Sintering

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Sintering is the process of compacting and forming solid material mass by heat or pressure without melting it up to the liquidation point.

Sintering occurs naturally in mineral deposits or as a manufacturing process used with metals, ceramics, plastics, and other materials. The atoms in the material diffuse across the boundaries of the particles, joining the particles together and creating a solid piece. Since the sintering temperature does not have to reach the melting point of the material, sintering is often chosen as the process of forming materials with very high melting points such as tungsten and molybdenum. The study of sintering in a process associated with a metallurgical powder is known as powder metallurgy. Examples of sintering can be observed when ice cubes in a glass of water are attached to each other, which is driven by the temperature difference between water and ice. Examples of pressure-induced sintering are the compaction of snow to glaciers, or the formation of hard snowballs by pressing loose snow together.

The word "sinter" comes from the Middle High German sinter , the English "cinder".

Video Sintering

Sintering umum

Sintering is effective when the process reduces porosity and improves properties such as strength, electrical conductivity, translucency and thermal conductivity; However, in other cases, it may be useful to increase its strength but maintain its gas absorption constant as in the filter or catalyst. During the combustion process, the diffusion of atoms encourages the removal of powdered surfaces in various stages, from the formation of the neck between the powders to the final elimination of the small pores at the end of the process.

The driving force for densification is the change in free energy from decreasing surface area and lowering the surface free energy by replacing solid vapor interface. It forms a new solid-solid interface but is lower in energy with a total fall in the free energy that occurs. On a microscopic scale, material transfer is affected by changes in pressure and the difference in free energy at the curved surface. If the particle size is small (and the curvature is high), this effect becomes very large. The energy changes are much higher when the radius of curvature is less than a few micrometers, which is one of the main reasons why many ceramic technologies are based on the use of fine particle materials.

For properties such as strength and conductivity, the bonding area in relation to particle size is the deciding factor. The controllable variables for each given material are the temperature and initial grain size, since the vapor pressure depends on the temperature. Through time, particle radii and vapor pressure are proportional to (p ₀ ) ^2/3 and to (p ₀ ) ^1/3 , respectively.

The resource for a solid-state process is the change of free or chemical potential energy between the neck and the surface of the particle. This energy creates material transfer in the fastest possible way; if transfer is made from particle volume or grain boundary between particles, particle reduction and pore destruction will occur. Pore ​​removal occurs faster for experiments with many pores of uniform size and higher porosity where the diffusion distance of the boundaries is smaller. For the last part of the process, the limits and diffusion of the lattice of the boundary become important.

Temperature control is essential for sintering, since the diffusion of the grains and the diffusion of the volume depend on the temperature, size and distribution of the material particles, material composition, and often the sintering environment to be controlled.

Maps Sintering

Ceramic Sintering

Sintering is part of the combustion process used in the manufacture of pottery and other ceramic objects. These objects are made of substances such as glass, alumina, zirconia, silica, magnesia, lime, beryllium oxide, and iron oxide. Some ceramic raw materials have a lower affinity for water and a lower plasticity index of clay, requiring organic additives in the pre-sintering stage. The general procedure of making ceramic objects through sintering powders include:

• Mix water, binder, deflocculant, and un-corroded ceramic powder to form a slurry;
• Spray-drying slurry;
• Put the spray dried powder into the mold and press to form a green body (unregistered ceramic items);
• Heating the green body at low temperatures to burn the binder;
• Sintered at high temperatures to unite ceramic particles.

All the characteristic temperatures associated with phase transformations, glass transitions, and melting points, occur during the sintering cycle of a particular ceramic formulation (ie, tail and frit) can be easily obtained by observing the expansion temperature curves during the thermal analysis of the optical dilatometer. In fact, sintering is concerned with the shrinkage of exceptional material because the glass phase flows after it reaches the transition temperature, and begins to consolidate the powder structure and greatly reduces the porosity of the material.

Sintering is done at high temperatures. In addition, a second and/or third external force (such as pressure, electric current) may be used. The second commonly used external force is pressure. Thus, sintering done only using temperatures is generally called "sintering without pressure". Pressure without pressure is possible with graded metal-ceramic composites, with the aid of sintering nanoparticles and bulk printing technology. The variant used for the 3D form is called hot isostatic pressure.

To allow efficient buildup of products in the furnace during sintering and prevent components from sticking together, many manufacturers separate the warehouse using ceramic powder separator sheets. These sheets are available in various materials such as alumina, zirconia and magnesia. They are also categorized by fine particle size, medium and coarse. By matching materials and particle size to sintered warehouses, surface damage and contamination can be reduced while maximizing furnace loading.

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Sintering metal powder

Most, if not all, metals can be sintered. This applies especially to pure metals produced in a vacuum that does not undergo surface contamination. Sintering under atmospheric pressure requires the use of protective gas, often enough endothermic gases. Sintering, with subsequent reworking, can produce a large number of material properties. Changes in density, alloys, or heat treatment may alter the physical characteristics of various products. For example, Young's modulus E _n of sintered iron powder remains somewhat insensitive to the time of sintering, alloying, or particle size in the original powder for lower sintering temperatures, on the density of the final product:

${\ displaystyle E_ {n}/E = (D/d) ^ {3.4}}  ÂÂ$

where D is density, E is Young modulus and d is the maximum iron density.

Sintering is static when metal powders under certain external conditions can show a mix, but return to normal behavior when the condition is removed. In most cases, the grain-collecting density increases as the material streams into the cavity, causing a decrease in overall volume. The mass movement that occurs during sintering consists of a reduction in total porosity by re-packing, followed by material transport due to evaporation and condensation of diffusion. At the last stage, metal atoms move along the crystal boundary to the walls of the internal pores, distributing the mass from the internal part of the object and refining the pore wall. Surface tension is the driving force for this movement.

A special sintering form (which is still considered part of a powder metallurgy) is a liquid-state sintering where at least one but not all elements are in liquid state. Liquid-conditioner sintering is required to make carbide cement or tungsten carbide.

The bronze sinter is particularly often used as a bearing material, since its porosity allows the lubricant to flow through it or to stay captured therein. Sintered copper can be used as a wicking structure on certain types of hot pipe construction, in which porosity allows a liquid to move through a porous material through capillary action. For materials with high melting points such as molybdenum, tungsten, rhenium, tantalum, osmium and carbon, sintering is one of several viable manufacturing processes. In this case, very low porosity is desirable and often achievable.

Sintered metal powders are used to create shifting gun shells called bullet breaking, as used by military and SWAT teams to quickly force entry into locked rooms. The gun rifle is designed to smash the latch, lock and hinge without risking a life by bouncing or flying at lethal speed through the door. They work by destroying the object they hit and then spreading to a relatively harmless powder.

Sintered bronze and stainless steel are used as filter materials in applications that require high temperature resistance while retaining the ability to regenerate filter elements. For example, sintered stainless steel elements are used to filter vapors in food and pharmaceutical, and bronze applications that are sintered in aircraft hydraulic systems.

Sintering powder containing precious metal like silver and gold is used to make small jewelry.

Profit

The special advantages of powder technology include:

1. High degree of purity and uniformity in the starting materials
2. Preservation of purity, as the next simpler fabrication process (fewer steps) allows
3. Stabilize the details of repeated operations, by controlling the grain size during the input stage
4. The absence of binding contacts between separate powder particles - or "inclusions" (called stringering) - as is often the case in the melting process
5. No deformation is needed to produce directed grain elongation
6. The ability to produce material from a controlled and uniform porosity.
7. The ability to produce almost a net-shaped object.
8. The ability to produce materials that can not be produced by other technologies.
9. Ability to create high-strength materials such as turbine blades.
10. After sintering mechanical strength for handling becomes higher.

The literature contains many references concerning sintering of different materials to produce solid/solid-phase compounds or mixtures of solids/melts at the processing stage. Almost all substances can be obtained in powder form, either through chemical, mechanical or physical processes, so basically all materials can be obtained by sintering. When the pure element is sintered, the remaining powder is still pure, so it can be recycled.

Losses

The specific disadvantages of powder technology include:

1. 100% sintered (iron ore) can not be filled in a blast furnace.
2. With sintering, you can not create a uniform size.
3. The micro and nano structures produced before sintering are often destroyed.

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Plastic sintering

Plastic materials are formed by sintering for applications requiring certain porosity materials. A porous plastic component used in filtration and for controlling the flow of fluid and gas. Sintered plastic is used in applications requiring caustic fluid separation processes such as nibs in whiteboard markers, inhaler filters, and vents for caps and liners on packaging materials. Sterilized ultra high molecular weight polyethylene materials are used as a base for skiing and snowboarding. The porous texture allows the wax to be retained in the structure of the base material, thus providing a more durable wax coating.

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Liquid phase synthesis

For materials that are difficult to sinter, a process called liquid phase sintering is commonly used. The materials for general liquid phase sintering are Si ₃ N ₄ , WC, SiC, and more. Sintering liquid phase is the process of adding additives to the powder that will melt before the matrix phase. The liquid phase sintering process has three stages:

• Rearrangements - When liquid melts the capillary it will draw fluid into the pores and also cause the grains to be rearranged into a more advantageous package arrangement.
• Solution-Precipitation - In areas where high capillary pressure (adjacent particles) the atoms will prefer to enter the solution and then settle in areas with lower chemical potential where the particles are not close or touch. This is called " horizontal contact ". This overloads the system in a manner similar to the grain boundary diffusion in solid state sintering. Ostwald ripening will also occur where smaller particles will enter into a special solution and settle on larger particles leading to densification.
• Final Densification - densification of solid skeletal tissue, movement of liquids from areas packed efficiently into the pores.

For the sintering liquid phase to be practical, the main phase must be at least slightly soluble in the liquid phase and the additive should melt before the main sintering of the solid particulate tissue occurs, otherwise a grain rearrangement will not occur. Liquid phase sintering was successfully applied to enhance the grain growth of the thin semiconductor layer of the nanoparticle precursor film.

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Electrical assisted sintering

These techniques use electric current to drive or increase sintering. The English engineer A. G. Bloxam enrolled in 1906 the first patent on sintering powders using direct current in a vacuum. The main object of the invention is the industrial scale production of filaments for incandescent lamps by soliding tungsten or molybdenum particles. The current used is very effective in reducing the surface oxide which increases the emissivity of the filaments.

In 1913, Weintraub and Rush patented a modified sintering method that combines electrical current with pressure. The benefits of this method are evident for sintering refractory metals as well as carbide powders or conductive nitrides. The first carbon-boron or silicon-carbon powder is placed in an electric insulating tube and compressed by two rods that also function as electrodes for current. The sintering temperature estimate is 2000 Â ° C.

In the United States, sintering was first patented by Duval d'Adrian in 1922. The three-step process aims to produce heat-resistant blocks of oxide materials such as zirconia, toria or tantalia. The steps are: (i) print the powder; (ii) rub it around 2500 ° C to make it perform; (iii) apply current pressure sintering as in Weintraub and Rush methods.

Sintering using an arc produced by the release of capacitance to remove the oxide prior to direct current heating, patented by G. F. Taylor in 1932. This sintering method derived using pulsation or alternating current, which is finally superimposed into direct current. These techniques have been developed over several decades and are summarized in more than 640 patents.

Of these the most famous technologies are sintering resistance (also called hot press) and sintering spark plasma, while electro sintering forging is the latest progress in this field.

Spark plasma sintering

In plasma spark sintering (SPS), external pressure and electric fields are applied simultaneously to increase metallic/ceramic compact powder densification. However, once commercialization is determined there is no plasma, so the exact name is sintering sparks such as those created by Lenel. Electrical field densification supplements are driven sintering with hot pressing shapes, to allow for lower temperatures and shorter amounts of time than typical sintering. For several years, it was speculated that the presence of sparks or plasma between the particles could help sintering; However, Hulbert and colleagues systematically prove that the electrical parameters used during spark plasma sintering make it (very) impossible. Given this, the name "spark plasma sintering" has been considered obsolete. Terms such as "Field Assisted Sintering Technique" (CEPAT), "Electric Field Assisted Sintering" (EFAS), and Direct Current Sintering (DCS) have been implemented by the sintering community. Using a DC pulse as an electric current, a plasma spark, a spark impact pressure, a joule heating, and electric field diffusion effects will be created. By modifying the die graphite design and assembly, it is shown to create a Pressureless sintering condition in splashing the plasma sintering facility. This modified die design setting is reported to synergize the advantages of sintering without conventional pressure and spark plasma sintering techniques.

Tuning of electro sinter

Electro-sintering electrodes are sintered assisted electric current technology (ECAS) derived from sintering capacitor discharges. It is used for the production of diamond metal matrix composites and under evaluation for the production of hard metals, nitinol and metals and other intermetallic. It is characterized by a very low sintering time which allows the machine to sinter at the same speed as compressive press.

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Sintered without pressure

Non-needle pressering is the sintering of the compact powder (sometimes at very high temperatures, depending on the powder) without the applied pressure. This avoids density variation in the final component, which occurs with more traditional heat suppression methods.

Compact powder (if ceramic) can be made by slip casting, injection molding, and cold isostatic presses. After pre-sintering, the final green compact can be worked up to the final shape before sintering.

Three different heating schedules can be performed with unstressed sintering: constant heating rate (CRH), rate-controlled sintering (RCS), and two-step sintering (TSS). The microstructure and size of the ceramic grains may vary depending on the materials and methods used.

Constant heating rate (CRH), also known as temperature controlled sintering, consists of a green compact heating at a constant rate up to sintering temperature. Experiments with zirconia have been performed to optimize the sintering temperature and sintering rate for the CRH method. The results show that the grain size is identical when the sample is sintered to the same density, proving that the grain size is a function of the density of the specimen rather than the CRH temperature mode.

In a rate-controlled sintering (RCS), the densification rate in the open porosity phase is lower than in the CRH method. By definition, relative density ,? _rel , in the open-porosity phase is lower than 90%. Although this should prevent the separation of pores from the grain boundaries, it has been proven statistically that RCS does not result in smaller grain size than CRH for alumina, zirconia, and cheerful samples.

Two-stage sintering (TSS) uses two different sintering temperatures. The first sintering temperature should ensure a relatively higher density of 75% of the theoretical sample density. This will remove the supercritical pores from the body. The sample will then be cooled and retained at a second sintering temperature until densification is complete. Cubic zirconia and cubic strontium titanate were significantly enhanced by TSS compared with CRH. However, changes in grain size on other ceramic materials, such as tetragonal zirconia and hexagonal alumina, are not statistically significant.

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Microwave sintering

In microwave sintering, heat is sometimes generated internally inside the material, rather than through the heat transfer of surface radiation from an external heat source. Some materials fail in pairs and others show blurry behavior, so it's limited in usability. The benefits of microwave sintering are faster heating for small loads, which means less time is needed to achieve sintering temperatures, less heating energy is required and improvements to product properties.

A microwave sintering failure is that generally only one synthetic is compact at a time, so the overall productivity turns out to be poor except for situations involving one type of sintering, as for the artist. Because microwaves can only penetrate short distances in materials with high conductivity and high permeability, microwave irradiation requires samples to be sent in a powder with particle size around the depth of microwave penetration in a particular material. Sintering and side reactions proceed several times faster during microwave sintering at the same temperature, resulting in different properties for sintered products.

This technique is recognized to be quite effective in maintaining fine grain/nano-sized grains in sintered biokeramics. Magnesium phosphate and calcium phosphate are examples that have been processed through microwave sintering techniques

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Densification, vitrification and grain growth

Sintering in practice is the control of both densification and grain growth. Densification is the action of reducing porosity in the sample making it denser. Grain growth is a process of grain boundary movement and Ostwald ripening to increase average grain size. Many properties (mechanical strength, power solving power, etc.) Benefit from relatively high density and small grain size. Therefore, being able to control this property during processing has high technical importance. Because densification of powders requires high temperatures, grain growth naturally occurs during sintering. The reduction of this process is key to many ceramic engineering.

For densification occurring at rapid speeds it is important to have (1) large amounts of liquid phase in size, (2) complete solubility near solids in liquids, and (3) wetting solids by liquids. The forces behind densification are derived from the liquid phase capillary pressures located between fine solid particles. When the liquid phase dries solid particles, each space between the particles becomes capillaries where large capillary pressures are developed. For particle size submicrometre, capillaries with diameters in the range of 0.1 to 1 micrometer develop a pressure in the range of 175 pounds per square inch (1,210 kPa) to 1,750 pounds per square inch (12,100 kPa) for silicate fluid and in the range of 975 pounds per inch square (6,720 kpa) to 9,750 pounds per square inch (67,200 kPa) for metals such as liquid cobalt.

Densification requires constant capillary pressure in which only solution-settling material transfer will not produce densification. For further densification, additional particle movement while particles grew growth and grain shape changes occurred. Depreciation will occur when the liquid slips between the particles and increases the pressure at the contact points causing the material to move away from the contact area which forces the center of the particles to close together.

Sintering of a liquid-phase material involves a fine-grained solid phase to create the required capillary pressure proportional to its diameter and the fluid concentration must also create the required capillary pressure within range, otherwise the process stops. The level of vitrification depends on pore size, viscosity and the amount of liquid phase leading to the viscosity of the overall composition, and the surface tension. Temperature dependence for densification controls the process because at higher viscosity temperatures decreases and increases the liquid content. Therefore, when the composition and processing changes are made, it will affect the vitrification process.

Sintering mechanism

Sintering occurs with the diffusion of atoms through the microstructure. This diffusion is caused by a chemical potential gradient - moving atoms from a higher area of ​​chemical potential to an area with a lower chemical potential. The different paths the atoms take to move from one place to another is the sintering mechanism. The six common mechanisms are:

• Diffusion surface - Diffusion of atoms along the surface of the particle
• Steam transport - Evaporating atoms that condense on different surfaces
• Lattice diffusion from surface - atom from diffuse surface through lattice
• The lattice diffusion from the grain boundary - the atoms of the grain boundary diffuse through the lattice
• Grain boundary diffusion - atoms spreading along grain boundaries
• Plastic deformation - dislocation movement causes material flow

It should also be distinguished between densification and non-compacting mechanisms. 1-3 above are not compacted - they take the atoms from the surface and rearrange them to the surface or other parts of the same surface. This mechanism only resets the material in the porosity and does not cause the pores to shrink. Mechanism 4-6 is the compaction mechanism - atoms are removed from most to the pore surface thereby eliminating porosity and increasing sample density.

Wheat Growth

The grain boundary (GB) is the transition area or interface between adjacent crystals (or grains) of the same lattice and lattice composition, not to be confused with phase boundaries. The adjacent granules do not have the same orientation of the lattice thus giving the atoms in GB shifted position relative to the lattice in the crystal. Because of the altered atomic positions in GB, they have a higher energy state when compared to atoms in the granular crystal lattice. It is this imperfection that makes it possible to selectively etch the GB when one wants the micro structure to be seen. Struggling to minimize its energy leads to the structuring of microstructures to achieve a metastable state within the specimen. This involves minimizing the GB area and changing the topology structure to minimize its energy. Growth of these grains can be normal or abnormal, normal grain growth is characterized by uniform growth and the size of all grains in the specimen. Abnormal grain growth is when some grains grow much larger than the remaining majority.

Energy/Grain boundary strain

Atom-atom dalam GB biasanya dalam keadaan energi yang lebih tinggi daripada yang setara dalam materi massal. Hal ini disebabkan ikatan mereka yang lebih membentang, yang menimbulkan ketegangan GB ${\ displaystyle \ sigma _ {GB}}  ÂÂ$ . Energi ekstra yang dimiliki atom disebut energi batas butir, ${\ displaystyle \ gamma _ {GB}}  ÂÂ$ . Biji-bijian akan ingin meminimalkan energi ekstra ini sehingga berusaha membuat batas butir lebih kecil dan perubahan ini membutuhkan energi.

"Or, in other words, force must be applied, in the grain boundary area and act along the line in the grain boundary area, to extend the grain boundary area to force force per unit length, ie voltage/voltage, along the line mentioned is? GB For this reason it will follow:

${\ displaystyle \ sigma _ {GB} dA {\ text {(selesai dikerjakan)}} = \ gamma _ {GB} dA {\ text {(perubahan energi)}} \, \!}  ÂÂ$

with dA as an increase in the grain boundary area per unit length along the line in the grain boundary area to be considered. "[pg 478]

GB strain can also be thought of as an attractive force between the atoms at the surface and the tension between these atoms is due to the fact that there is a greater inter-atomic distance between them on the surface than the bulk (ie the surface tension). As the surface area becomes larger, the bonds widen and GB tension increases. To cope with this increased tension there must be an atomic transport to the surface keeping a constant voltage of GB. The diffusion of these atoms causes a constant surface tension in the liquid. Then his argument,

${\ displaystyle \ sigma _ {GB} dA {\ text {(selesai dikerjakan)}} = \ gamma _ {GB} dA {\ text {(perubahan energi)}} \, \!}  ÂÂ$

apply. For solids, on the other hand, the diffusion of atoms to the surface may be insufficient and the surface tension may vary with increasing surface area. For a solid, one can gain expression for the free energy change of Gibbs, dG, on the GB area change, dA. dG given by

${\ displaystyle \ sigma _ {GB} dA {\ text {(selesai dikerjakan)}} = dG {\ text {(perubahan energi)}} = \ gamma _ {GB } dA Ad \ gamma _ {GB} \, \!}  ÂÂ$

which gift

${\ displaystyle \ sigma _ {GB} = \ gamma _ {GB} {\ frac {Ad \ gamma _ {GB}} {dA}} \, \!}  ÂÂ$

${\ displaystyle \ sigma _ {GB}}  ÂÂ$ biasanya dinyatakan dalam satuan ${\ displaystyle {\ frac {N} {m}}}  ÂÂ$ saat ${\ displaystyle \ gamma _ {GB}}  ÂÂ$ biasanya dinyatakan dalam satuan ${\ displaystyle {\ frac {J} {m ^ {2}}}}  ÂÂ$ ${\ displaystyle (J = Nm)}  ÂÂ$ karena mereka adalah properti fisik yang berbeda.

Ekuilibrium mekanis

In two-dimensional isotropic materials, the grain boundary voltage will be the same for the grain. This will provide a 120 ° angle at the GB intersection where three points meet. This will give the structure of a hexagonal pattern which is a metastable state (or mechanical balance) of a 2D specimen. The consequence of this is to keep trying as closely as possible with equilibrium. Grains with sides that are fewer than six will bend GB to try to keep the angle 120 Â ° between each other. This produces a curved boundary with curvature in that direction itself. A grain with six sides will, as mentioned, have a straight line while grains with more than six sides will have a curved border with its curvature away from itself. A grain with six boundaries (ie a hexagonal structure) is in a metastable state (ie local balance) in a 2D structure. In three dimensions the details of structures are similar but far more complex and the metastable structure for grains is non-regular 14-side polyhedra with multiple faces. In practice all grains are always unstable and thus always grow until they are prevented by the power of reply.

Grains try to minimize their energy, and the bending curve has a higher energy than a straight line. This means that the grain boundaries will migrate towards curvature. The consequence of this is that grains with less than 6 sides will decrease in size while grains with more than 6 sides will grow larger.

Grain growth occurs because the movement of an atom crosses the grain boundary. The convex surface has a higher chemical potential than the concave surface because the grain boundaries will move toward their center of curvature. Because smaller particles tend to have higher radius of curvature and this results in smaller grains losing atoms into larger and shrinking grains. This is a process called Ostwald ripening. Large grains grow at the expense of small grains. Grain growth in a simple model is found to follow:

${\ displaystyle G ^ {m} = G_ {0} ^ {m} Kt}  ÂÂ$

Here G is the final average grain size, G ₀ is the initial average grain size, is the time, m is the factor between 2 and 4, and K is a factor given by:

${\ displaystyle K = K_ {0} e ^ {\ frac {-Q} {RT}}}  ÂÂ$

Here Q is the molar activation energy, R is the ideal gas constant, T is the absolute temperature, and K ₀ are factors that depend on the material. In most materials the sintered grain size is the proportion to the inverse square root of fractional porosity, implying that the pores are the most effective retardant for grain growth during sintering.

Reduce grain growth

Dissolved ion

If the dopant is added to the material (eg: Nd in BaTiO ₃ ) impurity will tend to stick to the grain boundary. When the grain boundary tries to move (when the atoms jump from the convex surface to the hollow) the change of dopant concentration at the grain boundary will impose barriers on the boundary. The original concentration of solutes around the grain boundaries will be asymmetric in most cases. When the grain boundary tries to move the concentration on the opposite side of the movement it will have a higher concentration and therefore has a higher chemical potential. This increased chemical potential will act as a backforce to the original chemical potential gradient which is the reason for the grain boundary movement. A decrease in the net chemical potential decreases the grain boundary velocity and grain growth.

Fine second-phase particles

If the second phase particles insoluble in the matrix phase are added to the powder in the form of a much smoother powder than this will reduce the grain boundary movement. When the grain boundary tries to move through the diffusion diffusion of atoms from one grain to another the grains will be blocked by insoluble particles. It is therefore useful for particles to be at grain boundaries and they exert forces in opposite directions compared to grain boundary migrations. This effect is called the Zener effect after the man who predicted this drag style

${\ displaystyle F = \ pi r \ lambda \ sin (2 \ theta) \, \!}  ÂÂ$

where r is the radius of the particle and? the interfacial energy of the boundary if there are N particles per unit volume of the fraction of f

${\ displaystyle f = {\ frac {4} {3}} \ pi r ^ {3} N \, \!}  ÂÂ$

assuming they are randomly distributed. The unit area boundary will cut all the particles in volume 2r which is a 2Nr particle. So the number of n particles that cut one unit of grain boundary area is:

${\ displaystyle n = {\ frac {3f} {2 \ pi r ^ {2}}} \, \!}  ÂÂ$

Sekarang dengan asumsi bahwa biji-bijian hanya tumbuh karena pengaruh kelengkungan, kekuatan pendorong pertumbuhan adalah ${\ displaystyle {\ frac {2 \ lambda} {R}}}  ÂÂ$ di mana (untuk struktur butir homogen) R mendekati ke diameter rata-rata butir. Dengan ini diameter kritis yang harus dicapai sebelum biji-bijian berhenti tumbuh:

${\ displaystyle nF_ {max} = {\ frac {2 \ lambda} {D_ {crit}}} \, \!}  ÂÂ$

Ini dapat direduksi menjadi ${\ displaystyle D_ {crit} = {\ frac {4r} {3f}} \, \!}  ÂÂ$ sehingga diameter kritis butir tergantung dari ukuran dan fraksi volume partikel pada batas butir.

It has also been shown that small bubbles or cavities can act as inclusions

More complicated interactions that slow down grain boundary movement include the interaction of the surface energy of two grains and inclusions and are discussed in detail by C.S. Smith.

src: www.eurekalert.org

Natural sintering in geology

In geology, natural sintering occurs when the source of the spring brings precipitation of chemical or crust sediments, fo

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