KR20240048605A - OXIDE-BASED SOLID ELECTROLYTE FOR A Lithium SECONDARY BATTERIES AND PREPARATION METHOD THEREOF - Google Patents

Abstract

The present invention relates to a method for manufacturing an oxide-based solid electrolyte for an all-solid lithium secondary battery. More specifically, the present invention relates to a method for manufacturing an oxide-based solid electrolyte having a stable cubic phase while using an inexpensive raw material.

Description

Method for manufacturing oxide-based solid electrolyte for all-solid lithium secondary battery {OXIDE-BASED SOLID ELECTROLYTE FOR A Lithium SECONDARY BATTERIES AND PREPARATION METHOD THEREOF}

The present invention relates to a method for producing an oxide-based solid electrolyte for an all-solid lithium secondary battery. More specifically, the present invention relates to a method of manufacturing an oxide-based solid electrolyte with a stable cubic structure while using inexpensive raw materials.

Recently, the use of lithium secondary batteries has expanded from power sources for small mobile devices to power sources for mid- to large-sized electric vehicles (EVs) and power storage systems (ESS). In particular, interest in electric vehicles, which are eco-friendly vehicles, is increasing, and major automobile companies around the world are recognizing eco-friendly electric vehicles as the next generation growth technology and launching new models.

Battery specifications required for electric vehicles include high power density capable of rapid charging, high energy density per weight/volume, price, and safety. In particular, in the case of electric vehicles, they are devices that are directly ridden and controlled by humans, which can help with driving and accidents. Ensuring city safety is the most important requirement. In fact, in the case of the Model S, a commercial model of Tesla, a representative electric vehicle company in the United States, several incidents of fires occurring and burning down while driving were announced in the media, and there was a demand for batteries with high safety, and accordingly, the development of all-solid-state batteries was promoted. It is desperately needed.

All-solid-state lithium secondary batteries consist of a solid electrolyte as well as an anode and a cathode. In other words, an all-solid lithium secondary battery is a battery in which the electrolyte between the anode and cathode of the battery has been replaced with a solid one from the existing liquid. Since it does not use flammable organic solvents, there is a low risk of fire or explosion even if an internal short circuit occurs, and the size can be reduced. . In addition, not only is it superior in manufacturing cost and productivity, but it also has the feature of being able to achieve high voltage by stacking it in series within a cell. Additionally, in this solid electrolyte, since only Li ions do not move, side reactions due to movement of anions do not occur, and improvements in safety and durability are expected. In other words, all-solid-state lithium secondary batteries have features that increase safety compared to lithium secondary batteries that use liquid electrolyte.

Solid electrolytes of all-solid-state lithium secondary batteries include sulfide-based and oxide-based electrolytes. Among these, oxide-based solid electrolytes include LATP (Li _1.3 Al _0.3 Ti _1.7 (PO ₄ ) ₃ ), LLTO (Li _3x La _2/(3-x) TiO ₃ ), and LLZO (Li ₇ La ₃ Zr ₂ O ₁₂ ) systems are widely known, and among them, the LLZO system, which is known to have a relatively low grain boundary resistance and excellent dislocation window characteristics compared to the LLTO system, is attracting attention as a promising material.

Registered Patent 10-2241096

LLZO (Li ₇ La ₃ Zr ₂ O _12, lithium lanthanum zirconate) can be prepared by solid-state reaction through mixing and sintering of raw materials and is crystallized into a garnet structure or garnet-like structure. This solid-state reaction has a simple synthetic route, but the long mixing process, high sintering temperature, and long residence time required at such high temperature cause vaporization of lithium, which has the disadvantage of making it difficult to accurately control the stoichiometric content of the components. . In addition, since there is a large difference in ionic conductivity depending on the crystal structure, it is necessary to manufacture an LLZO-based solid electrolyte with a crystal structure that provides high ionic conductivity.

Accordingly, the present invention sought to provide a method for producing LLZO-based solid electrolyte by mixing raw materials well in a short time at relatively low energy.

Another object of the present invention is to provide a method for producing an LLZO-based solid electrolyte having a cubic phase.

The problem to be solved by the present invention is not limited here, and other problems not mentioned will be clearly understood by those skilled in the art from the description below.

In order to achieve the above object, the present invention

1) adding nitrate to the lithium precursor, lanthanum precursor, and zirconium precursor to obtain a precursor mixture,

2) mixing and pulverizing the precursor mixture through a milling process to obtain a mixed powder;

3) mixing, grinding and classifying the mixed powder of step 2) by adding a complex vibration mixing process,

4) Calcination step,

5) First crushing and classification step,

6) sintering step, and

7) A method for producing an LLZO-based oxide solid electrolyte including secondary grinding and classification steps is provided.

The lithium precursor may be LiCH ₃ COO, Li ₂ O, Li ₂ CO ₃ , LiOH, LiNO ₃ or a hydrate thereof, and is preferably Li ₂ CO ₃ .

The present invention has the advantage of shortening the manufacturing time and lowering the manufacturing cost by manufacturing a garnet-type LLZO-based solid electrolyte through a process that uses relatively low energy and mixes raw materials in a short time.

The LLZO-based solid electrolyte prepared by the manufacturing method of the present invention has the advantage of having a cubic phase with high crystallinity, excellent stability against lithium metal, and excellent ionic conductivity.

1 is a configuration diagram of an all-solid lithium secondary battery.
Figure 2 is an SEM photograph of the solid electrolyte prepared in Example 1, Comparative Example 1, and Comparative Example 2.
Figure 3 is an XRD graph of the solid electrolyte prepared in Example 1, Comparative Example 1, and Comparative Example 2.

Hereinafter, the present invention will be described in detail. Terms or words used in this specification and claims should not be construed as limited to their usual or dictionary meanings, and the inventor may appropriately define the concept of terms to explain his or her invention in the best way. It must be interpreted as meaning and concept consistent with the technical idea of the present invention based on principles.

Garnet-type LLZO (lithium lanthanum zirconate) is composed of oxides of lithium, lanthanum, and zirconium. Depending on its structure, it can be divided into cubic and tetragonal structures, among which the cubic structure is tetragonal. It is known that the ionic conductivity is about 10 to 100 times higher than that of . Therefore, various attempts are being made to produce LLZO solid electrolytes with a cubic structure with high ionic conductivity.

LLZO can be prepared by solid-phase reaction through mixing and sintering of raw materials and crystallized into a garnet structure or garnet-like structure. Although this solid-state reaction has a simple synthetic route, the long mixing process, high sintering temperature, and long residence time required at such high temperature cause vaporization of lithium, which has the disadvantage of making it difficult to accurately control the stoichiometric content of the components. .

In particular, when a milling process (planetary or ball mill) is used for mixing, a lot of energy is consumed due to milling for more than 5 hours, which raises the problem of increasing product costs. In addition, after milling, the overall yield is reduced due to loss of reactants on the wall of the milling pot, and there is a problem that the milling pot must be cleaned frequently.

Accordingly, the present invention sought to provide a method for producing an LLZO-based solid electrolyte with a cubic structure having a high degree of crystallinity by mixing raw materials well in a short time at relatively low energy. The present invention includes the step of mixing the raw materials through a complex vibration mixing process. A manufacturing method including was developed and completed.

This invention

1) adding nitrate to the lithium precursor, lanthanum precursor, and zirconium precursor to obtain a precursor mixture,

2) mixing and pulverizing the precursor mixture through a milling process to obtain a mixed powder;

3) mixing, grinding and classifying the mixed powder of step 2) by adding a complex vibration mixing process,

4) Calcination step,

5) First crushing and classification step,

6) sintering step, and

7) A method for producing an LLZO-based oxide solid electrolyte including secondary grinding and classification steps is provided.

The present invention produces an LLZO-based oxide solid electrolyte through a solid phase reaction, and is manufactured by mixing, pulverizing, classifying, and sintering precursors of solid electrolyte raw materials.

At this time, the conventional LLZO-based oxide solid electrolyte manufacturing method involves performing a milling process to mix raw material precursors, which is planetary milling or ball milling.

However, the present inventors recognized that when only a milling process is performed to mix raw material precursors, uniform mixing is not sufficiently achieved and a long time is required, and attempted to improve this problem. As a result, the present inventors discovered that when a complex vibration mixing process is performed along with a milling process, the raw material precursor mixture is homogeneously mixed to produce an LLZO-based solid electrolyte with a cubic structure with high ionic conductivity, and thus completed the present invention.

The present invention includes step 1) of adding nitrate to a lithium precursor, a lanthanum precursor, and a zirconium precursor to obtain a precursor mixture.

The lithium (Li) precursor may include LiCH ₃ COO, Li ₂ O, Li ₂ CO ₃ , LiOH, LiNO ₃ or hydrates thereof.

Conventionally, when expensive Li ₂ O is used as a lithium precursor, stable cubic LLZO can be produced and the performance of the solid electrolyte is excellent. However, when low-cost Li ₂ CO ₃ or LiNO ₃ is used as a lithium precursor, cubic and cubic LLZO can be produced. Due to the mixture of tetragonal structures, it was not possible to manufacture a solid electrolyte with excellent performance.

On the other hand, in the case of the present invention, by adding nitrate, preferably KNO ₃ , together with the lithium precursor, even when low-cost Li ₂ CO ₃ is used as the Li precursor, stable LLZO (cubic structure) is obtained at the same level as when using Li ₂ O. ) Solid electrolyte can be manufactured. In addition, by performing a complex vibration mixing process when adding KNO ₃ , the milling time is shortened, and a uniform KNO ₃ + LLZO precursor mixture is created even in the minimum amount to minimize crucible erosion by KNO ₃ and inflow of Al ₂ O ₃ components. It can be manufactured. In other words, the present invention can produce a solid electrolyte with excellent ionic conductivity even when using low-cost raw materials and shortening the milling time, which has the advantage of reducing costs and shortening the manufacturing process time. In addition, there is an advantage that sintering is possible at a lower temperature as the degree of sintering increases.

The lanthanum (La) precursor may be one or more compounds selected from the group consisting of acetate, nitrate, carbonate, chloride, hydroxide, and oxide containing lanthanum as a component, and is preferably La ₂ O ₃ .

The zirconium precursor may be one or more compounds selected from the group consisting of acetate, nitrate, carbonate, chloride, hydroxide, and oxide containing zirconium (Zr) as a component, and is preferably ZrO ₂ .

The solid electrolyte of the present invention further contains one or more elements selected from the group consisting of Ta, Ga, Nb, Nd, Sr, Al, Sc, Ti, V, Y and Ge as a dopant to increase ionic conductivity. It can be manufactured. To prepare a solid electrolyte containing the dopant, a precursor of one or more elements selected from the group consisting of Ta, Ga, Nb, Nd, Sr, Al, Sc, Ti, V, Y and Ge is added to the precursor mixture. Solid electrolytes can be manufactured. The precursor may be an acetate, nitrate, carbonate, chloride, hydroxide or oxide of Ta, Ga, Nb, Nd, Sr, Al, Sc, Ti, V, Y and Ge. Preferably it is an oxide.

The mixing ratio of the lithium precursor, lanthanum precursor, and zirconium precursor is 2.5 to 3.0 equivalents of lanthanum precursor and 1.7 to 2.0 equivalents of zirconium relative to 7 equivalents of lithium precursor. In this case, an LLZO oxide-based solid electrolyte with a cubic structure can be produced. When the nitrate is used in an amount greater than 0 to 10% by weight, preferably 2 to 7% by weight, based on the total precursor, an LLZO solid electrolyte with high ionic conductivity and a cubic structure can be produced. If nitrate is used in excess of 7% by weight relative to the total precursor, there may be a problem of inflow of alumina components due to erosion of the alumina crucible by nitric acid during calcination.

The present invention reduces the melting point of the LLZO precursor mixture and increases the degree of sintering by adding nitrate to the LLZO precursor mixture, thereby increasing the particle size of the final solid electrolyte. As a result, grain boundary resistance decreases and ionic conductivity increases.

In the present invention, when a dopant is included, it can be used in an amount of 1 to 10% by weight, preferably 1 to 5% by weight, and more preferably 1 to 4% by weight, based on the total amount of the precursor. The present invention has the advantage of being able to achieve the same performance and characteristics as the prior art by adding nitrate to the LLZO precursor mixture, even by adding a small amount of dopant compared to the prior art.

In step 2), the mixture from step 1) is initially mixed and pulverized through a milling process, and classification is performed if necessary. The milling process involves placing the precursor mixture and a zirconia ball of Φ3-Φ20 in a zirconia pot and mixing at a speed of 250-300 rpm for 0.5-3 hours, preferably 0.5-2 hours. Afterwards, the mixed precursor mixture is pulverized in a mortar and classified if necessary.

In the present invention, in step 3), a complex vibration mixing process is performed on the powder of the mixed and pulverized (or pulverized/classified) precursor mixture. In the present invention, when a sufficient amount of KNO ₃ is added to the LLZO production precursor, an LLZO solid electrolyte with a stable cubic structure can be manufactured compared to the case where KNO ₃ is not added, while adding KNO ₃ and performing a complex vibration mixing process The present invention was completed by discovering that an LLZO solid electrolyte with a stable cubic structure could be produced even by adding an appropriate amount of KNO ₃ .

The complex vibration mixing process involves simultaneously applying acoustic energy and vibration energy to the powder sample. Zirconia balls of Φ3-Φ10 are placed in the complex vibration mixing equipment and mixed under conditions of 10-100G, preferably 50-90G. This is a mixing process for 5-30 minutes. During the complex vibration mixing process, there may be a pause in the middle. If the complex vibration mixing process time is too long, it is not suitable due to overheating.

The complex vibration mixing equipment of the present invention simultaneously applies acoustic energy and vibration energy to the powder sample inside the equipment and uses rotational force, pressure, and high frequency to apply energy greater than gravitational acceleration to mix the powder in a short period of minutes to tens of minutes. The raw materials are crushed and mixed. When only planetary milling is performed, a milling process of more than 5 hours must be performed when mixing, and there is a problem in that the material is piled on the wall of the milling port. However, in the case of the present invention, the planetary milling time is shortened to less than 3 hours to form a milling process on the wall. Minimization of stacking is possible. In addition, by additionally performing a complex vibration mixing process, it is possible to homogeneously disperse and mix the materials for LLZO production in a shorter time compared to the process time of mixing by milling alone.

The present invention has the effect of obtaining powder with high homogeneity by effectively and quickly mixing the precursor mixture by additionally performing a complex vibration mixing process on the precursor mixture on which the milling process has been performed.

After the complex vibration mixing process, the precursor mixture is classified through a #100-#500 sieve, preferably #150-#250.

The present invention performs the calcination process in step 4).

The calcination process is a step of calcination in an electric furnace. Specifically, the mixed and classified powder was placed in an Al ₂ O ₃ crucible and the temperature was raised to 400-1000° C., preferably 700-1000° C., at a temperature increase rate of 5° C./min to 10° C./min, and then heated for 6 hours. This may be the stage where you maintain it for 10 hours. After the calcination step, a mortar pulverization process can be performed.

After the calcining process, a planetary milling or ball milling process is performed on the calcined powder. The milling process specifically involves placing a zirconia ball with a diameter of Φ3-Φ20 in a zirconia pot and mixing at a speed of 250-300 rpm for 3-5 hours. Afterwards, the pulverized precursor mixture is pulverized in a mortar and classified if necessary.

After grinding in a mortar, classify through a #100-#400 sieve.

The present invention carries out the sintering process in step 5).

The sintering process specifically involves placing the powder that has been pulverized/classified after calcination into an Al ₂ O ₃ crucible and heating at a temperature increase rate of 5° C./min to 10° C./min to 700-1300° C., preferably 1000-1200° C. ( This may be a step in which the temperature is raised to (the maximum sintering temperature can be reduced compared to the previous one through the addition of KNO ₃ ) and then maintained for 6 to 20 hours.

In the present invention, in step 6), after the sintering process, a planetary milling or ball milling process is performed on the sintered powder. The milling process specifically involves placing a zirconia ball with a diameter of Φ3-Φ20 in a zirconia pot and mixing at a speed of 250-300 rpm for 3-5 hours. Afterwards, the mixed powder is pulverized in a mortar and classified through a #100-#400 sieve to obtain an LLZO-based oxide-based solid electrolyte with a cubic structure.

The present invention can produce LLZO powder or pellets with a stable cubic structure by adding nitrate to the existing precursor composition for producing LLZO and applying a complex vibration mixing process to grind and mix.

The LLZO-based solid electrolyte prepared by the method of the present invention can be represented by the following formula (1).

[Formula 1]

Li _x La _y Zr _z D _w O ₁₂

Here, 6=x=9, 2=y=4, 1=z=3, 0=w=4

D is one or more elements selected from the group consisting of Ta, Ga, Nb, Nd, Sr, Al, Sc, Ti, V, Y and Ge.

The present invention provides an all-solid lithium secondary battery containing the LLZO solid electrolyte manufactured by the manufacturing method according to the present invention as described above.

Hereinafter, the present invention will be described with reference to an embodiment of the present invention. However, the present invention is not limited thereto, and in describing the present invention, descriptions of already known functions or configurations will be omitted to make the gist of the present invention clear.

[Example 1] Manufacturing of solid electrolyte using Li ₂ CO ₃ and complex vibration mixing process

23.9 g of Li ₂ CO ₃ powder, 46.0 g of La ₂ O ₃ powder, 23.1 g of ZrO ₂ powder, 2.2 g of Ga ₂ O ₃ powder, and 4.8 g of KNO ₃ powder were placed in a zirconia pot along with zirconia balls (Φ3-Φ20). and milled for 1 hour at a speed of 250-300 rpm. Afterwards, it was placed in a zirconia container along with zirconia balls (Φ3-Φ10), placed in a complex vibration mixer, mixed at 50-90G for 15 minutes, and then classified through a #200 sieve.

Afterwards, it was placed in an alumina crucible and calcined at 1000°C for 7 hours. The calcined powder was placed in a pot made of zirconia along with zirconia balls (Φ3-Φ20) and milled at a speed of 250-300 rpm for 4 hours.

This mixed powder was filled into a container, and this was sintered in an electric furnace at a sintering temperature of 1150°C for 10 hours. Afterwards, it was placed in a pot made of zirconia along with zirconia balls (Φ3-Φ20), milled and pulverized for 4 hours at a speed of 250-300 rpm, and classified through a #200 sieve to obtain an LLZO-based compound.

[Comparative Example 1] Preparation of solid electrolyte using Li ₂ O

An LLZO-based compound was prepared in the same manner as in Example 1, except that Li ₂ O was used instead of Li ₂ CO ₃ , KNO ₃ was not added, milling was performed for 5 hours, and the complex vibration mixing process was not performed. .

[Comparative Example 2] Preparation of solid electrolyte using Li ₂ CO ₃

An LLZO-based compound was prepared using Li ₂ CO ₃ in the same manner as in Example 1, except that KNO ₃ was not added, milling was performed for 5 hours, and a complex vibration mixing process was not performed.

[Comparative Example 3] Preparation of solid electrolyte using Li ₂ CO ₃

An LLZO-based compound was obtained in the same manner as in Example 1, except that milling using Li ₂ CO ₃ was performed for 5 hours and the complex mixing vibration process was not performed.

[Comparative Example 4] Preparation of solid electrolyte using LiOH·H ₂ O

An LLZO-based compound was prepared using LiOH·H ₂ O in the same manner as in Example 1, except that KNO ₃ was not added, milling was performed for 5 hours, and the complex vibration mixing process was not performed.

[Comparative Example 5] Preparation of solid electrolyte using LiNO ₃

An LLZO-based compound was prepared using LiNO ₃ in the same manner as in Example 1, except that KNO ₃ was not added, milling was performed for 5 hours, and the complex vibration mixing process was not performed.

Experimental Example 1.

The particle size and ionic conductivity of the obtained solid electrolyte material were measured and shown in Table 1 below.

<Particle size measurement>

Particle size was measured using a particle size analyzer (PSA).

The particle size dispersion (SPAN) was obtained by the following formula.

SPAN = (D ₉₀ -D ₁₀ )/D ₅₀

<Measurement of ionic conductivity>

Ion conductivity was measured under the conditions of 50mV, 1mHz to 4MHz using samples with the thicknesses in Table 1 below.

Li precursor Particle size (㎛) Ion conductivity note D ₁₀ D ₅₀ D ₉₀ SPAN thickness
(mm) resistance
(kO) LIC/sintering
[ x 10 ^-3 S/cm]
Sintering Example 1 1.975 6.21 13.18 1.80 2.22 0.224 1.26 -8.0% Comparative Example 1 3.22 6.67 12.13 1.34 1.75 0.163 1.37 Ref Comparative Example 2 0.491 5.93 30.62 5.08 2.24 0.399 0.77 -43.8% Comparative Example 3 2.86 7.74 13.94 1.43 1.98 0.460 0.55 -59.9% Comparative Example 4 0.441 4.39 20.76 4.63 2.43 1.763 0.18 -86.9% Comparative Example 5 0.229 5.56 18.81 3.34 2.24 1.163 0.25 -81.8%

According to Table 1, the oxide-based solid electrolyte of the present invention has a D ₅₀ of 6.21 ㎛, an ionic conductivity of 1.26 mS/cm, and the D ₅₀ of the LLZO electrolyte prepared by a conventional method using Li ₂ O of 6.67 ㎛ and ions. It can be seen that the conductivity is similar to 1.37 mS/cm. As a result, using the method of the present invention, it is possible to use Li ₂ CO ₃ , a raw material that is 10% cheaper than the price of Li ₂ O. Additionally, it is possible to shorten the process time by about 50% in the mixing process and reduce the sintering temperature in the sintering process, thereby providing excellent properties. It can be seen that there is an effect of economically manufacturing the LLZO-based solid electrolyte.

Experimental Example 2.

The size and shape of the particles were observed by measuring SEM images of the obtained LLZO solid electrolyte.

The shapes of the particles of Example 1 ((c)), Comparative Example 1 ((a)), and Comparative Example 2 ((b)) are shown in Figure 2. According to Figure 2, it can be seen that the solid electrolyte obtained in Example 1 is relatively homogeneous and has a similar shape to the solid electrolyte of Comparative Example 1, while having sufficiently larger particles than the solid electrolyte of Comparative Example 2.

Experimental Example 3.

The crystalline state of the prepared solid electrolyte was confirmed by XRD and is shown in Figure 3.

According to Figure 3, the LLZO oxide-based solid electrolyte of Example 1 has a crystallinity of a cubic structure similar to that of the solid electrolyte manufactured by the conventional method using expensive Li ₂ O as the raw material even when Li ₂ CO ₃ is used as the raw material. You can see what you have. On the other hand, when LLZO electrolyte is manufactured using Li ₂ CO ₃ using a conventional method, it can be seen that it contains undesirable phases (corresponding to “▼”) such as La ₂ Zr ₂ O ₇ (secondary phase).

Claims (11)

1) adding nitrate to the lithium precursor, lanthanum precursor, and zirconium precursor to obtain a precursor mixture,
2) mixing and pulverizing the precursor mixture through a milling process to obtain a mixed powder,
3) mixing, grinding and classifying the mixed powder of step 2) by adding a complex vibration mixing process,
4) Calcination step,
5) First crushing and classification step,
6) sintering step, and
7) Method for producing LLZO-based oxide solid electrolyte including secondary grinding and classification steps. The method of claim 1, wherein the lithium precursor is LiCH ₃ COO, Li ₂ O, Li ₂ CO ₃ , LiOH, LiNO ₃ or a hydrate thereof. The method of claim 2, wherein the lithium precursor is Li ₂ CO ₃ . The method for producing an LLZO-based oxide solid electrolyte according to claim 1, wherein the nitrate is KNO ₃ or NaNO ₃ . The method of claim 1, wherein the mixing ratio of the lithium precursor, lanthanum precursor, and zirconium precursor is 2.5 to 3.0 equivalents of the lanthanum precursor and 1.7 to 2.0 equivalents of zirconium relative to 7 equivalents of the lithium precursor. The method for producing an LLZO-based oxide solid electrolyte according to claim 1, wherein the nitrate is contained in an amount of more than 0 to 10% by weight based on the total precursor. The LLZO-based oxide solid electrolyte of claim 1, wherein the LLZO-based oxide solid electrolyte is prepared by further comprising at least one element selected from the group consisting of Ta, Ga, Nb, Nd, Sr, Al, Sc, Ti, V, Y, and Ge as a dopant. Manufacturing method. The method of claim 1, wherein the milling process of step 2) is performed for 0.5-3 hours at a speed of 250-300 rpm by inserting zirconia balls of Φ3-Φ20. The method of claim 1, wherein the composite vibration mixing process simultaneously applies acoustic energy and vibration energy to the mixed powder. The method of claim 1, wherein the complex vibration mixing process is a process of mixing for 5-30 minutes under conditions of 50-90G. An all-solid lithium secondary battery comprising an LLZO-based oxide solid electrolyte manufactured by the manufacturing method of claim 1.