American Mineralogist, Volume 89, pages 1304–1312, 2004

Nondestructive three-dimensional element-concentration mapping of a Cs-doped partiallymolten granite by X-ray computed tomography using synchrotron radiation
SUSUMU IKEDA,1,* TSUKASA NAKANO,2 AKIRA TSUCHIYAMA,3 KENTARO UESUGI,4 YOSHIO SUZUKI,4
KO-ICHI NAKAMURA,2 YOSHITO NAKASHIMA,2 AND HIDETO YOSHIDA5
Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwanoha 5-1-5,
Kashiwa, Chiba 277-8561, Japan
2
National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8567, Japan3
Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
4
Japan Synchrotron Radiation Research Institute (JASRI/SPring-8), Mikazuki, Hyogo 679-5198, Japan
5
Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan

1

ABSTRACT
Nondestructive, three-dimensional (3-D) element-concentration mapping was performed and highspatial resolution and quantitative applicability were demonstrated. X-ray computed tomographyusing synchrotron radiation developed at SPring-8 (SP-μCT) enabled us to acquire high-resolution
tomographic images with X-ray energies just above and below the absorption edge of an element.
Concentration of the element could be calculated from the difference of these images with a correction
using standard material. A 3-D Cs concentration map of a partially molten granite was obtained bythis technique and compared with a 2-D element map produced by an electron-probe X-ray microanalyzer (EPMA), with respect to spatial and compositional resolution. A spatial resolution of about
20 μm was achieved by SP-μCT. The compositional resolution of ±2.5 wt% was achieved using thefollowing two calibration processes of linear attenuation coefficients (LAC): (1) calibration based on
the empirical relationship between theoretical LACs and observed CT values, and (2) the calibrationof spatial variation of observed mass attenuation coefficients (MAC) due to X-ray energy shift using a standard material (Cs-bearing solution). Using the Cs2O map obtained by SP-μCT, 3-D image
analysis was demonstrated, for example, connectivity of melt was calculated and it was found that 88
vol% of melt was connected in three dimensions in the sample. Furthermore, the possibility of 3-D
diffusion studies by SP-μCT was discussed based on the spatial and compositional resolutions. This
“nondestructive” and “3-D” mapping technique can reveal the internal compositional distribution of
precious samples such as extraterrestrial materials and cultural assets, and can solve many 3-D issues
such as material transport in geological and industrial materials.

INTRODUCTION
X-ray computed tomography (CT) is a nondestructive technique for obtaining the spatial distribution of the X-ray linear
attenuation coefficient (LAC; denoted by μ) in an object. The
synchrotron radiation (SR) source provides highly collimated(parallel) and monochromatized X-ray beams useful for Xray CT (Flannery et al. 1987; Bonse and Busch 1996), and is
beginning to be used for mineralogical and petrological X-ray
CT studies (e.g., Uesugi et al. 1999; Tsuchiyama et al. 2001;
Paktunc et al. 2001). Collimated X-ray beams allow us to obtainhigh-spatial-resolution X-ray CT images straightforward without
data corrections required when using fan beams or cone beams(Herman 1980; Kak and Slaney 1988). The monochromatic X-ray
beams enable the calculation of quantitative values of the LAC
that depend on only the chemical composition and density of amaterial. Moreover, we can map the element concentration in an
object using the X-ray CT images measured at the tuned photon
energies. Using X-ray CT with an SR source, Thompson et al.
(1984) obtained a two-dimensional (2-D) map of I. The map consisted of a differential image of two X-ray CT images measured* E-mail: ikeda@epi.k.u-tokyo.ac.jp0003-004X/04/0809–1304$05.00

at photon energies just above and below the K-absorption edgeof I. The technique, generally called the “subtraction method,” isbased on the nature of X-ray absorption, whereby the changes inthe LACs of other elements are negligible within a small energy
range around the absorption edge. In later studies, the subtraction
method was applied to the imaging of Ni (Kinney et al. 1986), Cu(Flannery et al. 1987; Kinney et al. 1986), and Mo (Suzuki et al.
1988). In those studies, only qualitative images were obtained,
and no quantitative discussion of the concentration was involved.
The first demonstration that the internal element concentration
could be quantified by the subtraction method was performed by
Hirano et al. (1989). They acquired two CT images (below andabove Mo K-edge) of a set of several tubes containing Mo solution with different concentrations. They obtained a differential
image by subtraction and estimated the Mo concentrations using
the average CT value in each solution. They did not discuss thespatial resolution as a concentration map (whether each pixel had
quantitative meaning), though they mentioned that the spatial
resolution of their CT system was about 125 μm. In this paper, we
report three-dimensional (3-D) concentration mapping obtainedby the high-spatial-resolution X-ray CT system developed at
SPring-8 (Super Photon ring-8 GeV, Hyogo, Japan). Further-1304

IKEDA ET AL.: NONDESTRUCTIVE 3-D ELEMENT-CONCENTRATION MAPPING

more, we discuss the quantitative applicability of the mapping
technique by comparison with a 2-D element map measured byan electron-probe X-ray microanalyzer (EPMA).

X-RAY CT SYSTEM OF SPRING-8 (SP-ΜCT)
In recent years, an X-ray CT system named "SP-μCT"
with high spatial and contrast resolution, using SR, has beendeveloped at beam line BL20B2 of SPring-8 (e.g., Uesugi et al.
1999; Tsuchiyama et al. 1999). BL20B2 is a bending-magnet
beam line with a Si (311) double-crystal monochromator at
45 m from the light source, producing monochromatic X-rays
with a flux density of ~1 × 109 photons/s.mm2. The usableenergy range is 8.4−72 keV (Uesugi et al. 1999; Goto et al.
2001). The transmitted X-rays are converted to visible lightby a fluorescent screen of Tb-doped Gd2O2S, expanded by an
optical lens (magnification ×2), and detected by a CCD camera
with the pixels of 1000 × 1018 (Uesugi et al. 1999; Takano
et al. 2001). After the ordinary pre-processing for raw X-ray
intensities and their logarithm conversion, a convolution backprojection (CBP) method with a reconstruction filter using a
Hanning-window is used to reconstruct the CT images fromthe projection data (Uesugi et al. 1999; Nakano et al. 2000).
Each CT image (1000 × 1000 pixels as the maximum) has apixel size of 5.83 × 5.83 μm2 and a thickness of 5.83 μm. The
effective spatial resolution of the SP-μCT is about 13 μm,
according to the results of imaging tests with X-ray energies
less than 20 keV (Uesugi et al. 1999; Takano et al. 2001). The
spatial resolution of the image detector was slightly greaterthan 13 μm at the energy of 36 keV used in this study becauseof blur of the X-ray in the thin fluorescent screen. The contrast
resolution of the system was reported by Uesugi et al. (1999).
The diameter (maximum width) of samples must be less than
5 mm, as it is restricted by the field of view of the detector. A
sample height up to several centimeters is permitted, although
actual imaging area is less than 5 mm in height owing to thedivergent angle of X-ray beams. Imaging of samples up to
several centimeters is possible by connecting several data setswith vertical translations.

EXPERIMENTAL METHODS
Sample synthesis
A Cs-doped, partially molten sample was prepared using natural granite. The
Cs was expected to become concentrated in the melt and this would be useful for
imaging partial melt and for studying element diffusion in the melt. Fine-grained
biotite granite (adamellite having an aplite-like texture) from Hirukawa, GifuPrefecture, Japan, was used for sample preparation. Modal composition of thespecimen was K-feldspar 34%, plagioclase 31%, quartz 31%, and biotite 4%.
The cylindrically formed granite (3 mm in diameter and 10 mm in length) was
put into a platinum tube with Cs2CO3 powder reagent (2.1 wt% Cs2O) and purewater (10 wt%; supersaturated amount). First, the specimen was held isothermallyat 1000 °C and at an isostatic pressure of 228 MPa with Ar gas in an HIP (HotIsostatic Press produced by Kobe Steel, Ltd.). This condition (1000 °C) was meant
to completely melt the granite specimen in 50 h according to preliminary experiments. After holding for 16 h, when the melt fraction had reached about 10 vol%(based on the preliminary experiments), the temperature was dropped to 800 °C
in 2 h. The pressure decreased to 204 MPa with this drop in temperature. After
holding at 800 °C for 75 h, the specimen was quenched at room temperature
under high-pressure conditions. The volume fraction of the melt was about 10%.
If the preheating at 1000 °C is not performed at the first stage, the natural granite
specimen (not powder) does not begin melting, and the melt fraction cannot reach
10 vol% within several days. After removal from the platinum tube, the specimen
was used for the X-ray CT experiments.

1305

X-ray CT experimental procedure
The cylindrical specimen (3.5 mm in diameter and 6 mm in height) was placedon the rotation stage of the SP-μCT system so that the main axis of the sample
became almost the same as the rotation axis of the stage. The system settings were
the same as those reported by Uesugi et al. (1999). We obtained two sets of CT images for this sample. One set was obtained at an X-ray energy of 35.970 keV, which
is just below the Cs K-absorption edge (35.985 keV) (Hubbell and Seltzer 1996).
Another set was obtained at an X-ray energy of 36.000 keV, which is just above
the K-absorption edge. To obtain the CT images, 360 transmitted X-ray images (Iimages) were acquired with a rotation step angle of 0.5 degrees, and exposure timeof 35 seconds per rotation step. One image by a direct beam without the sample(I0 image) was acquired for every ten rotation steps by lowering the sample stage
to correct time drift of the X-ray beam intensity. Dark images were also obtained
before and after the experiment to eliminate the base intensity without the X-ray
beam. A total of 784 tomographic images (2-D slices) were then reconstructed fromthe 360 projection images. Note that the projection images consist of “projections”
as pixel values. The X-ray projection of every pixel, p, is defined by:�� �� � �� � � � � � � � � �� �� �

(1)

where I0 and I are the intensities of incident and transmitted X-ray beams, respectively. Projections in each projection image were calculated using the intensities
I and I0 of corresponding pixels in I and I0 images. The projection p equals to thesum of the LAC of material j (μj) multiplied by the path length through materialj (Lj).
Tsuchiyama et al. (2000; in preparation) obtained an empirical relationshipbetween the CT value (observed LAC by SP-μCT) and the theoretical LAC for
standard materials in the present CT system at the beam line BL20B2. CT-value, f,
is almost proportional to LAC, μ, for small μ (μ < ~20 cm–1) but deviates from thelinear relation for large μ (μ > ~20 cm–1). This nonlinear relation can be expressedby the following empirical formula (Tsuchiyama et al. in preparation):µ = � ����( ) + ( �� ) ���
�

�

�

�

�

(2)

where the parameter of a, b, c and n were determined by least-squares fitting (a= 1.127 ± 0.005, b= 0.5819 ± 0.1414, c = 1.227 ± 0.062 and n = 19.4). In thisstudy, the obtained CT value was converted to the LAC value for each voxel
using Equation 2.
Furthermore, we performed another experiment for data correction. We obtained projection images of a quartz glass cell filled with a CsCO3 aqueous solution(Cs = 2.95 wt%) at X-ray energies of 35.970 keV and 36.000 keV. This quartz
glass cell has a rectangular shape (outer dimensions: 12.7 × 12.5 × 45.0 mm3; innerdimensions: 10.0 × 10.1 × 43.7 mm3) and is usually used for ultraviolet - visible- near infrared spectrophotometers. First, the net projection of the solution was
calculated using the gross projection of the cell and solution and their parameters(chemical composition of the cell: SiO2, density of the cell = 2.08 g/cm3, and thickness of cell walls that X-rays pass through = 1.35 mm × 2 = 2.70 mm). Second, thedifference in the mass-attenuation coefficient (MAC; denoted by τ) above and below
the absorption edge was calculated for every pixel using the chemical composition,
density, and path length of the solution (10.00 mm). Here, the relationship between
MACs, τ, and LACs, μ, is represented by μ (cm–1) = τ (cm2/g) × ρ (g/cm3), whereρ is the density. This measurement of MACs above and below the absorption edge
is indispensable to obtain accurate data by the “subtraction method.” As discussed
later in detail, the difference in MAC (ΔτCs) had variation perpendicular to theground (the plane of the storage ring). This vertical shift of ΔτCs results from theshift of X-ray energy which is caused by the variation of the reflection position
and angle of the X-ray beam in the double-crystal monochromator with verticaldispersion geometry. The shift value depends on the geometry of the light source,
the monochromator, and the sample.

EPMA analysis

To evaluate the spatial and compositional resolution of the present 3-D concentration mapping by SP-μCT, conventional 2-D mapping by an electron-probe
X-ray microanalyzer (EPMA) was performed after the X-ray CT experiment. The
specimen was mounted in epoxy, ground, and polished. The surface obtained after
polishing corresponded to slice no. 252 of the CT images. A JEOL 8900 EPMAat the University of Tokyo was used for this 2-D precise mapping of the surface.
The acceleration voltage and beam current used were 15 keV and 1.2 × 10–7 A,
respectively. The beam diameter was set at 3 μm. The mapping step was set at 6 μm,
similar to the size of one voxel in the CT images. The intensity of the CsL X-rays was

1306

IKEDA ET AL.: NONDESTRUCTIVE 3-D ELEMENT-CONCENTRATION MAPPING

used to determine the concentration at each mapping point. We confirmed the linear
relationship between wt% Cs and the intensity of the CsL X-rays by conventional
point analysis, at many points in the sample, using ZAF correction. Pure CsI wasused as the standard sample to quantify the Cs concentration.

RESULTS AND DISCUSSION
LAC images and estimation of Cs-concentration
Figure 1a shows the CT image of slice no. 252, indicating
the 2-D distribution of the LAC converted from CT values.
Figure 1b shows the distribution of phases obtained by EPMA
element maps. By comparing the two figures, it is clear thatthe constituent minerals have different LACs and different
gray levels in Figure 1a, except for K-feldspar and plagioclase.

Pollucite (Cs2Al2Si4O12⋅nH2O) was crystallized in a Cs-bearing
melt, especially at the periphery of the sample. Table 1 shows
the chemical composition, density (Deer et al. 1966; Dana andFord 1959; Roberts et al. 1974; density of melt was estimatedas described later), and calculated attenuation coefficients ofminerals and melt. Based on the LACs in the table, K-feldspar
and plagioclase have similar LACs and it is theoretically difficult
to distinguish them. The ring artifact, one of the typical artifactsin X-ray CT images, is seen to some extent. However, beamhardening, an unavoidable CT artifact when using polychromatic
X-rays (Denison et al. 1997; Ketcham and Carlson 2001), does
not occur because of the use of monochromatic X-rays. If beamhardening occurs, apparent LAC becomes smaller as it goes tothe central part of the sample, and many problems result when

FIGURE 1. (a) One slice from CT images with the X-ray energy just below the Cs K-absorption edge of 35.970 keV (slice no. 252; 650 × 650
voxels). Gray level corresponds to LAC (1–5 cm–1) calculated from CT values by Equation 2 (in text) as indicated by the gray-scale bar. Theoretical
LACs (μ) of all phases are shown in Table 1. Mineral names are as follows: K-f = K-feldspar, Pl = plagioclase, Qz = quartz, Bt = biotite. (b) 2-D
distribution of mineral and melt phases determined based on the EPMA element maps of Si, Ti, Al, Fe, Ca, Na, K, and Cs. This polished plane
corresponds to slice no. 252 of the CT images. CT images c and d are of slice no. 252 at two X-ray energies just below (35.970 keV) and just above(36.000 keV) the Cs K-absorption edge, respectively, with gray scale 0–15 cm–1. Graphs under the images indicate variation of LAC along the lines
shown in the images. Note that a and c are the same image with different gray scales for LACs.

IKEDA ET AL.: NONDESTRUCTIVE 3-D ELEMENT-CONCENTRATION MAPPING1307

TABLE 1. Typical chemical composition (wt%), density and calculated attenuation coefficients of minerals and melt in the sample
QuartzK-feldspar

SiO2
TiO2
Al2O3
Fe2O3
MnO
MgO
CaO
Na2O
K2O
Cs2O
H2O*
Total

99.1
0.0
0.0
0.1
0.1
0.0
0.0
0.0
0.0
0.0
–
99.3

64.4
0.0
19.2
0.0
0.0
0.1
0.0
2.3
13.5
0.0
–
99.5

36.000 keV (above K-edge)
35.970 keV (below K-edge)

0.57
0.57

Density (g/cm3)

2.65†

Plagioclase
Chemical composition
58.2
0.1
24.6
0.2
0.1
0.0
5.4
10.0
0.3
0.2
–
99.1

BiotitePollucite

Melt

32.3
3.3
18.9
23.1
0.4
7.3
0.0
1.0
9.2
0.2
4.3
100.0

43.8
0.0
17.3
0.2
0.0
0.0
0.1
1.9
1.7
33.7
1.3
100.0

72.0
0.0
11.7
0.1
0.0
0.1
0.3
0.7
2.7
4.8
7.6
100.0

9.73
2.15

1.98
0.83

2.9§

2.4||

Theoretical MAC (cm2/g) at measured X-ray energies
0.72
0.69
1.44
0.72
0.64
1.40
2.56†

2.66‡

3.0†

Theoretical LAC (cm ) at measured X-ray energies
36.000 keV (above K-edge)
1.51
1.85
1.83
4.32
28.2
4.75
35.970 keV (below K-edge)
1.50
1.84
1.71
4.20
6.24
1.98
* For phases including water, H2O content was estimated by subtraction of total wt% from 100.
† Deer et al. (1966).
‡ Density of plagioclase depends on Ab-An ratio (Deer et al. 1966) and the value in the table was estimated using the measured Ab-An ratio (Ab77An23).
§ e.g., Dana and Ford (1959); Roberts et al. (1974).
|| Estimated from chemical composition (see text).
–1

quantitative analyses are carried out.
Figures 1c and 1d show CT images with two X-ray energies
just above and below the Cs K-absorption edge, respectively.
Because of the very small difference in X-ray energy between thetwo conditions (0.030 keV), there is little difference in the LAC
between the two images in the Cs-free regions. For example,
quartz grains that contain no Cs show the same gray level inthe two images. In contrast, considerable difference occurs in
Cs-bearing regions. These regions consist of pollucite crystals
and melt containing dissolved Cs. Such a difference in the LAC
is induced by the large difference in the MACs of Cs above andbelow the absorption edge. The MAC for Cs just above the Kabsorption edge is about 5 times greater than that just below theedge (Hubbell and Seltzer 1996). As described above, LACs (μ)
have the relationship with MACs (τ) represented by μ (cm–1) =τ (cm2/g) × ρ (g/cm3). We can derive the weight fraction of Cs
using the difference in the LAC (Δμ) between Figures 1c and1d as follows. The difference in LAC of each pixel above andbelow the absorption edge is:Δμ = (ΔτCs αCs + ΣiΔτi αi)ρ(3)where αCs is the weight fraction of Cs, ΔτCs is the differencein the MAC of Cs above and below the Cs K-absorption edge,
and i denotes all other elements (modified from Hirano et al.
1989). Because Δτi is very small, the second term is negligible
compared to the first term, and we obtain the following equation(Hirano et al. 1989):� �� �

���� �� � .

(4)

Although the X-rays used in the present study were monochromatic, a small degree of vertical variation of the X-ray
energy, which caused changes in ΔτCs, was inevitable in a large
beam area (Fig. 2d). The theoretical energy spread in the vertical

FIGURE 2. Variation in the X-ray projection (line integral of LAC
along the X-ray path) through the quartz glass cell filled with Cs-bearing
solution measured at X-ray energies of (a) 35.970 keV and (b) 36.000
keV. The sample was not rotated. Variation in the projection indicates theenergy shift in the actual X-ray beam. The energy shift is probably due tothe X-ray monochrometer system shown schematically as d. Using the
projection data, path length through the cell, and chemical compositionand densities of the solution and the cell, ΔτCs (the difference in the
MAC of Cs above and below the Cs K-edge) of every slice was obtained
as c. The projection and ΔτCs have vertical and horizontal variation.
Solid curves indicate mean value in each slice. The horizontal variation(standard deviation) in each slice is shown with gray bar. The horizontal
variation of projection and ΔτCs is negligibly small compared with thevertical one, excepting the top and bottom regions of the X-ray beam.

1308

IKEDA ET AL.: NONDESTRUCTIVE 3-D ELEMENT-CONCENTRATION MAPPING

direction (4 mm) is 0.019 keV assuming that the monochromatoris perfect. As described above, the actual vertical distribution ofΔτCs was measured by acquiring the X-ray projection image of aquartz glass cell filled with a Cs-bearing solution of known concentration. Figures 2a and 2b show actual variations in the X-ray
projections through the cell with the X-ray energy just above andbelow the Cs K-absorption edge, respectively. Figure 2c shows
the variation of ΔτCs obtained using the projection data. The horizontal deviation of ΔτCs was negligibly small compared with thevertical one as shown by the (horizontal) error bars. To improve
the quantitative accuracy of αCs, we used the measured ΔτCs in
Equation 4 for each slice (i.e. a ΔτCs value for each slice). Because
Δμ can be obtained from the CT images by using Equation 2,
the only unknown parameter was ρ. We assumed ρ to be 2.4
g/cm3 and 2.9 g/cm3 for the melt and pollucite, respectively. The
density of 2.4 g/cm3 is that of the melt, including 5 wt% Cs2O,
estimated by the method proposed by Bottinga et al. (1982). The
influences of pressure (about 0.05 g/cm3 increase at 200 MPa)
and water content (about 0.05 g/cm3 decrease at 5 wt% H2O)
(Johannes and Holtz 1996) were also taken into consideration.
According to the EPMA measurements, the solubility of Cs to
the partial melt in the specimen was less than 6 wt% as Cs2O.
The mapping points which had Cs2O concentrations greater than
6 wt% included the contribution from pollucite. The estimatedmelt density of 2.4 g/cm3 could be applicable to the regions with
Cs2O concentrations less than 6 wt%.
Cs-concentration maps and their resolutions
Figures 3a and 3b show Cs2O concentration maps obtainedby CT images (slice no. 252) with two estimated densities of
2.4 g/cm3 and 2.9 g/cm3, respectively. Figure 3c shows the Cs2O
concentration map by the EPMA, in a polished section corresponding to slice no. 252. The nondestructive Cs concentration
maps are in good agreement with the EPMA map, althoughsome ring artifacts affect the Cs maps. In particular, the Cs2O
concentration in the melt by SP-μCT (see blue areas in Fig. 3a)is almost the same as that by the EPMA. The Cs2O concentrationof pollucite crystals by SP-μCT (see high concentration areasin Fig. 3b) is also close to that by the EPMA. Owing to theseresults, we can conclude that this method has high quantitative
accuracy if the density of the material is known. Accordingly,
the quantitative error in this mapping technique depends largelyon the uncertainty of the density.
Figures 3d and 3e show images for comparison of the effective spatial resolution. As mentioned above, the voxel (3-Dpixel) size is similar for the EPMA and X-ray CT analyses. The
effective spatial resolution of EPMA mapping (electron probeof the X-ray emission area) is considered to be about 6 μm
(width) and 3 μm (depth) for the present measurement conditions(Castaing 1960). This 6 μm in-plane resolution of EPMA mapping corresponds to the pixel size (step distance) of the EPMA
map in this study. The boundary between the melt and pollucite
and that between the melt and quartz are sharp in the EPMA map(Fig. 3e), whereas they are diffuse with width of 3–4 pixels in the
SP-μCT map (Fig. 3d). Thus, the effective spatial resolution of
SP-μCT mapping is considered to be about 20 μm (3–4 voxels).
This spatial resolution is slightly poorer than the 13 μm effective
resolution of the SP-μCT system, mentioned previously (Uesugi

et al. 1999; Takano et al. 2001). This difference is probably due
to a subtle shift of the voxels (coordinates) between the images
above and below the absorption edge, depending on the sample
displacement or change in the X-ray path. This spatial resolutionof about 20 μm by “nondestructive method” is noteworthy.
Figure 4 shows the difference between Cs2O concentrations
measured by SP-μCT and EPMA. Concentrations estimated by
SP-μCT (slice no. 252) are compared pixel by pixel with the
EMPA map. Most of the data points plot on and around the 1:1
line, although a few points deviate significantly from the line.
There are four factors that produce the deviation. (1) The problemof the density estimation is the first factor of the deviation. Figure
4 uses an assumed density of ρ = 2.65 g/cm3, which is the medianvalue of the densities of Cs-bearing melt (2.4 g/cm3) and pollucite(2.9 g/cm3). For the first approximation, the assumed density isreasonable because almost all data points ranging from 6 to 30
wt% (larger than the amount dissolved in the melt and smaller
than the concentration in pollucite) plot on and around the 1:1
line. These data points include contributions from both melt andpollucite. On the other hand, the data points for concentrations
greater than 30 wt% plot far above the line (region A in the figure)because they originate only from pollucite with higher density.
(2) The second factor is the artifacts that characteristically appearin X-ray CT images. The deviant points in region B originate
mainly in the ring artifact. However, the number of points plottedin region B is very small as shown by the following regression
analysis. (3) The third factor is attributed to measurement error
by EPMA analysis. The EPMA map also has an error of about
1 wt% and shows larger deviations in some cases, for example,
by scratches on the polished surface. (4) The fourth factor is thetechnical problem of pixel-by-pixel comparison like Figure 4.
The complete pixel matching between two images acquired by
X-ray CT and EPMA is very difficult and is the principal causeof the deviation. Thus it should be noted that real uncertainties
of concentration by SP-μCT is better than that shown in the
figure. According to the regression analysis using all data points
in Figure 4, the correlation coefficient is 0.91 and the confidence
interval of 95.4% probability was estimated as ±2.5 wt%. In
this report, we use this confidence interval as the compositional
resolution of the 3-D mapping technique although real accuracy
ought to be better than that.
3-D concentration mapping and its usefulness
Figure 3f shows the 3-D Cs2O concentration map obtainedby stacking 300 slices. The concentration in each slice was corrected using the measured ΔτCs shown in Figure 2c. In the previous estimation of the element concentration by the subtraction
method (Hirano et al. 1989), the published value was used forΔτ. However, this value varies depending on the position in the
X-ray beam, the energy setting above and below the absorption
edge, and other factors. Thus, quantitative reliability in the present study has largely improved.
3-D concentration maps are particularly important for studying material transport in anisotropic materials or partially moltenmaterials. We can derive information on 3-D Cs diffusion fromthis 3-D concentration map. Of course, some Cs was transported
to the inside of the sample by H2O, because Cs was added aswater-soluble Cs2CO3 in this study. However, Cs is considered toIKEDA ET AL.: NONDESTRUCTIVE 3-D ELEMENT-CONCENTRATION MAPPING1309

F IGURE 3. Nondestructive
Cs2O concentration maps of sliceno. 252 obtained by SP-μCT (650× 650 voxels). Density is assumed
to be (a) 2.4 g/cm3 and (b) 2.9 g/
cm3. (c) Cs2O concentration mapof polished surface obtained by
EPMA (650 × 650 pixels). (d)Enlarged image of the box
region shown in CT image (b):voxel size is 5.83 × 5.83 × 5.83
μm. (e) Enlarged image of the box
region shown in EPMA image(c): pixel size is 6.0 × 6.0 μm.
Mineral names are as follows:
Pol = pollucite, Qz = quartz. (f)Bird eyeʼs view map of 3-D Cs2O
concentration map constructed bystacking 300 tomographic maps
(slice nos. 252–551; 650 × 650
× 300 voxels) with density ρ =2.9 g/cm3 (corresponding to b).
Concentration in each slice wascorrected using the measured ΔτCs,
obtained in Figure 2.

have been transported mainly by diffusion in the melt, because
the Cs2O concentration decreases toward the center of the sample.
Although we have not yet studied the details of the diffusion
process (for example, evaluation of the tortuousity of the melt
channel), the diffusion coefficient of Cs in partial melt is roughly
estimated as on the order of 10–10 m2/s. Such diffusion in partiallymolten materials has to be studied in three dimensions because
the 3-D network structure cannot be investigated precisely in
two dimensions (e.g., Ikeda et al. 2000).
3-D network structures of melt or crystals are important andhave been the targets of X-ray CT study. For example, Brown etal. (1999) identified the melt network in migmatite (strictly, thenetwork of leucosome in crystallized migmatites) and Philpotts

et al. (1999) discussed 3-D plagioclase chain networks using
X-ray CT. They used an ordinary X-ray CT technique, thus,
segmentation of leucosome or plagioclase by thresholding was
performed based on the difference of LACs. Although they could
obtain good binary images of the leucosome or plagioclase, theLACs of melt and minerals are generally very similar in silicate
systems and thresholding based on LACs are often difficult. 3-D
element-concentration maps are also useful from the point of thethresholding and making quantitative binary images. The 3-D
element mapping technique enables us to extract the material ofinterest by thresholding based on the element concentration. For
example, from the results of the 3-D image analysis technique(cluster labeling; Ikeda et al. 2000), 88 vol% of Cs-bearing melt

1310

IKEDA ET AL.: NONDESTRUCTIVE 3-D ELEMENT-CONCENTRATION MAPPINGFIGURE 4. Relationship between Cs2O concentrations measured by
EPMA and those by SP-μCT (slice no. 252). The concentrations by SPμCT were calculated using a density of 2.65 g/cm3, the median valueof melt (2.4) and pollucite (2.9). The corresponding pixels between theimages were determined by the appropriate coordinates conversions,scaling, rotation and parallel translation, because the size of pixels andpositions of the sample were different in the images. Actual comparison
was carried out using the average concentration of 4 × 4 = 16 (~ 24 ×
24 μm) pixels as one unit, which corresponds to the spatial resolutionof the SP-μCT mapping (20 μm). The central solid line indicates theleast-squares fitting in regression analysis and other solid lines indicate
the ±2σ (confidence interval of 95.4% probability). Regions A and B
are discussed in the text.

regions of 4–6 wt% Cs2O were connected as the 3-D network.
Thus, this 3-D concentration mapping technique is potentially apowerful tool for studying 3-D network structures.
Possibility of diffusion study by the 3-D mapping
The 3-D diffusion study is important and here we discuss thepossibility of diffusion studies by this nondestructive 3-D mapping technique. Figure 5a shows theoretical diffusion profiles
drawn for various (Dt)1/2, where D and t indicate the diffusion
coefficient (m2/s) and time (s), respectively. In the figure, horizontal and vertical intervals of the grid lines correspond to the spatial(~20 μm) and compositional resolution (±2.5 wt%) of the map,
respectively. Based on the spatial and compositional resolution,
the diffusion profiles of (Dt)1/2 ranging from 3 × 10–5 m to 3 × 10–4
m seem to be detected most precisely if the initial concentrationof the diffusion source is larger than 30 wt%. Figure 5b shows
the relationship between the time scale of geological events anddiffusion processes. As described above, diffusion processes plotting in the gray zone, where (Dt)1/2 = 3 × 10–5 – 3 × 10–4 m, arethe best candidates for the studies. For example, diffusion insilicate melt or glass in experimental samples (fast diffusion in
short time scale) is one of the potential targets. Partially molten
rocks prepared (quenched) in laboratories are proper samples
for investigating diffusion in complicated 3-D network systems.
Anisotropic material transport by the combination of diffusion
and advection in melt is also an important subject that can bestudied by the 3-D mapping technique. Moreover, “nondestructive measurement” enables the in situ diffusion studies. Using
the samples having appropriate diffusivity, time-resolved in situ
diffusion studies can be performed in the SP-μCT system. In such

FIGURE 5. (a) Diffusion profiles calculated using the error function
assuming an extended source of infinite extent (Crank 1975). The initialconcentration was fixed at 30 wt%. Diffusion profiles were drawn forvarious (Dt)1/2. The horizontal and vertical grid lines indicate the spatial
resolution and compositional resolution, respectively. (b) Relationshipbetween time scale and diffusion coefficients. The gray zone satisfies thecondition of (Dt)1/2 ranging from 3 × 10–5 to 3 × 10–4 m. The diffusion
processes that plot in the gray zone are potential targets of the 3-D
mapping technique. The ranges of diffusion processes are based on, forexample, Hofmann (1980), Lasaga (1998), and Nakashima (1995).

studies, time-resolution generally corresponds to the acquisition
time of one set of the projection images required for the reconstruction, that is, ranges from one to several hours (depending on
the target element, its concentration, and the sample diameter).
Volume diffusion that occurred in plutonic or metamorphic events(slow diffusion on long time scales) is also the target. Becausesuch slow diffusion cannot be investigated in situ, the traces ofanisotropic diffusion left in the natural specimens are candidates
for this mapping technique. Therefore, the nondestructive 3-D
mapping technique can be used for various 3-D and/or in situ
diffusion studies.
Other uses of the nondestructive 3-D mapping technique
Because all elements have absorption edges, this technique
can be applied to various samples and elements. As mentioned
above, “3-D” compositional information is important in many
scientific fields. The “nondestructive” feature of this technique
is also important, for example, for obtaining internal-elementconcentration maps of precious samples such as cultural assets,
which must not be cut. This technique is also useful for curation of extraterrestrial materials, such as precious meteorites

IKEDA ET AL.: NONDESTRUCTIVE 3-D ELEMENT-CONCENTRATION MAPPING

1311

FIGURE 6. Variation ofpenetration depths of X-ray
with the absorption energy
for different elements.
Data are plotted in orderof increasing atomic
number. The penetration
depths were calculated fora granitic rock, basalt, anda chondritic meteorite. The
chemical compositions ofJapanese standard granite(granodiorite) JG-1 (Imaiet al. 1995), mid-ocean
ridge basalt N-MORB (Sunet al. 1979), and Allendemeteorite CV3 (Jarosewich1990) were used. Density
was assumed to be 2.7 and2.9 g/cm3 for JG-1 and NMORB, respectively. The
density of Allende is 2.92 g/
cm3 (Consolmagno and Britt
1998). Penetration depth oftransmittance 10% and 90%
correspond to the maximum
and minimum sample
diameter, respectively.
Sample diameter is also
restricted by the field ofview of the detector (CCD
camera), spatial resolution,and usable X-ray energy.
These limitations are shownin the figure.

and samples returned by planetary missions. In addition, it is a
useful tool for investigation of samples that are easily deformed
or damaged by cutting, such as living tissues or fragile, porous
materials. So far, our research group has succeeded in obtaining
Fe distribution images of Antarctic micrometeorites of less than
100 μm (Tsuchiyama et al. 2001), with a spatial resolution of theorder of 1 μm, using the Fe K-absorption edge (7.112 keV) at“in-vacuum” type undulator beam line BL47XU (Uesugi et al.
2001) of which X-ray flux density is three orders of magnitudelarger than that of BL20B2. The monochromator is an Si (111)
double-crystal type. We are now investigating the quantitative
accuracy of the Fe concentration estimation in the minerals.
Restriction on sample diameter
Because the X-ray CT technique requires appropriate
transmittance of X-ray beams, the sample size (thickness) is
first restricted by the transmittance. Secondly, the sample size

is restricted by the field of view of the detector (CCD camera)
because the sample is rotated and projection images of the sample
should be acquired in all directions without any overflow into
the outside of the view (overflow into the direction of the rotation axis has no problem). Thirdly, the sample size is restrictedby the usable X-rays energy of the beam lines. Here, we discuss
the “sample diameter” as the sample size because a cylindricalshape is the most appropriate one for X-ray CT measurement.
If the sample is not cylindrical, the path length of X-ray varies
with sample rotation and further consideration is required forthis argument.
Figure 6 shows the relationships between energy of the X-ray
and penetration depth of which transmittance is 10% and 90%.
A transmittance of 10% is empirically the lower limit for obtaining the X-ray CT images sufficient for element concentration
measurement. Thus, the penetration depth of 10% transmittancemeans the maximum diameter (upper limit) of the sample. A

1312

IKEDA ET AL.: NONDESTRUCTIVE 3-D ELEMENT-CONCENTRATION MAPPINGtransmittance of 90% is the upper limit for obtaining the X-ray
CT images. Thus, the penetration depth of 90% transmittancemeans the minimum diameter (lower limit) of the sample. Because the energies of X-ray absorption edges are different fordifferent elements, the maximum and minimum sample diameter
varies depending upon the target element. These depth data were
calculated using the standard compositions of igneous rocks (JG1 as granitic rocks and N-MORB as basaltic rocks) and a meteorite (CV3) without any other components; thus, the penetration
depth decreases if the sample includes a large amount of target
heavy elements. According to these calculated data, the upper
limit of the sample diameter based on the X-ray penetration is
as following examples:
BL20B2 using K-edge (Cu-W are measurable)
Cu: 80 μm (CV3), 130 μm (MORB), 200 μm (JG-1)
Cs: 5 mm (CV3), 8 mm (MORB), 12 mm (JG-1)
W: 20 mm (CV3), 28 mm (MORB), 35 mm (JG-1)
BL20B2 using LIII-edge (Tm-U are measurable)
Tm: 90 μm (CV3), 150 μm (MORB), 220 μm (JG-1)
U: 600 μm (CV3), 1.0 mm (MORB), 1.7 mm (JG-1)
BL47XU using K-edge (Fe-Ba are measurable)
Fe: 60 μm (CV3), 90 μm (MORB), 130 μm (JG-1)
Ba: 5 mm (CV3), 9 mm (MORB), 13 mm (JG-1)
BL47XU using LIII-edge (Nd-U are measurable)
Nd: 100 μm (CV3), 85 μm (MORB), 100 μm (JG-1)
U: 600 μm (CV3), 1.0 mm (MORB), 1.7 mm (JG-1).
On the other hand, the lower limit of the sample diameter
due to the X-ray penetration is, for example, 10 μm, 600 μm and1.5 mm for Cu, Cs, and W, respectively, when using the JG-1
composition and the K-edge. Using the LIII-edge, the lower limit
is less than 100 μm even for the heaviest element U.
Besides these limitations due to the X-ray penetration (transmittance), maximum sample diameter is also restricted by thefield of view of the detector and by the usable X-ray energy. The
widths of the field of view of the detector are 5 mm and 0.45 mm
for BL20B2 and BL47XU, respectively. Thus, the actual sample
size for Cs measurement at BL20B2 is restricted to 5mm (or lesseven for the granitic samples). The minimum sample diameter,of course, must be larger than the spatial resolutions of themeasurement systems, that is, ~20 μm and ~1 μm for BL20B2and BL47XU, respectively. In Figure 6, the energy ranges ofusable X-ray at BL20B2 and BL47XU are shown. Owing to thisenergy restriction, the measurable lightest elements are Cu andFe for BL20B2 and BL47XU, respectively. Although elements
heavier than tungsten (W) have K-edges exceeding the usableenergy range (<72 keV at BL20B2), such heavy elements haveL-absorption edges greater than 12 keV, and therefore can beanalyzed by our method. Thus, our 3-D mapping technique is
useful in studying various subjects in the earth and materials
sciences.

ACKNOWLEDGMENTS
The synchrotron radiation experiments were performed at the SPring-8 withthe approval of the Japan Synchrotron Radiation Research Institute (JASRI) (proposal no. 2000B462-COM-np, 2001A0334-COM-np). Useful discussions with
M. Nakamura, T. Yoshino, and K. Mibe are gratefully acknowledged. We thankH. Nagahara, A. Yasuda, and M. Hamada for use of the HIP. We are grateful to
M. Rivers and B. Minarik for helpful and constructive comments which improved

the manuscript. This research was supported in part by a Research Fellowship of
the Japan Society for the Promotion of Science for Young Scientists (to S.I.). A
part of this study was financially supported by the Budget for Nuclear Researchof the Ministry of Education, Culture, Sports, Science and Technology, based on
the screening and counseling by the Atomic Energy Commission.

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