METHOD FOR PRODUCING ELECTROCHEMICAL CELLS OF A SOLID-STATE BATTERY

20170263980 · 2017-09-14

    Inventors

    Cpc classification

    International classification

    Abstract

    A method for producing at least one electrochemical cell of a solid-state battery, comprising a mixed-conducting anode, a mixed-conducting cathode, and an interposed electrolyte, is characterized in that a mixed-conducting anode and a mixed-conducting cathode are initially produced or provided. The surface of at least one of the two electrodes is modified by way of an additional method step in such a way that the electronic conductivity perpendicular to the cell is reduced to less than 10.sup.−8 S/cm in a layer of the electrode near the surface. The anode and cathode are then assembled to form a solid-state battery in such a way that the surface-modified layer of at least one electrode is disposed as an electrolyte layer between the anode and cathode, and the mixed-conducting electrodes are thereby electronically separated.

    Claims

    1. A method for producing at least one electrochemical cell of a solid-state battery, comprising a mixed-conducting anode, a mixed-conducting cathode, and an electrolyte layer interposed between the anode and the cathode, comprising the following steps: producing or providing a mixed-conducting anode; producing or providing a mixed-conducting cathode; modifying the surface of at least one of the two electrodes by way of an additional method step in such a way that the electronic conductivity perpendicular to the cell is reduced at room temperature to less than 10.sup.−8 S/cm in a layer of the electrode near the surface, while the ionic conductivity is more than 10.sup.−6 S/cm; wherein the modification of the surface of at least one electrode takes place by way of a chemical reaction with a liquid, gaseous or solid reagent or by way of a physical phase change; and subsequently assembling the anode and the cathode to form a solid-state battery in such a way that the surface-modified layer of at least one electrode is disposed on the boundary between the anode and the cathode as an electrolyte layer, and the mixed conducting electrodes are thereby electronically separated.

    2. The method according to the preceding claim, wherein an anode comprising LiC.sub.6, Li.sub.4 4, Sn, Li.sub.4.4Si, LiTi.sub.5O.sub.12, Na.sub.2Ti.sub.6O.sub.13Na or Li metal is used as the active material.

    3. The method according to claim 1, wherein a cathode comprising LiCoO.sub.2, LiMn.sub.2O.sub.4, Li(Ni, Co, Mn)O.sub.2, LiFePO.sub.4, LiNi.sub.xCo.sub.1−xO.sub.2, LiNi.sub.xMn.sub.2−xO.sub.4, NaFePO.sub.4, Na—CoO.sub.2, Na.sub.2/3[Ni.sub.1/3Mn.sub.2/3]O.sub.2, NaVPO.sub.4F or Na.sub.3V.sub.2(PO.sub.4).sub.3 is used as the active material.

    4. A method according to claim 1, wherein the modification of the surface of at least one electrode takes place by way of a chemical reaction of the electrode with a liquid reagent.

    5. A method according to claim 1, wherein the modification of the surface of at least one electrode takes place by way of a chemical reaction of the electrode with a solid.

    6. A method according to claim 1, wherein the modification of the surface of at least one electrode takes place by way of a chemical reaction of the electrode with a gaseous reagent.

    7. A method according to claim 1, wherein the modification of the surface of at least one electrode takes place by way of a physical phase change.

    8. A method according to claim 1, wherein both electrode surfaces are modified.

    9. A method according to claim 1, wherein the sum of the layer thickness of the modified surface or of the modified surfaces when assembled is a layer thickness of at least 0.1 nm and no more than 100 μm, and more particularly a layer thickness between 0.1 μm and 10 μm.

    10. A method according to claim 1, wherein the modification of the surface of at least one electrode at room temperature reduces the electronic conductivity perpendicular to the cell to less than 10.sup.−9 S/cm, and advantageously to less than 10.sup.−12 S/cm.

    11. A method according to claim 1, wherein when the two electrodes are assembled with at least one layer that is modified near the surface, an additional substance is introduced at the interface.

    12. A method according to claim 1, wherein the ionic conductivity at room temperature, after modification of the surface, in this region is at least 10.sup.−6 S/cm, however in particular more than 10.sup.−2 S/cm.

    Description

    SPECIFIC DESCRIPTION

    [0063] The invention will be described in more detail hereinafter based on suitable materials, exemplary embodiments and explanations about the process steps.

    [0064] Specific application examples for materials and further characteristics for this invention are provided hereafter, among other things, based on the example of a Li-ion battery, but are not limited to this example.

    [0065] a) Suitable cathode materials (active materials) for aLi-ion battery (commercially available) that may be used in the method according to the invention:

    TABLE-US-00001 Cathode material LiCoO.sub.2 LiMn.sub.2O.sub.4 Li(NiCoMn)O.sub.2 LiFePO.sub.4 Reversible capacity 140 100 150 145 (mAh/g) Working voltage (V) 3.6 3.8 3.8 3.2 Energy density of 180 100 170 130 the battery (Wh/kg)

    [0066] Further possible suitable mixed-conducting cathode materials that can be used and modified according to the invention include: LiNiO.sub.2, LiMn.sub.2O.sub.4 doped with Ni, Co, Fe, and LiAPO.sub.4 where A=Fe, Ni. Co, Mn.

    [0067] Suitable cathode materials for sodium-ion batteries include: NaFePO.sub.4, NaCoO.sub.2, Na.sub.2/3[Ni.sub.1/3Mn.sub.2/3]O.sub.2, NaVPO.sub.4F, Na.sub.3V.sub.2(PO.sub.4).sub.3.

    [0068] b) Suitable anode materials (active materials) for aLi-ion battery that may be used in the method according to the invention:

    TABLE-US-00002 Volume Mean Theor. Theor. expansion voltage vs. spec. capacity upon reaching Anode Limiting Li*/Li capacity density theor. capacity material joint (V) (mAh/g) (Ah/L) (%) Carbon- LiC.sub.6 0.1 374 760 12.8 based Tin-based Li.sub.4.4Sn 0.4 992 7240 260 Silicon- Li.sub.4.4Si 0.3 4200 9660 310 based Li.sub.4Ti.sub.5O.sub.12 Li.sub.7Ti.sub.5O.sub.12 1.5 175 610 <1

    [0069] Li metal, for example, should also be mentioned as a further possible mixed-conducting anode material that can be used and modified according to the invention.

    [0070] Suitable anode materials for sodium-ion batteries include: carbon, sodium metal, provided it is compatible with the electrolyte that is to be generated, and Na.sub.2Ti.sub.6O.sub.13-related materials.

    [0071] c) Suitable materials as the ion-conducting phase of the mixed-conducting anode or cathode (based on the example of a ceramic solid-state Li-ion conductor) that according to the invention form the electrolyte layer:

    [0072] phosphates: Li.sub.1+xAl.sub.xTi.sub.2−x(PO.sub.4).sub.3 (where x ˜0.2), Li-NASICON), Li.sub.3+xPO.sub.4−xN.sub.x (where x˜0.2),

    [0073] LiPON glass

    [0074] oxides: Li.sub.5 5La.sub.3Nb.sub.1 75In.sub.0 25O.sub.12, Li.sub.6 625La.sub.3Zr.sub.1 625Ta.sub.0 375O.sub.12 (garnet structure), Li.sub.3xLa.sub.(2/3)−xTiO.sub.3 (perovskite),

    [0075] sulfates: Li.sub.2S—P.sub.2S.sub.5 system, Li.sub.4−xGe.sub.1−xP.sub.xS.sub.4 system (thio-LISICON).

    [0076] Furthermore, materials suitable as solid electrolyte materials for sodium-ion batteries should be mentioned, such as β- or β′-alumina or Na.sub.1+xZr.sub.2Si.sub.xP.sub.3xO.sub.12 (NASICON materials).

    [0077] 1. Exemplary embodiment of the production method according to the invention for a lithium-ion solid-state battery cell:

    [0078] Production of a mixed-conducting cathode comprising:

    [0079] electronically conducting phase: 35 vol % C

    [0080] ionically conducting phase: 35 vol % Li.sub.7La.sub.3Zr.sub.2O.sub.12 (LLZ)

    [0081] active material: 30 vol. % LiFePO.sub.4

    [0082] The capacity of the cathode having a predefined layer thickness of 60 μm is calculated from the active material (LiFePO.sub.4) having a density of 3.6 g/cm.sup.3 and a reversible capacity of 145 (mAh/g) at 30 vol. % as:

    [00003] 0.3 .Math. 1.45 .Math. mAh .Math. 3.6 .Math. cm 3 .Math. 10 .Math. .Math. cm 2 .Math. 60 × 10 - 4 .Math. cm = 9.4 .Math. .Math. mAh

    [0083] Production of a mixed-conducting anode comprising:

    [0084] electronically conducting phase and active material: 50 vol % C

    [0085] ionicaliy conducting phase: 50 vol % Li.sub.7La.sub.3Zr.sub.2O.sub.12

    [0086] The minimum thickness of the anode (C), which should have the same capacity as the cathode, at a density (graphite) of 2.1 g/cm.sup.3 and a theoretical specific capacity of 374 (mAh/g) at 50 vol % is calculated as:

    [00004] 9.4 .Math. .Math. mAh 0.5 .Math. 374 .Math. mAh .Math. 2.1 .Math. cm 3 × 10 .Math. .Math. cm 2 = 24 × 10 - 4 .Math. cm = 24 .Math. .Math. μ .Math. .Math. m

    [0087] This results in the following specifications for a cell thus produced:

    TABLE-US-00003 cell voltage: 3.2 V dimensions thickness of the cathode: 60.0 μm thickness of the anode: 24.0 μm thickness of current conductor: 2x 20.0 μm total thickness of cell: 124.0 μm surface area: 10.0 cm.sup.2 possible capacity: cell 9.4 mAh 1 mm thick battery (8 cells) 75.2 mAh

    [0088] 2. Exemplary embodiment of the production method according to the invention for a sodium-ion solid-state battery cell:

    [0089] Cathode active material: NaFePO.sub.4 having 154 mAh/g and approximately 2.8 V against a C-anode having 187 mAh/g and a β-Al.sub.2O.sub.3 solid electrolyte.

    [0090] Production of a mixed-conducting cathode comprising:

    [0091] electronically conducting phase: 35 vol % C

    [0092] ionically conducting phase: 35 vol % β-Al.sub.2O.sub.3

    [0093] active material: 30 vol % NaFePO.sub.4

    [0094] The capacity of the cathode having a predefined layer thickness of 60 μm is calculated from the active material (NaFePO.sub.4) having a density of 3.66 g/cm.sup.3 and a reversible capacity of 154 (mAh/g) at 30 vol. % as:

    [00005] 0.3 .Math. 154 .Math. mAh .Math. 3.66 .Math. cm 3 .Math. 10 .Math. .Math. cm 2 .Math. 60 × 10 - 4 .Math. cm = 10.1 .Math. .Math. mAh

    [0095] Production of a mixed-conducting anode comprising:

    [0096] electronically conducting phase and active material: 50 vol % C

    [0097] ionically conducting phase: 50 vol % β-Al.sub.2O.sub.3

    [0098] The minimum thickness of the anode (C), which should have the same capacity as the cathode, at a density (graphite) of 2.1 g/cm.sup.3 and a theoretical specific capacity of 187 (mAh/g) at 50 vol %

    [0099] is calculated as:

    [00006] 10.1 .Math. .Math. mAh 0.5 .Math. 187 .Math. mAh .Math. 2.1 .Math. cm 3 .Math. 10 .Math. .Math. cm 2 = 51 × 10 - 4 .Math. cm = 51 .Math. .Math. μ .Math. .Math. m

    [0100] Specifications of a cell thus produced:

    TABLE-US-00004 cell voltage: 2.8 V dimensions: thickness of the cathode: 60.0 μm thickness of the anode: 51.0 μm thickness of current conductor: 2x 20.0 μm total thickness of cell: 151.0 μm surface area: 10.0 cm.sup.2 possible capacity: cell 10.1 mAh 1 mm thick battery (6.6 cells) 66.7 mAh

    [0101] d) Calculation of a potentially required depth to which the surface treatment according to the invention should reduce the electronic conductivity:

    [0102] The depth to which the electronic conductivity must be eliminated or considerably decreased depends on various parameters. The most important is the electronic conductivity of the electrolyte itself, =produced as a result of the modification of the electrodes. Sufficiently low self-discharge must be ensured for this purpose. Desirable values for the electronic conductivity of the electrolyte or of the modified surface are <1×10.sup.−8 S/cm, wherein a value of approximately 1×10.sup.−12 S/cm shall be regarded as particularly advantageous.

    [0103] As an exemplary calculation for the standard cell from the above 1st exemplary embodiment, a layer thickness of 500 μm results of an electrolyte for which the electronic conductivity could be reduced to 1×10.sup.−9 S/cm for a lithium-ion battery of 3.2 V, with a surface area of 10 cm.sup.2 and a maximum self-discharge current of 0.6 μA. If the electronic conductivity of the electrolyte can even be reduced to approximately 1×10.sup.−12 S/cm, this will result in an accordingly smaller required layer thickness of approximately 0.5 μm.

    [0104] The figure of the self-discharge current was estimated here at 0.6 μA, since 5% of the maximum capacity per month is a typical value for self-discharge in good lithium polymer (rechargeable batteries for MP3 players, cameras and the like).

    [0105] For the above-mentioned 1st exemplary embodiment of a lithium-ion solid-state battery cell, the self-discharge current that would result is:

    [00007] 5 .Math. % .Math. .Math. of .Math. .Math. 9.4 .Math. .Math. mAh .Math. .Math. per .Math. .Math. cell .Math. : .Math. .Math. 0.05 .Math. 9.40 .Math. .Math. mAh = 0.47 .Math. .Math. mAh per .Math. .Math. month .Math. .Math. ( 720 .Math. .Math. h ) .fwdarw. 0.47 × 10 - 3 .Math. Ah 720 .Math. .Math. h = 0.65 × 10 - 6 .Math. A = 0.65 .Math. .Math. μ .Math. .Math. A

    [0106] If the treated surface region could be reduced to an electronic conductivity of 1×10.sup.−9 S/cm, the required layer thickness of the electrolyte to be produced would be:

    [00008] d = AU I .Math. σ = 10 .Math. .Math. cm 2 .Math. 3.2 .Math. .Math. V 0.65 × 10 - 6 .Math. A .Math. 1 × 10 - 9 .Math. A Vcm = 0.05 .Math. .Math. cm = 500 .Math. .Math. μ .Math. .Math. m

    [0107] If the surface region to be treated could ultimately be reduced as far as an electronic conductivity of only 1×10.sup.−12 S/cm, the required layer thickness of the electrolyte to be produced would be decreased to;

    [00009] d = AU I .Math. σ = 10 .Math. .Math. cm 2 .Math. 3.2 .Math. .Math. V 0.65 × 10 - 6 .Math. A .Math. 1 × 10 - 12 .Math. A Vcm = 0.5 .Math. × 10 - 4 .Math. .Math. cm = 0.5 .Math. .Math. μ .Math. .Math. m

    [0108] Furthermore, it is also useful to select the required depth of the surface treatment in relation to the particle size and phase distribution of the mixed-conducting electrodes. The particle sizes of suitable common ceramic powders generally range between 1 nm and 1 mm. The subrange from 100 nm to 100 μm is useful, or more relevant, for the majority of conventional applications. An optimal range would be around a 1 μm particle size; however, this may vary depending on the specific requirements of an application.

    [0109] For the aforementioned exemplary embodiment having an electronic conductivity of the LLZ phase (ionically conducting phase) of approximately 1×10.sup.−11 S/cm at room temperature and a desired leakage current (self-discharge current) of 0.65 μA, the resulting required layer thickness for the surface region to be modified is approximately 5 μm. In the event that the surfaces of both electrodes are to be treated in the same manner by way of a surface treatment, the electronically conductive phase of each electrode should be eliminated to a respective depth of 2.5 μm, for example, or reduced to the corresponding predefined value.. This is a realistic value considering the desired particle size of approximately 1 μm of the LLZ matrix.

    [0110] e) Suitable surface treatment methods according to the invention:

    [0111] A specific treatment method that should be mentioned and could bring about the modification according to the invention of the mixed-conducting electrode surface is thermal treatment, in which carbon, as the electrically conductive phase, can be burned by heating to temperatures above 600° C. in an oxygen-containing atmosphere, for example. The of the surface can take place, for example, in a conventional furnace or a halogen furnace at a high heating rate, with air or oxygen blown into the furnace, or else by way of laser irradiation in air, and generally causes the carbon to burn out in the surface region, wherein the application time notably determines the depth of the removal.

    [0112] So as to ensure that not all sides of the electrodes are subjected to the thermal treatment during the heating in the furnace, the sides not intended to be treated can be protected as follows, for example: [0113] 1) heating in protective powder (such as ceramic or carbon or the like), which is to say the sample is embedded so that only the side intended to be treated is exposed. [0114] 2) wrapping the electrode in a thin foil (such as gold, platinum, another metal having a high melting point), which is to say the sample is placed with the side to be protected on the foil and the foil is folded up on the sides, without covering the side that is to be treated.

    [0115] The technology of these burn-off processes has already been studied in detail and burn-off rates have already been examined for a variety of carbon modifications, for example in the production of cavities in cast metal bodies (DE 19832718 Al) or for the resistance of carbon fiber composite materials (Untersuchungen zur Oxidationsbeständigkeit von Graphitfolien für Wärmespeicher Thomas Bauer (Analyses regarding the oxidation resistance of graphite foils for heat accumulators), Thomas Bauer, Deutsches Zentrurn für Luft-Lind Raumfahrt e.V. (DLR, German Aerospace Center), Institute of Engineering Thermodynamics, Thermophysics Working Group, Meeting, Karlsruhe, Germany, Mar. 4-5, 2010.

    [0116] The electrolyte material (ionically conducting phase) Li.sub.7La.sub.3Zr.sub.7O.sub.12 (LLZ), in contrast, does not start to decompose until >1250° C. and is consequently not affected.

    [0117] In addition, the temperature could be increased even further, for example up to 800° C. At this temperature, the active material LiFePO.sub.4 (LFP) in the cathode could also decompose, and thereby potential short circuits could also be prevented by the active material.

    [0118] Another possible alternative to the aforementioned method is dissolving the carbon out by way of a highly oxidizing acid, such as by way of sulfuric acid (optionally hot sulfuric acid) or nitric acid. The end product when nitric acid is used would be mellitic acid (C.sub.6(CO.sub.2H).sub.6), for example, which can further be used as a catalyst V.sub.2O.sub.5 to increase the reaction.

    [0119] Moreover, electrochemical oxidation of the carbon is also possible, for example with the aid of hydroxide melts (LiOH, KOH or NaOH) and the application of a voltage, as it is known from alkaline fuel cells (AFC) or direct carbon fuel cells (DCFC). Once again, the current intensity and application time determine the layer depth of the oxidation (operating temperature around 700° C., graphite in the mixed electrodes acts as the anode and “fuel,” typical current densities around 100 mA/cm.sup.2 at 0.45 V).

    [0120] Should the two previous methods not be compatible with the electrolyte material that is used, for example because the electrode comprises a material different from Li.sub.7La.sub.3Zr.sub.2O.sub.12 (LLZ), such as a phosphate which already decomposes at T>800° C., the carbon can also be removed more gently by way of ozone cleaning, for example. Such a method is carried out in a similar form with Si wafer cleaning in industry. Since carbon is frequently used as the electric phase even in mixed-conducting anodes, the same method can advantageously also be used for treating an anode.

    [0121] Suitable measures must be taken with all of the above-mentioned measures, notably also when heating in a furnace, to ensure that only the surface that is to be modified is indeed modified in the corresponding manner by the treatment.

    [0122] For example, when heating in the furnace, the electrode can be protected on the surfaces that are not to be modified by providing these surfaces with a protective layer, for example an additional graphite layer. In the case of a treatment with a liquid reagent, the electrode can be immersed in the liquid only at the surface to be modified, for example, or the surface to be modified can be wetted only superficially with the liquid.

    [0123] The following tables provide further mixed-conducting anodes and cathodes in combination with respective suitable surface treatment methods by way of example within the meaning of the invention.

    TABLE-US-00005 Conducting “Electrolyte” additive Treatment Anode to be produced (electrical) method Li.sub.4.4Sn Li.sub.1+xAl.sub.xTi.sub.2−x(PO.sub.4).sub.3 Sn (=anode) O.sub.3 plasma or HCl solution Li metal LiPON Li metal oxiding in air or (=anode) oxygen or nitriding in N.sub.2 Li.sub.4.4SI Li.sub.7La.sub.3Zr.sub.2O.sub.12 B (doped Si) oxidizing at 800° C. in air (furnace) Na metal β Al.sub.2O.sub.3 Na (=anode) Cl.sub.2 gas −> NaCl formation Na.sub.2Ti.sub.6O.sub.13 Na.sub.1+xZr.sub.2Si.sub.xP.sub.3XO.sub.12 C heating in oxygen/air or oxidizing acid Conducting “Electrolyte” additive Treatment Cathode to be produced (electrical) method LiMn.sub.2O.sub.4 Li.sub.1+xAl.sub.xTi.sub.2−x(PO.sub.4).sub.3 C O.sub.3 plasma or oxidizing acid LiCoO.sub.2 LiPON Co oxidizing in air or oxygen or HCl acid Li(NiCoMn)O.sub.2 Li.sub.7La.sub.3Zr.sub.2O.sub.12 Ni oxidizing in air or oxygen or HCl acid NaCoO.sub.2 β Al.sub.2O.sub.3 Co oxidizing in air or oxygen or HCl acid Na.sub.2/3[Ni.sub.1/3Mn.sub.2/3]O.sub.2 Na.sub.1+xZr.sub.2Si.sub.xP.sub.3XO.sub.12 C heating in oxygen/air or oxidizing acid

    [0124] f) Treatment of anode and/or cathode:

    [0125] The decision as to whether the anode and cathode surfaces that are to be joined for the solid-state battery require additional treatment and which decision produces optimal results depends, among other things, on the electronically conducting phases of the anode and the cathode and the compatibility of the electrode material and the treatment method.

    [0126] If the two mixed-conducting electrodes comprise the same phase that causes the electronic conductivity, it is possible in some circumstances to employ the same method for reducing the electronic conductivity on the surfaces of both the cathode and the anode. On a large scale, this could be advantageous in terms of process speed. For example, the treatment of double the surface area to a defined depth could be more advantageous than the treatment of only a single surface area to twice the depth.

    [0127] If the other phases, which is to say the active material and the ion-conductive phase, of the two electrodes are compatible with the selected surface method, advantageously identical methods can be employed for both electrodes. Otherwise optionally two different surface treatment methods must be selected to achieve the above-mentioned advantage of process speed, which could then potentially result in higher investment costs.

    [0128] If the anode and cathode to be used comprise two different materials for the electronic conductivity, or if one of these phases has two properties that cannot be influenced independently of one another, it might be prudent to treat only one of the mixed-conducting electrodes.

    [0129] g) Suitable methods for joining the anode and the cathode on the treated surface(s):

    [0130] In a specific exemplary embodiment of the invention, Li.sub.7La.sub.3Zr.sub.2O.sub.12 (LLZ) matrices, which may occur after the modification according to the invention of a surfaces of mixed-conducting anode and cathode, were placed on top of each other by way of example and sintered in air without pressure at 1200° C. for 35 hours. An equally sized sample made of LLZ matrix served as the comparison sample. The conductivity of the sample through the interface was examined, as were changes in the sample resulting from contact. The result that was found was that the overall conductivity was only reduced from 8.8×10.sup.−5 S/cm by a factor of 1.5 to 5.8×10.sup.−5 S/cm compared to the continuous comparison sample having the same size.

    [0131] FIGS. 1 to 4 show different embodiments of possibilities for joining the two electrodes to obtain an electrochemical cell. In the figures, E=mixed-conducting electrodes (anode or cathode) and E′=corresponding mixed-conducting counter electrode (cathode or anode), E.sub.m characterizes the modified surface region of the electrode E, and E′.sub.m the modified surface region of the counter electrode E′. CC identifies current collectors.

    [0132] FIGS. 1 and 2 are schematic illustrations of alternative production routes for an electrochemical cell, depending on whether only one mixed-conducting electrode surface is modified, or both that of the anode and that of the cathode are modified.

    [0133] FIGS. 3 and 4 show possible modifications or arrangement variants in the form of a sandwich unit, which advantageously yield higher voltages or current densities, and consequently higher energy densities or power densities, for certain material systems.

    [0134] h) Identifying features of a cell produced by way of this claim;

    [0135] The surface treatment ideally does not alter the ion-conducting phase, whereby the structure on what will later be the joining site is also maintained. If this is also not altered during the final joining of the mixed-conducting anode and cathode, this region may be easily identified using suitable microscopy methods. The different contrast of the modified phase, or the complete absence of the electrically conductive phase in the otherwise unmodified matrix of the ionically conducting phase can be taken advantage of for this purpose.