A bismuth-substituted rare earth iron garnet single crystal suitable for Faraday rotators and optical isolators with reduced insertion loss due to suppressed valence fluctuation of Fe ions is provided. The bismuth-substituted rare earth iron garnet single crystal of the present invention is characterized by the composition formula (Tb.sub.aLn.sub.bBi.sub.cMg.sub.3−(a+b+c))(Fe.sub.dGa.sub.eTi.sub.fPt.sub.5−(d+e+f))O.sub.12. In the composition formula above, 0.02≤f≤0.05, 0.02≤{3−(a+b+c)}≤0.08, and −0.01≤{3−(a+b+c)}−{f+5−(d+e+f)}≤0.01. Ln is a rare earth element and may be selected from Eu, Gd, Ho, Tm, Yb, Lu, and Y.

Method for producing a silicon ingot in which a horizontal magnetic field is generated are disclosed. A plurality of process parameters are regulated during ingot growth including a wall temperature of the crucible, a transport of silicon monoxide (SiO) from the crucible to the single crystal, and an evaporation rate of SiO from the melt. Regulating the plurality of process parameters may include controlling the position of a maximum gauss plane of the horizontal magnetic field, controlling the strength of the horizontal magnetic field, and controlling the crucible rotation rate.

Method for producing a silicon ingot in which a horizontal magnetic field is generated are disclosed. A plurality of process parameters are regulated during ingot growth including a wall temperature of the crucible, a transport of silicon monoxide (SiO) from the crucible to the single crystal, and an evaporation rate of SiO from the melt. Regulating the plurality of process parameters may include controlling the position of a maximum gauss plane of the horizontal magnetic field, controlling the strength of the horizontal magnetic field, and controlling the crucible rotation rate.

A 4H-SiC single crystal having good morphology while preventing heterogeneous polymorphs from being mixed in regardless of the presence or absence of doping in growing a 4H-SiC single crystal by the TSSG method is obtained. When the off-angle on the grown crystal in a method for producing a SiC single crystal by a TSSG method is set to 60 to 68°, heterogeneous polymorphs are less likely to be mixed in during the growth of 4H-SiC single crystal, and if, during that period, a meltback method is used to smooth the surface of the seed crystal and then grow the crystal, it is possible to obtain a grown crystal having good morphology.

A 4H-SiC single crystal having good morphology while preventing heterogeneous polymorphs from being mixed in regardless of the presence or absence of doping in growing a 4H-SiC single crystal by the TSSG method is obtained. When the off-angle on the grown crystal in a method for producing a SiC single crystal by a TSSG method is set to 60 to 68°, heterogeneous polymorphs are less likely to be mixed in during the growth of 4H-SiC single crystal, and if, during that period, a meltback method is used to smooth the surface of the seed crystal and then grow the crystal, it is possible to obtain a grown crystal having good morphology.

A method of producing an apatite crystal includes the steps of preparing an apatite single crystal expressed by the general formula M.sup.2.sub.5(PO.sub.4).sub.3X (M.sup.2 being at least atomic element selected from the group consisting of divalent alkaline-earth metals and Eu, and X is at least one atomic selected from the group consisting of halogens); placing the apatite single crystal into a space controllable to a predetermined atmosphere; supplying water vapor into the space; and heating such that the atmosphere in the space is within a 1000° C. to 1400° C. range.

A method of producing an apatite crystal includes the steps of preparing an apatite single crystal expressed by the general formula M.sup.2.sub.5(PO.sub.4).sub.3X (M.sup.2 being at least atomic element selected from the group consisting of divalent alkaline-earth metals and Eu, and X is at least one atomic selected from the group consisting of halogens); placing the apatite single crystal into a space controllable to a predetermined atmosphere; supplying water vapor into the space; and heating such that the atmosphere in the space is within a 1000° C. to 1400° C. range.

A bismuth-substituted rare earth iron garnet single crystal suitable for Faraday rotators and optical isolators with reduced insertion loss due to suppressed valence fluctuation of Fe ions is provided. The bismuth-substituted rare earth iron garnet single crystal of the present invention is characterized by the composition formula (Gd.sub.aLn.sub.bBi.sub.cMg.sub.3−(a+b+c))(Fe.sub.dGa.sub.eTi.sub.fPt.sub.5−(d+e+f))O.sub.12. In the composition formula above, 0.02≤f≤0.05, 0.02≤{3−(a+b+c)}≤0.08, and −0.01≤{3−(a+b+c)}−{f+5−(d+e+f)}≤0.01. Ln is a rare earth element and may be selected from Eu, Dy, Gd, Ho, Tm, Yb, Lu, and Y.

Systems and method for creating crystalline parts having a desired primary and secondary crystallographic orientations are provided. One embodiment may take the form of a method of manufacturing a part having a crystalline structure. The method includes melting aluminum oxide and drawing the melted aluminum oxide up a slit. Additionally, the method includes orienting the seed crystal relative to a growth apparatus such that a crystalline structure grows having a desired primary plane and a desired secondary plane orientation. Moreover, the method includes pulling the crystal as it forms to create a ribbon shaped crystalline structure and cutting a part from the crystalline structure.

Systems and method for creating crystalline parts having a desired primary and secondary crystallographic orientations are provided. One embodiment may take the form of a method of manufacturing a part having a crystalline structure. The method includes melting aluminum oxide and drawing the melted aluminum oxide up a slit. Additionally, the method includes orienting the seed crystal relative to a growth apparatus such that a crystalline structure grows having a desired primary plane and a desired secondary plane orientation. Moreover, the method includes pulling the crystal as it forms to create a ribbon shaped crystalline structure and cutting a part from the crystalline structure.