66 results about "Co-fired ceramic" patented technology

The invention provides an aerosol generating device and a coil assembly thereof, the coil assembly comprises a ceramic base body and a conductive heating body, the ceramic base body defines a heating cavity, and the heating cavity is used for accommodating an aerosol forming substrate; and the conductive heating body is arranged on the ceramic substrate, and is used for heating the aerosol forming substrate to generate aerosol. According to the coil assembly, the co-fired ceramic coil and the integrated design of the coil and the heating cavity are adopted, the distance between the coil and the cigarette is closer, meanwhile, a heating cavity base body is a ceramic base body, the heat conduction capacity is higher, heat generated by the coil can be better transmitted to a tobacco section, and effective utilization of the heat is facilitated.

The present invention discloses a low-temperature co-fired ceramic / glass composite material and its preparation method and application, belonging to the technical field of ceramic materials. The present invention uses aluminum oxide (Al2O3) as a ceramic phase, CaO-B2O3-SiO2 (CBS) and zinc-boron glass as a glass phase, and adds K2O, CuO, and Nb2O5. When the low-temperature co-fired ceramic / glass composite material is used to prepare microelectronic components, its firing temperature can be reduced to 800°C to 850°C, and the dielectric constant can be reduced to 7.0-8.5, and the dielectric loss can be reduced to 0.3×10 ‑3 ~0.7×10 ‑3 (1MHz).

The invention discloses a 3dB bridge which comprises a multi-layer dielectric body, and a first coupling line and a second coupling line are arranged on the two opposite sides of the multi-layer dielectric body respectively and are overlapped on the wide side of a coupling part. The first coupling line and the second coupling line are respectively divided into parallel finger-shaped conductor sections at the coupling part, and the adjacent finger sections correspond in a cross-layer staggered manner to form a multi-scale coupling channel of the same coupling part; corresponding input ends and output ends are respectively led out from the first coupling line and the second coupling line; and a parasitic resonance unit which is electromagnetically coupled with the finger section is arranged in the multilayer dielectric body at a distance d1 from the transverse edge of the coupling part. The 3dB bridge enables in-band coupling to be self-balanced along with frequency, a parasitic unit compensates a band edge in situ in a near field, the problem that single-scale coupling and boundary cannot be quantized is solved, wider fractional bandwidth, flatter amplitude and phase and improvement of band edge directivity and port isolation are achieved, repeatability and mass production consistency are ensured through d1, d2, T, k1 and k2 constraints, and the 3dB bridge adapts to co-fired ceramic packaging.

The application provides a low-temperature co-fired ceramic powder material and a preparation method and application thereof, and relates to the technical field of electronic ceramic materials.The low-temperature co-fired ceramic powder material provided by the application comprises the following raw material components in parts by weight: borosilicate glass powder 50-60 parts, quartz glass powder 30-40 parts, and powder additives 5-10 parts, wherein the powder additives comprise at least one of Al2O3, ZrO2, MgO and BaO.The low-temperature co-fired ceramic powder material prepared by compounding borosilicate glass powder, quartz glass powder and powder additives has a dielectric constant εr=3.8-4.5 after sintering, a low dielectric loss tan δ=0.001-0.0025, and a resistivity ρ=1.0-9.9*10 12 Ω*cm, the sintering temperature is in the range of 850-900 DEG C, and the density after sintering is good, and can be up to 99.8%.

This invention relates to the field of glass-ceramic technology, specifically providing a low-temperature co-fired ceramic, its preparation method, and its application. The raw materials for the low-temperature co-fired ceramic include VSBBS glass frit and ceramic frit, with the total weight of the VSBBS glass frit and ceramic frit being 100%. The mass percentages of the VSBBS glass frit and ceramic frit are 20-40% and 60-80%, respectively. The raw materials for the VSBBS glass frit, by mass percentage, include 10-30 wt% vanadium oxide, 10-30 wt% antimony oxide, 10-30 wt% barium oxide, 10-20 wt% boron oxide, and 30-50 wt% silicon oxide, with the sum of all oxides being 100%. The LTCC material obtained by this invention achieves excellent millimeter-wave dielectric properties, with a relative permittivity between 4.8 and 6.8, a dielectric loss less than or equal to 0.001, and a flexural strength of 180-230 MPa.

The invention discloses a first-tearing and second-pressing laminating machine for flexible low-temperature co-fired ceramics. The first-tearing and second-pressing laminating machine comprises a feeding mechanism, a fine adjustment mechanism, a first visual positioning mechanism, a cutting mechanism, a liftable adjusting mechanism, a second visual positioning mechanism, a film tearing mechanism, a waste recycling box, a laminating mechanism and a discharging bin. Ceramic in the feeding bin is grabbed through a feeding mechanical arm and placed on a fine adjustment platform of the fine adjustment mechanism; the fine tuning platform is combined with the first visual positioning mechanism to perform visual positioning adjustment on the ceramic on the fine tuning platform; the cutting mechanism is used for trimming the upper ceramic layer of the ceramic on the fine adjustment platform and transferring the upper ceramic layer to a liftable adjusting platform of the liftable adjusting mechanism after trimming is completed; the liftable adjusting platform is combined with the second visual positioning mechanism to carry out secondary visual positioning adjustment on the ceramic on the liftable adjusting platform; and the laminating mechanism receives the ceramic on the lifting adjusting platform, PET film tearing is carried out through the film tearing mechanism, and then laminating operation is carried out. The device is high in automation degree, high in production efficiency, high in quality and low in labor cost.

This invention relates to the field of special ceramic product manufacturing technology, specifically to a method for preparing an airtight ceramic base, comprising: a co-fired ceramic substrate, wherein the co-fired ceramic substrate is provided with a dense support layer, an interconnected functional layer, and a cavity sealing layer sequentially from bottom to top; the dense support layer is a high-purity alumina dense ceramic layer with a thickness ≥0.2mm; the interconnected functional layer is an integral sintered layer composed of a multi-layered stacked alumina ceramic dielectric layer and an embedded tungsten metallized three-dimensional interconnected structure; the cavity sealing layer is an alumina ceramic layer with a concave cavity structure, and the edge of the concave cavity is provided with an annular stress buffer groove. The airtight ceramic base of this invention, through structural innovation and synergistic optimization of the manufacturing process, adopts a three-layer integral co-fired ceramic substrate structure of the same material, combined with a rounded corner annular stress buffer groove design at the cavity edge, solving the problems of sintering warping, interlayer delamination, and stress concentration cracking.

This application discloses a method for fabricating conductive lines on a multilayer co-fired ceramic substrate and the multilayer co-fired ceramic substrate itself, relating to the field of electronic ceramic multilayer co-fired manufacturing technology. The method for fabricating conductive lines on the multilayer co-fired ceramic substrate includes: providing a green ceramic film strip for multilayer stacking and co-firing; forming conductive patterns on the surface of the green ceramic film strip using nanoimprinting technology, aligning and stacking it with at least one other green ceramic film strip, and laminating it to form a stack; and performing adhesive removal and co-firing treatment on the stack to form embedded conductive lines within the stack. The fabrication method proposed in this application can fabricate conductive lines with linewidths and spacings less than 50 μm, achieving embedded forming of conductive lines in multilayer structures. It can be used in conjunction with via drilling / filling and stack alignment processes for precision packaging of three-dimensional integrated circuits such as high-density multilayer wiring, high-frequency and high-speed circuits, and power electronic integration.

The invention provides an embedded fan-out packaging method and a packaging structure thereof, and the preparation method comprises the steps: S1, manufacturing a co-fired ceramic embedded substrate which is provided with a plurality of through cavities penetrating through the substrate, the thickness of the lower part of each through cavity is greater than the thickness of a chip, and the area of the upper part of each through cavity is greater than that of the lower part of each through cavity; s2, bonding the co-fired ceramic embedded substrate on the temporary bonding substrate by using a temporary bonding film; s3, the chip is attached into the through cavity, and the front face of the chip is tightly attached to the temporary bonding film; s4, filling glue is injected into the through cavity, and the height is larger than the height of the lower portion of the through cavity and smaller than the height of the upper portion of the through cavity; s5, the cover plate is placed on the upper portion of the through cavity, and the filling glue is extruded so that the gap between the cover plate and the through cavity can be filled with the filling glue; s6, carrying out de-bonding, so that the packaging body structure is separated from the temporary bonding film; s7, preparing single-layer or multi-layer fan-out rewiring on the lower surface of the packaging body structure; and S8, packaging components on the upper surface of the packaging body structure, and planting solder balls on the lower surface of the packaging body structure.

A copper powder having a surface treatment layer, the copper powder containing at least one organic acid salt from among organic acid salts containing Al and organic acid salts containing Ti.

According to the technical scheme, the aluminum oxide high-temperature co-fired ceramic with the double-layer cover plate comprises a ceramic substrate, an enclosure frame is welded to the upper surface of the ceramic substrate, the height of an internal partition wall of the enclosure frame is reduced, the height of an outer frame of the enclosure frame is increased, and a step table is formed. The shape of an internal partition wall of the enclosure frame can be designed in various shapes according to actual tube shell radio frequency requirements and internal component distribution, an outer frame of the enclosure frame is always kept in a regular shape, a lower-layer cover plate is bonded in the outer frame of the enclosure frame, and an upper-layer cover plate is welded to the upper surface of the outer frame of the enclosure frame in parallel in a sealing mode. According to the utility model, the original special-shaped cover plate can be divided into two parts through the stepped special-shaped enclosure frame, the lower-layer cover plate retains the special-shaped characteristic to be embedded into the partition wall and is fixed by conductive adhesive and the like, and the upper-layer cover plate is a cover plate with a regular appearance and can be packaged by adopting parallel seal welding, so that the cost of the parallel seal welding is lower than that of gold-tin welding; and the process difficulty is lower.

The embodiment of the invention provides a phased array system heat dissipation structure based on fan-out packaging and a working method. The heat dissipation structure comprises a fan-out packaged radio frequency chip and antenna array, a high-temperature co-fired ceramic substrate, a printed circuit board, a radio frequency feed network, a control and power supply network, a metal piece, a radio frequency interface and a power module. Wherein the fan-out packaged radio frequency chip and the antenna array are welded on the upper surface of the high-temperature co-fired ceramic substrate; the high-temperature co-fired ceramic substrate and the printed circuit board are respectively welded and fixed on the upper surface of the metal piece; the radio frequency feed network and the control and power supply network are embedded in the high-temperature co-fired ceramic substrate and the printed circuit board; the radio frequency interface and the power supply module penetrate through the metal piece and are welded to the lower surface of the printed circuit board.

The application discloses a method for electroless nickel-palladium-gold plating on an alumina high-temperature co-fired ceramic substrate, and belongs to the technical field of electroless nickel-palladium-gold plating. The method comprises the following steps: hanging, oil removal, micro-etching, glass micro-etching, acid pickling, palladium activation, inhibition, electroless nickel-boron plating, pre-plating of palladium, electroless palladium plating and electroless gold plating. The method is used for electroless nickel-palladium-gold plating on an alumina high-temperature ceramic tungsten metal to modify the metal, so that the workpiece has good weldability and bondability, the gold wire bonding strength can reach 280 mN, the average gold ribbon bonding tension is greater than 500 mN, and the average chip shear strength reaches 5.11 Kgf, all of which reach the relevant technical standards of the national military standard.

Provided in the present disclosure is a quantum random number generator integrated on the basis of a co-fired ceramic. The quantum random number generator comprises: a co-fired ceramic substrate, and a quantum state preparation unit, a quantum state measurement chip, a first processing unit and a second processing unit, which are jointly integrated on the co-fired ceramic substrate and are connected in sequence, wherein the quantum state preparation unit comprises a laser chip, the quantum state measurement chip comprises an end face coupler, and three-dimensional alignment is achieved between a light outlet of the laser chip and an input end of the end face coupler by means of a preset alignment structure formed on the co-fired ceramic substrate.

This copper powder having a surface treated layer contains a Si compound having a Si-O bond, an amphoteric metal X, and an alkaline earth metal Y, wherein the substance amount α (mol) of Si, the substance amount β (mol) of the amphoteric metal X, and the substance amount γ (mol) of the alkaline earth metal Y satisfy formula (I): α / β ≥ 0.8, formula (II): γ / β ≥ 0.4, and formula (III): 4α ≥ 2.4β +1.6γ.

The invention discloses a preparation method of a high-binding-force HTCC ceramic chemical nickel-gold plating layer, and belongs to the technical field of electronic components. The preparation method comprises the following steps: carrying out pretreatment on a tungsten slurry HTCC co-fired ceramic tube shell or a substrate through sand blasting, etching, Pd activation and other processes before chemical plating of a metal layer, immersing the pretreated substrate into a chemical nickel plating tank with adjusted parameters for chemical nickel plating to obtain a bright nickel layer, and then putting the bright nickel layer into a hydrogen atmosphere heat treatment furnace for heat treatment, the method comprises the following steps: carrying out heat treatment on a nickel / gold layer to obtain a nickel layer with high binding force strength, carrying out gold rolling plating, and finally carrying out heat treatment on the nickel / gold layer subjected to gold plating to obtain the HTCC metallized layer with high binding force strength. The binding force strength of the metalized layer manufactured by the technical scheme is greater than 35gf. The problems of low binding force and poor adhesive force of a chemical plating metallization nickel-gold layer on the surface of an existing HTCC ceramic substrate are solved. The method can be widely applied to the technical field of chemical plating of metallized layers of HTCC ceramic tube shells or substrates.

Disclosed in the present application are a power module, a power device, and a photovoltaic power generation system. The power module comprises a substrate, a first power device, a co-fired ceramic module, and a package body. The first power device is located on a surface of the substrate and is electrically connected to the substrate. The co-fired ceramic module is located on the side of the first power device facing away from the substrate, and the co-fired ceramic module and the first power device are spaced apart. The co-fired ceramic module comprises a co-fired ceramic base and a second power device, wherein the second power device is embedded in the co-fired ceramic base and is electrically connected to at least one of the substrate and the first power device. The package body encapsulates the substrate, the first power device, and the co-fired ceramic module. By means of the design scheme of the power module, the integration level and power density of the power module are improved while ensuring the structural reliability of the power module, and improvement to the power conversion performance of the power module is also facilitated, thereby improving the power density of the power device and thus improving the power generation efficiency of the photovoltaic power generation system.

This invention discloses a tungsten-copper electronic paste for medium-temperature co-fired ceramic substrates and its preparation method, belonging to the field of electronic pastes. By mass percentage, the paste consists of 80%–85% tungsten-copper powder, 5%–15% organic carrier, and 5%–10% binder phase. The preparation method includes: first preparing the organic carrier, then uniformly mixing the tungsten-copper powder and binder phase, followed by adding the organic carrier, and then thoroughly grinding and dispersing the mixture using a stirring and three-roll mill to obtain a uniform and stable tungsten-copper electronic paste. This invention, by optimizing the powder size and paste ratio, significantly reduces the sheet resistance of the conductive layer after sintering and improves conductivity while ensuring good co-firing compatibility with medium-temperature co-fired ceramics. The resulting paste exhibits excellent printability and rheological stability, with clear printed lines and a smooth surface. It shows no bubbling or delamination during sintering and is suitable for high-performance, high-reliability electronic packaging and substrate circuit manufacturing.

The invention provides a low-temperature co-fired ceramic filter. The low-temperature co-fired ceramic filter comprises a ceramic substrate, a filtering structure, an input electrode, an output electrode and a grounding electrode, the filtering structure is embedded into the ceramic substrate through a low-temperature co-firing process; one end of the input electrode is electrically connected with the input end of the filtering structure, and the other end extends to the outer surface of the ceramic substrate to form an external weldable end; one end of the output electrode is electrically connected with the output end of the filtering structure, and the other end extends to the outer surface of the ceramic substrate; one end of the grounding electrode is connected with the grounding end of the filtering structure, and the other end extends to the outer surface of the ceramic substrate to form a common-ground connection end. The filtering structure comprises a first capacitor, a second capacitor and a third capacitor which are sequentially connected in series to form a main signal channel, and first series resonance units are connected between the input end and the first capacitor and between the third capacitor and the output end respectively. And second series resonance units are respectively connected between the first capacitor and the second capacitor and between the second capacitor and the third capacitor.

The invention discloses a radiation refrigeration low-temperature co-fired Al2O3 ceramic chip and a preparation method thereof in the field of constructional engineering materials. The method comprises the following steps: 1) adding glass powder, an Al2O3 filler, an organic adhesive and a dispersing aid into a high-speed mixer, stirring and mixing at a low rotating speed, adding a plasticizer, starting high-speed stirring and mixing until the temperature reaches 70 + / -5 DEG C, rotating to a low rotating speed, adding a solvent, and continuously stirring and mixing to obtain tape casting slurry; 2) defoaming the tape casting slurry in a vacuum stirring defoaming machine, and discharging the slurry to a tape casting machine to obtain a tape casting belt; and 3) carrying out hot pressing on the casting belt according to requirements to obtain a green body, and placing the green body in a high-temperature kiln to remove organic matters in the green body to obtain the radiation refrigeration low-temperature co-fired Al2O3 ceramic material.The Al2O3 ceramic chip sintered at low temperature by the method has the effect of completely reflecting or approximately totally reflecting sunlight.

The invention belongs to the technical field of antennas, and relates to a four-arm helical antenna phased array, which is realized by using a low-temperature co-fired ceramic process, and comprises a plurality of antenna array elements, the plurality of antenna array elements are arranged in a rectangular array mode, and each antenna array element comprises an input coaxial structure, an antenna feed network structure and an antenna radiation structure, the input coaxial structure receives an external coaxial feed signal and transmits the external coaxial feed signal to the antenna feed network structure, the antenna feed network structure divides an input signal into four paths of circularly polarized output with the difference of 90 degrees, and the antenna radiation structure receives the circularly polarized output and generates circularly polarized radiation. Through combination of innovative designs such as a chain type structure, sequential rotation feeding, short circuit terminal optimization and an isolation assembly, the requirements of miniaturization and high integration level are met, the circular polarization characteristic and array expandability are improved, inter-unit coupling and array complexity can be reduced, and the antenna performance is improved. And the stable performance and the manufacturing consistency of the large array under the conditions of broadband and high scanning angle are ensured.

The invention provides a manufacturing method for preparing an organic packaging ceramic substrate from co-fired ceramic, and relates to the technical field of semiconductors. The invention discloses a manufacturing method for preparing an organic packaging ceramic substrate from co-fired ceramic. The manufacturing method comprises the following steps: S110, preparing ceramic slurry and metal conductor slurry; s210, preparing a raw ceramic chip; s310, circuit forming is carried out; s410, carrying out multi-layer lamination; s510, degreasing and sintering are carried out; and S610, post-treatment is carried out. S710, coating the ceramic core plate with a film; and S810, laying a solder mask layer. According to the manufacturing method for preparing the organic packaging ceramic substrate from the co-fired ceramic, the heat conductivity coefficient can be effectively increased, the temperature resistance range is enlarged, and the requirements for high-power heat dissipation and high temperature resistance can be effectively met.

The invention discloses a rare earth-microcrystalline glass-bio-fiber synergistic low-temperature sintering LTCC raw material belt and a preparation method thereof, and relates to the technical field of low-temperature co-fired ceramics, the rare earth-microcrystalline glass-bio-fiber synergistic low-temperature sintering LTCC raw material belt comprises an inorganic solid phase and an organic system; wherein the inorganic solid phase is prepared from the following components in percentage by mass: 55 to 70 weight percent of Li2Mg (1-x) RxTi3O8, 25 to 43 weight percent of Li2O-Al2O3-B2O3-SiO2-ZnO-MnO2, 0.2 to 1.0 weight percent of a grain boundary pinning agent and 0.3 to 1.2 weight percent of delignified nano cellulose; the organic system comprises the following components in percentage by mass: 6-14wt% of a binder, 1-3wt% of a dispersing agent and the balance of a mixed solvent of ethanol and butyl acetate. The method has the effects that the sintering temperature is reduced to 780 DEG C, the dielectric loss is reduced by 40%, and co-firing of the silver electrode is zero in diffusion and bubble.

The application relates to a high-precision cutting pre-laminating machine and relates to the technical field of low-temperature co-fired ceramic production. The pre-laminating machine comprises a rack and a control screen, the upper surface of the rack is provided with the control screen, and the pre-laminating machine further comprises a transmission module, a transfer assembly, a positioning and jacking cutting assembly and a pre-laminating assembly. The positioning and jacking cutting assembly comprises a supporting plate and a cutting knife, the upper surface of the rack is fixedly connected with a first fixed plate, and the upper surface of the first fixed plate is fixedly connected with two symmetrical second fixed plates. The iron frame positioning pin is adopted for positioning, the positioning precision is high, the total repeat error is small, and the laminating is positioned in comparison with visual positioning; the cutting function is added, the laminating and cutting functions are combined, the product inflow and outflow adopt the assembly line mode, a gluing machine and a laminating machine are respectively spliced in front and back, full-automatic production can be conveniently realized, the efficiency is high, and manual touching is avoided to cause dirt.

The invention discloses an inductor framework of an LTCC (Low Temperature Co-fired Ceramic) filter and a preparation method thereof, belongs to the technical field of LTCC, and solves the problem that the quality factor Q of a lamination structure inductor is lower than that of a winding structure inductor. The inductor specifically comprises a plurality of inductance coils which are transversely and spirally distributed; the inductance coil comprises a first layer inductance circuit, one end of the first layer inductance circuit is connected with a cylinder circuit, the top of the cylinder circuit is connected with a second layer inductance circuit, and the second layer inductance circuit is connected with the first layer inductance circuit of the next circle of inductance coil through another cylinder circuit. According to the LTCC filter inductor framework, the inductance coils are transversely and spirally distributed, the Q value of the LTCC filter inductor framework is increased through the transverse design, the degree of freedom of design space can be increased under the laminated structure design, and the purpose of miniaturization design is achieved. The preparation method of the inductor framework is simple in process, processing and preparation are carried out through conventional processes such as punching, hole filling, printing and laminating, and the inductor framework is suitable for large-scale production.

The invention discloses a preparation method of low-temperature co-fired ceramic with an adjustable thermal expansion coefficient and the low-temperature co-fired ceramic. The preparation method comprises the following steps: adding inorganic powder and an organic system into a solvent, carrying out ball milling to obtain ball-milled slurry, and carrying out tape casting, cutting and stacking, isostatic cool pressing and glue discharging sintering on the ball-milled slurry to obtain an LTCC ceramic matrix. According to the modified additive, gamma-spodumene and beta-spodumene can be separated out, a part of glass phase is reserved, the CTE adjustable range can be widened, dielectric loss is reduced, and the bending strength is enhanced.

The utility model discloses a flexible low-temperature co-fired ceramic straight-pull type laminating machine which comprises a machine frame, a stock bin, a material taking mechanism, a four-corner cutting mechanism, a transfer mechanism, a laminating mechanism, a discharging carrying mechanism and a discharging conveying mechanism, and the stock bin, the material taking mechanism, the four-corner cutting mechanism, the transfer mechanism, the laminating mechanism, the discharging carrying mechanism and the discharging conveying mechanism are arranged on the machine frame. The material taking mechanism is located on one side of the stock bin and the four-corner cutting mechanism, the to-be-machined ceramic chips in the stock bin are taken out through the material taking mechanism and placed on the four-corner cutting mechanism, and the four-corner cutting mechanism is used for cutting the four corners of the casting ceramic layers of the to-be-machined ceramic chips. The cut to-be-machined ceramic chips are transferred to the laminating mechanism through the transferring mechanism to be laminated, the laminating mechanism compacts the multiple to-be-machined ceramic chips through hydraulic pressure according to the laminating requirement, and the laminated finished products are carried to the discharging conveying mechanism through the discharging carrying mechanism to be discharged. According to the utility model, the connection strength between two adjacent layers of ceramic chips is high, and the ceramic chips are not easy to deform.

The application discloses a copper paste, a preparation method and application thereof, and a multilayer ceramic device and a preparation method thereof, and relates to the technical field of low-temperature co-fired ceramics, wherein the copper paste comprises the following components in the following mass fractions: resin: 3-8 parts; organic solvent: 6.7-19 parts; organic additive: 0.1-2 parts; copper powder: 60-90 parts; glass powder: 0.1-10 parts; inorganic additive: 0.1-10 parts; and the median particle size D50 of the copper powder is 0.5-10 microns. When the copper powder is co-fired with a green tape, the shrinkage rate of the copper powder is consistent with that of the green tape, so that the copper paste and the green tape can be perfectly co-fired, and the problems of cracking, delamination or warping of the finally-prepared ceramic device can be avoided.

This copper powder having a surface treated layer contains a Si compound having a Si-O bond, an amphoteric metal X, and an alkaline earth metal Y, wherein the substance amount α (mol) of Si, the substance amount β (mol) of the amphoteric metal X, and the substance amount γ (mol) of the alkaline earth metal Y satisfy formula (I): α / β ≥ 0.8, formula (II): γ / β ≥ 0.4, and formula (III): 4α ≥ 2.4β +1.6γ.