A nitride semiconductor free-standing substrate includes a diameter of not less than 40 mm, a thickness of not less than 100 μm, a dislocation density of not more than 5×10.sup.6/cm.sup.2, an impurity concentration of not more than 4×10.sup.19/cm.sup.3, and a nanoindentation hardness of not less than 19.0 GPa at a maximum load in a range of not less than 1 mN and not more than 50 mN.

A nitride semiconductor free-standing substrate includes a diameter of not less than 40 mm, a thickness of not less than 100 μm, a dislocation density of not more than 5×10.sup.6/cm.sup.2, an impurity concentration of not more than 4×10.sup.19/cm.sup.3, and a nanoindentation hardness of not less than 19.0 GPa at a maximum load in a range of not less than 1 mN and not more than 50 mN.

A method of fabricating a wafer according to the embodiment comprises the steps of growing an wafer on a surface of the wafer in a growth temperature; and cooling the wafer after the wafer has been grown, wherein a stepwise cooling is performed when cooling the wafer.

A method of fabricating a wafer according to the embodiment comprises the steps of growing an wafer on a surface of the wafer in a growth temperature; and cooling the wafer after the wafer has been grown, wherein a stepwise cooling is performed when cooling the wafer.

A method of increasing the luminescence efficiency of titanium-doped oxide crystal, used as a laser material, is disclosed. This is accomplished by tempering the crystal at a temperature from 1750° C. to 50° C. below the melting point of the oxide crystal in a hydrogen protecting atmosphere with a constant partial pressure of the aluminium suboxide Al.sub.2O gas. By applying the method of the present invention, its luminescence efficiency of titanium-doped oxide crystal increases by 10 to 50 percent, and possibly by as much as 100 percent or more compared to previous technological treatments.

Among other things, piezoelectric materials and methods of their manufacture are described; particularly methods of forming regions of varying crystal structure within a relaxor piezoelectric substrate. Such methods may including heating the piezoelectric substrate above the transition temperature and below the Curie temperature such that a first phase transition occurs to a first crystal structure; rapidly cooling the piezoelectric substrate below the transition temperature at a cooling rate that is sufficiently high for the first crystal structure to persist; and applying an electric field through one or more selected regions of the piezoelectric substrate, such that within the one or more selected regions, a second phase transition occurs and results in a second crystal structure.

Among other things, piezoelectric materials and methods of their manufacture are described; particularly methods of forming regions of varying crystal structure within a relaxor piezoelectric substrate. Such methods may including heating the piezoelectric substrate above the transition temperature and below the Curie temperature such that a first phase transition occurs to a first crystal structure; rapidly cooling the piezoelectric substrate below the transition temperature at a cooling rate that is sufficiently high for the first crystal structure to persist; and applying an electric field through one or more selected regions of the piezoelectric substrate, such that within the one or more selected regions, a second phase transition occurs and results in a second crystal structure.

A method of manufacturing a diamond substrate includes: forming an ion implantation layer at a side of a main surface of a diamond seed substrate by implanting ions into the main surface of the diamond seed substrate; producing a diamond structure by growing a diamond growth layer by a vapor phase synthesis method on the main surface of the diamond seed substrate, after implanting the ions; and performing heat treatment on the diamond structure. The performed heat treatment causes the diamond structure to be separated along the ion implantation layer into a first structure including the diamond seed substrate and failing to include the diamond growth layer, and a diamond substrate including the diamond growth layer. Thus, the method of manufacturing a diamond substrate is provided that enables a diamond substrate with a large area to be manufactured in a short time and at a low cost.

A method of manufacturing a diamond substrate includes: forming an ion implantation layer at a side of a main surface of a diamond seed substrate by implanting ions into the main surface of the diamond seed substrate; producing a diamond structure by growing a diamond growth layer by a vapor phase synthesis method on the main surface of the diamond seed substrate, after implanting the ions; and performing heat treatment on the diamond structure. The performed heat treatment causes the diamond structure to be separated along the ion implantation layer into a first structure including the diamond seed substrate and failing to include the diamond growth layer, and a diamond substrate including the diamond growth layer. Thus, the method of manufacturing a diamond substrate is provided that enables a diamond substrate with a large area to be manufactured in a short time and at a low cost.

Provided is a Ni-based single crystal superalloy containing 6% by mass or more and 12% by mass or less of Cr, 0.4% by mass or more and 3.0% by mass or less of Mo, 6% by mass or more and 10% by mass or less of W, 4.0% by mass or more and 6.5% by mass or less of Al, 0% by mass or more and 1% by mass or less of Nb, 8% by mass or more and 12% by mass or less of Ta, 0% by mass or more and 0.15% by mass or less of Hf, 0.01% by mass or more and 0.2% by mass or less of Si, and 0% by mass or more and 0.04% by mass or less of Zr, and optionally containing at least one element selected from B, C, Y, La, Ce, and V, with a balance being Ni and inevitable impurities.