Methods for recovery of critical minerals and rare earth elements from critical mineral or rare-earth-doped crystal materials

Abstract

In one aspect, the disclosure related to the recovery of rare earth metals from laser crystal waste. The laser crystal waste is dissolved in a phosphoric acid solution and subsequently treated with oxalic acid to form a precipitate. The precipitate can then be calcined to provide a rare earth metal oxide. This abstract is intended as a scanning tool for purposes of searching in the particular art and is not intended to be limiting of the present disclosure.

Description

METHODS FOR RECOVERY OF CRITICAL MINERALS AND RARE EARTH ELEMENTS FROM CRITICAL MINERAL OR RARE-EARTH-DOPED CRYSTAL MATERIALSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This Application claims the benefit of U.S. Provisional Application No. 63 / 532,209, filed on August 11 , 2023, which is incorporated herein by reference in its entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0002] This invention was made with government support under award DE-FE0032120 awarded by the US Department of Energy. The government has certain rights in the invention.BACKGROUND

[0003] Rare earth elements (REEs) are useful and necessary for the manufacture of batteries that power hybrid and electric vehicles, catalytic converters, computer memory, fluorescent lighting and lasers, smartphones and tablet computers, cameras including electronic components and lenses, e-readers, magnets, night-vision goggles, GPS and communications equipment, military applications including precision-guided weapons and vehicle armor, aircraft engines, personal protective equipment, and in other applications including defense applications. Some REEs can be used in air pollution control mechanisms, oil refineries, in medical diagnostic equipment such as, for example, X-ray and MRI machines, as phosphors, as catalysts, as components of ceramics and paints, and / or as polishing compounds. Although REEs and critical minerals (CM) can be extracted from many waste products and ores, few such resources are economically attractive. Due to current and possibly continuing export controls for REEs from China, it would be desirable to develop domestic sources of REEs.

[0004] Laser crystals are single crystal materials doped with either trivalent rare earth metal ions or transition metal ions. These crystals are at the heart of solid-state lasers, especially high power lasers. The requirements for laser crystals include transparency and high thermal stability. One of the most frequently used compositions is based on neodymium doped into a yttrium aluminum garnet (Y3AI5O12; also referred to as “YAG”). Other compositions include dopants such as ytterbium, erbium and holmium in the YAG lattice, and crystal matrices composed of yttrium vanadate (YVO4) and terbium gallium garnet (Tb3Ga50i2; also referred to as “TGG”). Production of synthesized laser crystals is often associated with problems such as light scattering from impurities, non-stoichiometric crystals, striae, and non-uniform doping along the crystal that leads to the generation of laser crystal production waste. As suggested above, the composition of most laser crystals includes critical minerals and / or rare earth elements, e.g., yttrium and gallium.

[0005] Despite advances in research directed to enhanced waste recovery of REEs fromproduction streams such as laser crystals, there is still a scarcity of methods and processes that are economical, scalable, and easily implemented. These needs and other needs are satisfied by the present disclosure.SUMMARY

[0006] In accordance with the purpose(s) of the disclosure, as embodied and broadly described herein, the disclosure, in one aspect, relates to phosphoric acid-based extraction methods of rare earth metals. In certain aspects, the disclosure relates to oxalic acid-based extraction methods of rare earth metals.

[0007] In certain aspects, the disclosure includes a method of extracting a rare earth metal oxide, a critical mineral metal oxide, or a combination thereof from a crystal material. In certain aspects, the disclosure includes admixing a crystal particulate composition with an aqueous composition consisting of from about 85% to about 99% w / w phosphoric acid and water in a crystal particulate / aqueous weightvolume (w / v) ratio wherein the crystal particulate / aqueous weightvolume (w / v) ratio is a ratio of grams of the crystal particulate composition to milliliters of the aqueous composition and where the crystal particulate / aqueous weightvolume (w / v) ratio is from about 0.1 to about 0.01 to form a first admixture.

[0008] In certain aspects, the disclosure includes raising the temperature of the first admixture to from about 200°C to about 400°C; and / or holding the temperature of the admixture at about 200°C to about 400°C until the crystal particulate composition dissolves in the aqueous composition; and / or lowering the temperature of the admixture to a temperature of the first admixture to about room temperature to not more than 100°C.

[0009] In certain aspects, the disclosure includes diluting the first admixture of phosphoric acid and the crystal particulates into water to provide a diluted aqueous admixture comprising a ratio of water to phosphoric acid of from about 10:1 to about 1 :10 by volume; and / or admixing an oxalic acid solution with the diluted aqueous admixture in a molar ratio of from about 4: 1 to about 2:1 of moles of the oxalic acid to the number of moles of rare earth metals to form a second admixture; and / or adding base to the second admixture such that the pH of the second admixture is from about 2 to about 5.

[0010] In certain aspects, the disclosure includes separating a rare earth metal oxide precipitate from the second admixture, wherein the rare earth metal oxide precipitate comprises at least one critical mineral metal oxide, at least one rare earth metal oxide, or combinations thereof.

[0011] Other systems, methods, features, and advantages of the present disclosure will be or become apparent to one with skill in the art upon examination of the following drawings anddetailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description, be within the scope of the present disclosure, and be protected by the accompanying claims. In addition, all optional and preferred features and modifications of the described aspects are usable in all aspects of the disclosure taught herein. Furthermore, the individual features of the dependent claims, as well as all optional and preferred features and modifications of the described aspects are combinable and interchangeable with one another.BRIEF DESCRIPTION OF THE FIGURES

[0012] Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.

[0013] FIG. 1 shows a process for the extraction and isolation of rare earth oxides according to the present description.

[0014] Additional advantages of the disclosure will be set forth in part in the description which follows, and in part will be obvious from the description, or can be learned by practice of the disclosure. The advantages of the disclosure 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 disclosure, as claimed.DETAILED DESCRIPTION

[0015] Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

[0016] As will be apparent to those of skill in the art upon reading this disclosure, each of the individual aspects described and illustrated herein has discrete components and features which may be readily separated from or combined with the features of any of the other several aspects without departing from the scope or spirit of the present disclosure.

[0017] Any recited method can be carried out in the order of events recited or in any other order that is logically possible. That is, unless otherwise expressly stated, it is in no way intended that any method or aspect set forth herein be construed as requiring that its steps be performed in a specific order. Accordingly, where a method claim does not specifically state in the claims or descriptions that the steps are to be limited to a specific order, it is no way intended that an order be inferred, in any respect. This holds for any possible non-expressbasis for interpretation, including matters of logic with respect to arrangement of steps or operational flow, plain meaning derived from grammatical organization or punctuation, or the number or type of aspects described in the specification.

[0018] All publications mentioned herein are incorporated herein by reference to disclose and describe the methods and / or materials in connection with which the publications are cited. The publications discussed herein are provided solely for their disclosure prior to the filing date of the present application. Nothing herein is to be construed as an admission that the present disclosure is not entitled to antedate such publication by virtue of prior disclosure. Further, the dates of publication provided herein can be different from the actual publication dates, which can require independent confirmation.

[0019] While aspects of the present disclosure can be described and claimed in a particular statutory class, such as the system statutory class, this is for convenience only and one of skill in the art will understand that each aspect of the present disclosure can be described and claimed in any statutory class.

[0020] 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. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the disclosed compositions and methods belong. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the specification and relevant art and should not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0021] Prior to describing the various aspects of the present disclosure, the following definitions are provided and should be used unless otherwise indicated. Additional terms may be defined elsewhere in the present disclosure.A. DEFINITIONS

[0022] As used herein, “comprising” is to be interpreted as specifying the presence of the stated features, integers, steps, or components as referred to, but does not preclude the presence or addition of one or more features, integers, steps, or components, or groups thereof. Moreover, each of the terms “by”, “comprising,” “comprises”, “comprised of,” “including,” “includes,” “included,” “involving,” “involves,” “involved,” and “such as” are used in their open, non-limiting sense and may be used interchangeably. Further, the term “comprising” is intended to include examples and aspects encompassed by the terms “consisting essentially of’ and “consisting of.” Similarly, the term “consisting essentially of’ is intended to include examples encompassed by the term “consisting of.

[0023] As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items. Expressions such as “at least one of,” when preceding a list of elements, modify the entire list of elements and do not modify the individual elements of the list.

[0024] As used herein, nomenclature for compounds, including organic compounds, can be given using common names, IUPAC, IUBMB, or CAS recommendations for nomenclature. When one or more stereochemical features are present, Cahn-lngold-Prelog rules for stereochemistry can be employed to designate stereochemical priority, E / Z specification, and the like. One of skill in the art can readily ascertain the structure of a compound if given a name, either by systemic reduction of the compound structure using naming conventions, or by commercially available software, such as CHEMDRAW™ (CambridgeSoft Corporation, U.S.A.).

[0025] Reference to "a" chemical compound refers to one or more molecules of the chemical compound rather than being limited to a single molecule of the chemical compound. Furthermore, the one or more molecules may or may not be identical, so long as they fall under the category of the chemical compound. Thus, for example, "a" chemical compound is interpreted to include one or more molecules of the chemical, where the molecules may or may not be identical (e.g., different isotopic ratios, enantiomers, and the like).

[0026] As used in the specification 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 metal,” “a metal oxide,” or “a metal oxalate,” includes, but is not limited to, two or more such metals, metal oxides, metal oxalates, and the like.

[0027] It should be noted that ratios, concentrations, amounts, and other numerical data can be expressed herein in a range format. 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. It is also understood that there are a number of values disclosed herein, and that each value is also herein disclosed as “about” that particular value in addition to the value itself. For example, if the value “10” is disclosed, then “about 10” is also disclosed. Ranges can be expressed herein as from “about” one particular value, and / or to “about” another particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms a further aspect. For example, if the value “about 10” is disclosed, then “10” is also disclosed.

[0028] When a range is expressed, a further aspect includes from the one particular value and / or to the other particular value. For example, where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in thedisclosure, e.g. the phrase “xto y” includes the range from ‘x’ to ‘y’ as well as the range greater than ‘x’ and less than ‘y’. The range can also be expressed as an upper limit, e.g. ‘about x, y, z, or less’ and should be interpreted to include the specific ranges of ‘about x’, ‘about y’, and ‘about z’ as well as the ranges of ‘less than x’, less than y’, and ‘less than z’. Likewise, the phrase ‘about x, y, z, or greater’ should be interpreted to include the specific ranges of ‘about x’, ‘about y’, and ‘about z’ as well as the ranges of ‘greater than x’, greater than y’, and ‘greater than z’. In addition, the phrase “about ‘x’ to ‘y’”, where ‘x’ and ‘y’ are numerical values, includes “about x’ to about ‘y’”.

[0029] It is to be understood that such a range format is used for convenience and brevity, and thus, should be interpreted in a flexible manner to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. To illustrate, a numerical range of “about 0.1 % to 5%” should be interpreted to include not only the explicitly recited values of about 0.1 % to about 5%, but also include individual values (e.g., about 1 %, about 2%, about 3%, and about 4%) and the sub-ranges (e.g., about 0.5% to about 1.1 %; about 5% to about 2.4%; about 0.5% to about 3.2%, and about 0.5% to about 4.4%, and other possible sub-ranges) within the indicated range.

[0030] As used herein, the terms “about,” “approximate,” “at or about,” and “substantially” mean that the amount or value in question can be the exact value or a value that provides equivalent results or effects as recited in the claims or taught herein. That is, it is understood that amounts, sizes, formulations, parameters, and other quantities and characteristics are not and need not be exact but may be approximate and / or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding off, measurement error and the like, and other factors known to those of skill in the art such that equivalent results or effects are obtained. In some circumstances, the value that provides equivalent results or effects cannot be reasonably determined. In such cases, it is generally understood, as used herein, that “about” and “at or about” mean the nominal value indicated ±10% variation unless otherwise indicated or inferred. In general, an amount, size, formulation, parameter or other quantity or characteristic is “about,” “approximate,” or “at or about” whether or not expressly stated to be such. It is understood that where “about,” “approximate,” or “at or about” is used before a quantitative value, the parameter also includes the specific quantitative value itself, unless specifically stated otherwise.

[0031] As used herein, the terms “optional” or “optionally” means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where said event or circumstance occurs and instances where it does not.

[0032] As used herein, the term “effective amount” refers to an amount that is sufficient to achieve the desired modification of a physical property of the composition or material. For example, an “effective amount” of an acid refers to an amount that is sufficient to achieve the desired improvement in the property modulated by the component, e.g. achieving and maintaining a desired solution pH. The specific level in terms of wt% or molarity in a composition required as an effective amount will depend upon a variety of factors including the amount and type of acid, amount and type of feedstock being utilized in the disclosed method or process, and economic considerations.

[0033] As used herein, the term “rare earth element” (REE), in the context of the present disclosure, refers to a composition comprising one or more rare earth elements, including one or more of a lanthanide chemical element, i.e., cerium, dysprosium, erbium, europium, gadolinium, holmium, lanthanum, lutetium, neodymium, praseodymium, samarium, scandium, terbium, thulium, ytterbium, and yttrium. The elements scandium and yttrium often occur in the same ore deposits as lanthanides and also have some similar chemical properties. Rare earth elements are useful in a variety of applications in the electronics, defense, and medical industries, as well as in other applications. An oxide of a rare earth element is a “rare earth oxide” and can be used for analytical purposes or may be useful as a component of ceramics, catalysts, and / or coatings, among other uses. It is to be understood that when referencing rare earth elements that any of the elements can be present in a zero valence or elemental state, or in an ionized or valence state associated in the art with the individual element, and all forms are understood to be collectively included within the meaning of “rare earth elements”. Moreover, it is to be understood that reference to any individual rare earth element, i.e., any one of lanthanum, cerium, praseodymium, neodymium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, lutetium, including scandium and yttrium, can be present in a zero valence or elemental state, or in an ionized or valence state associated in the art with the given element, and all forms are understood to be collectively included within the meaning of reference to said element. For example, reference to “lanthanum”, “an element such as lanthanum”, “a composition comprising lanthanum”, and the like, it is understood that the reference inclusive any or all forms of lanthanum such as La0, La+1, La+2, and La+3. It is further understood that a reference to any given rare earth element is inclusive of all isotopic forms of the element.

[0034] As used herein, the terms “heavy rare earth element” and “HREE”, in the context of the present disclosure, can be used interchangeably and refer to one or more element selected from dysprosium, erbium, holmium, lutetium, thulium, ytterbium, and yttrium. It is to be understood that yttrium can be classified as a heavy rare earth element due to chemical properties and co-location with other HREEs in ores but can also be yttrium is classified as alight rare earth element due to its lower atomic weight. However, in the context of segregation of REEs into only HREE and LREE (without separation of MREE), HREE refers to one or more element selected from dysprosium, erbium, holmium, lutetium, terbium, thulium, ytterbium, and yttrium.

[0035] As used herein, the terms “middle rare earth element” and “MREE”, in the context of the present disclosure, can be used interchangeably and refer to one or more element selected from europium, gadolinium, samarium, and terbium. In some aspects, these designations may differ slightly but are generally based on atomic weight.

[0036] As used herein, the terms “light rare earth element” and “LREE”, in the context of the present disclosure, can be used interchangeably and refer to one or more element selected from cerium, lanthanum, neodymium, and praseodymium. In some aspects, these designations may differ slightly but are generally based on atomic weight. However, in the context of segregation of REEs into only HREE and LREE (without separation of MREE), LREE refers to one or more element selected from cerium, europium, gadolinium, lanthanum, neodymium, praseodymium, samarium, and scandium.

[0037] As used herein, the term “total rare earth element” and “TREE”, in the context of the present disclosure, can be used interchangeably and refer to the total REE present in a disclosed composition or product of a disclosed process, method, or device, wherein the TREE comprises one or more of REE selected from lanthanum, cerium, praseodymium, neodymium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, lutetium, scandium and yttrium.

[0038] “Critical minerals” (CM) as used herein include minerals important to national security and the economy. REEs are considered critical minerals due to their numerous industrial uses. Other critical minerals may also be purified and concentrated using the disclosed process including, but not limited to, cobalt, gallium, germanium, hafnium, indium, niobium, rhenium, rubidium, tantalum, and tellurium.

[0039] A “feedstock” as used herein is a raw material processed to recover CMs and / or REEs that comprises crystal materials such as doped crystals, e.g., crystals doped with one or more critical mineral and / or rare earth element. A feedstock can be as disclosed herein, e.g., laser crystal waste (e.g., from production streams), recycled laser crystal materials (e.g., laser crystals recovered from discarded or broken equipment comprising a laser comprising a laser crystal), and the like. Other exemplary feedstocks rare-earth based quantum bits (qubits), comprising a doped crystal (including production streams, recycled materials recovered from quantum computing equipment, and the like), scintillation crystals, and other crystal materials and / or films comprising crystals that are doped with one or more critical mineral and / or rareearth element. In a particular aspect, the feedstock comprises laser crystal waste (e.g., from production streams), recycled laser crystal materials (e.g., laser crystals recovered from discarded or broken equipment comprising a laser comprising a laser crystal), and the like.

[0040] As used herein, “contacting” refers to the act of touching, making contact, or of bringing substances into immediate proximity.

[0041] As used herein, “decanting” or “decantation” includes pouring off a fluid, leaving a sediment or precipitate, thereby separating the fluid from the sediment or precipitate. The sediment or precipitate can be present as a slag.

[0042] As used herein, “filtering” or “filtration” refers to a mechanical method to separate solids from liquids by passing the feed stream through a porous sheet such as a ceramic or metal membrane, which retains the solids and allows the liquid to pass through. This can be accomplished by gravity, pressure or vacuum (suction). The filtering effectively separates the sediment and / or precipitate from the liquid.

[0043] As used herein, “average particle size” and “mean particle size” refer to particle size of particles in the particulate composition such that at least 50% or more of the compound particles are of the average particle size and as determined by methods as disclosed herein, e.g., microscopy and / or light scattering.

[0044] Unless otherwise specified, temperatures referred to herein are based on atmospheric pressure (i.e., one atmosphere).B. DISCLOSED METHOD FOR RECOVERY OF CRITICAL MINERALS FROM LASER CRYSTAL WASTE.

[0045] Laser crystals are single crystal materials doped with either trivalent rare earth metal ions or transition metal ions. The crystals are the heart of solid-state lasers, especially high power lasers. The requirements for laser crystals include transparency and high thermal stability. One of the most frequently used compositions is based on neodymium doped into a yttrium aluminum garnet (Y3AI5O12, YAG). Other compositions include dopants such as ytterbium, erbium and holmium in the YAG lattice, and crystal matrices composed of yttrium vanadate (YVO4) and terbium gallium garnet (Tb3Ga5Oi2, TGG).

[0046] Such crystals are grown by the Czocharalski growth process or the Bridgman gradient freeze process (Ref. 1). However, these processes present problems of their own. They include light scattering from impurities, non-stoichiometric crystals, striae, and non-uniform doping along the crystal. Because of these defects, these unsatisfactory results lead to the generation of laser crystal waste.

[0047] The composition of most laser crystals includes critical minerals such as the rare earthelements, yttrium and gallium. Terbium oxide is particularly expensive and is a valuable product from processing TGG waste. It is unacceptable to allows such valuable minerals to be discarded when the elements are so badly needed.

[0048] Thus, a problem the present description addresses is to develop a process for dissolving laser crystal waste and recovering the critical minerals. Many modifications and other aspects disclosed herein will come to mind to one skilled in the art to which the disclosed compositions and methods pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the disclosures are not to be limited to the specific aspects disclosed and that modifications and other aspects are intended to be included within the scope of the appended claims. The skilled artisan will recognize many variants and adaptations of the aspects described herein. These variants and adaptations are intended to be included in the teachings of this disclosure and to be encompassed by the claims herein.

[0049] In one aspect, with respect to FIG. 1 , the disclosure relates to a method 10 of extracting a rare earth metal oxide and / or a critical mineral metal oxide from a feedstock of a crystal particulate composition, such as a feedstock of a laser crystal particulate composition. The method comprises a step 100 of providing a feedstock of a laser crystal particulate composition having a particle size as disclosed herein, e.g., a laser crystal waste material. The method further comprises a step 101 that includes contacting the feedstock 100 (e.g., contacting can comprise admixing) with a composition consisting of from about 85% to about 99% w / w phosphoric acid and water at a ratio of phosphoric acid to feedstock as disclosed herein. In a further aspect, the phosphoric acid and water composition can consist of from about 85% to about 99%, about 85% to about 95%, about 85% to about 90%, about 90% to about 95%, or about 90% to about 99% w / w phosphoric acid and water. In one aspect, the feedstock of a laser crystal particulate composition can be admixed with the aqueous phosphoric acid and water composition in a laser crystal particulate composition / aqueous composition weightvolume (w / v) ratio of at least 1 :10 g / mL. In a further aspect, the laser crystal particulate composition / phosphoric acid and water composition weightvolume (w / v) ratio can range from about 1 :100 g / mL to about 1 :10 g / mL, about 1 :50 g / mL to about 1 :20 g / mL, about 1 :35 g / mL to about 1 :10 g / mL, about 1 :35 g / mL to about 1 :15 g / mL, about 1 :30 g / mL to about 1 :20 g / mL, or about 1 :27 g / mL to about 1 :22 g / mL.

[0050] The aqueous composition comprising the feedstock in contact with phosphoric acid is then heated as shown in step 102 at a temperature as disclosed herein, e.g., about 200-250 °C, followed by cooling the mixture as shown in step 103 to a desired temperature as disclosed herein, e.g., less than about 100 °C. In a further aspect, the aqueous composition can be heated to a temperature of about 200 °C to about 400 °C, about 200 °C to about 350 °C, about200 °C to about 300 °C, about 250 °C to about 400 °C, about 300 °C to about 400 °C, or about 200 °C to about 250 °C. In one aspect, the aqueous composition can be held at the elevated temperature until all or most of the laser crystal particulate composition has dissolved. In another aspect, the aqueous composition, after heating, can be cooled to a temperature of about room temperature to about 100 °C, about 20 °C to about 100 °C, about 23 °C to about 100 °C, about 40 °C to about 100 °C, about 60 °C to about 100 °C, about 80 °C to about 100 °C, about 20 °C to about 80 °C, about 20 °C to about 60 °C, or about 20 °C to about 40 °C.

[0051] Following cooling, as described in step 104, the cooled mixture is mixed with water, i.e., further diluted with water, at a desired ratio of water to feedstock / phosphoric acid mixture as disclosed herein, e.g., about a 3:1 ratio or greater (by volume) of water to the feedstock / phosphoric acid mixture, and allowed to cool further, e.g., to about 15-30 °C. In a further aspect, the cooled mixture is diluted with water in a ratio of water to phosphoric acid of from about 1 :10 to 10:1 , from about 1 :1 to about 1 :10, from about 1 :5 to 5:1 , from about 2:1 to 4:1 , from about 2.5:1 to 3.5:1 , from about 2:7 to about 3.7:1 , or about 3:1 by volume. In another aspect, the cooled mixture is diluted with water and allowed to cool further to a temperature of about 10 °C to about 40 °C, about 15 °C to about 40 °C, about 20 °C to about 40 °C, about 10 °C to about 35 °C, or about 10 °C to about 30 °C. As described in step 105, to the diluted and cooled mixture from step 104 is added an oxalic acid of suitable concentration as disclosed herein, e.g., about 1 M oxalic acid in water, in an amount as disclosed herein, e.g., a molar ratio of oxalic acid to anticipated molar amount of metal in the mixture such that the ratio is at least 3:1 oxalic acid to metal in the mixture (on a molar basis), to form an oxalic acid mixture. In a further aspect, the concentration of oxalic acid is from about 10 g / L to about 90 g / L, 20 g / L to about 90 g / L, 30 g / L to about 90 g / L, 40 g / L to about 90 g / L, about 50 g / L to about 90 g / L, about 60 g / L to about 90 g / L, about 70 g / L to about 90 g / L, about 80 g / L to about 90 g / L, or about 80 g / L to about 89 g / L. In another aspect, oxalic acid is added to the diluted and cooled mixture in a molar ratio of moles of oxalic acid to moles of rare earth metals in the mixture of from about 4:1 to about 2:1 , about 4:1 to about 3:1 , or about 3:1 to about 2:1 .

[0052] Next - as described in step 106 - a base is added to the oxalic acid mixture in an amount sufficient to bring the pH of the mixture to about pH 2.5 (or to a pH as further described herein) and allowed to cool. In one aspect, enough base is added to the oxalic mixture to bring the pH of the mixture to from about 2 to about 5, about 2 to about 4, about 2 to about 3, about 2.2 to about 2.8, about 2.3 to about 2.7, or about 2.4 to about 2.6. Following this step, the solution is subjected to a separation step, as described in step 107 to separate a rare earth precipitate from the mixture. Any suitable separation method can be utilized, e.g., filtration, but other separation methods as known to the skilled artisan can be used. In one aspect, the rare earth precipitate is a rare earth metal oxide precipitate comprising a rare earth metal oxalate.In a further aspect, the rare earth metal oxide precipitate can be selected from the group consisting of oxides of neodymium (Nd), yttrium (Y), lanthanum (La), dysprosium (Dy), cerium (Ce), praseodymium (Pr), scandium (Sc), terbium (Tb), samarium (Sm), europium (Eu), lutetium (Lu), gadolinium (Gd), ytterbium (Yb), erbium (Er), holmium (Ho), thulium (Tm), and combinations thereof. In another aspect, the rare earth metal oxide precipitate is a M(lll) oxide, where M represents a rare earth metal with the indicated valence state. In another aspect, the rare earth metal oxide precipitate is cerium, present as Ce(lll) oxide and / or Ce(IV) oxide. In one aspect, the rare earth metal oxide precipitate can comprise less than about 5 wt%, less than about 4 wt%, less than about 3 wt%, less than about 2 wt%, or less than about 1 wt% of a non-rare earth metal composition. In another aspect, the rare earth metal oxide precipitate can comprise from about 0.01 wt% to about 5 wt%, about 0.01 wt% to about 3 wt%, about 0.01 wt% to about 1 wt%, about 0.1 wt% to about 5 wt%, about 0.1 wt% to about 4 wt%, about 0.1 wt% to about 3 wt%, about 0.1 wt% to about 2 wt%, or about 0.1 wt% to about 1 wt% of a non-rare earth metal composition. In one aspect, the non-rare earth metal composition comprises Si, Al, Na, or any combination thereof.

[0053] The rare earth precipitate obtained in step 107 can be washed with an aqueous solution, e.g., water, as described in step 108. The washed rare earth precipitate from step 108 can be calcined as described in step 109. Calcining in step 109 can be carried out as described herein, e.g., about 400-800 °C for at least one hour (or as otherwise described in the present disclosure). In a further aspect, the calcining is carried out at a temperature of from about 400 °C to about 800 °C, about 400 °C to about 700 °C, about 400 °C to about 600 °C, or about 400 °C to about 500 °C for a time period of about 1 hour to about 24 hours, about 1 hour to about 21 hours, about 1 hour to about 18 hours, about 1 hour to about 15 hours, about 1 hour to about 12 hours, about 1 hour to about 9 hours, about 1 hour to about 6 hours, or about 1 hour to about 3 hours. An acid can be added to the calcined precipitate, as described in step 110, in an amount sufficient to obtain a solution having a pH as described herein, e.g, about 5-8, and can be followed by a separation step as described in step 111. In another aspect of step 110, the acid can be added to the rare earth precipitate prior to calcining or without a calcining step. In another aspect, an additional calcining step similar to that described in step 109 can be performed on a calcined precipitate after it has been treated with an acid, as described in step 110. Step 110 can comprise mixing a precipitate or a calcined precipitate with just enough of an aqueous mineral acid to dissolve the precipitate, where the aqueous mineral acid has a concentration of from about 0.1 M to about 1 M, about 0.1 M to about 0.5 M, or about 0.5 M to about 1 M. The aqueous mineral acid can comprise hydrochloric acid, sulfuric acid, nitric acid, hydrobromic acid, or a combination thereof. The precipitate and aqueous mineral acid solution can then be admixed with oxalic acid in a molar ratio of about2:1 oxalic acid to rare earth metal oxide. The admixture can then be titrated with a hydroxide base to a pH of about 5 to about 8, about 5 to about 7, about 5 to about 6, about 6 to about 8, or about 7 to about 8. For the separation step described in step 111 , any suitable separation method as known to the skilled artisan or as described in the present disclosure can be used, e.g., filtration. Finally, in step 112, the separated precipitate can be washed with an aqueous solution, e.g., water, and dried. Drying in step 112 can be done by evaporation at ambient temperature and can optionally include heating.

[0054] In one aspect, the crystal particulate composition comprises a doped crystal material. In a further aspect, the doped crystal material is doped with at least one rare earth metal oxide, at least one mineral metal oxide, or a combination thereof. In another aspect, the crystal particulate composition comprises material selected from a laser crystal. The crystal particulate composition can be substantially free of a fluoride ion. In one aspect, the crystal particulate composition is a yttrium aluminum garnet crystal, a terbium gallium garnet crystal, a neodymium-doped yttrium aluminum garnet crystal, a ytterbium-doped yttrium aluminum garnet crystal, or a holmium-doped yttrium aluminum garnet crystal. In one aspect, the methods disclosed herein can further comprise converting a laser crystal comprising at least one rare earth metal to a crystal particulate composition.

[0055] In certain aspects, the average particle size of the particulate composition in step 100 may be about 1 nm , about 2 nm, about 3 nm, about 4 nm, about 5 nm, about 6 nm, about 7 nm, about 8 nm, about 9 nm, about 10 nm, about 1 1 nm, about 12 nm, about 13 nm, about 14 nm, about 15 nm, about 16 nm, about 17 nm, about 18 nm, about 19 nm, about 20 nm, about 21 nm, about 22 nm, about 23 nm, about 24 nm, about 25 nm, about 26 nm, about 27 nm, about 28 nm, about 29 nm, about 30 nm, about 31 nm, about 32 nm, about 33 nm, about 34 nm, about 35 nm, about 36 nm, about 37 nm, about 38 nm, about 39 nm, about 40 nm, about 41 nm, about 42 nm, about 43 nm, about 44 nm, about 45 nm, about 46 nm, about 47 nm, about 48 nm, about 49 nm, about 50 nm, about 51 nm, about 52 nm, about 53 nm, about 54 nm, about 55 nm, about 56 nm, about 57 nm, about 58 nm, about 59 nm, about 60 nm, about 61 nm, about 62 nm, about 63 nm, about 64 nm, about 65 nm, about 66 nm, about 67 nm, about 68 nm, about 69 nm, about 70 nm, about 71 nm, about 72 nm, about 73 nm, about 74 nm, about 75 nm, about 76 nm, about 77 nm, about 78 nm, about 79 nm, about 80 nm, about 81 nm, about 82 nm, about 83 nm, about 84 nm, about 85 nm, about 86 nm, about 87 nm, about 88 nm, about 89 nm, about 90 nm, about 91 nm, about 92 nm, about 93 nm, about 94 nm, about 95 nm, about 96 nm, about 97 nm, about 98 nm, about 99 nm, about 100 nm, about 101 nm, about 102 nm, about 103 nm, about 104 nm, about 105 nm, about 106 nm, about 107 nm, about 108 nm, about 109 nm, about 110 nm, about 1 1 1 nm, about 1 12 nm, about 113 nm, about 1 14 nm, about 1 15 nm, about 1 16 nm, about 1 17 nm, about 118 nm, about 119 nm,about 120 nm, about 121 nm, about 122 nm, about 123 nm, about 124 nm, about 125 nm about 126 nm, about 127 nm, about 128 nm, about 129 nm, about 130 nm, about 131 nm about 132 nm, about 133 nm, about 134 nm, about 135 nm, about 136 nm, about 137 nm about 138 nm, about 139 nm, about 140 nm, about 141 nm, about 142 nm, about 143 nm about 144 nm, about 145 nm, about 146 nm, about 147 nm, about 148 nm, about 149 nm about 150 nm, about 151 nm, about 152 nm, about 153 nm, about 154 nm, about 155 nm about 156 nm, about 157 nm, about 158 nm, about 159 nm, about 160 nm, about 161 nm about 162 nm, about 163 nm, about 164 nm, about 165 nm, about 166 nm, about 167 nm about 168 nm, about 169 nm, about 170 nm, about 171 nm, about 172 nm, about 173 nm about 174 nm, about 175 nm, about 176 nm, about 177 nm, about 178 nm, about 179 nm about 180 nm, about 181 nm, about 182 nm, about 183 nm, about 184 nm, about 185 nm about 186 nm, about 187 nm, about 188 nm, about 189 nm, about 190 nm, about 191 nm about 192 nm, about 193 nm, about 194 nm, about 195 nm, about 196 nm, about 197 nm about 198 nm, about 199 nm, about 200 nm, about 201 nm, about 202 nm, about 203 nm about 204 nm, about 205 nm, about 206 nm, about 207 nm, about 208 nm, about 209 nm about 210 nm, about 211 nm, about 212 nm, about 213 nm, about 214 nm, about 215 nm about 216 nm, about 217 nm, about 218 nm, about 219 nm, about 220 nm, about 221 nm about 222 nm, about 223 nm, about 224 nm, about 225 nm, about 226 nm, about 227 nm about 228 nm, about 229 nm, about 230 nm, about 231 nm, about 232 nm, about 233 nm about 234 nm, about 235 nm, about 236 nm, about 237 nm, about 238 nm, about 239 nm about 240 nm, about 241 nm, about 242 nm, about 243 nm, about 244 nm, about 245 nm about 246 nm, about 247 nm, about 248 nm, about 249 nm, about 250 nm, about 251 nm about 252 nm, about 253 nm, about 254 nm, about 255 nm, about 256 nm, about 257 nm about 258 nm, about 259 nm, about 260 nm, about 261 nm, about 262 nm, about 263 nm about 264 nm, about 265 nm, about 266 nm, about 267 nm, about 268 nm, about 269 nm about 270 nm, about 271 nm, about 272 nm, about 273 nm, about 274 nm, about 275 nm about 276 nm, about 277 nm, about 278 nm, about 279 nm, about 280 nm, about 281 nm about 282 nm, about 283 nm, about 284 nm, about 285 nm, about 286 nm, about 287 nm about 288 nm, about 289 nm, about 290 nm, about 291 nm, about 292 nm, about 293 nm about 294 nm, about 295 nm, about 296 nm, about 297 nm, about 298 nm, about 299 nm about 100 nm, about 301 nm, about 302 nm, about 303 nm, about 304 nm, about 305 nm about 306 nm, about 307 nm, about 308 nm, about 309 nm, about 310 nm, about 311 nm about 312 nm, about 313 nm, about 314 nm, about 315 nm, about 316 nm, about 317 nm about 318 nm, about 319 nm, about 320 nm, about 321 nm, about 322 nm, about 323 nm about 324 nm, about 325 nm, about 326 nm, about 327 nm, about 328 nm, about 329 nm about 330 nm, about 331 nm, about 332 nm, about 333 nm, about 334 nm, about 335 nm about 336 nm, about 337 nm, about 338 nm, about 339 nm, about 340 nm, about 341 nmabout 342 nm, about 343 nm, about 344 nm, about 345 nm, about 346 nm, about 347 nm, about 348 nm, about 349 nm, about 350 nm, about 351 nm, about 352 nm, about 353 nm, about 354 nm, about 355 nm, about 356 nm, about 357 nm, about 358 nm, about 359 nm, about 360 nm, about 361 nm, about 362 nm, about 363 nm, about 364 nm, about 365 nm, about 366 nm, about 367 nm, about 368 nm, about 369 nm, about 370 nm, about 371 nm, about 372 nm, about 373 nm, about 374 nm, about 375 nm, about 376 nm, about 377 nm, about 378 nm, about 379 nm, about 380 nm, about 381 nm, about 382 nm, about 383 nm, about 384 nm, about 385 nm, about 386 nm, about 387 nm, about 388 nm, about 389 nm, about 390 nm, about 391 nm, about 392 nm, about 393 nm, about 394 nm, about 395 nm, about 396 nm, about 397 nm, about 398 nm, about 399 nm, about 100 nm, about 401 nm, about 402 nm, about 403 nm, about 404 nm, about 405 nm, about 406 nm, about 407 nm, about 408 nm, about 409 nm, about 410 nm, about 411 nm, about 412 nm, about 413 nm, about 414 nm, about 415 nm, about 416 nm, about 417 nm, about 418 nm, about 419 nm, about 420 nm, about 421 nm, about 422 nm, about 423 nm, about 424 nm, about 425 nm, about 426 nm, about 427 nm, about 428 nm, about 429 nm, about 430 nm, about 431 nm, about 432 nm, about 433 nm, about 434 nm, about 435 nm, about 436 nm, about 437 nm, about 438 nm, about 439 nm, about 440 nm, about 441 nm, about 442 nm, about 443 nm, about 444 nm, about 445 nm, about 446 nm, about 447 nm, about 448 nm, about 449 nm, about 450 nm, about 451 nm, about 452 nm, about 453 nm, about 454 nm, about 455 nm, about 456 nm, about 457 nm, about 458 nm, about 459 nm, about 460 nm, about 461 nm, about 462 nm, about 463 nm, about 464 nm, about 465 nm, about 466 nm, about 467 nm, about 468 nm, about 469 nm, about 470 nm, about 471 nm, about 472 nm, about 473 nm, about 474 nm, about 475 nm, about 476 nm, about 477 nm, about 478 nm, about 479 nm, about 480 nm, about 481 nm, about 482 nm, about 483 nm, about 484 nm, about 485 nm, about 486 nm, about 487 nm, about 488 nm, about 489 nm, about 490 nm, about 491 nm, about 492 nm, about 493 nm, about 494 nm, about 495 nm, about 496 nm, about 497 nm, about 498 nm, about 499 nm, about 400 nm, about 501 nm, about 502 nm, about 503 nm, about 504 nm, about 505 nm, about 506 nm, about 507 nm, about 508 nm, about 509 nm, about 510 nm, about 511 nm, about 512 nm, about 513 nm, about 514 nm, about 515 nm, about 516 nm, about 517 nm, about 518 nm, about 519 nm, about 520 nm, about 521 nm, about 522 nm, about 523 nm, about 524 nm, about 525 nm, about 526 nm, about 527 nm, about 528 nm, about 529 nm, about 530 nm, about 531 nm, about 532 nm, about 533 nm, about 534 nm, about 535 nm, about 536 nm, about 537 nm, about 538 nm, about 539 nm, about 540 nm, about 541 nm, about 542 nm, about 543 nm, about 544 nm, about 545 nm, about 546 nm, about 547 nm, about 548 nm, about 549 nm, about 550 nm, about 551 nm, about 552 nm, about 553 nm, about 554 nm, about 555 nm, about 556 nm, about 557 nm, about 558 nm, about 559 nm, about 560 nm, about 561 nm, about 562 nm, about 563 nm,about 564 nm, about 565 nm, about 566 nm, about 567 nm, about 568 nm, about 569 nm, about 570 nm, about 571 nm, about 572 nm, about 573 nm, about 574 nm, about 575 nm, about 576 nm, about 577 nm, about 578 nm, about 579 nm, about 580 nm, about 581 nm, about 582 nm, about 583 nm, about 584 nm, about 585 nm, about 586 nm, about 587 nm, about 588 nm, about 589 nm, about 590 nm, about 591 nm, about 592 nm, about 593 nm, about 594 nm, about 595 nm, about 596 nm, about 597 nm, about 598 nm, about 599 nm, about 600 nm, about 601 nm, about 602 nm, about 603 nm, about 604 nm, about 605 nm, about 606 nm, about 607 nm, about 608 nm, about 609 nm, about 610 nm, about 611 nm, about 612 nm, about 613 nm, about 614 nm, about 615 nm, about 616 nm, about 617 nm, about 618 nm, about 619 nm, about 620 nm, about 621 nm, about 622 nm, about 623 nm, about 624 nm, about 625 nm, about 626 nm, about 627 nm, about 628 nm, about 629 nm, about 630 nm, about 631 nm, about 632 nm, about 633 nm, about 634 nm, about 635 nm, about 636 nm, about 637 nm, about 638 nm, about 639 nm, about 640 nm, about 641 nm, about 642 nm, about 643 nm, about 644 nm, about 645 nm, about 646 nm, about 647 nm, about 648 nm, about 649 nm, about 650 nm, about 651 nm, about 652 nm, about 653 nm, about 654 nm, about 655 nm, about 656 nm, about 657 nm, about 658 nm, about 659 nm, about 660 nm, about 661 nm, about 662 nm, about 663 nm, about 664 nm, about 665 nm, about 666 nm, about 667 nm, about 668 nm, about 669 nm, about 670 nm, about 671 nm, about 672 nm, about 673 nm, about 674 nm, about 675 nm, about 676 nm, about 677 nm, about 678 nm, about 679 nm, about 680 nm, about 681 nm, about 682 nm, about 683 nm, about 684 nm, about 685 nm, about 686 nm, about 687 nm, about 688 nm, about 689 nm, about 690 nm, about 691 nm, about 692 nm, about 693 nm, about 694 nm, about 695 nm, about 696 nm, about 697 nm, about 698 nm, about 699 nm, about 700 nm, about 701 nm, about 702 nm, about 703 nm, about 704 nm, about 705 nm, about 706 nm, about 707 nm, about 708 nm, about 709 nm, about 710 nm, about 711 nm, about 712 nm, about 713 nm, about 714 nm, about 715 nm, about 716 nm, about 717 nm, about 718 nm, about 719 nm, about 720 nm, about 721 nm, about 722 nm, about 723 nm, about 724 nm, about 725 nm, about 726 nm, about 727 nm, about 728 nm, about 729 nm, about 730 nm, about 731 nm, about 732 nm, about 733 nm, about 734 nm, about 735 nm, about 736 nm, about 737 nm, about 738 nm, about 739 nm, about 740 nm, about 741 nm, about 742 nm, about 743 nm, about 744 nm, about 745 nm, about 746 nm, about 747 nm, about 748 nm, about 749 nm, about 750 nm, about 751 nm, about 752 nm, about 753 nm, about 754 nm, about 755 nm, about 756 nm, about 757 nm, about 758 nm, about 759 nm, about 760 nm, about 761 nm, about 762 nm, about 763 nm, about 764 nm, about 765 nm, about 766 nm, about 767 nm, about 768 nm, about 769 nm, about 770 nm, about 771 nm, about 772 nm, about 773 nm, about 774 nm, about 775 nm, about 776 nm, about 777 nm, about 778 nm, about 779 nm, about 780 nm, about 781 nm, about 782 nm, about 783 nm, about 784 nm, about 785 nm,about 786 nm, about 787 nm, about 788 nm, about 789 nm, about 790 nm, about 791 nm, about 792 nm, about 793 nm, about 794 nm, about 795 nm, about 796 nm, about 797 nm, about 798 nm, about 799 nm, about 100 nm, about 801 nm, about 802 nm, about 803 nm, about 804 nm, about 805 nm, about 806 nm, about 807 nm, about 808 nm, about 809 nm, about 810 nm, about 811 nm, about 812 nm, about 813 nm, about 814 nm, about 815 nm, about 816 nm, about 817 nm, about 818 nm, about 819 nm, about 820 nm, about 821 nm, about 822 nm, about 823 nm, about 824 nm, about 825 nm, about 826 nm, about 827 nm, about 828 nm, about 829 nm, about 830 nm, about 831 nm, about 832 nm, about 833 nm, about 834 nm, about 835 nm, about 836 nm, about 837 nm, about 838 nm, about 839 nm, about 840 nm, about 841 nm, about 842 nm, about 843 nm, about 844 nm, about 845 nm, about 846 nm, about 847 nm, about 848 nm, about 849 nm, about 850 nm, about 851 nm, about 852 nm, about 853 nm, about 854 nm, about 855 nm, about 856 nm, about 857 nm, about 858 nm, about 859 nm, about 860 nm, about 861 nm, about 862 nm, about 863 nm, about 864 nm, about 865 nm, about 866 nm, about 867 nm, about 868 nm, about 869 nm, about 870 nm, about 871 nm, about 872 nm, about 873 nm, about 874 nm, about 875 nm, about 876 nm, about 877 nm, about 878 nm, about 879 nm, about 880 nm, about 881 nm, about 882 nm, about 883 nm, about 884 nm, about 885 nm, about 886 nm, about 887 nm, about 888 nm, about 889 nm, about 890 nm, about 891 nm, about 892 nm, about 893 nm, about 894 nm, about 895 nm, about 896 nm, about 897 nm, about 898 nm, about 899 nm, about 900 nm, about 901 nm, about 902 nm, about 903 nm, about 904 nm, about 905 nm, about 906 nm, about 907 nm, about 908 nm, about 909 nm, about 910 nm, about 911 nm, about 912 nm, about 913 nm, about 914 nm, about 915 nm, about 916 nm, about 917 nm, about 918 nm, about 919 nm, about 920 nm, about 921 nm, about 922 nm, about 923 nm, about 924 nm, about 925 nm, about 926 nm, about 927 nm, about 928 nm, about 929 nm, about 930 nm, about 931 nm, about 932 nm, about 933 nm, about 934 nm, about 935 nm, about 936 nm, about 937 nm, about 938 nm, about 939 nm, about 940 nm, about 941 nm, about 942 nm, about 943 nm, about 944 nm, about 945 nm, about 946 nm, about 947 nm, about 948 nm, about 949 nm, about 950 nm, about 951 nm, about 952 nm, about 953 nm, about 954 nm, about 955 nm, about 956 nm, about 957 nm, about 958 nm, about 959 nm, about 960 nm, about 961 nm, about 962 nm, about 963 nm, about 964 nm, about 965 nm, about 966 nm, about 967 nm, about 968 nm, about 969 nm, about 970 nm, about 971 nm, about 972 nm, about 973 nm, about 974 nm, about 975 nm, about 976 nm, about 977 nm, about 978 nm, about 979 nm, about 980 nm, about 981 nm, about 982 nm, about 983 nm, about 984 nm, about 985 nm, about 986 nm, about 987 nm, about 988 nm, about 989 nm, about 990 nm, about 991 nm, about 992 nm, about 993 nm, about 994 nm, about 995 nm, about 996 nm, about 997 nm, about 998 nm, about 999 nm, or about 1 pm, about 2 m, about 3 pm , about 4 pm about 5 pm, about 6 pm, about 7 pm, about 8 pm, about 9 pm, about 10pm, about 11 pm, about 12 pm, about 13 pm, about 14 pm, about 15 pm, about 16 pm, about 17 pm, about 18 pm, about 19 pm, about 20 pm, about 21 pm, about 22 pm, about 23 pm, about 24 pm, about 25 pm, about 26 pm, about 27 pm, about 28 pm, about 29 pm, about 30 pm, about 31 pm, about 32 pm, about 33 pm, about 34 pm, about 35 pm, about 36 pm, about 37 pm, about 38 pm, about 39 pm, about 40 pm, about 41 pm, about 42 pm, about 43 pm, about 44 pm, about 45 pm, about 46 pm, about 47 pm, about 48 pm, about 49 pm, about 50 pm, about 51 pm, about 52 pm, about 53 pm, about 54 pm, about 55 pm, about 56 pm, about 57 pm, about 58 pm, about 59 pm, about 60 pm, about 61 pm, about 62 pm, about 63 pm, about 64 pm, about 65 pm, about 66 pm, about 67 pm, about 68 pm, about 69 pm, about 70 pm, about 71 pm, about 72 pm, about 73 pm, about 74 pm, about 75 pm, about 76 pm, about 77 pm, about 78 pm, about 79 pm, about 80 pm, about 81 pm, about 82 pm, about 83 pm, about 84 pm, about 85 pm, about 86 pm, about 87 pm, about 88 pm, about 89 pm, about 90 pm, about 91 pm, about 92 pm, about 93 pm, about 94 pm, about 95 pm, about 96 pm, about97 m, about 98 pm, about 99 pm, about 100 pm, about 101 pm, about 102 pm, about 103 pm, about 104 pm, about 105 pm, about 106 pm, about 107 pm, about 108 pm, about 109 pm, about 110 pm, about 111 pm, about 112 pm, about 113 pm, about 114 pm, about 115 pm, about 116 pm, about 117 pm, about 118 pm, about 119 pm, about 120 pm, about 121 pm, about 122 pm, about 123 pm, about 124 pm, about 125 pm, about 126 pm, about 127 pm, about 128 pm, about 129 pm, about 130 pm, about 131 pm, about 132 pm, about 133 pm, about 134 pm, about 135 pm, about 136 pm, about 137 pm, about 138 pm, about 139 pm, about 140 pm, about 141 pm, about 142 pm, about 143 pm, about 144 pm, about 145 pm, about 146 pm, about 147 pm, about 148 pm, about 149 pm, about 150 pm, about 151 pm, about 152 pm, about 153 pm, about 154 pm, about 155 pm, about 156 pm, about 157 pm, about 158 pm, about 159 pm, about 160 pm, about 161 pm, about 162 pm, about 163 pm, about 164 pm, about 165 pm, about 166 pm, about 167 pm, about 168 pm, about 169 pm, about 170 pm, about 171 pm, about 172 pm, about 173 pm, about 174 pm, about 175 pm, about 176 pm, about 177 pm, about 178 pm, about 179 pm, about 180 pm, about 181 pm, about 182 pm, about 183 pm, about 184 pm, about 185 pm, about 186 pm, about 187 pm, about 188 pm, about 189 pm, about 190 pm, about 191 pm, about 192 pm, about 193 pm, about 194 pm, about 195 pm, about 196 pm, about 197 pm, about 198 pm, about 199 pm, about 200 pm, about 201 pm, about 202 pm, about 203 pm, about 204 pm, about 205 pm, about 206 pm, about 207 pm, about 208 pm, about 209 pm, about 210 pm, about 211 pm, about 212 pm, about 213 pm, about 214 pm, about 215 pm, about 216 pm, about 217 pm, about 218 pm, about 219 pm, about 220 pm, about 221 pm, about 222 pm, about 223 pm, about 224 pm, about 225 pm, about 226 pm, about 227 pm, about 228 pm, about 229 pm, about 230 pm, about 231 pm, about 232 pm, about 233 pm, about 234 pm, about 235 pm, about 236 pm, about 237 pm, about 238 pm, about 239 pm, about 240 pm, about 241pm, about 242 pm, about 243 pm, about 244 m, about 245 pm, about 246 pm, about 247 pm, about 248 pm, about 249 pm, about 250 pm, about 251 pm, about 252 pm, about 253 pm, about 254 pm, about 255 pm, about 256 pm, about 257 pm, about 258 pm, about 259 pm, about 260 pm, about 261 pm, about 262 pm, about 263 pm, about 264 pm, about 265 pm, about 266 pm, about 267 pm, about 268 pm, about 269 pm, about 270 pm, about 271 pm, about 272 pm, about 273 pm, about 274 pm, about 275 pm, about 276 pm, about 277 pm, about 278 pm, about 279 pm, about 280 pm, about 281 pm, about 282 pm, about 283 pm, about 284 pm, about 285 pm, about 286 pm, about 287 pm, about 288 pm, about 289 pm, about 290 pm, about 291 pm, about 292 pm, about 293 pm, about 294 pm, about 295 pm, about 296 pm, about 297 pm, about 298 pm, about 299 pm, about 100 pm, about 301 pm, about 302 pm, about 303 pm, about 304 pm, about 305 pm, about 306 pm, about 307 pm, about 308 pm, about 309 pm, about 310 pm, about 311 pm, about 312 pm, about 313 pm, about 314 pm, about 315 pm, about 316 pm, about 317 pm, about 318 pm, about 319 pm, about 320 pm, about 321 pm, about 322 pm, about 323 pm, about 324 pm, about 325 pm, about 326 pm, about 327 pm, about 328 pm, about 329 pm, about 330 pm, about 331 pm, about 332 pm, about 333 pm, about 334 pm, about 335 pm, about 336 pm, about 337 pm, about 338 pm, about 339 pm, about 340 pm, about 341 pm, about 342 pm, about 343 pm, about 344 pm, about 345 pm, about 346 pm, about 347 pm, about 348 pm, about 349 pm, about 350 pm, about 351 pm, about 352 pm, about 353 pm, about 354 pm, about 355 pm, about 356 pm, about 357 pm, about 358 pm, about 359 pm, about 360 pm, about 361 pm, about 362 pm, about 363 pm, about 364 pm, about 365 pm, about 366 pm, about 367 pm, about 368 pm, about 369 pm, about 370 pm, about 371 pm, about 372 pm, about 373 pm, about 374 pm, about 375 pm, about 376 pm, about 377 pm, about 378 pm, about 379 pm, about 380 pm, about 381 pm, about 382 pm, about 383 pm, about 384 pm, about 385 pm, about 386 pm, about 387 pm, about 388 pm, about 389 pm, about 390 pm, about 391 pm, about 392 pm, about 393 pm, about 394 pm, about 395 pm, about 396 pm, about 397 pm, about 398 pm, about 399 pm, about 100 pm, about 401 pm, about 402 pm, about 403 pm, about 404 pm, about 405 pm, about 406 pm, about 407 pm, about 408 pm, about 409 pm, about 410 pm, about 411 pm, about 412 pm, about 413 pm, about 414 pm, about 415 pm, about 416 pm, about 417 pm, about 418 pm, about 419 pm, about 420 pm, about 421 pm, about 422 pm, about 423 pm, about 424 pm, about 425 pm, about 426 pm, about 427 pm, about 428 pm, about 429 pm, about 430 pm, about 431 pm, about 432 pm, about 433 pm, about 434 pm, about 435 pm, about 436 pm, about 437 pm, about 438 pm, about 439 pm, about 440 pm, about 441 pm, about 442 pm, about 443 pm, about 444 pm, about 445 pm, about 446 pm, about 447 pm, about 448 pm, about 449 pm, about 450 pm, about 451 pm, about 452 pm, about 453 pm, about 454 pm, about 455 pm, about 456 pm, about 457 pm, about 458 pm, about 459 pm, about 460 pm, about 461 pm, about 462 pm, about 463pm, about 464 pm, about 465 pm, about 466 m, about 467 pm, about 468 pm, about 469 pm, about 470 pm, about 471 pm, about 472 pm, about 473 pm, about 474 pm, about 475 pm, about 476 pm, about 477 pm, about 478 pm, about 479 pm, about 480 pm, about 481 pm, about 482 pm, about 483 pm, about 484 pm, about 485 pm, about 486 pm, about 487 pm, about 488 pm, about 489 pm, about 490 pm, about 491 pm, about 492 pm, about 493 pm, about 494 pm, about 495 pm, about 496 pm, about 497 pm, about 498 pm, about 499 pm, about 400 pm, about 501 pm, about 502 pm, about 503 pm, about 504 pm, about 505 pm, about 506 pm, about 507 pm, about 508 pm, about 509 pm, about 510 pm, about 511 pm, about 512 pm, about 513 pm, about 514 pm, about 515 pm, about 516 pm, about 517 pm, about 518 pm, about 519 pm, about 520 pm, about 521 pm, about 522 pm, about 523 pm, about 524 pm, about 525 pm, about 526 pm, about 527 pm, about 528 pm, about 529 pm, about 530 pm, about 531 pm, about 532 pm, about 533 pm, about 534 pm, about 535 pm, about 536 pm, about 537 pm, about 538 pm, about 539 pm, about 540 pm, about 541 pm, about 542 pm, about 543 pm, about 544 pm, about 545 pm, about 546 pm, about 547 pm, about 548 pm, about 549 pm, about 550 pm, about 551 pm, about 552 pm, about 553 pm, about 554 pm, about 555 pm, about 556 pm, about 557 pm, about 558 pm, about 559 pm, about 560 pm, about 561 pm, about 562 pm, about 563 pm, about 564 pm, about 565 pm, about 566 pm, about 567 pm, about 568 pm, about 569 pm, about 570 pm, about 571 pm, about 572 pm, about 573 pm, about 574 pm, about 575 pm, about 576 pm, about 577 pm, about 578 pm, about 579 pm, about 580 pm, about 581 pm, about 582 pm, about 583 pm, about 584 pm, about 585 pm, about 586 pm, about 587 pm, about 588 pm, about 589 pm, about 590 pm, about 591 pm, about 592 pm, about 593 pm, about 594 pm, about 595 pm, about 596 pm, about 597 pm, about 598 pm, about 599 pm, about 600 pm, about 601 pm, about 602 pm, about 603 pm, about 604 pm, about 605 pm, about 606 pm, about 607 pm, about 608 pm, about 609 pm, about 610 pm, about 611 pm, about 612 pm, about 613 pm, about 614 pm, about 615 pm, about 616 pm, about 617 pm, about 618 pm, about 619 pm, about 620 pm, about 621 pm, about 622 pm, about 623 pm, about 624 pm, about 625 pm, about 626 pm, about 627 pm, about 628 pm, about 629 pm, about 630 pm, about 631 pm, about 632 pm, about 633 pm, about 634 pm, about 635 pm, about 636 pm, about 637 pm, about 638 pm, about 639 pm, about 640 pm, about 641 pm, about 642 pm, about 643 pm, about 644 pm, about 645 pm, about 646 pm, about 647 pm, about 648 pm, about 649 pm, about 650 pm, about 651 pm, about 652 pm, about 653 pm, about 654 pm, about 655 pm, about 656 pm, about 657 pm, about 658 pm, about 659 pm, about 660 pm, about 661 pm, about 662 pm, about 663 pm, about 664 pm, about 665 pm, about 666 pm, about 667 pm, about 668 pm, about 669 pm, about 670 pm, about 671 pm, about 672 pm, about 673 pm, about 674 pm, about 675 pm, about 676 pm, about 677 pm, about 678 pm, about 679 pm, about 680 pm, about 681 pm, about 682 pm, about 683 pm, about 684 pm, about 685pm, about 686 pm, about 687 pm, about 688 m, about 689 pm, about 690 pm, about 691 pm, about 692 pm, about 693 pm, about 694 pm, about 695 pm, about 696 pm, about 697 pm, about 698 pm, about 699 pm, about 700 pm, about 701 pm, about 702 pm, about 703 pm, about 704 pm, about 705 pm, about 706 pm, about 707 pm, about 708 pm, about 709 pm, about 710 pm, about 711 pm, about 712 pm, about 713 pm, about 714 pm, about 715 pm, about 716 pm, about 717 pm, about 718 pm, about 719 pm, about 720 pm, about 721 pm, about 722 pm, about 723 pm, about 724 pm, about 725 pm, about 726 pm, about 727 pm, about 728 pm, about 729 pm, about 730 pm, about 731 pm, about 732 pm, about 733 pm, about 734 pm, about 735 pm, about 736 pm, about 737 pm, about 738 pm, about 739 pm, about 740 pm, about 741 pm, about 742 pm, about 743 pm, about 744 pm, about 745 pm, about 746 pm, about 747 pm, about 748 pm, about 749 pm, about 750 pm, about 751 pm, about 752 pm, about 753 pm, about 754 pm, about 755 pm, about 756 pm, about 757 pm, about 758 pm, about 759 pm, about 760 pm, about 761 pm, about 762 pm, about 763 pm, about 764 pm, about 765 pm, about 766 pm, about 767 pm, about 768 pm, about 769 pm, about 770 pm, about 771 pm, about 772 pm, about 773 pm, about 774 pm, about 775 pm, about 776 pm, about 777 pm, about 778 pm, about 779 pm, about 780 pm, about 781 pm, about 782 pm, about 783 pm, about 784 pm, about 785 pm, about 786 pm, about 787 pm, about 788 pm, about 789 pm, about 790 pm, about 791 pm, about 792 pm, about 793 pm, about 794 pm, about 795 pm, about 796 pm, about 797 pm, about 798 pm, about 799 pm, about 100 pm, about 801 pm, about 802 pm, about 803 pm, about 804 pm, about 805 pm, about 806 pm, about 807 pm, about 808 pm, about 809 pm, about 810 pm, about 811 pm, about 812 pm, about 813 pm, about 814 pm, about 815 pm, about 816 pm, about 817 pm, about 818 pm, about 819 pm, about 820 pm, about 821 pm, about 822 pm, about 823 pm, about 824 pm, about 825 pm, about 826 pm, about 827 pm, about 828 pm, about 829 pm, about 830 pm, about 831 pm, about 832 pm, about 833 pm, about 834 pm, about 835 pm, about 836 pm, about 837 pm, about 838 pm, about 839 pm, about 840 pm, about 841 pm, about 842 pm, about 843 pm, about 844 pm, about 845 pm, about 846 pm, about 847 pm, about 848 pm, about 849 pm, about 850 pm, about 851 pm, about 852 pm, about 853 pm, about 854 pm, about 855 pm, about 856 pm, about 857 pm, about 858 pm, about 859 pm, about 860 pm, about 861 pm, about 862 pm, about 863 pm, about 864 pm, about 865 pm, about 866 pm, about 867 pm, about 868 pm, about 869 pm, about 870 pm, about 871 pm, about 872 pm, about 873 pm, about 874 pm, about 875 pm, about 876 pm, about 877 pm, about 878 pm, about 879 pm, about 880 pm, about 881 pm, about 882 pm, about 883 pm, about 884 pm, about 885 pm, about 886 pm, about 887 pm, about 888 pm, about 889 pm, about 890 pm, about 891 pm, about 892 pm, about 893 pm, about 894 pm, about 895 pm, about 896 pm, about 897 pm, about 898 pm, about 899 pm, about 900 pm, about 901 pm, about 902 pm, about 903 pm, about 904 pm, about 905 pm, about 906 pm, about 907m, about 908 pm, about 909 pm, about 910 pm, about 91 1 pm, about 912 pm, about 913 pm, about 914 pm, about 915 pm, about 916 pm, about 917 pm, about 918 pm, about 919 pm, about 920 pm, about 921 pm, about 922 pm, about 923 pm, about 924 pm, about 925 pm, about 926 pm, about 927 pm, about 928 pm, about 929 pm, about 930 pm, about 931 pm, about 932 pm, about 933 pm, about 934 pm, about 935 pm, about 936 pm, about 937 pm, about 938 pm, about 939 pm, about 940 pm, about 941 pm, about 942 pm, about 943 pm, about 944 pm, about 945 pm, about 946 pm, about 947 pm, about 948 pm, about 949 pm, about 950 pm, about 951 pm, about 952 pm, about 953 pm, about 954 pm, about 955 pm, about 956 pm, about 957 pm, about 958 pm, about 959 pm, about 960 pm, about 961 pm, about 962 pm, about 963 pm, about 964 pm, about 965 pm, about 966 pm, about 967 pm, about 968 pm, about 969 pm, about 970 pm, about 971 pm, about 972 pm, about 973 pm, about 974 pm, about 975 pm, about 976 pm, about 977 pm, about 978 pm, about 979 pm, about 980 pm, about 981 pm, about 982 pm, about 983 pm, about 984 pm, about 985 pm, about 986 pm, about 987 pm, about 988 pm, about 989 pm, about 990 pm, about 991 pm, about 992 pm, about 993 pm, about 994 pm, about 995 pm, about 996 pm, about 997 pm, about 998 pm, about 999 pm, or about 1000 pm. In a further aspect, the average particle size may be from one value to another a value within the foregoing array of average particle sizes. For example, the average particle size can be less than about 1000 pm, less than about 300 pm, or less than about 100 pm. In another example, the average particle size can range from about 10 pm to about 1000 pm, about 100 pm to about 1000 pm, about 100 pm to about 500 pm, about 100 pm to about 300 pm, In one aspect, the average particle size can represent the average particle size in the longest dimension of the particles.

[0056] In various aspects, average particle size of the particulate composition may be determined by a method as disclosed herein or as known to the skilled artisan. For example, suitable methods include microscopy such as physical sieving / screening methods using standard sieve sizes and techniques; light microscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM) and / or field emission scanning electron microscopy (FESEM); light scattering methods such as quasi-electric light scattering (QELS) and / or dynamic light scattering (DLS); and / or using laser light diffusion methods, e.g., photon correlation spectroscopy.

[0057] In a further aspect, as appropriate, the particulate composition can be further characterized for various parameters and characteristics using methods such as, but not limited to, ultraviolet-visible spectroscopy (UV-Vis), atomic force microscopy (AFM), X-ray photoelectron spectroscopy (XPS), X-ray fluorescence (XRF), powder X-ray diffraction (XRD), energy-dispersive X-ray spectroscopy (EDX), thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy (FTIR), matrix-assisted laser desorption / ionization time-of-flight mass spectrometry (MALDI-TOF), Rutherford backscattering spectrometry (RBS), dual polarization interferometry and nuclear magnetic resonance or combinations thereof.

[0058] In certain pointed aspects, a laser crystal / aqueous weightvolume (w / v) ratio wherein the laser crystal / aqueous weightvolume (w / v) ratio is a ratio of grams of the laser crystal particulate composition to milliliters of the aqueous composition and where the laser crystal / aqueous weightvolume (w / v) ratio is about 0.1 , about 0.09, about 0.08, about 0.07, about 0.06, about 0.05, about 0.04, about 0.03, about 0.02, or about 0.01 to form a first admixture. In a particular aspect, the average particle size may be from one value to another a value within the foregoing array of average particle sizes.

[0059] In certain aspects, the aqueous solution may comprise from about 80%, about 81%, about 82%, about 83%, about 84%, about 85, about 86%, about 87%, about 88%, about 89%, about 90%, about 91%, about 92%, about 93%, about 94%, about 95%, about 96%, about 97%, about 98%, about 99%, or about 100% phosphoric acid. In a particular aspect, the average particle size may be from one value to another a value within the foregoing array of average particle sizes.

[0060] In certain aspects, the temperature of the resulting mixture may be raised to about 200 °C, about 201 °C, about 202 °C, about 203 °C, about 204 °C, about 205 °C, about 206 °C, about 207 °C, about 208 °C, about 209 °C, about 210 °C, about 211 °C, about 212 °C, about 213 °C, about 214 °C, about 215 °C, about 216 °C, about 217 °C, about 218 °C, about 219 °C, about 220 °C, about 221 °C, about 222 °C, about 223 °C, about 224 °C, about 225 °C, about 226 °C, about 227 °C, about 228 °C, about 229 °C, about 230 °C, about 231 °C, about 232 °C, about 233 °C, about 234 °C, about 235 °C, about 236 °C, about 237 °C, about 238 °C, about 239 °C, about 240 °C, about 241 °C, about 242 °C, about 243 °C, about 244 °C, about 245 °C, about 246 °C, about 247 °C, about 248 °C, about 249 °C, about 250 °C, about 250 °C, about 251 °C, about 252 °C, about 253 °C, about 254 °C, about 255 °C, about 256 °C, about 257 °C, about 258 °C, about 259 °C, about 250 °C, about 260 °C, about 261 °C, about 262 °C, about 263 °C, about 264 °C, about 265 °C, about 266 °C, about 267 °C, about 268 °C, about 269 °C, about 260 °C, about 270 °C, about 271 °C, about 272 °C, about 273 °C, about 274 °C, about 275 °C, about 276 °C, about 277 °C, about 278 °C, about 279 °C, about 270 °C, about 280 °C, about 281 °C, about 282 °C, about 283 °C, about 284 °C, about 285 °C, about 286 °C, about 287 °C, about 288 °C, about 289 °C, about 280 °C, about 290 °C, about 291 °C, about 292 °C, about 293 °C, about 294 °C, about 295 °C, about 296 °C, about 297 °C, about 298 °C, about 299 °C, about 290 °C, about 290 °C, about 291 °C, about 292 °C, about 293 °C, about 294 °C, about 295 °C, about 296 °C, about 297 °C, about 298 °C, about 299 °C, about 290 °C, about 290 °C, about 291 °C, about 292 °C, about 293 °C, about 294 °C, about 295 °C, about 296 °C, about 297 °C, about 298 °C, about 299 °C,about 300 °C, about 301 °C, about 302 °C, about 303 °C, about 304 °C, about 305 °C, about 306 °C, about 307 °C, about 308 °C, about 309 °C, about 310 °C, about 311 °C, about 312 °C, about 313 °C, about 314 °C, about 315 °C, about 316 °C, about 317 °C, about 318 °C, about 319 °C, about 320 °C, about 321 °C, about 322 °C, about 323 °C, about 324 °C, about 325 °C, about 326 °C, about 327 °C, about 328 °C, about 329 °C, about 330 °C, about 331 °C, about 332 °C, about 333 °C, about 334 °C, about 335 °C, about 336 °C, about 337 °C, about 338 °C, about 339 °C, about 340 °C, about 341 °C, about 342 °C, about 343 °C, about 344 °C, about 345 °C, about 346 °C, about 347 °C, about 348 °C, about 349 °C, about 350 °C, about 350 °C, about 351 °C, about 352 °C, about 353 °C, about 354 °C, about 355 °C, about 356 °C, about 357 °C, about 358 °C, about 359 °C, about 350 °C, about 360 °C, about 361 °C, about 362 °C, about 363 °C, about 364 °C, about 365 °C, about 366 °C, about 367 °C, about 368 °C, about 369 °C, about 360 °C, about 370 °C, about 371 °C, about 372 °C, about 373 °C, about 374 °C, about 375 °C, about 376 °C, about 377 °C, about 378 °C, about 379 °C, about 370 °C, about 380 °C, about 381 °C, about 382 °C, about 383 °C, about 384 °C, about 385 °C, about 386 °C, about 387 °C, about 388 °C, about 389 °C, about 380 °C, about 390 °C, about 391 °C, about 392 °C, about 393 °C, about 394 °C, about 395 °C, about 396 °C, about 397 °C, about 398 °C, about 399 °C, about 390 °C, about 390 °C, about 391 °C, about 392 °C, about 393 °C, about 394 °C, about 395 °C, about 396 °C, about 397 °C, about 398 °C, about 399 °C, about 390 °C, about 390 °C, about 391 °C, about 392 °C, about 393 °C, about 394 °C, about 395 °C, about 396 °C, about 397 °C, about 398 °C, about 399 °C, or about 400 °C. In a particular aspect, the temperature may be from one value to another a value within the foregoing array of temperatures.C. REFERENCES

[0061] References are cited herein throughout using the format of reference number(s) enclosed by parentheses corresponding to one or more of the following numbered references. For example, citation of references numbers 1 and 2 immediately herein below would be indicated in the disclosure as (Refs. 1 and 2).

[0062] Ref. 1. Oxide and Fluoride Laser Crystals, L. Jeffery Atherton, Stephen A. Payne, C. David Brandie, Ann. Rev. Mater. Sci. 1993, 23, 453-502.

[0063] Ref. 2. Effect of hot acid etching on the mechanical strength of ground YAG laser elements, Revital Feldman, Yehoshua Shimony, Eyal Lebiush, Yuval Golan, Journal of Physics and Chemistry of Solids 2008, 69, 839-846.

[0064] Ref. 3. A novel methodology for rapid digestion of rare earth element ores and determination by microwave plasma-atomic emission spectrometry and dynamic reaction cel I- inductively coupled plasma-mass spectrometry, Erick Helmeczi, Yong Wang, Ian D. Brindle,Taianta 2016, 160, 521-527.

[0065] Ref. 4. Hydrofluoric Acid-Free Digestion of Geological Samples for the Quantification of Rare Earth Elements by Inductively Coupled Plasma-Optical Emission Spectrometry, Bezerra de Oliveira, Andrey Linhares; Afonso, Julio Carlos; da Silva, Lilian; Alcover Neto, Arnaldo; Castro Carneiro, Manuel; Dias da Silva, Lilian Irene; Couto Monteiro, Maria Ines, Geostandards and Geoanalytical Research (2019), 43(4), 689-699.

[0066] Ref. 5. Dissolution of geological material with orthophosphoric acid for major-element determination by flame atomic-absorption spectroscopy and inductively-coupled plasma atomic-emission spectroscopy, Hannaker, Philip; Hou, Qing Lie, Taianta (1984), 31 (12), 1 153- 1 157.

[0067] Ref. 6. Method for recycling of rare earth and zirconium oxide materials, Burlingame, Nicholas H.; Burlingame, Samuel, United States, US20130171047 A1 2013-07-04.D. ASPECTS

[0068] The following listing of exemplary aspects supports and is supported by the disclosure provided herein.

[0069] Aspect 1 . A method of obtaining a critical mineral metal oxide, a rare earth metal oxide, or combinations thereof from a crystal material, the method comprising: admixing a crystal particulate composition with an aqueous composition consisting of from about 85% to about 99% w / w phosphoric acid and water in a crystal particulate / aqueous weightvolume (w / v) ratio wherein the crystal particulate / aqueous weightvolume (w / v) ratio is a ratio of grams of the crystal particulate composition to milliliters of the aqueous composition and where the crystal particulate / aqueous weightvolume (w / v) ratio is from about 0.1 to about 0.01 to form a first admixture; raising the temperature of the first admixture to a first temperature from about 200 °C to about 400 °C; holding the temperature of the first admixture at the first temperature until the crystal particulate composition dissolves in the aqueous composition; lowering the temperature of the first admixture to a second temperature from about room temperature to not more than 100°C; diluting the first admixture into water to provide a diluted aqueous admixture comprising a ratio of water to phosphoric acid of from about 1 :10 to about 10:1 by volume; admixing an oxalic acid solution with the diluted aqueous admixture in a molar ratio of from about 4:1 to about 2:1 of moles of the oxalic acid to the number of moles of rare earth metals to form a second admixture; adding base to the second admixture such that the pH of the second admixture is from about 2 to about 5; and separating a rare earth metal oxide precipitate from the second admixture; wherein the rare earth metal oxide precipitate comprises at least one critical mineral metal oxide, at least one rare earth metal oxide, or combinations thereof.

[0070] Aspect 2. The method of Aspect 1 , wherein the crystal particulate composition comprises particulates comprising a doped crystal material.

[0071] Aspect 3. The method of Aspect 2, wherein the particulates comprising the doped crystal material are doped with at least one rare earth metal oxide, at least one critical mineral metal oxide, or a combination thereof.

[0072] Aspect 4. The method of Aspect 1 or Aspect 2, wherein the crystal particulate composition comprises particulates comprising a material selected from a laser crystal.

[0073] Aspect 5. The method of any one of Aspect 1 -Aspect 4, wherein the raising the temperature of the first admixture to a first temperature is to from about 200°C to about 350°C.

[0074] Aspect 6. The method of any one of Aspect 1 -Aspect 4, wherein the raising the temperature of the first admixture to a first temperature is to from about 200°C to about 300°C.

[0075] Aspect 7. The method of any one of Aspect 1 -Aspect 4, wherein the raising the temperature of the first admixture to a first temperature is to from about 200°C to about 250°C.

[0076] Aspect 8. The method of any one of Aspect 1 -Aspect 7, wherein the percentage of phosphoric acid in the aqueous composition is from about 85 wt% to 90 wt%.

[0077] Aspect 9. The method of Aspect 8, wherein the percentage of phosphoric acid in the aqueous composition is from about 90 wt% to about 95 wt%.

[0078] Aspect 10. The method of Aspect 8, wherein the percentage of phosphoric acid in the aqueous composition is from about 90 wt% to about 99 wt%.

[0079] Aspect 1 1 . The method of any one of Aspect 1 -Aspect 10, wherein the rare earth metal oxide precipitate is selected from the group consisting of neodymium (Nd), yttrium (Y), lanthanum (La), dysprosium (Dy), cerium (Ce), praseodymium (Pr), scandium (Sc), terbium (Tb), samarium (Sm), europium (Eu), lutetium (Lu), gadolinium (Gd), ytterbium (Yb), erbium (Er), holmium (Ho), thulium (Tm) oxides, and combinations thereof.

[0080] Aspect 12. The method of Aspect 1 1 , wherein the rare earth metal oxide precipitate is selected from the group consisting of Nd, Y and Tb oxides.

[0081] Aspect 13. The method of Aspect 1 1 or Aspect 12, wherein the rare earth metal oxide precipitate is a M(lll) oxide; and wherein M represents a rare earth metal with the indicated valence state.

[0082] Aspect 14. The method of Aspect 1 1 , wherein the rare earth metal oxide precipitate is cerium (Ce), and wherein the cerium (Ce) is present as Ce(lll) oxide and / or Ce(IV) oxide.

[0083] Aspect 15. The method of any one of Aspect 1 -Aspect 14, wherein the concentrationof the oxalic acid solution is from about 10 g / L to about 90 g / L.

[0084] Aspect 16. The method of Aspect 15, wherein the concentration of the oxalic acid solution is from about 50 g / L to about 90 g / L.

[0085] Aspect 17. The method of Aspect 15, wherein the concentration of the oxalic acid solution is from about 60 g / L to about 90 g / L.

[0086] Aspect 18. The method of Aspect 15 wherein the concentration of the oxalic acid solution is from about 70 g / L to about 90 g / L.

[0087] Aspect 19. The method of Aspect 15, wherein the concentration of the oxalic acid solution is from about 80 g / L to about 90 g / L.

[0088] Aspect 20. The method of Aspect 15, wherein the concentration of the oxalic acid solution is from about 80 g / L to about 89 g / L.

[0089] Aspect 21. The method of any one of Aspect 1 -Aspect 20, wherein the crystal particulate composition has an average particle size of from about 0.01 millimeter to about 1 millimeter in the longest dimension.

[0090] Aspect 22. The method of any one of Aspect 1 -Aspect 21 , wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 : 100 g / mL to about 1 :10 g / mL.

[0091] Aspect 23. The method of Aspect 22, wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 :50 g / mL to about 1 :20 g / mL.

[0092] Aspect 24. The method of Aspect 22, wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 :35 g / mL to about 1 :10 g / mL.

[0093] Aspect 25. The method of Aspect 22, wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 :35 g / mL to about 1 :15 g / mL.

[0094] Aspect 26. The method of Aspect 22, wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 :30 g / mL to about 1 :20 g / mL.

[0095] Aspect 27. The method of Aspect 22, wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 :27 g / mL to about 1 :22 g / mL.

[0096] Aspect 28. The method of any one of 1 -Aspect 27, wherein the ratio of water to phosphoric acid is from about 1 :9 to about 9:1 by volume.

[0097] Aspect 29. The method of Aspect 28, wherein the ratio of water to phosphoric acid is from about 1 :5 to about 5:1 by volume.

[0098] Aspect 30. The method of Aspect 28, wherein the ratio of water to phosphoric acid is from about 2:1 to about 4:1 by volume.

[0099] Aspect 31 . The method of Aspect 28, wherein the ratio of water to phosphoric acid is from about 2.5:1 to about 3.5:1 by volume.

[0100] Aspect 32. The method of Aspect 28, wherein the ratio of water to phosphoric acid is from about 2:7 to about 3.7:1 by volume.

[0101] Aspect 33. The method of Aspect 28, wherein the ratio of water to phosphoric acid is from about 3:1 .

[0102] Aspect 34. The method of any one of Aspect 1 -Aspect 33, wherein the pH is from about 2 to about 4.

[0103] Aspect 35. The method of Aspect 34, wherein the pH is from about 2 to about 3.

[0104] Aspect 36. The method of Aspect 34, wherein the pH is from about 2.2 to about 2.8.

[0105] Aspect 37. The method of Aspect 34, wherein the pH is from about 2.3 to about 2.7.

[0106] Aspect 38. The method of Aspect 34, wherein the pH is from about 2.4 to about 2.6.

[0107] Aspect 39. The method of Aspect 34, wherein the pH is about 2.5.

[0108] Aspect 40. The method of any one of Aspect 1 -Aspect 39, wherein the rare earth metal oxide precipitate is dissolved in a minimum amount of a 0.1 M to a 1 M aqueous mineral acid selected from the group consisting of hydrochloric acid, sulfuric acid, nitric acid, and hydrobromic acid; admixed with oxalic acid in about a 2:1 molar ratio of oxalic acid to rare earth metal oxide; and titrated with a hydroxide base to a pH of from pH 5 to pH 8.

[0109] Aspect 41. The method of any one of Aspect 1-Aspect 40, further comprising calcining the precipitate in air at a third temperature of from about 400°C to about 800°C for a time period of from about 1 hour to about 24 hours.

[0110] Aspect 42. The method of any one of Aspect 1 -Aspect 41 , wherein the crystal particulate composition is substantially free of a fluoride ion.

[0111] Aspect 43. The method of any one of Aspect 1 -Aspect 41 , wherein the crystal particulate composition is an yttrium aluminum garnet crystal.

[0112] Aspect 44. The method of any one of Aspect 1 -Aspect 41 , wherein the crystalparticulate composition is a terbium gallium garnet crystal.

[0113] Aspect 45. The method of any one of Aspect 1-Aspect 41 , wherein the crystal particulate composition is a neodymium-doped yttrium aluminum garnet crystal.

[0114] Aspect 46. The method of any one of Aspect 1-Aspect 41 , wherein the crystal particulate composition is an ytterbium-doped yttrium aluminum garnet crystal.

[0115] Aspect 47. The method of any one of Aspect 1-Aspect 41 , wherein the crystal particulate composition is a holmium-doped yttrium aluminum garnet crystal.

[0116] Aspect 48. The method of any one of Aspect 1-Aspect 41 , further comprising the step of converting a laser crystal comprising at least one rare earth metal to a laser crystal particulate composition.

[0117] Aspect 49. The method of Aspect 48, wherein the laser crystal particulate composition has particles having an average particle size less than about 1 millimeter in the longest dimension.

[0118] Aspect 50. The method of Aspect 48, wherein the laser crystal particulate composition has particles having an average particle size less than 0.3 millimeter in the longest dimension.

[0119] Aspect 51. The method of Aspect 48, wherein the laser crystal particulate composition has particles having an average particle size less than 0.1 millimeter in the longest dimension.

[0120] Aspect 52. The method of Aspect 48, wherein the laser crystal particulate composition has particles having an average particle size from about 0.1 millimeter to about 1.0 millimeter in the longest dimension.

[0121] Aspect 53. The method of Aspect 48, wherein the laser crystal particulate composition has particles having an average particle size from about 0.1 millimeter to about 0.5 millimeter in the longest dimension.

[0122] Aspect 54. The method of Aspect 48, wherein the laser crystal particulate composition has particles having an average particle size from about 0.1 millimeter to about 0.3 millimeter in the longest dimension.

[0123] Aspect 55. The method of any one of Aspect 1-Aspect 54, wherein the rare earth metal oxide precipitate comprises less than about 5 wt% of a non-rare earth metal composition.

[0124] Aspect 56. The method of Aspect 55, wherein the rare earth metal oxide precipitate comprises less than about 4 wt% of a non-rare earth metal composition.

[0125] Aspect 57. The method of Aspect 55, wherein the rare earth metal oxide precipitate comprises less than about 3 wt% of a non-rare earth metal composition.

[0126] Aspect 58. The method of Aspect 55, wherein the rare earth metal oxide precipitate comprises less than about 2 wt% of a non-rare earth metal composition.

[0127] Aspect 59. The method of Aspect 55, wherein the rare earth metal oxide precipitate comprises less than about 1 wt% of a non-rare earth metal composition.

[0128] Aspect 60. The method of any one of Aspect 56-Aspect 59, wherein the non-rare earth metal composition comprises Si, Al, Na, or combinations thereof.

[0129] Aspect 61 . A composition comprising a critical mineral metal oxide, a rare earth metal oxide, or a combination thereof obtained by the method of any one of Aspect 1 -Aspect 60.

[0130] From the foregoing, it will be seen that aspects herein are well adapted to attain all the ends and objects hereinabove set forth together with other advantages which are obvious and which are inherent to the structure.

[0131] While specific elements and steps are discussed in connection to one another, it is understood that any element and / or steps provided herein is contemplated as being combinable with any other elements and / or steps regardless of explicit provision of the same while still being within the scope provided herein.

[0132] It will be understood that certain features and subcombinations are of utility and may be employed without reference to other features and subcombinations. This is contemplated by and is within the scope of the claims.

[0133] Since many possible aspects may be made without departing from the scope thereof, it is to be understood that all matter herein set forth or shown in the accompanying drawings and detailed description is to be interpreted as illustrative and not in a limiting sense.

[0134] 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. The skilled artisan will recognize many variants and adaptations of the aspects described herein. These variants and adaptations are intended to be included in the teachings of this disclosure and to be encompassed by the claims herein.

[0135] Now having described the aspects of the present disclosure, in general, the following Examples describe some additional aspects of the present disclosure. While aspects of the present disclosure are described in connection with the following examples and the corresponding text and figures, there is no intent to limit aspects of the present disclosure to this description. On the contrary, the intent is to cover all alternatives, modifications, and equivalents included within the spirit and scope of the present disclosure.E. EXAMPLES

[0136] The following examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and description of how the compounds, compositions, articles, devices and / or methods claimed herein are made and evaluated, and are intended to be purely exemplary of the disclosure and are not intended to limit the scope of what the inventors regard as their disclosure. 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.1 . DISSOLUTION OF LASER CRYSTAL WASTE

[0137] A manufacturer of laser crystals provides granulated products of the following compounds: a) neodymium-doped yttrium aluminum garnet (Y3AI5O12 or “YAG”); ytterbium- doped YAG, erbium-doped YAG, terbium-doped YAG, yttrium vanadate (YVO4), and terbium gallium garnet (Tb3Ga50i2, or“TGG”) as separate waste streams.

[0138] A neodymium-doped yttrium aluminum garnet powder is ground to about 0.1 mm average diameter size. The powder is added to 85% phosphoric acid (85% H3PO4, or “PA”) and heated to about from 200-250°C until substantially all the powder is dissolved. The w / v ratio of powder to PA is varied from about 1 g / 10mL to about 1 g / 25 mL. The reaction is cooled and water added such that the volumetric ratio of water to PA is from about 1 : 1 to about 10:1.2. PRECIPITATION OF OXALATES

[0139] An oxalic acid solution in water with a concentration of from about 10 g / L to about 90 g / L is added. The pH of the solution is adjusted to about 2-3 using ammonium hydroxide. The resulting precipitate is collected by filtration and dried in air.3. CALCINATION

[0140] The precipitate is heated to about 400°C-600°C for one hour in air.4. TESTING AND WASHING

[0141] The resulting calcined product is tested for the amount of base cation. If there is a significant concentration of sodium or potassium ions, the solid is suspended in water, the pH adjusted by HCI or nitric acid, and the resulting precipitate collected.5. EXEMPLARY DISCLOSED METHOD AND DATA

[0142] In several trials, 4 to 6 grams of terbium gallium garnet (TGG) was mixed with 100 milliliters of ortho-phosphoric acid (85%). The mixture was heated to 250°C until the solid TGG has dissolved. After cooling, the solution was diluted with 300 milliliters of water and mixed.Oxalic acid solution (90 g / L) was added to achieve a 3:1 mole ratio of oxalic acid to terbium + gallium. Precipitation started upon mixing the two solutions. The mixture was titrated with ammonium hydroxide to pH 2.5. The precipitate was collected by filtration, washed with water, and dried at 1 10°. Analysis of the filtrate revealed that greater than 95% of the terbium was precipitated while greater than 96% of the gallium remained in solution. The oxalate salt was calcined in air by heating to slowly to 450°C and holding at that temperature for 6 hours. The brown color of the calcined solid indicated that some of the solid was Tb4O? in addition to Tb2O3. In one trial, the product composition was close to the theoretical mass percent of terbium in these solids (85% and 87% respectively). In another trial, the product was impure with 54 mass% Tb and 13% phosphorus. In the latter trial, the product was purified by dissolving the solid in dilute nitric acid, adding oxalic acid, precipitating the oxalate salt and calcining the oxalate salt. The product composition rose to 83% Tb. In all trials, 0.5% lutetium was present in the TGG and in the final terbium oxide product. Other impurities (gallium, aluminum, silicon) were present at the 1% level in the terbium oxide product. Overall recovery of Tb from TGG was greater than 90%. The mass percent composition of the Nd:YAG, calcined material, and final washed solid are given in Table 1 below.Table 1. calcined washedNd:YAG solid solidY 40.08% 42.29% 52.88%Nd 5.01% 5.26% 6.59%Al 20.98% 0.06% 0.09%Si 0.91% 0.03% 0.03%Na 0.16% 11.95% 0.85%

[0143] It will be apparent to those skilled in the art that various modifications and variations can be made in the present disclosure without departing from the scope or spirit of the disclosure. Other aspects of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.

Claims

CLAIMSWhat is claimed is:

1. A method of obtaining a critical mineral metal oxide, a rare earth metal oxide, or combinations thereof from a crystal material, the method comprising: admixing a crystal particulate composition with an aqueous composition consisting of from about 85% to about 99% w / w phosphoric acid and water in a crystal particulate / aqueous weightvolume (w / v) ratio wherein the crystal particulate / aqueous weightvolume (w / v) ratio is a ratio of grams of the crystal particulate composition to milliliters of the aqueous composition and where the crystal particulate / aqueous weightvolume (w / v) ratio is from about 0.1 to about 0.01 to form a first admixture; raising the temperature of the first admixture to a first temperature from about 200 °C to about 400 °C; holding the temperature of the first admixture at the first temperature until the crystal particulate composition dissolves in the aqueous composition; lowering the temperature of the first admixture to a second temperature from about room temperature to not more than 100°C; diluting the first admixture into water to provide a diluted aqueous admixture comprising a ratio of water to phosphoric acid of from about 1 : 10 to about 10:1 by volume; admixing an oxalic acid solution with the diluted aqueous admixture in a molar ratio of from about 4:1 to about 2:1 of moles of the oxalic acid to the number of moles of rare earth metals to form a second admixture; adding base to the second admixture such that the pH of the second admixture is from about 2 to about 5; and separating a rare earth metal oxide precipitate from the second admixture; wherein the rare earth metal oxide precipitate comprises at least one critical mineral metal oxide, at least one rare earth metal oxide, or combinations thereof.

2. The method of claim 1 , wherein the crystal particulate composition comprises particulates comprising a doped crystal material.

3. The method of claim 2, wherein the particulates comprising the doped crystal materialare doped with at least one rare earth metal oxide, at least one critical mineral metal oxide, or a combination thereof.

4. The method of claim 1 , wherein the crystal particulate composition comprises particulates comprising a material selected from a laser crystal.

5. The method of claim 1 , wherein the raising the temperature of the first admixture to a first temperature is to from about 200°C to about 350°C.

6. The method of claim 1 , wherein the raising the temperature of the first admixture to a first temperature is to from about 200°C to about 300°C.

7. The method of claim 1 , wherein the raising the temperature of the first admixture to a first temperature is to from about 200°C to about 250°C.

8. The method of claim 1 , wherein the percentage of phosphoric acid in the aqueous composition is from about 85 wt% to 90 wt%.

9. The method of claim 8, wherein the percentage of phosphoric acid in the aqueous composition is from about 90 wt% to about 95 wt%.

10. The method of claim 8, wherein the percentage of phosphoric acid in the aqueous composition is from about 90 wt% to about 99 wt%.1 1. T The method of claim 1 , wherein the rare earth metal oxide precipitate is selected from the group consisting of neodymium (Nd), yttrium (Y), lanthanum (La), dysprosium (Dy), cerium (Ce), praseodymium (Pr), scandium (Sc), terbium (Tb), samarium (Sm), europium (Eu), lutetium (Lu), gadolinium (Gd), ytterbium (Yb), erbium (Er), holmium (Ho), thulium (Tm) oxides, and combinations thereof.

12. The method of claim 1 1 , wherein the rare earth metal oxide precipitate is selected from the group consisting of Nd, Y and Tb oxides.

13. The method of claim 1 1 , wherein the rare earth metal oxide precipitate is a M(lll) oxide; and wherein M represents a rare earth metal with the indicated valence state.

14. The method of claim 1 1 , wherein the rare earth metal oxide precipitate is cerium (Ce), and wherein the cerium (Ce) is present as Ce(lll) oxide and / or Ce(IV) oxide.

15. The method of claim 1 , wherein the concentration of the oxalic acid solution is from about 10 g / L to about 90 g / L.

16. The method of claim 15, wherein the concentration of the oxalic acid solution is from about 50 g / L to about 90 g / L.

17. The method of claim 15, wherein the concentration of the oxalic acid solution is from about 60 g / L to about 90 g / L.

18. The method of claim 15 wherein the concentration of the oxalic acid solution is from about 70 g / L to about 90 g / L.

19. The method of claim 15, wherein the concentration of the oxalic acid solution is from about 80 g / L to about 90 g / L.

20. The method of claim 15, wherein the concentration of the oxalic acid solution is from about 80 g / L to about 89 g / L.

21. The method of claim 1 , wherein the crystal particulate composition has an average particle size of from about 0.01 millimeter to about 1 millimeter in the longest dimension.

22. The method of claim 1 , wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 : 100 g / mL to about 1 :10 g / mL.

23. The method of claim 22, wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 :50 g / mL to about 1 :20 g / mL.

24. The method of claim 22, wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 :35 g / mL to about 1 :10 g / mL.

25. The method of claim 22, wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 :35 g / mL to about 1 :15 g / mL.

26. The method of claim 22, wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 :30 g / mL to about 1 :20 g / mL.

27. The method of claim 22, wherein the first admixture has a w / v ratio of the crystal particulate composition to the aqueous composition consisting of 85% phosphoric acid of from about 1 :27 g / mL to about 1 :22 g / mL.

28. The method of claim 1 , wherein the ratio of water to phosphoric acid is from about 1 :9 to about 9:1 by volume.

29. The method of claim 28, wherein the ratio of water to phosphoric acid is from about 1 :5 to about 5:1 by volume.

30. The method of claim 28, wherein the ratio of water to phosphoric acid is from about 2:1 to about 4:1 by volume.

31. The method of claim 28, wherein the ratio of water to phosphoric acid is from about 2.5:1 to about 3.5:1 by volume.

32. The method of claim 28, wherein the ratio of water to phosphoric acid is from about 2:7 to about 3.7:1 by volume.

33. The method of claim 28, wherein the ratio of water to phosphoric acid is from about 3:1.

34. The method of claim 1 , wherein the pH is from about 2 to about 4.

35. The method of claim 34, wherein the pH is from about 2 to about 3.

36. The method of claim 34, wherein the pH is from about 2.2 to about 2.8.

37. The method of claim 34, wherein the pH is from about 2.3 to about 2.7.

38. The method of claim 34, wherein the pH is from about 2.4 to about 2.6.

39. The method of claim 34, wherein the pH is about 2.5.

40. The method of claim 1 , wherein the rare earth metal oxide precipitate is dissolved in a minimum amount of a 0.1 M to a 1 M aqueous mineral acid selected from the group consisting of hydrochloric acid, sulfuric acid, nitric acid, and hydrobromic acid; admixed with oxalic acid in about a 2:1 molar ratio of oxalic acid to rare earth metal oxide; and titrated with a hydroxide base to a pH of from pH 5 to pH 8.

41. The method of claim 1 , further comprising calcining the rare earth metal oxide precipitate in air at a third temperature of from about 400 °C to about 800 °C for a time period of from about 1 hour to about 24 hours.

42. The method of claim 1 , wherein the crystal particulate composition is substantially free of a fluoride ion.

43. The method of claim 1 , wherein the crystal particulate composition is an yttrium aluminum garnet crystal.

44. The method of claim 1 , wherein the crystal particulate composition is a terbium gallium garnet crystal.

45. The method of claim 1 , wherein the crystal particulate composition is a neodymium- doped yttrium aluminum garnet crystal.

46. The method of claim 1 , wherein the crystal particulate composition is an ytterbium- doped yttrium aluminum garnet crystal.

47. The method of claim 1 , wherein the crystal particulate composition is a holmium-doped yttrium aluminum garnet crystal.

48. The method of claim 1 , further comprising the step of converting a laser crystal comprising at least one rare earth metal to a laser crystal particulate composition.

49. The method of claim 48, wherein the laser crystal particulate composition has particles having an average particle size less than about 1 millimeter in the longest dimension.

50. The method of claim 48, wherein the laser crystal particulate composition has particles having an average particle size less than 0.3 millimeter in the longest dimension.51 . The method of claim 48, wherein the laser crystal particulate composition has particles having an average particle size less than 0.1 millimeter in the longest dimension.

52. The method of claim 48, wherein the laser crystal particulate composition has particles having an average particle size from about 0.1 millimeter to about 1.0 millimeter in the longest dimension.

53. The method of claim 48, wherein the laser crystal particulate composition has particles having an average particle size from about 0.1 millimeter to about 0.5 millimeter in the longest dimension.

54. The method of claim 48, wherein the laser crystal particulate composition has particles having an average particle size from about 0.1 millimeter to about 0.3 millimeter in the longest dimension.

55. The method of claim 1, wherein the rare earth metal oxide precipitate comprises less than about 5 wt% of a non-rare earth metal composition.

56. The method of claim 55, wherein the rare earth metal oxide precipitate comprises less than about 4 wt% of a non-rare earth metal composition.

57. The method of claim 55, wherein the rare earth metal oxide precipitate comprises less than about 3 wt% of a non-rare earth metal composition.

58. The method of claim 55, wherein the rare earth metal oxide precipitate comprises less than about 2 wt% of a non-rare earth metal composition.

59. The method of claim 55, wherein the rare earth metal oxide precipitate comprises less than about 1 wt% of a non-rare earth metal composition.

60. The method of claim 1 , wherein the non-rare earth metal composition comprises Si, Al, Na, or combinations thereof.61 . A composition comprising a critical mineral metal oxide, a rare earth metal oxide, or a combination thereof obtained by the method of claim 1 .

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