A lithium-ion solid-state electrolyte and its chemical composition

Abstract

This invention belongs to the field of solid-state electrolyte technology, and discloses a lithium-ion solid-state electrolyte, its preparation method, and a lithium-ion battery. The lithium-ion solid-state electrolyte is β-euryptite and its derivative system, with the chemical formula β-euryptiteLi. 1+x Al 1+x Si 1‑x O4; where x ranges from -0.75 to 1.00; the Al and Si elements in the original LiAlSiO4 are replaced to determine the ratio of Al to Si elements, thus obtaining the β-euryptite Li aluminosilicate lithium-ion solid electrolyte. 1+x Al 1+x Si 1‑x O4, x = 1.00, 0.50, 0.25, 0.08, 0, -0.25, -0.50, or -0.75. This invention lowers the activation energy barrier and increases the Li content of β-LiAlSi2O4 material by adjusting the Al to Si element content ratio. + Electrical conductivity.

Description

Technical Field

[0001] This invention belongs to the field of solid electrolyte technology and relates to a lithium-ion solid electrolyte and its chemical composition. Background Technology

[0002] Currently, solid-state lithium batteries are a new generation of energy storage devices with high energy density and high safety. To develop high-performance solid-state lithium batteries, solid electrolytes, as a crucial component of all-solid-state batteries, still face many unresolved issues. One of these is the need to improve ionic conductivity at room temperature. Solid-state lithium-ion conductors are key components. After decades of extensive research, various solid-state lithium conductors have been studied, including LISICON-like materials, spodumene, garnet, NASION-like materials, lithium nitride, hydrides, and perovskite lithium halides. However, these materials still struggle to meet the requirements for conductivity and stability. For example, inorganic compound solid electrolytes such as LLZO, LLZTO, and LATP have high interfacial impedance with the electrode, resulting in high preparation and processing costs, which hinders their commercial development. LISICON-like sulfide materials exhibit very good lithium-ion conductivity, even better than the 10 mS / cm conductivity of commercial liquid electrolytes. However, sulfide materials are sensitive to moisture and have a narrow electrochemical window, making them difficult to operate in air and unstable at high-voltage cathodes. Garnet materials typically exhibit good stability, but their room-temperature conductivity is usually far below 1 mS / cm, making them unsuitable for high-energy, high-rate solid-state batteries. Therefore, developing novel solid-state lithium-ion conductors with high lithium conductivity and superior mechanical, thermal, chemical, and electrochemical stability has become a key research focus and challenge.

[0003] Silicon-based materials are potential candidates for lithium conductors. Silicate-based materials are widely distributed on Earth and exhibit diverse structures. They demonstrate excellent mechanical, thermal, chemical, and electrochemical stability. In recent years, silicate materials have once again attracted attention as lithium-ion conductors. For example, β-lithium garnet MAlSi2O6 (M = Li, Na, K, Rb, or Cs) has been synthesized as an alkali metal ion conductor with diffusion barriers between 0.56 eV and 0.83 eV. Mo et al., through ab initio molecular dynamics (AIMD) calculations and experiments, found that LiTaSiO5, LiAlSiO4, and Li2ZnSiO4 may possess high Li conductivity at room temperature, indicating that Li... 1.125 Ta 0.875 Zr 0.125 The theoretical diffusion barrier of SiO5 is 0.21 eV, and the experimental value is 0.38 eV. Doping can significantly reduce the Li diffusion barrier in Li2ZnSiO4. If the diffusion barrier of silicate materials can be significantly reduced, silicate materials will become very promising solid-state lithium-ion conductors.

[0004] Due to the widespread application and excellent electrochemical stability of silicon-based materials, there is no need to focus too much on their stability; rather, the focus should be on improving the conductivity of lithium ions. In particular, understanding the diffusion mechanism of Li in silicate materials from both theoretical and experimental perspectives will help in the rational design of silicate-based Li conductors with high RT conductivity and significantly reduced diffusion barriers.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0006] (1) Many existing solid electrolytes have high diffusion barriers for lithium-ion transport and low ion conductivity at room temperature.

[0007] (2) Solid-state lithium conductor materials are difficult to meet the requirements of conductivity and stability. The stability of the electrolyte interface is beneficial to extending the cycle life of all-solid-state lithium batteries. At present, there is no electrolyte material that has both a high oxidation limit and a low reduction limit. Among them, inorganic compound solid electrolytes have a large interfacial impedance with the electrode, and the preparation and processing costs are high; LISICON-like sulfide materials are sensitive to moisture, have a narrow electrochemical window, are difficult to work in air, and are unstable for high-voltage cathodes; garnet materials have a conductivity at room temperature that is far below 1 mS / cm, and cannot be used in high-energy, high-rate solid-state batteries. Summary of the Invention

[0008] To address the problems existing in the prior art, this invention provides a lithium-ion solid electrolyte and its chemical composition, and particularly relates to a lithium-ion solid electrolyte based on β-lithium nepheline and its optimized composition method.

[0009] This invention is achieved by providing a lithium-ion solid electrolyte, wherein the lithium-ion solid electrolyte is β-euryptite and its derivatives, with the chemical formula: β-euryptite Li 1+x Al 1+x Si 1-x O4; where x takes values ​​ranging from -0.75 to 1.00, x ≠ 0.

[0010] Furthermore, when x takes a value of -0.75, the lithium-ion solid electrolyte is Li 0.25 Al 0.25 Si 1.75 O4.

[0011] When x takes the value -0.50, the lithium-ion solid electrolyte is Li 0.5 Al 0.5 Si 1.5 O4.

[0012] When x takes the value -0.25, the lithium-ion solid electrolyte is Li 0.75 Al0.75 Si 1.25 O4.

[0013] Furthermore, when x is 0.08, the lithium-ion solid electrolyte is Li 1.08 Al 1.08 Si 0.92 O4.

[0014] Furthermore, when x is 0.25, the lithium-ion solid electrolyte is Li 1.25 Al 1.25 Si 0.75 O4.

[0015] Furthermore, when x takes the value of 0.50, the lithium-ion solid electrolyte is Li 1.5 Al 1.5 Si 0.5 O4.

[0016] Furthermore, when x is 1.00, the lithium-ion solid electrolyte is Li2Al2O4.

[0017] Another object of the present invention is to provide a lithium-ion battery, wherein the lithium-ion battery is a primary lithium-ion battery or a secondary lithium-ion battery, and both the primary lithium-ion battery and the secondary lithium-ion battery are made of the aforementioned lithium-ion solid electrolyte. The primary lithium-ion solid electrolyte is made of the aforementioned lithium-ion solid electrolyte.

[0018] Another object of the present invention is to provide a method for preparing the lithium-ion solid electrolyte, the method comprising:

[0019] By substituting the Al and Si elements in the original LiAlSiO4 and determining the Si to Al element ratio, a β-euryptite lithium-ion solid electrolyte was obtained. 1+x Al 1+x Si 1-x O4, x = 1.00, 0.50, 0.25, 0.08, -0.25, -0.50 or -0.75.

[0020] Based on the above technical solutions and the technical problems solved, please analyze the advantages and positive effects of the technical solution to be protected by this invention from the following aspects:

[0021] First, addressing the technical problems existing in the prior art and the difficulty in solving them, this paper closely analyzes, in conjunction with the technical solution to be protected by this invention and the results and data obtained during the research and development process, how the technical solution of this invention solves the technical problems, and the inventive technical effects brought about by solving these problems. The specific description is as follows:

[0022] This invention analyzes Li 1+x Al 1+x Si 1-x The molecular dynamics of Li in O4, with different values ​​of x in the range of (-0.75 to 1, x ≠ 0), can be used to adjust the Si / Al ratio, thereby reducing the diffusion barrier of Li and improving the conductivity of lithium ions. The all-solid-state electrolyte predicted in this invention contains the following components: Li 0.25 Al 0.25 Si 1.75 O4, Li 0.75 Al 0.75 Si 1.25 O4, LiAlSiO4, Li 1.25 Al 1.25 Si 0.75 O4, Li 0.5 Al 0.5 Si 1.5 O4, Li 1.08 Al 1.08 Si 0.92 O4, Li 1.5 Al 1.5 Si 0.5 O4.

[0023] In this invention, the added components are inexpensive, the prediction and calculation methods are mature, and the optimal Al / Si element ratio in the electrolyte obtained can significantly improve the lithium-ion conductivity of the solid electrolyte in all-solid-state batteries.

[0024] This invention utilizes first-principles calculations for theoretical design, altering the Si / Al ratio to lower the lithium-ion diffusion barrier and improve lithium-ion conductivity. The lithium-ion solid electrolyte provided by this invention can be used in the energy field as an all-solid-state lithium-ion battery, comprising both primary and secondary batteries.

[0025] Second, considering the technical solution as a whole or from a product perspective, the technical effects and advantages of the technical solution to be protected by this invention are specifically described as follows:

[0026] This invention lowers the activation energy barrier and increases the Li content of β-LiAlSi2O4 material by adjusting the Al to Si ratio. + Electrical conductivity. Used in solid-state batteries, it can significantly improve battery rate and reduce battery internal resistance.

[0027] Third, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0028] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0029] Significantly improved the all-solid-state electrolyte Li of β-LiAlSi2O4 materials 1+x Al 1+x Si 1-x The lithium-ion conductivity of O4 at room temperature; for example: when x = 0.25, the diffusion barrier of Li is 0.24, only 0.39 times that of LiAlSiO4, while the ionic conductivity is 37730 times that of LiAlSiO4; when x = -0.50, the diffusion barrier of Li is 0.20, only 0.33 times that of LiAlSiO4, while the ionic conductivity is 66760 times that of LiAlSiO4; when x = 1, the ionic conductivity is also 860 times that of LiAlSiO4. For other values ​​of x in Table 1, the ionic conductivity is more than an order of magnitude larger than that of LiAlSiO4. (Calculations show that the diffusion barrier of LiAlSiO4 at room temperature is 0.61 eV, and the ionic conductivity is 0.0001 mS / cm.)

[0030] β-LiAlSi2O4 materials are widely available and inexpensive, and the calculated all-solid-state electrolyte Li... 1+ x Al 1+x Si 1-x O4 (x≠0) has higher ionic conductivity and can significantly improve the battery rate and reduce the battery internal resistance when applied to all-solid-state lithium-ion batteries. Attached Figure Description

[0031] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 These are several Li provided in the embodiments of the present invention. 1+x Al 1+x Si 1-x Schematic diagram of the crystal structure of O4 and lithium-ion diffusion channels; Figures (a) to (f) show the crystal structure of Li4 ​​and lithium-ion diffusion channels. 1+x Al 1+x Si 1-x The crystal structure of O4, and Figures (g) to (i) show the crystal structure of Li. 1+x Al1+x Si 1-x Lithium-ion diffusion channels in O4. It can be seen that adjusting the silicon-to-aluminum ratio alters the crystal structure, and all electrolytes exhibit one-dimensional ion diffusion channels along the c-axis.

[0033] Figure 2 The Li provided in the embodiments of the present invention 1+x Al 1+x Si 1-x The graph shows the relationship between lithium-ion conductivity and temperature of O4 and the relationship between lithium-ion diffusion barrier and electrolyte composition; Figure (a) shows the relationship between Li and temperature. 1+x Al 1+x Si 1-x The lithium-ion conductivity of O4, Figure (b) shows the conductivity of Li. 1+x Al 1+x Si 1-x The diffusion barrier of O4; Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0035] To address the problems existing in the prior art, the present invention provides a lithium-ion solid electrolyte and its preparation method. The present invention will be described in detail below with reference to the accompanying drawings.

[0036] I. Explanatory and Illustrative Embodiments. To enable those skilled in the art to fully understand how the present invention is specifically implemented, this section provides an explanatory and illustrative description of the embodiments described in the claims.

[0037] β-euryptite (LiAlSiO4) has a hexagonal structure and a space group of P6222. LiAlSiO4 exhibits very small thermal expansion, even anisotropic negative thermal expansion (NTE) behavior. Primitive LiAlSiO4 is a one-dimensional (1D) lithium-ion conductor along the c-axis, with a typical diffusion barrier of 0.6–0.95 eV, and cannot be used as a lithium-ion conductor at room temperature.

[0038] The lithium-ion solid electrolyte provided in this embodiment of the invention is β-euryptite and its derivative system, with the chemical formula: β-euryptite Li 1+x Al 1+x Si 1-x O4; where x takes values ​​ranging from -0.75 to 1.00, x ≠ 0.

[0039] When x takes the value -0.75, the lithium-ion solid electrolyte is Li 0.25Al 0.25 Si 1.75 O4.

[0040] When x takes the value -0.50, the lithium-ion solid electrolyte is Li 0.5 Al 0.5 Si 1.5 O4.

[0041] When x takes the value -0.25, the lithium-ion solid electrolyte is Li 0.75 Al 0.75 Si 1.25 O4.

[0042] When x is 0.08, the lithium-ion solid electrolyte is Li 1.08 Al 1.08 Si 0.92 O4.

[0043] When x is 0.25, the lithium-ion solid electrolyte is Li 1.25 Al 1.25 Si 0.75 O4.

[0044] When x is 0.50, the lithium-ion solid electrolyte is Li 1.5 Al 1.5 Si 0.5 O4.

[0045] When x is 1.00, the lithium-ion solid electrolyte is Li2Al2O4.

[0046] The method for preparing lithium-ion solid electrolyte provided in this embodiment of the invention includes:

[0047] By substituting the Al and Si elements in the original LiAlSiO4 and determining the Al to Si element ratio, a β-euryptite lithium-ion solid electrolyte was obtained. 1+x Al 1+x Si 1-x O4, x = 1.00, 0.50, 0.25, 0.08, -0.25, -0.50 or -0.75.

[0048] II. Application Examples. To demonstrate the inventiveness and technical value of the technical solution of this invention, this section provides application examples of the technical solution of the claims on specific products or related technologies.

[0049] Li with different values ​​of x 1+x Al 1+x Si 1-x Lithium-ion batteries using O4 material as an all-solid-state electrolyte; for example, Li-ion batteries with x = -0.5.0.5 Al 0.5 Si 1.5 Li at O4, x = 0.25 1.25 Al 1.25 Si 0.75 Li at O4, x = -0.75 0.25 Al 0.25 Si 1.75 Li at O4, x = -0.25 0.75 Al 0.75 Si 1.25 Li at O4, x = 0.08 1.08 Al 1.08 Si 0.92 Li at O4, x = 0.50 1.5 Al 1.5 Si 0.5 O4 or Li2Al2O4 when x = 1.00, etc.

[0050] III. Evidence of the Relevant Effects of the Embodiments. The embodiments of the present invention have achieved some positive effects during research and development or use, and indeed possess significant advantages compared to existing technologies. The following description, in conjunction with data, charts, and other materials from the experimental process, illustrates these advantages.

[0051] (1) At different temperatures from 573K to 973K, the effects of β-euryptite Li 1+x Al 1+x Si 1-x AIMD simulations were performed on O4 (x = -0.75 to 1). Structural optimization and dynamic analysis were performed using the Vienna Ab initio Simulation Package (VASP). Projected augmented wave (PAW) pseudopotentials and the generalized gradient approximation (GGA) parameterized by Perdew, Burke, and Emzerhof (PBE) were used in all simulations. The PAW pseudopotential cutoff energy for structural optimization was 520 eV, and the cutoff energy for AIMD simulations was 400 eV. Structural optimization was performed using a 3×3×3 Monkhorst k-point mesh, and the integration of the Burri flow region was sampled. The force convergence criterion was... AIMD simulations used the Nosé-Hoover temperature controller's NVT integration with a time step of 2 fs, and the total AIMD simulation time was in the range of 50-200 ps.

[0052] (2) The Li diffusion coefficient is obtained from the mean square displacement (MSD) data obtained by AIMD simulation based on the Einstein-Smoluchowski equation:

[0053]

[0054] Where D is the diffusivity and D is the lattice dimension in which diffusion occurs. Let be the displacement of the atom at time t. The conductivity can be obtained from the Nernst-Einstein equation:

[0055]

[0056] In the formula, σ is the ionic conductivity, n is the carrier density, q is the carrier charge, and k is the carrier charge. B Where is Boltzmann constant, T is temperature, D0 is a constant, and E is the diffusion barrier.

[0057] (3) The AIMD calculation method was used to analyze the Li in β-euryptite Li 1+x Al 1+x Si 1-x Diffusion in LiAlSiO4. The results show that by changing the Si / Al ratio, the Li diffusion barrier in LiAlSiO4 significantly decreased from 0.61 eV to [a lower value]. 0.5 Al 0.5 Si 1.5 Li in O4 0.5 Al 0.5 Si 1.5 O4 and Li 1.25 Al 1.25 Si 0.75 The diffusion barrier of Li in O4 is 0.24 eV.

[0058] (4) The Li content can be adjusted by the Si / Al ratio, denoted by x. For other Si / Al ratios, the optimized Li... 1+x Al 1+x Si 1-x The structure of O4 (x = -0.75 to 1, x ≠ 0). The β-pyroxene structure remains relatively unchanged with varying silicon-to-aluminum ratios. As x increases, the lattice parameters a and c, as well as the cell volume, all increase due to the increased number of Li atoms in the cell. In a LiAlSiO4 cell, there are 12 Li atoms, 12 Al atoms, 12 Si atoms, and 48 O atoms. When the Si / Al ratio decreases from 7 to 0, the number of Li atoms in the cell ranges from 0 to 24. There are four Li diffusion channels along the c-direction. These channels are formed by the shared edges of Si-O tetrahedra and Al-O tetrahedra, creating a double-helix structure. The number of Li atoms in each diffusion channel can vary from 0 to 6 depending on the number of Li atoms within the cell. Figure 1 (g) to (h) show diffusion channels containing one Li atom, two Li atoms, and four Li atoms, referred to as the 1Li channel, 3Li channel, and 4Li channel, respectively. The Li-Li distance varies with the number of Li atoms in the diffusion channel.

[0059] The composition, lithium-ion diffusion barrier, and predicted room-temperature conductivity of the solid electrolyte provided in this embodiment of the invention are shown in Table 1.

[0060] Table 1. Composition of solid electrolytes, lithium-ion diffusion barriers, and predicted room-temperature conductivity.

[0061]

[0062]

[0063] Figure 1 This represents β-euryptite Li 1+x Al 1+x Si 1-x The optimized structure diagram of O4 (x = -0.75 to 1, x ≠ 0). The Li content can be adjusted by the Si / Al ratio, which is represented by x. Figure 1 ac is Li 0.75 Al 0.75 Si 1.25 O4, LiAlSiO4 and Li 1.25 Al 1.25 Si 0.75 The side view of O4 is shown in Figure df, which is the top view of the corresponding structure. In a LiAlSiO4 unit cell, there are 12 Li atoms, 12 Al atoms, 12 Si atoms, and 48 O atoms. When the Si / Al ratio decreases from 7 to 0, the range of Li atoms in the unit cell is 0–24. There are four Li diffusion channels along the c-axis. One Li diffusion channel on the (0.5,0.5)c-axis (where (0.5,0.5) represents the coordinates of (x,y)) is called the central channel. One Li diffusion channel on the (0,0)c-axis is called the edge channel. The two Li diffusion channels on the (0,0.5) and (0.5,0)c-axis are called surface channels. The diffusion channels are formed by the shared edges of Si-O tetrahedra and Al-O tetrahedra, creating a double-helix structure, as shown in Figure df. Figure 1 As shown in gh. With the change of intracellular Li number, the Li number of each diffusion channel can range from 0 to 6. Figure 1 The graph gh shows diffusion channels containing one Li atom, two Li atoms, and four Li atoms, referred to as the 1Li channel, 3Li channel, and 4Li channel, respectively. The Li-Li distance varies with the number of Li atoms in the diffusion channel.

[0064] Figure 2 Li was shown 1+x Al 1+x Si 1-x AIMD results for Li conductivity and diffusion barrier in O4. Figure 2a shows the linear fit of the curve lg(σT) versus 1000 / T. Conductivity was calculated based on the slopes of MSD at 573 K, 673 K, 773 K, and 873 K. The slopes of all fitted curves decrease when x is simultaneously negative or positive. The Li diffusion barrier was obtained using the linear fit of the curve lg(σT) versus 1000 / T according to the Nernst-Einstein equation. Diffusion barrier data are shown below. Figure 2 As shown in b. Calculations show that when x = 0, the diffusion barrier of the original LiAlSiO4 is the highest, at 0.61 eV. When x is both negative and positive, the diffusion barrier decreases significantly. When x = -0.5, Li... 0.5 Al 0.5 Si 1.5 The diffusion barrier of O4 is as low as 0.20 eV. As x increases from 0 to 1, the diffusion barrier decreases rapidly, and the diffusion barrier of Li... 1.25 Al 1.25 Si 0.75 The minimum value of O4 is 0.26 eV, and the diffusion barrier of Li2Al2O4 steadily increases to 0.42 eV.

[0065] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A lithium-ion solid electrolyte, characterized in that, The lithium-ion solid electrolyte is a derivative system of nepheline, with the chemical formula: Li 1+x Al 1+x Si 1-x O4; where x ranges from -0.75 to 1.00 and x ≠ 0; The preparation method of the lithium-ion solid electrolyte includes: replacing the Al and Si elements in the original LiAlSiO4, determining the ratio of Al to Si elements, and obtaining aluminosilicate lithium-ion solid electrolyte as β-euryptiteLi 1+ x Al 1+x Si 1-x O4, x = 1.00, 0.50, 0.25, 0.08, -0.25, -0.50 or -0.75; The lithium-ion solid electrolyte achieves performance improvements through the following methods: first-principles theoretical design is used to change the Si / Al ratio, reducing the lithium-ion diffusion barrier and improving the lithium-ion conductivity; Li... 1+x Al 1+x Si 1-x The molecular dynamics of Li in O4 were investigated. Different values ​​of x within the range of -0.75 to 1 (x≠0) were used to adjust the Si / Al ratio, thereby lowering the diffusion barrier of Li and increasing the conductivity of lithium ions. Furthermore, adjusting the Al to Si ratio in β-LiAlSiO4 materials lowered the activation energy barrier and increased the Li-to-Li conductivity of the β-LiAlSiO4 material. + Electrical conductivity; used in solid-state batteries, it can significantly improve battery rate and reduce battery internal resistance.

2. The lithium-ion solid electrolyte as described in claim 1, characterized in that, When x takes the value -0.75, the lithium-ion solid electrolyte is Li 0.25 Al 0.25 Si 1.75 O4.

3. The lithium-ion solid electrolyte as described in claim 1, characterized in that, When x takes the value -0.50, the lithium-ion solid electrolyte is Li 0.5 Al 0.5 Si 1.5 O4.

4. The lithium-ion solid electrolyte as described in claim 1, characterized in that, When x takes the value -0.25, the lithium-ion solid electrolyte is Li 0.75 Al 0.75 Si 1.25 O4.

5. The lithium-ion solid electrolyte as described in claim 1, characterized in that, When x is 0.08, the lithium-ion solid electrolyte is Li 1.08 Al 1.08 Si 0.92 O4.

6. The lithium-ion solid electrolyte as described in claim 1, characterized in that, When x is 0.25, the lithium-ion solid electrolyte is Li 1.25 Al 1.25 Si 0.75 O4.

7. The lithium-ion solid electrolyte as described in claim 1, characterized in that, When x is 0.50, the lithium-ion solid electrolyte is Li 1.5 Al 1.5 Si 0.5 O4.

8. The lithium-ion solid electrolyte as described in claim 1, characterized in that, When x is 1.00, the lithium-ion solid electrolyte is Li2Al2O4.

9. A lithium-ion battery, characterized in that, The lithium-ion battery is a primary lithium-ion battery or a secondary lithium-ion battery, and the primary lithium-ion battery or the secondary lithium-ion battery is made from the lithium-ion solid electrolyte as described in any one of claims 1 to 7 or a mixture thereof in any proportion.

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