
LEHMANN et al.: Key Eng. Mater. 264-268, 1387 (2004)
2 µm 5 µm
10 µm 10 µm
fraction< 2 µm
fraction6.3 – 20 µm
fraction2 – 6.3 µm
fraction20 – 63 µm
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2
• Although most real anisometric particles have an irregular shape, many of them can approximatelybe considered as rotationally symmetric.
• The most convenient model shapes for platelets are circular disks and oblate spheroids.
• In this case shape can be characterized by a single number, the aspect ratio:
(maximum and minimum extension DM – “diameter” and H – “height”)
Introduction 6 – Oblate particles
EBERHARD KARLS
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EBERHARD KARLS
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HD
R M≡
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 1 – Size distributions
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0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Rel
ativ
e vo
lum
e [%
/ m
icro
n]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 2 – Size distributions
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0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Rel
ativ
e vo
lum
e [%
/ m
icro
n]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 3 – Size distributions
EBERHARD KARLS
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EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Rel
ativ
e vo
lum
e [%
/ m
icro
n]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 4 – Size distributions
EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Rel
ativ
e vo
lum
e [%
/ m
icro
n]
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Rel
ativ
e vo
lum
e [%
/ m
icro
n]
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 5 – Size distributions
EBERHARD KARLS
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EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Rel
ativ
e vo
lum
e [%
/ m
icro
n]
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Rel
ativ
e vo
lum
e [%
/ m
icro
n]
Dirac distribution Heaviside step function
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
3
Theory 6 – Size distributions
EBERHARD KARLS
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EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 7 – Size distributions
EBERHARD KARLS
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EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
spheres
DM=DL=DS
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 8 – Size distributions
EBERHARD KARLS
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EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
circular disks (aspect ratio 10)
DM
DS
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 9 – Size distributions
EBERHARD KARLS
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EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
circular disks (aspect ratio 30)
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 10 – Size distributions
EBERHARD KARLS
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EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [microns]
Cum
ulat
ive
volu
me
[%]
circular disks (aspect ratio 10)
perpendicularorientation
randomorientation
in-planeorientation
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 11 – Stokes equation
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Classical Stokes equation for sedimentation analyses:
(dynamic shear viscosity η, steady-state settling velocity V, density of solid particles ρS and liquid ρL, gravitational acceleration g,
equivalent sphere diameter / Stokes diameter DS )
Derivation of the Stokes equation via force equilibrium:
0=+−=∑ RGB FFFF
gDF LSB ρπ 3
6= gDF SSG ρπ 3
6= SR DVF ηπ3=
lift force (buoyancy) gravitational force resistance force
gVD
LSS )(
18ρρη−
=
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4
Theory 12 – Stokes equation
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Modified Stokes equation for circular disks:
(dynamic shear viscosity η, steady-state settling velocity V, density of solid particles ρS and liquid ρL, gravitational acceleration g,
(equivalent) disk diameter DM and aspect ratio R )
Derivation of the Stokes equation via force equilibrium:
0=+−=∑ RGB FFFF
lift force (buoyancy) gravitational force resistance force
MrandomR DVF η6≈
gRVDLS
M )(24
ρρπη−
=
gR
DF L
MB ρπ 3
4⋅= g
RDF S
MG ρπ 3
4⋅=
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Theory 13 – Stokes equation
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Modified Stokes equation for oblate spheroids:
(dynamic shear viscosity η, steady-state settling velocity V, density of solid particles ρS and liquid ρL, gravitational acceleration g,(equivalent) spheroid diameter DM and aspect ratio R )
Derivation of the Stokes equation via force equilibrium:
0=+−=∑ RGB FFFF
lift force (buoyancy) gravitational force resistance force
MrandomR DVF η6≈gR
DF L
MB ρπ 3
6⋅= g
RDF S
MG ρπ 3
6⋅=
gRVDLS
M )(36
ρρπη−
=
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Theory 14 – Aspect ratio formulae
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• for circular disks:
(PABST et al.: Brit. Ceram. Trans. 2001, LEHMANN: M.Sc. Thesis (kaolins), Tübingen / Germany 2003, LOBATO: Ph.D. Thesis (on talc), Blacksburg / USA 2005)
• for oblate spheroids:
DS is the ordinary Stokes diameter (equivalent sphere diameter), DM can be measured by image analysis.
gRVDLS
M )(36
ρρπη−
=
2
2 ⎟⎟⎠
⎞⎜⎜⎝
⎛⋅=
S
M
DDR π
2
43
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅=
S
M
DDR π
gVD
LSS )(
18ρρη−
=
gVD
LSS )(
18ρρη−
=
gRVDLS
M )(24
ρρπη−
=
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Theory 15 – Aspect ratio formulae
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In practice, these formulae are applied to compare sedimentation results with laser diffraction results (with the laser diffraction equivalent diameter DL instead of
the true disk or spheroid diameter DM).
Problem: The shape factor (degree of anisometry) thus calculated can be called an aspect ratio only when the particles are oriented with their planes perpendicular to
the laser beam direction.
Solution: When the particle orientation in the laser beam is random, Cauchy’s stereological theorem has to
be invoked to obtain the correct aspect ratio formula.
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
In the case of circular disks and oblate spheroids with large aspect ratio the surface area is approximately:
Cauchy’s stereological theorem says, that the average projected area of randomly oriented,
monodisperse convex particles is just one quarter of the surface area of these particles.
⇔ laser diffraction:
⇒ for large aspect ratios (approximately):
Theory 16 – Aspect ratio formulae
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2
4 Lprojection DA ⋅=π
2
2 MDS ⋅≈π
2
84 Mprojection DSA ⋅≈=π
LM DD ⋅≈ 2
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Theory 17 – Aspect ratio formulae
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2
43
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅=
S
M
DDR π
2
23
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅=
S
L
DDR π
2
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅=
S
L
DDR π
2
2 ⎟⎟⎠
⎞⎜⎜⎝
⎛⋅=
S
M
DDR π
disks spheroids
oriented oriented
randomrandom
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5
Theory 18 – Aspect ratio formulae
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Our simple aspect ratio formula for spheroids in randomorientation,
can be considered as an approximation of the exactsolution given by Jennings and Parslow (1988),
JENNINGS & PARSLOW: Proc. Roy. Soc. London 419, 137 (1988)
because for large aspect ratios we have
( )( ) ( )[ ]1ln1
1arctan222
2
−++−
−=
RRRR
RRDD
L
S
∞→R
( ) RR ≈−12
RRRR
DD
L
S
2lnarctan2
2 += 2arctan π≈R22ln RR <<
2
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅=
S
L
DD
R π
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Theory 19 – Aspect ratio formulae
EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
DL/DS [1]
Aspe
ct ra
tio [1
]
our formula (approximation)
Jennings-Parslowsolution (exact)
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 20 – Aspect ratio formulae
EBERHARD KARLS
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EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
DL/DS [1]
Aspe
ct ra
tio [1
]
our formula (approximation)
Jennings-Parslowsolution (exact)
0
1
2
3
4
5
6
7
8
9
10
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
DL/DS [1]
Aspe
ct ra
tio [1
]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Theory 21 – Aspect ratio formulae
EBERHARD KARLS
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EBERHARD KARLS
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0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
DL/DS [1]
Aspe
ct ra
tio [1
]
our formula (approximation)
Jennings-Parslowsolution (exact)
0
1
2
3
4
5
6
7
8
9
10
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
DL/DS [1]
Aspe
ct ra
tio [1
]
SL DD / Jennings & Parslow
Our formula Relative error [%]
1 1 3.140 214 % 1.1 2.301 3.799 65 % 1.2 3.195 4.522 42 % 1.3 4.088 5.307 30 % 1.4 5.013 6.154 23 % 1.5 5.984 7.065 18 % 1.6 7.005 8.038 15 % 1.7 8.081 9.075 12 % 1.8 9.213 10.174 10 % 1.9 10.403 11.335 9 % 2.0 11.652 12.560 8 % 2.2 14.331 15.198 6 % 2.4 17.251 18.086 5 % 2.6 20.418 21.226 4 % 2.8 23.831 24.618 3 % 3.0 27.492 28.260 3 %
(same graph,zoomed)
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Experimental 1 – SiC platelets
EBERHARD KARLS
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EBERHARD KARLS
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In practice, aspect ratio formulae are usually applied to sedimentation and laser diffraction results (DS and DL).
Key question: Are the particles randomly orientedduring the laser diffraction experiment ?
Methodological approach to find the answer:Perform a microscopic image analysis and find out
whether coincidence with laser diffraction data can beachieved with or without the Cauchy theorem.
⇒ if coincidence is achieved only with Cauchy then the particle orientation in the laser beam is random !
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Experimental 2 – SiC platelets
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Optical micrograph of SiC platelets lying flatside on the object slide.
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6
Experimental 3 – SiC platelets
EBERHARD KARLS
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EBERHARD KARLS
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Cumulative size distribution of SiC platelets measured by laser diffraction.
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [µm]
Cum
ulat
ive
perc
enta
ge [%
]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Experimental 4 – SiC platelets
EBERHARD KARLS
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EBERHARD KARLS
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0
50
100
150
200
250
300
350
27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 92.5
Projected area diameter [µm]
Rel
ativ
e nu
mbe
r [1]
Number-weighted size distribution (frequency histogram of DM).
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Experimental 5 – SiC platelets
EBERHARD KARLS
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EBERHARD KARLS
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Frequency histogram of the aspect ratio.
0
2
4
6
8
10
12
14
16
0 5 10 15 20 25 30 35 40 45
Aspect ratio [1]
Freq
uenc
y [1
] y = 0.3905x - 1.3141
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60 70 80 90 100
Projected area diameter [µm]
Asp
ect r
atio
[1]
In order to transform the number-weighted (q0) distribution to a volume-weighted distribution (q3) via the equation
the size dependence of the aspect ratio must be known.
iiii qDRq 03
3 ⋅⋅=
Size dependence of the aspect ratio.
3.14.0 −⋅= MDR
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Experimental 6 – SiC platelets
EBERHARD KARLS
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EBERHARD KARLS
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Frequency histogram of the aspect ratio.
0
2
4
6
8
10
12
14
16
0 5 10 15 20 25 30 35 40 45
Aspect ratio [1]
Freq
uenc
y [1
] y = 0.3905x - 1.3141
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60 70 80 90 100
Projected area diameter [µm]
Asp
ect r
atio
[1]
In order to transform the number-weighted (q0) distribution to a volume-weighted distribution (q3) via the equation
the size dependence of the aspect ratio must be known.
iiii qDRq 03
3 ⋅⋅=
Size dependence of the aspect ratio.
3.14.0 −⋅= MDR
Measured by focusing on the upper and lower basal plane of SiC platelets !
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Experimental 7 – SiC platelets
EBERHARD KARLS
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EBERHARD KARLS
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Volume-weighted size distribution obtained by transformation.
0
200000
400000
600000
800000
1000000
1200000
1400000
1600000
27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 92.5
Projected area diameter [µm]
Rel
ativ
e vo
lum
e [1
]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Experimental 8 – SiC platelets
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
Cumulative size distribution of SiC platelets measured by image analysis.
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Equivalent diameter [µm]
Cum
ulat
ive
perc
enta
ge [%
]
dotted: measured Q0 distributiondashed: Q3 calculated with constant R (22)full: Q3 calculated with size-dependent R
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
7
Experimental 9 – SiC platelets
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
Size distribution of SiC platelets after applying the Cauchy theorem.
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Equivalent diameter [µm]
Cum
ulat
ive
perc
enta
ge [%
]
dotted: measured Q0 distributiondashed: Q3 calculated with constant R (22)full: Q3 calculated with size-dependent Rgreen: Q3 after application of the Cauchy theorem
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Experimental 10 – SiC platelets
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
Comparison of size distributions of SiC platelets.
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Equivalent diameter [µm]
Cum
ulat
ive
perc
enta
ge [%
]
Laser diff. Q0 Q3 (const. R) Q3 (var. R) Q3 (Cauchy)
blue dotted: measured Q0 distribution, blue full: Q3 calculated with size-dependent R,green: Q3 after application of the Cauchy theorem, red: Q3 measured by laser diffraction
DM (Q3 without Cauchy) = 49.5–51.3 µmDM (Q3 with Cauchy) = 36.9–39.9 µmDL = 38.3 µm
median values
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Summary and Conclusion – 1• New simple formulae have been proposed to
calculate the average aspect ratio of oblate particleswhen the size distribution is known fromsedimentation analysis (DS). and either microscopicimage analysis (DM) or laser diffraction (DL). All ofthese approximate formulae are of the general form:
where the prefactor C (shape factor) is 3/2 for disksand 1 for spheroids and the prefactor K (orientationfactor) is π/2 for perpendicular orientation (typically DM) and π for random orientation (typically DL).
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
2
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅=
S
L
DD
KCR2
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅=
S
M
DDKCR
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Summary and Conclusion – 2• Our formula for randomly oriented spheroids,
is an approximation to the Parslow-Jennings solution,
for the case of large aspect ratios.
In practice, the error is < 10 % for aspect ratios > 10.
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
( )( ) ( )[ ]1ln1
1arctan222
2
−++−
−=
RRRR
RRDD
L
S
2
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅=
S
L
DDR π
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Summary and Conclusion – 3• For SiC platelets it has been shown that after
application of Cauchy’s sterological theorem the size distribution measured by image analysis coincides well with the laser diffraction result:
– median value of DL: 38 µm,– median value of DM without Cauchy: 49-51 µm,– median value of DM with Cauchy: 37-40 µm.
⇒ SiC platelets are randomly oriented in the measuring cell of the laser diffraction instrument; this situation is typical for laser diffraction, unless special conditions are chosen / special equipment is used to enforce particle orientation.
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 1
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
Inte
nsitä
t (o.
E.)
2 7 12 17 22 2 7 32 37 4 2 4 7
2 Theta
( )011
( )001
( )131
( )131( )020
( )002
( )003( )200( )113
( )120( )011 ( )031
Illit/Muskovit
Quarz
Inte
nsitä
t (o.
E.)
2 7 12 17 22 2 7 32 37 4 2 4 7
2 Theta
( )011
( )001
( )131
( )131( )020
( )002
( )003( )200( )113
( )120( )011 ( )031
Illit/Muskovit
Quarz
X-ray reflexes of kaolinite (example: kaolin Imperial, Czech Republic); note that the quartz main reflex (101) is at 26.41 ° 2θ, the illite / muscovite (001) and
(002) reflexes are at 8.57 and 17.47 ° 2θ, respectively [Lehmann 2003].
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
8
X-ray and SEM studies of kaolins – 2
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
Influence of orientation texture on X-ray diffractograms (examples: kaolinsKDK / Podbořany and Sedlec Ia, Karlovy Vary, Czech Republic): due to a higher
degree of orientation some reflexes are suppressed in KDK [Lehmann 2003].
2 12 22 32 42 52 62
2 Theta
Inte
nsitä
t (o.
E.)
Kaolin KDK (0-2µm)
Kaolin Sedlec 1a (6,3-20µm)
2 12 22 32 42 52 62
2 Theta
Inte
nsitä
t (o.
E.)
Kaolin KDK (0-2µm)
Kaolin Sedlec 1a (6,3-20µm)
Very low intensities due to orientation texture
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 3
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
SEM micrographs of the coarse fraction of a kaolin (size fraction 20-63 µm ofkaolin KD 50, Podbořany / Czech Republic) [Lehmann 2003].
50 µmKaolinit-Stapel
Quarz-Aggregat
alterierterFeldspat
50 µmKaolinit-Stapel
50 µmKaolinit-Stapel
Quarz-Aggregat
alterierterFeldspat
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 4
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
SEM micrographs of different size fractions (< 2 µm, 2–6.3 µm and 6.3–20 µm) of kaolin KD 50 (Podbořany / Czech Republic) [Lehmann 2003].
10 µm
Kaolinit-Plättchen
10 µm
Kaolinit-Plättchen
10 µm
Kaolinit
Quarz-Aggregate
10 µm
Kaolinit
Quarz-Aggregate
20 µmQuarz-Aggregate
Kaolinit-Stapel
20 µmQuarz-Aggregate
Kaolinit-Stapel
< 2 µm 2 – 6.3 µm 6.3 – 20 µm
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 5
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
SEM micrographs of the different size fractions of kaolin KDK(Podbořany / Czech Republic) [Lehmann 2003].
2 µm2 µmKaolinit-Plättchen
Quarz
Smektit. Komponente?
2 µm2 µmKaolinit-Plättchen
Quarz
Smektit. Komponente?
Quarz-Aggregate
Kaolinit-Plättchen
6 µmQuarz-Aggregate
Kaolinit-Plättchen
6 µm
10 µmKaolinit-Stapel
Quarz-Aggregate
10 µmKaolinit-Stapel
Quarz-Aggregate
10 µm
Kaolinit-Stapel
10 µm
Kaolinit-Stapel
< 2 µm
6.3–20 µm 20–63 µm
2–6.3 µm
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 6
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
X-ray diffractograms of kaolin KDK (Podbořany, Czech Republic), total sample, textured sample and individual size fractions [Lehmann 2003].
2 1 2 2 2 3 2 4 2 5 2 6 2
2 Theta
Inte
nsitä
t (o.
E.)
Gesamtprobe
Texturpräparat (Gesamtprobe)
0 –2µm
6,3 –20µm
2 –6,3µm
Kaolinit
Kaolinit
Quarz
FeldspatIllit
Mont-morillonit
MixedLayer
2 1 2 2 2 3 2 4 2 5 2 6 2
2 Theta
Inte
nsitä
t (o.
E.)
Gesamtprobe
Texturpräparat (Gesamtprobe)
0 –2µm
6,3 –20µm
2 –6,3µm
Kaolinit
Kaolinit
Quarz
FeldspatIllit
Mont-morillonit
MixedLayer
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 7
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
X-ray diffractogram of the fine size fraction (< 2 µm) of kaolin KDK (Podbořany, Czech Republic) after swelling in glycol (in order to emphasize
the smectite and mixed layer minerals) [Lehmann 2003].
2 12 22 32 42 52 622 Theta
Inte
nsitä
t (o.
E.)
Illit
Kaolinit
KaolinitMont-morillonit
Quarz
MixedLayer
2 12 22 32 42 52 622 Theta
Inte
nsitä
t (o.
E.)
Illit
Kaolinit
KaolinitMont-morillonit
Quarz
MixedLayer
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
9
X-ray and SEM studies of kaolins – 8
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
Particle size distributions of kaolin KDK (Podbořany, Czech Republic); comparison of sedimentation and laser diffraction results [Lehmann 2003].
Äquivalentdurchmesser [µm]
Kum
ulat
ive
Mas
se [%
]
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
1 0 0
0 , 1 1 1 0 1 0 0
M a l v e r n
A n a l y s e t t e
S e d i g r a p h
Äquivalentdurchmesser [µm]
Kum
ulat
ive
Mas
se [%
]
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
1 0 0
0 , 1 1 1 0 1 0 0
M a l v e r n
A n a l y s e t t e
S e d i g r a p h
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 9
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
SEM micrographs of the different size fractions of kaolin Imperial(Karlovy Vary / Czech Republic) [Lehmann 2003].
< 2 µm
6.3–20 µm 20–63 µm
2–6.3 µm
2 µm
Kaolinit-Plättchen
Kaolinit-Stapel
2 µm
Kaolinit-Plättchen
Kaolinit-Stapel
10 µmKaolinit-Stapel Illit/Muskovit ?
Kaolinit-Plättchen
10 µmKaolinit-Stapel Illit/Muskovit ?
Kaolinit-Plättchen
20 µm
Kaolinit-Stapel
AlterierterGlimmer
20 µm
Kaolinit-Stapel
AlterierterGlimmer
20 µm
Kaolinit-Stapel
alterierter Glimmeroder umgewandelterFeldspat 20 µm
Kaolinit-Stapel
alterierter Glimmeroder umgewandelterFeldspat
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 10
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
SEM and chemical analysis by EDX of single grains; note that the K-containing mineral could be mica or feldspar, cleavage suggests mica [Lehmann 2003].
< 2 µm
6.3–20 µm 20–63 µm
2–6.3 µm
2 µm
Kaolinit-Plättchen
Kaolinit-Stapel
2 µm
Kaolinit-Plättchen
Kaolinit-Stapel
10 µmKaolinit-Stapel Illit/Muskovit ?
Kaolinit-Plättchen
10 µmKaolinit-Stapel Illit/Muskovit ?
Kaolinit-Plättchen
20 µm
Kaolinit-Stapel
AlterierterGlimmer
20 µm
Kaolinit-Stapel
AlterierterGlimmer
20 µm
Kaolinit-Stapel
alterierter Glimmeroder umgewandelterFeldspat 20 µm
Kaolinit-Stapel
alterierter Glimmeroder umgewandelterFeldspat
PTPT
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 11
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
X-ray diffractograms of kaolin Imperial (Karlovy Vary, Czech Republic), total sample and individual size fractions [Lehmann 2003].
2 12 22 32 42 52 62
Inte
nsitä
t (o.
E.)
0 – 2µm
Gesamtprobe
2 – 6,3µm
6,3 – 20µm
2 Theta
Illit/Muscovit
Kaolinit
Kaolinit
Quarz
2 12 22 32 42 52 62
Inte
nsitä
t (o.
E.)
0 – 2µm
Gesamtprobe
2 – 6,3µm
6,3 – 20µm
2 Theta
Illit/Muscovit
Kaolinit
Kaolinit
Quarz
Inte
nsitä
t (o.
E.)
0 – 2µm
Gesamtprobe
2 – 6,3µm
6,3 – 20µm
2 Theta
Illit/Muscovit
Kaolinit
Kaolinit
Quarz
0 – 2µm
Gesamtprobe
2 – 6,3µm
6,3 – 20µm
2 Theta
Illit/Muscovit
Kaolinit
Kaolinit
Quarz
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 12
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
Particle size distributions of kaolin Imperial (Karlovy Vary, Czech Republic); comparison of sedimentation and laser diffraction results [Lehmann 2003].
0
10
20
30
40
50
60
70
80
90
100
0,1 1 10 100
Malvern AnalysetteSedigraph
Äquivalentdurchmesser [µm]
Kum
ulat
ive
Mas
se [%
]
0
10
20
30
40
50
60
70
80
90
100
0,1 1 10 100
Malvern AnalysetteSedigraph
Äquivalentdurchmesser [µm]
Kum
ulat
ive
Mas
se [%
]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 13
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
Typical particle size distributions of kaolin; (left h.s.: sedimentation, right h.s.: laser diffraction) [Lehmann et al. 2003].
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100
Equivalent diameter [µm]
Cum
ulat
ive
mas
s[%
]
Sedimentation
Laser scattering×8
×3
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
10
X-ray and SEM studies of kaolins – 14
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
• Use of three different types of Czech kaolins:Imperial®, KDK® and Sedlec 1a®.
• Particle size analysis using laser diffraction(Malvern Mastersizer µ) and sedimentation(Micromeritics Sedigraph 5100).
• Separation of size fractions < 2µm, 2 – 6.3 µm, 6.3 – 20 µm and > 20 µm by sedimentation with Atterberg cylinders.
• Quantitative phase analysis (determination of mineral content) of whole sample as well asindividual size fractions with XRD using the Rietveld-based software SIROQUANT®.
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 15
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
0.1 1 10 100
Kaolin KDKKaolin Sedlec 1aKaolin Imperial
LSsh
ape
fact
or
Stokes diameter [µm]
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 16
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
°2 Theta2 7 12 17 22 27
<2µm
2-6.3µm
6.3-20µm
Inte
nsity
(a.u
.)
°2 Theta2 7 12 17 22 27
<2µm
2-6.3µm
6.3-20µm
Inte
nsity
(a.u
.)
95-7Feldspar
-2113Smectite/ML
6.3 – 20 µm
2 – 6.3 µm
0 – 2 µm
Bulk sample
Mineral
3142Illite
2726818Quartz
61667770Kaolinite
Weight%
95-7Feldspar
-2113Smectite/ML
6.3 – 20 µm
2 – 6.3 µm
0 – 2 µm
Bulk sample
Mineral
3142Illite
2726818Quartz
61667770Kaolinite
Weight%
• High amounts of smectite / mixed-layer silicates in the fraction < 2 µm.
• Increasing quartz content with increasing grain size.
KDK (Podbořany, CZ)
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 17
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
• Increasing quartz contentand decrasing kaolinitecontent with increasing grain size.
°2 Theta2 7 12 17 22 27
<2µm
2-6.3µm
6.3-20µm
Inte
nsity
(a.u
.)
°2 Theta2 7 12 17 22 27
<2µm
2-6.3µm
6.3-20µm
Inte
nsity
(a.u
.)
Sedlec Ia (Karlovy Vary, CZ)6.3 – 20
µm2 – 6.3
µm0 – 2 µm
Bulk sample
Mineral
6533Illite
12322Quartz
82929595Kaolinite
Weight%
6.3 – 20 µm
2 – 6.3 µm
0 – 2 µm
Bulk sample
Mineral
6533Illite
12322Quartz
82929595Kaolinite
Weight%
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 18
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
• Increasing quartz content with increasing grain size
• Increased mica (illite) content in the fraction 6.3– 20 µm.
°2Theta
Inte
nsity
(a.u
.)
2 7 12 17 22 27
<2µm
2-6.3µm
6.3-20µm
°2Theta
Inte
nsity
(a.u
.)
2 7 12 17 22 27
<2µm
2-6.3µm
6.3-20µm
Imperial (Karlovy Vary, CZ)
-Detectionlimit
11Smectite
6.3 – 20 µm
2 – 6.3 µm
0 – 2 µm
Bulk sample
Mineral
9458Illite
10525Quartz
81919286Kaolinite
Weight%
-Detectionlimit
11Smectite
6.3 – 20 µm
2 – 6.3 µm
0 – 2 µm
Bulk sample
Mineral
9458Illite
10525Quartz
81919286Kaolinite
Weight%
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
X-ray and SEM studies of kaolins – 19
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
0
20
40
60
80
100
120
140
160
180
0.1 1 10
Kaolin KDKKaolin Sedlec 1aKaolin Imperial
LS-s
hape
fact
or
Stokes diameter [µm]
Extermely high shape factors (average aspect ratios) in KDK due to high smectite / ML content
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
11
Acknowledgement
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
Bilateral Czech-German cooperation project D2-CZ21/06-07 “Characterization of AnisometricParticles and the Microstructure of Heterogeneous Materials”, DAAD (Germany) and Academy of Sciences of the Czech Republic, and research programme “Preparation and Research of Functional Materials and Material Technologies using Micro- and Nanoscopic Methods”, Czech Ministry of Education, Youth and Sports (Grant MSM 6046137302) and project “Tvorba předmětu Charakterizace částic a částicových soustav“, Czech Ministry of Education, Youth and Sports (Grant FRVŠ F1b 674).
The support is gratefully acknowledged.Special thanks to M. Lehmann for his careful investigation of Czech kaolins,
T. Török for the creation of 3D figures,J. Hostaša for calculating the statistic exercise problems
and many of our students for performing time-consuming measurements.
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)
Acknowledgement
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
EBERHARD KARLS
UNIVERSITÄTTÜBINGEN
Selected references:[1] Pabst W., Kuneš K., Havrda J., Gregorová E.: J. Eur. Ceram. Soc. 20 (2000), 1429.[2] Pabst W., Kuneš K., Gregorová E., Havrda J.: Brit. Ceram. Trans. 100 (2001), 106. [3] Pabst W., Kuneš K., Gregorová E., Havrda J.: Key Eng. Mater. 206-213 (2002), 743.[4] Lehmann M.: Korngrössen- und Kornformcharakterisierung an Kaolinen (Grain size and shape characterization of kaolins, in German). M.Sc. Thesis, Universität Tübingen 2003.[5] Lehmann M., Berthold C., Pabst W., Nickel K.G.: Key Eng. Mater. 264-268 (2004), 1387.[6] Nováková M.: Velikostní a tvarová charakterizace destičkovitých částic (Size and shape characterization of oblate particles, in Czech). M.Sc. Thesis, ICT Prague 2007.[7] Pabst W., Berthold C., Gregorová E.: J. Eur. Ceram. Soc. 27 (2007), 1759.[8] Pabst W., Berthold C.: Part. Part. Syst. Charact. 24 (2007), 458.
PABST, GREGOROVÁ, BERTHOLD et al.ICT Prague (Czech Republic) & Universität Tübingen (Germany)