Embodiments provide a method of growing a silicon single crystal ingot, the method including growing a silicon single crystal ingot having crystal orientation of (111) using the Czochralski method, measuring a diameter of the silicon single crystal ingot, calculating a length of a facet of the silicon single crystal ingot, calculating a correction formula for a rotation speed of a seed and a correction formula for a pulling speed of the silicon single crystal ingot based on the calculated facet length, and correcting the rotation speed of the seed and the pulling speed of the silicon single crystal ingot based on a result of the calculation.

Growth of single crystal epitaxial films of the perovskite crystal structure by liquid- or vapor-phase means can be accomplished by providing single-crystal perovskite substrate materials of improved lattice parameter match in the lattice parameter range of interest. Current substrates do not provide as good a lattice match, have inferior properties, or are of limited size and availability because cost of materials and difficulty of growth. This problem is solved by the single-crystal perovskite solid solutions described herein grown from mixtures with an indifferent melting point that occurs at a congruently melting composition at a temperature minimum in the melting curve in the pseudo-binary molar phase diagram. Accordingly, single-crystal perovskite solid solutions, structures, and devices including single-crystal perovskite solid solutions, and methods of making single-crystal perovskite solid solutions are described herein.

Growth of single crystal epitaxial films of the perovskite crystal structure by liquid- or vapor-phase means can be accomplished by providing single-crystal perovskite substrate materials of improved lattice parameter match in the lattice parameter range of interest. Current substrates do not provide as good a lattice match, have inferior properties, or are of limited size and availability because cost of materials and difficulty of growth. This problem is solved by the single-crystal perovskite solid solutions described herein grown from mixtures with an indifferent melting point that occurs at a congruently melting composition at a temperature minimum in the melting curve in the pseudo-binary molar phase diagram. Accordingly, single-crystal perovskite solid solutions, structures, and devices including single-crystal perovskite solid solutions, and methods of making single-crystal perovskite solid solutions are described herein.

An RAMO.sub.4 substrate including a single crystal represented by a general formula RAMO.sub.4, wherein R represents one or more trivalent elements selected from a group consisting of Sc, In, Y, and lanthanide elements, A represents one or more trivalent elements selected from a group consisting of Fe(III), Ga, and Al, and M represents one or more divalent elements selected from the group consisting of Mg, Mn, Fe(II), Co, Cu, Zn, and Cd, in which a main plane of the RAMO.sub.4 substrate has an off-angle a tilted a with respect to an M-axis direction from a C-plane and 0.05|a|0.8 is satisfied.

Methods for preparing an ingot in an ingot puller apparatus are disclosed. Thermal simulations are performed with the length of the ingot puller apparatus side heater being varied in the thermal simulations. A side heater is selected based on the thermal simulations. An ingot puller apparatus having the selected side heater length is provided. A seed crystal is lowered into a melt within a crucible of the ingot puller apparatus and an ingot is withdrawn from the melt.

Methods for preparing an ingot in an ingot puller apparatus are disclosed. Thermal simulations are performed with the length of the ingot puller apparatus side heater being varied in the thermal simulations. A side heater is selected based on the thermal simulations. An ingot puller apparatus having the selected side heater length is provided. A seed crystal is lowered into a melt within a crucible of the ingot puller apparatus and an ingot is withdrawn from the melt.

Growth of single crystal epitaxial films of the perovskite crystal structure by liquid- or vapor-phase means can be accomplished by providing single-crystal perovskite substrate materials of improved lattice parameter match in the lattice parameter range of interest. Current substrates do not provide as good a lattice match, have inferior properties, or are of limited size and availability because cost of materials and difficulty of growth. This problem is solved by the single-crystal perovskite solid solutions described herein grown from mixtures with an indifferent melting point that occurs at a congruently melting composition at a temperature minimum in the melting curve in the pseudo-binary molar phase diagram. Accordingly, single-crystal perovskite solid solutions, structures, and devices including single-crystal perovskite solid solutions, and methods of making single-crystal perovskite solid solutions are described herein.

Growth of single crystal epitaxial films of the perovskite crystal structure by liquid- or vapor-phase means can be accomplished by providing single-crystal perovskite substrate materials of improved lattice parameter match in the lattice parameter range of interest. Current substrates do not provide as good a lattice match, have inferior properties, or are of limited size and availability because cost of materials and difficulty of growth. This problem is solved by the single-crystal perovskite solid solutions described herein grown from mixtures with an indifferent melting point that occurs at a congruently melting composition at a temperature minimum in the melting curve in the pseudo-binary molar phase diagram. Accordingly, single-crystal perovskite solid solutions, structures, and devices including single-crystal perovskite solid solutions, and methods of making single-crystal perovskite solid solutions are described herein.

A method for casting comprising: providing a seed, the seed characterized by: an arcuate form and a crystalline orientation progressively varying along an arc of the form; providing molten material; and cooling and solidifying the molten material so that a crystalline structure of the seed propagates into the solidifying material.

A method for casting comprising: providing a seed, the seed characterized by: an arcuate form and a crystalline orientation progressively varying along an arc of the form; providing molten material; and cooling and solidifying the molten material so that a crystalline structure of the seed propagates into the solidifying material.