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DOI: 10.1016/j.jmrt.2018.10.003
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Quantitative X-ray microtomography technique to evaluate high-temperature transient diffusion of Iron diffusants in high alumina-silicate porous refractory media
Carlos Eduardo Guedes Catunda
Corresponding author
, Roberto Ribeiro de Avillez, Marcos Henrique de Pinho Mauricio
Department of Chemical and Materials Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil
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Figures (6)
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Tables (5)
Table 1. Chemical analysis of media and diffusants [38].
Table 2. Phase analysis of media and diffusants [38].
Table 3. Physical properties of high alumina-silicate porous refractory media [38].
Table 4. Acquisition parameters of the 3DμCT test and operating limits of the equipment.
Table 5. Adjustment parameters of the quantitative experimental data by the Levenberg–Marquardt (LMA) method for the diffusing couple subjected to high-temperature conditions.
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Diffusion tests were performed with solid diffusants of Iron oxides in contact with porous silico-aluminous refractory castables in high-temperature conditions. A non-destructive X-ray computer microtomography technique with digital 3D reconstruction (3DμCT) was used for spatial monitoring the diffusion into the media. A particle tracking (PT) method was applied to evaluate diffusion through porous materials and to quantify its diffusive properties based on 3D images over time. The influence of temperature was examined in the range from 1100°C to 1300°C. Each sample was heat treated for 100h in the investigated temperature. The normalized concentration of diffusants as a function of the penetration was obtained by 3DμCT images and compared with the concentration profile determined by elementary microanalysis with energy dispersive spectroscopy and surface chemical mapping (MAP/EDS). Thus, the diffusivity of the porous media was quantified from the experimental data. It was observed a variation less than 3.52% between the MAP/EDS and 3DμCT, i.e., between the destructive and non-destructive methods, suggesting that the 3DμCT method may be extended to other media and diffusants.

High-temperature diffusion
High alumina-silicate refractory
Mechanical properties
X-ray microtomography
Image analysis
Full Text

The study of the mass flow and its different transport mechanisms has aroused great interest in the materials science community. The determination of the diffusivity [1–8] and the effective penetration of solid diffusants in various porous media [5,9,10] is of fundamental importance in materials engineering studies. Porous media, such as refractory materials, represent a strategic segment of outstanding importance in the scientific field [11–13] of mass transport phenomena and the industrial field [14–17]. The chemical study of the diffusion couple (medium/diffusant) interaction subjected to different thermal conditions is fundamental, especially in the base industry. Thus, this study sought to conduct transient diffusion experiments with diffusive etching of Iron(II), Iron(II, III) and Iron(III) oxide for porous media composed of alumina-silicate refractory materials of high alumina (SiO2–Al2O3), to quantify the respective diffusivity (diffusion coefficient) under high-temperature conditions. In the case of porous heterogeneous substrates, such as high alumina-silicate castables refractories, the diffusive mass propagation is favored by the temperature [7,13,18–20] which ranges from 1100°C to 1300°C. Thus, to predict the transient concentration of diffusant based on the diffusive model, it is necessary to know the spatial and temporal arrangement of each diffusant particle in the media for each thermal condition.

X-ray 3DμCT is fast becoming a consolidated tool within the materials science community for the acquisition of 3D images and as a quantitative diagnostic tool [21–26]. As a non-destructive technique, 3DμCT is an ideal means to trace diffusion over time.

This study first considers the image acquisition process, followed by the segmentation stages, where the samples were examined for the quantification of the 3D image data to extract key topological parameters such as density variations from attenuation-based microtomography. These data are needed to highlight the proclivity of the specific diffusion process under high-temperature conditions, such as the evolution of chemical etching in refractory media. Particle tracking (PT) methods allow the mapping of the diffusion phenomenon in 3D over time [27,28]. Finally, the use of 3DμCT images is considered as the starting point to predict diffusion through porous materials and to quantify its diffusive properties by the normalized concentration of diffusants as a function of penetration based on realistic media under high-temperature conditions [3–6,14,15]. The diffusivity was also compared with the standard destructive surface microscopy technique, in this case, elementary microanalysis by EDS with spectral imaging and surface chemical mapping (MAP/EDS).

This study could be synthesized according to its primary objectives, as follows:

  • Demonstrate the behavior of the diffusional interaction between the diffusants and the porous media (diffusion couple) subjected to service under high-temperatures;

  • Predict and quantify the diffusivity and penetration of diffusants along the depth of the porous media as a function of temperature;

  • Present practical applications for 3DμCT/PT method, associated with the fundamental concept of diffusivity; and

  • Compare the values obtained by different methods (destructive and non-destructive experimental techniques) and discuss them based on the results obtained in this study.

2Materials and experimental procedures2.1Fabrication of high alumina-silicate porous refractory media

The powdered refractory material of SiO2–αAl2O3 (Tables 1 and 2) was prehydrated with demineralized water at 20°C in the ratio of 5×10−2L/kg. Homogenized in the mechanical mixer and prepared in a ϕ25.4(1″)×200mm mold by a free casting process with the subsequent application of 0.2MPa pressure (Dynisco/LMI4000/USA) to favor the subsequent drying process. The monolithic ceramic was dried at 70°C for 24h with a subsequent sintering process of 70h in a tubular furnace (Maitec/FTEI6004/Brazil). The maximum temperature was 1450°C for 5h with a heating ramp of 0.5°C/min in standard air atmosphere and maximum shrinkage of −0.4%. This procedure tries to simulate the formation of the alumina-silicate bed in the large steel slabs reheating furnaces [29,30]. Twenty cylindrical-shaped samples of 10mm were cut for diffusion test according to Fig. 1a and physical properties as shown in Table 3.

Table 1.

Chemical analysis of media and diffusants [38].

Chemical analysis  Al2O3  SiO2  CaO  TiO2  ZrO2  NaO2  K2P2O5  MgO  Fe2O3  Fe3O4  FeO 
Mediaa  91.31  4.53  1.64  1.33  0.43  0.15  0.07  0.05  0.04  0.44     
Diffusant                    38.96  39.76  21.28 

Granulometry (Tyler mesh −25+230); temperature of use (°C): max. 1375°C [TG-DTA]; pyrometric cone equivalent: cone>35 (>1785°C).

Table 2.

Phase analysis of media and diffusants [38].

(XRD) X-ray crystallography  Corundum  Anorthite  Grossite  Mullite  Hematite  Magnetite  Wustite 
Media (%)  90.15  6.23  2.68  0.93       
Diffusant (%)          38.96  39.76  21.29 
Fig. 1.

Diffusion couple sample and digital image processing and analysis: (a) Monolithic cylindrical-shaped sample ϕ25.4(1″)×10mm for diffusion test by chemical etching, (b) digital diffusion couple reconstruction, (c) RoI segmentation and identification of the diffusants, and (d) RoI cross section ϕ20mm slice converted into monochromatic 8-bit image [43] to quantify the concentration of diffusants.

Table 3.

Physical properties of high alumina-silicate porous refractory media [38].

Physical properties  Bulk density (g/cm3Cold crushing strength (MPa)  Cold modulus of rupture (MPa)  Total linear change (%) 
After drying at 70°C  3.17±0.03  62.46±1.16  19.96±0.34  0.0 (−0.4 at 1300°C) 
2.2Iron diffusants

The Iron diffusants (Tables 1 and 2) were steel scrap collected from an industry furnace (Gerdau/Brazil). The material was ground to pass mesh 65 to 270 (−65+270) and improve its dispersion on the top of the ceramic samples. The XRD data for the solid diffusant characterize a material composed mainly of Iron(II), Iron(II, III) and Iron(III) oxide [31–34] in the proportion of 1:2:2. The diffraction pattern was generated by the BRUKER diffractometer D8 Discover, operating with CuKα radiation, angular step of 0.02° (2θ) from 10° to 90° and acquisition time for each point of 0.4s. The phases were identified in the software EVA [35] and adjusted by the Rietveld refinement method [36] with the software TOPAS 4.2 [37].

2.3Diffusion couple

The experimental sample setup and furnace temperature simulated the conditions present inside the industrial reheating furnaces. The sintered ceramic cylindrical samples were covered with 5mm thick layer of the Iron oxide solid diffusant powder. This geometry is similar to the classical diffusion couple. The diffusion pairs were subjected to 5 different temperature regimes per 100h, respectively, 1300°C, 1275°C, 1250°C, 1200°C, and 1100°C. The maximum heating and cooling rate was 2°C/min, error ±0.1°C. The diffusion was modeled by two semi-infinite media [13,18,39,40]. It was assumed an initial concentration of 100% of Iron oxide on etching side and 0% of Iron oxide in the silico-aluminous substrate.

The solution is the complementary error functions (erfc), Eq. (1), if the diffusion coefficients are temperature independent [13] and θ is the relative concentration, z is the penetration, t is the time, and DAB is the effective diffusion coefficient, function of temperature.

2.43DμCT analysis

This study uses the 3DμCT data to reconstruct the diffusion couple samples (Figs. 1b and 2) and to segregate the region of interest (RoI) of diffusants [6,9,23,41,42] as shown in Fig. 1c. The concentration of diffusants in a series of thin sections was obtained by extracting critical topological parameters from attenuation based 3DμCT by digital crop in concentric ϕ20mm slices, to avoid edge adverse effects, as shown in Fig. 1d [43]. The penetration data so obtained were analyzed by fitting them with Eq. (1) to extract the diffusivity from the concentration curves (Fig. 3).

Fig. 2.

3DμCT reconstructed images for diffusion couple cylindrical-shaped sample (M1_T1100_S5B) before diffusion test: (a) XY view, (b) XZ view, and (c) XYZ view.

Fig. 3.

Generalized solution of the diffusivity by 3DμCT method: (a) pore concentration scatter data of experimental condition 1100°C as a function of penetration; (b) concentration of diffusants scatter data of experimental condition 1100°C as a function of penetration, (c) relative concentration (θ) as a function of penetration; and (d) generalized surface of relative (dimensionless) diffusivity as a function of penetration and temperature.

The XRADIA 510 VERSA (ZEISS) microtomograph [44] was used with: X-ray source (NORDSON) model NT1626 with micro focal tube and copper (Cu) anode [24,45]; macro lens detector (ANDOR) model DW936N-BV-558 with matrix 2048×2048 pixels coupled to CCD camera; and a 4-degree sample micropositioning system (NEWMARK SYSTEMS) model WLE. The test acquisition parameters are set out in Table 4.

Table 4.

Acquisition parameters of the 3DμCT test and operating limits of the equipment.

Acquisition parameters  [unit]  Real  Min  Max. 
Voltage  kV  140.17  30  160 
Current  μA  71.07  15  70 
Power  9.96  10 
Exposition time [22]  1.00  0.2  – 
Total scan time  4.38  –  – 
Source-object distance  mm  52.00     
Object-detector distance  mm  68.01     
Pixel sizea  μm  30  0.35  – 
Angular pitch  rad.  0.004  0.628  – 
Slice thickness  μm  30  –  – 
Amplification factor  ×  0.4  0.4  40 
Number of projections  n°  1601  10  – 
Camera binningb  × 
Image size  Matrix  1024×1024  512×512  2048×2048 
Source filter  Type  HE2  LE1  HE6 
Filter thickness  mm  0.12  0.03  0.32 

The pixel size depends on the lens used. The best achievable resolution for each lens is: (i) 5μm for 0.4× objective; (ii) 0.7μm for objective 4×; (iii) 0.45μm for objective 20×; and (iv) 0.35μm for objective 40×.


Binning 2 was used as a way to maximize the signal by reducing the exposition time with the image resolution.

The software SCOUT-AND-SCAN [44], version 10.7.3245 (ZEISS XRADIA), was used for the control and capture of the 3DμCT images. The software XMRECONSTRUCTOR [44], version 10.7.3245 (ZEISS XRADIA), was used for the reconstruction of the 3DμCT images. The ORS software [46], version (OBJECT RESEARCH SYSTEMS INC), was used for the digital image processing and analysis.

The digital processing of 3D images (Fig. 1b) starts applying the Non-Local Means (NLM-5K) algorithm, an edge-preserving denoising filter, available in the ORS [46], and further threshold segmentation (Fig. 1c). The NLM-5K was applied to each slice (2D) and replicated to the entire volume (3D). The densitometric difference, and therefore the X-ray attenuation of the Iron oxide diffusants in the medium, was quite evident, justifying the application of the NLM filter. As a result, the post-filtering images are obtained with a minimal loss of detail and preserved edges [47].

Quantification of the concentration of diffusants in each slice (thin sections) as a function of the penetration was obtained by the software FIJI [48] in the version 1.51f (IMAGEJ). A sequence of images was generated and converted to 8-bit monochromatic as shown in Fig. 1d. The percentage of area occupied by the segmented objects can be interpreted as the concentration of diffusants A in B medium (CAB), or calculated for relative concentration penetration curve, θ, as used in Eq. (1), as a function of the penetration [2,13,38,40,49].

2.5Microanalysis by energy dispersive spectroscopy (spectral imaging and surface chemical mapping [MAP/EDS])

The JSM-6510L MEV JEOL scanning electron microscope coupled to the Thermo scientific NSS Spectral Imaging (THERMO FISHER SCIENTIFIC INC.) was used for the chemical surface mapping by EDS scanning through spectral image analysis with NanoTrace detector microprobe. The diffusion couples were sectioned exposing the central plane of penetration of the diffusants. The sections were embedded in epoxy resin with vacuum impregnation with 24h cure followed by deposition of Au film in the BALZERS SCD050 equipment at 25°C with a potential difference of 500V, in a vacuum system operating at 4×10−1mbar. For the quantification of the diffusant, back scatted electrons (BSE) with 15kV primary beam acceleration voltage were used in in-line micro scanning along the sample depth (Fig. 4). The objective of this destructive analysis (MAP/EDS) was to compare the quantitative results with the 3DμCT analysis.

Fig. 4.

Penetration analysis by energy dispersive spectroscopy (EDS): (a) backscattered electron (BSE) images showing in-line cross-sectional scanning along the depth; (b) elementary chemical mapping of Fe diffusant by X-ray energy dispersive spectroscopy coupled with spectral analysis mode (EDS/NSS), and (c) spectral pattern.

3Results and discussion3.1Penetration analysis by 3DμCT over time with PT method

The 3DμCT reconstructed images of the diffusing species is shown in Fig. 2, for one of the cases analyzed.

The percentage of diffusant occupied area in the monochromatic 8-bit digital slices was converted to the diffusants concentration in the medium along the depth of the samples for each experimental condition [2,49], respectively, 1100°C, 1200°C, 1250°C, 1275°C and 1300°C. Thus, the approximated concentration profile along the depth was obtained by the non-linear adjustment of the erfc function [13,18,39,40]. The Levenberg–Marquardt scaled algorithm (LMA) without weighting methods was used [8,50]. The obtained adjusted values are in Table 5.

Table 5.

Adjustment parameters of the quantitative experimental data by the Levenberg–Marquardt (LMA) method for the diffusing couple subjected to high-temperature conditions.

Parameters  1300°C  1275°C  1250°C  1200°C  1100°C 
C0  4,24E+01  3,28E+00  1,51E−01  3,03E−01  3,03E−01 
Def  1,74E+01  1,61E+01  1,45E+01  1,41E+01  1,17E+01 
DAB [mm2/s]  5,00E+03  4,82E+03  4,57E+03  4,50E+03  4,11E+03 
DAB [cm2/s]  5,00E−05  4,82E−05  4,57E−05  4,50E−05  4,11E−05 

The data scatter a lot due to the heterogeneous microstructure, very large grains and porosity, as visible in Figs. 1a and 3a. The porosity required the correction of the penetration profile by the pore concentration, according to Eq. (2) (Fig. 3b), and the generalized solution of the relative concentration penetration curve as shown in Fig. 3c. This correction method allows its correlation with the diffusion models for semi-infinite media.

A more comprehensive way of looking at the relative concentration as a dimensionless diffusivity data (Fig. 3c) is to correlate all experimental quantitative data to form a generalized surface of the concentration as a function of temperature and penetration (Fig. 3d). In this way, it is possible to trace the relative diffusivity behavior to highlight the proclivity of specific diffusion process depending on the thermal condition, depth (penetration) and also on the medium (material).

3.2Penetration analysis by energy dispersive spectroscopy (EDS)

A chemical surface line analysis of the diffusants was carried out on the sample heat treated at 1300°C along the depth (Fig. 4a). The other elements, Al, Si, Mn, O, Ca, and C, were also quantified along the same line. However, only the Fe diffusant was mapped (MAP/EDS), highlighted and quantified as shown in Fig. 4b and c.

These data also showed larger scatter, similar to the data obtained by 3DμCT (Fig. 3a). The data were also fitted by the erfc function (Fig. 5a) and the fitting compared to the one obtained from 3DμCT data. The two fitted results are almost the same within the fitting errors, as shown in Fig. 5b.

Fig. 5.

Comparative analysis for the relative dimensionless concentration profile of the diffusant at 1300°C in the porous medium by different methods (3DμCT and MAP/EDS).

Thus, it is possible to ratify the proposed model for high-temperature transient diffusion of Iron diffusants in high alumina-silicate porous refractory media evaluated by quantitative X-ray 3DμCT since it was subjected to a standard destructive test by elementary EDS microanalysis obtaining comparable results. The confirmation of one method by the other ratifies not only the core of this study but also the data for the inferences of the phenomenological behavior of the diffusivity in porous media itself, reported here. Fig. 5b shows that the most significant difference in the relative concentration of diffusant along the depth of the medium occurred at the greatest depth of the samples in ∼10mm. The maximum difference, Δmax, between the methods was 3.52%, with the relative concentration of 0.463 by the 3DμCT method and 0.480 by EDS.

3.3Diffusion properties

By the adjustment function, C0 and Def, it was possible to calculate the diffusivity DAB, that is, the diffusivity of A in the media B (Table 5), as a thermally activated process. Thus, in agreement with the diffusion models [2,13,20,51], and ratified by this study, the graph of the effective diffusivity was plotted, Def, as a function of the reciprocal temperature, 1/T, as shown in Fig. 6. The activation energy was 208kJmol−1 (inset Fig. 6) with comparable literature results [3,15] for high alumina-silicate porous refractory media and solid Iron diffusants.

Fig. 6.

Effective diffusivity as a function of the reciprocal temperature for the diffuser couple subjected to high-temperature conditions.


The feasibility of quantitative X-ray 3DμCT non-destructive method to measure the Iron oxide distribution inside a silico-aluminous substrate was demonstrated through the comparison of X-ray 3DμCT and EDS microanalysis (as shown in Fig. 5b). So this technique was used to measure the Iron oxide effective diffusivity for temperature from 1100°C to 1300°C (see Table 5). The difference that allowed the RoI segmentation between the absorbers for X-ray waves was 3.86× (KαCu) [52]. The minimum densitometric difference for segmentation was 2.6× [52]. The 3DμCT method provided a detailed reconstruction of the diffusive phenomenon through 3D digital image processing with the NLM K-5 filter, which resulted in minimal detail loss.

The prediction model of the diffusant penetration in porous media showed adherence to the experimental data for the quantification of the relative concentration of diffusants along the depth in the destructive (MAP/EDS) and non-destructive (3DμCT) analysis, with a deviation less than 3.52% between experimental methods. The activation energy (208kJmol−1) was obtained by a linear adjustment between the effective diffusivity (Def) as a function of the reciprocal temperature (1/T), as already assumed in a thermally activated physical situation, with comparable literature results [3,15].

The quantitative X-ray 3DμCT technique is validated as characterization method to study the high-temperature transient diffusion of Iron diffusants in high alumina-silicate porous refractory media and their respective interactive phenomena. This characterization method may be extended to other diffusants and porous media.

Conflicts of interest

The authors declare no conflicts of interest.


This study was financed in part by the CAPES/Brazil (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) – Finance Code 001 and CNPq/Brazil (Conselho Nacional de Desenvolvimento Científico e Tecnológico) – No. 305095/2015-3.

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