Alloy nanoparticles, assembly of alloy nanoparticles, catalyst, and method for producing alloy nanoparticles

Abstract

Provided are novel alloy nanoparticles that include five or more elements (however, cases in which the alloy nanoparticles are directly supported on a carbon-material support exclude cases in which the carbon-material support is made of graphene or carbon fiber), an aggregate of alloy nanoparticles, a catalyst, and a method for producing alloy nanoparticles.

Description

[Technical field]

[0001] The present invention relates to alloy nanoparticles, an aggregate of alloy nanoparticles, a catalyst, and a method for producing alloy nanoparticles. [Background technology]

[0002] High-entropy alloys are a new material that have only been proposed for about 20 years, and are used in a variety of structural metal materials, including steel and aluminum alloys. The name high-entropy alloys comes from the fact that the sum of thermodynamic entropy when mixing and alloying multiple elements is higher than that of conventional solid-solution strengthened alloys.

[0003] High-entropy alloys are expected to be materials that exhibit excellent mechanical properties and functionality, but their development has mainly focused on 3D alloys (Patent Document 1).

[0004] Patent Document 2 discloses multi-element solid solution alloy microparticles in which a third element M (M = at least one of Rh, Ir, Au, Ag, and Pt) is added to PdRu, and a method for producing the same; however, in the examples, it only discloses quaternary solid solution microparticles, and does not mention high-entropy alloys.

[0005] Non-Patent Document 1 discloses a method for producing high-entropy alloy nanoparticles by supporting a metal salt on a carbon material, applying a large current thereto, rapidly heating the material to a high temperature of 2000 K or higher, and then rapidly cooling the material.

[0006] Patent Document 3 discloses a carbon monoxide resistant catalyst material including a binary alloy represented by PtX [X is rhodium or osmium] and a support material in which the PtX alloy is dispersed, but does not disclose alloys of ternary or higher elements. In addition, this alloy is produced by an impregnation method and is not a solid solution.

[0007] Patent Document 4 discloses a method for producing a catalyst including a ruthenium-containing catalyst layer formed on the surface of a structure, and the ruthenium (Ru) precursor-containing solution used in producing the catalyst layer may contain platinum (Pt), palladium (Pd), rhodium (Rh), iridium (Ir), osmium (Os) or mixed metal precursors thereof, but in the examples, no catalyst layer containing a precious metal other than ruthenium is produced.

[0008] Patent Document 5 discloses a platinum alloy catalyst PtX, in which X is one or more metals selected from the group consisting of precious metals, ruthenium, rhodium, palladium, iridium, osmium, gold, silver, and transition metals. However, in the examples, only an example in which X is Ru is disclosed, and no ternary or higher alloy catalyst is produced.

[0009] Patent Document 6 discloses a catalyst for hydrogen purification containing (a) at least one of ruthenium, rhodium, and iridium, (b) platinum, and (c) osmium. However, in the examples, ternary or quaternary catalysts of Pt-Ru-Os, Pt-Rh-Os, and Pt-Ru-Os-Ir are produced, and there is no description of alloy catalysts of quinary or more elements, nor is there any disclosure of solid solutions.

[0010] Non-Patent Document 2 describes a manufacturing method in which a graphene support and a metal are mechanically pulverized to form high-entropy alloy nanoparticles on the graphene support. Note that the elemental composition of the FeCrCoCuNi nanoparticles shown in Fig. 9 did not show a uniform mixture.

[0011] Non-Patent Document 3 describes a manufacturing method for obtaining nanoparticles by irradiating a laser on a target of a bulk high-entropy alloy of 3d transition metals (fourth period). Note that, although Table 2 describes the composition of CoCrFeMnNi nanoparticles, the uniformity of the mixture is not shown.

[0012] Non-Patent Document 4 describes a manufacturing method for obtaining nanoparticles by solvothermal synthesis at about 200° C. using organometallic salts of platinum group elements. Note that Fig. 5 shows scanning transmission electron microscope (STEM)-energy dispersive X-ray analysis (EDS, also known as EDX) images of PtRhRu and PtPdIrRhRu particles, but the images do not indicate the uniformity of the mixture at the atomic level. [Prior art documents] [Patent documents]

[0013] [Patent Document 1] Re-table 2017 / 098848 [Patent Document 2] WO2017 / 150596 [Patent Document 3] Special Publication No. 2016-511920 [Patent Document 4] JP 2017-13040 A [Patent Document 5] Special Publication No. 2010-534130 [Patent Document 6] JP 2003-146617 A [Non-patent literature]

[0014] [Non-Patent Document 1] Science (2018) 359, 1489-1494 [Non-Patent Document 2] SCIENTIFIC REPORTS (2018) 8:8737 [Non-Patent Document 3] RSC Adv. (2019) 9, 18547-18558 [Non-Patent Document 4] Adv.Funct.Mater. (2019) 1905933 Summary of the Invention [Problem to be solved by the invention]

[0015] The effect of the invention described in Patent Document 2 is that "by adding an additional element to a PdRu solid solution alloy that cannot be obtained in bulk, the solid solution state of Pd and Ru is stabilized, and catalyst deterioration during high temperature conditions or long-term reactions is prevented" (see

[0028] ). In other words, the problem that Patent Document 2 aims to solve is to increase the catalytic efficiency of PdRu. It was difficult to derive the idea of ​​quinary or higher alloy nanoparticles from the disclosure of the examples of quaternary solid solution microparticles in Patent Document 2, as the problem is different, since it is unclear whether the catalytic efficiency of PdRu increases when the number of dissolved elements is increased. In Non-Patent Document 1, a conductive carbon fiber (carbon nanofiber) support is required to react metal salts by pulse voltage, while in Non-Patent Document 2, a graphene support is required, and only alloy nanoparticles supported by these are obtained. In addition, in Non-Patent Document 2, mechanical milling is used, so particles with non-uniform particle sizes and uniform particles of several nm cannot be produced. In the lower left part of page 6 of Non-Patent Document 4, it is stated that the obtained nanoparticles are stable up to 700K (427℃). In particular, an XRD pattern corresponding to hcp appears from 800K, which suggests that a hcp Ru-rich phase has appeared. On the other hand, it is stated that the positions of the fcc peaks remain almost unchanged. If a uniform alloy is formed at first and Ru is mainly precipitated, as shown in Table S1, the atomic radius of Ru is smaller than the others, so its lattice constant expands according to Beggars' law. In addition, Fig. S16 shows the relationship between melting point and crystallite size, and Ru is a single metal and is 2nm or less. From these, Non-Patent Document 4 handles that an fcc alloy with large crystallites and small Ru-rich particles are precipitated unevenly at first, but due to the small size of the crystals, a uniform fcc alloy is formed by XRD. When the nanoparticles are heated, the small hcp particles become coarse and a prominent peak appears in the XRD, but the peak position of the fcc does not change, so it is thought that there is almost no change in the metal composition ratio (Ru does not precipitate from the alloy and exists as a separate particle). In other words, the nanoparticles obtained in Non-Patent Document 4 are not mixed uniformly, and cannot be said to be alloy nanoparticles containing five or more elements mixed at the atomic level. In the case of batch-type solvothermal synthesis, the sealed vial is gradually heated, so that metals that are easily decomposed or reduced react gradually, and the reduction speed differs for each metal, making it difficult to produce a uniform alloy.

[0016] The problem to be solved by the present invention is to provide novel alloy nanoparticles containing five or more elements, which may be supported on a support other than a carbon fiber support or a graphene support. [Means for solving the problem]

[0017] The configuration of the present invention, which is a specific means for solving the above problems, and a preferred configuration of the present invention will be described below.

[0018] [1] Alloy nanoparticles containing five or more elements; However, when the alloy nanoparticles are directly supported on the carbon material support, this does not include the case where the carbon material support is graphene or carbon fiber. [2] The alloy nanoparticles according to [1], wherein the elements constituting the alloy nanoparticles include a combination of elements that are not solid-soluble in a phase equilibrium diagram. [3] The alloy nanoparticles according to [1] or [2], wherein the elements constituting the alloy nanoparticles include at least five elements selected from the group consisting of platinum group metals (Ru, Rh, Pd, Os, Ir, Pt), Ag, Au, Cd, Hg, In, Tl, Sn, Pb, Sb, Bi, Mo, W, Tc, Re, 3d metals (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn), Ga, Ge, As, H, B, Al, C, Si, N, P, Y, Zr, Nb, lanthanides, Hf, and Ta. [4] The alloy nanoparticles according to any one of [1] to [3], wherein the elements constituting the alloy nanoparticles include at least one selected from the group consisting of Ru, Rh, Pd, Os, Ir, Pt, Ag, Au, Cu, and Ni. [5] The alloy nanoparticles according to any one of [1] to [4], wherein the elements constituting the alloy nanoparticles include five or more kinds of platinum group elements. [6] The alloy nanoparticles according to any one of [1] to [5], wherein the ratio of the platinum group element in the alloy nanoparticles is 5 atomic % or more. [7] The alloy nanoparticles have the following formula (1): Ru p Rh q Pd r Os x Ir y Pt z (1) (p+q+r+x+y+z=1, 0≦p, q, r, x, y, z<1, either one of p, q, r, x, y, z is 0, or p, q, r, x, y, z are all numbers between 0 and 1.) The alloy nanoparticles according to any one of [1] to [6], wherein the alloy nanoparticles are represented by the formula: [8] The alloy nanoparticles according to any one of [1] to [7], having an average particle size of 0.5 to 30 nm. [9] The alloy nanoparticles according to any one of [1] to [8], which are an aggregate of alloy nanoparticles.

[10] The alloy nanoparticles according to any one of [1] to [8], wherein the alloy nanoparticles are supported on a non-carbon material support or a particulate carbon support.

[11] An aggregate of alloy nanoparticles, comprising 98% or more by number of the alloy nanoparticles according to any one of [1] to [8].

[12] A catalyst comprising the alloy nanoparticles according to any one of [1] to

[10] , or an aggregate of the alloy nanoparticles according to

[11] .

[13] The catalyst according to

[12] , wherein any alloy nanoparticle contained in the catalyst contains all of five or more elements as constituent elements.

[14] A method for producing alloy nanoparticles, comprising the step of adding an aqueous solution containing salts of five or more elements to a liquid reducing agent heated to 200°C to 300°C to react with the solution to obtain alloy nanoparticles containing five or more elements; However, when the alloy nanoparticles are directly supported on the carbon material support, the case where the carbon material support is graphene or carbon fiber is excluded.

[0019] A preferred embodiment of the present invention is as follows. Item 1. A platinum group multi-element solid solution containing five or more platinum group elements or an alloy nanoparticle according to any one of [1] to

[10] . Item 2. The platinum group multi-element solid solution according to Item 1 or the alloy nanoparticles according to any one of [1] to

[10] , wherein the platinum group multi-element solid solution is fine particles having an average particle size of 0.5 nm to 0.5 μm. Item 3. The platinum group multi-element solid solution according to Item 1 or the alloy nanoparticles according to any one of [1] to

[10] , wherein the content of the platinum group element is 5 at % or more. Item 4. The platinum group multi-element solid solution according to any one of Items 1 to 3 or the alloy nanoparticles according to any one of [1] to

[10] , which are covered with a protective agent. Item 5. The platinum group multi-element solid solution according to any one of Items 1 to 4 or the alloy nanoparticles according to any one of Items [1] to

[10] , which are supported on a carrier. Item 6. The platinum group multi-component solid solution has the following formula (1): Ru p Rh q Pd r Os x Ir y Pt z (1) (p+q+r+x+y+z=1, 0≦p, q, r, x, y, z<1, either one of p, q, r, x, y, z is 0, or p, q, r, x, y, z are all numbers between 0 and 1.) The platinum group multi-element solid solution according to any one of items 1 to 5, or the alloy nanoparticles according to any one of items [1] to

[10] , Item 7. The platinum group multi-element solid solution according to Item 6, wherein x is a number between 0 and 1. Item 8. The platinum group multi-element solid solution according to any one of items 1 to 7 or the alloy nanoparticles according to any one of items [1] to

[10] , wherein the crystal structure is fcc or hcp. Item 9. A catalyst comprising, as a component, the platinum group multi-element solid solution according to any one of items 1 to 8 or the alloy nanoparticles according to any one of items [1] to

[10] . Item 10. A supported catalyst comprising the solid solution according to item 5 or the alloy nanoparticles according to any one of items [1] to

[10] . Item 11. The catalyst according to Item 10, which is a hydrogenation catalyst, a hydrogen oxidation catalyst, an oxygen reduction reaction (ORR) catalyst, an oxygen evolution reaction (OER) catalyst, a nitrogen oxide (NOx) reduction catalyst, a carbon monoxide (CO) oxidation catalyst, a dehydrogenation catalyst, a VVOC or VOC oxidation catalyst, an exhaust gas purification catalyst, a water electrolysis catalyst, or a hydrogen fuel cell catalyst. Item 12. A method for producing a platinum group multi-element solid solution, comprising the step of adding an aqueous solution containing five or six salts selected from the group consisting of Ru salts, Rh salts, Pd salts, Os salts, Ir salts, and Pt salts to a liquid reducing agent heated to 200°C to 300°C and reacting the solution to obtain a platinum group multi-element solid solution containing five or more platinum group elements. Item 13. A method for producing a supported catalyst, comprising the steps of adding an aqueous solution containing five or six salts selected from the group consisting of Ru salts, Rh salts, Pd salts, Os salts, Ir salts, and Pt salts to a liquid reducing agent heated to 200°C to 300°C and reacting the solution with a support, to obtain a support having a platinum group multi-element solid solution containing five or more platinum group elements. Effect of the Invention

[0020] According to the present invention, it is possible to provide novel alloy nanoparticles containing five or more elements, which may be supported on a support other than a carbon fiber support or a graphene support. [Brief description of the drawings]

[0021] [Figure 1] A method for producing platinum group hexavalent solid solution fine particles, which are the alloy nanoparticles of Example 1, will be described. [Diagram 2] Energy dispersive X-ray analysis (EDS) map of the platinum group hexavalent solid solution microparticles obtained in Example 1. The six platinum group elements (Ru, Rh, Pd, Os, Ir, Pt) are uniformly distributed in the microparticles, indicating that they are a solid solution. [Diagram 3] The following shows the (a) powder X-ray diffraction (PXRD) pattern, (b) EDS line analysis, and (c) quantitative analysis (at%) of the six platinum group elements by fluorescent X-ray analysis of the platinum group hexavalent solid solution fine particles obtained in Example 1. It was confirmed that all elements were solid-dissolved in each particle with almost the same composition. The crystal structure was a single fcc. [Figure 4] FIG. 4 is an in situ XRD pattern of the alloy nanoparticles of Example 1. [Diagram 5] Application of the platinum group hexavalent solid solution particles obtained in Example 1 to an ORR catalyst. [Figure 6] FIG. 6 is a graph showing a comparison of current density when the ethylene glycol oxidation electrocatalytic activity of the alloy nanoparticles obtained in Example 1 was measured with that of a commercially available Pt / C catalyst. [Figure 7-1] Fig. 7(a) is a graph showing a comparison of current density with that of single metal particles when the initial ethanol oxidation electrocatalytic activity of the alloy nanoparticles obtained in Example 1 was measured, and Fig. 7(b) is a graph showing a comparison of current density with that of a commercially available catalyst when the initial ethanol oxidation electrocatalytic activity of the alloy nanoparticles obtained in Example 1 was measured. [Figure 7-2] Fig. 7(c) is a graph showing a comparison of current densities at 0.45 V (left side) and 0.60 V (right side) when the initial ethanol oxidation electrocatalytic activity of the alloy nanoparticles obtained in Example 1 is measured. Fig. 7(d) is a graph showing a comparison of current densities with Au@PtIr / C when the initial ethanol oxidation electrocatalytic activity of the alloy nanoparticles obtained in Example 1 is measured. [Figure 7-3] FIG. 7(e) is a graph showing a comparison of current densities when the electrocatalytic activity of the alloy nanoparticles obtained in Example 1 was measured for the first and 50th time for ethanol oxidation. [Figure 8] FIG. 8 is a graph showing a comparison of current densities when the electrocatalytic activity of the alloy nanoparticles obtained in Example 3 for ethylene glycol oxidation was measured. [Figure 9-1] Fig. 9(a) is a graph showing a comparison of current densities when measuring the hydrogen evolution electrode catalytic activity when an aqueous H2SO4 solution is used for the alloy nanoparticles obtained in Example 3. Fig. 9(b) is a graph showing a comparison of current densities (mA cm-2) per electrode area when measuring the hydrogen evolution electrode catalytic activity when an aqueous H2SO4 solution is used for the alloy nanoparticles obtained in Example 3. [Figure 9-2]Fig. 9(c) is a graph showing a comparison of current densities when measuring the hydrogen generation electrode catalytic activity when an aqueous KOH solution is used for the alloy nanoparticles obtained in Example 3. Fig. 9(d) is a graph showing a comparison of current densities per electrode area when measuring the hydrogen generation electrode catalytic activity when an aqueous KOH solution is used for the alloy nanoparticles obtained in Example 3. [Figure 10] FIG. 10 is a STEM-EDS map of the alloy nanoparticles obtained in Example 4. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] The present invention will be described in detail below. The following description of the constituent elements may be based on representative embodiments or specific examples, but the present invention is not limited to such embodiments. In this specification, a numerical range expressed using "~" means a range including the numerical values ​​before and after "~" as the lower and upper limits.

[0023] [Alloy nanoparticles] The alloy nanoparticles of the present invention are alloy nanoparticles containing five or more elements, except when the alloy nanoparticles are directly supported on a carbon material support, in which case the carbon material support is graphene or carbon fiber. This configuration makes it possible to provide novel alloy nanoparticles containing five or more elements, which may be supported on a support other than a carbon fiber support or a graphene support. In this specification, alloy nanoparticles refer to alloy particles having an average particle size of 0.5 nm to 0.5 μm. It is preferable that the alloy nanoparticles have high material uniformity, and it is more preferable that they show a stable structure when heated and have high material uniformity. In particular, in a high-entropy alloy of five or more elements, the entropy S of the configuration is large, and therefore a uniform solid solution phase is stable at high temperatures due to the Gibbs free energy G=H-TS (where H is enthalpy, T is absolute temperature, and S is entropy). It is particularly preferable that the alloy nanoparticles show a stable structure and have high material uniformity when heated, for example, to 500K or more (preferably 700K or more, more preferably 900K or more). The material uniformity can be confirmed by in situ XRD or STEM-EDS. In addition, it is preferable that the alloy nanoparticles have constituent elements mixed at the atomic level. Specifically, when the alloy nanoparticles are used as an aggregate, it is preferable that the aggregate of the alloy nanoparticles contains 98% or more of the alloy nanoparticles of the present invention. Alternatively, it is preferable that any alloy nanoparticle constituting the aggregate of the alloy nanoparticles contains all of five or more elements as constituent elements. In addition, when the alloy nanoparticles are used as a catalyst containing a large number of alloy nanoparticles, it is preferable that the alloy nanoparticles contained in the catalyst contain 98% or more of the alloy nanoparticles of the present invention. Alternatively, it is preferable that any alloy nanoparticles contained in the catalyst contain all of five or more elements as constituent elements. The alloy nanoparticles of the present invention are preferably novel high-entropy alloy nanoparticles. Preferred embodiments of the present invention will now be described.

[0024] <Element> The alloy nanoparticles of the present invention are composed of five or more elements, preferably composed of 5 to 50 elements, more preferably composed of 5 to 25 elements, particularly preferably composed of 5 to 10 elements, and even more particularly preferably composed of 5 or 6 elements.

[0025] There is no particular limitation on the types of elements constituting the alloy nanoparticles of the present invention, however, it is preferable that the alloy nanoparticles do not have a combination of elements that will become an insulator (including an insulating oxide). The elements constituting the alloy nanoparticles may include a combination of elements that are not solid-soluble in the phase equilibrium diagram, or may not include a combination of elements that are not solid-soluble in the phase equilibrium diagram. That is, the alloy nanoparticles may be a combination of elements that cannot easily form a solid solution, or may be a combination of elements that can easily form a solid solution. Phase equilibrium diagrams are also called phase diagrams, state diagrams, alloy phase diagrams, etc., and all diagrams similar to these can be used as phase equilibrium diagrams in this specification. The phase equilibrium diagram may be a phase equilibrium diagram of two elements or a phase equilibrium diagram of three or more elements.

[0026] According to the present invention, it is possible to provide novel alloy nanoparticles containing five or more elements, in which a wide variety of elements are used and the constituent elements are mixed at the atomic level. Therefore, it is preferable that the elements constituting the alloy nanoparticles include a combination of elements that are not solid-soluble in a phase equilibrium diagram. In a phase equilibrium diagram, a combination of elements that does not form a solid solution is a combination that has an immiscible region of 30 atomic % or more at 1000°C and a pressure of 1 atm (normal pressure). It is more preferable that the elements constituting the alloy include a combination of elements that are not dissolved in a binary or ternary phase equilibrium diagram, and it is particularly preferable that the elements constituting the alloy include a combination of elements that are not dissolved in a binary or ternary phase equilibrium diagram. Of the combinations of two elements constituting the alloy, it is preferable to include a combination of elements that are not dissolved in at least one binary phase equilibrium diagram, and it is more preferable to include a combination of elements that are not dissolved in two or more binary phase equilibrium diagrams.

[0027] Among the combinations of two elements constituting the alloy nanoparticles, the combinations of elements that are not solid-soluble in at least one set of binary phase equilibrium diagrams include PdRu, AuIr, AgRh, AuRh, AuRu, CuRu, CuIr, AgCu, FeCu, AgIr, AgRu, MoRu, RhC, RuN, RuSn, PdOs, CuOs, AgOs, AuOs, CuRh, IrRh, IrPd, AgPt, AuPt, and other combinations of precious metals and most non-precious metals. Among the five or more elements constituting the alloy nanoparticles, the combinations of two elements that are not solid-soluble in a binary phase equilibrium diagram include the combination of PdRuRhOsIr and Pt, the combination of RuRhPdIr and Pt, and AuRuRhIrPt. Among the three combinations of elements constituting the alloy nanoparticles, combinations of elements that do not form a solid solution in at least one ternary phase equilibrium diagram include PdRuB, AuRuIr, RuRhAu, PtIrRu, FeRuRh, AuIrRh, and AgIrRh. Even for combinations of elements for which no binary phase equilibrium diagram is known, if there is a region of immiscibility of 30 atomic % or more at 1000 °C and 1 atm pressure, it is included in the combinations of elements that are not dissolved in a phase equilibrium diagram.

[0028] The elements constituting the alloy nanoparticles preferably contain an oxidation-resistant metal. An oxidation-resistant metal is a metal that maintains a metallic state (where the metallic structure, such as fcc, bcc, or hcp, can be confirmed) with a particle size of 50 nm or less, such as precious metals and Ni.

[0029] The alloy nanoparticles of the present invention preferably contain at least five elements selected from the group consisting of platinum group metals (Ru, Rh, Pd, Os, Ir, Pt), Ag, Au, Cd, Hg, In, Tl, Sn, Pb, Sb, Bi, Mo, W, Tc, Re, 3d metals (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn), Ga, Ge, As, H, B, Al, C, Si, N, P, Y, Zr, Nb, lanthanides, Hf and Ta. It is more preferable that the elements constituting the alloy nanoparticles of the present invention include at least five elements selected from the group consisting of platinum group metals (Ru, Rh, Pd, Os, Ir, Pt), Ag, Au, Cd, Hg, In, Tl, Sn, Pb, Sb, Bi, Mo, W, Tc, Re, 3d metals (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn), Ga, Ge, As, B, Al, C, Si, N, P, and lanthanides. Among these, it is particularly preferable that the elements constituting the alloy nanoparticles include at least five elements selected from the group consisting of platinum group metals (Ru, Rh, Pd, Os, Ir, Pt), Ag, Au, In, Tl, Sn, Bi, Mo, W, Re, 3d metals (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn), Ga, B, C, N, and lanthanides. It is particularly preferable that the elements constituting the alloy nanoparticles include at least five kinds selected from the group consisting of Ru, Rh, Pd, Os, Ir, Pt, Ag, Au, Cu, and Ni. It is even more particularly preferable that the elements constituting the alloy nanoparticles include at least five elements selected from the group consisting of the platinum group metals (Ru, Rh, Pd, Os, Ir, and Pt). However, an even more particularly preferred embodiment other than alloy nanoparticles consisting only of platinum group metals is one in which the elements constituting the alloy nanoparticles include at least five elements selected from the group consisting of Rh, Ru, Os, Ir, Pt, Au, Ag, Mo, W, Re, Fe, Co, Ni, Cu, C, N, and B, or an even more particularly preferred embodiment is one in which the elements constituting the alloy nanoparticles include at least five elements selected from the group consisting of Rh, Pd, Os, Ir, Pt, Au, Ag, Mo, W, Re, Fe, Co, Ni, Cu, C, N, and B.

[0030] On the other hand, the elements constituting the alloy nanoparticles preferably include at least one of the group consisting of platinum group metals (Ru, Rh, Pd, Os, Ir, Pt), Ag, Au, and Ni, and more preferably include two of them. Also, it is particularly preferable that the elements constituting the alloy nanoparticles include at least one of the group consisting of platinum group metals (Ru, Rh, Pd, Os, Ir, Pt), and more particularly preferable that the elements constituting the alloy nanoparticles include two of them. When the alloy nanoparticles of the present invention are a platinum group multi-component solid solution, the proportion of platinum group elements is preferably 5 atomic % or more, 10 atomic % or more, 15 atomic % or more, 20 atomic % or more, 25 atomic % or more, 30 atomic % or more, 35 atomic % or more, 40 atomic % or more, 45 atomic % or more, 50 atomic % or more, 55 atomic % or more, 60 atomic % or more, 65 atomic % or more, 70 atomic % or more, 75 atomic % or more, 80 atomic % or more, 85 atomic % or more, 90 atomic % or more, 95 atomic % or more, 98 atomic % or more, or 100 atomic %.

[0031] According to a preferred embodiment of the present invention, a stable high entropy solid solution containing platinum group elements (PGM-HEA) can be obtained. In a preferred embodiment of the alloy nanoparticles of the present invention, the alloy nanoparticles contain five or six platinum group elements, which makes it possible to control the adsorption energy to the catalyst substrate over a wide energy range, and provides an optimal surface for the target reaction, and is expected to have unprecedented properties. In addition, it becomes possible to use Os, which was previously difficult to handle.

[0032] A platinum group multi-element solid solution according to one preferred embodiment of the alloy nanoparticles of the present invention has the following formula (1): Ru p Rh q Pd r Os x Ir y Pt z (1) (p+q+r+x+y+z=1, 0≦p, q, r, x, y, z<1, either one of p, q, r, x, y, z is 0, or p, q, r, x, y, z are all numbers between 0 and 1.) It is expressed as:

[0033] In one preferred embodiment of the present invention, when five platinum group elements are contained, there are six specific cases as follows: (i) p = 0, 0 < q, r, x, y, z < 1, preferably 0.03 ≤ q ≤ 0.5, 0.03 ≤ r ≤ 0.5, 0.03 ≤ x ≤ 0.5, 0.03 ≤ y ≤ 0.5, 0.03 ≤ z ≤ 0.5, more preferably 0.05 ≤ q ≤ 0.4, 0.05 ≤ r ≤ 0.4, 0.05 ≤ x ≤ 0.4, 0.05 ≤ y ≤ 0.4, 0.05 ≤ z ≤ 0.4, even more preferably 0.1 ≤ q ≤ 0.3, 0.1 ≤ r ≤ 0.3, 0.1 ≤ x ≤ 0.3, 0.1 ≤ y ≤ 0.3, 0.1 ≤ z ≤ 0.3; (ii) q = 0, 0 < p, r, x, y, z < 1, preferably 0.03 ≤ p ≤ 0.5, 0.03 ≤ r ≤ 0.5, 0.03 ≤ x ≤ 0.5, 0.03 ≤ y ≤ 0.5, 0.03 ≤ z ≤ 0.5, more preferably 0.05 ≤ q ≤ 0.4, 0.05 ≤ r ≤ 0.4, 0.05 ≤ x ≤ 0.4, 0.05 ≤ y ≤ 0.4, 0.05 ≤ z ≤ 0.4, even more preferably 0.1 ≤ p ≤ 0.3, 0.1 ≤ r ≤ 0.3, 0.1 ≤ x ≤ 0.3, 0.1 ≤ y ≤ 0.3, 0.1 ≤ z ≤ 0.3; (iii) r = 0, 0 < p, q, x, y, z < 1, preferably 0.03 ≤ p ≤ 0.5, 0.03 ≤ q ≤ 0.5, 0.03 ≤ x ≤ 0.5, 0.03 ≤ y ≤ 0.5, 0.03 ≤ z ≤ 0.5, more preferably 0.05 ≤ p ≤ 0.4, 0.05 ≤ q ≤ 0.4, 0.05 ≤ x ≤ 0.4, 0.05 ≤ y ≤ 0.4, 0.05 ≤ z ≤ 0.4, even more preferably 0.1 ≤ p ≤ 0.3, 0.1 ≤ q ≤ 0.3, 0.1 ≤ x ≤ 0.3, 0.1 ≤ y ≤ 0.3, 0.1 ≤ z ≤ 0.3; (iv) x = 0, 0 < p, q, r, y, z < 1, preferably 0.03 ≤ p ≤ 0.5, 0.03 ≤ q ≤ 0.5, 0.03 ≤ r ≤ 0.5, 0.03 ≤ y ≤ 0.5, 0.03 ≤ z ≤ 0.5, more preferably 0.05 ≤ p ≤ 0.4, 0.05 ≤ q ≤ 0.4, 0.05 ≤ r ≤ 0.4, 0.05 ≤ y ≤ 0.4, 0.05 ≤ z ≤ 0.4, even more preferably 0.1 ≤ p ≤ 0.3, 0.1 ≤ q ≤ 0.3, 0.1 ≤ r ≤ 0.3, 0.1 ≤ y ≤ 0.3, 0.1 ≤ z ≤ 0.3; (v) y = 0, 0 < p, q, r, x, z < 1, preferably 0.03 ≤ p ≤ 0.5, 0.03 ≤ q ≤ 0.5, 0.03 ≤ r ≤ 0.5, 0.03 ≤ x ≤ 0.5, 0.03 ≤ z ≤ 0.5, more preferably 0.05 ≤ p ≤ 0.4, 0.05 ≤ q ≤ 0.4, 0.05 ≤ r ≤ 0.4, 0.05 ≤ x ≤ 0.4, 0.05 ≤ z ≤ 0.4, even more preferably 0.1 ≤ p ≤ 0.3, 0.1 ≤ q ≤ 0.3, 0.1 ≤ r ≤ 0.3, 0.1 ≤ x ≤ 0.3, 0.1 ≤ z ≤ 0.3; (vi) z = 0, 0 < p, q, r, x, y < 1, preferably 0.03 ≤ p ≤ 0.5, 0.03 ≤ q ≤ 0.5, 0.03 ≤ r ≤ 0.5, 0.03 ≤ x ≤ 0.5, 0.03 ≤ y ≤ 0.5, more preferably 0.05 ≤ p ≤ 0.4, 0.05 ≤ q ≤ 0.4, 0.05 ≤ r ≤ 0.4, 0.05 ≤ x ≤ 0.4, 0.05 ≤ y ≤ 0.4, even more preferably 0.1 ≤ p ≤ 0.3, 0.1 ≤ q ≤ 0.3, 0.1 ≤ r ≤ 0.3, 0.1 ≤ x ≤ 0.3, 0.1 ≤ y ≤ 0.3.

[0034] When containing six platinum group elements, (vii) 0 < p, q, r, x, y, z < 1, preferably 0.03 ≤ q ≤ 0.5, 0.03 ≤ r ≤ 0.5, 0.03 ≤ x ≤ 0.5, 0.03 ≤ y ≤ 0.5, 0.03 ≤ z ≤ 0.5, more preferably 0.05 ≤ p ≤ 0.4, 0.05 ≤ q ≤ 0.4, 0.05 ≤ r ≤ 0.4, 0.05 ≤ x ≤ 0.4, 0.05 ≤ y ≤ 0.4, 0.05 ≤ z ≤ 0.4, even more preferably 0.1 ≤ p ≤ 0.3, 0.1 ≤ q ≤ 0.3, 0.1 ≤ r ≤ 0.3, 0.1 ≤ x ≤ 0.3, 0.1 ≤ y ≤ 0.3, 0.1 ≤ z ≤ 0.3.

[0035] The crystal structure of the alloy nanoparticles is not particularly limited. Depending on the composition of the alloy nanoparticles and the overall average valence electron number, etc., the alloy may have a crystal structure such as fcc (face-centered cubic lattice), hcp (hexagonal close-packed lattice), bcc (body-centered cubic lattice), etc. The alloy nanoparticles of one preferred embodiment of the present invention are solid solutions with an fcc structure or an hcp structure. However, when the alloy nanoparticles become an ordered alloy (i.e., have an ordered phase), form an amorphous structure, or form an intermetallic compound, they can maintain structures other than those mentioned above. When elements with significantly different atomic radii or electronegativity are mixed, an intermetallic compound may be formed. In the case of an intermetallic compound, the atomic arrangement is not random, but the alloy becomes an ordered alloy. Examples of combinations of two types of elements that make up the alloy nanoparticles include RhC, PdB, a combination of a noble metal and a transition metal, and a combination of a noble metal and a typical metal, such as RuSn. However, in the case of an ordered alloy with many constituent elements, the atomic sites in the ordered alloy may be randomly composed of specific multiple elements. For example, elements with large atomic radii may be randomly arranged at the atomic sites of elements with large atomic radii, and elements with small atomic radii may be randomly arranged at the atomic sites of elements with small atomic radii. Among the six elements of the platinum group, four elements are fcc (face-centered cubic lattice), namely Rh, Pd, Ir, and Pt, and two elements are hcp (hexagonal close-packed lattice), namely Os and Ru. The alloy nanoparticles of one preferred embodiment of the present invention are solid solutions of fcc structure containing elements of the platinum group. The alloy nanoparticles of another preferred embodiment of the present invention are solid solutions of hcp structure containing elements of the platinum group. Even when the six elements of the platinum group are used, the proportion of the fcc structure may be high as in the original proportion, or the proportion of the hcp structure may be high.

[0036] Since the alloy nanoparticles of the present invention have high uniformity of solid solution, it is preferable that five or more elements are uniformly distributed and solid-dissolved. Here, "uniformly distributed" means that there is no bias in the distribution of five or more elements, and it is preferable that the distribution of each element (atom) is not biased by an energy dispersive X-ray analysis map. It is also preferable that a single fcc or hcp pattern can be confirmed by powder X-ray diffraction (XRD). Note that even if fcc and hcp coexist, if the interatomic distances of both structures are equal, the constituent elements are considered to be uniformly distributed in each structure. At that time, the metal compositions of both fcc and hcp structures are equivalent, so the interatomic distances are equal to each other.

[0037] (percentage of elements) The alloy nanoparticles of the present invention are not particularly limited in terms of the ratio of each element constituting the alloy nanoparticles, i.e., the average composition of the alloy nanoparticles of the present invention is not particularly limited. In one preferred embodiment of the present invention, the upper limit of the proportion of the most abundant element when the entire alloy nanoparticle is taken as 100 atomic % is 80 atomic % or less, 70 atomic % or less, 60 atomic % or less, 50 atomic % or less, 45 atomic % or less, 40 atomic % or less, or 35 atomic % or less. In one preferred embodiment of the present invention, the lower limit of the proportion of the smallest element when the entire alloy nanoparticle is taken as 100 atomic % is 1 atomic % or more, 5 atomic % or more, 9 atomic % or more, 10 atomic % or more, or 15 atomic % or more. Furthermore, the element with the highest atomic ratio is preferably 1 to 500 times, more preferably 1 to 5 times, even more preferably 1 to 3 times, particularly preferably 1 to 2 times, and most preferably 1 to 1.5 times that of the element with the lowest atomic ratio. When the alloy nanoparticles of the present invention are high-entropy solid solution alloys, it is preferable that the atomic ratios of five or more elements are as close as possible, and in particular, it is more preferable that the atomic ratios of five or six platinum group elements are as close as possible.

[0038] In one preferred embodiment of the present invention, the alloy nanoparticles of the present invention contain Os. Among the platinum group elements, Os is easily oxidized and can become a toxic oxide such as OsO4, but by forming a solid solution alloy with the other four or five platinum group elements, the generation of a toxic oxide such as OsO4 can be suppressed.

[0039] <Shape of alloy nanoparticles> The alloy nanoparticles of the present invention may have various shapes such as a sphere, an ellipsoid, a rectangular tube, a cylinder, a cube, a rectangular parallelepiped, or a scale, and are preferably spherical or ellipsoidal. The average particle size of the alloy nanoparticles is preferably 0.5 to 50 nm, more preferably 0.5 to 30 nm, and further preferably 1.0 to 20 nm. The average particle size of the particles can be calculated as an arithmetic mean by direct observation with, for example, a transmission electron microscope (TEM). The above average particle size of the particles is the average particle size of the alloy nanoparticles, and in the case where the alloy nanoparticles are supported on a carrier, it is the average particle size of the alloy nanoparticle portion other than the carrier. The particle size distribution of the particles is preferably within the range of the average particle size ±0.1 to 15 nm, more preferably ±0.3 to 15 nm, and particularly preferably ±0.5 to 10 nm.

[0040] The alloy nanoparticles of the present invention may be in the form of an aggregate of alloy nanoparticles, or may be in the form of being supported on a carrier.

[0041] (Aggregation of alloy nanoparticles) The aggregate of alloy nanoparticles refers to a powder consisting of a large number of alloy nanoparticles. For example, it is preferable that the assembly of alloy nanoparticles does not substantially contain a carrier or the like, or is not supported on a carrier. The collection of alloy nanoparticles may include a protective agent, such as a polymer. Furthermore, the aggregate of alloy nanoparticles may have an oxide coating or the like on the surface of each alloy nanoparticle. The assembly of alloy nanoparticles may contain impurity particles in addition to the alloy nanoparticles of the present invention, but the assembly of alloy nanoparticles preferably contains 90% by number or more of the alloy nanoparticles of the present invention, more preferably 98% by number or more, particularly preferably 99% by number or more, and even more particularly preferably 100% by number. The alloy nanoparticle aggregate may contain alloy nanoparticles in which all of the five elements contained in the compound used for production are dissolved, as well as alloy nanoparticles in which only some of the five elements contained in the compound used for production are dissolved. However, it is preferable that the proportion of alloy nanoparticles in which the same elements are dissolved is high. Of the alloy nanoparticles constituting the alloy nanoparticle aggregate, it is preferable that 90% or more by number, more preferably 98% or more by number, particularly preferably 99% or more by number, and even more particularly preferably 100% by number, of the alloy nanoparticles containing all of the five or more elements as constituent elements. The ratio of each particle contained in the alloy nanoparticle aggregate is determined within a visual field in which a part of the alloy nanoparticle aggregate is observed. For example, it is preferable that the alloy nanoparticles constituting the alloy nanoparticle aggregate, which contain all of five or more elements as constituent elements, are contained within the above range within a certain visual field in which a part of the alloy nanoparticle aggregate is observed. However, it is more preferable to determine the ratio of each particle contained in the alloy nanoparticle aggregate as an average within a plurality of visual fields in which a part of the alloy nanoparticle aggregate is observed.

[0042] (Carrier) The support includes, when the alloy nanoparticles are directly supported on a carbon material support, except when the carbon material support is graphene or carbon fiber. Specific examples of the support used include oxides, nitrides, carbides, elemental carbon (excluding graphene or carbon fiber), and elemental metals. Examples of oxides used for the support include oxides such as silica, alumina, ceria, titania, zirconia, and niobia, and composite oxides such as silica-alumina, titania-zirconia, ceria-zirconia, and strontium titanate. Examples of elemental carbon include activated carbon, carbon black, graphite, and carbon nanotubes. The nitrides include boron nitride, silicon nitride, gallium nitride, indium nitride, aluminum nitride, zirconium nitride, vanadium nitride, tungsten nitride, molybdenum nitride, titanium nitride, and niobium nitride. The carbides include silicon carbide, gallium carbide, indium carbide, aluminum carbide, zirconium carbide, vanadium carbide, tungsten carbide, molybdenum carbide, titanium carbide, niobium carbide, and boron carbide. Examples of elemental metals include pure metals such as iron, copper, and aluminum, and alloys such as stainless steel. In the present invention, when the alloy nanoparticles are directly supported on the carbon material support, the carbon material support is not limited to graphene or carbon fiber. That is, the support is preferably a non-carbon fiber support (a material that is not made of elemental carbon) or a particulate carbon support, and a non-carbon material support is more preferable from the viewpoint that the support does not burn in a high-temperature oxidizing atmosphere, and an oxide support is particularly preferable. Activated carbon or the like can be used as the particulate carbon support.

[0043] <Protective agent> The alloy nanoparticles of the present invention may be coated with a protective agent (preferably a surface protective agent) such as polymers such as polyvinylpyrrolidone (PVP) and polyethylene glycol (PEG), amines such as oleylamine, and carboxylic acids such as oleic acid.

[0044] <Method of manufacturing alloy nanoparticles> The method for producing alloy nanoparticles of the present invention includes a step of adding an aqueous solution containing salts of five or more elements to a liquid reducing agent heated to 200°C to 300°C and reacting the solution to obtain alloy nanoparticles containing five or more elements, except when the alloy nanoparticles are directly supported on a carbon material support, in which case the carbon material support is graphene or carbon fiber. The method for producing alloy nanoparticles of the present invention is preferably a method for producing a multi-component platinum group solid solution, comprising the step of adding an aqueous solution containing five or six salts selected from the group consisting of Ru salts, Rh salts, Pd salts, Os salts, Ir salts and Pt salts to a liquid reducing agent heated to 200°C to 300°C and reacting them to obtain a multi-component platinum group solid solution containing five or more platinum group elements. A preferred embodiment of the method for producing alloy nanoparticles will now be described.

[0045] (Preparation of raw material solution) The method for producing alloy nanoparticles preferably includes a step of preparing a solution (raw material solution) of compounds containing each of the elements that constitute the alloy nanoparticles. Each element constituting the alloy nanoparticles is dissolved in a solvent. Examples of polar solvents that can be used include water, alcohols (methanol, ethanol, isopropanol, etc.), polyols (ethylene glycol, diethylene glycol, triethylene glycol, propylene glycol, glycerin, etc.), polyethers (polyethylene glycol, etc.), acetonitrile, acetone, dimethylformamide, dimethylsulfoxide, N-methylpyrrolidone, etc. Among these, water and alcohol are preferred. As the non-polar solvent, hexane, benzene, toluene, diethyl ether, chloroform, ethyl acetate, THF, etc. can be used. As the raw material solution, it is preferable to use an aqueous solution containing a water-soluble salt of a metal element or a water-soluble salt of an element other than a metal, but in the case of a combination of non-polar metal salts, a non-polar solvent containing a non-polar metal salt may be used. By adjusting the molar ratio of the compounds containing each element, the molar ratio of each element in the resulting alloy nanoparticles can be adjusted.

[0046] Water-soluble salts of elements include: Known water-soluble salts (e.g., sulfates, nitrates, acetates, chlorides, bromides, iodides, potassium cyanates, sodium cyanates, hydroxides, carbonates, etc.) of platinum group metals (Ru, Rh, Pd, Os, Ir, Pt), Ag, Au, Cd, Hg, In, Tl, Sn, Pb, Sb, Bi, Mo, W, Tc, Re, 3d metals (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn), Ga, Ge, As, B, Al, C, Si, N, P, Y, Zr, Nb, lanthanides, Hf and Ta. In particular, the following are preferred: Ru: RuCl3, RuCl3·nH2O, RuBr3, K2RuCl5(NO), and other ruthenium halides, ruthenium nitrate, and Ru3(CO) 12, Ru(NO)(NO3) a (OH) b , Ru(acac)3, etc. Rh: Rhodium acetate, rhodium nitrate, rhodium chloride (RhCl3), RhCl3·3H2O, etc. Pd: K2PdCl4, Na2PdCl4, K2PdBr4, Na2PdBr4, palladium nitrate, etc. Os: Osmium halides such as OsCl3, OsBr3, etc. Ir: iridium chloride, iridium acetylacetonate (acac; it is preferable to dissolve the acac system in a non-polar solvent), potassium iridium cyanate, potassium iridate, H2IrCl6, etc. Pt: K2PtCl4, (NH4)2K2PtCl4, (NH4)2PtCl6, Na2PtCl6, H2PtCl6, Pt(acac)2 etc. Au: AuCl3, HAuCl4, K[AuCl4], Na[AuCl4], K[Au(CN)2], K[Au(CN)4], AuBr3, HAuBr4, etc. Ag: AgNO3, Ag(CH3COO), etc. In: InCl3 4H2O, etc. Sn: SnCl3·2H2O, Sn(ethyhex)2, etc. Mo: Mo(CO)6, etc. Cu: Cu(NO3)2, CuSO4, Cu(CH3COO)2, CuCO3, CuCl, CuCl2, etc. Fe: FeCl3·6H2O, FeCl2·4H2O, Fe(NO3)3, etc. Co: CoCl2 6H2O, etc. Ni: NiCl2 6H2O, etc. B: BH3, etc. N: Ru(NO)(NO3) a (OH) b , ammonia, nitric acid, hydrazine, etc.

[0047] (Ultrasonic Treatment) It is preferable to include a step of ultrasonically treating a solution (raw material solution) of compounds containing each element constituting the alloy nanoparticles. However, as an alternative to the step of ultrasonically treating the raw solution, if there is a method capable of preparing a uniform raw solution at a speed equivalent to that of ultrasonically treating the raw solution, that method may be used.

[0048] (Preparation of reducing agent) The method for producing alloy nanoparticles preferably includes a step of preparing a reducing agent. The reducing agent is preferably a liquid reducing agent. Examples of liquid reducing agents include polyhydric alcohols such as ethylene glycol, glycerin, diethylene glycol, and triethylene glycol; lower alcohols such as methanol, ethanol, n-propanol, isopropanol, n-butanol, and isobutanol under high pressure; water-containing alcohols such as water-containing ethanol under high pressure; a THF solution of BH3 (THF complex); or hydrazine, a NaBH4 solution, and a sodium naphthalenide solution. In addition, each element constituting the alloy nanoparticles may be used as a reducing agent. For example, a THF solution of BH3 (THF complex) may be used as a reducing agent to form alloy nanoparticles containing the B element. When mixing and heating are performed under pressure using a flow device described later, a reducing agent with a low boiling point can be preferably used. The boiling point of the lower alcohol, which is a preferred reducing agent, is from room temperature to about 130°C, more preferably about 40 to 120°C, and even more preferably about 60 to 100°C. Since these reducing agents have a low boiling point under normal pressure, it is difficult to reduce compounds (metal compounds, etc.) containing each element constituting the alloy nanoparticles to form alloy nanoparticles composed of metals that do not form a solid solution in the phase equilibrium diagram. By reacting at high temperature under pressure, they acquire reducing properties and can function as a reducing agent for obtaining alloy nanoparticles composed of metals that do not form a solid solution in the phase equilibrium diagram. The reducing agent is used in an amount of at least one equivalent, preferably an excess amount, for reducing the compounds (preferably water-soluble salts) containing the elements that constitute the alloy nanoparticles.

[0049] (mixture) The method for producing alloy nanoparticles preferably includes a step of mixing raw material solutions to obtain a mixed solution. It is preferable to mix a reducing agent into the raw material solution before or when the mixed solution is heated. The method for producing alloy nanoparticles preferably includes a step of heating the mixed solution to cause a reaction. The reaction time during heating can be about 1 minute to 12 hours. The heating is preferably carried out with stirring. The reaction temperature during heating is preferably about 170 to 300° C., more preferably about 180 to 250° C. When a reducing agent such as NaBH4 is used, it may be used at room temperature or after cooling.

[0050] The method of mixing or heating is not particularly limited. For example, either or both of the reducing agent and the mixed solution may be heated before mixing. In addition, the method for producing alloy nanoparticles preferably includes a step of heating the reducing agent, and the reducing agent heated in this step is preferably mixed with the raw material solution to cause a thermal reaction. For example, the reducing agent may be heated, and the mixed solution may be mixed by dropping it with a pump (syringe pump) or spraying it with a spray device. Alternatively, the ultrasonically treated raw material solution and a solution of a reducing agent may be supplied to a reaction vessel, and mixed and heated using a flow device (flow reactor) that heats and reacts under pressure. When pressurizing with a flow device, the pressure of the raw material solution and the reducing agent solution is preferably about 0.1 to 20 MPa, more preferably about 0.2 to 10 MPa, and particularly preferably about 0.2 to 9 MPa. The pressure in the reaction vessel is preferably about 0.1 to 20 MPa, more preferably about 0.2 to 10 MPa, and particularly preferably about 0.2 to 9 MPa. The pressure in the reaction vessel is about the same as the back pressure of the back pressure valve installed downstream of the reaction vessel, and can be controlled by adjusting the back pressure valve. The temperature (reaction temperature) of the reaction vessel when pressurizing is about 100 to 400°C, preferably about 150 to 300°C, and more preferably about 180 to 240°C.

[0051] (Separation of alloy nanoparticles) The method for producing alloy nanoparticles preferably includes a step of separating and collecting a precipitate from the solution after the heating reaction. This process makes it possible to obtain alloy nanoparticles that contain five or more metals in a solid solution state. Methods for separating and isolating the precipitate include drying under reduced pressure, centrifugation, filtration, sedimentation, reprecipitation, and separation using a powder separator (cyclone). Before separating out the precipitate, it is preferable to allow the reaction solution to cool or to rapidly cool it.

[0052] By adding a protective agent to the mixed solution, the reducing agent, or a reaction solution in which these are mixed, it is possible to obtain particles (preferably nanoparticles) in which aggregation is suppressed. When a protective agent is used, the protective agent is contained in a reaction solution obtained by mixing a mixture of the raw material solutions and a reducing agent at a concentration of preferably 0.01 to 100 times, more preferably 0.5 to 50 times, and even more preferably 1 to 10 times the total amount of metal compounds in terms of mass ratio. The protective agent may be contained in the raw material solution, the reducing agent, or both the raw material solution and the reducing agent.

[0053] Furthermore, by making a support coexist in the mixed solution, the reducing agent, or a reaction solution in which these are mixed, it is possible to obtain a supported catalyst in which alloy nanoparticles are supported on a support. By making the support coexist in the reaction solution, a supported catalyst in which the multi-element solid solution is supported on the support can be obtained. When the multi-element solid solution is in the form of fine particles, a supported catalyst in which aggregation of the fine particles is suppressed can be obtained by adding a protective agent simultaneously with the support to the reaction solution for producing the multi-element solid solution fine particles.

[0054] On the other hand, neither a protective agent nor a carrier may be added to the mixed solution, the reducing agent, or a reaction solution obtained by mixing these. In this way, it is possible to obtain alloy nanoparticles that are an aggregate of alloy nanoparticles. In this case, the alloy nanoparticles, which are an aggregate of the alloy nanoparticles, and the support are mixed in a solution or the powders are mixed in a non-solvent system or a solvent system, and then molded to obtain a supported catalyst in which the alloy nanoparticles are supported on the support. When a solvent is used, the mixture may be filtered and then dried as necessary.

[0055] [catalyst] The alloy nanoparticles of the present invention can be used as catalysts that exhibit excellent performance. There is no particular limitation on the shape of the alloy nanoparticles when used as catalysts. The catalyst may be used as a supported catalyst.

[0056] There is no particular limit to the catalytic reactions in which the alloy nanoparticles of the present invention exhibit excellent catalytic performance, but examples of such reactions include those known to use catalysts containing platinum group elements. Specific examples include chemical reactions such as reduction reactions including hydrogenation reactions, dehydrogenation reactions, oxidation reactions including combustion, and coupling reactions. In addition, by utilizing these catalytic performances, the alloy nanoparticles can be suitably used in various processes, devices, and other applications. There is no particular limit to the applications in which the alloy nanoparticles can be suitably used, but examples of such applications include catalysts for hydrogen generation reactions (HER), catalysts for hydrogenation reactions, catalysts for hydrogen oxidation reactions, catalysts for oxygen reduction reactions (ORR), catalysts for oxygen generation reactions (OER), catalysts for nitrogen oxide (NOx) reduction reactions, catalysts for carbon monoxide (CO) oxidation reactions, catalysts for dehydrogenation reactions, catalysts for VVOC or VOC oxidation reactions, catalysts for exhaust gas purification, catalysts for water electrolysis reactions, and catalysts for hydrogen fuel cells. EXAMPLES

[0057] The present invention will be described in more detail below with reference to examples and comparative examples. The materials, amounts used, ratios, processing contents, processing procedures, etc. shown in the following examples can be appropriately changed without departing from the spirit of the present invention. Therefore, the scope of the present invention should not be interpreted as being limited by the specific examples shown below.

[0058] [Device] In the examples, the following equipment was used: (i-1)Powder X-ray Diffraction (PXRD) Rigaku Miniflex600 (Cu Kα) (i-2)PXRD SPring-8 BL02B2 (measurement wavelength: 0.62938(6) angstroms) (ii)Energy-dispersive x-ray spectroscopy in scanning transmission electron microscopy (STEM-EDS) JEOL JEM-ARM200CF (accelerating voltage: 120 kV) (iii) X-ray fluorescence analysis (XRF) X-ray fluorescence analyzer ZSX Primus IV

[0059] [Example 1]: Production of platinum group hexavalent solid solution particles <Preparation of alloy nanoparticles> 300 ml of triethylene glycol (TEG) was heated and stirred at 230°C, and a metal ion mixture solution (40 ml) of ion exchange water solution of K2PdCl4 (0.167 mmol), RuCl3·nH2O (0.167 mmol), RhCl3·3H2O (0.167 mmol), OsCl3·3H2O (0.167 mmol), IrCl4·xH2O (0.167 mmol), and K2[PtCl4] (0.167 mmol) was sprayed into the solution, which was then maintained at 230°C for 5 minutes and then allowed to cool. The resulting precipitate was separated by centrifugation (Fig. 1). For a part of the separated platinum group six - element solid - solution nanoparticles in the solid - solution state (alloy nanoparticles of Example 1; also referred to as PGM - HEA), they are shown in the EDS map (Figure 2), powder X - ray diffraction (PXRD) pattern (Figure 3(a)) and EDS line analysis (Figure 3(b)). Also, XRF analysis of the nanoparticles was performed to calculate the metal composition of the six platinum group elements (Figure 3(c)). From Figure 2, as far as observed in the STEM image, it was confirmed that all elements were dissolved in each alloy nanoparticle. That is, within the range of the field of view confirmed in this example, it can be seen that the aggregate of alloy nanoparticles contains 100% of alloy nanoparticles in which all five elements contained in the compound used in the production as constituent elements are dissolved. Also, it can be seen that any alloy nanoparticle constituting the aggregate of the alloy nanoparticles of the present invention contains all five elements contained in the compound used in the production as constituent elements. From Figure 3(a), Figure 3(b) and Figure 3(c), it was confirmed that all elements were dissolved in each alloy nanoparticle with almost the same composition. The crystal structure of the alloy nanoparticles was a single fcc.

[0060] <Elemental analysis by STEM - EDS> Perform STEM - EDS analysis on the alloy nanoparticles of Example 1. Elemental analysis by line scan using multiple fields of view of a scanning transmission electron microscope is performed to calculate the metal composition of six elements. The average composition is obtained.

[0061] <XRD analysis> In - situ XRD analysis was performed on the obtained alloy nanoparticles of Example 1 (measurement wavelength at SPring - 8 BL02B2: 0.62938(6) Å). The obtained results are shown in Figure 4. From Figure 4, it was found that the alloy nanoparticles of Example 1 showed a stable structure up to 923K, and both the material uniformity and the solid - solution uniformity were high. In particular, it was found that the alloy nanoparticles of Example 1 had better material uniformity than the non - uniform particles obtained by the method described in Adv. Funct. Mater. 2019, 1905933.

[0062] <tem> A TEM photograph of the alloy nanoparticles of Example 1 obtained was taken. The average particle size of the alloy nanoparticles of Example 1 was 3.1 ± 0.6 nm.

[0063] [Example 2]: Production of Platinum Group Quinary System Solid Solution Fine Particles <Preparation of Alloy Nanoparticles> 300 ml of triethylene glycol (TEG) was heated and stirred at 230 °C, and a metal ion mixed solution, which was an ion-exchanged aqueous solution (40 ml) of K2PdCl4 (0.3 mmol), RuCl3·nH2O (0.3 mmol), RhCl3·3H2O (0.2 mmol), IrCl4·xH2O (0.1 mmol), and K2[PtCl4] (0.1 mmol), was sprayed and added thereto. After maintaining at 230 °C for 5 minutes, it was allowed to cool, and the resulting precipitate was separated by centrifugation to obtain platinum group quinary system solid solution fine particles RuRhPdIrPt (Ru:Rh:Pd:Ir:Pt (mol%) = 28.9:19.6:32.0:10.2:9.30) which were the alloy nanoparticles of Example 2.

[0064] <Elemental Analysis by STEM-EDS> A part of the STEM-EDS analysis of all the alloy nanoparticles obtained in Example 2 was carried out in the same manner as in Example 1. The average composition was determined. As long as observed in the STEM image, it was confirmed that all the elements were solid-solved in each of the alloy nanoparticles of the present invention. That is, within the range of the visual field confirmed in this example, it can be seen that the aggregate of the alloy nanoparticles contains 100% of alloy nanoparticles in which all five kinds of elements contained in the compound used in the production as constituent elements are solid-solved. Further, it can be seen that any of the alloy nanoparticles constituting the aggregate of the alloy nanoparticles of the present invention contains all five kinds of elements contained in the compound used in the production as constituent elements.

[0065] <tem> Photographs of the alloy nanoparticles of Example 2 obtained were taken by TEM. The average particle size of the alloy nanoparticles of Example 2 was 6.3 ± 1.1 nm.

[0066] [Reference Example 1] 300 ml of triethylene glycol (TEG) was heated and stirred at 230 °C. An aqueous solution in which K2PdCl4 (0.8 mmol) and RuCl3·nH2O (0.2 mmol) were dissolved in ion-exchanged water (40 ml) was sprayed and added thereto, and the mixture was maintained at 230 °C for 5 minutes and then allowed to cool. The resulting precipitate was separated by centrifugation to obtain platinum group binary solid solution fine particles PdRu (Pd:Ru (mol%) = 81.7:18.3).

[0067] [Test Example 1] <Manufacture of Electrode> A solid solution electrode catalyst (solid solution / C: metal amount 20 wt%) in which the alloy nanoparticles obtained in Examples 1 to 2 and Reference Example 1 were supported on carbon particles was manufactured. The synthesized alloy nanoparticles were mixed in water with carbon particles (Vulcan-XC-72R) at a ratio of 20 wt%, supported on carbon by ultrasonic dispersion, recovered by centrifugation, and dried to produce a catalyst powder. 2.5 mg of this catalyst powder was dispersed in a mixed solution of 6.55 ml of isopropanol and 3.44 ml of water, and 0.01 ml of a 5 wt% Nafion (registered trademark) solution (manufactured by Fujifilm Wako Pure Chemical Corporation) was added and mixed well to prepare a catalyst ink. By applying an appropriate amount of this ink to a working electrode such as a rotating ring disk electrode or a glassy carbon electrode, a catalyst electrode was fabricated. <ORR Catalytic Activity> Current measuring device: Potentiostat (ALS760E manufactured by BAS) Measurement method: A rotating ring-disk electrode in which the alloy nanoparticles of Examples 1-2 and Reference Example 1 were supported on carbon particles was used as the cathode, and a three-electrode cell (counter electrode: platinum wire, reference electrode: silver-silver chloride electrode (Ag / AgCl), electrolyte: 0.1 M HClO4 aqueous solution, 25°C, oxygen saturated) was used to measure the current value I when the potential E was swept from 1.0 V to -0.0 V (vs. RHE) at 5 mV / s, and the ORR catalytic activity was evaluated. The results are shown in Figure 5. From Figure 5, it was found that the quinary alloy nanoparticles obtained in Example 2 showed higher activity than the binary alloy nanoparticles obtained in Reference Example 1, and furthermore, the hexameric alloy nanoparticles obtained in Example 1 showed higher activity.

[0068] [Test Example 2] <Ethylene glycol oxidation electrocatalytic reaction> Current measuring device: Potentiostat (BAS ALS760E) Measurement method: A glassy carbon electrode with the alloy nanoparticles of Example 1 supported on carbon particles was used as the anode, and a three-electrode cell (counter electrode: platinum wire, reference electrode: silver-silver chloride electrode (Ag / AgCl), electrolyte: ethylene glycol, 25°C, oxygen saturated) was used to sweep the potential E from 0.30 V to 0.70 V (vs. RHE) at 5 mV / s, measuring the current density jgeo (unit: mA / cm 2 ) was measured to evaluate the electrocatalytic activity of ethylene glycol oxidation. The results are shown in Figure 6. From Figure 6, it was found that the alloy nanoparticles (PGM-HEA) of Example 1 exhibited higher activity than the commercially available Pt / C catalyst (manufactured by Alfa Acer).

[0069] [Test Example 3] <Electrocatalytic reaction of ethanol oxidation> Current measuring device: Potentiostat (BAS ALS760E) Measurement method: A glassy carbon electrode with the alloy nanoparticles of Example 1 supported on carbon particles was used as the anode, and a three-electrode cell (counter electrode: platinum wire, reference electrode: silver-silver chloride electrode (Ag / AgCl), electrolyte: ethanol, 25°C, oxygen saturated) was used to sweep the potential E from -0.0 V to 1.10 V (vs. RHE) at 20 mV / s, measuring the current density jgeo (unit: mA / cm 2 ) was measured, and the ethanol oxidation electrode catalytic activity was evaluated 50 times. The results of the initial ethanol oxidation electrode catalytic activity are shown in FIGS. 7(a) to 7(d). From FIGS. 7(a), 7(b), and 7(c), it was found that the alloy nanoparticles (PGM-HEA) of Example 1 exhibited higher activity than Pd. From FIG. 7(d), it was found that the alloy nanoparticles (PGM-HEA) of Example 1 exhibited higher activity than the previously reported highest activity catalyst Au@PtIr / C (J. Am. Chem. Soc. 2019, 141, 24, 9629-9636). It was found that the reaction initiation at low potential suggested a 12-electron reaction. Also, the results of comparing the initial ethanol oxidation electrode catalytic activity with the ethanol oxidation electrode catalytic activity after 50 times are shown in FIG. 7(e). From FIG. 7(e), it was found that the alloy nanoparticles (PGM-HEA) of Example 1 also had high durability. In addition, the durability was also high when compared with Pd particles not shown in the figure.

[0070] [Example 3]: Preparation of Platinum Group 5-Element Solid Solution Fine Particles (2) <Preparation of Alloy Nanoparticles> 300 ml of triethylene glycol (TEG) was heated and stirred at 230 °C, and a metal ion mixed solution, which was an ultrapure aqueous solution (50 ml) of K2PdCl4 (0.2 mmol), RuCl3·nH2O (0.2 mmol), RhCl3·nH2O (0.2 mmol), H2IrCl6 (0.2 mmol), and K2[PtCl4] (0.2 mmol), was sprayed and added thereto. After maintaining at 230 °C for 10 minutes, it was allowed to cool to room temperature, and the resulting precipitate was separated by centrifugation to obtain the alloy nanoparticles of Example 3.

[0071] <Elemental Analysis by STEM-EDS> The STEM-EDS analysis of all some of the alloy nanoparticles obtained in Example 3 was carried out in the same manner as in Example 1. The average composition was determined. As far as the STEM image is concerned, it was confirmed that all elements of the alloy nanoparticles of the present invention are dissolved in each alloy nanoparticle. That is, within the field of view confirmed in this embodiment, it is understood that the assembly of alloy nanoparticles contains 100% by number of alloy nanoparticles in which all five elements contained in the compound used in the production as constituent elements are dissolved. It is also understood that any alloy nanoparticle constituting the assembly of the alloy nanoparticles of the present invention contains all five elements contained in the compound used in the production as constituent elements.

[0072] <tem> A TEM photograph was taken of the obtained alloy nanoparticles of Example 3. The average particle size of the alloy nanoparticles of Example 3 was 5.5±1.2 nm.

[0073] [Test Example 4] <Electrocatalytic activity for the oxidation of ethylene glycol> An electrode catalyst (alloy / C: metal amount 20 wt%) was produced in which the obtained alloy nanoparticles of Example 3 were supported on carbon particles. The amount of nanoparticles was 0.05 mg. Current measuring device: Potentiostat (BAS ALS760E) Measurement method: A glassy carbon electrode with the alloy nanoparticles of Example 3 supported on carbon particles was used as the anode, and a three-electrode cell (counter electrode: platinum wire, reference electrode: silver-silver chloride electrode (Ag / AgCl), electrolyte: ethylene glycol, 25°C, oxygen saturated) was used to sweep the potential E from 0.30 V to 0.70 V (vs. RHE) at 5 mV / s, measuring the current density jgeo (unit: mA / cm 2 ) was measured to evaluate the electrocatalytic activity of ethylene glycol oxidation. The results are shown in Figure 8. From Figure 8, it was found that the quinary alloy nanoparticles of Example 3 exhibited higher activity than a commercially available Pt / C catalyst (manufactured by Alfa Acer).

[0074] [Test Example 5] <Hydrogen generation electrode catalytic reaction> An electrode catalyst (alloy / C: metal amount 20 wt%) was produced in which the obtained alloy nanoparticles of Example 3 were supported on carbon particles. The amount of nanoparticles was 0.05 mg. Current measuring device: Potentiostat (BAS ALS760E) Measurement method: A rotating ring-disk electrode with the alloy nanoparticles of Example 3 supported on carbon particles was used as the cathode, and a three-electrode cell (counter electrode: platinum wire, reference electrode: silver-silver chloride electrode (Ag / AgCl), electrolyte: 0.05 M H2SO4 aqueous solution or 1.0 M KOH aqueous solution, 25°C, oxygen saturated) was used to measure the current density jgeo (unit: mA / cm) when the potential E was swept at 5 mV / s from 0.0 V to -0.12 V in Figure 9(a) and from 0.0 V to -0.4 V (vs. RHE) in Figure 9(c). 2 ) was measured to evaluate the hydrogen evolution electrode catalytic activity. Figures 9(a) and 9(b) show the results when an H2SO4 aqueous solution was used. Figures 9(c) and 9(d) show the results when an KOH aqueous solution was used. FIG. 9 shows that the quinary alloy nanoparticles of Example 3 are more active than the single metals in both acidic and alkaline conditions, and also have extremely high chemical durability.

[0075] [Example 4]: Production of nine-element FeCoNiCuRuRhPdIrPt solid solution particles using a flow reactor <Preparation of alloy nanoparticles> An aqueous hydrochloric acid solution was prepared by adding 0.14 ml of HCl to 50 ml of ion-exchanged water. Nine metal salt solutions with a pH of 1.60 were prepared by dissolving K2PdCl4 (0.05 mmol), RuCl3·nH2O (0.05 mmol), IrCl4·nH2O (0.05 mmol), K2PtCl4 (0.05 mmol), RhCl3·3H2O (0.05 mmol), FeCl2·4H2O (0.05 mmol), CoCl2·6H2O (0.05 mmol), CuCl2·2H2O (0.05 mmol), and NiCl2·6H2O (0.05 mmol) in 2 ml of aqueous hydrochloric acid and mixing them. Polyvinylpyrrolidone (PVP) K30 (5 mmol; Fujifilm Wako Pure Chemical Industries, Ltd.) was completely dissolved in 20 ml of an aqueous hydrochloric acid solution to prepare a PVP solution. The PVP solution was mixed with nine kinds of metal salt solutions to prepare a raw solution (metal ion mixed solution). The obtained raw solution was stored in a raw solution container.

[0076] A 10.5 mM reducing agent solution was prepared by adding a 15.75 mol / L KOH aqueous solution to a 25% by volume aqueous solution of ethanol, and stored in a reducing agent solution tank. Using a flow device (flow reactor), a reducing agent solution was fed from a reducing agent solution tank through pump A at a set flow rate of 30 mL / min and heated with a heater set at a temperature of 375°C. A metal ion mixed solution was fed from a precursor solution container through pump B at 3.0 mL / min, and the two solutions were mixed in a reaction vessel. Thereafter, the mixed solution was cooled in a cooling section, and the back pressure of a back pressure valve provided downstream of the cooling section was set to 9.9 - 10.1 MPa to collect a product containing alloy nanoparticles. The solution temperature during the collection of the alloy nanoparticles was 285°C. The solution recovered as a product was concentrated with an evaporator and centrifuged to recover the alloy nanoparticles.

[0077] <Elemental analysis by STEM-EDS> A part of the STEM-EDS analysis of all the alloy nanoparticles obtained in Example 4 was carried out in the same manner as in Example 1. The results obtained are shown in Fig. 10. From Fig. 10, as far as observed in the STEM image, it was confirmed that all elements were solid-solved in each alloy nanoparticle. That is, within the range of the field of view confirmed in this example, it can be seen that the aggregate of alloy nanoparticles contains 100% by number of alloy nanoparticles in which all nine elements contained in the compound used in the production as constituent elements are solid-solved. Also, it can be seen that any alloy nanoparticle constituting the aggregate of the alloy nanoparticles of the present invention contains all nine elements contained in the compound used in the production as constituent elements.< / tem> < / tem> < / tem>

Claims

1. Alloy nanoparticles containing five or more elements, represented by the following formula (1): Ru p Rh q Pd r Os x Iry Pt z (1) (p+q+r+x+y+z=1, 0≦p, q, r, x, y, z<1, any one of p, q, r, x, y, and z is 0, or p, q, r, x, y, and z are all numbers between 0 and 1.) The alloy nanoparticles are represented by However, when the alloy nanoparticles are directly supported on a carbon material support, except when the carbon material support is graphene or carbon fiber, and when the alloy nanoparticles represented by formula (1) contain five types of platinum group elements, any one of (i) to (vi) is satisfied, and when they contain six types of platinum group elements, (vii) is satisfied. (i) p=0, 0<q, r, x, y, z<1, 0.03≦q≦0.5, 0.03≦r≦0.5, 0.03≦x≦0.5, 0.03≦y≦0.5, 0.03≦z≦0.5; (ii) q=0, 0<p, r, x, y, z<1, 0.03≦p≦0.5, 0.03≦r≦0.5, 0.03≦x≦0.5, 0.03≦y≦0.5, 0.03≦z≦0.5; (iii) r=0, 0<p, q, x, y, z<1, 0.03≦p≦0.5, 0.03≦q≦0.5, 0.03≦x≦0.5, 0.03≦y≦0.5, 0.03≦z≦0.5; (iv) x=0, 0<p, q, r, y, z<1, 0.03≦p≦0.5, 0.03≦q≦0.5, 0.03≦r≦0.5, 0.03≦y≦0.5, 0.03≦z≦0.5; (v) y=0, 0<p, q, r, x, z<1, 0.03≦p≦0.5, 0.03≦q≦0.5, 0.03≦r≦0.5, 0.03≦x≦0.5, 0.03≦z≦0.5; (vi) z=0, 0<p, q, r, x, y<1, 0.03≦p≦0.5, 0.03≦q≦0.5, 0.03≦r≦0.5, 0.03≦x≦0.5, 0.03≦y≦0.

5. (vii) 0<p, q, r, x, y, z<1, 0.03≦q≦0.5, 0.03≦r≦0.5, 0.03≦x≦0.5, 0.03≦y≦0.5, and 0.03≦z≦0.

5.

2. The alloy nanoparticles according to claim 1 , wherein the elements constituting the alloy nanoparticles include a combination of elements that are not solid-soluble in a phase equilibrium diagram.

3. The alloy nanoparticles according to claim 1 or 2, having an average particle size of 0.5 to 30 nm.

4. The alloy nanoparticles according to any one of claims 1 to 3, which are used as a catalyst for an oxidation electrocatalytic reaction or a hydrogen evolution electrocatalytic reaction using an electrolyte.

5. The alloy nanoparticles according to claim 1, wherein the alloy nanoparticles are RuRhPdOsIrPt particles or RuRhPdIrPt particles.

6. The alloy nanoparticles according to any one of claims 1 to 5, which are an aggregate of the alloy nanoparticles.

7. The alloy nanoparticles according to any one of claims 1 to 6, wherein the alloy nanoparticles are supported on a non-carbon material support or a particulate carbon support.

8. An aggregate of alloy nanoparticles, comprising 98% or more by number of the alloy nanoparticles according to any one of claims 1 to 7.

9. A catalyst comprising the alloy nanoparticles according to any one of claims 1 to 7, or an aggregate of the alloy nanoparticles according to claim 8.

10. A method for producing alloy nanoparticles comprising the steps of adding an aqueous solution containing salts of five or more elements to a liquid reducing agent heated to 200°C to 300°C and reacting the solution to obtain alloy nanoparticles containing five or more elements, The alloy nanoparticles have the following formula (1): Ru p Rh q Pd r Os x Iry Pt z (1) (p+q+r+x+y+z=1, 0≦p, q, r, x, y, z<1, any one of p, q, r, x, y, and z is 0, or p, q, r, x, y, and z are all numbers between 0 and 1.) Represented by Method for producing alloy nanoparticles; However, when the alloy nanoparticles are directly supported on a carbon material support, except when the carbon material support is graphene or carbon fiber, and when the alloy nanoparticles represented by formula (1) contain five types of platinum group elements, any one of (i) to (vi) is satisfied, and when they contain six types of platinum group elements, (vii) is satisfied. (i) p=0, 0<q, r, x, y, z<1, 0.03≦q≦0.5, 0.03≦r≦0.5, 0.03≦x≦0.5, 0.03≦y≦0.5, 0.03≦z≦0.5; (ii) q=0, 0<p, r, x, y, z<1, 0.03≦p≦0.5, 0.03≦r≦0.5, 0.03≦x≦0.5, 0.03≦y≦0.5, 0.03≦z≦0.5; (iii) r=0, 0<p, q, x, y, z<1, 0.03≦p≦0.5, 0.03≦q≦0.5, 0.03≦x≦0.5, 0.03≦y≦0.5, 0.03≦z≦0.5; (iv) x=0, 0<p, q, r, y, z<1, 0.03≦p≦0.5, 0.03≦q≦0.5, 0.03≦r≦0.5, 0.03≦y≦0.5, 0.03≦z≦0.5; (v) y=0, 0<p, q, r, x, z<1, 0.03≦p≦0.5, 0.03≦q≦0.5, 0.03≦r≦0.5, 0.03≦x≦0.5, 0.03≦z≦0.5; (vi) z=0, 0<p, q, r, x, y<1, 0.03≦p≦0.5, 0.03≦q≦0.5, 0.03≦r≦0.5, 0.03≦x≦0.5, 0.03≦y≦0.

5. (vii) 0<p, q, r, x, y, z<1, 0.03≦q≦0.5, 0.03≦r≦0.5, 0.03≦x≦0.5, 0.03≦y≦0.5, and 0.03≦z≦0.5.

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