Abstract: An abrasive article includes a backing, abrasive particles secured to the backing, and a size coat provided over the abrasive particles, the size coat comprises a binder resin, at least one filler material and at least one lubricant material having a melting temperature of at least about 200 degrees F. A method of grinding aluminum using such an abrasive article is also described.

Abstract: An abrasive grain is disclosed and may include a body. The body may include a central portion and 3 radial arms extending outwardly from the central portion along the entire length of the central portion of the body. A first radial arm, a second radial arm, and a third radial arm can define a total angle of less than 180 degrees. The body may also include at least one groove extending from a base surface along a first side of the body.

Abstract: A coated cutting tool is provided which allows for satisfactory machining over a long period of time, particularly in the machining of difficult-to-machine materials with low thermal conductivity. The coated cutting tool includes a substrate and a coating layer formed on a surface of the substrate, wherein: at least one layer of the coating layer comprises a predetermined layer containing a compound having a composition represented by the formula: (AlXTi1-X)N [wherein x denotes an atomic ratio of the Al element based on a total of the Al element and the Ti element, and x satisfies 0.60?x?0.85]; a value of an orientation index TC (311) of a cubic (311) plane of the predetermined layer is from 2.5 or more to 4.2 or less; and an average thickness of the predetermined layer is from 1.0 ?m or more to 12.0 ?m or less.

Abstract: A CMP slurry composition for polishing a tungsten pattern wafer and a method of polishing a tungsten pattern wafer, the composition including a solvent, the solvent including a polar solvent or a non-polar solvent; an abrasive agent; and an oxidizing agent, wherein the abrasive agent includes silica modified with an amino silane that includes three nitrogen atoms.

Abstract: The invention relates to an imide polymer-based solid film lubricant, a method for producing same, a sliding element comprising same and the use thereof. According to the method, difunctional or cyclized difunctional compounds and optionally functional fillers are added to a non-imidized or partly imidized polyamide acid prepolymer or an imidized short-chain blocked prepolymer in a solvent or solvent mixture and then, depending on the prepolymer, a polymerization reaction or an imidization reaction and in both cases a crosslinking reaction is carried out. The solid film lubricant comprises an imide polymer as the resin matrix and optionally functional fillers, the molecules of the imide polymer comprising groups (R1) of the difunctional compounds that additionally contribute to the crosslinking.

Abstract: A method of making abrasive particles includes: providing a slurry comprising non-colloidal solid particles and a liquid vehicle; forming at least a portion of the slurry into shaped bodies contacting a substrate; at least partially drying the shaped bodies to provide shaped abrasive precursor particles; separating at least a portion of the shaped abrasive precursor particles from the substrate; and converting at least a portion of the shaped abrasive precursor particles into shaped abrasive particles. The shaped abrasive particles comprise alpha alumina having an average crystal grain size of 0.8 to 8 microns and an apparent density that is at least 92 percent of the true density. Each shaped abrasive particle has a respective surface comprising a plurality of smooth sides that form at least four vertexes. Shaped abrasive particles, abrasive articles including them, and methods of using are also disclosed.

Abstract: Various embodiments disclosed relate to an abrasive article (10). The abrasive article (10 includes a backing (12) defining a major surface. The abrasive article (10) includes an abrasive layer including a plurality of tetrahedral abrasive particles (16) attached to the backing (12). The tetrahedral abrasive particles (16) include four faces joined by six edges terminating at four vertices (40, 42, 44, 46). Each one of the four faces contacts three of the four faces, and a major portion of the tetrahedral abrasive particles (16) have at least one of the vertices (40, 42, 44, 46) oriented in substantially a same direction.

Abstract: Articles and methods regarding the making and use of low-shedding nonwoven abrasive articles, such as abrasive wheels and hand pads, that have a low shed rate and achieve a high grind ratio. The abrasive articles comprise a blend of a plurality of primary abrasive particles and a plurality of reinforcing abrasive particles that is disposed on a nonwoven web substrate. The primary abrasive particles have an average particle size equal to or larger than the average fiber diameter of the substrate fibers, and the reinforcing abrasive particles have an average particle size smaller than the average fiber diameter.

Abstract: A cutting insert may include a base member and a coating layer thereon. The coating layer may include a first layer including a titanium compound on the base member, a second layer including alumina and an upper surface on the first layer, and a third layer including a titanium compound on the upper surface. The coating layer may include a crack at a top surface and therein. In a cross section orthogonal to the top surface, the crack may be present in the third layer and the second layer; in the third layer it may have a width of 1 ?m or more. In the upper surface it may have a width of 0.5 ?m or more—smaller than the width of the crack in the third layer. Another part may have a width of 0.2 ?m or less closer to the base member than the upper surface.

Abstract: A shaped abrasive agglomerate particle includes a shaped abrasive particle bonded in a vitreous matrix. The shaped abrasive particles have a longest particle lineal dimension on a surface and a shortest particle dimension perpendicular to the longest particle lineal dimension, and the longest particle lineal dimension is at least twice the shortest particle dimension. The shaped abrasive agglomerate particle has a longest agglomerate lineal dimension on a surface and a shortest agglomerate dimension perpendicular to the longest agglomerate lineal dimension, and the longest agglomerate lineal dimension is at least twice the shortest agglomerate dimension. The abrasive agglomerate particles are useful in abrasive articles. Methods of making the shaped abrasive agglomerate particle and abrading a workpiece are also described.

Abstract: A method for electrostatically scattering an abrasive grain includes applying at least one electro-conductive material to the abrasive grain. The electro-conductive material is in the form of at least one organic compound.

Abstract: Provided is, for example, a cleaner sheet including: a cleaning surface that is configured to be brought into sliding contact with a surface of an object to be cleaned. The cleaning surface has unevenness, and includes projections respectively having distal ends configured to be in sliding contact with the object to be cleaned when in use. The projections are constituted by a member formed to have the projections arranged at intervals from each other in a plane direction of the cleaning surface. The member has a hardness of 0.4 MPa or more measured by a nano-indentation method. The cleaning surface further includes adhesive recesses that have higher adhesive force than that of the member and are exposed on the cleaning surface.

Abstract: Compositions for forming polymer layers useful in the manufacture of display devices, particularly flexible display, and methods of forming such devices are provided.

Abstract: The present disclosure relates to abrasive buffing articles (“abrasive buffs”) and methods of making the same. The abrasive buffs include a substrate, such as a fabric, that has been impregnated with an abrasive polymeric composition that includes abrasive particles, such as primary abrasive particles and/or abrasive aggregates, such as spray dried abrasive aggregates. The abrasive buffs are flexible and capable of conforming to and effectively abrading, polishing, and buffing workpieces possessing a complex geometry.

Abstract: An abrasive tool includes a support, on which a plurality of abrasive flaps is arranged. The abrasive flaps each have a base and abrasive material, which is attached to the base by means of a binder. To increase the useful life and total material abrasion, the abrasive flaps are reinforced by a cured filling resin. The reinforcement of the abrasive flaps reduces the cyclical deflection thereof around a zero position due to workpiece machining, thereby avoiding increased wear on the abrasive flaps.

Abstract: A fixed abrasive article having a body including abrasive particles contained within a bond material, the abrasive particles including shaped abrasive particles or elongated abrasive particles having an aspect ratio of length:width of at least 1.1:1, each of the shaped abrasive particles or elongated abrasive particles having a predetermined position or a predetermined three-axis orientation, including a placement angle ranging from +90 degrees to ?90 degrees and a rake angle ranging from +90 degrees to ?90 degrees.

Abstract: A method for coating a metal based component surface wherein said metal based component has an inner and/or outer surface portion that is to be coated, and which surface portion comprises a carbide forming composition. A cavity having one or more cavity walls, wherein said at least one inner and/or outer surface portion forms at least a portion of said one or more cavity walls is provided, and a portion of the cavity is filled with diamond powder. Thereafter gas is removed from the interface between said diamond powder and said at least one inner and/or outer surface portion, and the cavity is subjected to a hot pressing process for a predetermined time at a predetermined pressure and a predetermined temperature such that said diamond powder diffusion bonds to said at least one one inner and/or outer surface portion. Finally at least a part of said diamond powder is removed from said at least one cavity.

Abstract: An abrasive article comprising a first group including a plurality of shaped abrasive particles overlying a backing, wherein the plurality of shaped abrasive particles of the first group define a first non-shadowing distribution relative to each other.

Abstract: The present disclosure involves apparatuses and methods for coating a lapping plate with an aqueous composition. The apparatus can be configured and the aqueous composition can be formulated so that the aqueous composition can flow to a spray nozzle device solely due to gravity in a batchwise manner.

Abstract: A super hard construction comprises a substrate comprising a peripheral surface, an interface surface and a longitudinal axis extending in a plane and a super hard material layer formed over the substrate and having an exposed outer surface, a peripheral surface extending therefrom and an interface surface. One of the interface surface of the substrate or the interface surface of the super hard material layer comprises one or more projections arranged to project from the interface surface, the one or more projections being spaced from the peripheral surface of the substrate and a peripheral flange extending between the peripheral side edge and the interface surface. The peripheral flange is inclined at an angle of between around 5 degrees to around 30 degrees to a plane substantially perpendicular to the plane through which the longitudinal axis extends.

Abstract: Various embodiments disclosed relate to pore inducers and porous abrasive forms made using the same. In various embodiments, the present invention provides a method of forming a porous abrasive form including heating an abrasive composition including pore inducers to form the porous abrasive form. During the heating the pore inducers in the porous abrasive form reduce in volume to form induced pores in the porous abrasive form.

Abstract: A resin composition (X), which is a curable resin composition according to the present invention, contains a curable resin component (10), a surface-modified nanodiamond (20), and an organic medium. The surface-modified nanodiamond (20) includes a ND particle (21), which is a nanodiamond particle, and a silane coupling agent (22). The silane coupling agent (22) has a (meth)acryloyl-containing organic chain and is bonded to the ND particle (21). The resin composition (X) is suitable for forming a nanodiamond-dispersed cured resin portion having both high transparency and high scratch resistance. An optical element according to the present invention has a light-transmitting region and includes a cured resin portion, which is a cured product of the resin composition (X), in at least part of the light-transmitting region. The optical element is advantageous for actually providing an optical element including a cured resin portion or cured resin layer having both high transparency and high scratch resistance.

Abstract: A method for signifying a selected cumulative scrubbing action between a device and a surface, the cumulative scrubbing action being signified by a signaling element, wherein the signaling element is configured to provide an observable signal when the selected cumulative scrubbing action has been provided to the surface. The method may comprise applying scrubbing action to the signaling element to release and/or expose at least a first portion of an indicator, and observing the device and/or surface for the signal. The present disclosure also relates to signaling elements and devices for use according to the methods of the present disclosure, and to methods of preparing the same.

Abstract: A drilling tip according to the disclosure has a tip body which is provided with a tip portion tapered toward a tip side of the tip body; and a hard layer which is formed on a surface of the tip portion of the tip body, an outermost layer of the hard layer is a cBN sintered material having 70 to 95 vol % of cBN grains, and when a cross-sectional structure of the outermost layer is observed, a binder phase having a width of 1 nm or greater and 30 nm or less and containing Al, B, and N, and in which a ratio of an O content to an Al content is 0.1 or less exists between neighboring cBN grains.

Abstract: An optical element for deflecting X-rays comprising a multilayer structure including amorphous first WC layers and amorphous second SiC layers, wherein each two adjacent ones of the first layers are separated by a respective one of the second layers such that the first and second layers are arranged alternatingly, wherein at least some of the first layers and at least some of the second layers have a thickness of at least 3 nm. A method of producing such an optical element and to use of such an optical element is also disclosed.

Abstract: Nonwoven abrasive articles comprise a nonwoven abrasive member having an overlayer composition comprising a fatty acid metal salt disposed thereon adjacent to a working surface. The nonwoven abrasive member comprises abrasive particles adhered to a fiber web by a binder. The abrasive particles may be exposed and/or the nonwoven abrasive member may have suitable frictional properties. Methods of making the same are also disclosed.

Abstract: A coated abrasive article includes a backing, a make layer, crushed abrasive particles, and a size layer. The crushed abrasive particles include: 35 to 100 weight percent of initial crushed abrasive particles having a first composition and first size grade, wherein a majority of the initial crushed abrasive particles are platey crushed abrasive particles, and wherein each platey crushed abrasive particle has a respective length, width, and thickness; and 0 to 65 weight percent of crushed filler particles having a second composition and a second size grade. The first and second compositions and/or size grades are different. The coated abrasive article has a direction of intended use, a majority of the platey crushed abrasive particles of the coated abrasive article are positioned with their thickness oriented substantially parallel to the direction of intended use. A method of making the coated abrasive article is also disclosed.

Abstract: The present disclosure relates to abrasive articles that include abrasive aggregates of silicon carbide with a vitrified bond, and methods of making and using such abrasive articles and abrasive aggregates. In particular, the abrasive aggregates can possess a combination of beneficial properties and comprise a vitreous binder composition having a specific composition, sintering temperature, glass transition temperature, or a combination thereof.

Abstract: The application relates to bond materials for a grinding wheel, in particular a glass ceramic and a preparation method thereof, and a bond for the composite grinding wheel. The glass ceramic is prepared from raw materials comprising kaolin, silica, diboron trioxide, lithium superoxide, albite, potassium feldspar, talc, dolomite, phosphorus pentoxide, and yttrium oxide. A glass ceramic composed entirely of microcrystalline phases is obtained from the glass prepared by the above raw materials at 900-1020° C., achieving a complete conversion of the glass phase at a low temperature. The application also provides a bond for a composite grinding wheel, comprising glass ceramic and glass with mass ratio of (20-50):(50-80), the glass phase having a low flow temperature and, together with the glass ceramic phase, forming encapsulation of the abrasive particles, realizing low-temperature sintering of the grinding wheel.

Abstract: Methods of making an abrasive article. Abrasive particles are loaded to a distribution tool including a plurality of walls defining a plurality of slots. Each slot is open to a lower side of the tool. The loaded particles are distributed from the distribution tool to a major face of a backing web below the lower side and moving relative to the tool. At least a majority of the particles distributed from the tool undergo an orientation sequence in which each particle first enters one of the slots. The particle then passes partially through the slot such that a first portion is beyond the lower side and in contact with the major face, and a second portion within the slot. The sequence then includes the particle remaining in simultaneous contact with one of the walls and the major face for a dwell period while the web moves relative to the tool.

Abstract: Provided are abrasive articles that include a plurality of layers, in the following order: a backing; an abrasive layer; and a supersize coat. The supersize coat contains a metal salt of a long-chain fatty acid and clay particles dispersed therein. Advantageously, the clay particles enhance the optical clarity of the supersize coat, allowing printed abrasive articles to be made with thicker supersize coatings. The addition of clay was also found to improve cut performance of the abrasive article relative to articles in which the clay particles are absent.

Abstract: The present disclosure relates to a polycrystalline diamond compact (PDC) cutter with protective barrier coating. The PDC cutter consists of an unleached or leached polycrystalline diamond (PCD) table, a cemented carbide body substrate, and a coating disposed on the cutter. The coating covers at least partially the exterior surfaces of the PCD table of the PDC cutter, and it may also extend over partially or entirely the exterior surfaces of the cemented carbide body. The coating is either a single layer or multilayer. The coating has a thickness of 0.4 ?m-100 ?m. The coating may have a strong metallurgical bonding with PDC cutter. The coating comprises an oxidation-resistant layer that protects the PDC cutter from thermal and mechanical degeneration during brazing and cutting applications. Methods for preparing such the coating comprise physical vapor deposition, chemical vapor deposition, thermoreactive deposition and diffusion, electrical plating, electroless plating, or their combinations.

Abstract: A method of manufacturing an abrasive sponge for cleaning, the method comprising the steps of: a) applying a cross-linking agent comprising one or more cyanoacrylate or isocyanate groups per molecule of crosslinking agent and mixtures thereof on at least a portion of a surface of a foam body comprising a open-cell foam material; and b) curing the cross-linking agent to form an abrasive layer on the at least a portion of the surface of the foam body.

Abstract: A method of making shaped abrasive particles including forming an abrasive flake comprising a plurality of precursor shaped abrasive particles and a frangible support joining the precursor shaped abrasive particles together; transporting the abrasive flake through a rotary kiln to sinter the abrasive flake; and breaking the sintered abrasive flake into individual shaped abrasive particles. The method is useful to make small shaped abrasive particles having insufficient mass to be efficiently individually sintered in a rotary kiln without joining two or more of the shaped abrasive particles together.

Abstract: An abrasive article (100) comprising a backing (102); a make resin (112) contacting the backing (102); abrasive particles (114) contacting the make resin (112); and a size resin (116) contacting both the abrasive particles (114) and the make resin (112), wherein the make resin (112) includes an alkyl quaternary ammonium clay, which can take the form of Garamite.

Abstract: Embodiments of the invention relate to polycrystalline diamond compacts (“PDC”) exhibiting enhanced diamond-to-diamond bonding. In an embodiment, a PDC includes a polycrystalline diamond (“PCD”) table bonded to a substrate. At least a portion of the PCD table includes a plurality of diamond grains defining a plurality of interstitial regions. The plurality of interstitial regions includes a metal-solvent catalyst. The plurality of diamond grains exhibit an average grain size of about 30 ?m or less. The plurality of diamond grains and the metal-solvent catalyst collectively exhibit an average electrical conductivity of less than about 1200 S/m. Other embodiments are directed to PCD, employing such PCD, methods of forming PCD and PDCs, and various applications for such PCD and PDCs in rotary drill bits, bearing apparatuses, and wire-drawing dies.

Abstract: It is an object of the present invention to provide an abrasive material which enables: processing efficiency and finished planarity of a substrate material to be simultaneously improved at a high level; polishing costs to be reduced; and a difficult-to-process substrate composed of sapphire or silicon carbide to be polished efficiently and precisely. An abrasive material comprises a substrate and an abrasive layer laminated on a front face side of the substrate, wherein the abrasive layer includes a binder containing an inorganic substance as a principal component, and abrasive particles dispersed in the binder, wherein a front face of the abrasive layer comprises a plurality of regions provided through dividing by grooves, and wherein a maximum peak height (Rp) on the front face of the abrasive layer is no less than 2.5 ?m and no greater than 70 ?m.

Abstract: A polycrystalline diamond body contains diamond particles, the diamond particles have a mean particle size of 50 nm or less, and a crack initiation load is 10 N or more as measured in a fracture strength test by pressing a diamond indenter D with a tip radius Dr of 50 ?m against a surface of the polycrystalline diamond body at a load rate F of 100 N/min. Accordingly, a polycrystalline diamond body that is tough and has a small diamond particle size, a cutting tool, a wear-resistant tool, a grinding tool, and a method for producing the polycrystalline diamond body are provided.

Abstract: Disclosed is a composition of matter comprising a biologically active substance bound to a graphene-coated dielectric-core particle, and methods for making and using the same.

Abstract: A cutting blade for cutting a workpiece includes a base and a cutting edge fixed to a peripheral portion of the base. The cutting edge is formed by bonding a mixture of abrasive grains and photocatalyst particles with a binder. In cutting the workpiece by using the cutting blade, a cutting water is supplied to the cutting blade and light is applied to the cutting blade to excite the photocatalyst particles. The cutting water supplied to the cutting blade comes into contact with the photocatalyst particles excited, so that the cutting water is given an oxidizing power due to hydroxy radicals.

Abstract: A composite polycrystal contains polycrystalline diamond formed of diamond grains that are directly bonded mutually, and non-diamond carbon dispersed in the polycrystalline diamond, and has a concentration of contained hydrogen of greater than 1000 ppm and less than or equal to 20000 ppm.

Abstract: The present invention relates to a polycrystalline diamond compact. A method for manufacturing a polycrystalline diamond compact includes: preparing primary sintering by mixing and assembling first diamond particles and metal binder particles; sintering the mixed and assembled particles; leaching the upper surface of the sintered polycrystalline diamond compact; preparing secondary sintering by mixing second diamond particles and the metal binder particles and assembling the mixed particles on the upper surface of the primarily sintered polycrystalline diamond compact; sintering the sintered polycrystalline diamond compact and the mixed particles of the upper part; and a grinding step of grinding the reassembled second diamond particles and metal binder particles so as to remove the same.

Abstract: A sintered polycrystalline body and a method of forming the sintered polycrystalline body are disclosed. The sintered polycrystalline body comprises a plurality of particles cubic boron nitride dispersed in a matrix. The matrix includes materials selected from compounds of any of titanium and aluminium. The polycrystalline body further comprises 0.1 to 5.0 volume % of lubricating chalcogenide particles dispersed in the matrix. The chalcogenide particles have a coefficient of friction of less than 0.1 with respect to a workpiece material. Preferably sulfide particles are used as lubricant. Preferably 30-70 vol.-% cBN is contained. Sintering takes place at 1100-1600° C. and 4-8 GPa.

Abstract: A vehicle part or component includes a surface that is configured to contact a fuel containing ethanol. The surface has a layer of non-hydrogenated diamond like carbon (NH-DLC) material disposed on the surface. The layer of NH-DLC has a thickness of from greater than or equal to about 100 nm to less than or equal to about 100 ?m. The NH-DLC material has a carbon content of greater than or equal to about 90 atomic % (at. %), a carbon-carbon sp3 hybrid bond content of from greater than or equal to about 60% to less than or equal to about 100%, and a carbon-carbon sp2 hybrid bond content of from greater than or equal to about 0 to less than or equal to about 40%. The NH-DLC material is substantially free of hydrogen atoms. Methods for manufacturing the vehicle part or component are also provided.

Abstract: The present disclosure relates to an industrial device, such as a drill bit including a thermally stable polycrystalline diamond (TSP) table coupled to a substrate via an attachment joint, with at least one attachment material located in the attachment joint. At least one of the attachment materials includes a metal or metal alloy and an additive material having a hardness higher than the metal or metal alloy or a coefficient of thermal expansion lower than that of the metal or metal alloy.

Abstract: A method to produce a sintered metal carbide article containing diamond particles throughout said article is disclosed. In one embodiment, the method involves creating a mixture of metal carbide (MC) particles, metallic binder (MB) particles and coated diamond (D) particles is compacted into a desired shape and then heated at a temperature below the graphitization temperature of the D particles to produce an under sintered MC-MB-D article which is then rapidly heated in an induction heating device to surprisingly produce a sintered MC-MB-D article containing diamond particles throughout the article. The MC-MB-D article exhibits excellent drilling/cutting capacity and surprisingly high impact resistance. One useful MC-B-D article made according to the disclosed invention is a tungsten carbide-cobalt (WC—Co) article containing diamonds WC—Co-D throughout the article.

Abstract: A coated abrasive article comprising a backing, an adhesive layer disposed in a discontinuous distribution on at least a portion of the backing, wherein the discontinuous distribution comprises a plurality of adhesive contact regions having at least one of a lateral spacing or a longitudinal spacing between each of the adhesive contact regions; and at least one abrasive particle disposed on each adhesive contact region, the abrasive particle having a tip, and there being at least one of a lateral spacing or a longitudinal spacing between each of the abrasive particles, and wherein at least 65% of the at least one of a lateral spacing and a longitudinal spacing between the tips of the abrasive particles is within 2.5 standard deviations of the mean.

Abstract: A hot-melt adhesive composition comprises 35 wt % to 40 wt % of petroleum resin, 10 wt % to 14 wt % of polyester elastomer resin, 10 wt % to 14 wt % of ethylene vinyl acetate resin, 14 wt % to 19 wt % of polyether polyol, 15 wt % to 21 wt % of polyester polyol, 8 wt % to 10 wt % of methylene diphenyl diisocyanate, and 0.1 wt % to 0.5 wt % of an amine catalyst, wherein the hot-melt adhesive composition has a melt viscosity of 20,000 cps to 50,000 cps as measured at 150° C.

Abstract: Dressing tool including a main body having a working surface covered with hard-material grains distributed on the main body. Recesses for accommodating the hard-material grains are created in the main body and then filled with an adhesive, the excess adhesive is removed across the main body, and thereafter the hard-material grains are flung onto the main body so that only the grains located in the recesses remain adherent to the working surface of the tool. The hard-material grains can then be bonded to the main body by a physical and/or chemical bond. Thus, a distribution of the grains over the working surface of the tool that can be precisely defined in advance is ensured.

Abstract: Cutting elements include a substrate, a thermally stable polycrystalline table comprising a superhard material secured to the substrate, and a layer of metal interposed between, and attaching the substrate and the thermally stable polycrystalline table. Methods of forming a cutting element include providing a thermally stable polycrystalline table in a mold, providing a layer of metal on the thermally stable polycrystalline table, distributing a mixture of particles comprising a plurality of hard particles and a plurality of particles comprising a matrix material on the layer of metal, and heating the mold while applying pressure to the mixture of particles to cause the mixture of particles to coalesce and form a substrate and at least partially melt the layer of metal to flow and wet the thermally stable polycrystalline table and the substrate to form an attachment therebetween.