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| | The author is known as Wilber Pegues. To play lacross is something he would by no means give up. Distributing manufacturing is exactly where her primary earnings comes from. Ohio is where his house is and his family members enjoys it.<br><br>Feel free to visit my web-site; free psychic reading - [http://www.light4america.com/profile.php?u=Ro0506 www.light4america.com] - |
| [[image:LDClinkerScaled.jpg|thumb|200px|right|[[Clinker (cement)|Clinker]] nodules produced by sintering]]
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| '''Sintering''' is a method for creating objects from [[Powder (substance)|powders]], including [[powdered metal|metal]] and [[ceramic]] powders. It is based on atomic [[diffusion]]. Diffusion occurs in any material above [[absolute zero]], but it occurs much faster at higher temperatures. In most sintering processes, the powdered material is held in a mold and then heated to a temperature below the melting point. The atoms in the powder particles diffuse across the boundaries of the particles, fusing the particles together and creating one solid piece. Because the sintering temperature does not have to reach the melting point of the material, sintering is often chosen as the shaping process for materials with extremely high melting points such as [[tungsten]] and [[molybdenum]].
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| Sintering is traditionally used for manufacturing [[ceramic]] objects but finds applications in almost all fields of industry. The study of sintering and of powder-related processes is known as [[powder metallurgy]]. A simple, intuitive example of sintering can be observed when ice cubes in a glass of water adhere to each other.
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| The word "sinter" comes from the [[Middle High German]] ''Sinter'', a [[cognate]] of English "[[cinder]]".
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| ==Advantages==
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| Particular advantages of the powder technology include:
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| # Very high levels of [[wiktionary:Purity|purity]] and uniformity in starting materials
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| # Preservation of purity, due to the simpler subsequent [[Manufacturing|fabrication]] process (fewer steps) that it makes possible
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| # Stabilization of the details of repetitive operations, by control of [[Crystallite|grain]] size during the input stages
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| # Absence of binding contact between segregated powder particles – or "inclusions" (called stringering) – as often occurs in melting processes
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| # No [[Deformation (engineering)|deformation]] needed to produce directional elongation of grains
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| # Capability to produce materials of controlled, uniform porosity.
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| # Capability to produce nearly net-shaped objects.
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| # Capability to produce materials which cannot be produced by any other technology.
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| # Capability to fabricate high-strength material like turbine blades.
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| # After sintering the mechanical strength to handling becomes higher.
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| The literature contains many references on sintering dissimilar materials to produce solid/solid-phase compounds or solid/melt mixtures at the processing stage. Almost any substance can be obtained in powder form, through either chemical, mechanical or physical processes, so basically any material can be obtained through sintering. When pure elements are sintered, the leftover powder is still pure, so it can be recycled.
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| ==Disadvantages==
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| Particular disadvantages of the powder technology include:
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| # 100% sintered (iron ore) can not be charged in the blast furnace.
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| # By sintering one cannot create uniform sizes.
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| ==General sintering==
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| Sintering is effective when the process reduces the porosity and enhances properties such as strength, electrical conductivity, translucency and thermal conductivity; yet, in other cases, it may be useful to increase its strength but keep its gas absorbency constant as in filters or catalysts. During the firing process, atomic diffusion drives powder surface elimination in different stages, starting from the formation of necks between powders to final elimination of small pores at the end of the process.
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| The driving force for densification is the change in free energy from the decrease in surface area and lowering of the surface free energy by the replacement of solid-vapor interfaces. It forms new but lower-energy solid-solid interfaces with a total decrease in free energy occurring on sintering 1-micrometre particles a 1 cal/g decrease. On a microscopic scale, material transfer is affected by the change in pressure and differences in free energy across the curved surface. If the size of the particle is small (and its curvature is high), these effects become very large in magnitude. The change in energy is much higher when the radius of curvature is less than a few micrometres, which is one of the main reasons why much ceramic technology is based on the use of fine-particle materials.<ref name=Kingery/>
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| For properties such as strength and conductivity, the bond area in relation to the particle size is the determining factor. The variables that can be controlled for any given material are the temperature and the initial grain size, because the vapor pressure depends upon temperature. Through time, the particle radius and the vapor pressure are proportional to (p<sub>0</sub>)<sup>2/3</sup> and to (p<sub>0</sub>)<sup>1/3</sup>, respectively.<ref name=Kingery/>
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| The source of power for solid-state processes is the change in free or chemical potential energy between the neck and the surface of the particle. This energy creates a transfer of material through the fastest means possible; if transfer were to take place from the particle volume or the grain boundary between particles, then there would be particle reduction and pore destruction. The pore elimination occurs faster for a trial with many pores of uniform size and higher porosity where the boundary diffusion distance is smaller. For the latter portions of the process, boundary and lattice diffusion from the boundary become important.<ref name=Kingery/>
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| Control of temperature is very important to the sintering process, since grain-boundary diffusion and volume diffusion rely heavily upon temperature, the size and distribution of particles of the material, the materials composition, and often the sintering environment to be controlled.<ref name=Kingery>{{Cite journal|last1 =Kingery|first1 =W. David|last2 = Bowen|first2 = H. K.|last3 = Uhlmann|first3 = Donald R.|title = Introduction to Ceramics|publisher = [[John Wiley & Sons]], [[Academic Press]]|date = April 1976|edition = 2nd|location =|url =|doi =|id = |isbn = 0-471-47860-1}}</ref>
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| ==Ceramic sintering==
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| Sintering is part of the firing process used in the manufacture of [[pottery]] and other ceramic objects. These objects are made from substances such as [[glass]], [[alumina]], [[zirconia]], [[silica]], [[magnesia (mineral)|magnesia]], [[Lime (mineral)|lime]], [[beryllium oxide]] and [[ferric oxide]]. Some ceramic raw materials have a lower [[Chemical affinity|affinity]] for water and a lower [[plasticity index]] than [[clay]], requiring organic additives in the stages before sintering. The general procedure of creating ceramic objects via sintering of powders includes:
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| *Mixing water, [[Binder (material)|binder]], [[deflocculant]], and unfired ceramic powder to form a [[slurry]];
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| *[[Spray drying|Spray-drying]] the slurry;
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| *Putting the spray dried powder into a mold and pressing it to form a ''green body'' (an unsintered ceramic item);
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| *Heating the green body at low temperature to burn off the binder;
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| *Sintering at a high temperature to fuse the ceramic particles together.
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| All the characteristic temperatures associated to phases transformation, glass transitions and melting points, occurring during a sinterisation cycle of a particular ceramics formulation (i.e., tails and frits) can be easily obtained by observing the expansion-temperature curves during [[optical dilatometer]] thermal analysis. In fact, sinterisation is associated to a remarkable shrinkage of the material because glass phases flow, once their transition temperature is reached, and start consolidating the powdery structure and considerably reducing the porosity of the material.
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| There are two types of sintering: with pressure (also known as [[hot pressing]]), and without pressure. Pressureless sintering is possible with graded metal-ceramic composites, with a nanoparticle sintering aid and bulk molding technology. A variant used for 3D shapes is called [[hot isostatic pressing]].
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| To allow efficient stacking of product in the furnace during sintering and prevent parts sticking together, many manufacturers separate ware using Ceramic Powder Separator Sheets. These sheets are available in various materials such as alumina, zirconia and magnesia. They are additionally categorized by fine, medium and coarse particle sizes. By matching the material and particle size to the ware being sintered, surface damage and contamination can be reduced while maximizing furnace loading.
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| ==Sintering of metallic powders==
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| [[File:Iron powder.JPG|thumb|right|250px|[[Iron powder]]]]
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| Most, if not all, metals can be sintered. This applies especially to pure metals produced in vacuum which suffer no surface contamination. Sintering under atmospheric pressure requires the usage of a protective gas, quite often [[endothermic gas]].<ref>{{cite web|url=http://www.crystec.com/kllendoe.htm|title=endo gas}}</ref> Sintering, with subsequent reworking, can produce a great range of material properties. Changes in density, [[alloy]]ing, or heat treatments can alter the physical characteristics of various products. For instance, the [[Young's Modulus]] ''E<sub>n</sub>'' of sintered [[iron]] powders remains insensitive to sintering time, alloying, or particle size in the original powder, but depends upon the density of the final product:
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| <math>E_n/E = (D/d)^{3.4}</math>
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| where ''D'' is the density, ''E'' is [[Young's modulus]] and ''d'' is the maximum density of iron. | |
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| Sintering is static when a metal powder under certain external conditions may exhibit coalescence, and yet reverts to its normal behavior when such conditions are removed. In most cases, the density of a collection of grains increases as material flows into voids, causing a decrease in overall volume. Mass movements that occur during sintering consist of the reduction of total porosity by repacking, followed by material transport due to [[evaporation]] and [[condensation]] from [[diffusion]]. In the final stages, metal atoms move along crystal boundaries to the walls of internal pores, redistributing mass from the internal bulk of the object and smoothing pore walls. [[Surface tension]] is the driving force for this movement.
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| A special form of sintering, still considered part of powder metallurgy, is liquid-state sintering. In liquid-state sintering, at least one but not all elements are in a liquid state. Liquid-state sintering is required for making [[cemented carbide]] or [[tungsten carbide]].
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| Sintered [[bronze]] in particular is frequently used as a material for [[bearing (mechanical)|bearings]], since its porosity allows lubricants to flow through it or remain captured within it. For materials that have high melting points such as [[molybdenum]], [[tungsten]], [[rhenium]], [[tantalum]], [[osmium]] and [[carbon]], sintering is one of the few viable manufacturing processes. In these cases, very low porosity is desirable and can often be achieved.
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| Sintered metal powder is used to make [[frangibility|frangible]] shotgun shells called [[breaching round]]s, as used by military and SWAT teams to quickly force entry into a locked room. These are shotgun shells designed to destroy door deadbolts, locks and hinges without risking lives by ricocheting or by flying on at lethal speed through the door. They work by destroying the object they hit and then dispersing into a relatively harmless powder.
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| Sintered bronze and stainless steel are used as filter materials in applications requiring high temperature resistance while retaining the ability to regenerate the filter element. For example, sintered stainless steel elements are employed for filtering steam in food and pharmaceutical applications, and sintered bronze in aircraft hydraulic systems.
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| Sintering of powders containing precious metals such as [[silver]] and [[gold]] is used to make small jewelry items.
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| ==Plastics sintering==
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| Plastic materials are formed by sintering for applications that require materials of specific porosity.
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| Sintered plastic porous components are used in filtration and to control fluid and gas flows. Sintered plastics are used in applications requiring wicking properties, such as marking pen nibs. Sintered [[ultra high molecular weight polyethylene]] materials are used as [[ski]] and [[snowboard]] base materials. The porous texture allows wax to be retained within the structure of the base material, thus providing a more durable wax coating.
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| ==Liquid phase sintering==
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| For materials which are hard to sinter a process called liquid phase sintering is commonly used. Materials for which liquid phase sintering is common are [[Silicon nitride|Si<sub>3</sub>N<sub>4</sub>]], [[Tungsten carbide|WC]], [[Silicon carbide|SiC]], and more. Liquid phase sintering is the process of adding an additive to the powder which will melt before the matrix phase. The process of liquid phase sintering has three stages:
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| *'''Rearrangement''' – As the liquid melts capillary action will pull the liquid into pores and also cause grains to rearrange into a more favorable packing arrangement.
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| *'''Solution-Precipitation''' – In areas where capillary pressures are high (particles are close together) atoms will preferentially go into solution and then precipitate in areas of lower chemical potential where particles are non close or in contact. This is called "''contact flattening''" This densifies the system in a way similar to grain boundary diffusion in solid state sintering. [[Ostwald ripening]] will also occur where smaller particles will go into solution preferentially and precipitate on larger particles leading to densification.
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| *'''Final Densification''' – densification of solid skeletal network, liquid movement from efficiently packed regions into pores.
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| For liquid phase sintering to be practical the major phase should be at least slightly soluble in the liquid phase and the additive should melt before any major sintering of the solid particulate network occurs, otherwise rearrangement of grains will not occur.
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| ==Electric current assisted sintering==
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| These techniques employ electric currents to drive or enhance sintering.<ref>{{cite web|url=http://www.sciencedirect.com/science/article/pii/S0927796X08000995 |title=Materials Science and Engineering: R: Reports : Consolidation/synthesis of materials by electric current activated/assisted sintering |publisher=ScienceDirect |date= |accessdate=2011-09-30}}</ref> English engineer A. G. Bloxam registered in 1906 the first [[patent]] on sintering powders using [[direct current]] in [[vacuum]]. The primary purpose of his inventions was the industrial scale production of filaments for [[Incandescent light bulb|incandescent lamp]]s by compacting [[tungsten]] or [[molybdenum]] particles. The applied current was particularly effective in reducing surface [[oxide]]s that increased the [[emissivity]] of the filaments.<ref name=grasso/>
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| In 1913, Weintraub and Rush patented a modified sintering method which combined electric current with [[pressure]]. The benefits of this method were proved for the sintering of [[Refraction (metallurgy)|refractory metals]] as well as conductive [[carbide]] or [[nitride]] powders. The starting [[boron]]–[[carbon]] or [[silicon]]–carbon powders were placed in an [[Insulator (electrical)|electrically insulating]] tube and compressed by two rods which also served as [[electrode]]s for the current. The estimated sintering temperature was 2000 °C.<ref name=grasso/>
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| In the US, sintering was first patented by Duval d’Adrian in 1922. His three-step process aimed at producing heat-resistant blocks from such oxide materials as [[Zirconium dioxide|zirconia]], [[Thorium dioxide|thoria]] or [[Tantalum|tantalia]]. The steps were: (i) [[Molding (process)|molding]] the powder; (ii) [[Annealing (metallurgy)|annealing]] it at about 2500 °C to make it conducting; (iii) applying current-pressure sintering as in the method by Weintraub and Rush.<ref name=grasso/>
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| Sintering which uses an [[Electric arc|arc]] produced via a [[capacitance]] discharge to eliminate oxides before direct current heating, was patented by G. F. Taylor in 1932. This originated sintering methods employing pulsed or [[alternating current]], eventually superimposed to a direct current. Those techniques have been developed over many decades and summarized in more than 640 patents.<ref name=grasso>{{cite journal|format=free download pdf|journal=Sci. Technol. Adv. Mater.|volume= 10|year=2009|page=053001|title=Electric current activated/assisted sintering (ECAS): a review of patents 1906–2008|author=Salvatore Grasso ''et al.''|doi= 10.1088/1468-6996/10/5/053001|issue=5}}</ref>
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| Of these technologies the most well known is resistance sintering (also called [[hot pressing]]) and [[spark plasma sintering]], while [[capacitor discharge sintering]] is the latest advancement in this field.
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| ===Spark plasma sintering===
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| [[Spark plasma sintering]] (SPS) external pressure and an electric field are applied simultaneously to enhance the densification of the metallic/ceramic powder compacts. This densification uses lower temperatures and shorter amount of time than typical sintering.<ref name = Tuan>{{Cite journal|last1 = Tuan|first1 = W.H.|last2 =Guo|first2 =J.K.|publisher =Springer|year = 2004 |isbn = 3-540-40516-X|title = Multiphased ceramic materials: processing and potential}}</ref> For a number of years, it was speculated that the existence of sparks or plasma between particles could aid sintering; however, Hulbert and coworkers systematically proved that the electric parameters used during spark plasma sintering make it (highly) unlikely.<ref>Hulbert, D. M. et al. The Absence of Plasma in‘ Spark Plasma Sintering’. Journal of Applied Physics 104, 3305 (2008).</ref> In light of this, the name "spark plasma sintering" has been rendered obsolete. Terms such as "Field Assisted Sintering Technique" (FAST), "Electric Field Assisted Sintering" (EFAS), and Direct Current Sintering (DCS) have been implemented by the sintering community.<ref>Anselmi-Tamburini, U. et al. in Sintering: Nanodensification and Field Assisted Processes (Castro, R. & van Benthem, K.) (Springer Verlag, 2012).</ref> Using a DC pulse as the electrical current, spark plasma, spark impact pressure, joule heating, and an electrical field diffusion effect would be created.<ref name=Palmer/>
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| Certain ceramic materials have low density, chemical inertness, high strength, hardness and temperature capability; nanocrystalline ceramics have even greater strength and higher superplasticity.<ref name=Palmer/>
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| Many microcrystalline ceramics that were treated and had gained facture toughness lost their strength and hardness, with this many have created ceramic composites to offset the deterioration while increasing strength and hardness to that of nanocrystalline materials. Through various experiments it has been found that in order to design the mechanical properties of new material, controlling the grain size and its distribution, amount of distribution and other is pinnacle.<ref name=Palmer>{{Cite journal|last1 = Palmer|first1 = R.E.|last2 = Wilde|first2 = G.|title = Mechanical Properties of Nanocomposite Materials|publisher = Elsevier Ltd.|date = December 22, 2008|location =EBL Database|isbn = 978-0-08-044965-4}}</ref>
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| ==Pressureless sintering==
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| Pressureless sintering is the sintering of a powder compact (sometimes at very high temperatures, depending on the powder) without applied pressure. This avoids density variations in the final component, which occurs with more traditional hot pressing methods.
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| The powder compact (if a ceramic) can be created by [[Slipcasting|slip casting]] into a plaster mould, then the final green compact can be machined if necessary to final shape before being heated to sinter.
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| ==Densification, vitrification and grain growth==
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| {{Main|Crystallite}}
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| Sintering in practice is the control of both densification and grain growth. Densification is the act of reducing porosity in a sample thereby making it more dense. Grain growth is the process of grain boundary motion and [[Ostwald ripening]] to increase the average grain size. Many properties ([[mechanical strength]], electrical breakdown strength, etc.) benefit from both a high relative [[density]] and a small grain size. Therefore, being able to control these properties during processing is of high technical importance. Since densification of powders requires high temperatures, [[grain growth]] naturally occurs during sintering. Reduction of this process is key for many engineering ceramics.
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| For densification to occur at a quick pace it is essential to have (1) an amount of liquid phase that is large in size, (2) a near complete solubility of the solid in the liquid, and (3) wetting of the solid by the liquid. The power behind the densification is derived from the capillary pressure of the liquid phase located between the fine solid particles. When the liquid phase wets the solid particles, each space between the particles becomes a capillary in which a substantial capillary pressure is developed. For submicrometre particle sizes, capillaries with diameters in the range of 0.1 to 1 micrometres develop pressures in the range of {{convert|175|psi}} to {{convert|1750|psi}} for silicate liquids and in the range of {{convert|975|psi}} to {{convert|9750|psi}} for a metal such as liquid cobalt.<ref name=Kingery/>
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| Densification requires constant [[capillary pressure]] where just solution-precipitation material transfer would not produce densification. For further densification, additional particle movement while the particle undergoes grain-growth and grain-shape changes occurs. Shrinkage would result when the liquid slips between particles and increase pressure at points of contact causing the material to move away from the contact areas forcing particle centers to draw near each other.<ref name=Kingery/>
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| The sintering of liquid-phase materials involve a fine-grained solid phase to create the needed capillary pressures proportional to its diameter and the liquid concentration must also create the required capillary pressure within range, else the process ceases. The vitrification rate is dependent upon the pore size, the viscosity and amount of liquid phase present leading to the viscosity of the overall composition, and the surface tension. Temperature dependence for densification controls the process because at higher temperatures viscosity decreases and increases liquid content. Therefore, when changes to the composition and processing are made, it will affect the vitrification process.<ref name=Kingery/>
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| ===Sintering mechanisms===
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| Sintering occurs by diffusion of atoms through the microstructure. This diffusion is caused by a gradient of chemical potential – atoms move from an area of higher chemical potential to an area of lower chemical potential. The different paths the atoms take to get from one spot to another are the sintering mechanisms. The six common mechanisms are:
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| *Surface diffusion – Diffusion of atoms along the surface of a particle
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| *Vapor transport – Evaporation of atoms which condense on a different surface
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| *Lattice diffusion from surface – atoms from surface diffuse through lattice
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| *Lattice diffusion from grain boundary – atom from grain boundary diffuses through lattice
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| *Grain boundary diffusion – atoms diffuse along grain boundary
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| *Plastic deformation – dislocation motion causes flow of matter
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| Also one must distinguish between densifying and non-densifying mechanisms. 1–3 above are non-densifying – they take atoms from the surface and rearrange them onto another surface or part of the same surface. These mechanisms simply rearrange matter inside of porosity and do not cause pores to shrink. Mechanisms 4–6 are densifying mechanisms – atoms are moved from the bulk to the surface of pores thereby eliminating porosity and increasing the density of the sample.
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| ===Grain growth===
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| A [[grain boundary]](GB) is the transition area or interface between adjacent [[crystallites]] (or [[Food grain|grain]]s) of the same chemical and lattice composition, not to be confused with a [[phase boundary]]. The adjacent grains do not have the same orientation of the lattice thus giving the atoms in GB shifted positions relative to the lattice in the crystals. Due to the shifted positioning of the atoms in the GB they have a higher energy state when compared with the atoms in the crystal lattice of the grains. It is this imperfection that makes it possible to selectively etch the GBs when one wants the microstructure visible.<ref name=Smallman>{{cite book|last=Smallman R. E.|first=Bishop, Ray J|title=Modern physical metallurgy and materials engineering: science, process, applications|year=1999|publisher=Oxford : Butterworth-Heinemann|isbn=978-0-7506-4564-5}}</ref>
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| Striving to minimize its energy leads to the coarsening of the [[microstructure]] to reach a metastable state within the specimen. This involves minimizing its GB area and changing its [[topological]] structure to minimize its energy. This [[grain growth]] can either be normal or abnormal, a normal grain growth is characterized by the uniform growth and size of all the grains in the specimen. [[Grain growth#Normal vs abnormal|Abnormal growth]] is when a few grains grow much larger than the remaining majority.<ref name="Fundamentals of Materials Science">{{cite book|last=Mittemeijer|first=Eric J.|title=Fundamentals of Materials Science The Microstructure–Property Relationship Using Metals as Model Systems|year=2010|publisher=Springer Heidelberg Dordrecht London New York|isbn=978-3-642-10499-2|pages=463–496}}</ref>
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| ====Grain boundary energy/tension====
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| The atoms in the GB are normally in a higher energy state than their equivalent in the bulk material. This is due to their more stretched bonds, which gives rise to a GB tension <math>\sigma_{GB}</math>. This extra energy that the atoms possess is called the grain boundary energy, <math>\gamma_{GB}</math>. The grain will want to minimize this extra energy thus striving to make the grain boundary area smaller and this change requires energy.<ref name="Fundamentals of Materials Science" />
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| “Or, in other words, a force has to be applied, in the plane of the grain boundary and acting along a line in the grain-boundary area, in order to extend the grain-boundary area in the direction of the force. The force per unit length, i.e. tension/stress, along the line mentioned is σGB. On the basis of this reasoning it would follow:
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| <math>\sigma_{GB} dA \text{ (work done)} = \gamma_{GB} dA \text{ (energy change)}\,\!</math>
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|
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| with dA as the increase of grain-boundary area per unit length along the line in the grain-boundary area considered.”<ref name="Fundamentals of Materials Science" /> [pg 478]
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| The GB tension can also be thought of as the attractive forces between the atoms at the surface and the tension between these atoms is due to the fact that there is a larger interatomic distance between them at the surface compared to the bulk (i.e. [[surface tension]]). When the surface area becomes bigger the bonds stretch more and the GB tension increases. To counteract this increase in tension there must be a transport of atoms to the surface keeping the GB tension constant. This diffusion of atoms accounts for the constant surface tension in liquids. Then the argument,
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| <math>\sigma_{GB} dA \text{ (work done)} = \gamma_{GB} dA \text{ (energy change)}\,\!</math>
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| holds true. For solids, on the other hand, diffusion of atoms to the surface might not be sufficient and the surface tension can vary with an increase in surface area.<ref name=Sintering>{{cite book|last=Kang|first=Suk-Joong L.|title=Sintering: Densification, Grain Growth, and Microstructure|year=2005|publisher=Elsevier Ltd.|isbn=978-0-7506-6385-4|pages=9–18}}</ref>
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| For a solid, one can derive an expression for the change in Gibbs free energy, dG, upon the change of GB area, dA. dG is given by
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| <math>\sigma_{GB} dA \text{ (work done)} = dG \text{ (energy change)} = \gamma_{GB} dA + A d\gamma_{GB}\,\!</math>
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| which gives
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|
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| <math>\sigma_{GB} = \gamma_{GB} + \frac{Ad\gamma_{GB}}{dA}\,\!</math>
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| <math>\sigma_{GB}</math> is normally expressed in units of <math>\frac{N}{m}</math> while <math>\gamma_{GB}</math> is normally expressed in units of <math>\frac{J}{m^2}</math> <math>(J = Nm)</math> since they are different physical properties.<ref name="Fundamentals of Materials Science" />
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| ====Mechanical equilibrium====
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| In a two-dimensional [[isotropic material]] the grain boundary tension would be the same for the grains. This would give angle of 120° at GB junction where three grains meet. This would give the structure a [[hexagonal]] pattern which is the [[metastable]] state (or [[mechanical equilibrium]]) of the 2D specimen. A consequence of this is that to keep trying to be as close to the equilibrium as possible grains with fewer sides than six will bend the GB to try keep the 120° angle between each other. This results in a curved boundary with its [[curvature]] towards itself. A grain with six sides will as mentioned have straight boundaries while a grain with more than six sides will have curved boundaries with its curvature away from itself. A grain with six boundaries (i.e. hexagonal structure) are in a metastable state (i.e. local equilibrium) within the 2D structure.<ref name="Fundamentals of Materials Science" /> In three dimensions structural details are similar but much more complex and the [[metastable]] structure for a grain is a non-regular 14-sided [[polyhedra]] with doubly curved faces. In practice all arrays of grains are always unstable and thus always grows until its prevented by a counterforce.<ref name="Physical Metallurgy ch 28">{{cite book|last=Robert W. Cahn|first=Peter Haasen|title=Physical Metallurgy (Fourth Edition)|year=1996|isbn=978-0-444-89875-3|pages=2399–2500}}</ref>
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| Since the grains strive to minimize their energy and a curved boundary has a higher energy than a straight boundary. This means that the grain boundary will migrate towards the <!--clarify--> the curvature.{{clarify|date=September 2012|reason="the curvature" is wrong, but I'm not sure how to fix it}} The consequence of this is that grains with less than 6 sides will decrease in size while grains with more than 6 sides will increase in size.<ref name="Ceramic materials ch sintering">{{cite book|last=C. Barry Carter|first=M. Grant Norton|title=Ceramic Materials: Science and Engineering|year=2007|publisher=Springer Science+Business Media, LLC.|isbn=978-0-387-46270-7|pages=427–443}}</ref>
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| Grain growth happens due to motion of atoms across a grain boundary. Convex surfaces have a higher chemical potential than concave surfaces therefore grain boundaries will move toward their center of curvature. As smaller particles tend to have a higher radius of curvature and this results in smaller grains losing atoms to larger grains and shrinking. This is a process called Ostwald ripening. Large grains grow at the expense of small grains.
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| Grain growth in a simple model is found to follow:
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| <math>G^m= G_0^m+Kt</math>
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| Here ''G'' is final average grain size, ''G<sub>0</sub>'' is the initial average grain size, ''t'' is time, ''m'' is a factor between 2 and 4, and ''K'' is a factor given by:
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| <math>K= K_0 e^{\frac{-Q}{RT}}</math>
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| Here ''Q'' is the molar activation energy, ''R'' is the ideal gas constant, ''T'' is absolute temperature, and ''K<sub>0</sub>'' is a material dependent factor.
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| ===Reducing grain growth===
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| '''Solute ions'''
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| If a dopant is added to the material (example: Nd in BaTiO<sub>3</sub>) the impurity will tend to stick to the grain boundaries. As the grain boundary tries to move (as atoms jump from the convex to concave surface) the change in concentration of the dopant at the grain boundary will impose a drag on the boundary. The original concentration of solute around the grain boundary will be asymmetrical in most cases. As the grain boundary tries to move the concentration on the side opposite of motion will have a higher concentration and therefore have a higher chemical potential. This increased chemical potential will act as a backforce to the original chemical potential gradient that is the reason for grain boundary movement. This decrease in net chemical potential will decrease the grain boundary velocity and therefore grain growth.
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| '''Fine second phase particles'''
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| If particles of a second phase which are insoluble in the matrix phase are added to the powder in the form of a much finer powder than this will decrease grain boundary movement. When the grain boundary tries to move past the inclusion diffusion of atoms from one grain to the other will be hindered by the insoluble particle. Since it is beneficial for particles to reside in the grain boundaries and they exert a force in opposite direction compared to the grain boundary migration. This effect is called the Zener effect after the man who estimated this drag force to
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| <math> F = \pi r \lambda \sin (2\theta)\,\!</math>
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| where r is the radius of the particle and λ the interfacial energy of the boundary if there are N particles per unit volume their volume fraction f is
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| <math> f = \frac{4}{3} \pi r^3 N\,\!</math>
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| assuming they are randomly distributed. A boundary of unit area will intersect all particles within a volume of 2r which is 2Nr particles. So the number of particles n intersecting a unit area of grain boundary is:
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| <math>n = \frac{3f}{2 \pi r^2}\,\!</math>
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| Now assuming that the grains only grow due to the influence of curvature, the driving force of growth is <math>\frac{2 \lambda}{R} </math> where (for homogeneous grain structure) R approximates to the mean diameter of the grains. With this the critical diameter that has to be reached before the grains ceases to grow:
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| <math>n F_{max} = \frac{2 \lambda}{D_{crit}}\,\!</math>
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| This can be reduced to
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| <math>D_{crit} = \frac{4r}{3f} \,\!</math>
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| so the critical diameter of the grains is dependent of the size and volume fraction of the particles at the grain boundaries.<ref name="Physical Metallurgy">{{cite book|last=Robert W. Cahn|first=Peter Haasen|title=Physical Metallurgy(Fourth Edition)|year=1996|isbn=978-0-444-89875-3}}</ref>
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| It has also been shown that small bubbles or cavities can act as inclusion
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| More complicated interactions which slow grain boundary motion include interactions of the surface energies of the two grains and the inclusion and are discussed in detail by C.S. Smith.<ref name="C. S. Smith">{{cite journal|last=Smith|first=Cyril S.|title=Introduction to Grains, Phases and Interphases: an Introduction to Microstructure|date=February 1948}}</ref>
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| == Natural sintering in geology ==
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| <!-- Sinter (geology) redirects here -->
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| [[Image:Source pétrifiante.jpg|thumb|right|200px|Petrifying spring in Réotier near [[Mont-Dauphin]], [[France]]]]
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| In [[geology]] a natural sintering occurs when a mineral spring brings about a deposition of chemical sediment or crust, for example as of porous silica.<ref name="freedicsinter">[http://www.thefreedictionary.com/sinter Sinter] in thefreedictionary.com.</ref>
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| A sinter is a mineral deposit that presents a porous or vesicular texture; its structure shows small cavities. Two types of deposits are referenced: [[silica|siliceous]] deposits, and [[calcareous]] deposits.<ref name="britanica">[http://www.britannica.com/EBchecked/topic/546308/sinter sinter] in Encyclopedia Britanica.</ref>
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| [[Siliceous sinter]] is a deposit of [[opal]]ine or [[amorphous]] [[silica]], that shows as incrustations near [[hot spring]]s and [[geyser]]s. It sometimes forms conical mounds, called geyser cones, but can also shape as a [[Terrace (geology)|terrace]]. The main agents responsible for the deposition of siliceous sinter are [[algae]] and other vegetation in the water. Altering of wall rocks can also form sinters near [[fumarole]]s and in the deeper channels of [[hot spring]]s. Examples of siliceous sinter are [[geyserite]] and [[fiorite]]. They can be found in many places, including [[Iceland]], [[New Zealand]], [[U.S.A.]] ([[Yellowstone National Park]] - Wyo., [[Steamboat Springs, Colorado|Steamboat Springs]] - Colo.),...
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| [[Calcareous sinter]] is also called [[tufa]], calcareous tufa, or calc-tufa. It is a deposit of [[calcium carbonate]], as with [[travertine]]. Called petrifying springs, they are quite common in limestone districts. Their calcareous waters deposit a sintery incrustation on surrounding objects. The precipitation being assisted with mosses and other vegetable structures, thus leaving cavities in the calcareous sinter after they have decayed.<ref name="britanica"/>
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| Petrifying spring at [[Pamukkale]], [[Turkey]] :
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| <gallery>
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| Image:Pamukkale3.jpg
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| Image:Pamukkale1.jpg
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| </gallery>
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| ==See also==
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| {{colbegin|2}}
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| *[[Capacitor Discharge Sintering]]
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| *[[Ceramic engineering]]
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| * [[Energetically modified cement]]
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| *[[Selective laser sintering]], a [[rapid prototyping]] technology.
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| *[[Spark plasma sintering]]
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| *[[Frit]]
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| *[[Yttria-stabilized zirconia]]
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| *High-temperature [[Superconductivity|superconductors]]
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| *[[Metal clay]]
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| *[[W. David Kingery]] - a pioneer of si§§§§ntering methods
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| For the geological aspect :
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| * [[Petrifying well]]
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| {{colend}}
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| ==References==
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| {{Reflist}}
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| ==Further reading==
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| *{{Cite journal
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| |last1 = Chiang|first1 = Yet-Ming
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| |last2 = Birnie|first2 = Dunbar P.
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| |last3 = Kingery|first3 = W. David
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| |title = Physical Ceramics: Principles for Ceramic Science and Engineering
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| |publisher = John Wiley & Sons
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| |date = May 1996
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| |location =
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| |url =
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| |doi =
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| |id =
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| |isbn = 0-471-59873-9}}
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| *{{cite book
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| |last = Green
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| |first = D.J.
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| |coauthors = Hannink, R.; Swain, M.V.
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| |year = 1989
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| |title = Transformation Toughening of Ceramics
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| |location = Boca Raton
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| |publisher = CRC Press
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| |isbn = 0-8493-6594-5
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| }}
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| *{{cite book
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| |last = German
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| |first = R.M.
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| |year = 1996
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| |title = Sintering Theory and Practice
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| |publisher = John Wiley & Sons, Inc
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| |isbn = 0-471-05786-X
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| }}
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| *{{Cite journal
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| |last1 = Kang|first1 = Suk-Joong L.
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| |title = Sintering
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| |publisher = [[Elsevier]], Butterworth Heinemann
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| |year = 2005
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| |edition = 1st
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| |location = Oxford
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| |url =
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| |doi =
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| |id =
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| |isbn = 0-7506-6385-5}}
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| ==External links==
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| {{Wiktionary}}
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| *[http://www.roentzsch.org/SintPP/index.html Particle-Particle-Sintering – a 3D lattice kinetic Monte Carlo simulation]
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| *[http://www.roentzsch.org/SintSP/index.html Sphere-Plate-Sintering – a 3D lattice kinetic Monte Carlo simulation]
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| *[http://www.thickfilmtech.com Thick Film Technologies- A Manufacturer of Ceramic Sintering Separator Sheets]
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| [[Category:Industrial processes]]
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| [[Category:Metalworking]]
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| [[Category:Plastics industry]]
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| [[Category:Geology]]
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