CN117551424A - Oil-based thermosensitive active grinding fluid and microwave-assisted fixed abrasive grinding method - Google Patents

Abstract

The invention discloses an oil-based thermosensitive active grinding fluid and a microwave-assisted fixed abrasive grinding method, wherein the oil-based thermosensitive active grinding fluid comprises the following components: the mass percent of the propylene glycol is 0.5-5%, the mass percent of the triethanolamine is 0.5-5%, the mass percent of the thermosensitive oxidant is 1-10%, and the balance is vegetable oil. The thermal decomposition initiator in the thermally-induced thermosensitive active grinding fluid is decomposed to generate free radicals with strong chemical activity, so that the hard and brittle materials under the action of mechanical force are quickly subjected to chemical modification, and a relatively softer modification layer is generated on the surface of the matrix; under the action of microwave heating, the thermosensitive active grinding fluid is used as a conducting medium to transfer heat to the surface of a workpiece to be processed, so that the plastic deformation capacity of the surface modified layer material of the workpiece is improved; the diamond fixed abrasive millstone mechanically removes the surface material of the workpiece softened by microwave heating, the low-hardness modified layer is broken and peeled off in a layered manner, and the rapidly exposed new surface is further modified and removed, so that high processing efficiency is obtained.

Description

An oil-based heat-sensitive active grinding fluid and microwave-assisted bonded abrasive grinding method

Technical field

The invention relates to the technical field of ultra-precision machining of difficult-to-machine materials, and relates to an oil-based heat-sensitive active grinding fluid and a microwave-assisted bonded abrasive grinding method. The grinding fluid and grinding method are particularly suitable for brittle crystal materials.

Background technique

The statements herein merely provide background information related to the present invention and do not necessarily constitute prior art.

Brittle crystal materials, such as single crystal silicon, alumina, silicon carbide, and gallium nitride, are core materials in the fields of energy, communications, transportation, and medical care. Power devices and radio frequency devices made of brittle semiconductor materials are widely used in modern industrial fields such as new energy vehicles, 5G communications, photovoltaic power generation, rail transportation, smart grids, and aerospace. However, the above-mentioned brittle crystalline materials have the characteristics of high hardness, great brittleness and stable chemical properties, and are typically difficult-to-process materials. The surface quality and processing accuracy of the workpiece will significantly affect the performance, energy consumption and life of semiconductor devices. Therefore, it is particularly important to achieve high efficiency, low damage and ultra-precision processing of brittle materials.

Grinding, grinding and polishing are mainly used at home and abroad for ultra-precision processing of brittle crystal materials made by wire cutting to control shape accuracy, surface quality and sub-surface damage depth. Grinding usually uses 1 to 15 μm free diamond abrasives to mechanically remove the damage layer generated during the grinding process. CN110421481A provides a method of mechanical grinding and processing of hard and brittle sapphire with free abrasives, but the material properties of high hardness and strong wear resistance and three-body wear The processing method of material removal results in extremely low material removal rate and poor surface accuracy of the workpiece when grinding sapphire with free abrasives. CN110539209A provides a method for processing sapphire wafers by combining free abrasive grinding and fixed abrasive grinding. Fixed abrasive disc grinding can effectively increase the grinding pressure, improve the material removal rate, and obtain high processing accuracy at the same time. However, the two-body method The processing method of abrasive mechanical removal of material results in relatively poor grinding surface and subsurface quality, significantly increasing the time and cost of subsequent chemical mechanical polishing treatments. In view of the material characteristics of third-generation semiconductor materials such as high hardness, strong wear resistance, and high brittleness, existing grinding methods for processing hard and brittle materials have problems such as extremely low efficiency or poor surface quality. There is an urgent need to develop a method that can take into account both surface quality and processing. Efficient grinding methods reduce the manufacturing and processing costs of brittle materials, especially hard and brittle materials, and accelerate the development of high-efficiency semiconductor devices.

Contents of the invention

In view of the prominent contradiction between grinding efficiency and surface quality of difficult-to-process brittle crystalline materials, the present invention provides an oil-based heat-sensitive active grinding fluid and a microwave-assisted fixed abrasive grinding method.

In order to achieve the above objects, the present invention is achieved through the following technical solutions:

In a first aspect, the present invention provides an oil-based heat-sensitive active grinding fluid, which includes the following components: a mass percentage of propylene glycol of 0.5% to 5%, a mass percentage of triethanolamine of 0.5% to 5%, and a mass percentage of heat-sensitive oxidant. The percentage is 1% to 10%, and the balance is vegetable oil.

In some embodiments, the heat-sensitive oxidant is selected from one or a combination of one or more of hydrogen peroxide, dicyclohexyl peroxycarbonate (DCPD), or diisopropyl peroxydicarbonate (IPP).

Thermal decomposition initiator refers to a thermal decomposition initiator that can be thermally decomposed to produce free radicals for controllable chemical modification of hard and brittle materials under the action of mechanical force.

The main working principle of oil-based thermally active polishing fluid: microwave-induced thermal decomposition initiator in the thermally active polishing fluid decomposes to produce highly chemically active free radicals, which can quickly chemically modify hard and brittle materials under the action of mechanical force, and promote A relatively softer modified layer is produced on the surface of the substrate; under the action of microwave heating, the heat-sensitive active grinding fluid acts as a conductive medium to transfer heat to the surface of the workpiece to be processed, improving the plastic deformation ability of the modified layer material on the surface of the workpiece; diamond consolidation The abrasive disc mechanically removes the surface material of the workpiece softened by microwave heating. The modified layer with low hardness is broken and peeled off in layers. The newly exposed surface is further modified and removed to obtain high processing efficiency. Propylene glycol and triethanolamine are used to synergistically regulate diamond. The contact stress between the abrasive particles and the modified layer enables high-efficiency, low-damage ultra-precision grinding of hard and brittle materials that are difficult to machine.

The details are as follows: The thermal decomposition reaction equations of the organic peroxy thermal decomposition initiators dicyclohexyl peroxycarbonate (DCPD) and diisopropyl peroxydicarbonate (IPP) are as follows:

The equation for the thermal decomposition reaction of hydrogen peroxide, an inorganic peroxy thermal decomposition initiator, is as follows:

The chemical equation for the reaction between the surface of brittle crystalline materials and free radicals is as follows:

Among them, B is the brittle workpiece material.

In some embodiments, the vegetable oil is soybean oil, palm oil, or rapeseed oil.

In a second aspect, the present invention provides a method for preparing the oil-based heat-sensitive active grinding fluid, which includes the following steps:

After mixing propylene glycol, triethanolamine and vegetable oil in proportion, add a heat-sensitive oxidant to the mixture and mix evenly to obtain a grinding liquid.

In a third aspect, the present invention provides a microwave-assisted fixed abrasive grinding method, which includes the following steps: adding the oil-based heat-sensitive active grinding fluid to the fixed abrasive grinding disc;

Drive the workpiece to be ground and the grinding disc to rotate and grind against each other;

Use microwaves to heat the grinding system, and at the same time induce the decomposition of the oil machine's thermally active grinding fluid in the thermally active grinding fluid to produce active free radicals to chemically modify the workpiece under mechanical stress;

Grinding removes the softened material from the surface of the workpiece.

Chemical modification can reduce the hardness of the surface material of the workpiece and improve the fracture toughness of brittle materials. At the same time, the heating effect of microwave is used to improve the plasticity of the modified layer material.

By configuring an oil-based thermally active grinding fluid, a microwave-consolidated diamond abrasive grinding system with microwave heating function and adjustable temperature is constructed, using microwave energy to heat the workpiece to be processed, improving the plastic deformation ability of the material, and inducing thermally active grinding at the same time The thermal decomposition initiator in the liquid decomposes to generate active free radicals to chemically modify the surface material of the workpiece under mechanical stress, causing the surface of the brittle workpiece material to form a modified layer with low hardness, low elastic modulus and high fracture toughness. Increase the critical cutting depth for material brittle-plastic transition removal, reduce or even eliminate processing damage caused by single mechanical stress removal, and improve material removal rate and processing surface quality.

In some embodiments, the expression of the critical grinding depth d _c for grinding to remove softened material from the workpiece surface is as follows:

d _c =λ(H/E) ^1/2 (K _c /H) ² ;

Among them, λ is the brittleness-plastic transition factor of brittle materials, H is the hardness of the microwave-softened material, E is the elastic modulus of the microwave-softened material, and K _c is the fracture toughness of the microwave-softened material.

In some embodiments, microwaves are used to heat the grinding system to 40-300°C.

In some embodiments, the particle size of the diamond abrasive in the grinding disc is 0.2-3.0 μm.

In some embodiments, the grinding pressure is 50-100g/cm ² ;

Preferably, the rotation speed of the grinding disc is 150-300 rpm;

Preferably, the rotation speed of the workpiece is 100-150 rpm;

Preferably, the flow rate of the grinding liquid is 50-100 mL/min.

In some embodiments, the method further includes the steps of measuring the surface roughness S _a of the polished workpiece using an atomic force microscope and observing the subsurface of the polished workpiece using focused ion beam-transmission electron microscopy technology.

In some embodiments, the construction steps of the microwave-assisted fixed abrasive grinding system are:

Set a microwave radiation shield with a visible window outside the grinding platform;

Inside the shielding cover, one or more microwave generators are concentrated or evenly arranged along the grinding platform. The distance between the microwave generator and the workpiece to be processed is 5 to 10 cm;

Install the workpiece to be processed and the grinding disc separately for subsequent operations.

The beneficial effects achieved by one or more embodiments of the present invention are as follows:

1. The present invention uses heat-sensitive active grinding fluid to carry out microwave-assisted controllable chemical modification of the workpiece under the action of mechanical force, soften the surface material of the workpiece, increase the critical cutting depth for material brittle-plastic transition removal, thereby reducing or even Eliminates processing damage caused by single mechanical stress removal while increasing material removal rate. There is no microcrack damage or breakage on the surface of the workpiece after grinding, and the surface roughness _Sa of the workpiece can reach 1.0~10.0nm. The material removal rate can reach 15.0~30.0μm/min. The invention can simultaneously achieve ultra-precision grinding processing of high surface quality, low mechanical damage and high material removal rate of difficult-to-machine materials.

2. The present invention uses a fixed abrasive grinding disc. The density distribution of the abrasive particles is controllable, the grinding efficiency is high, the grinding disc has good wear resistance and high durability. At the same time, the active grinding fluid provides microwave assistance to the workpiece under the action of mechanical force. Controllable chemical modification can expand the controllable speed range of chemical reactions, adapt to mechanical forces under different parameters, regulate the synergistic effect of chemical and mechanical grinding, effectively improve the surface quality and processing efficiency of materials, and achieve high performance for hard, brittle and difficult-to-machine materials. Efficient, low-damage ultra-precision grinding processing.

Description of the drawings

The description and drawings that constitute a part of the present invention are used to provide a further understanding of the present invention. The illustrative embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention.

Figure 1: SEM micrographs (a and b) of diamond abrasive grains (a and b) and pictures of diamond fixed abrasive discs (c) prepared in the microwave-assisted bonded abrasive grinding method of the present invention;

Figure 2 is a schematic diagram of the grinding platform in the microwave-assisted fixed abrasive grinding method of the present invention, 1-workbench, 2-workpiece to be processed, 3-liquid pool, 4-diamond fixed abrasive grinding disc, 5-grinding dust filtering device, 6- Thermal active grinding liquid supply device, 7-thermal initiator concentration indicating device, 8-microwave generating device;

Figure 3 is a comparison chart of the material removal rates of diamond-bonded abrasives grinding silicon carbide and alumina crystals under the action of deionized water and oil-based heat-sensitive active grinding fluid in the microwave-assisted bonded abrasive grinding method of the present invention;

Figure 4 is an SEM micrograph of alumina single crystals ground by diamond-bonded abrasives under the action of deionized water and oil-based heat-sensitive active polishing fluid in the microwave-assisted bonded abrasive grinding method of the present invention;

Figure 5 is a process flow chart for the preparation of oil-based heat-sensitive active grinding fluid and the microwave-assisted fixed abrasive grinding processing of brittle materials in the microwave-assisted fixed abrasive grinding method of the present invention.

Detailed ways

It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings commonly understood by one of ordinary skill in the art to which this invention belongs.

Example 1

A microwave-assisted fixed abrasive grinding method for brittle materials and an oil-based heat-sensitive active grinding fluid of the present invention will be further described with reference to the examples:

In this embodiment, a 2-inch hard and brittle silicon carbide and alumina wafer is selected as the workpiece to be processed. A grinding and polishing machine designed and customized in the laboratory is used as the test platform. The microwave generator can heat the workpiece to be processed and the active grinding fluid to 80°C. , a diamond bonded abrasive disc with an average particle size of 3 μm is used to grind the above workpiece, as shown in Figure 2, for grinding processing. After grinding, the samples were ultrasonically cleaned with alcohol for 10 minutes. Use a balance (accuracy 0.001 mg) to weigh the mass of the workpiece material before and after grinding, and calculate the material removal rate; use an atomic force microscope to measure the surface roughness S _a of the workpiece after grinding, with a measurement range of 50 μm × 50 μm, and use a field emission scanning electron microscope to observe the workpiece after grinding. The surface of the workpiece.

The specific implementation steps are as follows:

S1. Based on the chemical principle that thermal decomposition initiators interact with heat to generate free radical active species, and the chemical principle that free radical active species and inert materials react with each other to form a softening layer, for hard and brittle materials with high hardness, brittleness, and chemical properties Stable characteristics, equipped with active grinding fluid that generates free radical active species by microwave heating and can perform controllable chemical modification of workpiece materials under mechanical stress:

S11. Pour a certain amount of propylene glycol, triethanolamine and vegetable oil into a beaker in sequence in the chemical experiment operation box, and mechanically stir and mix at room temperature for 3 to 5 minutes to obtain a propylene glycol-triethanolamine mixed oil solution;

S12. Slowly add a certain amount of the thermal decomposition initiator compound to the propylene glycol-trolamine mixed oil solution, stir mechanically at room temperature for 1 to 2 minutes, and dissolve or disperse the thermal decomposition initiator compound into the propylene glycol-trolamine mixed oil solution. , a grinding fluid with heat-sensitive activity is obtained;

S13. Pour the prepared heat-sensitive active grinding fluid into a light-proof reagent bottle for later use.

S2. Build a microwave-consolidated diamond abrasive grinding platform with microwave heating function and adjustable temperature:

S21. Fix the microwave generator 5cm from the contact interface between the workpiece and the grinding disc. The microwave generator can rotate and move to focus the energy on the designated area;

S22. Use a balance to weigh the mass of the workpiece before grinding, then install the double-door shielding cover directly in front of the grinding table, clamp the workpiece to the workbench connected to the upper drive motor through vacuum adsorption, and place the 3 μm particle size solid The bonded diamond abrasive grinding disc is fixed to the turntable connected to the lower drive motor;

S23. Add the heat-sensitive active grinding fluid configured in S1 to the diamond bonded abrasive grinding disc at a certain flow rate.

S3. Set the microwave generator respectively according to the composition, content and flow rate of the initiator compound in the heat-sensitive active grinding fluid obtained in S1, as well as the hardness, elastic modulus, fracture toughness and interface separation strength of the workpiece material modification layer. Process parameters such as power, grinding pressure, grinding disc rotation speed and workpiece rotation speed. The selection of process parameters is based on the mechanical properties of the workpiece modification layer. The automatic grinding and polishing machine is started to perform microwave heating chemical modification and mechanical grinding removal of the workpiece material. Microwave-assisted mechanical grinding processing of dynamically removing material from the sexual layer:

The specific steps for grinding the workpiece include:

S31. Start the lower drive motor to drive the fixed diamond abrasive grinding disc to rotate, start the upper drive motor to drive the workpiece to rotate, and at the same time apply positive pressure to control the fixed diamond abrasive grinding disc and the workpiece to grind against each other.

S32. Adjust the microwave generator, use microwave energy to heat the workpiece to be processed, and at the same time induce the thermal decomposition initiator in the heat-sensitive active grinding fluid to decompose to generate active free radicals to chemically modify the workpiece under the action of mechanical stress and reduce the deterioration of the surface material of the workpiece. Hardness and elastic modulus, while improving the fracture toughness of brittle materials.

On the basis of step S3, the softened material on the surface of the workpiece is removed by grinding. The expression of the critical cutting depth d _c for mechanically removing the softened material on the surface of the workpiece with diamond abrasive grains is as follows:

d _c =λ(H/E) ^1/2 (K _c /H) ² ;

Among them, λ is the brittle-plastic transition factor of the photosensitive material, H is the hardness of the photosensitive material, E is the elastic modulus of the photosensitive material, and K _c is the fracture toughness of the photosensitive material.

S33. After 10 to 30 minutes, turn off the testing machine, remove the workpiece, and then clean the workpiece ultrasonically with alcohol for 10 minutes. Use a balance to weigh the mass of the ground workpiece, calculate the removal rate of the workpiece material, and use an atomic force microscope to measure the surface roughness of the ground workpiece. Degree _Sa , measuring range 50μm×50μm, use field emission scanning electron microscope to observe the surface of the workpiece after grinding.

S34. Use an atomic force microscope to measure the surface roughness S _a of the polished workpiece, use a field emission scanning electron microscope to observe the surface of the polished workpiece, and use focused ion beam-transmission electron microscopy technology to observe the subsurface of the polished workpiece.

Grinding liquid: Grinding liquid C, composed of: 94% soybean oil, 5% dicyclohexyl peroxycarbonate (DCPD), 0.5% propylene glycol, and 0.5% triethanolamine.

Grinding method: grinding temperature 80°C, grinding pressure 100g/cm ² , grinding disc rotation speed 200rpm, workpiece rotation speed 50rpm, grinding fluid flow 50mL/min, grinding time 20 minutes, the microwave generator is in working condition, and the grinding disc surface temperature is guaranteed to be 80°C Fluctuates left and right; the particle size of the diamond abrasive grains in the fixed abrasive disc is 250nm ~ 1000nm.

Comparative example 1

Grinding liquid A is deionized water, and everything else is the same as in Example 1.

Comparative example 2

Grinding liquid B includes: 99% soybean oil, 0.5% propylene glycol, and 0.5% triethanolamine; everything else is the same as in Example 1.

test results:

As shown in Figure 3, the surface roughness S a of silicon carbide and alumina wafers processed by microwave-assisted fixed abrasive grinding with polishing liquid _A is 41.3nm and 36.6nm, and the workpiece material removal rate MRR is 7.3μm/min and 3.9μm. /min.

The surface roughness S _a of silicon carbide and alumina wafers processed by polishing liquid B with microwave-assisted fixed abrasive grinding is 33.1nm and 24.8nm, and the workpiece material removal rate MRR is 6.3μm/min and 2.3μm/min.

The surface roughness S _a of silicon carbide and alumina wafers processed by polishing liquid C microwave-assisted fixed abrasive grinding is 11.3nm and 8.6nm, and the workpiece material removal rate MRR is 20.5μm/min and 10.9μm/min.

Figure 4 further proves that microwave-assisted fixed abrasive grinding processing based on oil-based thermally active grinding fluid can effectively reduce the brittle fracture of silicon carbide and aluminum oxide crystal surfaces and improve the mechanical damage of the grinding surface.

Through the above three sets of tests to compare the processing effects of diamond fixed abrasive mechanical grinding and microwave-assisted fixed abrasive grinding, it was found that the processing effect of the grinding processing method of the present invention is significantly better than the traditional mechanical grinding processing method.

In particular, control group A uses deionization. Microwave heating exceeding 100°C will produce high-temperature water vapor, which poses certain safety risks. Therefore, this example only controls the temperature around 80°C. However, in the actual processing process, due to the use of large Vegetable oils such as soybean oil and olive oil are used as the base liquid, and the temperature can be further increased to 300°C, which will be more conducive to the dislocation slip of the surface material of the modified layer, thereby improving the plastic deformation ability and obtaining better grinding performance.

Example 2

Grinding liquid: composed of: 93% soybean oil, 2% diisopropyl peroxydicarbonate, 4% propylene glycol, and 1% triethanolamine. Others are the same as Example 1.

Example 3

Grinding fluid: composed of: 87% soybean oil, 7% hydrogen peroxide, 2% propylene glycol, and 4% triethanolamine. Others are the same as Example 1.

Example 4

Grinding method: grinding temperature 200°C, grinding pressure 50g/cm ² , grinding disc rotation speed 300rpm, workpiece rotation speed 150rpm, grinding fluid flow 70mL/min, grinding time 20 minutes, microwave generator in working condition, ensure the grinding disc surface temperature is 200°C Fluctuate left and right.

Example 5

Grinding method: grinding temperature 300°C, grinding pressure 100g/cm ² , grinding disc rotation speed 150rpm, workpiece rotation speed 150rpm, grinding fluid flow 100mL/min, grinding time 20 minutes, the microwave generator is in working condition, and the surface temperature of the grinding disc is guaranteed to be 300°C. Fluctuate left and right.

The above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims (11)

1. An oil-based thermosensitive active grinding fluid is characterized in that: the composition comprises the following components: the mass percent of the propylene glycol is 0.5-5%, the mass percent of the triethanolamine is 0.5-5%, the mass percent of the thermosensitive oxidant is 1-10%, and the balance is vegetable oil.

2. The oil-based heat sensitive active abrasive slurry of claim 1, wherein: the thermosensitive oxidant is selected from one or a combination of more of hydrogen peroxide, dicyclohexyl peroxycarbonate or diisopropyl peroxydicarbonate;

preferably, the vegetable oil is soybean oil, palm oil or rapeseed oil.

3. The method for preparing the oil-based thermosensitive active polishing liquid according to claim 1 or 2, characterized in that: the method comprises the following steps:

and (3) uniformly mixing propylene glycol, triethanolamine and vegetable oil according to a proportion, adding a thermosensitive oxidant into the mixed solution, and uniformly mixing to obtain the grinding fluid.

4. A microwave-assisted fixed abrasive grinding method is characterized in that: the method comprises the following steps: adding the oil-based heat-sensitive active abrasive slurry of claim 1 or 2 to a fixed abrasive grinding disc;

driving a workpiece to be ground and a grinding disc to rotate and perform counter grinding;

heating the grinding system by utilizing microwaves, and simultaneously inducing the decomposition of the thermosensitive active grinding fluid of the oil machine in the thermosensitive active grinding fluid to generate active free radicals to chemically modify the workpiece under the action of mechanical stress;

grinding to remove the softened material on the surface of the workpiece.

5. A method of microwave-assisted fixed abrasive lapping according to claim 3, wherein: critical grinding depth d for grinding and removing workpiece surface softening material _c The expression of (2) is as follows:

d _c ＝λ(H/E) ^1/2 (K _c /H) ² ；

wherein lambda is the brittle-plastic transition factor of the brittle material, H is the hardness of the material after microwave softening, E is the elastic modulus of the material after microwave softening, K _c Is the fracture toughness of the material after microwave softening.

6. A method of microwave-assisted fixed abrasive lapping according to claim 3, comprising the steps of: and heating the grinding system to 40-300 ℃ by adopting microwaves.

7. A method of microwave-assisted fixed abrasive lapping according to claim 3, comprising the steps of: the granularity of the diamond abrasive in the grinding disc is 0.2-3.0 mu m.

8. A method of microwave-assisted fixed abrasive lapping according to claim 3, comprising the steps of: the grinding pressure is 50-100 g/cm ² 。

9. The method for microwave-assisted fixed abrasive lapping according to claim 7, comprising the steps of: the rotating speed of the grinding disc is 150-300 rpm;

preferably, the rotating speed of the workpiece is 100-150 rpm;

preferably, the flow rate of the grinding fluid is 50-100 mL/min.

10. A method of microwave-assisted fixed abrasive lapping according to claim 3, comprising the steps of: further comprises measuring the surface roughness S of the workpiece after grinding by using an atomic force microscope _a And observing the subsurface of the workpiece after grinding by using a focused ion beam-transmission electron microscope technique.

11. A method of microwave-assisted fixed abrasive lapping according to claim 3, comprising the steps of: the method for constructing the microwave-assisted fixed abrasive grinding system comprises the following steps of:

a microwave radiation shielding cover with a visible window is arranged outside the grinding platform;

one or more microwave generators are arranged in the shielding cover in a centralized or uniform manner along the grinding platform, and the distance between the microwave generators and a workpiece to be processed is 5-10 cm;

and respectively installing the workpiece to be processed and the grinding disc, and then carrying out subsequent operation.