Abstract: A hydrometallurgical process for the removal of arsenic and antimony from a so-called “dirty” copper concentrate (101) is described. The process comprises the following steps: Step 1: repulping (100) the “dirty” copper concentrate with an alkaline lixiviant (102, 103), and subjecting the “dirty” copper concentrate to an alkaline leaching process (“the Leach”) in a Leach reactor (110). The arsenic and antimony are dissolved in the Leach to produce a “clean” copper concentrate (138) and leach discharge liquor (132). Step 2: subjecting the Leach discharge liquor (132) to a lime treatment step (151) in order to regenerate (150) the alkaline lixiviant as well as precipitate an impurity rich precipitate (161) containing arsenic and antimony. Then the impurity rich precipitate (161) is separated (160) from the regenerated alkaline lixiviant (162). The impurity rich precipitate is washed and disposed of in an environmentally safe condition.

Abstract: The present invention provides a process for extracting noble metals from anode slime, comprising: mixing sodium carbonate, quartz and coke powder and impurity-removed anode slime, and subjecting the mixture to smelting and converting to obtain alloys of noble metals. The present invention avoids problem of lead pollution by using metallic bismuth to collect noble metals; meanwhile, metallic bismuth has low melting point, high specific gravity, and formation heat of bismuth oxide of 45.6 kcal/g atomic oxygen, thus it is easy to be reduced and the reduction temperature is low, which are beneficial for saving energy consumption and reduction time; the much smaller amounts of copper, nickel, antimony and arsenic entering noble bismuth in a slightly reductive smelting atmosphere than those entering noble lead make the converting of noble bismuth become simple, thereby decreasing smelting time and increasing the direct recovery rate of noble metals in anode slime.

Abstract: A method for recovery of platinum group metals from a spent catalyst is described. The method includes crushing the spent catalyst to obtain a catalyst particulate material including particles having a predetermined grain size. The method includes subjecting the catalyst particulate material to a chlorinating treatment in the reaction zone at a predetermined temperature for a predetermined time period by putting the catalyst particulate material in contact with the chlorine containing gas. The method also includes applying an electromagnetic field to the chlorine-containing gas in the reaction zone to provide ionization of chlorine; thereby to cause a chemical reaction between platinum group metals and chlorine ions and provide a volatile platinum group metal-containing chloride product in the reaction zone. Following this, the volatile platinum group metal-containing chloride product is cooled to convert the product into solid phase platinum group metal-containing materials.

Abstract: A process for the beneficiation of Manganese ore which includes the step of leaching of the ore with acid to remove Calcium Carbonate and Magnesium Carbonate. The ore is first broken down to the required particle size by conventional means. Selective leaching of Calcium oxide and Magnesium carbonate occurs leaving an ore having a higher Manganese content.

Abstract: The invention relates to brass alloys that are substantially lead-free. In the alloys of the invention, lead is replaced with tellurium resulting in alloys that exhibit excellent machinability and conductivity.

Abstract: New heat treatable aluminum alloys having magnesium and zinc are disclosed. The new aluminum alloys generally contain 3.0-6.0 wt. % Mg, 2.5-5.0 wt. % Zn, where (wt. % Mg)/(wt. % Zn) is from 0.60 to 2.40.

Abstract: Provided is an aluminum alloy clad sheet that resolves the contradiction between a high strength level and ductility in a single sheet of the existing 7000-series aluminum alloy or the like, and has high strength, good formability (high ductility), and a good BH property through short-time artificial age hardening. An aluminum alloy clad sheet subjected to diffusion heat treatment includes a plurality of aluminum alloy layers being laminated. In the clad sheet, aluminum alloy layers having specific compositions are adjacently laminated such that the contents of Mg or Zn are different from each other, and a microstructure after the diffusion heat treatment has fine grain size and an interdiffusion region of Mg and Zn. In addition, the clad sheet has a specific DSC characteristic. Consequently, high strength and good formability (high ductility) are exhibited, and a BH property through short-time artificial age hardening is improved.

Abstract: Alloys, processes for preparing the alloys, and articles including the alloys are provided. The alloys can include, by weight, about 0% to about 8% nickel, about 1% to about 6% tungsten, about 1% to about 4% copper, about 0.1% to about 2% chromium, about 0.01% to about 1% vanadium, about 0.01% to about 0.5% carbon, about 0.01% to about 0.1% titanium, about 0.001% to about 0.01% boron, about 0% to about 1% silicon, and about 0% to about 0.1% calcium, the balance essentially iron and incidental elements and impurities.

Abstract: An austenitic stainless steel having low nickel and molybdenum and exhibiting comparable corrosion resistance and formability properties to higher nickel and molybdenum alloys comprises, in weight %, up to 0.20 C, 2.0-9.0 Mn, up to 2.0 Si, 16.0-23.0 Cr, 1.0-5.0 Ni, up to 3.0 Mo, up to 3.0 Cu, 0.1-0.35 N, up to 4.0 W, up to 0.01 B, up to 1.0 Co, iron and impurities, the steel having a ferrite number of less than 10 and a MD30 value of less than 20° C.

Abstract: The invention relates to a high-tensile brass alloy comprising 58-66 wt % Cu; 1.6-7 wt % Mn; 0.2-6 wt % Ni; 0.2-5.1 wt % Al; 0.1-3 wt % Si; ?1.5 wt % Fe; ?0.5 wt % Sn; ?0.5 wt % Pb; and the remainder Zn together with unavoidable impurities. Also described are a high-tensile brass product with such an alloy composition, and a method for manufacturing such a product made of a high-tensile brass alloy.

Abstract: The present disclosure relates to methods for forming a golf club head assembly using a combination of different, but separate heat treatments for the golf club head body and high strength faceplate, and vibrational waves to relive stress in the weld heat affected zones of the golf club body and face.

Abstract: The present invention relates to the use of an alkaline, aqueous coating composition for coating of zinc or zinc alloy coated steel substrates, comprising one or more alkaline sulfates, and one or more alkaline carbonates, wherein the pH of the composition ranges from 9-12. The present invention also defines a method for the non-reactive coating of zinc or zinc alloy coated steel substrates by use of said compositions and further relates to the application of said method as a surrogate for pre-phosphating of zinc or zinc alloy coated steel substrates in industrial applications.

Abstract: A method of manufacturing a laminate in which a spray coating film made of a material different from a base material is laminated on the base material includes: a base material heating step of heating the base material; an intermediate layer forming step of forming, on a surface of the heated base material, an intermediate layer made of a material different from the base material and the spray coating film; and a spray coating film forming step of forming the spray coating film on a surface of the intermediate layer.

Abstract: Implementations of the present disclosure relate to an improved shield for use in a processing chamber. In one implementation, the shield includes a hollow body having a cylindrical shape that is substantially symmetric about a central axis of the body, and a coating layer formed on an inner surface of the body. The coating layer is formed the same material as a sputtering target used in the processing chamber. The shield advantageously reduces particle contamination in films deposited using RF-PVD by reducing arcing between the shield and the sputtering target. Arcing is reduced by the presence of a coating layer on the interior surfaces of the shield.

Abstract: A metal substrate (71) is coated with an enamel or other coating material (72) by irradiating the coating material (72) and substrate (71) with electromagnetic radiation to melt an underlying surface of the metal substrate (71) before melting the coating material (72) to create, after cooling, a fusion bond between the solidified substrate and coating material, whereby the fusion bonded interface (73) has an intermeshing irregular tongue and groove like microstructure profile shown in FIG. 7. The electromagnetic radiation may be unfocussed, circulinear or focussed at a point located within the metal substrate (71) to first melt the substrate (71).

Abstract: Methods of applying aluminum coating layers over copper wires are disclosed. A first method may include applying aluminum powder to the surface of a rod, passing the rod through a first set of compression rolls thereby forcing the aluminum powder into a compacted preform around the rod, and heating the rod covered by the preform at 550° C. to 620° C. Further, the heated preform coated rod is passed through a second set of compression rolls thereby obtaining an aluminum coated copper rod. A second method includes disposing a copper rod inside an aluminum tube having an inner layer formed of brazing aluminum alloy, reducing the diameter of the tube's inner surface to match the copper rod, and heating the composite tube-rod such that the inner layer of the brazing alloy fuses to the rod. Another method includes passing the copper rod through a spray of metallic aluminum.

Abstract: A coated cutting tool includes a body and a hard and wear resistant PVD coating on the body, wherein the body is made from a cemented carbide, cermet, ceramics, polycrystalline diamond or polycrystalline cubic boron nitride based materials. Th coating includes a first (Ti,Al)-based nitride sub-coating and a second (Ti,Al)-based nitride sub-coating. The first (Ti,Al)-based nitride sub-coating can be a single layer, and the second (Ti,Al)-based nitride sub-coating can be a laminated structure, wherein the first (Ti,Al)-based nitride sub-coating includes a (Ti1-xAlx)Nz-layer where 0.1<x<0.4, 0.6<z<1.2, and wherein the second (Ti,Al)-based nitride sub-coating includes a (Ti1-x1-y1Alx1Cry1)Nz1 layer where 0.5<x1<0.75, 0.05<y1<0.2, 0.6<z1<1.2.

Abstract: An embodiment of an apparatus includes a deposition chamber, a workpiece fixture including a first workpiece holder, and a first crucible. The workpiece holder is configured to retain a first workpiece in the deposition chamber. The first crucible includes a body including at least one wall defining a non-circular upper recess with a base. A first lower recess is formed below the base of the upper recess and configured to retain a first primary coating feedstock therein.

Abstract: A drying device includes a first cylindrical member and a second cylindrical member. The first cylindrical member has an outer peripheral surface having a surface temperature that is higher on one width wise side where an end is present than on the other widthwise side where another end is present, whereas the second cylindrical member has an outer peripheral surface having a surface temperature that is lower on the one widthwise side where an end is present than on the other widthwise side where another end is present.

Abstract: A drying roller includes: a cylindrical member for drying a separator original sheet, with hot water which is supplied into the cylindrical member and ejected from inside the cylindrical member, the separator original sheet being wrapped on an outer peripheral surface of the cylindrical member; and a discharge pipe for discharging the hot water toward one inner end surface of the cylindrical member, the heating medium being discharged at a position where a distance to the one end surface of the cylindrical member is longer than a distance to the other inner end surface of the cylindrical member.

Abstract: A method can include applying a mask to a CMC structure, and subjecting the structure having an applied mask to a process for repair. In one embodiment, the applying a mask to a CMC structure can include applying a mask to a feature of a CMC structure.

Abstract: Embodiments of the present technology include graphene-metal composites. An example graphene-metal composite comprises a porous metal foam substrate, a graphene layer deposited to the porous metal foam substrate, a metal layer applied to the graphene layer, and another graphene layer deposited to the metal layer; the multilayered porous metal foam substrate being compressed to form a graphene-metal composite.

Abstract: Embodiments of the present technology include graphane-metal composites. An example graphane-metal composite comprises a porous metal foam substrate, a graphane layer deposited to the porous metal foam substrate, a metal layer applied to the graphane layer, and another graphane layer deposited to the metal layer; the multilayered porous metal foam substrate being compressed to form a graphane-metal composite.

Abstract: A machining tool comprising at least one diamond-coated functional region having a substrate surface composed of a hard metal or a ceramic material arranged beneath the diamond layer. The substrate surface contains hard material particles on the basis of carbide and/or nitride and/or oxide, which are embedded in a cobalt-containing binding matrix. The diamond layer is directly arranged on the substrate surface without cobalt having been removed by chemical or physical methods in substantial amounts out of the binding matrix of the substrate surface. Such a tool is produced by pre-treating a hard metal substrate surface with a positively charged ion beam, followed by conventional CVD-diamond coating directly onto the ion beam-pre-treated cobalt-containing substrate surface. The ion-underlying atoms thereby largely remain in the substrate. The tools according to the invention have good diamond layer bonding to the substrate and a high wear resistance.

Abstract: An improved ALD system usable for low vapor pressure liquid and sold precursors. The ALD system includes a precursor container and inert gas delivery elements configured to increase precursor vapor pressure within a precursor container by injecting an inert gas pulse into the precursor container while a precursor pulse is being removed to the reaction chamber. A controllable inert gas flow valve and a flow restrictor are disposed along an inert gas input line leading into the precursor container below its fill level. A vapor space is provided above the fill level. An ALD pulse valve is disposed along a precursor vapor line extending between the vapor space and the reaction chamber. Both valves are pulsed simultaneously to synchronously remove precursor vapor from the vapor space and inject inert gas into the precursor container below the fill level.

Abstract: A system and method for continuous atomic layer deposition. The system and method includes a housing, a moving bed which passes through the housing, a plurality of precursor gases and associated input ports and the amount of precursor gases, position of the input ports, and relative velocity of the moving bed and carrier gases enabling exhaustion of the precursor gases at available reaction sites.

Abstract: Disclosed are methods and systems for forming a layer on a web with reduced levels of particulates. The layer is formed from a fluid mixture(s) or solution of chemical reagents that react to form the layer. The system includes a conveyor device provided configured to carry the web within the chamber while the first surface of the web undergoes one or more processing steps; a first fluid delivery apparatus and a second fluid delivery apparatus, and a first fluid removal apparatus. The first fluid removal apparatus is positioned within a space arranged between the first and the second delivery apparatuses.

Abstract: A solution comprising a palladium compound and a polyaminocarboxylic compound has been found to be suitable as a bath for electroless plating of palladium onto copper. Use of such a solution produces a plated component comprising a copper surface and a palladium plated coating having a thickness of between 0.01 micrometers (?m) and 5 ?m. A method for electroless plating of palladium onto a copper surface of a component includes preparing a bath having a palladium compound and a polyaminocarboxylic compound. The copper component is submerged in the bath to plate a palladium layer on the copper surface of the component. The component resulting from the plating method has a palladium layer plated on the copper surface.

Abstract: A metal-based/diamond laser composite coating preparation method includes: first selecting high-hardness metal powder and diamond powder of a proper grain size and shape; then uniformly mixing the high-hardness metal powder and diamond powder via a ball-milling method; and finally preparing a composite coating on a substrate by synchronously combining laser texturing technology, laser thermal treatment technology and cold spraying technology. The thickness of the composite coating is greater than 1 mm, and the volume content of diamond in the coating is greater than 45%. A metal-based/diamond laser composite coating is also provided.

Abstract: The coated metal plate pertaining to the present invention is a coated metal plate for exterior use, and has a metal plate and a top coating film disposed on the metal plate. The top coating film contains 0.01-15 vol % of porous particles as a gloss adjusting agent, and the coated metal plate satisfies the expressions below. In the expressions below, R is the number-average particle diameter (?m), D97.5 is the diameter (?m) of 97.5% of the particles, Ru is the upper limit particle diameter (?m), and T is the film thickness (?m) of the top coating film in the number particle size distribution of the gloss adjusting agent. D97.5/T?0.7; Ru?1.2T; R?1.0; 3?T?20.

Abstract: A method for operating and electrolytic system may include an electrolyzer for generating hydrogen and oxygen as product gas. Hydrogen and oxygen produced during the electrolytic process are discharged from the electrolyzer. As a result, the efficiency of the electrolytic system is improved, at least one of the product gases in the expansion turbine is expanded, and a generator is driven by the expansion turbine.

Abstract: An electrolysis device of the present invention includes an electrolysis unit. The electrolysis unit includes a channel for fluid to be treated, at least one electrolysis electrode pair, a flow inlet, and a flow outlet. The electrolysis electrode pair is disposed so as to incline with respect to a vertical direction and includes an upper electrode and a lower electrode disposed so as to face each other. The channel for fluid to be treated is disposed so that a fluid that has flowed in from the flow inlet flows through an interelectrode channel between the upper electrode and the lower electrode from a lower side to an upper side and flows out from the flow outlet.

Abstract: Electrochemical and photoelectrochemical cells for the oxidation of 5-hydroxymethylfurfural to 2,5-furandicarboxylic acid and/or 2,5-diformylfuran are provided. Also provided are methods of using the cells to carry out the electrochemical and photoelectrochemical oxidation of 5-hydroxymethylfurfural to 2,5-furandicarboxylic acid and/or 2,5-diformylfuran.

Abstract: A membrane module and method of making are provided, including a mold therefor. Exemplarily, the module, which comprises a membrane around which is formed a frame, is adapted for use with an electrochemical apparatus. The membrane comprises a fabric made from a synthetic fiber such as nylon, where the nylon is woven into ripstop nylon fabric. The frame, which comprises, exemplarily, high-density polyethylene (HDPE) or polypropylene, includes a wedge-shaped portion to facilitate collection of evolved gases and which provides support to the membrane as well as support to internal electrodes. The mold is adapted to suspend and secure the membrane during formation of the module and to provide a module which secures the membrane within the frame after formation of the module.

Abstract: The invention relates to nonferrous metallurgy and may be suitable for controlling the feed of alumina to electrolytic cells for producing aluminum to maintain the alumina concentration in the electrolytic melt equal or close to the saturation value. To maintain the alumina concentration within the set range, reduced voltage U or pseudo-resistance R is measured. The measured values are recorded at fixed time intervals, underfeeding or overfeeding phases compared to a theoretical alumina feeding rate during electrolysis are formed, whereas the duration of underfeeding phases is selected depending on the alumina concentration in the electrolytic melt, and the duration of overfeeding phases is determined according to the change of one or more electrolytic cell parameters being recorded: reduced voltage, U, pseudo-resistance. R, rates of reduced voltage, dU/dt, pseudo-resistance, dR/dt, change.

Abstract: A non alpha controlled plating bath including Tin species and a trace amount of Polonium species is utilized in a plating tool. The plating tool includes a Polonium filter element to remove Polonium species from the plating bath to selectively plate Tin upon a plating cathode. The filter may include a Titanium inner portion surrounding by a stannic oxide exterior. The filter may reduce the Polonium species by having the polonium absorb and then enter within the stannic oxide matrix. The filter may be located within the plating tool reservoir or filter housing. The filter may be fabricated by forming Tin upon a Titanium backbone and converting the Tin to stannic oxide.

Abstract: A non alpha controlled plating bath including Tin species and a trace amount of Polonium species is utilized in a plating tool. The plating tool includes a Polonium filter element to remove Polonium species from the plating bath to selectively plate Tin upon a plating cathode. The filter may include a Titanium inner portion surrounding by a stannic oxide exterior. The filter may reduce the Polonium species by having the polonium absorb and then enter within the stannic oxide matrix. The filter may be located within the plating tool reservoir or filter housing. The filter may be fabricated by forming Tin upon a Titanium backbone and converting the Tin to stannic oxide.

Abstract: Thin film substrates are electroplated with copper from low internal stress, high ductility acid copper electroplating baths. During the copper electroplating process the thin film substrates can warp or bow. To address the problem of warping or bowing during copper electroplating the thin film substrate is held by a securing means which inhibits the thin film substrate from excessive activity.

Abstract: An apparatus for stereo-electrochemical deposition of metal layers consisting of an array of anodes, a cathode, a positioning system, a fluid handling system for an electrolytic solution, communications circuitry, control circuitry and software control. The anodes are electrically operated to promote deposition of metal layers in any combination on the cathode to fabricate a structure.

Abstract: A non alpha controlled plating bath including Tin species and a trace amount of Polonium species is utilized in a plating tool. The plating tool includes a Polonium filter element to remove Polonium species from the plating bath to selectively plate Tin upon a plating cathode. The filter may include a Titanium inner portion surrounding by a stannic oxide exterior. The filter may reduce the Polonium species by having the polonium absorb and then enter within the stannic oxide matrix. The filter may be located within the plating tool reservoir or filter housing. The filter may be fabricated by forming Tin upon a Titanium backbone and converting the Tin to stannic oxide.

Abstract: A system and a process for continuously electrolytically coating a light metal coil is provided. The system includes a bath containing a precursor for an electroceramic coating on a light metal coil and containing a cathodic connection, at least one motor connected to at least one motive assembly to impart movement to the coil. A power source provides voltage and current to the coil through the electrification device, and through the coil in the bath to the cathode connection via the aqueous electrolytic solution. The process includes electrifying bare coil with a voltage and a current, passing the electrified bare light metal coil through a bath having a cathodic connection and containing an aqueous solution with a precursor for an electroceramic coating, and electrochemically reacting the light metal coil with the precursor thereby generating a coated light metal coil having an electroceramic coating on at least one surface.

Abstract: Disclosed is a method of treating the surface of an aluminum substrate, including (a) forming a porous oxide film on the surface of the aluminum substrate and (b) applying a corrosion inhibitor on the surface of the aluminum substrate having the oxide film formed thereon. The method of treating the surface of the aluminum substrate enables the formation of the porous oxide film on the surface of the aluminum substrate through surface treatment so that the applied corrosion inhibitor is partially absorbed into the porous oxide film, thus exhibiting superior corrosion resistance and anti-fouling effects of the metal substrate, compared to conventional surface treatment methods involving coating only with a corrosion inhibitor.

Abstract: A seal ring for an electrochemical processor does not slip or deflect laterally when pressed against a wafer surface. The seal ring may be on a rotor of the processor, with the seal ring having an outer wall joined to a tip arc through an end. The outer wall may be a straight wall. A relatively rigid support ring may be attached to the seal ring, to provide a more precise sealing dimension. Knife edge seal rings that slip or deflect laterally on the wafer surface may also be used. In these designs, the slipping is substantially uniform and consistent, resulting in improved performance.

Abstract: A non alpha controlled Tin including Tin and a trace amount of Polonium is utilized as a plating anode to selectively plate Tin upon a plating cathode. Tin may be selectively plated by pulse plating the non alpha controlled Tin with current control to suppress plating of Polonium upon the plating cathode. Tin may also be selectively plated by pulse plating the non alpha controlled Tin with potential control to suppress plating of Polonium upon the plating cathode. Tin may also be selectively plated by pulse and reverse plating to plate out Polonium upon a filtering cathode. Tin may also be selectively plated by plating out Polonium upon a filtering cathode within a concentrate. Tin may also be selectively plated by plating out purified Tin upon a filtering cathode, separating the purified Tin from the filtering cathode, and utilizing the purified Tin to plate Tin upon the plating cathode.

Abstract: An apparatus for stereo-electrochemical deposition of metal layers consisting of an array of anodes, a cathode, a positioning system, a fluid handling system for an electrolytic solution, communications circuitry, control circuitry and software control. The anodes are electrically operated to promote deposition of metal layers in any combination on the cathode to fabricate a structure.

Abstract: Techniques for processing materials in supercritical fluids including processing in a capsule disposed within a high-pressure apparatus enclosure are disclosed. The disclosed techniques are useful for growing crystals of GaN, AlN, InN, and their alloys, including InGaN, AlGaN, and AlInGaN for the manufacture of bulk or patterned substrates, which in turn can be used to make optoelectronic devices, lasers, light emitting diodes, solar cells, photoelectrochemical water splitting and hydrogen generation devices, photodetectors, integrated circuits, and transistors.

Abstract: Present embodiments include an additive manufacturing tool configured to receive a metallic material and to supply a plurality of droplets to a part at a work region of the part, wherein each droplet of the plurality of droplets comprises the metallic material and a heating system comprising a primary laser system configured to generate a primary laser beam to heat a molten zone of a substrate of the part and a secondary laser system configured to generate a secondary laser beam to heat a transition zone of the substrate of the part, wherein the molten zone and the work region are colocated, and wherein the transition zone is disposed about the molten zone.

Abstract: A crystal pulling system for growing a monocrystalline ingot from a melt of semiconductor or solar-grade material includes a housing defining a growth chamber, a crucible disposed within the growth chamber containing the melt of semiconductor or solar-grade material, a vacuum pump for drawing exhaust gases out of the growth chamber, and a fluid-cooled exhaust tube connected between the growth chamber and the vacuum pump.

Abstract: The present invention provides a film formation method and a film formation apparatus which can fabricate an epitaxial film with +c polarity by a sputtering method. In one embodiment of the present invention, the film formation method of epitaxially growing a semiconductor thin film with a wurtzite structure by the sputtering method on an epitaxial growth substrate heated to a predetermined temperature by a heater includes the following steps. First, the substrate is disposed on a substrate holding portion including the heater to be located at a predetermined distance away from the heater. Then, the epitaxial film of the semiconductor film with the wurtzite structure is formed on the substrate with the impedance of the substrate holding portion being adjusted.

Abstract: Some aspects relate to methods of forming an epitaxial layer. In some examples, the methods include ejecting atoms from a molten metal sputtering material onto a heated crystalline substrate and growing a single epitaxial layer on the substrate from the ejected atoms, where the atoms are ejected with sufficient energy that the grown epitaxial layer has at least a partial rhombohedral lattice, and wherein the crystalline substrate is heated to a temperature of about 600 degrees Celsius or less, or about 500 degrees or less. Other aspects relate to materials, such as a material including a single epitaxial layer on top of a crystalline substrate, the layer including one or more semiconductor materials and having at least a partial rhombohedral lattice, or a substantially rhombohedral lattice.