Floating zone crystal growth of inorganic oxide materials and methods of use thereof

Abstract

Disclosed herein is floating zone crystal growth of inorganic oxide materials and methods of use thereof. For example, disclosed herein are methods of making a single crystal of a composition by floating zone crystal growth, the composition comprising A2O3, wherein A is a metal; wherein the single crystal has a lattice dimension of from 3.900 to 4.100 Å. Also disclosed herein are methods of making a single crystal of a composition by floating zone crystal growth, the composition comprising AMO3, wherein A is Ca, Sr, Ba, or a combination thereof, and M is Ti, Zr, Hf, or a combination thereof. Also disclosed herein are single crystals grown by any of the methods disclosed herein and wafers formed from any of the single crystals disclosed herein. Also disclosed herein are devices and / or articles of manufacture comprising any of the single crystals disclosed herein and / or any of the wafers disclosed herein.

Description

[0001]FLOATING ZONE CRYSTAL GROWTH OF INORGANIC OXIDE MATERIALS AND METHODS OF USE THEREOF CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of priority to U.S. Provisional Application No. 63 / 686,968 filed August 26, 2024, which is hereby incorporated herein by reference in its entirety. STATEMENT OF GOVERNMENT SUPPORT This invention was made with government support under grant number W911NF-19-2- 0119 awarded by the Army Research Laboratory. The government has certain rights in the invention. BACKGROUND In the field of thin films, there is a great demand for substrates (crystal wafers) with a lattice dimension of 4.00 Angstroms (4.00 Å). At present only a few materials are used, but are expensive and / or undergo detrimental phase transitions. Alternative crystal wafers having a lattice dimension of 4.00 Angstroms (4.00 Å) are needed. The compositions, devices, systems, and methods disclosed herein address these and other needs. SUMMARY In accordance with the purposes of the disclosed devices, methods, and systems as embodied and broadly described herein, the disclosed subject matter relates to floating zone crystal growth of inorganic oxide materials and methods of use thereof. For example, disclosed herein are methods of making a single crystal of a composition, the method comprising floating zone crystal growth, the composition comprising: A2O3, wherein A is a metal (e.g., one or more metals); wherein the single crystal has a lattice dimension of from 3.900 to 4.100 Å, such as 4.000 Å; with the proviso that A2O3is not Ga2O3. In some examples, A is selected from the group consisting of Ca, Sr, Ba, Ti, Zr, Hf, Ga, Al, and combinations thereof. In some examples, the composition comprises AMO3, wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and M is selected from the group consisting of Ti, Zr, Hf, and combinations thereof. Also disclosed herein are methods of making a single crystal of a composition, the method comprising floating zone crystal growth, the composition comprising: AMO3, wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and M is selected from the group consisting of Ti, Zr, Hf, and combinations thereof. In some examples, the single crystal has a lattice dimension of from 3.900 to 4.100 Å, In some examples, the single crystal has a lattice dimension of 4.000 Å. In some examples, the composition comprises AZr1-xHFxO3, wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and x is from 0 to 1. In some examples, the composition comprises CaZr1-xHFxO3, BaZr1-xHFxO3, SrZr1- xHFxO3, or a combination thereof, wherein each x independently is from 0 to 1. In some examples, the composition comprises CaZr1-xHFxO3, wherein x is from 0 to 1. In some examples, the composition comprises CaZrO3, CaHfO3, or a combination thereof. In some examples, the composition comprises CaZrO3. In some examples, the composition comprises CaHfO3. In some examples, the composition comprises BaZr1-xHFxO3, wherein x is from 0 to 1. In some examples, the composition comprises BaZrO3, BaHfO3, or a combination thereof. In some examples, the composition comprises BaZrO3. In some examples, the composition comprises BaHfO3. In some examples, the composition comprises SrZr1-xHFxO3, wherein x is from 0 to 1. In some examples, the composition comprises SrZrO3. In some examples, the composition comprises SrHfO3. In some examples, the composition comprises (AlyGa1-y)2O3 where y is from greater than 0 to 1. In some examples, the composition comprises Al2O3. In some examples, the composition further comprises a dopant. In some examples, the dopant is selected from the group consisting of Si, Fe, Cu, Tm, Al, Ce, Ga, and combinations thereof. In some examples, the composition comprises (AlyGa1-y)2O3 doped with a dopant, wherein the dopant is selected from the group consisting of Si, Fe, Cu, Tm, Ce, and combinations thereof. In some examples, the composition comprises (AlyGa1-y)2O3 doped with a dopant. In some examples, the composition has a melting point of 2200°C or more. In some examples, the single crystal has an average diameter of from 5 to 50 mm and an average length of 10 to 100 mm. In some examples, the method comprises: preparing a polycrystalline precursor of the composition; heat treating the polycrystalline precursor to form a powder comprising the composition; pressing the powder into a rod and heating the rod, to thereby form a feed rod comprising the composition; introducing the feed rod and a seed rod into a float zone of a floating zone crystal furnace under a growth atmosphere, the seed rod being a single crystal of the composition; and growing the single crystal of the composition via floating zone crystal growth. In some examples, the method further comprises: rotating the feed rod in the float zone at a rate of from 5 to 30 rpm, such as from 10 to 20 rpm (e.g., 15 rpm); rotating the seed rod in the float zone at a rate of from 5 to 30 rpm, such as from 20 to 30 rpm (e.g., 25 rpm); and moving the seed rod linearly within the float zone at a speed of from 10 to 60 mm / h, such as from 25 to 35 mm / h (e.g., 30 mm / h). In some examples, preparing the polycrystalline precursor comprises mixing the precursors with or without the dopant(s) for several hours before heating. In some examples, heat treating the polycrystalline precursor to form a powder comprising the composition comprises heating the sample in air to a temperature of from 400 to 1200°C. In some examples, pressing the powder into a rod comprises placing the powder into a tube, subsequently pressing the powder at 400-600 atm of pressure (for example using a hydrostatic press), and subsequently sintering the rods. In some examples, the growth atmosphere comprises Ar, O2, N2, and / or air, and optionally a dopant. Also disclosed herein are single crystals grown by any of the methods disclosed herein. Also disclosed herein are methods of use of any of the single crystals disclosed herein (e.g., single crystals grown by any of the methods disclosed herein). In some examples, the method comprises cutting the single crystal to thereby form a wafer. Also disclosed herein are wafers formed (e.g., cut) from any of the single crystals disclosed herein (e.g., single crystals grown by any of the methods disclosed herein). Also disclosed herein are wafers formed by any of the methods disclosed herein. Also disclosed herein are methods of use of any of the wafers disclosed herein. In some examples, the method comprises using the wafer as a substrate for thin film growth. Also disclosed herein are devices and / or articles of manufacture comprising any of the single crystals disclosed herein and / or any of the wafers disclosed herein. Also disclosed herein are devices and / or articles of manufacture comprising a thin film grown on any of the single crystals disclosed herein and / or any of the wafers disclosed herein. Additional advantages of the disclosed compositions, devices, systems, and methods will be set forth in part in the description which follows, and in part will be obvious from the description. The advantages of the disclosed compositions, devices, systems, and methods will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosed systems and methods, as claimed. The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims. BRIEF DESCRIPTION OF THE FIGURES The accompanying figures, which are incorporated in and constitute a part of this specification, illustrate several aspects of the disclosure, and together with the description, serve to explain the principles of the disclosure. Figure 1. Photograph of an example crystal from the floating zone crystal growth methods described herein. Figure 2. Photograph of example wafers. Figure 3. Photograph of an example crystal from the floating zone crystal growth methods described herein. Figure 4. Photograph of an example crystal from the floating zone crystal growth methods described herein. Figure 5. Photograph of an example wafer. Figure 6. Photograph of example CaZrO3wafers made by the methods described herein. DETAILED DESCRIPTION The compositions, devices, methods, and systems described herein may be understood more readily by reference to the following detailed description of specific aspects of the disclosed subject matter and the Examples included therein. Before the present compositions, devices, methods, and systems are disclosed and described, it is to be understood that the aspects described below are not limited to specific synthetic methods or specific reagents, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting. Also, throughout this specification, various publications are referenced. The disclosures of these publications in their entireties are hereby incorporated by reference into this application in order to more fully describe the state of the art to which the disclosed matter pertains. The references disclosed are also individually and specifically incorporated by reference herein for the material contained in them that is discussed in the sentence in which the reference is relied upon. In this specification and in the claims that follow, reference will be made to a number of terms, which shall be defined to have the following meanings. Throughout the description and claims of this specification the word “comprise” and other forms of the word, such as “comprising” and “comprises,” means including but not limited to, and is not intended to exclude, for example, other additives, components, integers, or steps. As used in the description and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a composition” includes mixtures of two or more such compositions, reference to “an agent” includes mixtures of two or more such agents, reference to “the component” includes mixtures of two or more such components, and the like. “Optional” or “optionally” means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where the event or circumstance occurs and instances where it does not. Ranges can be expressed herein as from “about” one particular value, and / or to “about” another particular value. By “about” is meant within 5% of the value, e.g., within 4, 3, 2, or 1% of the value. When such a range is expressed, another aspect includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another aspect. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. Values can be expressed herein as an “average” value. “Average” generally refers to the statistical mean value. By “substantially” is meant within 5%, e.g., within 4%, 3%, 2%, or 1%. “Exemplary” means “an example of” and is not intended to convey an indication of a preferred or ideal embodiment. “Such as” is not used in a restrictive sense, but for explanatory purposes. It is understood that throughout this specification the identifiers “first” and “second” are used solely to aid in distinguishing the various components and steps of the disclosed subject matter. The identifiers “first” and “second” are not intended to imply any particular order, amount, preference, or importance to the components or steps modified by these terms. References in the specification and concluding claims to parts by weight of a particular element or component in a composition denotes the weight relationship between the element or component and any other elements or components in the composition or article for which a part by weight is expressed. Thus, in a compound containing 2 parts by weight of component X and 5 parts by weight component Y, X and Y are present at a weight ratio of 2:5, and are present in such ratio regardless of whether additional components are contained in the compound. A weight percent (wt. %) of a component, unless specifically stated to the contrary, is based on the total weight of the formulation or composition in which the component is included. The term “or combinations thereof” as used herein refers to all permutations and combinations of the listed items preceding the term. For example, “A, B, C, or combinations thereof” is intended to include at least one of: A, B, C, AB, AC, BC, or ABC, and if order is important in a particular context, also BA, CA, CB, CBA, BCA, ACB, BAC, or CAB. Continuing with this example, expressly included are combinations that contain repeats of one or more item or term, such as BB, AAA, AB, BBC, AAABCCCC, CBBAAA, CABABB, and so forth. The skilled artisan will understand that typically there is no limit on the number of items or terms in any combination, unless otherwise apparent from the context. As used herein the term “plurality” means 2 or more (e.g., 3 or more; 4 or more; 5 or more; 10 or more; 15 or more; 20 or more; 25 or more; 30 or more; 40 or more; 50 or more; 75 or more; 100 or more; 150 or more; 200 or more; 250 or more; 300 or more; 400 or more; 500 or more; 750 or more; 1000 or more; 1500 or more; 2000 or more; 2500 or more; 3000 or more; 4000 or more; or 5000 or more). Floating Zone Crystal Growth of Inorganic Oxide Materials Described herein is floating zone crystal growth of inorganic oxide materials and methods of use thereof. For example, described herein are methods of making a single crystal of a composition, the method comprising floating zone crystal growth, the composition comprising: A2O3wherein A is a metal (e.g., one or more metals). In some examples, A is an alkaline earth metal (e.g., one or more alkaline earth metals), a transition metal (e.g., one or more transition metals), a post-transition metal (e.g., one or more post-transition metals), or a combination thereof. Examples of alkaline earth metals include, but are not limited to, Ca, Sr, and Ba. Examples of transition metals include, but are not limited to, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd, Hf, Ta, W, Re, Os, Ir, Pt, Au, and Hg. Examples of post-transition metals include, but are not limited to, Al, Ga, In, Sn, Pb, Bi, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb. In some examples, the post- transition metal comprises Al, Ga, In, Sn, Pb, Bi, or a combination thereof. In some examples, A is selected from the group consisting of Ca, Sr, Ba, Ti, Zr, Hf, Ga, Al, and combinations thereof. In some examples, the composition comprises: AMO3 wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and M is selected from the group consisting of Ti, Zr, Hf, and combinations thereof. In some examples, the composition comprises AZr1-xHFxO3, wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and x is from 0 to 1. For example, x can be 0 or more (e.g., 0.1 or more, 0.2 or more, 0.3 or more, 0.4 or more, 0.5 or more, 0.6 or more, 0.7 or more, or 0.8 or more). In some examples, x can be 1 or less (e.g., 0.9 or less, 0.8 or less, 0.7 or less, 0.6 or less, 0.5 or less, 0.4 or less, 0.3 or less, or 0.2 or less). The value of x can range from any of the minimum values described above to any of the maximum values described above. For example, x can be from 0 to 1 (e.g., from 0 to 0.5, from 0.5 to 1, from 0 to 0.2, from 0.2 to 0.4, from 0.4 to 0.6, from 0.6 to 0.8, from 0.8 to 1, from 0 to 0.8, from 0 to 0.6, from 0 to 0.4, from 0.2 to 1, from 0.4 to 1, from 0.6 to 1, from 0.1 to 0.9, or from 0.2 to 0.8). In some examples, x is 0. In some examples, x is 1. In some examples, the composition comprises CaZr1-xHFxO3, BaZr1-xHFxO3, SrZr1-xHFxO3, or a combination thereof, wherein each x independently is from 0 to 1. In some examples, the composition comprises CaZr1-xHFxO3, wherein x is from 0 to 1. In some examples, the composition comprises CaZrO3, CaHfO3, or a combination thereof. In some examples, the composition comprises CaZrO3. In some examples, the composition comprises CaHfO3. In some examples, the composition comprises BaZr1-xHFxO3, wherein x is from 0 to 1. In some examples, the composition comprises BaZrO3, BaHfO3, or a combination thereof. In some examples, the composition comprises BaZrO3. In some examples, the composition comprises BaHfO3. In some examples, the composition comprises SrZr1-xHFxO3, wherein x is from 0 to 1. In some examples, the composition comprises SrZrO3, SrHfO3, or a combination thereof. In some examples, the composition comprises SrZrO3. In some examples, the composition comprises SrHfO3. In some examples, the composition comprises (AlyGa1-y)2O3, where y is from 0 to 1. For example, y can be 0 or more (e.g., 0.1 or more, 0.2 or more, 0.3 or more, 0.4 or more, 0.5 or more, 0.6 or more, 0.7 or more, or 0.8 or more). In some examples, y can be 1 or less (e.g., 0.9 or less, 0.8 or less, 0.7 or less, 0.6 or less, 0.5 or less, 0.4 or less, 0.3 or less, or 0.2 or less). The value of y can range from any of the minimum values described above to any of the maximum values described above. For example, y can be from 0 to 1 (e.g., from 0 to 0.5, from 0.5 to 1, from 0 to 0.2, from 0.2 to 0.4, from 0.4 to 0.6, from 0.6 to 0.8, from 0.8 to 1, from 0 to 0.8, from 0 to 0.6, from 0 to 0.4, from 0.2 to 1, from 0.4 to 1, from 0.6 to 1, from 0.1 to 0.9, or from 0.2 to 0.8). In some examples, y is 0. In some examples, y is 1. In some examples, the composition comprises Al2O3, Ga2O3, or a combination thereof. In some examples, the composition comprises Al2O3. In some examples, the composition comprises Ga2O3. In some examples, the composition comprises (AlyGa1-y)2O3, where y is from greater than 0 to 1. In some examples, the composition is not Ga2O3. In some examples, the composition further comprises a dopant. Examples of dopants include, but are not limited to, Al, Ga, In, Sn, Pb, Bi, Si, Fe, Cu, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb. In some examples, the dopant comprises Si, Fe, Cu, Tm, Al, Ce, Ga, and combinations thereof. In some examples, the composition comprises CaZr1-xHFxO3 doped with a dopant. In some examples, the composition comprises BaZr1-xHFxO3 doped with a dopant. In some examples, the composition comprises SrZr1-xHFxO3doped with a dopant. In some examples, the composition comprises (AlyGa1-y)2O3doped with a dopant, wherein the dopant is selected from the group consisting of Si, Fe, Cu, Tm, Ce, and combinations thereof. In some examples, the composition has a melting point of 2200°C or more (e.g., 2300°C or more, 2400°C or more, 2500°C or more, 2600°C or more, 2700°C or more, 2800°C or more, or 2900°C or more). In some examples, the composition has a melting point of 3000°C or less (e.g., 2900°C or less, 2800°C or less, 2700°C or less, 2600°C or less, 2500°C or less, or 2400°C or less). The melting point of the composition can range from any of the minimum values described above to any of the maximum values described above. For example, the composition can have a melting point of from 2200°C to 3000°C (e.g., from 2200°C to 2600°C, rom 2600°C to 3000°C, from 2200°C to 2400°C, from 2400°C to 2600°C, from 2600°C to 2800°C, from 2800°C to 3000°C, from 2300°C to 3000°C, from 2400°C to 3000°C, from 2500°C to 3000°C, or from 2700°C to 3000°C). In some examples, the single crystal has a lattice dimension of 3.900 Å or more (e.g., 3.920 Å or more, 3.940 Å or more, 3.960 Å or more, 3.980 Å or more, 4.000 Å or more, 4.020 Å or more, 4.040 Å or more, 4.060 Å or more, or 4.080 Å or more). In some examples, the single crystal has a lattice dimension of 4.100 Å or less (e.g., 4.080 Å or less, 4.060 Å or less, 4.040 Å or less, 4.020 Å or less, 4.000 Å or less, 3.980 Å or less, 3.960 Å or less, 3.940 Å or less, or 3.920 Å or less). The lattice dimension of the single crystal can range from any of the minimum values described above to any of the maximum values described above. For example, the single crystal can have a lattice dimension of from 3.900 to 4.100 Å (e.g., from 3.900 to 4.000 Å, from 4.000 to 4.100 Å, from 3.900 to 3.950 Å, from 3.950 to 4.000 Å, from 4.000 to 4.050 Å, from 4.050 to 4.100 Å, from 3.950 to 4.050 Å). In some examples, the single crystal has a lattice dimension of 4.00 Å. In some examples, the single crystal has an average diameter of 5 millimeters (mm) or more (e.g., 10 mm or more, 15 mm or more, 20 mm or more, 25 mm or more, 30 mm or more, 35 mm or more, 40 mm or more, or 45 mm or more). In some examples, the single crystal has an average diameter of 50 mm or less (e.g., 45 mm or less, 40 mm or less, 35 mm or less, 30 mm or less, 25 mm or less, 20 mm or less, 15 mm or less, or 10 mm or less). The average diameter of the single crystal can range from any of the minimum values described above to any of the maximum values described above. For example, the single crystal can have an average diameter of from 5 to 50 mm (e.g., from 5 to 25 mm, from 25 to 50 mm, from 5 to 15 mm, from 15 to 25 mm, from 25 to 35 mm, from 35 to 50 mm, from 5 to 40 mm, from 5 to 30 mm, from 5 to 20 mm, from 10 to 50 mm, from 20 to 50 mm, from 30 to 50 mm, from 10 to 45 mm, or from 15 to 40 mm). In some examples, the single crystal has an average length of 10 mm or more (e.g., 15 mm or more, 20 mm or more, 25 mm or more, 30 mm or more, 35 mm or more, 40 mm or more, 45 mm or more, 50 mm or more, 55 mm or more, 60 mm or more, 65 mm or more, 70 mm or more, 75 mm or more, 80 mm or more, 85 mm or more, 90 mm or more, or 95 mm or more). In some examples, the single crystal has an average length of 100 mm or less (e.g., 95 mm or less, 90 mm or less, 85 mm or less, 80 mm or less, 75 mm or less, 70 mm or less, 65 mm or less, 60 mm or less, 55 mm or less, 50 mm or less, 45 mm or less, 40 mm or less, 35 mm or less, 30 mm or less, 25 mm or less, 20 mm or less, or 15 mm or less). The average length of the single crystal can range from any of the minimum values described above to any of the maximum values described above. For example, the single crystal can have an average length of 10 to 100 mm (e.g., from 10 to 55 mm, from 55 to 100 mm, from 10 to 40 mm, from 40 to 70 mm, from 70 to 100 mm, from 10 to 90 mm, from 10 to 80 mm, from 10 to 70 mm, from 10 to 60 mm, from 10 to 50 mm, from 10 to 30 mm, from 20 to 100 mm, from 30 to 100 mm, from 40 to 100 mm, from 50 to 100 mm, from 60 to 100 mm, from 80 to 100 mm, from 20 to 90 mm, or from 30 to 80 mm). In some examples, the single crystal has an average diameter of from 5 to 50 mm and an average length of 10 to 100 mm. The methods comprise floating zone crystal growth, for example using a floating zone crystal furnace. In some examples, the method comprises: preparing a polycrystalline precursor of the composition; heat treating the polycrystalline precursor to form a powder comprising the composition; pressing the powder into a rod and heating the rod, to thereby form a feed rod comprising the composition; introducing the feed rod and a seed rod into a float zone of a floating zone crystal furnace under a growth atmosphere, the seed rod being a single crystal of the composition; and growing the single crystal of the composition via floating zone crystal growth. In some examples, the method further comprises rotating the feed rod in the float zone at a rate of 5 rpm or more (e.g., 10 rpm or more, 15 rpm or more, 20 rpm or more, or 25 rpm or more). In some examples, the method further comprises rotating the feed rod in the float zone at a rate of 30 rpm or less (e.g., 25 rpm or less, 20 rpm or less, 15 rpm or less, or 10 rpm or less). The rate at which the feed rod is rotated in the float zone can range from any of the minimum values described above to any of the maximum values described above. For example, the method can further comprise rotating the feed rod in the float zone at a rate of from 5 to 30 rpm (e.g., from 5 to 15 rpm, from 15 to 30 rpm, from 5 to 10 rpm, from 10 to 15 rpm, from 15 to 20 rpm, from 20 to 25 rpm, from 25 to 30 rpm, from 10 to 30 rpm, from 20 to 30 rpm, from 5 to 25 rpm, from 5 to 20 rpm, from 10 to 25 rpm, or from 10 to 20 rpm). In some examples, the method further comprises rotating the feed rod in the float zone at a rate of from 10 to 20 rpm. In some examples, the method further comprises rotating the feed rod in the float zone at a rate of 15 rpm. In some examples, the method further comprises rotating the seed rod in the float zone at a rate of 5 rpm or more (e.g., 10 rpm or more, 15 rpm or more, 20 rpm or more, or 25 rpm or more). In some examples, the method further comprises rotating the seed rod in the float zone at a rate of 30 rpm or less (e.g., 25 rpm or less, 20 rpm or less, 15 rpm or less, or 10 rpm or less). The rate at which the seed rod is rotated in the float zone can range from any of the minimum values described above to any of the maximum values described above. For example, the method can further comprise rotating the seed rod in the float zone at a rate of from 5 to 30 rpm (e.g., from 5 to 15 rpm, from 15 to 30 rpm, from 5 to 10 rpm, from 10 to 15 rpm, from 15 to 20 rpm, from 20 to 25 rpm, from 25 to 30 rpm, from 10 to 30 rpm, from 20 to 30 rpm, from 5 to 25 rpm, from 5 to 20 rpm, from 10 to 25 rpm, or from 10 to 20 rpm). In some examples, the method further comprises rotating the seed rod in the float zone at a rate of from 20 to 30 rpm. In some examples, the method further comprises rotating the seed rod in the float zone at a rate of 25 rpm. In some examples, the method further comprises moving the seed rod linearly within the float zone at a speed of 10 millimeters per hour (mm / h) or more (e.g., 15 mm / h or more, 20 mm / h or more, 25 mm / h or more, 30 mm / h or more, 35 mm / h or more, 40 mm / h or more, 45 mm / h or more, 50 mm / h or more, or 55 mm / h or more). In some examples, the method further comprises moving the seed rod linearly within the float zone at a speed of 60 mm / h or less (e.g., 55 mm / h or less, 50 mm / h or less, 45 mm / h or less, 40 mm / h or less, 35 mm / h or less, 30 mm / h or less, 25 mm / h or less, 20 mm / h or less, or 15 mm / h or less). The speed at which the seed rod is moved linearly within the float zone can range from any of the minimum values described above to any of the maximum values described above. For example, the method can further comprise moving the seed rod linearly within the float zone at a speed of from 10 to 60 mm / h (e.g., from 10 to 35 mm / h, from 35 to 60 mm / h, from 10 to 20 mm / h, from 20 to 30 mm / h, from 30 to 40 mm / h, from 40 to 50 mm / h, from 50 to 60 mm / h, from 10 to 50 mm / h, from 10 to 40 mm / h, from 10 to 30 mm / h, from 20 to 60 mm / h, from 30 to 60 mm / h, from 40 to 60 mm / h, from 20 to 50 mm / h, from 20 to 40 mm / h, or from 25 to 35 mm / h). In some examples, the method further comprises moving the seed rod linearly within the float zone at a speed of 25 to 35 mm / h. In some examples, the method further comprises moving the seed rod linearly within the float zone at a speed of 30 mm / h. In some examples, the method further comprises: rotating the feed rod in the float zone at a rate of from 5 to 30 rpm, such as from 10 to 20 rpm (e.g., 15 rpm); rotating the seed rod in the float zone at a rate of from 5 to 30 rpm, such as from 20 to 30 rpm (e.g., 25 rpm); and / or moving the seed rod linearly within the float zone at a speed of from 10 to 60 mm / h, such as from 25 to 35 mm / h (e.g., 30 mm / h). In some examples, the method further comprises: rotating the feed rod in the float zone at a rate of from 10 to 20 rpm (e.g., 15 rpm); rotating the seed rod in the float zone at a rate of from 20 to 30 rpm (e.g., 25 rpm); and / or moving the seed rod linearly within the float zone at a speed of from 25 to 35 mm / h (e.g., 30 mm / h). In some examples, the method further comprises: rotating the feed rod in the float zone at a rate of 15 rpm; rotating the seed rod in the float zone at a rate of e.g., 25 rpm; and / or moving the seed rod linearly within the float zone at a speed of e.g., 30 mm / h. In some examples, the method further comprises: rotating the feed rod in the float zone at a rate of from 5 to 30 rpm, such as from 10 to 20 rpm (e.g., 15 rpm); rotating the seed rod in the float zone at a rate of from 5 to 30 rpm, such as from 20 to 30 rpm (e.g., 25 rpm); and moving the seed rod linearly within the float zone at a speed of from 10 to 60 mm / h, such as from 25 to 35 mm / h (e.g., 30 mm / h). In some examples, the method further comprises: rotating the feed rod in the float zone at a rate of from 10 to 20 rpm (e.g., 15 rpm); rotating the seed rod in the float zone at a rate of from 20 to 30 rpm (e.g., 25 rpm); and moving the seed rod linearly within the float zone at a speed of from 25 to 35 mm / h (e.g., 30 mm / h). In some examples, the method further comprises: rotating the feed rod in the float zone at a rate of 15 rpm; rotating the seed rod in the float zone at a rate of e.g., 25 rpm; and moving the seed rod linearly within the float zone at a speed of e.g., 30 mm / h. In some examples, preparing the polycrystalline precursor comprises mixing the precursors with or without the dopant(s) for several hours before heating. In some examples, heat treating the polycrystalline precursor to form a powder comprising the composition comprises heating the sample in air to a temperature of 400°C or more (e.g., 450°C or more, 500°C or more, 550°C or more, 600°C or more, 650°C or more, 700°C or more, 750°C or more, 800°C or more, 850°C or more, 900°C or more, 950°C or more, 1000°C or more, 1050°C or more, 1100°C or more, or 1150°C or more). In some examples, heat treating the polycrystalline precursor to form a powder comprising the composition comprises heating the sample in air to a temperature of 1200°C or less (e.g., 1150°C or less, 1100°C or less, 1050°C or less, 1000°C or less, 950°C or less, 900°C or less, 850°C or less, 800°C or less, 750°C or less, 700°C or less, 650°C or less, 600°C or less, 550°C or less, 500°C or less, or 450°C or less). The temperature at which the sample is heated in air can range from any of the minimum values described above to any of the maximum values described above. For example, heat treating the polycrystalline precursor to form a powder comprising the composition comprises heating the sample in air to a temperature of from 400 to 1200°C (e.g., from 400°C to 800°C, from 800°C to 1200°C, from 400°C to 600°C, from 600°C to 800°C, from 800°C to 1000°C, from 1000°C to 1200°C, from 400°C to 1000°C, from 600°C to 1200°C, or from 600°C to 1000°C). In some examples, pressing the powder into a rod comprises placing the powder into a tube, subsequently pressing the powder at 400-600 atm of pressure (for example using a hydrostatic press), and subsequently sintering the rods. In some examples, the powder can be pressed at a pressure of 400 atm or more (e.g., 425 atm or more, 450 atm or more, 475 atm or more, 500 atm or more, 525 atm or more, 550 atm or more, or 575 atm or more). In some examples, the powder can be pressed at a pressure of 600 atm or less (e.g., 575 atm or less, 550 atm or less, 525 atm or less, 500 atm or less, 475 atm or less, 450 atm or less, or 425 atm or less). The pressure at which the powder is pressed can range from any of the minimum values described above to any of the maximum values described above. For example, the powder can be pressed at a pressure of from 400 to 600 atm (e.g., from 400 to 500 atm, from 500 to 600 atm, from 400 to 450 atm, from 450 to 500 atm, from 500 to 550 atm, from 550 to 600 atm, from 400 to 550 atm, from 450 to 600 atm, or from 450 to 550 atm). In some examples, the growth atmosphere comprises Ar, O2, N2, and / or air, and optionally a dopant. In some examples, the growth atmosphere comprises a first gas and a second gas, the first and second gas being Ar, O2, N2, air, or a combination thereof. In some examples, the first gas is provided at a flow rate of 0.1 ml / min or more (e.g., 0.2 ml / min or more, 0.3 ml / min or more, 0.4 ml / min or more, 0.5 ml / min or more, 0.6 ml / min or more, 0.7 ml / min or more, 0.8 ml / min or more, or 0.9 ml / min or more). In some examples, the first gas is provided at a flow rate of 1 ml / min or less (e.g., 0.9 ml / min or less, 0.8 ml / min or less, 0.7 ml / min or less, 0.6 ml / min or less, 0.5 ml / min or less, 0.4 ml / min or less, 0.3 ml / min or less, or 0.2 ml / min or less). The flow rate of the first gas can range from any of the minimum values described above to any of the maximum values described above. For example, the first gas can be provided at a flow rate of from 0.1 to 1 ml / min (e.g., from 0.1 to 0.5 ml / min, from 0.5 to 1 ml / min, from 0.1 to 0.4 ml / min, from 0.4 to 0.7 ml / min, from 0.7 to 1 ml / min, from 0.1 to 0.8 ml / min, from 0.1 to 0.6 ml / min, from 0.2 to 1 ml / min, from 0.4 to 1 ml / min, from 0.2 to 0.8 ml / min, or from 0.4 to 0.6 ml / min). In some examples, the first gas is provided at a flow rate of from 0.4 to 0.6 ml / min. In some examples, the first gas is provided at a flow rate of 0.5 ml / min. In some examples, the second gas is provided at a flow rate of 10 ml / min or more (e.g., 15 ml / min or more, 20 ml / min or more, 25 ml / min or more, 30 ml / min or more, 35 ml / min or more, 40 ml / min or more, 45 ml / min or more, 50 ml / min or more, 55 ml / min or more, 60 ml / min or more, or 65 ml / min or more). In some examples, the second gas is provided at a flow rate of 70 ml / min or less (e.g., 65 ml / min or less, 60 ml / min or less, 55 ml / min or less, 50 ml / min or less, 45 ml / min or less, 40 ml / min or less, 35 ml / min or less, 30 ml / min or less, 25 ml / min or less, 20 ml / min or less, or 15 ml / min or less). The flow rate of the second gas can range from any of the minimum values described above to any of the maximum values described above. For example, the second gas can be provided at a flow rate of from 10 to 70 ml / min (e.g., from 10 to 40 ml / min, from 40 to 70 ml / min, from 10 to 20 ml / min, from 20 to 30 ml / min, from 30 to 40 ml / min, from 40 to 50 ml / min, from 50 to 60 ml / min, from 60 to 70 ml / min, from 10 to 60 ml / min, from 10 to 50 ml / min, from 20 to 70 ml / min, from 30 to 70 ml / min, from 50 to 70 ml / min, from 20 to 60 ml / min, from 30 to 60 ml / min, or from 40 to 60 ml / min). In some examples, the second gas is provided at a flow rate of 40 to 60 ml / min. In some examples, the second gas is provided at a flow rate of 50 ml / min. In some examples, the growth atmosphere comprises a first gas and a second gas, the first and second gas being Ar, O2, N2, air, or a combination thereof, wherein the first gas is provided at a flow rate of from 0.1 to 1 ml / min (e.g., 0.5 ml / min), and the second gas being provided at a flow rate of from 10 to 70 ml / min, such as from 40 to 60 ml / min (e.g., 50 ml / min). In some examples, the growth atmosphere comprises a first gas and a second gas, the first and second gas being Ar, O2, N2, air, or a combination thereof, wherein the first gas is provided at a flow rate of from 0.4 to 0.6 ml / min (e.g., 0.5 ml / min), and the second gas being provided at a flow rate of from 40 to 60 ml / min (e.g., 50 ml / min). In some examples, the growth atmosphere comprises a first gas and a second gas, the first and second gas being Ar, O2, N2, air, or a combination thereof, wherein the first gas is provided at a flow rate of 0.5 ml / min, and the second gas being provided at a flow rate of 50 ml / min. In some examples, the growth atmosphere comprises Ar and O2, wherein the Ar is provided at a flow rate of from 0.1 to 1 ml / min (e.g., 0.5 ml / min), and the O2 provided at a flow rate of from 10 to 70 ml / min, such as from 40 to 60 ml / min (e.g., 50 ml / min). In some examples, the growth atmosphere comprises Ar and O2, wherein the Ar is provided at a flow rate of from 0.4 to 0.6 ml / min (e.g., 0.5 ml / min), and the O2provided at a flow rate of from 40 to 60 ml / min (e.g., 50 ml / min). In some examples, the growth atmosphere comprises Ar and O2, wherein the Ar is provided at a flow rate of 0.5 ml / min, and the O2provided at a flow rate of from 50 ml / min. Also disclosed herein are single crystals grown by any of the methods disclosed herein (e.g., single crystals comprising any of the compositions disclosed herein grown by any of the methods disclosed herein). Also disclosed herein are methods of use of any of the single crystals disclosed herein. For example, the methods can comprise cutting the single crystal to thereby form a wafer. Also disclosed herein are wafers formed (e.g., cut) from any of the single crystals disclosed herein. Also disclosed herein are methods of use of any of the wafers disclosed herein. For example, the methods can comprise using the wafer as a substrate for thin film growth. Also disclosed herein are device and / or articles of manufacture comprising any of the single crystals and / or wafers disclosed herein. Also disclosed herein are device and / or articles of manufacture comprising thin films grown on any of the single crystals and / or wafers disclosed herein. A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims. The examples below are intended to further illustrate certain aspects of the systems and methods described herein, and are not intended to limit the scope of the claims. EXAMPLES The following examples are set forth below to illustrate the methods and results according to the disclosed subject matter. These examples are not intended to be inclusive of all aspects of the subject matter disclosed herein, but rather to illustrate representative methods and results. These examples are not intended to exclude equivalents and variations of the present invention which are apparent to one skilled in the art. Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.) but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in °C or is at ambient temperature, and pressure is at or near atmospheric. There are numerous variations and combinations of measurement conditions, e.g., component concentrations, temperatures, pressures and other measurement ranges and conditions that can be used to optimize the described process. Example 1 - Floating zone crystal growth of inorganic oxide materials The correct conditions to grow crystals of CaZrO3, CaHfO3, and CaZr1-xHfxO3 were successfully determined. Crystals of the materials are very difficult to grow owing to their high melting points(> 2200°C). Using flux type synthesis for the precursors, a floating zone furnace was used to grow the crystals. In addition, the correct conditions to grow crystals of Ga2O3, Al2O3, and doped Ga2O3with dopants such as Si, Fe, Cu, Tm, Al, Ce, Ga, and combinations thereof, were also determined. In the field of thin films, there is a great demand for substrates (crystal wafers) with a lattice dimension of 4.00 Angstroms (4.00 Å). At present only a few materials are used such as MScO3 (M = Dy, Tb, Gd, Eu, Sm, Nd, and Pr) and LiTaO3. However the Sc materials are very expensive (e.g., Sc2O3 is cost prohibitive), and LiTaO3 undergoes detrimental phase transitions. Because of this, there is a need for a different substrate. CaZrO3and CaHfO3have lattice dimensions of 4.00 Å. The issue to date has been their crystal growth. With A2O3 (wherein A = Ga or Al) , the issue is the reproducibility of the crystal growth. Described herein is a method to grow transparent A2O3, and doped A2O3 crystals using a floating zone furnace. Examples of good materials for a substrate for thin film growth are CaZrO3 and CaHfO3. Both have a lattice dimension of 4.00 Å, and are far less expensive than what is currently available. The problem is that both materials melt at very high temperatures (e.g., CaZrO3 melts at 2550°C and CaHfO3melts at 2390°C). Because of the high melting points, crystals are very difficult to grow. Herein, these materials, as well as other high melting oxides, were successfully grown. Although A2O3and doped A2O3are commercially available, the cost is very high (e.g., > $1500 for one crystal wafer). The floating zone method described herein, makes these crystals available at a much cheaper cost (e.g., $300 – 500 per wafer). Polycrystalline precursors of AMO3 (A = Sr, Ca, Ba; M = Ti, Zr, Hf) were synthesized by using the alkaline earth carbonate and transition metal oxide in a mixed halide flux at a 1:1 ratio of oxide to flux. The mixture was heated to 1200°C at a rate of 5°C per min for 900 minutes and cooled to room temperature at 5°C per minute. The resulting powder was pressed into a rods (feed and seed rods) and heated to 1650°C for several hours. Rods (feed and seed) are made are placing the powder in a tube, and subsequently pressing the powder at 400-600 atm of pressure using a hydrostatic press. Once the rods are formed, they are heated (sintered) as follows: A. Heating in muffle furnace with heating rate 2.0^ / min up to 1200 ^; B. Held at 1200 ^ for 10 hours; C. Cooling down with an average rate of 5^ / min to room temperature; D. Heating in Carbolit Gero HTF-18 / 04 muffle furnace with heating rate 5^ / min up to 1650 ^; E. Held at 1650 ^ for 12 hours; and F. Cooling down with an average rate of 5^ / min to room temperature. Crystal growth • the growth atmosphere: Ar and O2 flow (0.5 l / min and 50 ml / min, respectively); • the rate of seed rod moving was 30 mm / h; • the feed rod and seed rod rotation speeds were 15 and 25 rpm, respectively. Crystals are typically 5-15 mm in diameter and 10-40 mm in length. A photograph of an example resulting crystal is shown in Figure 1. A crystal of such a size can then be subsequently cut into wafers (e.g., 10 mm x 10 mm x 1 mm thick) (Figure 2). The resulting wafers are large enough to be used as substrates for thin film growth. Crystals of Ga2O3, Al2O3, and doped Ga2O3 were also grown by the floating zone method. Dopants included, but are not limited to, Si, Fe, Cu, Tm, Al, Ce, Ga. A feed rod of the required material was created with the polycrystalline powder. The feed and seed rods are sintered well; there is no loose powdered remaining. The density of the feed and seed rods are 95% or more for high quality crystal growth. Crystal growth was performed on a Model: FZ-T-12000-X-VIII-VPO-PC-UH Floating Zone furnace. For A2O3crystals, O2was used as the growth atmosphere, whereas for AMO3crystals a mixture of Ar and O2was used as the growth atmosphere. The feed and seed rod rotation speeds were faster for A2O3 compared with the AMO3 materials. Typical crystals are shown in Figure 3 and Figure 4. Crystals range from 5-25 mm in diameter and 10-60 mm in length. Wafers were also cut from these crystals (Figure 5). Example CaZrO3 wafers made by the methods described herein are shown in Figure 6. EXEMPLARY ASPECTS In view of the described compositions, devices, systems, and methods, herein below are described certain more particularly described aspects of the inventions. The particularly recited aspects should not, however, be interpreted to have any limiting effect on any different claims containing different or more general teachings described herein or that the “particular” aspects are somehow limited in some way other than the inherent meanings of the language and formulas literally used therein. Example 1: A method of making a single crystal of a composition, the method comprising floating zone crystal growth, the composition comprising: A2O3, wherein A is a metal (e.g., one or more metals); wherein the single crystal has a lattice dimension of from 3.900 to 4.100 Å, such as 4.000 Å; with the proviso that A2O3 is not Ga2O3. Example 2: The method of any examples herein, particularly example 1, wherein A is selected from the group consisting of Ca, Sr, Ba, Ti, Zr, Hf, Ga, Al, and combinations thereof. Example 3: The method of any examples herein, particularly example 1 or example 2, wherein the composition comprises AMO3, wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and M is selected from the group consisting of Ti, Zr, Hf, and combinations thereof. Example 4: A method of making a single crystal of a composition, the method comprising floating zone crystal growth, the composition comprising: AMO3, wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and M is selected from the group consisting of Ti, Zr, Hf, and combinations thereof. Example 5: The method of any examples herein, particularly example 4, wherein the single crystal has a lattice dimension of from 3.900 to 4.100 Å, Example 6: The method of any examples herein, particularly examples 1-5, wherein the single crystal has a lattice dimension of 4.000 Å. Example 7: The method of any examples herein, particularly examples 1-6, wherein the composition comprises AZr1-xHFxO3, wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and x is from 0 to 1. Example 8: The method of any examples herein, particularly examples 1-7, wherein the composition comprises CaZr1-xHFxO3, BaZr1-xHFxO3, SrZr1-xHFxO3, or a combination thereof, wherein each x independently is from 0 to 1. Example 9: The method of any examples herein, particularly examples 1-8, wherein the composition comprises CaZr1-xHFxO3, wherein x is from 0 to 1. Example 10: The method of any examples herein, particularly examples 1-9, wherein the composition comprises CaZrO3, CaHfO3, or a combination thereof. Example 11: The method of any examples herein, particularly examples 1-10, wherein the composition comprises CaZrO3. Example 12: The method of any examples herein, particularly examples 1-11, wherein the composition comprises CaHfO3. Example 13: The method of any examples herein, particularly examples 1-12, wherein the composition comprises BaZr1-xHFxO3, wherein x is from 0 to 1. Example 14: The method of any examples herein, particularly examples 1-13, wherein the composition comprises BaZrO3, BaHfO3, or a combination thereof. Example 15: The method of any examples herein, particularly examples 1-14, wherein the composition comprises BaZrO3. Example 16: The method of any examples herein, particularly examples 1-15, wherein the composition comprises BaHfO3. Example 17: The method of any examples herein, particularly examples 1-16, wherein the composition comprises SrZr1-xHFxO3, wherein x is from 0 to 1. Example 18: The method of any examples herein, particularly examples 1-17, wherein the composition comprises SrZrO3. Example 19: The method of any examples herein, particularly examples 1-18, wherein the composition comprises SrHfO3. Example 20: The method of any examples herein, particularly examples 1-19, wherein the composition comprises (AlyGa1-y)2O3 where y is from greater than 0 to 1. Example 21: The method of any examples herein, particularly examples 1-20, wherein the composition comprises Al2O3. Example 22: The method of any examples herein, particularly examples 1-21, wherein the composition further comprises a dopant. Example 23: The method of any examples herein, particularly example 22, wherein the dopant is selected from the group consisting of Si, Fe, Cu, Tm, Al, Ce, Ga, and combinations thereof. Example 24: The method of any examples herein, particularly examples 1-23, wherein the composition comprises (AlyGa1-y)2O3 doped with a dopant, wherein the dopant is selected from the group consisting of Si, Fe, Cu, Tm, Ce, and combinations thereof. Example 25: The method of any examples herein, particularly examples 1-24, wherein the composition comprises (AlyGa1-y)2O3 doped with a dopant. Example 26: The method of any examples herein, particularly examples 1-25, wherein the composition has a melting point of 2200°C or more. Example 27: The method of any examples herein, particularly examples 1-26, wherein the single crystal has an average diameter of from 5 to 50 mm and an average length of 10 to 100 mm. Example 28: The method of any examples herein, particularly examples 1-27, wherein the method comprises: preparing a polycrystalline precursor of the composition; heat treating the polycrystalline precursor to form a powder comprising the composition; pressing the powder into a rod and heating the rod, to thereby form a feed rod comprising the composition; introducing the feed rod and a seed rod into a float zone of a floating zone crystal furnace under a growth atmosphere, the seed rod being a single crystal of the composition; and growing the single crystal of the composition via floating zone crystal growth. Example 29: The method of any examples herein, particularly example 28, wherein the method further comprises: rotating the feed rod in the float zone at a rate of from 5 to 30 rpm, such as from 10 to 20 rpm (e.g., 15 rpm); rotating the seed rod in the float zone at a rate of from 5 to 30 rpm, such as from 20 to 30 rpm (e.g., 25 rpm); and moving the seed rod linearly within the float zone at a speed of from 10 to 60 mm / h, such as from 25 to 35 mm / h (e.g., 30 mm / h). Example 30: The method of any examples herein, particularly example 28 or example 29, wherein preparing the polycrystalline precursor comprises mixing the precursors with or without the dopant(s) for several hours before heating. Example 31: The method of any examples herein, particularly examples 28-30, wherein heat treating the polycrystalline precursor to form a powder comprising the composition comprises heating the sample in air to a temperature of from 400 to 1200°C. Example 32: The method of any examples herein, particularly examples 28-31, wherein pressing the powder into a rod comprises placing the powder into a tube, subsequently pressing the powder at 400-600 atm of pressure (for example using a hydrostatic press), and subsequently sintering the rods. Example 33: The method of any examples herein, particularly examples 28-32, wherein the growth atmosphere comprises Ar, O2, N2, and / or air, and optionally a dopant. Example 34: A single crystal grown by the method of any examples herein, particularly examples 1-33. Example 35: A method of use of the single crystal of any examples herein, particularly example 34. Example 36: The method of any examples herein, particularly example 35, wherein the method comprises cutting the single crystal to thereby form a wafer. Example 37: A wafer formed (e.g., cut) from the single crystal of any examples herein, particularly example 34. Example 38: A wafer formed by the method of any examples herein, particularly example 36. Example 39: A method of use of the wafer of any examples herein, particularly example 37 or example 38. Example 40: The method of any examples herein, particularly example 39, wherein the method comprises using the wafer as a substrate for thin film growth. Example 41: A device and / or article of manufacture the single crystal of any examples herein, particularly example 34, and / or the wafer of any examples herein, particularly example 37 or example 38. Example 42: A device and / or an article of manufacture comprising a thin film grown on the single crystal of any examples herein, particularly example 34, and / or the wafer of any examples herein, particularly example 37 or example 38. Other advantages which are obvious and which are inherent to the invention will be evident to one skilled in the art. It will be understood that certain features and sub-combinations are of utility and may be employed without reference to other features and sub-combinations. This is contemplated by and is within the scope of the claims. Since many possible embodiments may be made of the invention without departing from the scope thereof, it is to be understood that all matter herein set forth or shown in the accompanying drawings is to be interpreted as illustrative and not in a limiting sense. The devices and methods of the appended claims are not limited in scope by the specific devices and methods described herein, which are intended as illustrations of a few aspects of the claims and any devices and methods that are functionally equivalent are intended to fall within the scope of the claims. Various modifications of the devices and methods in addition to those shown and described herein are intended to fall within the scope of the appended claims. Further, while only certain representative method steps disclosed herein are specifically described, other combinations of the method steps also are intended to fall within the scope of the appended claims, even if not specifically recited. Thus, a combination of steps, elements, components, or constituents may be explicitly mentioned herein or less, however, other combinations of steps, elements, components, and constituents are included, even though not explicitly stated.

Claims

CLAIMS What is claimed is:

1. A method of making a single crystal of a composition, the method comprising floating zone crystal growth, the composition comprising: A2O3 wherein A is a metal (e.g., one or more metals); wherein the single crystal has a lattice dimension of from 3.900 to 4.100 Å, such as 4.000 Å; with the proviso that A2O3is not Ga2O3.

2. The method of claim 1, wherein A is selected from the group consisting of Ca, Sr, Ba, Ti, Zr, Hf, Ga, Al, and combinations thereof.

3. The method of claim 1 , wherein the composition comprises AMO3, wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and M is selected from the group consisting of Ti, Zr, Hf, and combinations thereof.

4. The method of claim 1, wherein the composition comprises AZr1-xHFxO3, wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and x is from 0 to 1.

5. The method of claim 1, wherein the composition comprises CaZr1-xHFxO3, BaZr1-xHFxO3, SrZr1-xHFxO3, or a combination thereof, wherein each x independently is from 0 to 1.

6. The method of claim 1, wherein the composition comprises CaZr1-xHFxO3, wherein x is from 0 to 1.

7. The method of claim 1, wherein the composition comprises (AlyGa1-y)2O3where y is from greater than 0 to 1.

8. The method of claim 1, wherein the composition further comprises a dopant and / or has a melting point of 2200°C or more.

9. A method of making a single crystal of a composition, the method comprising floating zone crystal growth, the composition comprising: AMO3 whereinA is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and M is selected from the group consisting of Ti, Zr, Hf, and combinations thereof.

10. The method of claim 9, wherein the single crystal has a lattice dimension of from 3.900 to 4.100 Å.

11. The method of claim 9, wherein the composition comprises AZr1-xHFxO3, wherein A is selected from the group consisting of Ca, Sr, Ba, and combinations thereof, and x is from 0 to 1.

12. The method of claim 9, wherein the composition comprises CaZr1-xHFxO3, BaZr1-xHFxO3, SrZr1-xHFxO3, or a combination thereof, wherein each x independently is from 0 to 1.

13. The method of claim 9, wherein the composition comprises CaZr1-xHFxO3, wherein x is from 0 to 1.

14. The method of claim 9, wherein the composition comprises CaZrO3, CaHfO3, or a combination thereof.

15. The method of claim 9, wherein the composition comprises (AlyGa1-y)2O3 where y is from greater than 0 to 1.

16. The method of claim 9, wherein the composition further comprises a dopant and / or has a melting point of 2200°C or more.

17. The method of any one of claims 1-16, wherein the method comprises: preparing a polycrystalline precursor of the composition; heat treating the polycrystalline precursor to form a powder comprising the composition; pressing the powder into a rod and heating the rod, to thereby form a feed rod comprising the composition; introducing the feed rod and a seed rod into a float zone of a floating zone crystal furnace under a growth atmosphere, the seed rod being a single crystal of the composition; and growing the single crystal of the composition via floating zone crystal growth.

18. The method of claim 17, wherein the method further comprises: rotating the feed rod in the float zone at a rate of from 5 to 30 rpm, such as from 10 to 20 rpm (e.g., 15 rpm); rotating the seed rod in the float zone at a rate of from 5 to 30 rpm, such as from 20 to 30 rpm (e.g., 25 rpm); andmoving the seed rod linearly within the float zone at a speed of from 10 to 60 mm / h, such as from 25 to 35 mm / h (e.g., 30 mm / h).

19. The method of claim 17, wherein preparing the polycrystalline precursor comprises mixing the precursors with or without the dopant(s) for several hours before heating; wherein heat treating the polycrystalline precursor to form a powder comprising the composition comprises heating the sample in air to a temperature of from 400 to 1200°C; wherein pressing the powder into a rod comprises placing the powder into a tube, subsequently pressing the powder at 400-600 atm of pressure (for example using a hydrostatic press), and subsequently sintering the rods; or a combination thereof.

20. The method of claim 17, wherein the growth atmosphere comprises Ar, O2, N2, and / or air, and optionally a dopant.

21. A single crystal grown by the method of any one of claims 1-20. A method of use of the single crystal of claim 21.

23. A wafer formed (e.g., cut) from the single crystal of claim 21.

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