JP3587262B2 - Method for producing columnar rare earth silicate single crystal - Google Patents
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本発明は、希土類珪酸塩単結晶の育成方法に関する。 The present invention relates to a method for growing a rare earth silicate single crystal.
珪酸ガドリニウム単結晶等の希土類珪酸塩単結晶は、シンチレータ、蛍光体等として広く用いられている。この単結晶系に属する珪酸ガドリニウム単結晶等は、原料融液からチョクラルスキー法によって作ることができる。すなわち、原料を入れたるつぼを加熱して融液とし、るつぼ内の融液に種結晶を接触させ、種結晶を引き上げることにより、種結晶に更に単結晶を成長させることにより製造された。また、シンチレータ等として用いられる場合には、一般に円柱あるいは直方体の形状に加工して使用される。実際には更に、１面〜全面を鏡面研磨し、鏡面研磨を施した１面を除いて反射材を塗布あるいは巻き付けた状態で、反射材の無い面を光電子増倍管に密着させて使用される。しかしながら、この単斜晶系に属する珪酸ガドリニウム単結晶等は、ａ面（（１００）面）にへき開性があり、またｂ軸（［０１０］軸）方向の熱膨張係数が他の方向に比べ方向に比べ大きいという異方性があるために、結晶育成冷却中に（１００）面及び（０１０）面に沿って割れ易く、加工中にも新たな割れが発生し易い。割れのない希土類珪酸塩単結晶を育成する方法として、引上軸を単結晶のｂ軸（［０１０］軸）またはその近傍（ｂ軸からの傾きの角度が０〜３０°）とする方法（特許文献１参照）、及び引上軸を（１００）面に平行でかつ、ｃ軸（［００１］軸）からの傾きの角度が０°〜２５°の方向とする方法（特許文献２参照）が提案されている。 Rare earth silicate single crystals such as gadolinium silicate single crystals are widely used as scintillators, phosphors and the like. The gadolinium silicate single crystal belonging to this single crystal system can be produced from the raw material melt by the Czochralski method. That is, it was manufactured by heating a crucible in which the raw materials were put into a melt, bringing a seed crystal into contact with the melt in the crucible, pulling up the seed crystal, and further growing a single crystal on the seed crystal. When used as a scintillator or the like, it is generally used after being processed into a cylindrical or rectangular parallelepiped shape. In practice, one surface to the entire surface is mirror-polished, and the surface without the reflection material is used in close contact with the photomultiplier tube in a state where the reflection material is applied or wound except for one surface which has been subjected to the mirror polishing. You. However, gadolinium silicate single crystal belonging to this monoclinic system has a cleaving property on the a-plane ((100) plane) and has a thermal expansion coefficient in the b-axis ([010] axis) direction which is lower than that in other directions. Because of the anisotropy that is larger than the direction, the crystal is easily cracked along the (100) plane and the (010) plane during crystal growth cooling, and new cracks are easily generated during processing. As a method for growing a rare-earth silicate single crystal without cracks, a method in which the pulling axis is set to the b-axis ([010] axis) of the single crystal or in the vicinity thereof (the angle of inclination from the b-axis is 0 to 30 °) ( And a method in which the pulling axis is parallel to the (100) plane and the angle of inclination from the c-axis ([001] axis) is 0 ° to 25 ° (see Patent Document 2). Has been proposed.
しかし、これら従来法では、希土類珪酸塩単結晶の育成冷却中あるいは加工時に依然割れが発生する問題がある。すなわち、引上軸を［０１０］軸またはその近傍とした場合には、育成冷却中に種結晶や育成結晶の途中に割れが発生し、結晶が落下してしまう。更に、この方向に育成した結晶から長い円柱形試料を採取する場合には、育成結晶の長さ方向に（円柱の軸方向を引上軸方向にして）試料を採取するが、この場合側面の円筒研削時に割れが発生し易く、歩留りが低下する問題がある。一方、引上軸を［００１］軸またはその近傍とした場合には、育成結晶から試料を採取、加工する際に、引上方向に垂直な面を研磨する時にへき開割れが発生してしまう。この試料面の割れを防止するためには、引上軸方向に対し試料の中心軸を十分傾けて試料を採取する必要があり、試料採取の歩留りが低下し作業も面倒になるという問題がある。本発明は、引上軸方向を選択することにより、育成中に割れが発生することがなく、かつ育成結晶の側面及び断面（引上方向に垂直な面）の加工時に割れが発生しにくいため、結晶育成及び試料採取が容易な単結晶が得られる希土類珪酸塩単結晶の育成方法を提供するものである。 However, these conventional methods have a problem that cracks still occur during the growth and cooling of the rare earth silicate single crystal or during processing. That is, when the pulling axis is the [010] axis or in the vicinity thereof, cracks occur in the seed crystal or the grown crystal during the growth and cooling, and the crystal falls. Further, when collecting a long cylindrical sample from the crystal grown in this direction, the sample is collected in the length direction of the grown crystal (with the axial direction of the cylinder being the pull-up axis direction). There is a problem that cracks are easily generated during cylindrical grinding, and the yield is reduced. On the other hand, if the pull-up axis is the [001] axis or its vicinity, cleavage and cracking will occur when a surface perpendicular to the pull-up direction is polished when collecting and processing a sample from the grown crystal. In order to prevent the crack on the sample surface, it is necessary to collect the sample by sufficiently tilting the center axis of the sample with respect to the pulling-up axis direction, and there is a problem that the yield of the sample collection is reduced and the operation is troublesome. . In the present invention, by selecting the pulling axis direction, cracks do not occur during growth, and cracks do not easily occur during processing of the side surface and cross section (plane perpendicular to the pulling direction) of the grown crystal. Another object of the present invention is to provide a method for growing a rare earth silicate single crystal, which can provide a single crystal that is easy to grow and sample.
上記目的を達成するために、本発明者らは、原料を入れたるつぼを加熱して融液とし、その融液に種結晶の下端を接触させ、種結晶を引き上げながら単結晶を育成する希土類珪酸塩単結晶の育成において、引上軸の方位による育成中及び加工時の割れの発生し易さについて検討した。その結果、引上軸を単結晶のｂ軸（［０１０］軸）とｃ軸（［００１］軸）の間のある範囲（ｂ軸からの傾きの角度が３０°以上、かつｃ軸からの角度が２５°以上）で、かつ（１００）面との傾きの角度が０〜２５°の方向にすることにより、育成中及び加工時の割れを防止することができることを見いだすことによって、本発明は成されたものである。 In order to achieve the above object, the present inventors heated a crucible containing raw materials to form a melt, contacted the lower end of the seed crystal with the melt, and grown a single crystal while pulling up the seed crystal. In the growth of silicate single crystals, the possibility of cracking during growth and during processing according to the orientation of the pulling axis was examined. As a result, the pulling axis is set to a certain range between the b-axis ([010] axis) and the c-axis ([001] axis) of the single crystal (the angle of inclination from the b-axis is 30 ° or more, and The present invention is based on the finding that cracks during growth and during processing can be prevented by setting the angle of inclination with respect to the (100) plane to 0 to 25 °. Is made.
即ち本発明は、原料を入れたるつぼを加熱して融液とし、その融液に種結晶の下端を接触させ、種結晶を引き上げながら単結晶を育成する際に、引上軸を、単結晶のｂ軸（［０１０］軸）からの傾きの角度が３０°以上、かつｃ軸（［００１］軸）からの傾きの角度が２５°以上の方向として希土類珪酸塩単結晶を育成し、該希土類珪酸塩単結晶の側面を（００１）−１７°面から傾けて円筒研削した後、更に両端面を（００１）−１７°面から傾けて鏡面研磨することを特徴とする円柱状希土類珪酸塩単結晶の製造方法を提供する。 That is, the present invention heats the crucible containing the raw material and melt, the melt is brought into contact with the lower end of the seed crystal, when a single crystal is grown while pulling the seed crystal, the pulling member, single-crystal of b-axis ([010] axis) angle of inclination from 30 ° or more, and c-axis angle of inclination from ([001] axis) is a direction of 25 ° or more to foster a rare earth silicate single crystal after the cylindrical grinding tilted side of the rare earth silicate single crystal from (001) -17 ° plane, cylindrical rare earth, characterized in that the mirror-polishing by tilting further both end faces from the (001) -17 ° plane Provided is a method for producing a silicate single crystal .
本発明の育成方法により、結晶の育成・冷却中に割れの発生しない、かつ加工の円筒研削時や研磨時に割れが発生しない、育成及び加工が容易な希土類珪酸塩単結晶を得ることができる。 According to the growing method of the present invention, it is possible to obtain a rare-earth silicate single crystal that does not generate cracks during crystal growth and cooling and that does not generate cracks during cylindrical grinding or polishing, and that is easy to grow and process.
原料を入れたるつぼを加熱して融液とし、その融液に種結晶の下端を接触させ、種結晶を引き上げながら単結晶を育成する希土類珪酸塩単結晶の育成において、引上軸を単結晶のｂ軸（［０１０］軸）とｃ軸（［００１］軸）の間のある範囲で、かつ（１００）面との傾きの角度が０〜２５°の方向にすることにより、育成中及び加工時の割れを防止することができる原因は次のように考えられる。希土類珪酸塩単結晶の材料力学特性を調べた結果、［００１］軸方向の熱膨張係数が他の方向よりも大きいことがわかっている。そのため、引上軸を［０１０］軸またはその近傍とした場合には、この［０１０］軸方向が温度勾配の大きい方向になるために、熱応力により育成中に種結晶や育成結晶の途中に割れが発生し、結晶が落下してしまうと考えられる。そこで、結晶の落下を防止するためには、引上軸の［０１０］軸からの傾きをある角度以上にすればよい。また、希土類珪酸塩単結晶には、へき開面（（１００）面）に垂直方向から荷重し、［００１］軸方向に引っ張りの応力が作用する場合に塑性変形が発生すること、そして、へき開割れ方向の破壊靱性値は（０１０）面よりも（００１）−１７°面（［００１］軸を法線方向とする面）の方が約１桁小さく、へき開割れは（０１０）面側からよりも（００１）−１７°面側から非常に発生し易いことが今回新たにわかった。これらのへき開面に関する異方性のある特性から、［０１０］軸近傍を引上軸とした結晶から長さ方向に長い円柱状試料を採取する場合には、（００１）−１７°面に近い面（傾きの小さい面）が側面になるために、へき開割れ及びへき開面の剥がれが発生し易い。そこで、円筒研削時の側面の割れ及び剥がれを防止するためには、引上軸の［０１０］軸からの傾きをある角度以上にすればよい。 The crucible containing the raw materials is heated to form a melt.The lower end of the seed crystal is brought into contact with the melt, and the seed crystal is pulled up to grow a single crystal. In a certain range between the b-axis ([010] axis) and the c-axis ([001] axis), and the angle of inclination with respect to the (100) plane is in a direction of 0 to 25 °, during growth and The reason why cracking during processing can be prevented is considered as follows. As a result of examining the material mechanical properties of the rare earth silicate single crystal, it has been found that the coefficient of thermal expansion in the [001] axis direction is larger than that in other directions. Therefore, when the pulling axis is the [010] axis or in the vicinity thereof, the [010] axis direction becomes a direction with a large temperature gradient. It is considered that cracks occur and crystals fall. Therefore, in order to prevent the crystal from falling, the inclination of the pulling axis from the [010] axis may be set to a certain angle or more. In addition, a rare earth silicate single crystal is subjected to a plastic deformation when a tensile stress is applied in the [001] axial direction when a load is applied from a direction perpendicular to the cleavage plane ((100) plane). The fracture toughness value in the direction is about one order of magnitude smaller on the (001) -17 ° plane (the plane with the [001] axis as the normal direction) than on the (010) plane, and the cleavage cracking is greater from the (010) plane side. This time, it was newly found that this was also very likely to occur from the (001) -17 ° plane side. Due to the anisotropic properties of these cleavage planes, when collecting a columnar sample long in the length direction from a crystal with the pull-up axis near the [010] axis, it is close to the (001) -17 ° plane. Since the surface (the surface with a small inclination) is a side surface, cleavage cleavage and peeling of the cleavage surface are liable to occur. Therefore, in order to prevent cracking and peeling of the side surface during cylindrical grinding, the inclination of the pulling shaft from the [010] axis may be set to a certain angle or more.
一方、同じくへき開割れの破壊靱性値の異方性により、引上軸を［００１］軸近傍とした場合には、（００１）−１７°面に近い面（傾きの小さい面）が引上方向に垂直になるために、加工に便利なこの面で切断し試料を採取すると、この面を研磨する時にへき開割れが発生してしまう。そこで、引上軸に垂直な面で試料を採取しても、研磨する際に割れが入らないようにするためには、すなわち、試料採取に便利な（歩留りも良い）結晶方向の育成結晶を得るためには、引上軸の［００１］軸からの傾きをある角度以上にすればよい。へき開性のある（１００）面と引上軸の関係については、引上軸を［００１］−１７°軸（（１００）面の法線方向）近傍とすると、［０１０］軸近傍とした場合と同様に、引上軸にほぼ垂直な面の割れによる結晶落下の問題が発生し、（０１０）面割れよりも発生し易いために、引上軸（１００）面に平行にした方向が最も結晶育成がし易い。しかし、引上軸との傾きの角度か０〜２５°までは結晶の育成が可能であり、結晶の加工にも支障の無い方向であるので、引上軸の方向として選択することができる。以上が、引上軸をｂ軸（［０１０］軸）からの傾きの角度が３０°以上、ｃ軸（［００１］軸）からの角度が２５°以上、かつ（１００）面との傾きの角度が０〜２５°の方向にすることにより、育成中及び加工時の割れを安定して防止できることの理由と考えられる。 On the other hand, when the pulling axis is set near the [001] axis due to the anisotropy of the fracture toughness value of the cleavage crack, the plane close to the (001) -17 ° plane (the plane with a small inclination) is in the pulling direction. When the sample is cut and cut on this surface, which is convenient for processing, a cleavage crack occurs when this surface is polished. Therefore, in order to prevent cracks during polishing even when a sample is taken on a plane perpendicular to the pulling axis, a crystal grown in a crystal direction that is convenient for sample collection (good in yield) is used. In order to obtain it, the inclination of the pull-up axis from the [001] axis may be set to a certain angle or more. Regarding the relationship between the cleaving (100) plane and the pulling axis, assuming that the pulling axis is near the [001] -17 ° axis (the normal direction of the (100) plane), it is near the [010] axis. Similarly to the above, the problem of crystal falling due to cracks in a plane substantially perpendicular to the pulling axis occurs, and the crystal is more likely to occur than the (010) plane crack. Therefore, the direction parallel to the pulling axis (100) plane is most likely. Crystal growth is easy. However, the crystal can be grown up to an angle of inclination of 0 to 25 ° with respect to the pulling axis, and it is a direction that does not hinder the crystal processing. Therefore, the direction can be selected as the direction of the pulling axis. As described above, the angle of inclination of the pull-up axis from the b-axis ([010] axis) is 30 ° or more, the angle from the c-axis ([001] axis) is 25 ° or more, and the inclination with respect to the (100) plane. It is considered that setting the angle to a direction of 0 to 25 ° can stably prevent cracking during growth and during processing.
珪酸ガドリニウム単結晶以外の、化１の一般式
［化１］
Ｒ２ＳｉＯ５
（但し、ＲはＬａ、Ｃｅ、Ｐｒ、Ｎｄ、Ｐｍ、Ｓｍ、Ｅｕ、Ｔｂ、Ｄｙ、Ｈｏ、Ｅｒ、Ｔｍ、Ｙｂ、Ｌｕ、Ｙ、Ｓｃから選ばれる１種以上の希土類元素）
で示される希土類珪酸塩単結晶についても、結晶の力学特性は同様であり、同様の結果となる。更に、これらの希土類珪酸塩単結晶にＣｅ等の希土類元素やＣｒ等の鉄属遷移金属をドープした場合も、効果は同様である。以上の希土類珪酸塩単結晶は、珪酸ガドリニウム単結晶の結晶構造と同じ結晶構造を持ち、その構造は空間群Ｐ２／ｃに属する。
General formula of Chemical Formula 1 other than gadolinium silicate single crystal
R 2 SiO 5
(Where R is one or more rare earth elements selected from La, Ce, Pr, Nd, Pm, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu, Y and Sc)
The mechanical properties of the rare-earth silicate single crystal represented by are similar, and the same result is obtained. The same effect is obtained when these rare earth silicate single crystals are doped with a rare earth element such as Ce or an iron-based transition metal such as Cr. The above rare earth silicate single crystal has the same crystal structure as the gadolinium silicate single crystal, and the structure belongs to the space group P2 / c.
（比較例１）
セリウム付活珪酸ガドリニウム単結晶（Ｃｅ：Ｇｄ２ＳｉＯ５）の場合の例を説明する。原料として、Ｇｄ２Ｏ３約３２６０ｇ、ＳｉＯ２約５４０ｇ、ＣｅＯ２約１０ｇをφ１００のＩｒるつぼ中に採り、φ５０×１８０ｍｍ３の結晶をチョクラルスキー法で育成した。種結晶の引上軸は［０１０］軸とし、引上速度は１〜３ｍｍ／ｈ、回転速度は３０〜５０ｒｐｍとした。育成の切り離し後、２０〜６０時間かけて室温まで結晶を冷却した。しかし、その途中で、結晶直胴部の上部で引上軸にほぼ垂直に割れが発生し、割れ発生位置から下の結晶部分が落下してしまった（図２）。このような結晶の落下は９０％以上の確率で発生した。直胴部とは、融液に種結晶の下端を接触させ種結晶を引き上げながら単結晶を育成する場合、種結晶から目的径まで結晶径を広げ目的径になった後育成される部分である。更に、育成結晶の割れのない部分から、φ４０×１２０ｍｍ３の試料の採取を試みた。育成結晶を引上軸に約１２０ｍｍの長さに切断した。その後、円筒研削機により側面の円筒研削を行いφ４０の円柱に加工したが、側面にへき開面（（１００）面）方向の割れ及び剥がれが発生してしまった（図３）。
(Comparative Example 1)
An example of a cerium-activated gadolinium silicate single crystal (Ce: Gd 2 SiO 5 ) will be described. As raw materials, about 3260 g of Gd 2 O 3 , about 540 g of SiO 2 , and about 10 g of CeO 2 were placed in a φ100 Ir crucible, and crystals of φ50 × 180 mm 3 were grown by the Czochralski method. The pulling axis of the seed crystal was the [010] axis, the pulling speed was 1 to 3 mm / h, and the rotation speed was 30 to 50 rpm. After separating the growth, the crystals were cooled to room temperature over a period of 20 to 60 hours. However, on the way, a crack was generated almost perpendicularly to the pulling axis at the upper part of the crystal straight body part, and the lower crystal part dropped from the crack occurrence position (FIG. 2). Such a crystal drop occurred with a probability of 90% or more. When growing a single crystal while bringing the seed crystal into contact with the lower end of the seed crystal and pulling up the seed crystal, the straight body portion is a portion grown after the crystal diameter is expanded from the seed crystal to the target diameter and reaches the target diameter. . Further, a sample of φ40 × 120 mm 3 was sampled from a portion where the grown crystal had no crack. The grown crystal was cut into a length of about 120 mm around a pulling shaft. After that, the side surface was cylindrically ground by a cylindrical grinder and processed into a φ40 cylinder, but cracks and peeling occurred on the side surface in the direction of the cleavage plane ((100) plane) (FIG. 3).
（比較例２）
比較例１と同様にＧＳＯ単結晶をチョクラルスキー法で育成した。種結晶の引上軸は［００１］軸とし、引上速度は１〜３ｍｍ／ｈ、回転速度は３０〜５０ｒｐｍとした。育成の切り離し後、２０〜５０時間かけて室温まで結晶を冷却した。約５０％の確率で冷却途中に割れは発生せず、直胴部がφ５０×１８０ｍｍ３の単結晶が得られた。育成結晶から、φ４０×１３０ｍｍ３の試料の採取するために切断加工を行った。育成結晶を引上軸に垂直に約１３０ｍｍの長さに切断した。その後、円筒研削機により側面の円筒研削を行いφ４０の円柱に加工し、割れの無い側面を得ることができた。次に、鏡面研磨を行ったところ、側面は割れが発生すること無く研磨することができたが、両端面（底面）の研磨時には、へき開面（（１００）面）方向の割れが発生してしまった（図４）。
(Comparative Example 2)
A GSO single crystal was grown by the Czochralski method as in Comparative Example 1. The pulling axis of the seed crystal was the [001] axis, the pulling speed was 1 to 3 mm / h, and the rotation speed was 30 to 50 rpm. After the growth was separated, the crystals were cooled to room temperature over 20 to 50 hours. With a probability of about 50%, no cracks occurred during cooling, and a single crystal having a straight body portion of φ50 × 180 mm 3 was obtained. A cutting process was performed to collect a sample of φ40 × 130 mm 3 from the grown crystal. The grown crystal was cut to a length of about 130 mm perpendicular to the pulling axis. Thereafter, the side surface was cylindrically ground by a cylindrical grinder and processed into a φ40 cylinder, whereby a crack-free side surface could be obtained. Next, when mirror polishing was performed, the side surfaces could be polished without cracking. However, when polishing both end surfaces (bottom surface), cracks were generated in the cleavage plane ((100) plane) direction. (Fig. 4).
（実施例１）
比較例１と同様にＧＳＯ単結晶をチョクラルスキー法で育成した。種結晶の引上軸は、［０１０］軸からの傾きが６０°で［００１］軸からの傾きが３０°、かつ（１００）面に平行な方向とした。引上速度は１〜３ｍｍ／ｈ、回転速度は３０〜５０ｒｐｍとした。育成の切り離し後、２０〜６０時間かけて室温まで結晶を冷却した。約８０％の確率で冷却途中に割れは発生せず、直胴部がφ５０×１８０ｍｍ３の単結晶が得られた。育成結晶から、φ４０×１３０ｍｍ３の試料の採取するために切断加工を行った。育成結晶を引上軸に垂直に約１３０ｍｍの長さに切断した。その後、円筒研削機により側面の円筒研削を行いφ４０の円柱に加工し、割れの無い側面を得ることができた。次に、鏡面研磨を行ったところ、側面及び両端面（底面）とも割れが発生すること無く研磨することができた（図１）。
(Example 1)
A GSO single crystal was grown by the Czochralski method as in Comparative Example 1. The pull-up axis of the seed crystal was set to a direction in which the inclination from the [010] axis was 60 °, the inclination from the [001] axis was 30 °, and parallel to the (100) plane. The pulling speed was 1 to 3 mm / h, and the rotation speed was 30 to 50 rpm. After separating the growth, the crystals were cooled to room temperature over a period of 20 to 60 hours. About 80% of the time cracks during cooling is not generated, the straight body portion is a single crystal of ø50 × 180 mm 3 was obtained. A cutting process was performed to collect a sample of φ40 × 130 mm 3 from the grown crystal. The grown crystal was cut to a length of about 130 mm perpendicular to the pulling axis. Thereafter, the side surface was cylindrically ground by a cylindrical grinder and processed into a φ40 cylinder, whereby a crack-free side surface could be obtained. Next, when mirror polishing was performed, the side and both end faces (bottom face) could be polished without cracking (FIG. 1).
（実施例２）
比較例１と同様にＧＳＯ単結晶をチョクラルスキー法で育成した。種結晶の引上軸は、［０１０］軸からの傾きが６０°で［００１］軸からの傾きが３０°、かつ（１００）面との傾きの角度が２５°の方向とした。引上速度は１〜３ｍｍ／ｈ、回転速度は３０〜５０ｒｐｍとした。育成の切り離し後、２０〜６０時間かけて室温まで結晶を冷却した。約６０％の確率で冷却途中に割れは発生せず、直胴部がφ５０×１８０ｍｍ３の単結晶が得られた。育成結晶から、φ４０×１３０ｍｍ３の試料の採取するために切断加工を行った。育成結晶を引上軸に垂直に約１３０ｍｍの長さに切断した。その後、円筒研削機により側面の円筒研削を行いφ４０の円柱に加工し、割れの無い側面を得ることができた。次に鏡面研磨を行ったところ、側面及び両端面（底面）とも割れが発生すること無く研磨することができた。
(Example 2)
A GSO single crystal was grown by the Czochralski method as in Comparative Example 1. The pulling axis of the seed crystal was a direction in which the tilt from the [010] axis was 60 °, the tilt from the [001] axis was 30 °, and the tilt angle with the (100) plane was 25 °. The pulling speed was 1 to 3 mm / h, and the rotation speed was 30 to 50 rpm. After separating the growth, the crystals were cooled to room temperature over a period of 20 to 60 hours. With a probability of about 60%, cracks did not occur during cooling, and a single crystal having a straight body portion of φ50 × 180 mm 3 was obtained. A cutting process was performed to collect a sample of φ40 × 130 mm 3 from the grown crystal. The grown crystal was cut to a length of about 130 mm perpendicular to the pulling axis. Thereafter, the side surface was cylindrically ground by a cylindrical grinder and processed into a φ40 cylinder, whereby a crack-free side surface could be obtained. Next, when mirror polishing was performed, the side and both end faces (bottom face) could be polished without cracking.
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