Читать книгу Processing of Ceramics - Группа авторов - Страница 15

The translucent ceramics that began to be developed in the late 1950s are used in high‐pressure sodium vapor lamp, and PLZT ((PbLa)ZrO₃) ceramics are applied to flash‐protecting shutters utilizing the electro‐optic effect, after that development on various types of materials and application research were conducted, but research and development stagnated because fundamental problems related to optical technology cannot be solved. The purpose of writing this book is to describe; (i) how the author challenged with what kind of idea to develop the “optical grade polycrystalline ceramics” which is far superior to the conventional translucent ceramics and comparable to the optical grade single crystalline materials, (ii) how to evaluate the optical quality of fabricated optical ceramic materials, and (iii) how to feedback the obtained information from the evaluation into the fabrication process and so on.

Conventionally, optical grade single crystalline materials are produced by various methods such as Verneuil (VN), floating zone (FZ), Bridgman (BM), and Czochralski (Cz), and basically, the crystals are grown after melting the raw materials. Industrial manufacturing methods are also established, and relatively high‐quality crystal materials can be easily obtained but there are also various disadvantages. The optical quality of conventional optical ceramics represented by translucent alumina ceramics is remarkably poorer than that of the above mentioned single crystals, but if there is a technology that can produce a ceramic material that can compete with single crystal, then the fabrication of new materials that was impossible by the conventional single crystal growth technology and also other advantages such as fabrication of large size and mass productivity will become possible. The question is what kind of idea is to carry out with material development. It is said that the single crystal fabrication method has limitations on the homogeneity of the grown single crystalline material because segregation tends to occur at the solid–liquid interface during crystal growth under gravitational field, and it is difficult to synthesize more homogeneous materials unless it is synthesized under zero gravity (for example, outer space). In addition, since the conventional method basically is a process of solidifying from a temperature higher than the melting point, there is also a problem that lattice defects inside the material are likely to be involved. However, it is also a fact that the optical performance of a single crystal is much higher than the conventional transparent ceramics. Despite the fact that ceramic specialists have carried out various researches so far, they were in the dark and had no direction where they should open the key of technology.

First, I would like to mention how I was able to challenge the development of laser ceramics which was considered “thoughtless.” Please refer Figure 1.6 again. This figure shows a microstructure image of common ceramics, but the material is composed of microcrystals (small crystal grains) with random orientations, and there are also many scattering sources. Dr. Coble succeeded in getting translucent Al₂O₃ ceramics for the first time by aiming at reduction of pores by microstructure control (especially by inhibition of grain growth during sintering process). Even after that, development was carried out by the same method, but many scattering sources remain in the material that cannot be removed by Coble's method, and the application was still limited. Although the idea on the development of laser ceramics is not largely different from the past, firstly “complete removal of macroscopic structure defects causing Mie scattering” is essential. Here, removal of residual pores will be described as a typical example.

Dr. Coble outlined the removal of residual pores when he developed translucent alumina by pressureless sintering. In the case of translucent alumina, when the relationship between (1) grain growth rate and (2) moving speed of pores is (1) > (2), pores are trapped inside the grains as explained in Figure 1.8a, and these residual pores become main scattering sources. As he introduced a trace amount of MgO as a grain growth inhibitor (pinning center), the above relationship is changed to (1) ≤ (2) and he succeeded to reduce the number of residual pores in the ceramics. However, in the case of laser materials even if there is “a small number of pores” remained inside, it severely affects the laser function and therefore it is still necessary to develop the materials with “zero pores.” Also, it is necessary to control the grain boundary phase in nano‐size and dislocations at grain boundaries. Figure 1.8b shows the product of the research applied to the discharge tube of a high‐pressure sodium lamp. From here, it will be a different part from Coble.

Figure 1.9a shows granules obtained by spray drying an Al₂O₃‐Y₂O₃ system (composition is YAG) slurry with a spray dryer. Figure 1.9b‐1 and b‐2 show the fracture surface after the granules were molded in a metal mold observed by SEM. Granules of about 50 μm diameter exhibit a real spherical structure in which Al₂O₃ and Y₂O₃ are homogeneously mixed. When these granules are press‐molded inside the metal mold, the granules collapse, and finally, the spherical granule shape disappears, and a green powder compact with a uniform structure is obtained. Figure 1.9b‐1 shows a granule using a binder with good crushing property (a binder having excellent plastic deformability is used in this case), and it has a homogeneous structure with a molding pressure of 20 MPa. Figure 1.9b‐2 shows the fracture surface structure of the powder compacted body when granules with poor crushing characteristics (i.e., binders having high elastic deformability are used in this case) are similarly molded at 20 MPa. Since it is a hard granule, the strength of powder compact after molding is strong, but the form of granules (the part where the granules are not collapsed) can be confirmed inside the green powder compact.

Figure 1.8 (a) First demonstration of translucent alumina ceramics by Dr. Coble (he explained how to remove pores from inside of polycrystalline ceramics) and (b) topical application for translucent alumina ceramics.

Figure 1.9 (a) Appearance of granulated Al₂O₃‐Y₂O₃ powders by spray drier and (b) internal structure of Al₂O₃‐Y₂O₃ powder compact after uniaxial press under 20 MPa.

The powder compact showed in the above figure is further pressed in CIP (cold isostatic press) machine at 140 MPa. Then, the pore size distribution of this sample after CIP was measured by using the mercury penetration method. The result is shown in Figure 1.10. The pore diameter of the sample using a binder with good crushing characteristics is concentrated at 30–40 nm, but large voids of μm size are detected in the other samples without a binder, resulting in structure defects (which induce light scattering sources at the end product). Once large structural defects are formed, it is difficult to completely remove them even by high‐pressure sintering techniques such as HP (hot press) and HIP (hot isostatic press) treatments.

In order to effectively eliminate residual pores on the fracture surface of the green powder compacts, it is necessary to prepare before sintering the green compact with pore size smaller than the particle size of the raw powder materials to be used and to have a narrow and sharp distribution in the pore diameter. By subsequent preliminary sintering, it is necessary to prepare a sintered body having a relative density 98–99%, and further, it must be subjected to HIP treatment to prepare a sintered body having almost no residual pores. It depends on the sintering properties of the raw materials.

Figure 1.10 Pore distribution of Al₂O₃‐Y₂O₃ green body after cold isostatic press (140 MPa) by mercury penetration method.

The residual pore volume inside the Nd:YAG ceramics at 1995 (by the time the ceramic laser was firstly developed) was at the level of several ppm, but recently it has become possible to control to the residual pore volume below the ppt level, which is essential for larger size with higher quality. It is a remarkable numerical value that the residual pore volume is as low as 10⁻⁸ as compared with the translucent alumina. HIP (hot isostatic press) has been used since the 1980s, and it has been confirmed that it is effective for densification of materials. When the sintered material is heat‐treated at high temperature and high pressure, the material is densified, and the density is increased. It seems that HIP is an effective densification (pore removal) process, but in most cases, it compresses residual pores to reduce the pore size inside the materials, and apparently, its density was increased. In the case of only apparently densified samples, rebound of shrunken pores occurs when heated in a pressureless condition, and in the worst case, the transparency returns to the opaque body again. In some cases, the high‐pressure Ar gas which introduced from the grain boundaries or trapped in the pores expands rapidly during the heat treatment process, and finally, the HIP‐treated sintered body may explode. For example, even if the residual pores shrink due to HIP pressure, Mie scattering and Rayleigh scattering certainly occur; therefore, “pore removal process” is essential.

Figure 1.11 shows the image of pore removal by HIP (hot isostatic pressing) treatment. The relationship between the pore size and the grain size is important, and the key point is timing of HIP treatment. This point is determined by the sintering properties of the raw materials, type of sintering additives, and its adding amount. In addition, the most important point is to clarify that the residual pores are totally removed from the materials after the HIP treatment or whether the pores were merely shrunk and still remained inside the materials. If the pores can be completely removed, the transmittance of the material will be improved from Type A (Mie scattering) to Type B (Rayleigh scattering), and hence, the remaining technical issue will be only how to control Rayleigh scattering inside the transparent materials.

Figure 1.11 (a) Image of removing pores from polycrystalline ceramics by hot isostatic press. (b) Typical transmittance spectrum by “Mie” and “Rayleigh” scattering.

In synthesizing Nd:YAG ceramics with high transparency, a trace amount of SiO₂ is added as a sintering aid, but even if only a slight excess of sintering aid (SiO₂) is introduced, the grain boundary phase tends to be precipitated. Figure 1.12a is a TEM image of the grain boundary part. Although the grain boundary phase is only 70 nm, Rayleigh scattering certainly occurs, and the transmission spectrum behavior will be like Type B. Detection of the grain boundary phase of nm size is difficult with SEM observation, but even by the transmission polarizing microscope, it is possible to detect nano‐sized heterogeneous phase (grain boundary phase) observed by TEM. Figure 1.12b is a transmission microscope (open nicol) photograph. Only transmitted light through the inside of the material can be observed. Since the crystal structure of Nd:YAG is cubic, there is no birefringence unless there is a heterogeneous phase. Therefore, when it is observed under polarized light (cross nicol condition), the whole image gets black. However, as shown in Figure 1.12c, needle shape birefringence was detected in this material; its position corresponds to the grain boundary area, so it can be judged as a grain boundary phase. Also, when the specimen stage of the optical microscope is rotated, light and dark (angle dependence of birefringence) are repeated alternately, so that the crystal structure of the grain boundary phase can be easily found out. In addition, since the distribution of grain boundary phases can also be understood, it is a promising method for inspecting Rayleigh scattering sources. In general, the grain boundary phase is determined by many factors such as impurities incorporated in raw material, kind, and amount of sintering aids, and sintering process (especially cooling process condition), so it is necessary to set up procedures to control these parameters so that grain boundary phases do not generate inside the materials.

Figure 1.12 (a) TEM image of Y₃Al₅O₁₂(YAG) ceramics including excess SiO₂ near grain boundary, (b) transmission microscopy image of YAG ceramics under open nicol, and (c) transmission polarizing microscope image of YAG ceramics. We can clearly see secondary phase on grain boundaries.

Rayleigh scattering arises from nano‐sized scatterers near grain boundaries. Figure 1.13 shows transmission spectra of single crystal and polycrystalline ceramics of the same composition (0.6% Nd:YAG). Laser generation is a process of extracting laser light (coherent light) with a wavelength of 1064 nm by exciting a gain medium with an LD (laser diode) with a wavelength of 808 or 885 nm; hence, scattering characteristics around 1 μm is particularly important. If there is grain boundary scattering in the transmission spectrum, the wavelength dependence of the transmittance occurs (that is, the transmittance of the ceramic decreases as the wavelength becomes shorter). But in this case, the transmission spectrum of both shows exactly the same behavior and does not obey the Rayleigh scattering law. Even when compared with a material with a thickness of 100 mm, the transmittance of both of them in the 1 μm region is nearly the theoretical limit (about 83%), and it can be understood that there exist “material sciences” having different concepts from the conventional ceramics.

Figure 1.14a shows a SEM photograph of the fracture surface of the fabricated Nd:YAG ceramics, and Figure 1.14b shows the HR‐TEM image near the grain boundary of this material. Although the material undergoes intergranular fracture, the presence of fine pores and grain boundary phases cannot be recognized, and even in HR‐TEM, the grain boundary has a clean structure with no grain boundary phase (it is not just a clean grain boundary that has been told so far, and in fact it has been proven in terms of its properties). Since Nd:YAG grains have different crystal orientations, dislocations are present near grain boundaries, so it is important to verify whether or not that dislocation parts cause optical scattering in the laser oscillation wavelength region.

Figure 1.13 Transmission spectra of Nd:YAG single crystal and polycrystalline ceramics with same Nd content and thickness between 400 and 1200 nm wavelength.

Figure 1.14 (a) Fracture surface of Nd:YAG ceramics by SEM and (b) lattice structure of Nd:YAG ceramics around grain boundary by high‐resolution transmission electron microscopy.

Figure 1.15 (a) Schematic setup of laser tomography with 1 μm light source, (b) sample with grain boundary phase, and (c) sample with no including anisotropic phase measured by tomography.

Figure 1.15a shows the setup of the laser tomography used for detecting the light scattering inside the material (the light source has a wavelength of 1 μm). Here, the material is irradiated with a laser beam, and scattered light inside the material is captured with a CCD camera installed in a perpendicular direction. Figure 1.15b shows a material with a grain boundary phase, Figure 1.15c shows a sample with no grain boundary phase and a scattering coefficient equivalent to that of a single crystal. In the sample shown in Figure 1.15b, scattering from the grain boundary area can be easily detected, but in the sample of Figure 1.15c it is difficult to detect scattered light. Recently, we fabricated Yb:YAG ceramics (size 80 × 190 × t6 mm) for high power laser oscillation. After optical polishing and AR coating, then its optical loss at 1 μm was measured. Its scattering loss was as low as 0.02%/cm. We confirmed extremely low scattering. Generally, the optical loss of a single crystal is 0.1%/cm, but nowadays, the optical loss of polycrystalline ceramics is significantly lower than that of the single crystal. Although the obtained results cannot be understood from the conventional material science, actually how to consider these real facts is to open the “further science doors.” As stated at the beginning, “pursuing the truth of natural science and fully understanding the theory” leads to a conclusion. In other words, there seems to be a possibility that the pursuit of natural science has been insufficient, and that the future of ceramic materials could be easily predicted with insufficient understanding of the theory.

In Figure 1.16a, the outside landscape can be clearly observed through the fabricated Nd:YAG ceramic rod with a length of 300 mm (size is 10 × 10 × L300 mm), because scattering of this material is equal to or higher than that of high‐quality single crystal. The Schlieren image and the transmitted wavefront image of this material are also shown in Figure 1.16b,c, respectively, but the inhomogeneous parts cannot be detected inside the material and very low scattering and high uniformity guarantee the optical quality. Figure 1.16d shows the result of irradiating the ceramic sample with a He–Ne laser. It is understood that the quality of this material is so high that internal scattering cannot be visually observed.

Figure 1.16 (a) Appearance of Nd:YAG ceramics with 300 mm length, (b) Schlieren image and (c) transmitted wavefront image of this ceramics, (d) condition of internal scattering line when He–Ne laser irradiated into Nd:YAG ceramics (we cannot detect scattering line in this ceramic)

Figure 1.17 shows an appearance of a high‐quality Nd:YAG single crystal (manufactured by the Cz method, 10 × 10 × L 25 mm) having the same composition as the 1% Nd:YAG ceramics (Φ10 × L25 mm) produced in this study and the transmitted wave front distortion measured by the interferometer.

The laser beam pattern when irradiated with He–Ne laser (wavelength 633 nm) is also shown. Although it is difficult to distinguish the appearance of ceramics and single crystal, the transmitted wavefront distortion per inch length of ceramics is λ/19.5, that is, 0.051λ/in. (λ = 633 nm, the smaller the wavefront distortion is, the more uniform the gain material). It is generally about 0.10λ/in. for single crystals. In fact, this result is the most advantageous condition since the wavefront distortion measurement was taken with respect to the crystal growth direction after cutting off the high‐quality part of the produced single crystal ingot. There are countless facets (nonuniform parts) in the direction perpendicular to crystal growth, which makes it difficult to measure wavefront distortion. When these materials are irradiated with a Gaussian mode, He–Ne laser, the beam patterns of the transmitted lasers of both samples were similar to the initials (this meaning is considered to be some reasons that (i) the optical quality of both materials happens to be similar accidentally at the irradiated part and (ii) the difference cannot be detected by using only one pass of detection light for both materials with different wavefront distortion). However, the same result is obtained even when the laser is irradiated in the direction perpendicular to the main measurement direction in ceramics (that is, there is no optical anisotropy of the optical quality), whereas in the case of the single crystal material, the laser is irradiated in the vertical direction, distinctive beam distortion is confirmed. By excluding the anisotropy of the optical quality, the single crystal material is utilized so that there is no big problem in laser application. Without limiting to YAG materials, single crystals remain a major problem as optical materials, and even as long as 50 years have passed since the report of laser oscillation by Nd:YAG single crystal in 1964, even an idea for solving those conventional problems has not been proposed.

Figure 1.17 Comparative data of (a) Polycrystalline and (b) single crystal by Czochralski growth of 1%Nd:YAG materials by appearance, wave front distortion, beam patter of He–Ne laser which passed through test sample.

The author has advanced further research even in materials systems other than YAG. As shown in Figure 1.18, the transmission behavior of single crystal and ceramics of spinel ceramics was investigated. Both of the transmission characteristics in the infrared to visible wavelength range are equivalent, but the transmission characteristics of ultraviolet wavelength range of ceramics composed of fine grains exceeded single crystal.

Furthermore, as seen in the above inset figure, ceramics could transmit through to shorter than 200 nm, where the single crystal was hard to transmit. The optical band gap of spinel ceramics is 6.8 eV (absorption edge is 180 nm), far superior to 4.9 and 5.5 eV of the same single crystal fabricated by Bernoulli method or CZ method. It has been reported that the lasing characteristics of ceramics have also approached that of single crystals as the transmission properties of ceramics have approached single crystals, and some scientific understandings have been achieved. In conventional perception; however, it is theoretically impossible for the optical characteristics of polycrystalline ceramics to exceed that of single crystals in the short wavelength region, in particular, in the ultraviolet region where Rayleigh scattering is significant due to the presence of grain boundaries (dislocations). Nevertheless, the achievements in this invention fundamentally reverse the conventional perception.

Figure 1.18 Transmittance spectra between UV (vacuum) ~ infrared wavelength of most excellent polycrystalline Spinel ceramics, single crystal Spinel by Verneuil and Czochralski method.

Figure 1.19a is a setup diagram using a He–Ne laser having a wavelength of 633 nm. In order to observe the scattering sources existing inside the material, a laser is irradiated to the surface‐polished material, and the scattering state and the intensity of the scattering are measured from a direction perpendicular to the laser irradiation direction using a CCD camera and a power meter. For this material, the laser‐irradiated surface was AR‐coated, and the internal loss of each material was measured from the intensity of the initial beam and the intensity of the laser emitted through the material.

As shown in Figure 1.19b, the optical loss of spinel ceramics shows extremely low scattering of 0.07%/cm, which is much lower than that of the same single crystal produced by the Verneuil or Czochralski method. In Figure 1.19c, the scattering state inside the material was observed with a CCD camera installed perpendicular to the laser irradiation direction. For any materials, the scattering state could not be detected as an image by the laser tomography. Figure 1.19d shows the measurement of weak scattering using a light‐receiving element instead of a CCD camera. The detected scattered light was normalized by setting the scattering intensity from the crystal by the Czochralski method to 100. As a result, the scattering intensity becomes smaller in the order of Verneuil crystal → Czochralski crystal → polycrystalline spinel ceramics by sintering method. Since only one residual pore (approximately 1 μm) is observed in the spinel ceramics, the porosity is at the level of 10⁻¹³, and it can be considered that there is no Mie scattering in this material. The residual pore can be detected by a transmission microscope, and when it is irradiated with a He–Ne laser (from the left side of the image), the light is scattered from the vicinity of the interface between the base material and the residual pores (the portion where the refractive index fluctuation exists). In this state, when the light of the transmission microscope is turned off and the observation is continued while irradiating the He–Ne laser, circular Mie scattering can be clearly confirmed scattered from the interface of residual pores and the base material. This scattering conditions are shown in Figure 1.19e. Ceramic materials have numerous grain boundaries, and even though the He–Ne laser passes through the grain boundaries, the scattered light cannot be detected by a normal tomography or a tomography using an optical microscope. This means that scattering from the grain boundaries is very insignificant or almost nonexistent (not limited to the spinel ceramics). Therefore, it is still necessary to seriously discuss grain boundary scattering phenomenon in ceramics, which has been doubted to be used as an optical material.

Figure 1.19 (a) Optical loss at 1064 nm and laser tomography at 633 nm of polycrystalline and single crystal, (b) residual pore and Mie scattering from pore by He–Ne laser.

By the way, Rayleigh scattering is expressed as follows.

where θ is the scattering angle, I₀ is the light intensity before transmission, n is the refractive index; R is the distance between the measurement point and the scattering source, d is the scatterer size, and λ is the measuring wavelength. Basically, light scattering increases in proportion to the power of the scatterer size to the sixth power, the reciprocal of the measurement wavelength to the fourth power. In common sense which is well recognized by almost all material scientists until now, “There are many dislocations at the grain boundaries in the ceramics and their dislocations become scattering sources causing grain boundary scattering, so the transmittance of the ceramics increases as the wavelength becomes shorter.” However, the obtained result is opposite to the conventional common sense that “polycrystalline ceramics having grain boundaries are superior in optical properties to single crystals, and in particular, in the short wavelength region, they show a significant difference in optical properties.”

It is important that the optical material must be “extremely low scattering,” but optical uniformity is also a very important parameter. Laser beam patterns after passing through the spinel ceramic (25 mm‐thick), Czochralski and Verneuil single crystals irradiated with a He–Ne laser having a Gaussian mode are observed with a beam profiler, and these results are summarized in Figure 1.20. When laser irradiation is performed, no scattering line is detected inside the spinel ceramic material (see Figure 1.20a), and only Fresnel scattering (surface scattering due to the difference in refractive index between air and the base material) is observed at the input and output surface of laser irradiation. As a reference, the original beam pattern is shown in Figure 1.20b‐1. The beam that has passed through the Verneuil spinel single crystal with significant optical inhomogeneity showed the greatest distortion (see Figure 1.20b‐2). The beam that has passed through the spinel single crystal by the Czochralski method is also deformed into an elliptical (vertical) shape (see Figure 1.20b‐3). Only the beam that has passed through the ceramic maintains a concentric shape similar to the original beam (see Figure 1.20b‐4) (because the material surface is not AR‐coated, the laser beam that has passed through any material is attenuated by about 24% compared to the original beam due to surface reflection). Beam quality is a critical parameter for optical materials, and the superiority of ceramics, which is different from the conventional understanding, has been proved. The fact that spinel ceramics exhibit extremely low scattering and high beam quality is closely related to the microstructure of the material. As can be seen from the laser tomography shown in above Figure 1.19, a clean grain boundary in which no grain boundary phase exists reduces Rayleigh scattering. In addition, since there is almost no residual pore as a main scattering source, Mie scattering can be almost completely eliminated.

Figure 1.20 (a) He–Ne laser irradiation test and (b‐1) original and (b‐2‐4) changing of beam pattern via various specimens.

The following results clearly indicate that high beam quality, one of the lifelines of optical materials, can be guaranteed. The internal optical stress of the spinel single crystals prepared by the Verneuil method and the Czochralski method was observed using a polarizer. In addition, the uniformity of the refractive index inside these crystalline materials was observed with a Schlieren imaging system. These observation results are summarized in Figure 1.21b‐1, b‐2, c‐1 and c‐2. The Verneuil single crystal shows significant optical inhomogeneity as well as significant optical stress. Since the single crystal of the Czochralski method has a core at the center of the grown crystal ingot, a high‐quality peripheral portion is used as a sample. However, optical distortion is also observed in this part. Although the optical uniformity is better than the crystal grown by the Verneuil method, “a domain structure of around Φ1 mm having a nonuniform refractive index” is still observed inside the material.

Figure 1.21 Optical inspection of polycrystalline Spinel Ceramics by sintering method and Spinel crystal by Verneuil and Czochralski (Cz) methods.

Figure 1.21a‐1–4 show the appearance of polycrystalline spinel ceramics of ϕ20 × t10 mm produced by the sintering method. It is very transparent and has a lower optical loss than the Czochralski single crystal even in the visible region. The transmitted wavefront image by the interferometer showed a straight fringe (<0.1λ/cm [λ = 633 nm]). In the measurement using the polarizer, the optical stress was below the detection limit. Furthermore, there is no inhomogeneous part in the Schlieren observation. Finally, the reason why the absorption edge of polycrystalline ceramics becomes shorter and the band gap shows a larger value than that of a single crystal will be described in the following. As shown in the Figure 1.21b,c, the spinel single crystals have a domain structure with nonuniform refractive index. The chemical formula of the spinel is MgAl₂O₄, and this material can also be a solid solution with “a large composition tolerance.” When the chemical composition of the spinel single crystal is analyzed, MgO/Al₂O₃ (M/A Ratio) was 1.00, and the average composition of the material is almost stoichiometric.

It is considered that the cause of the nonuniform refractive index domain structure observed by Schlieren observation is that the M/A ratio in each domain is different. When materials having different spinel M/A ratios are formed, cation or anion defect structures are induced to form inside the material, and these defect structures certainly affect the band gap. Therefore, it is considered that the absorption edge of the single crystal shifted to the longer wavelength side. Since the refractive index domain structure could not be detected in the spinel ceramics, the shift of the absorption edge due to defects inside the material was small, and this result was similar to the transmission spectrum behavior by computational science. This result breaks the conventional outline that the optical uniformity of single crystals is absolutely superior to ceramics.

The optical uniformity of ceramics reported to date (2020) is far superior to single crystals regarding different types of materials, and the superiority of optical quality of single crystal material which has been regarded as common sense began to collapse. It is extremely difficult to explain by classical theory about the optical properties of ceramics produced by modern science. Rayleigh's scattering theory was built in the nineteenth century, but it is a mathematical expression of the atmospheric scattering phenomena by calculation. The author thinks that the Rayleigh's scattering theory is still correct in the sense of its theory, but when applying the theory by computational science to a practical material, we should consider again the contradictions existing in theory and in reality, etc., and therefore, it is essential to predict the future of material science in this way.

Some technological examples which changed the material science will be described in Chapter 4. It is difficult to produce TAG (Tb₃Al₅O₁₂) and YIG (Y₃Fe₅O₁₂) single crystals by FZ method, and it is not easy to synthesize high‐quality crystals because these single crystals are incongruent materials. The optical quality of ceramics prepared by sintering method for these materials is equal to or superior to those of single crystals, demonstrating the scale‐up and high productivity of optical performance and size that cannot be realized with single crystals. For optical isolators used in laser processing in the 1 μm band (especially for fiber lasers), TO (Tb₂O₃) and TYO (Tb₂O₃‐Y₂O₃) ceramics could be expected to become Faraday rotation elements having the largest Verdet constant, but their melting point is as high as around 2400 °C and also have phase transition point just below the melting point; therefore, the synthesis of single crystals is virtually impossible. For this reason, the representative of the Faraday rotation element is TGG (Tb₃Ga₅O₁₂) crystal. But the TO and TYO ceramics which the author first demonstrated in the world show Verdet constants which are nearly four times that of the TGG single crystal, and this fundamental performance makes the isolator device much smaller. An isolator device using this material has already been put to practical use and contributes to the high reliability of a fiber laser for processing.