Heterogeneities and defects in powder compacts and sintered alumina bodies visualized by using the synchrotron X-ray CT

in powder packing structure. Here we applied the synchrotron X-ray multiscale-CT to characterize the complex domain structures, i


Introduction
The sintering of submicron-and nano-sized powders [1,2] is of interest in the development of miniaturized electronic devices [3], and optical and mechanical components with greater reliability and lifetime. Ultrafine powders are used for making dense materials with finest grain size by pressureless sintering [4][5][6] and two-step sintering [7][8][9]. Fully dense and transparent ceramic materials are fabricated by pressure-assisted sintering such as hot isostatic pressing (HIP) [10,11], hot pressing (HP), and spark plasma sintering (SPS) [12][13][14][15]. However, the submicron-and nano-sized particles easily form agglomerates by interparticle forces (the Van der Waals and electrostatic) during synthesis, storage, and powder handling. The agglomerates and aggregates in powder compact affects the densification and grain growth during sintering [16][17][18][19]. The inhomogeneity in powder compacts induces nonuniform sintering rates and internal local stresses, thereby, may create microstructural defects [20,21]. When the densification rate of an agglomerate is different from the surrounding matrix, a defect will be formed along the boundary between the agglomerate and the matrix. It has been supposed that the pore size distribution is bimodal with small inter-particle pores and large inter-agglomerate pores. As the number of inter-particle pore decreases with densification, the pore drag effect on grain boundary migration [22] is reduced leading to faster grain growth in the denser domain than that in the porous domain in the final stage of sintering. The characterization and control of the heterogeneities of particle packing in the green bodies are critical for obtaining the desired microstructure by sintering [23]. While the wet process or colloidal processing is effective to obtain agglomerate-free powder compacts [3,5,23], it is important to examine the heterogeneous structure of powder compacts formed by dry pressing.
The synchrotron X-ray multiscale computed tomography (X-ray-CT) consists of an X-ray microtomography (micro-CT) as a wide-field and low-resolution system and a phase-contrast high-energy X-ray nanotomography (nano-CT) as a narrow-field and high-resolution system [24,25]. This technique was applied to investigate the strength-limiting defects in sintered samples prepared by compaction of spray-dried granules [26]. Granules are used to improve the flowability of powders in the industrial process of die filling. The synchrotron X-ray multiscale-CT revealed that branched crack-like defects and circular crack-like defects were formed along boundaries of granules and cavities of hollow granules, respectively. This imaging technique was also applied to study the microstructural evolution in sintering of multi-layer ceramic capacitors (MLCC) [27].
The purpose of this study is to examine how inhomogeneous pore distribution evolves from powder packing during sintering by using the synchrotron X-ray multiscale computed tomography. Here we show that the distribution of small residual pores results from the heterogeneous domain structure of powder compacts even in the pressureless sintering of an alumina powder, which has been supposed to be agglomerate-free [6]. This characterization technique will be applied to optimize the powder processing for developing materials with uniform microstructures.

Experimental procedures
The as-received commercial α-alumina (Al 2 O 3 ) powder (TM-DAR, Taimei Chemicals Co., Ltd, Japan), with a purity of 99.99% and an average particle size of 0.15 μm, was used for this study. Cylindrical compacts of 15 mm diameter and 5 mm height were formed by uniaxial pressing at 40 MPa and cold isostatic pressing at 200 MPa. The powder compact was heated to the sintering temperature (800 -1300 • C) at a heating rate of 5 • C/min, and held for 2 h in air in an electric furnace. The relative density, which was measured by the Archimedes method, increases from 67.7% at 800 • C (initial stage) to 98.9% at 1300 • C (final stage). For the X-ray CT observation, cylindrical samples with a diameter of 0.85 mm were extracted from the sintered body by laser beam machining. Laser cutting was carried out using a Nd:YAG pulsed laser with a wavelength of 1064 nm. The beam diameter of 30-40 µm was chosen to reduce damage to the sample.
The synchrotron X-ray CT experiments were performed at BL20XU,  of the Japanese synchrotron radiation facility, SPring-8, using the X-ray energy of 20 keV for micro-and nano-CT mode. The micro-CT mode is based on a simple X-ray projection optics. Optical system of nano-CT mode was based on a phase contrast X-ray full field microscope, consisting of a hollow-cone illumination system using a condenser zone plate (CZP), sample stages, a Fresnel zone plate (FZP) objective, a Zernike phase plate (phase ring), and a visible-light conversion type X-ray image detector [24,25]. Because the phase-shift cross section in the X-ray region is up to about thousand times larger than that of absorption [28], phase contrast X-ray imaging is employed for the high-sensitive observation of fine structures. The sample was rotated by steps of 0.1 • up to 180 • . Voxel sizes for micro-and nano-CT mode were 0.5 µm and 40 nm, respectively. The measuring time for one sample was 8 min for micro-CT. A region of interest in the sample was observed by nano-CT with a measuring time of 30 min. The 3D visualization and geometrical measurements were performed using Amira (VSG, Burlington, MA) in the present study. A Gaussian filtering was applied to reduce the noise in 2D images. Local thresholding method was used to segment the gray value image into pore and material, so as to measure the defect size. The surface was discretized using triangular meshing, from which the volume and surface area of defects were calculated. The 2D microstructural features were observed using field emission scanning electron microscopy (FE-SEM, ZEISS GeminiSEM 300, Germany) equipped with EBSD. The image analysis of pore features was performed for 400 high-resolution SEM images covering a 1.16 × 0.86 mm wide area by using ImageJ software. The Schwartz-Saltykov model was used to convert the size distribution of circular pores in the cross section to that of spherical pores in 3D space [29,30].  Fig. 1(a) shows the 2D cross section of sintered alumina with the relative density of 67.7% observed by micro-CT. The gray scale image of micro-CT represents local density variation, since the attenuation of the X-ray through a body is linked to its absorption coefficient. High-density regions look brighter, while low-density regions look darker. The local density variation reveals that the initial structure of powder compact consists of domains with different sizes and shapes bounded by darker boundaries. There were four types of domains; (i) Large domains with the size of a few hundreds μm, (ii) small irregular shaped domains with 10-100 µm, (iii) long rectangular domains with the width of ~ 10 µm, (iv) round white domains smaller than 10 µm. Fig. 1(b), (c) are enlarged views observed by nano-CT. Zernike phase contrast technique enhances the appearance of shapes and interfaces between materials with different refractive index. The figures indicate the spatial distribution of primary particles. Its number density is low in dark boundary regions among irregular domains (ii) in Fig. 1(b). The round white domain (iv) is a region of high number density as shown in Fig. 1(c). There are cracklike defects inside and around the dense domain. We term these  heterogeneous domain structures as agglomerates in this paper. The terms "soft agglomerate", "hard agglomerate", and "aggregate" are widely used to distinguish various types of assemblages of particles in powder technology. However, as we cannot know whether these domains are soft or hard from X-ray CT images, we simply use the term agglomerates only [31]. The origin of agglomerates will be discussed later. Fig. 2 shows the SEM image of a cross section of the sintered alumina with relative density of 98.9%. The microstructure was apparently homogeneous, and there was no large defect (> 10 µm) in the wide view ( Fig. 2(a)). While some regions were fully dense ( Fig. 2(b)), the local distribution of fine pores was observed in some places at higher magnification (Fig. 2(c)). Most pores were smaller than 0.2 µm. The fine pores are located mainly at grain boundaries. The average grain size was 0.97 µm. The grain size in the porous region was smaller than that in the dense region. The average porosity was 0.9% calculated from the area fraction of pores in the total cross-section.

Heterogeneous distribution of residual pores
The heterogeneous distribution of porous regions was clearly imaged by using micro-CT in Fig. 3(a). Large uniform domains were surrounded by many small domains with different sizes and shapes bounded by dark areas. This dark area indicates the porous region. The distribution of porous regions corresponds to the boundary between domains in powder compact in the initial stage. Here, it should be noted that the individual fine pore cannot be imaged by micro-CT, because its size is smaller than the voxel size of micro-CT. Squares in Fig. 2(c) indicate the voxel size. The gray scale image of a voxel depends on the volume fraction of fine pores. The brightness of the voxel is in the order A > B > C. The spatial resolution to separate two objects is approximately two times larger than the voxel size. If the distance among pores is smaller than about 1 µm, the region containing many small pores looks as if it was a single large dark area. The gray scale of the micro-CT image in Fig. 3(a) is related to the spatial distribution of number density of fine pores. The micro-CT is a powerful method to detect the heterogeneous distribution of fine pores in a large scale, which cannot be discerned by SEM (Fig. 2(a)). The 3D distribution of defects is illustrated in Fig. 3(b). The large domain was dense with the residual porosity of 0.1% containing only a few spherical pores. Small defects distributed outside the large domain. Fig. 3(c) is the enlarged view of a square region observed by micro-CT in Fig. 3(b). The same region was also observed by nano-CT and shown in Fig. 3(d). Defects observed by micro-CT are exaggerated images of porous regions containing fine pores, so that they do not represent the accurate shape of individual pore. Nevertheless, Fig. 3(a) revealed that porous regions consisting of fine pores are formed along the boundary between the large agglomerate and its surroundings. The fine residual pore is also formed among small irregular shaped agglomerates. It is important that almost fully dense microstructure could be obtained inside the large agglomerate by pressureless sintering. This result suggests that the as-received powder was homogeneous. The small agglomerates and the disordered agglomerate structure may be formed when the large lumps of bulk powder break easily during die filling.

Types of pore distribution
Several types of pore distribution are classified based on the initial agglomerate structure of powder compact. The SEM micrograph in Fig. 4 (a) illustrates the coalescence of several cavities at grain boundary facets along the interface between a large agglomerate and the surrounding region of small agglomerates. This defect is formed by tensile stress due to differential sintering rates between the large agglomerate and the surrounding region. Fig. 4(b) shows the formation of defects on both sides of a long rectangular agglomerate. A cluster of small pores in Fig. 4 (c) locates at a junction where several agglomerates meet. The different shrinkage rate of a small agglomerate makes a gap in Fig. 4(d). This process accompanies the formation of fine pores around it. This composite structure is regarded as a large void.
The isolated single pore in Fig. 4(e) has a complicated structure containing several grains inside, which we term complex pore. The complexity of a single pore can be described by its connectivity or genus g. Roughly speaking, it is the number of holes in the pore surface. A spherical pore is characterized by a genus-zero surface. A doughnutshaped pore (torus) has genus 1. There is a grain inside the crosssection of the doughnut-shaped pore, when it is cut perpendicular to the axis of revolution. Since there are several grains inside the pore in Fig. 4(e), this complex pore is described by g > 3. It was the largest one found by SEM observation.
The largest defect structure was observed by micro-CT as shown in Fig. 5. It looked like a crack along the boundary of a plate-shaped agglomerate, which is the long rectangular agglomerate in the crosssection. This crack-like structure consists of many fragments, each of them is probably either coalesced cavities at grain boundaries facets ( Fig. 4(a)) or a collection of fine pores. It should be noted that the defect may not be a real crack.

Size distribution of pores and defects
The size distribution of pores in three dimensions was estimated from that observed on cross sections by SEM using Schwartz-Saltykov method [29,30], and plotted in Fig. 6(a). The relation between the number of pores per unit volume (N V ) and the diameter (D) of spherical pore could be approximated by the inverse power law We obtained the exponent of b = 9.4 in a range 0.34μm < D < 1.42μm. The inverse power law is shown as broken line in Fig. 6(a).
The defect size observed by synchrotron X-ray CT was defined by the diameter of the equivalent sphere. The histogram in Fig. 6(b) shows the size distribution of defects in the porous region in Fig. 3(d) observed by nano-CT. It agreed with the inverse power law for the pore size observed by SEM fairly well in the range from 0.4 µm to 0.9 µm. However, the number of defects larger than 1 µm was much larger than that of pores observed by SEM.
The size distribution of defects observed by micro-CT is shown in Fig. 6(c). The maximum defect size of 15 µm was about ten times larger than the maximum pore size. It indicates that the defect observed by micro-CT is not a real pore, but a porous region with a collection of fine pores. The size distribution was fitted by the inverse power law with exponent 8.6. It could be approximated by the exponential law also The fitting curves are plotted in Fig. 6(c) as broken lines and dashed lines for the inverse power law and the exponential law, respectively. The comparison between the structure observed by SEM and CT will be discussed in 4.2.

Visualization of the mesoscopic defect structure by SEM
An appropriate visualization technique supports the understanding of the heterogeneous structures. Whereas the micro-CT revealed the distribution of fine pores related to the complicated agglomerate structures, such nonuniform mesoscopic structure looked homogeneous in the SEM micrograph in Fig. 2(a). We present a technique based on a SEM micrograph (Fig. 7(a)) for analyzing the agglomerate structure here. As a first step we do a binary segmentation of the high-resolution gray-scale image with a pixel size of 17 nm into material (white) and pore (black) by using the global thresholding method in Image J software ( Fig. 7(b)). The binary image is resampled to make the pixel size 0.41 µm, which is approximately equal to the voxel size of the micro-CT. This procedure converts the binary image into a gray-scale image. The gray-level of a pixel is a function of local porosity or number density of fine pores. Fig. 7(c) represents a contrast-enhanced image similar to that obtained by the micro-CT. This technique can enhance the heterogeneous porous region for the perception of agglomerate structure without the access to the synchrotron X-ray micro-CT.

Comparison between SEM and synchrotron X-ray CT
The elimination of residual porosity was heterogeneous in pressureless sintering of dry pressed submicron TM-DAR powder. The regions containing very fine pores remained in the material, even though some regions were almost fully densified. Bodišová et al. [8] observed such heterogeneous microstructure in two-step sintering also by using SEM. The present micro-CT observation clearly proved that the complete elimination of fine pores was prevented by the differential sintering of agglomerate structures in the green body. The synchrotron X-ray multiscale-CT has an advantage over SEM for observing cross-sections of both green body and sintered body non-destructively.
The shape and size of residual pore in the final stage can be characterized by SEM most accurately (Fig. 2(c)). On the other hand, although some pores could be distinguished from others in the crosssection imaged by nano-CT ( Fig. 3(f)), the collection of pores looked as a large defect when the separation between close pores was small. The micro-CT could image only the shape of porous region as a large defect in Fig. 3(e). Therefore, the size distributions of defects observed by nano-CT and micro-CT ( Fig. 6(b), (c)) were different from that of pores observed by SEM (Fig. 6(a)). The authors suppose that the size distribution of defects by micro-CT indicates the multi-scale nature of spatial pore distribution.
The microstructure of a sintered body is characterized by the relative density and the average grain size usually. In addition to them, the combination of SEM and synchrotron X-ray CT provides the spatial distribution of pores and the pore size distribution. This knowledge will be used for optimizing the process to develop materials with tailored microstructures. Of course, the wet processing is an effective method to obtain the uniform green body, as TM-DAR powder can be easily disintegrated into the primary particles [5,32,33]. The dense microstructures with the residual porosity of 0.1% can be obtained by pressureless sintering of a uniform green body. Such microstructure will be similar to the SEM micrograph in Fig. 2(b) and micro-CT images inside large agglomerates in Fig. 3(a) and (b).

Large defects in the sintered body
The 3D multiscale-imaging technique enables us to obtain the detailed knowledge of defects (size, shape, and distribution) in sintered alumina directly. The defect in Fig. 5 was largest defect observed by micro-CT. Even though the defect may not be a real crack, the crack-like distribution of fine pores may enhance the stress concentration. Although we do not have the strength data, we suppose that this defect can be a fracture origin. The micro-CT observation revealed that this crack-like defect was formed by the differential sintering of a plateshaped agglomerate. We do not know why the as-received TM-DAR powder contained such plate-shaped agglomerates with the thickness about 10 µm. But it is well known that fine powders adhere on the wall of the container and the equipment surface easily [34]. The plate-shaped agglomerates may be fragments of removed adhesion layer.

Summary
The synchrotron X-ray multiscale-CT and the scanning electron microscopy were used to investigate how heterogeneous distribution of residual pores evolved from the initial structure of powder compact during pressureless sintering of a submicron α-alumina powder (TM-DAR). The powder compact, which was made by uniaxial pressing and cold isostatic pressing, consisted of several types of domains, or agglomerates, bounded by low-density regions among them. The initial packing structure suggested that a lump of uniform bulk powder broke easily, forming small irregularly shaped agglomerates. The as-received powder contained several plate-shaped agglomerates also. The distribution of residual pores was heterogeneous in a sintered sample with relative density of 98.9%. While large agglomerates were densified almost completely, porous regions containing fine pores were formed along the boundary of agglomerates. The size distribution of pore was expressed by the inverse power law with the maximum diameter of 2 µm. The elimination of fine pores was prevented by the differential sintering of agglomerates in the powder compact. The largest defect observed by micro-CT was a crack-like defect formed along the interface of a plate-shaped agglomerate.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.