CN113403567B - Nano yttrium oxide stabilized zirconia thermal barrier coating and preparation method thereof - Google Patents
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Abstract
The invention relates to a nanometer yttria-stabilized zirconia thermal barrier coating and a preparation method thereof, comprising the following steps: step 1, zrOCl is configured 2 ·8H 2 O and Y (NO) 3 ) 3 ·6H 2 O, mixing the solution A; step 2, dropwise adding excessive ammonia water into the mixed solution A gradually and continuously stirring until Zr (OH) is generated 4 And Y (OH) 3 Mixed white precipitate of (2); step 3, adding a PVA aqueous solution into the mixed white precipitate to obtain a mixture; step 4, placing the mixture on a roller ball mill for ball milling to obtain ball-milled slurry; and 5, granulating the ball-milled slurry on a spray granulator, and removing water to obtain dry Zr (OH) 4 And Y (OH) 3 The spherical mixed powder of (1); step 6, placing the spherical mixed powder obtained after granulation into a powder feeder, performing thermal spraying on the surface of the metal substrate in an atmospheric plasma spraying mode, and performing Zr (OH) under the condition of high-temperature flame 4 And Y (OH) 3 After pyrolysis, Y 3+ Incorporation into ZrO 2 In the crystal lattice, a high-density nanometer yttria-stabilized zirconia thermal barrier coating is formed.
Description
Technical Field
The invention belongs to the technical field of high-temperature protection, and particularly relates to a nano yttrium oxide stabilized zirconia thermal barrier coating and a preparation method thereof.
Background
In recent years, gas turbines have been rapidly developed, and are widely used as a new generation of energy power devices following internal combustion engines and steam engines in various fields such as energy, power generation, and ship power. With the increasing thermal efficiency of gas turbines, the machine will generate more heat during operation, which brings more requirements and challenges to the high temperature resistance, high pressure resistance, wear resistance, oxidation resistance and other performances of important components in the gas turbines. The thermal barrier coating is used as a high-temperature protection technology, can effectively isolate huge heat from a protected component, and protects an internal component from being influenced by high temperature.
ZrO 2 As a thermal barrier coating material, the material has the advantages of high melting point, large thermal expansion coefficient, small thermal conductivity, excellent mechanical property and the like, but ZrO 2 In the process from room temperature to higher service temperature, zrO 2 A phase transition occurs, which results in ZrO during each thermal cycle 2 Irreversible volume shrinkage of the coating occurs, eventually leading to peeling of the coating. And Y is 2 O 3 Y in (1) 3+ Due to its ionic radius and Zr 4+ Therefore, the YSZ type thermal barrier coating can replace the Zr position in the crystal lattice, introduce oxygen defects, form a phonon scatterer, reduce the thermal conductivity, prevent the crystal lattice from being transformed, and avoid the problems of thermal expansion and the like in service, so that the YSZ type thermal barrier coating can be used as one of thermal barrier materials with development potential. At present, the preparation of the YSZ coating is usually carried out by a plasma spraying method, wherein spherical YSZ powder particles are melted by high-temperature flame, and then molten or semi-molten liquid drops are blown on the surface of a workpiece by using compressed air. But due to ZrO 2 The melting point of the YSZ powder is higher, the residence time in flame is shorter, and the YSZ powder cannot be completely melted, so that the prepared YSZ thermal barrier coating has the problems of low density, uneven particle distribution, poor coating adhesion and the like.
Disclosure of Invention
The invention aims to provide a nano-yttria stabilized zirconia thermal barrier coating and a preparation method thereof, which solve the problem of common ZrO 2 The thermal barrier coating particles have the problems of incomplete melting, low density, uneven distribution, poor coating adhesion and the like.
The invention is realized by adopting the following technical scheme:
a preparation method of a nanometer yttria-stabilized zirconia thermal barrier coating comprises the following steps:
in the step 1, the method comprises the following steps of,configuration of ZrOCl 2 ·8H 2 O and Y (NO) 3 ) 3 ·6H 2 O, mixing the solution A;
step 2, dropwise adding excessive ammonia water into the mixed solution A obtained in the step 1 step by step and continuously stirring until Zr (OH) is generated 4 And Y (OH) 3 Mixed white precipitate of (2);
step 3, adding a PVA aqueous solution into the mixed white precipitate obtained in the step 2 to obtain a mixture;
step 4, placing the mixture obtained in the step 3 on a roller ball mill for ball milling to obtain ball-milled slurry;
and 5, granulating the ball-milled slurry obtained in the step 4 on a spray granulator, and removing water to obtain dry Zr (OH) 4 And Y (OH) 3 The spherical mixed powder of (4);
step 6, placing the spherical mixed powder obtained after granulation in the step 5 into a powder feeder, performing thermal spraying on the surface of the metal substrate in an atmospheric plasma spraying mode, and performing Zr (OH) under the condition of high-temperature flame 4 And Y (OH) 3 After pyrolysis, Y 3+ Incorporated into ZrO 2 In the crystal lattice, a high-density nanometer yttria-stabilized zirconia thermal barrier coating is formed.
In a further improvement of the invention, in step 1, zrOCl is added according to the volume of the mixed solution A being 1000mL 2 ·8H 2 O and Y (NO) 3 ) 3 ·6H 2 The mass fraction of O is 10-50 wt.%, zr 4+ Y of (A) is 3+ The molar concentration ratio is 89:11 to 97:3.
the invention is further improved in that in the step 2, the volume concentration of the ammonia water is 30-50%.
The further improvement of the invention is that in the step 3, the mass concentration of the PVA aqueous solution is 5-10%, and the adding amount is 100-200 mL.
The further improvement of the invention is that in the step 4, the rotating speed of the roller ball mill is 40-80 r/min, and the working time is 12-24 h.
In a further improvement of the invention, in step 5, the granulation parameters are as follows: the inlet temperature of the spray granulator is 300-350 ℃, the outlet temperature is 120-150 ℃, the temperature in the cavity is 180-200 ℃, the nozzle speed is 28000-35000 r/min, and the feeding speed is 100-150 g/min.
The further improvement of the invention is that in step 6, the parameters of the plasma spraying are as follows: current 240-280A, voltage 30-50V, primary gas Ar and N 2 The flow rate is 14.0-18.0L/min, and secondary gas N 2 The flow rate is 2.0-4.0L/min, the spraying distance is 80-100 mm, the flow rate of the powder carrier gas is 3.0-5.0L/min, and the powder feeding rate is 2.0-2.5 g/min.
A nanometer yttria-stabilized zirconia thermal barrier coating is prepared by the preparation method.
The invention has at least the following beneficial technical effects:
1. the invention provides a preparation method of a nanometer yttria-stabilized zirconia thermal barrier coating, which directly utilizes generated nanometer Zr (OH) 4 And Y (OH) 3 White coprecipitation is used as a precursor, and mixed spherical feed is prepared by spray granulation after ball milling, so that the components of the white coprecipitation and the mixed spherical feed are uniform, coarse grains in a high-temperature sintering process are avoided, melting is easier in a spraying process, and a coating is more compact.
2. Compared with the traditional high-temperature calcination powder preparation, spray granulation and zirconia coating plasma spraying processes, the preparation method of the nano yttria-stabilized zirconia thermal barrier coating provided by the invention directly utilizes Zr (OH) 4 And Y (OH) 3 The spherical mixed powder of (2) is decomposed by the high temperature action of a plasma torch as a spray coating material, Y 3+ Incorporation into ZrO 2 In the crystal lattice, a YSZ thermal barrier coating is formed. The yttria-stabilized zirconia thermal barrier coating is prepared by a one-step method, the production steps are simple and convenient, the energy is saved, and the cost is low;
3. compared with the traditional thermal barrier coating process, the nano-grade zirconia powder is used as the raw material, the relative density of the obtained coating is increased from 62.3% to 84.5%, and the bonding force between the coating and a substrate is increased from 35.2N to 52.4N. The feed has more complete melting degree, high density and stronger adhesive force with the substrate, and solves the problem of common ZrO 2 The thermal barrier coating particles have the problems of incomplete melting, low density, uneven distribution, poor coating adhesion and the like.
Drawings
FIG. 1 shows Zr (OH) according to the present invention 4 And Y (OH) 3 SEM picture of the ball feedstock;
FIG. 2 is an XRD pattern of a yttria-stabilized zirconia thermal barrier coating prepared in accordance with the present invention;
FIG. 3 is an SEM image of a yttria-stabilized zirconia thermal barrier coating prepared in accordance with the present invention;
FIG. 4 is a graph of the mechanical properties of a yttria-stabilized zirconia thermal barrier coating prepared in accordance with the present invention, wherein FIG. 4 (a) is a graph of relative density of the coating and FIG. 4 (b) is a graph of bonding force.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. It should be noted that the embodiments and features of the embodiments of the present invention may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
The invention provides a preparation method of a nano yttria-stabilized zirconia thermal barrier coating, which is implemented by the following steps:
step 1, configuring ZrOCl according to a certain proportion 2 ·8H 2 O/Y(NO 3 ) 3 ·6H 2 O, mixing the solution; the volume of the mixed solution is 1000mL, zrOCl 2 ·8H 2 O and Y (NO) 3 ) 3 ·6H 2 The mass fraction of O is 10-50 wt.%, and Zr 4+ Y of (A) is 3+ The molar concentration ratio is 89:11 to 97:3.
step 2, dropwise adding excessive ammonia water into the mixed solution in the step 1 step by step and continuously stirring until Zr (OH) is generated 4 And Y (OH) 3 Mixed white precipitate of (2); wherein the concentration of the ammonia water is 30-50%.
Step 3, adding a certain amount of PVA aqueous solution into the solution in the step 2; the concentration of PVA is 5-10%, and the addition amount is 100-200 mL.
Step 4, placing the mixture obtained in the step 3 on a roller ball mill for ball milling; the rotating speed of the roller ball mill is 40-80 r/min, and the working time is 12-24 h.
And 5, granulating the ball-milled slurry obtained in the step 4 on a spray granulator, and removing water to obtain dry Zr (OH) 4 And Y (OH) 3 The spherical mixed powder of (4); wherein the granulation parameters are as follows: the inlet temperature of the spray granulator is 300-350 ℃, the outlet temperature is 120-150 ℃, the temperature in the cavity is 180-200 ℃, the nozzle speed is 28000-35000 r/min, and the feeding speed is 100-150 g/min;
step 6, putting the spherical powder obtained after granulation in the step 5 into a powder feeder, performing thermal spraying on the surface of the metal substrate in an atmospheric plasma spraying mode, and performing Zr (OH) under the condition of high-temperature flame 4 And Y (OH) 3 After pyrolysis, Y 3+ Incorporation into ZrO 2 In the crystal lattice, a high-density nanometer yttria-stabilized zirconia (YSZ) thermal barrier coating is formed. Wherein the parameters of plasma spraying are as follows: current 240-280A, voltage 30-50V, primary gas (Ar + N) 2 ) The flow rate is 14.0-18.0L/min, and secondary gas (N) 2 ) The flow rate is 2.0-4.0L/min, the spraying distance is 80-100 mm, the flow rate of the powder carrier gas is 3.0-5.0L/min, and the powder feeding rate is 2.0-2.5 g/min.
Example 1
Step 1, preparing ZrOCl with a certain proportion 2 ·8H 2 O/Y(NO 3 ) 3 ·6H 2 O mixed solution: preparing 1000mL of mixed solution ZrOCl 2 ·8H 2 O/Y(NO 3 ) 3 ·6H 2 Mass fraction of O10 wt.%, zr 4+ Y of (A) is 3+ The molar concentration ratio is 89:11.
step 2, adding excessive ammonia water dropwise into the mixed solution in the step 1 and continuously stirring until Zr (OH) is generated 4 And Y (OH) 3 Mixed white precipitate of (2): whereinThe concentration of ammonia was 30wt.%.
Step 3, adding a certain amount of PVA aqueous solution into the solution in the step 2; the PVA concentration was 5% and the amount added was 200mL.
Step 4, placing the mixture obtained in the step 3 on a roller ball mill for ball milling; the rotating speed of the roller ball mill is 40r/min, and the working time is 12h.
And 5, granulating the ball-milled slurry obtained in the step 4 on a spray granulator, and removing water to obtain dry Zr (OH) 4 And Y (OH) 3 The spherical mixed powder of (4); wherein the granulation parameters are as follows: the inlet temperature of the spray granulator is 350 ℃, the outlet temperature is 150 ℃, the temperature in the cavity is 200 ℃, the nozzle speed is 28000r/min, and the feeding speed is 100g/min;
step 6, putting the spherical powder obtained after granulation in the step 5 into a powder feeder, performing thermal spraying on the surface of the metal substrate in an atmospheric plasma spraying mode, and performing Zr (OH) under the condition of high-temperature flame 4 And Y (OH) 3 After pyrolysis, Y 3+ Incorporated into ZrO 2 In the crystal lattice, a high-density nanometer yttria-stabilized zirconia (YSZ) thermal barrier coating is formed. Wherein the parameters of plasma spraying are as follows: current 240A, voltage 50V, primary gas (Ar + N) 2 ) Flow rate 14.0L/min, secondary gas (N) 2 ) The flow rate is 2.0L/min, the spraying distance is 80mm, the flow rate of the powder carrier gas is 3.0L/min, and the powder feeding rate is 2.0g/min.
Example 2
Step 1, preparing ZrOCl with a certain proportion 2 ·8H 2 O/Y(NO 3 ) 3 ·6H 2 O mixed solution: preparing 1000mL of mixed solution ZrOCl 2 ·8H 2 O/Y(NO 3 ) 3 ·6H 2 Mass fraction of O30 wt.%, zr 4+ Y of (2) 3+ The molar concentration ratio is 97:3.
step 2, dropwise adding excessive ammonia water into the mixed solution in the step 1 step by step and continuously stirring until Zr (OH) is generated 4 And Y (OH) 3 Mixed white precipitate of (2); wherein the concentration of ammonia water is 50%.
Step 3, adding a certain amount of PVA aqueous solution into the solution in the step 2; the PVA concentration was 10% and the amount added was 100mL.
Step 4, placing the mixture obtained in the step 3 on a roller ball mill for ball milling; the rotating speed of the roller ball mill is 80r/min, and the working time is 12h.
And 5, granulating the ball-milled slurry obtained in the step 4 on a spray granulator, and removing water to obtain dry Zr (OH) 4 And Y (OH) 3 The spherical mixed powder of (1); wherein the granulation parameters are as follows: the inlet temperature of the spray granulator is 300 ℃, the outlet temperature is 120 ℃, the temperature in the cavity is 180 ℃, the nozzle speed is 35000r/min, and the feeding speed is 150g/min;
step 6, placing the spherical powder obtained after granulation in the step 5 into a powder feeder, performing thermal spraying on the surface of the metal substrate in an atmospheric plasma spraying manner, and performing Zr (OH) under the condition of high-temperature flame 4 And Y (OH) 3 After pyrolysis, Y 3+ Incorporated into ZrO 2 In the crystal lattice, a high-density nanometer yttria-stabilized zirconia (YSZ) thermal barrier coating is formed. Wherein the parameters of plasma spraying are as follows: current 280A, voltage 30V, primary gas (Ar + N) 2 ) Flow rate 18.0L/min, secondary gas (N) 2 ) The flow rate is 4.0L/min, the spraying distance is 100mm, the flow rate of the powder carrier gas is 5.0L/min, and the powder feeding rate is 2.5g/min.
Example 3
Step 1, preparing ZrOCl with a certain proportion 2 ·8H 2 O/Y(NO 3 ) 3 ·6H 2 O mixed solution: preparing 1000mL of mixed solution ZrOCl 2 ·8H 2 O/Y(NO 3 ) 3 ·6H 2 Mass fraction of O40 wt.%, zr 4+ Y of (A) is 3+ The molar concentration ratio is 95:5.
step 2, dropwise adding excessive ammonia water into the mixed solution in the step 1 step by step and continuously stirring until Zr (OH) is generated 4 And Y (OH) 3 Mixed white precipitate of (2); wherein the concentration of ammonia water is 50%.
Step 3, adding a certain amount of PVA aqueous solution into the solution in the step 2; the PVA concentration was 10%, and the amount added was 150mL.
Step 4, placing the mixture obtained in the step 3 on a roller ball mill for ball milling; the rotating speed of the roller ball mill is 80r/min, and the working time is 12h.
And 5, granulating the ball-milled slurry obtained in the step 4 on a spray granulator, and removing water to obtain dry Zr (OH) 4 And Y (OH) 3 The spherical mixed powder of (4); wherein the granulation parameters are as follows: the inlet temperature of the spray granulator is 320 ℃, the outlet temperature is 130 ℃, the temperature in the cavity is 190 ℃, the nozzle speed is 30000r/min, and the feeding speed is 120g/min;
step 6, placing the spherical powder obtained after granulation in the step 5 into a powder feeder, performing thermal spraying on the surface of the metal substrate in an atmospheric plasma spraying manner, and performing Zr (OH) under the condition of high-temperature flame 4 And Y (OH) 3 After pyrolysis, Y 3+ Incorporated into ZrO 2 In the crystal lattice, a high-density nanometer yttria-stabilized zirconia (YSZ) thermal barrier coating is formed. Wherein the parameters of plasma spraying are as follows: current 260A, voltage 40V, primary gas (Ar + N) 2 ) Flow rate of 16.0L/min, secondary gas (N) 2 ) The flow rate is 3.0L/min, the spraying distance is 90mm, the flow rate of the powder carrier gas is 40L/min, and the powder feeding rate is 2.3g/min.
Example 4
Step 1, preparing ZrOCl with a certain proportion 2 ·8H 2 O/Y(NO 3 ) 3 ·6H 2 O mixed solution: preparing 1000mL of mixed solution ZrOCl 2 ·8H 2 O/Y(NO 3 ) 3 ·6H 2 Mass fraction of O40 wt.%, zr 4+ Y of (A) is 3+ The molar concentration ratio is 95:5.
step 2, dropwise adding excessive ammonia water into the mixed solution in the step 1 step by step and continuously stirring until Zr (OH) is generated 4 And Y (OH) 3 Mixed white precipitate of (2); wherein the concentration of the ammonia water is 40 percent.
Step 3, adding a certain amount of PVA aqueous solution into the solution in the step 2; the PVA concentration was 5% and the amount added was 150mL.
Step 4, placing the mixture obtained in the step 3 on a roller ball mill for ball milling; the rotating speed of the roller ball mill is 60r/min, and the working time is 18h.
Step (ii) of5, granulating the ball-milled slurry obtained in the step 4 on a spray granulator, and removing water to obtain dry Zr (OH) 4 And Y (OH) 3 The spherical mixed powder of (4); wherein the granulation parameters are as follows: the inlet temperature of the spray granulator is 330 ℃, the outlet temperature is 130 ℃, the temperature in the cavity is 180 ℃, the nozzle speed is 32000r/min, and the feeding speed is 120g/min;
step 6, placing the spherical powder obtained after granulation in the step 5 into a powder feeder, performing thermal spraying on the surface of the metal substrate in an atmospheric plasma spraying manner, and performing Zr (OH) under the condition of high-temperature flame 4 And Y (OH) 3 After pyrolysis, Y 3+ Incorporated into ZrO 2 In the crystal lattice, a high-density nanometer yttria-stabilized zirconia (YSZ) thermal barrier coating is formed. Wherein the parameters of plasma spraying are as follows: current 280A, voltage 40V, primary gas (Ar + N) 2 ) Flow rate 18.0L/min, secondary gas (N) 2 ) The flow rate is 4.0L/min, the spraying distance is 80mm, the flow rate of the powder carrier gas is 3.5L/min, and the powder feeding rate is 2.3g/min.
Zr (OH) of high-density nano yttrium oxide stabilized zirconia thermal barrier coating prepared by the method 4 And Y (OH) 3 As shown in fig. 1, it can be seen that the spherical feed is composed of countless fine nanoparticles without fine particles, which is favorable for melting in plasma high temperature flame.
The invention directly utilizes Zr (OH) 4 And Y (OH) 3 The spherical mixed powder is used as a spray coating, is decomposed under the high-temperature action of a plasma spray gun, and is used for preparing the yttria-stabilized zirconia thermal barrier coating by a one-step method, so that the production steps are simple and convenient, the energy is saved, and the cost is lower.
XRD and SEM images of the yttria zirconia thermal barrier coating obtained by the method of the invention; as shown in FIGS. 2 and 3, it can be seen that only tetragonal ZrO was present in the coating obtained after spraying 2 Description of Zr (OH) after passing through the high temperature spray gun 4 And Y (OH) 3 Are all completely decomposed, and Y 3+ Is dissolved in ZrO 2 In the crystal lattice of (1), stabilized ZrO 2 The function of the crystal form; in addition, the prepared coating has high melting degree,the coating is very compact, has almost no obvious air holes and is very uniformly distributed, which is beneficial to improving the service life of the thermal barrier coating and the direct bonding strength of the coating and the substrate.
FIG. 4 is a graph of the mechanical properties of a yttria-stabilized zirconia thermal barrier coating prepared in accordance with the present invention. It can be seen that the YSZ coating prepared by the present invention, whether it is denser or has higher bonding strength to the substrate than commercial YSZ coatings. The relative density of the coating obtained by the invention is increased from 62.3% to 84.5%, and the bonding force between the coating and the substrate is increased from 35.2N to 52.4N.
Although the invention has been described in detail with respect to the general description and the specific embodiments thereof, it will be apparent to those skilled in the art that modifications and improvements can be made based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (5)
1. A preparation method of a nanometer yttria-stabilized zirconia thermal barrier coating is characterized by comprising the following steps:
step 1, preparing ZrOCl 2 ·8H 2 O and Y (NO) 3 ) 3 ·6H 2 O, mixing the solution A; zrOCl according to the volume of the mixed solution A of 1000mL 2 ·8H 2 O and Y (NO) 3 ) 3 ·6H 2 The mass fraction of O is 10-50 wt.%, zr 4+ Y of (A) is 3+ The molar concentration ratio is 89:11 to 97:3;
step 2, dropwise adding excessive ammonia water into the mixed solution A obtained in the step 1 step by step and continuously stirring until Zr (OH) is generated 4 And Y (OH) 3 Mixed white precipitate of (2);
step 3, adding PVA aqueous solution into the mixed white precipitate obtained in the step 2 to obtain a mixture;
step 4, placing the mixture obtained in the step 3 on a roller ball mill for ball milling to obtain ball-milled slurry;
step 5, granulating the ball-milled slurry obtained in the step 4 on a spray granulator, and removing waterObtaining dry Zr (OH) after separation 4 And Y (OH) 3 The spherical mixed powder of (4); the granulation parameters were: the inlet temperature of the spray granulator is 300-350 ℃, the outlet temperature is 120-150 ℃, the temperature in the cavity is 180-200 ℃, the nozzle speed is 28000-35000 r/min, and the feeding speed is 100-150 g/min;
step 6, placing the spherical mixed powder obtained after granulation in the step 5 into a powder feeder, performing thermal spraying on the surface of the metal substrate in an atmospheric plasma spraying manner, and performing Zr (OH) under the condition of high-temperature flame 4 And Y (OH) 3 After pyrolysis, Y 3+ Incorporated into ZrO 2 In the crystal lattice, a high-density nanometer yttria-stabilized zirconia thermal barrier coating is formed; the parameters of plasma spraying are as follows: current 240-280A, voltage 30-50V, primary gas Ar and N 2 The flow rate is 14.0-18.0L/min, and secondary gas N 2 The flow rate is 2.0-4.0L/min, the spraying distance is 80-100 mm, the flow rate of the powder carrier gas is 3.0-5.0L/min, and the powder feeding rate is 2.0-2.5 g/min.
2. The method for preparing a nano yttria-stabilized zirconia thermal barrier coating according to claim 1, wherein in the step 2, the volume concentration of ammonia water is 30-50%.
3. The method for preparing a nano yttria-stabilized zirconia thermal barrier coating according to claim 1, wherein in the step 3, the PVA aqueous solution has a mass concentration of 5-10% and is added in an amount of 100-200 mL.
4. The method for preparing a nano yttria-stabilized zirconia thermal barrier coating according to claim 1, wherein in the step 4, the rotation speed of the roller ball mill is 40-80 r/min, and the working time is 12-24 h.
5. A nano yttria-stabilized zirconia thermal barrier coating, characterized by being prepared by the preparation method of any one of claims 1 to 4.
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