MEASUREMENT OF DENSITY DISTRIBUTION IN ALUMINA GREEN BODIES
BY X-RAY TOMOGRAPHY
Meulenyzer S.2, Gonon M.1, Descamps J-C.1, Cambier F.2
1
Faculté Polytechnique de Mons, Service de Science des Materiaux,
56 rue de l'Epargne, B-7000 Mons, Belgique.
2
Belgium Ceramic Research Centre,
5 avenue du gouverneur Cornez, B-7000 Mons (Belgique)
ABSTRACT
The objective of this study is to investigate the feasibility and the accuracy of density
measurements on ceramics green bodies by using high-resolution X-ray CT (Computed
Tomography). At a first stage, experimental parameters were investigated in order to define
the best conditions to observe density gradients in single axe pressed alumina green samples.
Then measurements were performed from 2D projection X-ray radiography. Axial and radial
gradients in alumina cylinders shaped under various pressures an of various aspect ratios were
characterised. Finally 3D X-ray CT were performed and compared to the results obtained in
two dimensions.
KEY WORDS
X-ray Computed Tomography, Density gradients, Ceramics green bodies, Alumina.
INTRODUCTION
High-resolution X-ray CT is a non-destructive technique for visualising volume defects and
heterogeneities in opaque solids. Information on the 3D geometries is translated into twodimensional slices of elemental thickness [1]. On that point high-resolution X-ray CT is
equivalent to medical CAT-scanning but it differs in the resolution that reaches a few tens of
microns, even when investigated parts are made of high density materials.
For many advanced ceramic applications, the knowledge of the density and density gradients
is of major importance. Indeed, density variations in green bodies may influence the final
properties and also yields to uncontrolled shrinkage and deformation during sintering [2] [3].
Density gradients are linked to the shape and the green forming technique, they can be
modelised but rare are the techniques that allow measurements as X-ray CT does [4].
EXPERIMENTAL PROCEDURES
1. X-ray CT System
The X-Tech X-ray CT system used is composed of (figure 1):
- a microfocus Tungsten X-ray source (5 µm diameter) 40–225 KeV,
- a CsI scintillation X-ray detection screen coupled with a photomultiplier and a CCD
camera (1024x1024 pixels),
- a five axis manipulator (x, y, z, translations; y tilt; z rotation).
Samples can take any position between X-ray source and detector (890 mm). However
geometric shade due to source dimension must be considered for high enlargements (>1 pixel
when enlargement is > x40).
Geometric deformations due to polar projection are corrected with regard to a reference grid
picture.
Shading, variation of intensity between pixels detector due to different distances source-pixel,
is corrected with regard to a white reference picture taken without sample.
3D CT reconstruction is operated by filtered backprojection [1] from series of 360 images
taken at 1° steps.
z
Iy,z
I0
x
y
x-ray source
detector
Figure 1: X-ray CT system
2. Density measurement
2.1 Measurement by conventional 2D projection radiography
During a sample examination, the intensity I y , z of the X-ray beam hitting the screen detector
at pixel y,z is attenuated with regard to the intensity I y0, z at the same pixel when no sample is
introduced along the beam path (figure 1). This attenuation follows the Beer-Lambert’s law :
I y,z
I y0, z
 

 exp    . y , z .t y , z 
    y , z

{1}
ty,z :
thickness of crossed sample,
()y,z: mean masse absorption coefficient of sample along ty,z.
In the CT System, the intensity I y , z is converted into a grey levels N y , z ranging between 0
(black, no radiation) and 4096 (white, saturation of the detector). If there is a linear
dependence between the intensity and the grey level and if the mass absorption coefficient is
known, the mean density along the tx,y direction can be calculated.
2.2 Measurement by 3D CT
In 3D CT the information in grey levels obtained is proportional to the linear absorption
coefficients µ = (µ/). for all elemental volume associated to each voxel. Assuming an
homogeneous chemical composition of the sample (µ/ = cste), the grey level is proportional
to the local density.
RESULTS AND DISCUSSION
In a first stage, the system X-ray detection linearity was checked. As previously said, the grey
levels given by the image must be proportional to the intensities striking the detector.
Then, to carry out precise measurement of the density, the accurate value of the mass
absorption coefficient () must be known. Therefore, attenuation measurements of the
radiation according to the mass thickness were carried out on densified alumina samples.
Thereafter, a first evaluation of density gradients present in green bodies was carried out by
direct measurements in 2D radiography.
Finally, 3D representation of density gradients of density were realised.
1. Linearity of the X-ray detector
In this part of the study, no sample was introduced between the source and the detector. The
grey level N introduced in the calculations corresponds to an average values measured around
the centre of the detection screen on a surface y,z of ~ 10 x 10 mm2 (50 x 50 pixels). It
corresponds to an average intensity I.
For a given X-ray energy the X-ray tube current was set to obtain saturation of the detector
(X-ray intensity I0, grey level N0 = 4096). The X-ray tube current was then decreased to
reduce intensity I at the screen detector and the corresponding grey level N was measured.
The experimental curves confirm the linear dependence between N/N0 and I/I0 (Figure 2),
however the grey level Nb corresponding to no X-ray intensity is not 0 so that the following
correction appears as necessary:
I
N Nb

I0 N0 Nb
{2}
2 Mass absorption coefficient
This part of the study aims to determine accurate values of () for the alumina as function
of the tube tension but also the effects of beam hardening. Dense alumina pellets of various
mass thickness .t obtained by isostatic pressing and sintering were introduced in the CT
system between source and detector.
The grey level N.t introduced in the calculations corresponds to an average values measured
around the centre of the detection screen on a surface y.z of ~ 10 x 10 mm2 (50 x 50 pixels). It
corresponds to an average intensity I.t. Considering the distance source / detector (890 mm),
the variations in t with the pixel position y,z are negligible and ty,z ~ t, thickness of the
alumina pellet over all the y,z range of measurement.
In that conditions, mass absorption coefficients are calculated according to equation:
  
 
 .t
 I0 
 N0 Nb 
ln   .t  ln   .t
b 
I 
N  N 


 .t
 .t
{3}
According to the experimental conditions, high variation of the mass absorption coefficient
are observed due to beam hardening (figure 3). The use of Cu filters reduces this phenomenon
and will avoid CT reconstruction artefacts [1] [9].
3500
0.50
3000
0.45
2500
E= 60 kV
E= 70 kV
E= 80 kV
E= 80 kV + Cu filter
0.40
2
 (cm /g)
Grey level N
4000
2000
1500
1000
NG
NG correction
500
0.35
0.30
0.25
0
0
20
40
60
80
100
I/Imax (%)
Figure 2: Linearity of X-ray detector
0.20
0
5
2
x (g/cm )
10
Figure 3: Variation in µ/
15
3 Measurement of density gradients by 2D radiography
Alumina cylinders of two diameters (30 and 40 mm) uniaxially pressed under various
pressures (10, 32 and 56 MPa) were introduced in the CT system.
The X-ray tube setting was 80 kV and 290µA for all tests. Cu filter (0.4 mm) was used to
reduce beam hardening (figure 3).
Grey levels N were measured in the same conditions than in §2.
Average densities  along diameter at different heights of the cylinder and along the height at
different points of the diameter were calculated (figure 4).
Sample
motion
Sample
motion
I0
I0
I
I
X-rays
X-rays
Figure 4: Principle of density measurement by 2D radiography
Densities were calculated with reference to the average grey level N to which is associated
the average density  of the sample :
  
  
I
I
 exp   . .t  ; 0  exp   ..t 
0
I
I
  
  
;
 

I N Nb

 exp   .t.   
b
I N N
 

N  Nb 
ln 
b 
N  N 
    
  .t
 
{4}
Axial gradients show that with single axe single effect die pressing the density is higher under
punch that at the sample base. An axial density gradient of 0.20 is measured with a shaping
pressure of 10 MPa and an aspect ratio H/D (height / diameter) of 1.16 (figure 5). The radial
gradient show a minimum in density along the cylinder axis and a maximum near the surface
(figure 5) The curve show a more or less high symmetry according to the measurement
direction what can be linked to a non homogeneous distribution of the powder in the die
before shaping.
1.92
2.00
1.90
1.95
1.90
1.86
Density
Density
1.88
1.84
1.82
Average value geometricaly measured
1.85
1.80
1.80
1.75
Average value geometricaly measured
1.78
1.76
1.70
0
5
10
15
Position (mm)
20
25
30
0
5
10
15
20
25
30
35
Position (mm)
Figure 5: Density gradients in alumina cylinders pressed at 10 MPa (a: axial; b: radial).
Additional measurements show the decrease in axial and radial gradients with the increase in
pressure and also with a decrease in aspect ratio H/D (figure 6).
2.20
density
2.10
2.00
1.90
10 MPa
32 MPa
32 MPa
56 MPa
1.80
1.70
0
5
H/D=1,16
H/D=1,15
H/D=0,67
H/D=1,1
10
15
20
25
30
35
Distance from top ( mm)
Figure 6: Density gradients according to shaping pressure and aspect ratio (H/D)
Density resolution depends on the experimental conditions throughout accuracy of the grey
scale measurement (radiography quality) and the mass absorption coefficient (equation 4). In
the present work the accuracy is about ± 0.01.
4. Measurement of density gradient by 3D X-ray CT
At that point of the investigations, 3D characterisation of the density gradients have been
done in a qualitative way. X-ray radiographies were collected using the same experimental
parameters than previously for 2D characterisation.
A 3D representation of the sample pressed at 10 MPa is given in figure 7. The grey levels
distribution is decomposed into segments: from white to dark red according to increasing
densities. These results confirm the density distribution characterised from 2D measurements
but a low density zone is observed juste under the punch around the cylinder axis.
Top (punch)
Bottom
Figure 7: Density gradients in an alumina cylinder pressed under 10 MPa (aspect ratio 1.16)
(white = low density, black = high density)
5. Conclusions
A methodology for density gradients characterisation in ceramic green bodies by X-ray 2D
radiography has been investigated. The protocol proposed uses an autocalibration of the
measurement with regard to the average density of the samples. Measurement realised on
alumina green bodies uniaxilay pressed agree with theory.
Qualitative 3D density distributions were characterised for the same samples. Results agree
with the 2D measurements.
Actual work focuses on the tridimentional quantitative measurement by computed
tomography
Acknowledgements
The authors would like to express their sincere gratitude to Hakim Djerba 3rd year student in
material science at UVMH – Maubeuge (France) for his help in the collection of the data used
in this project.
References
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