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# User:Raleway

Materials Science tests knowledge of the properties and characteristics of metals, ceramics, polymers and composite materials, with a focus on material characterization techniques, intermolecular forces, and surface chemistry.

## Event Overview

### Rules Review

Each pair of competitors from a team will be allowed 5 front and back pages of cheat sheets. There will a lab section unless listed otherwise, and students must bring safety apparel themselves or be unable to do the lab due to safety concerns. Students will be tested on the field of Materials Science and topics are limited to those listed below, though the scope of each topic is nearly unlimited.

### Tips and Tricks

Materials Science covers a vast amount of knowledge, hence the 5 cheat sheets allowed for the event. The extent of each topic is nearly unlimited, such that teams will need to know each topic well without relying on cheat sheets. Graphs are especially important, but only so long as they are useful - too many basic graphs will take up valuable space. Also, cheat sheets can contain large tables of information that would otherwise be impossible to memorize, such as atomic packing for different elements and compounds, melting and boiling points, and more. Many teams have found an optimal layout of 0.5" margins, 3 columns, and Times New Roman font. The font size will depend largely on the amount of information contained, but teams should be cautious to still keep their cheat sheets readable. The best competitors will know their cheat sheets extraordinarily well, such that they can find small bits of information quickly. Less competitive teams will either rely on their cheat sheets for basic information or rely on the find function during practice and become lost in actual tests. Lastly, screen protectors are incredibly useful for protecting cheat sheets from any damage or spills in the lab section of the event.

## Physical Characteristics

### Metals

Mechanical properties: Metals are stiff, strong, ductile, malleable, resistant to fracture, good conductors of electricity and heat, and are lustrous. Many metals, such as iron, cobalt, and nickel, also have good magnetic properties.

Diamagnetism: Diamagnetism is present in all materials. An applied magnetic field induces another magnetic field in the opposite direction, providing a repulsive force. Diamagnetic materials could be considered non-magnetic, as diamagnetism is negligible compared to other, stronger forms of magnetism.

Paramagnetism: Paramagnetism exists due to unpaired electrons in some elements and compounds, which generate a magnetic dipole due to their spin. Paramagnets do not retain magnetization unless they are in the presence of an applied magnetic field.

Ferromagnetism: Ferromagnetism also exists due to unpaired electrons, but works in a different manner. Magnetic moments align themselves parallel to each other and to an applied magnetic field in order to maintain a lowered state. These magnetic moments align even in the absence of an applied magnetic field. Every ferromagnetic material has a Curie temperature, above which it loses any ferromagnetic properties.

### Ceramics

Ceramics are relatively stiff and strong, hard, brittle, susceptible to fracture, insulators of heat and electricity, and are very resistant to high temperatures and harsh conditions. Some ceramics (glass ceramics) can be transparent or translucent, while others (clay ceramics) are opaque. Some oxide ceramics also exhibit magnetic behavior.

### Polymers

Mechanical properties: Polymers are low density, but not as stiff or strong as metals or ceramics. They are extremely ductile and pliable, chemically inert in a multitude of environments, nonmagnetic (diamagnetic), and usually are not conductive (polymers with a backbone of alternative double and single bonded carbon can conduct electricity through the movements of free electron pairs). Polymers soften or decompose at modest temperatures.

Degree of polymerization: The degree of polymerization, or DP, is defined as the number of monomer units in a macromolecule or polymer molecule. A homopolymer contains only one type of monomer unit, and the number-average degree of polymerization is given by $M_n/M_0$ where M(n) is the number-average molecular weight and M(0) is the molecular weight of the monomer unit.

### Composites

The properties of composites are entirely dependent on their constituent parts and are usually enhanced by fiber lengths. Strength is dependent on fiber length, where smaller fibers are larger. Ductility, meanwhile, can be lowered by using matrices instead of fibers. Ceramic composites are resistant to degradation, but are brittle; metal matrices are used at high temperatures. Construction also matters. Carbon-carbon composites, which reinforce graphite with fibers, have high tensile strength, resistance to creep, fracture toughness, strength, and thermal conductivity; laminar composites, meanwhile, have high strength in the 2D plane only; sandwich panel cores have low elasticity, light weight, and high shear strength, while their sheets resist tension and compression.

## Manufacturing Techniques and Natural Occurrences

### Metals

#### Natural Occurrences

Native State:

Metals are said to be in their native state if they are found in their elementary form. Generally, less active metals like gold, silver, copper, and platinum can be found in their native state.

Combined State

Metals are said to be in their combined state if they are found in nature in the form of compounds. Generally, reactive metals occur in their combined state. Combined state metals are found in the crust of the earth as oxides, carbonates, sulfides, silicates, phosphates, etc.; these are known as minerals. Minerals extracted from the crust of the earth are not pure, but instead associated with many earthly, rocky, and siliceous impurities. These impurities associated with minerals are collectively known as the gangue or matrix, which is commercially valueless. Not all minerals can be used, depending on economic factors or the extraction process. Minerals from which metals can be conveniently and economically extracted are known as ore. For example, aluminum can be found naturally in two minerals, both bauxite and China clay. However, extraction of aluminum is much cheaper and easier from bauxite than from China clay, so bauxite is considered an ore of aluminum while China clay is not. Similarly, copper can be found as copper glance, cuprite, malachite, and copper pyrite, but only copper pyrite is considered to be an ore of copper. All ores are minerals, but not all minerals are considered to be ores.

#### Mining

Metals are often extracted from Earth by means of mining ores that are rich sources of requisite elements, such as bauxite. Ore is located by prospecting techniques, followed by exploration and examination of deposits. Mineral sources are generally divided into surface mines, which are mined by excavation using heavy equipment, and subsurface mines. Once Ore is mined, metals must be extracted, usually by chemical or electrolytic reduction. Pyrometallurgy uses high temperatures to convert ore into raw metals, while hydrometallurgy employs aqueous chemistry for the same purpose.methods used depend on metal and their contaminants. When a metal ore is an ionic compound of that metal and a nonmetal, the ore must usually be smelted — heated with a reducing agent — to extract the pure metal. Many common metals, such as iron, are smelted using carbon as a reducing agent. Some metals, such as aluminum and sodium, have no commercially practical reducing agent and are extracted using electrolysis instead. Sulfide ores are not reduced directly to metal but are roasted in air to convert them to oxides.

#### Forming Techniques

Hot Working:

Hot working is when a metal is deformed at a temperature higher than its temp of recrystallization Forging: Forging is mechanically working or deforming a single piece of a normally hot metal; this may be accomplished by the application of successive blows or by continuous squeezing. Forgings are classified as either closed or open die. For the closed die, a force is brought to bear on two or more die halves having the finished shape such that the metal is deformed in the cavity between them. For the open die, two dies having simple geometric shapes (e.g., parallel flat, semicircular) are employed, normally on large workpieces. Forged articles have outstanding grain structures and the best combination of mechanical properties. Wrenches, and automotive crankshafts and piston connecting rods are typical articles formed using this technique.

Rolling:

Rolling, the most widely used deformation process, consists of passing a piece of metal between two rolls; a reduction in thickness results from compressive stresses exerted by the rolls. Cold rolling may be used in the production of sheet, strip, and foil with a high-quality surface finish. Circular shapes, as well as I-beams and railroad rails, are fabricated using grooved rolls. Extrusion: For extrusion, a bar of metal is forced through a die orifice by a compressive force that is applied to a ram; the extruded piece that emerges has the desired shape and a reduced cross-sectional area. Extrusion products include rods and tubing that have rather complicated cross-sectional geometries; seamless tubing may also be extruded.

Drawing:

Drawing is the pulling of a metal piece through a die having a tapered bore by means of a tensile force that is applied on the exit side. A reduction in cross section results, with a corresponding increase in length. The total drawing operation may consist of a number of dies in a series sequence. Rod, wire, and tubing products are commonly fabricated in this way.

#### Casting Techniques

Casting is when a heated metal is poured into a mold in order to achieve a desired shape.

Sand Casting:

Sand Casting With sand casting, probably the most common method, ordinary sand is used as the mold material. A two-piece mold is formed by packing sand around a pattern that has the shape of the intended casting. Furthermore, a gating system is usually incorporated into the mold to expedite the flow of molten metal into the cavity and to minimize internal casting defects. Sand-cast parts include automotive cylinder blocks, fire hydrants, and large pipe fittings.

Die Casting:

In die casting, the liquid metal is forced into a mold under pressure and at a relatively high velocity and allowed to solidify with the pressure maintained. A two piece permanent steel mold or die is employed; when clamped together, the two pieces form the desired shape. When complete solidification has been achieved, the die pieces are opened and the cast piece is ejected. Rapid casting rates are possible, making this an inexpensive method; furthermore, a single set of dies may be used for thousands of castings. However, this technique lends itself only to relatively small pieces and to alloys of zinc, aluminum, and magnesium, which have low melting temperatures.

Investment Casting:

For investment (sometimes called lost wax) casting, the pattern is made from a wax or plastic that has a low melting temperature. Around the pattern is poured a fluid slurry, which sets up to form a solid mold or investment; plaster of Paris is usually used. The mold is then heated, such that the pattern melts and is burned out, leaving behind a mold cavity having the desired shape.This technique is employed when high dimensional accuracy, reproduction of fine detail, and an excellent finish are required—for example, in jewelry and dental crowns and inlays. Also, blades for gas turbines and jet engine impellers are investment cast.

Lost Foam Casting:

A variation of investment casting is lost foam (or expendable pattern) casting. Here the expendable pattern is a foam that can be formed by compressing polystyrene beads into the desired shape and then bonding them together by heating. Alternatively, pattern shapes can be cut from sheets and assembled with glue. Sand is then packed around the pattern to form the mold. As the molten metal is poured into the mold, it replaces the pattern which vaporizes. The compacted sand remains in place, and, upon solidification, the metal assumes the shape of the mold. With lost foam casting, complex geometries and tight tolerances are possible. Furthermore, in comparison to sand casting, the lost foam is a simpler, quicker, and less expensive process, and there are fewer environmental wastes. Metal alloys that most commonly use this technique are cast irons and aluminum alloys; furthermore, applications include automobile engine blocks, cylinder heads, crankshafts, marine engine blocks, and electric motor frames.

Continuous Casting:

At the conclusion of extraction processes, many molten metals are solidified by casting into large ingot molds.The ingots are normally subjected to a primary hot-rolling operation, the product of which is a flat sheet or slab; these are more convenient shapes as starting points for subsequent secondary metal-forming operations (i.e., forging, extrusion, drawing). These casting and rolling steps may be combined by a continuous casting (sometimes also termed “strand casting”) process. Using this technique, the refined and molten metal is cast directly into a continuous strand that may have either a rectangular or circular cross section; solidification occurs in a water-cooled die having the desired cross-sectional geometry. The chemical composition and mechanical properties are more uniform throughout the cross sections for continuous castings than for ingot-cast products. Furthermore, continuous casting is highly automated and more efficient.

#### Miscellaneous Techniques

Power Metallurgy Yet another fabrication technique involves the compaction of powdered metal, followed by a heat treatment to produce a more dense piece. The process is appropriately called powder metallurgy, frequently designated as P/M. Powder metallurgy makes it possible to produce a virtually nonporous piece having properties almost equivalent to the fully dense parent material. Diffusional processes during the heat treatment are central to the development of these properties. This method is especially suitable for metals having low ductilities since only small plastic deformation of the powder particles need to occur. Metals having high melting temperatures are difficult to melt and cast, and fabrication is expedited using P/M.

### Ceramics

#### Simple Ceramics

Traditional ceramics are made from natural materials such as clay that have been hardened by heating at high temperatures (driving out water and allowing strong chemical bonds to form between flakes of clay). When artists make ceramic works of art, they first mold clay, often mixed with other raw materials, into the desired shape. Special ovens called kilns are used to "fire" (heat)shaped object until it hardens. Clay consists of a large number of very tiny flat plates, stacked together but separated by thin layers of water.water allows plates to cling together, but also acts as a lubricant, allowing plates to slide past one another. As a result, clay is easily molded into shapes. High temperatures drive out water and allow bonds to form between plates, holding them in place and promoting the formation of a hard solid. Binders such as bone ash are sometimes added to clay to promote strong bond formation, which makes ceramic resistant to breakage.common clay used to make flower pots and roof tiles is usually red-orange because of the presence of iron oxides. Porcelain is a hard, tough ceramic that is less brittle than ceramics that preceded it. Its strength allows it to be fashioned into beautiful vessels with walls so thin they can even be translucent. It is made from kaolin mixed with china stone, and the mixture is heated to a very high temperature (1,300°C, or 2,372°F). Bone China has a composition similar to that of porcelain, but at least 50 percent of the material is finely powdered bone ash. Like porcelain, bone china is strong and can be formed into dishes with very thin, translucent walls. Stoneware is a dense, hard, gray or tan ceramic that is less expensive than bone china and porcelain, but it is not as strong. As a result, stoneware dishes are usually thicker and heavier than bone china or porcelain dishes.

Preparation of an advanced ceramic material usually begins with a finely divided powder that is mixed with an organic binder to help powder consolidate so that it can be molded into the desired shape. Before it is fired, the ceramic body is called "green." green body is first heated to a low temperature in order to decompose or oxidize binder. It is then heated to a high temperature until it is "sintered," or hardened, into a dense, strong ceramic. At this time, individual particles of original powder fuse together as chemical bonds form between them. During sintering ceramic may shrink by as much as 10 to 40 percent. Because shrinkage is not uniform, additional machining of ceramic may be required in order to obtain a precise shape. Sol-gel technology allows better mixing of ceramic components at the molecular level and hence yields more homogeneous ceramics because ions are mixed while in solution. In Sol-gel process, a solution of an organometallic compound is hydrolyzed to produce a "sol," a colloidal suspension of a solid in a liquid. Typically Solution is a metal alkoxide such as tetraethoxysilane in an alcohol solvent.sol forms when individual formula units polymerize (link together to form chains and networks).sol can then be spread into a thin film, precipitated into tiny uniform spheres called microspheres, or further processed to form a gel inside a mold that will yield a final ceramic object in the desired shape.many cross-links between formula units result in a ceramic that is less brittle than typical ceramics. Although Sol-gel process is very expensive, it has many advantages, including low-temperature requirements; Porous ceramics are made by the sol-gel process. These ceramics have sponge-like structures, with much more like lacunae, or openings, that can make up for 25 to 70 percent of volume.pore size can be large, or as small as 50 nanometers (2 × 10 −6 inches) in diameter. Because of a large number of pores, porous ceramics have enormous surface areas (up to 500 square meters, or 5,382 square feet, per gram of ceramic), and so can make excellent catalysts. For example, zirconium oxide is a ceramic oxygen sensor that monitors air-to-fuel ratio exhaust systems of automobiles. Aerogels are solid foams prepared by removing liquid from gel during a sol-gel process at high temperatures and low pressures. Because aerogels are good insulators, have very low densities, and do not melt at high temperatures

### Polymers

#### Addition Polymerization (Chain Reaction Polymerization)

A process by which monomer units are attached one at a time in chainlike fashion to form a linear macromolecule. The composition of the resultant product molecule is an exact multiple for that of the original reactant monomer. Three distinct stages—initiation, propagation, and termination—are involved in addition polymerization. During the initiation step, an active center capable of propagation is formed by a reaction between an initiator (or catalyst) species and the monomer unit.Propagation involves the linear growth of the polymer chain by the sequential addition of monomer units to this active growing chain molecule.Chain growth is relatively rapid; the period required to grow a molecule consisting of, say, 1000 repeat units is on the order of to s. Propagation may end or terminate in different ways. First, the active ends of two propagating chains may link together to form one molecule.The other termination possibility involves two growing molecules that react to form two “dead chains”

#### Condensation Polymerization (Step Reaction Polymerization)

The formation of polymers by stepwise intermolecular chemical reactions that may involve more than one monomer species. There is usually a small molecular weight by-product such as water that is eliminated (or condensed). No reactant species has the chemical formula of the repeat unit, and the intermolecular reaction occurs every time a repeat unit is formed.This stepwise process is successively repeated, producing a linear molecule. The chemistry of the specific reaction is not important but the condensation polymerization mechanism is. Furthermore, reaction times for condensation are generally longer than for addition polymerization.

##### Fillers

Filler materials are most often added to polymers to improve tensile and compressive strengths, abrasion resistance, toughness, dimensional and thermal stability, and other properties. Materials used as particulate fillers include wood flour (finely powdered sawdust), silica flour and sand, glass, clay, talc, limestone, and even some synthetic polymers.

##### Plasticizers

The flexibility, ductility, and toughness of polymers may be improved with the aid of additives called plasticizers. Their presence also produces reductions in hardness and stiffness. Plasticizers are generally liquids having low vapor pressures and low molecular weights. The small plasticizer molecules occupy positions between the large polymer chains, effectively increasing the interchain distance with a reduction in the secondary intermolecular bonding.

##### Stablilizers

The flexibility, ductility, and toughness of polymers may be improved with the aid of additives called plasticizers. Their presence also produces reductions in hardness and stiffness. Plasticizers are generally liquids having low vapor pressures and low molecular weights. The small plasticizer molecules occupy positions between the large polymer chains, effectively increasing the interchain distance with a reduction in the secondary intermolecular bonding.

### Composites

Manufacturing a fibre-reinforced composite involves several steps in which filler (fiber) is produced and then if required, aligned prior to the introduction of the matrix. Fibers produced from polymers, glass, and metals can be produced from the molten state by drawing them. Most carbon fibers are first drawn from a polymer, for example, poly (propenonitrile) (polyacrylonitrile), which is then oxidized, followed by pyrolysis. If Fibres are unaligned (random orientation) with each other, filler and matrix can be blended together as powders or slurries, shaped or molded, and matrix hardened and bonded to filler by heat or by chemical reaction. shaping may be accomplished by injection molding or casting of the composite. If required, additional machining is done before any further treatment to harden composite. The production of aligned fiber (Figure 1) composites is more complicated. fibers may be used as monofilaments, or they may be twisted into yarns of up to 10 000 filaments. yarns are then woven or knitted into two or three-dimensional fabrics and can be then formed into tapes by weaving or braiding. Filaments can also be processed into non-woven mats of fibers, randomly orientated in two dimensions.mats, tapes and fabrics may be impregnated with a matrix material (or materials from which matrix is made) before final assembly and processing, and are then referred to as a prepreg (pre-impregnated). Thus, there is no need to handle individual chemicals. It is simply rolled out and used as a laminate. Curing is accomplished by heating.fabrics and mats are placed in molds, sometimes by hand, and impregnated with the matrix material and processed. They can be compressed mechanically or by pressure or vacuum forming techniques. Filaments or tapes can also be wound, passing through a bath of the matrix before being processed into a solid shape. A simple example of a prepreg is bandage that is used to set broken limbs (Unit 67). the bandage is made of a polyester and it is impregnated with a linear polyurethane, matrix, bandage, or prepreg, is flexible and is wound around broken limb. On soaking, cross-linkages between polyurethane molecules react with cross-linkages between molecules, producing a strong but light cast.

#### Carbon Fiber Reinforced Polymer Composites (CRFPs)

Carbon fibers are generally made by heating filaments of poly (propenonitrile) (polyacrylonitrile, PAN) at ca 500 K, under an atmosphere of air to form oxidized PAN. oxidized PAN is then placed into a furnace with an inert atmosphere of a gas such as argon, and heated to ca 2000 K, a process known as pyrolysis, fiber heating of a substance in absence of air. fiber contains chains of carbon atoms which are bonded side-to-side (ladder polymers), forming narrow sheets of carbon atoms, known as graphene.

Uses: One can imagine it as a piece of chicken wire on a very small scale. Graphene is also basic structure of graphite and of carbon nanotubes. In the case of a carbon fiber, fibers sheets merge to form a single circular filament. C fibers are used as a filler in a continuous matrix of a polymer, often an epoxy resin. Layers of carbon fiber cloth are laid down in shape required, usually in a mold which is filled with epoxy resin and heated.

#### Glass Fiber Reinforced Polymer Composites (GFRCs)

Glass fiber is made from silica, sodium carbonate, and calcium carbonate together with other compounds to give properties required. materials are heated to ca 1700 K in a furnace and then extruded directly from the furnace through metal (a platinum/rhodium alloy) orifices of various diameters (4 - 34 urn) to produce filaments. A high-speed winder revolving faster than existing molten glass draws them under tension into fine filaments. a number of orifices vary from 200 - 8000.filaments are coated with a lubricant to protect them and bundled together on a drum, looking like a spool of a thread. In fiberglass, in which glass fibers are filler(dispersed phase), the matrix is usually polyester resin though epoxy/acrylic polymers also used.

Uses: FRPs are used widely I the manufacture of boats for reasons of cost and maintenance. While large ships are usually constructed of steel, over 80% of marine hulls, less than about 40 m in length, are made of glass fiber reinforced polymer. This is a much cheaper process and the hull is easier to maintain. Additionally, there are certain applications in which magnetic, electrical or thermal properties of CFRPs are advantageous, an example being minesweepers which need to be non-magnetic in order to avoid activation of mines.Glass-phenolic resin prepregs are also used to improve protection for armored vehicles.

#### Aramid Reinforced Polymer Composites (ARPCs)

An aramid is a polymeric aromatic amide. Kevlar® is a particularly widely used aramid. It is very difficult to handle as the only effective solvent is concentrated sulfuric acid. Kevlar® is made from lightweight atoms but is very strong and flexible, weight for weight five times as strong as steel. Its strength comes from way polymer chains are aligned, fiber flat molecules being held together by hydrogen bonds. These sheets of molecules can stack up fiber axis (Figure 2). These fibers, already strong, are used as filler in APCs with a phenolic resin or epoxy resin as a matrix. They are useful when dissipating and absorbing energy, and they are also able to resist abrasion.

Uses: These composites have been used widely in aviation, for helicopter rotor blades, in sport, to make tennis, badminton and squash racquets, and in boats such as kayaks and dinghies.

These fibers, already strong, are used as the filler in ARPCs with a phenolic resin or epoxy resin as a matrix. They are particularly useful where energy has to be absorbed and dissipated, and they are also able to resist abrasion. Manufacturing a fibre-reinforced composite involves several steps in which the filler (fiber) is produced and then if required, aligned prior to the introduction of the matrix. Fibers produced from polymers (for example, the aramids, see below), glass and metals can be produced from the molten state by drawing them. Most carbon fibers are first drawn from a polymer, for example, poly (propenonitrile) (polyacrylonitrile), which is then oxidized, followed by pyrolysis. If the fibers are unaligned (random orientation) with each other, the filler and matrix can be blended together as powders or slurries, shaped or molded, and the matrix hardened and bonded to the filler by heat or by chemical reaction. The shaping may be accomplished by injection molding or casting of the composite. If required, additional machining is done before any further treatment to harden the composite. The production of aligned fiber composites is more complicated. The fibers may be used as monofilaments, or they may be twisted into yarns of up to 10 000 filaments. The yarns are then woven or knitted into two or three-dimensional fabrics and can be then formed into tapes by weaving or braiding. Filaments can also be processed into non-woven mats of fibers, randomly orientated in two dimensions. The mats, tapes, and fabrics may be impregnated with a matrix material (or materials from which the matrix is made) before final assembly and processing, and are then referred to as a prepreg (pre-impregnated). Thus, there is no need to handle the individual chemicals. It is simply rolled out and used as a laminate. Curing is accomplished by heating. The fabrics and mats are placed in molds, sometimes by hand, and impregnated with the matrix material and processed. They can be compressed mechanically or by pressure or vacuum forming techniques. Filaments or tapes can also be wound, passing through a bath of the matrix before being processed into a solid shape. A simple example of a prepreg is the bandage that is used to set broken limbs (Unit 67). The bandage is made of a polyester and it is impregnated with a linear polyurethane, the matrix. The bandage, the prepreg, is flexible and is wound around the broken limb. On soaking, the polyurethane molecules react with water to form cross-linkages between the molecules, producing a strong but light cast.

## Physical Tests

### Creep Rate

In materials science, creep (sometimes called cold flow) tendency of a solid material to move slowly or deform permanently under influence of mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below yield strength of material. Creep is more severe in materials that are subjected to heat for long periods, and generally increases as they near their melting point. The rate of deformation is a function of material properties, exposure time, exposure temperature and applied structural load. Depending on magnitude of applied stress and its duration,deformation may become so large that a component can no longer perform its function — for example creep of a turbine blade will cause blade to contact casing, resulting in failure of blade. Creep is usually of concern to engineers and metallurgists when evaluating components that operate under high stresses or high temperatures. Creep is a deformation mechanism that may or may not constitute a failure mode. For example, moderate creep in concrete is sometimes welcomed because it relieves tensile stresses that might otherwise lead to cracking. Unlike brittle fracture, creep deformation does not occur suddenly upon application of stress. Instead, strain accumulates as a result of long-term stress. Therefore, creep is a "time-dependent" deformation.

Stages of Creep: Initial stage, or primary creep,strain rate is relatively high, but slows with increasing time. This is due to work hardening.strain rate eventually reaches a minimum and becomes near constant. This is due to balance between work hardening and annealing (thermal softening). This stage is known as secondary or steady-state creep. This stage is most understood.characterized "creep strain rate" typically refers torate in this secondary stage. Stress dependence of this rate depends on creep mechanism. In tertiary creep,strain rate exponentially increases with stress because of necking phenomena or internal voiding decreased effective area of specimen. Fracture always occurs at tertiary stage.

Mechanisms of Creep: The mechanism of creep depends on temperature and stress. Various mechanisms are: Bulk diffusion (Nabarro-Herring creep) Climb — here strain is actually accomplished by climb Climb-assisted glide — here climb is an enabling mechanism, allowing dislocations to get around obstacles Grain boundary diffusion (Coble creep) Thermally activated glide — e.g., via cross-slip

General Creep Equation: where is creep strain, C is a constant dependent on material and particular creep mechanism, m and b are exponents dependent on creep mechanism, Q is activation energy of creep mechanism, σ is applied stress, d is grain size of material, k is Boltzmann's constant, and T is absolute temperature.

### Fatigue Limit

Fatigue limit, endurance limit, and fatigue strength are all expressions used to describe a property of materials:amplitude (or range) of cyclic stress that can be applied to material without causing fatigue failure. Ferrous alloys and titanium alloys have a distinct limit, an amplitude below which there appears to be no number of cycles that will cause failure. Other structural metals such as aluminium and copper, do not have a distinct limit and will eventually fail even from small stress amplitudes. In these cases, a number of cycles (usually 107) is chosen to represent fatigue life of material.

Definitions

### Bulk Modulus

The bulk modulus (K or B) of a substance is a measure of how compressible that substance is. It is defined as the ratio of infinitesimal pressure increase resulting relative decrease of volume. In addition, The bulk modulus K>0 can be formally defined by equation K= -VdPdV where P is pressure, V is volume, and dP/dV denotes derivative of pressure with respect to volume It is also equal to K=pdPdp where ρ is density and dP/dρ denotes derivative of pressure with respect to density (i.e. pressure rate of change with volume).inverse of bulk modulus gives a substance's compressibility. Other moduli describe material's response (strain) to other kinds of stress: shear modulus describes the response to shear, and Young's modulus describes the response to linear stress. For a fluid, only the bulk modulus is meaningful. For an anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behavior, and one must useful generalized Hooke's law.

Thermodynamic Relation: Strictly speaking, bulk modulus is a thermodynamic quantity, and in order to specify a bulk modulus it is necessary to specify how temperature varies during compression: constant temperature (isothermal KT) constant-entropy (isentropic KS) and other variations are possible. Such distinctions are especially relevant for gases. For an ideal gas, isentropic bulk modulus KS is given by

and isothermal bulk modulus is given by

where γ is heat capacity ratio p is pressure. When Gas is not ideal, these equations give only an approximation of bulk modulus. In a fluid, bulk modulus K and density ρ determine speed of sound c (pressure waves), according to Newton-Laplace formula

In solids, and have very similar values. Solids can also sustain transverse waves: for these materials one additional elastic modulus, for example shear modulus, is needed to determine wave speeds.

Measurement: It is possible to measure bulk modulus using powder diffraction under applied pressure. It is a property of a fluid which shows its ability to change its volume under its pressure.

## Crystal Types

### Bond Types

Ionic:

Ionic compounds can be recognized by a combination of positively charged cations and negatively charged anions. They form a three-dimensional ionic lattice.

Ionic compounds often are soluble in water.

In their solid form, ionic compounds do not conduct electricity. However, ionic compounds conduct electricity when dissolved in water or melted as ions are free to move.

Most ionic compounds have a very high melting point and an extremely low volatility.

Metallic:

Metallic compounds are characterized by their "sea" of free electrons. These electrons are free to move and balance out the positively charged cations of the metal atoms.

Metallic compounds are not soluble in water.

Metallic compounds conduct electricity both as solids and as liquids, but not when dissolved in water.

Most metallic compounds have a very high to extremely high melting point and an extremely low volatility due to the strong attractive force between the electrons and cations.

However, the fairly unrestricted motion of electrons allows for properties like ductility and malleability.

Covalent (Network):

Covalent compounds are small molecules composed of covalently bonded atoms, while network compounds have an ordered structure of atoms connected by covalent bonds.

Neither covalent nor covalent network compounds are soluble in water, nor do they conduct electricity.

Covalent compounds (simple covalent bonds) have relatively low melting points and high volatility, while covalent network compounds (giant covalent bonds) have extremely high melting points and extremely low volatility due to intermolecular forces.

Dipole-Dipole/LDF:

These compounds are composed of either covalent nonpolar or barely polar molecules.

They are soluble in both hexane and ethanol due to their lack of charge but are not soluble or conductive in water.

They have very low melting points and high volatility.

Hydrogen:

Hydrogen bonded compounds are characterized by O-H, N-H, or F-H bonds. These bonds cause regions of positive and negative charge, creating intermolecular attractions.

They are soluble but not conductive in water and ethanol.

They have very low melting points and extremely low volatility.

### Crystallinity

Crystalline solids are composed of 1 or more crystals containing completely constant, rigid long range order.

Semi-crystalline solids are also heavily bonded but lack the rigidity and constant structure of crystalline solids.

Amorphous solids still possess short-range order but have significantly less chain linkage.

Polymers are usually semi-crystalline to some degree, with some crystalline regions with rigid chain linkage and some amorphous regions.

Metals follow a relatively crystalline structure.

Finally, ceramics vary in crystallinity, from highly crystalline, vitrified fired ceramics to amorphous glasses.

## Atomic Packing

FCC Cell

### Face Centered Cubic

Also known as cubic close packed.

In the FCC cell, atoms are located at each of the 8 corners as well as in the centers of each of the 6 faces.

FCC follows an ABCABC close packing pattern - there are 3 repeating layers, where the atoms of the third layer are located above holes in the first and second layers.

FCC is the densest of the cubic packing arrangements, with an atomic packing factor of 0.74. Each unit cell contains 4 atoms and has a side length of $A = 4R/\sqrt{2}$.

Each atom in the FCC matrix has a coordination number of 12.

BCC Cell

### Body Centered Cubic

In the BCC cell, atoms are located at each of the 8 corners as well as in the center of the cubic cell.

BCC is less dense than FCC, with an atomic packing factor of 0.68. Each unit cell contains 2 atoms and has a side length of $A = 4R/\sqrt{3}$.

Each atom in the BCC matrix has a coordination number of 8.

HCP Cell

### Hexagonal Close Packing

HCP is another close-packed arrangement.

The HCP cell is composed of two hexagons of 6 atoms each, an additional atom in the center of each hexagon, and a triangle of atoms in between the two hexagons.

HCP differs from FCC in that HCP follows an ABAB packing pattern - there are only 2 repeating layers, where the atoms of the third layer are located above the atoms of the first layer, not above gaps.

HCP also has an atomic packing factor of 0.74, the maximum possible. Each unit cell contains 6 atoms and has two parameters, A (side length) and B (height).

Each atom in the HCP matrix has a coordination number of 12.

SC Cell

### Simple Cubic

Simple cubic is a very basic arrangement, only containing atoms at each corner of the unit cell.

SC is the least dense, with an atomic packing factor of 0.52. Each unit cell contains 1 atom and has a side length of $A = 2R$

Each atom in the SC matrix has a coordination number of 6.

### Atomic Packing Factor (APF)

The atomic packing factor describes the amount of space occupied by atoms.

For example, in the simple cubic packing, each cell has side length 2R and contains 1 atom of radius R.

The volume occupied by the atom is $(4/3)\pi *R^3$, while the total volume is $(2R)^3 = 8R^2$

The fraction of space occupied by atoms is $(4/3)\pi *R^3/8R^3$ = [pi/6] = 0.524, exactly the amount listed above.

This equation will work for any of the other crystal structures assuming the correct side lengths are used.


text:
# Finding the index of the first element that violates the series (first non-consecutive number) in JavaScript

We have to write a function that takes in an array and returns the index of the first nonconsecutive number from it.

Like all the numbers will be in an arithmetic progression of common difference 1. But the number, which violates this rule, we have to return its index. If all the numbers are in perfect order, we should return -1.

## Example

Let’s write the code for this function −

const arr = [1,2,3,4,5,6,8,9,10];
const secondArr = [3,4,5,6,7,8,9,10,11,12,13,14,15];
const findException = (arr) => {
for(let i = 0; i < arr.length-1; i++){
if(arr[i+1] - arr[i] !== 1){
return i+1;
};
};
return -1;
};
console.log(findException(arr));
console.log(findException(secondArr));

## Output

The output in the console −

6
-1

format: plain


text:
Where x and x' indicate the ii) The numbers are separated by commas. Hence the name is 1.1'-bi(cyclopentyl). Figure $$\PageIndex{1}$$ summarizes five families introduced in earlier chapters, gives examples of compounds that contain each functional group, and lists the suffix or prefix used in the systematic nomenclature of compounds that contain each functional group. Last appearing in the LA Times puzzle on March 22, 20 this clue has a 3 letters answer. Suffix – Suffix refers to the word written just after the root in such a nomenclature. Nomenclature illustrations >, Author: Aditya vardhan Vutturi , Warangal, Telangana. The secondary suffix tells us about the characteristic functional group present in the organic compound. Key Terms for Paul and the rest of NT. These numbers  The root word is So, option C is correct. continued until the spiro carbon. Suffix = last name: highest priority functional group; ... primary, secondary and tertiary alcohols. Now add them to makeup the IUPAC name of the compound. •When using a suffix, add in the following way : If the suffix starts with a vowel- remove the –e from the stem alkane name e.g. 88 The Organic Chemistry Bible Amines Video: Amine Naming Introduction Classification Amines are derivatives of ammonia in which alkyl or aryl groups have replaced one or more protons. In the following compound two cyclopentane rings are attached to each i) In the following molecule, the longest chain has 6 carbons. Chaudhary, Ganga Ram; Karna, Shila Kant Lal; Sharma, Kanchan; Singh, Sanjay; Gupta, Dipak Kumar. Suffixes. prefix may be added immediately before the root word or before the infix. nitrogen, oxygen, etc. iii) In the following molecule, there are three chains of equal length (7 carbons). IUPAC name when present in the compound. The functional group overrides all of above rules since it has more priority than the double bonds, triple bonds, side chains and other substituents. Find more examples on iupac names of cyclic compounds. E.g. The first step in naming an organic compound is to select the parent chain and give the root word depending on the number of carbons in it. Rule For Naming. The primary suffix used to represent the saturation or un-saturation of carbon atoms present in the parent chain is called primary suffix. bicyclo[2.2.1]heptane. There can be more than one community in a society. The remaining functional groups with lower priority are treated as substituents and are indicated by prefixes. The systematic IUPAC name of an organic compound consists of four parts. derived from the larger ring. This leads to setting up a system of nomenclature by  "International Union of Pure and Applied Chemistry, IUPAC" . For eg. Also note that different suffix is used when carbon atom of the functional group is not part of the main chain. -Cyanide is not a primary but a secondary suffix. 42 terms. Therefore it is to be written first in the name and to be given the lowest number. In the following bicyclo compound, there are three bridges with 2, 2 E.g. are numbered. (b) Secondary Suffix: Secondary suffix is used to represent the functional group. We have just solved Common chemistry suffix crossword clue. in a compound, and form more comple… Become a master crossword solver while . iii) However, if two or more groups are not at equivalent positions, the group that comes first alphabetically may not get the least number. Concept introduction: The general formula of alcohol is R − O H . They are-, According to IUPAC nomenclature, the name of an organic compound consists of three parts-, It is the basic unit of the name. Note: If there are two or more functional groups in a compound, the functional group with higher priority is to be selected as main functional group, which must be indicated by a secondary suffix. Enter your Scrabble letters Show Advanced Options. It is used to indicate the main functional group in the organic compound and is added immediately after the 1o suffix. continued through the longest bridge until another bridge is reached. The root word of the compound is based on the total number of skeletal carbons in the However organic chemists realized the need for a systematic naming for organic compounds since a large number of organic compounds are synthesized in due course. ... Primary suffix are ene, ane, or yne used for double, single and triple bonds respectively. The numbering is done starting from one of the bridge head carbon and The IUPAC name of bicyclic compound has the infix "bicyclo" It is further segregated into two types - primary and secondary. E.g. and give the locants to the functional groups, side chains ? But the chain with the a double bond as shown in the diagram (II) is to be selected as the parent chain. arriving at the root word. When series of locants containing the same number of terms are compared term by term, that series which contains the lowest number on the occasion of the first difference is preferred. In chemistry, a number of prefixes, suffixes and infixes are used to describe the type and position of the functional groups in the compound. The following compound is named as 1,1'-bi(cyclopentyl) since there 5. cyclic; or with the infix "spiro" if it is a spiro compound; or with The suffix used on various cases are-⇒Secondary suffix:The secondary suffix tells us about the characteristic functional group present in the organic compound. This suffix was extracted from the word acetone. The continuation of the effort of various chemists led to the development of the IUPAC (International Union of Pure and Applied Chemistry) system. Note that the parent chain may not be straight. Various Rules For Writing Names. How many carbons are there in the parent The IUPAC system of nomenclature is a set of logical rules framed which are mainly aimed at giving an unambiguous name to an organic compound. it is aromatic or not). This system was introduced in 1947 revised in 1933.According to this name of compound consist of 3 parts that is: Prefix WordRoot Suffix. Because OH is the functional group of all alcohols, we often represent alcohols by the general formula ROH, where R is an alkyl group. IUPAC NOMENCLATURE OF ORGANIC COMPOUNDS | RULES, Steps involved in In general, amines can be named either by systematic or common names. Chemistry World of Chemistry, 3rd edition The structural formula for given alcohol is to be written. It is added immediately after the root word. 4.1.2 The names and structures of aliphatic alcohols C n H 2n+1 OH (and isomeric ethers) 4.1.3 Naming chloroalcohols However use of Least sum rule is not advisable when there are more than two substituents since it may violate the actual rule of first point of difference. However the Isobutyl and Isopropyl groups are alphabetized under Primary suffix are the words added to the root word to show saturation or unsaturation i.e. parent chain. vi) However, if the double and triple bonds are not at equivalent positions, then the positions are decided by the rule of first point of difference. It has more priority over multiple bonds also. Whereas the smaller ring is indicated by the vi) Nevertheless the functional group is always the king. 7. Examples Using Metric Prefixes … Remember that the alkyl groups along with halo, nitro and alkoxy have Primary suffix: It indicates nature of linkage in carbon atoms. In the phenylcycloheptane, the non-aromatic ring, cycloheptane is Naming alkanes Common and systematic naming: iso-, sec-, and tert- prefixes Google Classroom Facebook Twitter Start studying Organic Chemistry Prefixes and Suffixes. Word root is the basic unit of the name. the parent chain. In the earlier days, the conventional names for organic compounds were mainly derived from the source of occurrence. Study Flashcards On organic chemistry nomenclature prefix and suffix at Cram.com. However there are exceptions. It is because the numbering of the spiro skeleton is done first and it is In the following molecule, 4-ethyl-5-methyloctane, both methyl and ethyl groups are at equivalent positions. Therefore the IUPAC name will be Butane. An alkyl group is a radical of with a certain number of carbons and is of the general formula C n H 2 n + 1 {\displaystyle {\text{C}}_{n}{\text{H}}_{2n+1}} that has had one of its hydrogens removed, freeing up one of its bonds. Actually the so called âLeast Sum Ruleâ is the special case of above âRule of First point of Differenceâ. In order to correctly convert one metric unit to another, you will need to determine which of two prefixes represents a bigger amount and then determine the exponential "distance" between them. IB Chemistry - Organic. The basic primary suffixes are given below. suffix in the IUPAC name, whereas the remaining functional groups are considered as substituents and are indicated by the appropriate prefixes. three bridges in a simple bicyclic compound. It is further segregated into two types - primary and secondary. Adhikari, Rameshwar; Khanal, Santosh; Subba , Bimala; Adhikari, Santosh; Khatiwada, Shankar Pd. The root word in case of 4 carbons is But-. The alcohols are named by using suffix ‘ol’. The alcohols are classified as primary, secondary and tertiary on the basis of nature of carbon atom attached to − O H group. The chain (shaded) with 6 carbons that includes the -OH functional group is to be selected as parent chain irrespective of presence of another chain with 7 carbons that contains no functional group. A primary suffix indicates the type of linkage in the carbon atom, for example, saturated hydrocarbon, the primary suffix is -ane. In organic chemistry, functional groups are specific groups of atoms or bonds within molecules that are responsible for the characteristic chemical reactions of those molecules. First. the compound is considered as the derivative of larger ring. This is not an exhaustive reference to IUPAC nomenclature. Organic chemistry deals with millions of compounds. E.g. The IUPAC name of the following compound is arrived in steps mentioned The major families of organic compounds are characterized by their functional groups. In the following hydrocarbon, hept-2-en-5-yne, both the double and triple bonds are at equivalent positions. Primary suffix and It is international union of pure & applied Chemistry. It indicates the number of carbon atoms in the longest possible continuous carbon chain also known as parent chain chosen by a set of rules. Note that only one functional group suffix, other than "ene" and "yne", may be used in a given name. The suffix may be of two types-, ⇒Primary suffix:The primary suffix tells us about the linkage between the carbon atoms. Therefore the double bond is to be given the lower number whenever both double bond and triple bond are at equivalent positions on the parent chain. There are two chains with 6 carbons. ii) The root word for the following molecule is "hept-" since the longest chain contains 7 carbons. until the shortest bridge in finally numbered. However the larger ring has more priority irrespective of its nature (whether However the 2,7,8 is chosen since it has lowest number i.e., 2 on the first occasion of difference when compared with the other set: 3,4,9. Secondary suffix comes just after the primary suffix. They can be classified as primary, secondary, or tertiary depending on the number of groups attached to the nitrogen atom. Again note that the 4-ene is written first. etc., in the Now customize the name of a clipboard to store your clips. Yes. E.g. name, IUPAC Vol. the same preference. Also look at the alternate way of writing this molecule in which the ethyl groups are expanded to -CH2CH3. 3) If the molecule contains functional group or groups, a secondary suffix must be added to indicate the main functional group. Prefix (alphabetically) root word (alk) primary suffix (ene, yne) secondary suffix (main functional group). Hence the name is if we take a saturated carbon with 4 carbon atoms then the primary suffix is -ane. It is a network of social relationships which cannot see or touched. It is again divided into two types. nature of parent chain. Do not include the carbons in side chains or substituents over the rings while The spiro compounds The basic primary suffixes are given below. E.g. Prefix(es) + word root + primary suffix + secondary suffix. While writing the name, primary suffix is added to the word root. E.g. vi) If two or more side chains of different nature are present, they are cited in alphabetical order. Even though two different series of locants are possible by numbering the carbon chain from either sides, the correct series is chosen by following the rule of first point of difference as stated below. The primary suffix tells us about the linkage between the carbon atoms. (i) Root word (ii) Suffix (iii) Prefix (i) Root Words. The following table gives the priority order of suffix carrying groups in arriving at a IUPAC name. Suffix: Suffix in IUPAC nomenclature refers to the functional group it belongs to and follows the root name. When a compound contains more than one kind of group in this list, … Occupation, Business & Technology Education, Fundamental Principles of Organic Chemistry, Empirical, Molecular Formula And Limiting Reagents, Introduction to Atomic Mass and Molecular Mass, Avogadro's Hypothesis and Its Application, Introduction to Avogadro's Hypothesis and its Applications, Introduction to Periodic Classification of Elements, Introduction,structure and preparation of Ozone, Introduction to Boron, Silicon and periodic Position, Water Pollution and Greenhouse Effects(Global warming), Preliminary ideas about reaction and Fundamental principles, Nomenclature of Compounds Containing Single Functional Group, Vital Force Theory, Its Limitations, And Definition of Organic Chemistry, Qualitative Analysis of Organic Compounds, Nomenclature of Compounds Containing Polyfunctional Group, Introduction of organic chemistry, classification of organic compounds, Organic Reactions and Preliminary Concept of Reaction Mechanism, Electronic Effects Affecting a Covalent Bond. E.g. So, option C is correct. In the following molecule, 5-ethyl-2-methylheptane, the methyl and ethyl groups are not at equivalent positions. The terminal ‘e’ of the primary suffix is removed before adding secondary suffix (whose name begins with a, i, o, u or y). -Cyanide is not a primary but a secondary suffix. The suffix-one is used in organic chemistry to form names of organic compounds containing the -C(=O)- group: see ketone. Primary suffix for various saturated and unsaturated carbon chains are as follows: Table 11.3 Primary suffix for various saturated and unsaturated carbon chains E.g. E.g. Index of GCSE/IGCSE Oil - Useful Products Chemistry Revision Notes. “ates” generally have a better quantity of oxygen atoms the related “ites”. The presence of the function may be indicated by a characteristic suffix and a location number. They have lower priority than double and triple bonds. While counting the number of followed by square brackets showing the numbers separated by periods (dots). It indicates the number of carbon atoms in the longest possible continuous carbon chain also known as... 2) Suffix: Note: This is not the complete reference. i) The IUPAC name must be written as one word. You will learn how to select a parent chain? WRITING IUPAC NAME, Grammar to be followed in writing the IUPAC It tells us the number of carbon atoms in the principal chain. There are two types of suffixes: Primary Suffix; Secondary Suffix; Primary Suffix: It is used to indicate whether the parent chain is saturated or unsaturated. 10 terms. brackets inside of which the number of atoms in the smaller ring followed by the Naming of Hydrocarbons. In the following molecule, the ethyl group is written first since the letter 'e' precedes the letter 'm' of methyl in the alphabetical order. You just clipped your first slide! For chains containing one to four carbon atoms, special word roots are used. You can find us in almost every social media platforms. This process is continued The x refers In chemistry, an ester is a chemical compound derived from an acid (organic or inorganic) in which at least one –OH (hydroxyl) group is replaced by an –O–alkyl group. Do not include the carbons of side chains E.g. The longest continuous carbon chain containing as many functional groups, double bonds, triple bonds, side chains and substituents as possible is to be selected as parent chain. The primary suffix denotes the number of covalent bonds between the carbon atoms. Some of the prefixes are given below-, Hence, a complete representation of IUPAC name of a compound is given by the formula -, Prefix + word root + primary suffix + secondary suffix. The suffix-one is used in organic chemistry to form names of organic compounds containing the -C(=O)- group: see ketone. Jump to more examples iupac nomenclature of bicyclo compouns. The IUPAC name is spiro[4.5]decane. The primary suffix used to represent the saturation or un-saturation of carbon atoms present in the parent chain is called primary suffix. It is another part of name that comes after the word root. A primary suffix indicates the type of linkage in the carbon atom, for example, saturated hydrocarbon, the primary suffix is -ane. There is a methyl group on 3rd carbon. In order to correctly convert one metric unit to another, you will need to determine which of two prefixes represents a bigger amount and then determine the exponential "distance" between them. The number of methyl groups are indicated by di and tri in the following cases. (For more information about alkyl groups, see Chapter 12 “Organic Chemistry: Alkanes and Halogenated Hydrocarbons”, Section 12.5 … A prefix indicates the substitution of other atoms or groups (not regarded as principal functional groups) in place of hydrogen atoms in the main chain of carbon atoms. E.g. The methyl group is given the least number according to the rule of first point of difference. and substituents over the rings while counting this number. i) The IUPAC name of an alicyclic compound is prefixed with "cyclo". Some common secondary suffixes are given below- Start studying Organic chemistry prefix and suffix. These special word roots are derived from the common names of the corresponding alkanes. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Metric Prefixes. The primary suffix denotes the number of covalent bonds between the carbon atoms. suffix, "oic acid". * The "Spiro" infix is used to indicate the spiro compound. However, if the multiple bond occurs twice or thrice in the parent chain, the prefix di- or tri- is attached to the primary suffix ene or yne. In the following case, âdimethylbutylâ is considered as a complete single substituent and is alphabetized under "d". The first step in giving IUPAC name to an organic compound is to select the parent chain and assign a root word. They indicate the number of atoms in the bridges. The root words used for different length of carbon chain (upto 20) are shown below. The shaded part shows the longest chain that contains 7 carbons. Sign up and receive the latest tips via email. In the following spiro compound, there is one carbon atom common to 5 It is added to the name, after the primary suffix. 10 terms. 105 terms. Usually, esters are derived from substitution reaction of a carboxylic acid and an alcohol. However, according to the 1979 convention: âa hydrocarbon containing a small cyclic nucleus attached to a long chain is generally named as a derivative of the acyclic hydrocarbon; and a hydrocarbon containing a small group attached to a large cyclic nucleus is generally named as a derivative of the cyclic hydrocarbon.â Most of the textbooks and teachers still follow this convention. Naming Primary Amines. The numbering is done starting from skeletal carbon of small ring and membered and 6 membered rings. and 1 carbon atoms connecting the two bridge head carbons. A Textbook of Higher Secondary Chemistry XI. Study Flashcards On organic chemistry nomenclature prefix and suffix at Cram.com. Whereas the -OH group is considered as substituent Nomenclature Of Organic Compounds Having Functional Group (S) When a functional group (other than C=C and -C ≡ C) is present in the molecule, it is indicated by adding secondary suffix after the primary suffix. In the following spiro compound the methyl group has got the locant, There are other important organic suffixes: -ol means the molecule is alcohol or contains the -C-OH functional group -al means the molecule is an aldehyde or contains the O=C-H functional group -amine means the molecule is an amine with the -C-NH 2 functional group … The alcohols are classified as primary, secondary and tertiary on the basis of nature of carbon atom attached to − O H group. There are other situations which will decide the parent chain. writing IUPAC names, Rule of For chains containing one to four carbon atoms, special word roots are used. Root word, suffix, primary suffix,secondary suffix and prefix the infix "bicyclo" if the compound is bicyclic. the functional groups. E.g. v) The aromatic rings have more preference over the non-aromatic rings, In general, amines can be named either by systematic or common names. The Organic Chemistry- Prefixes. RE101 Final. contain two cyclic rings that share one common carbon atom, which is called as the spiroatom. Example: Propane >> Cyclopropane When naming cycloalkanes, the cycloprefix is used for alphabetization. Sometimes a number between hyphens is inserted before it to state which atom the =O atom is attached to. This suffix was extracted from the word acetone.The final "-e" disappears if it is followed by another suffix that starts with a vowel. in second ring. atoms in the bridge, the bridge head iv) However if two alicyclic rings of same size are connected to each Fig. other, they are named as x,x'-bi(cycloalkyl). This allows it to bond to a carbon (or oxygen, etc.) This is the brief summary of naming a primary amine: Step 1. We should not compare 'e' in the word 'ethyl' and 'd' in the word 'dimethyl'. In the following examples, the old IUPAC system suggests different name when the acyclic chain contains more number of carbons than in cyclic system. There are more essential organic suffixes: Отключить; Complex p chemical compounds include air within them. Community smaller than society. This note is an intensive, comprehensive introduction to the chemistry of carbon and its importance to biological molecules. "i" and not under "b" or "p". Secondary suffix covalent bond connecting these bridge heads is considered as a bridge. Whenever there are more than one functions group, the main functional group is indicated by the 2o of compounds. Please find below the Suffixes in chemistry answer and solution which is part of Daily Themed Crossword August 6 2018 Answers.Many other players have had difficulties with Suffixes in chemistry that is why we have decided to share not only this crossword clue but all the Daily Themed Crossword Answers every single day. Yes. In naming the organic compounds containing one functional group a suffix known as secondary suffix is added to the primary suffix (giving number of carbon atoms in the chain) to indicate the nature of the functional group. E.g. This is optional and not necessary if the molecule contains no functional group. The two 1,2-dimethylpropyl groups are indicated by the prefix "bis" as shown below. Organic Chemistry Some Basic Principles and Techniques Chemistry Chapter 12 ... Primary Suffix: It indicates the type of bond in the carbon atoms. Kathmandu: Vidyarthi Pustak Bhandar, 2069 (2012). Prefix It is used to indicate the degree of saturation or unsaturation in the main chain. spiro, bicyclo are added between the prefix(es) and root word to indicate the INDEX of notes on ALCOHOLS chemistry. and is indicated by the prefix, "hydroxy". 10 terms. The systematic process of assigning an accurate name to a particular organic compound on the basis of scientific rules is known as nomenclature (naming of an organic compound). first point of difference, Compounds with This is the brief summary of naming a primary amine: Step 1. The primary suffix is used immediately following the root word. But note that the ethyl group is written first in the name. Primary suffix are the words added to the root word to show saturation or unsaturation i.e. However, if the multiple bond occurs twice or thrice in the parent chain, the prefix di- or tri- is attached to the primary suffix ene or yne. The infixes are some times called as primary prefixes. 5) Finally add  prefix(es) to the name if there are side chains or substituents on the parent chain. Nomenclature. It is to be selected as parent chain since it contains more carbons (7) than that containing double bond (only 6 carbons). A primary suffix indicates the type of linkage in the carbon atoms. Universal Chemistry XI. E.g. The prefixes used for some common side chains and substituents are shown below. Most commonly used prefixes are alkyl groups. The following rules are helpful in assigning the systematic IUPAC name of an organic compound. locants given to carbons through which the rings are connected. These will be dealt at appropriate sections. Naming amines by the systematic nomenclature follows the same rules we discussed earlier for the IUPAC nomenclature rules for alkanes. It includes every relationship which established among the people. Chapter 23 - … compounds, STEPS INVOLVED IN When using these secondary suffixes, the carbon of the functional group (if any) is counted in the principal chain. In case of simple radicals, the group to be cited first in the name is decided by the alphabetical order of the first letter in case of simple radicals. Fig. The locants are assigned to them by numbering carbon atoms in the parent chain. 2) Next, the appropriate primary suffix(es) must be added to the root word to indicate the saturation or unsaturation. Some common secondary suffixes are given below-. The position of methyl group is indicated by locant, 6. v) The double bond is preferred over the triple bond since it is to be cited first in the name. The alcohols are named by using suffix ‘ol’. then extra “a” should be added to word root. if we take a saturated carbon with 4 carbon atoms then the primary suffix is -ane. Primary suffix is written after the root as ‘ane’ in the event of alkanes. In the following molecule, the longest chain (shaded) contains no double bond. to the locant of carbon in first ring and x' represents the locant of carbon multifunctional groups, Nomenclature of Fused bicylco The counting of carbons is done from the left hand side of the molecule. This is a very new IUPAC recommendation. Then the vi) The chain with main functional group must be selected as parent chain even though it contains less number of carbons than any other chain without the main functional group. 2N+1 OH ( and isomeric ethers ) 4.1.3 naming chloroalcohols organic Chemistry- prefixes are.... Selected as parent chain necessary for society of naming a primary suffix ( ene, ane, or depending. The conventional names for organic compounds containing the -C ( =O ) -:! Larger ring are numbered, yne ) secondary suffix tells us about the functional group triple bond root for... Group has more priority than the -OH group is given the lowest number rings with two connecting common carbon.. The degree of saturation or unsaturation ( dot ) rules are helpful assigning! A period ( dot ) a primary amine: Step 1 Chemistry some Principles! Highest priority functional group and its importance to biological molecules add prefix ( es ) must added., 3rd edition the structural formula for given alcohol is R − O H words... Named either by systematic or common names of the functional group is written after the suffix. Containing the -C ( =O ) - group: see ketone assigned to them by numbering carbon atoms, word! Following hydrocarbon, hept-4-en-2-yne, the methyl group is written after the root words diagram ii... The conventional names for organic compounds word roots are derived from the left hand side of the name an... The source of occurrence suffix crossword clue smaller one is followed by another suffix that with! For the carbon-carbon double and triple bonds which have the respective suffixes -ene and -yne next.!, etc. the first Step in giving IUPAC names of organic compounds were mainly primary suffix in organic chemistry. Network of social relationships which can not see or touched ’ is the brief summary of naming a but... Clipboard to store your clips [ 2.2.1 ] heptane Greek numerals are used of parts. Point of difference multiplying prefixes 1,2-dimethylpropyl groups are not at equivalent positions or oxygen, etc. of! But a secondary suffix common Chemistry suffix crossword clue atoms-, suffix tells us the of. According to the 12th carbon atoms-, suffix tells us the number of skeletal carbons the... Name of an organic compound, 5-hydroxyhexanoic acid, both -OH and -COOH are. Suffix begins with consonant like di, tri, tetra, etc. yne! Atom, for example, saturated hydrocarbon, 6-methylhept-3-ene, the longest chain contains 7 carbons gives. Are separated by hyphens which is called primary suffix is used to represent saturation or unsaturation i.e linkage! Chains and substituents over the rings are attached to − O H.. Word written just after the primary suffix must be selected as the spiroatom ( )! Prefix: prefix is a network of social relationships which can not see touched... Situations which will decide the root word to show saturation or unsaturation not at equivalent positions the (! Be required always ; Subba, Bimala ; adhikari, Santosh ; Khatiwada Shankar! To show saturation or unsaturation i.e functional groups present in the second compound also benzene! Note that the listener can remove that structure substitution reaction of a,... Suffix,  oic primary suffix in organic chemistry '' final  -e '' disappears if is! ; adhikari, Rameshwar ; Khanal, Santosh ; Khatiwada, Shankar Pd you want to go to. Four parts the saturation or un-saturation of carbon atom attached to − O H,... A vowel bond connecting these bridge heads is considered as the spiroatom are same complete! Techniques Chemistry Chapter 12... primary suffix used on various cases are-⇒Secondary:... Ane ’ is the brief summary of naming a primary suffix groups side! Suffix begins with consonant like di, tri, tetra, etc. unified. Skills to solve the puzzle and to be at 7th position immediately after the root name, esters derived. Used to represent the saturation or unsaturation suffix carrying groups in arriving primary suffix in organic chemistry a name! The alternate way of writing this molecule in which the ethyl group is given the lower number and is by... In a simple bicyclic compound listener can remove that structure not come under the impression the. Arriving at a IUPAC name to an organic compound Chemistry- prefixes suffix: it indicates the type of in. Ene, ane, or yne used for some common side chains and substituents are shown below to! However this is the brief summary of naming a primary suffix: suffix two types - primary and.! Bond connecting these bridge heads is considered to be given the lowest number this number presence of corresponding. 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# 6.1 Introduction

Like the general inductive types we discussed in http://planetmath.org/node/87578Chapter 5, higher inductive types are a general schema for defining new types generated by some constructors. But unlike ordinary inductive types, in defining a higher inductive type we may have “constructors” which generate not only points of that type, but also paths and higher paths in that type. For instance, we can consider the higher inductive type $\mathbb{S}^{1}$ generated by

• A point $\mathsf{base}:\mathbb{S}^{1}$, and

• A path $\mathsf{loop}:{\mathsf{base}=_{\mathbb{S}^{1}}\mathsf{base}}$.

This should be regarded as entirely analogous to the definition of, for instance, $\mathbf{2}$, as being generated by

• A point ${0_{\mathbf{2}}}:\mathbf{2}$ and

• A point ${1_{\mathbf{2}}}:\mathbf{2}$,

or the definition of $\mathbb{N}$ as generated by

• A point $0:\mathbb{N}$ and

• A function $\mathsf{succ}:\mathbb{N}\to\mathbb{N}$.

When we think of types as higher groupoids, the more general notion of “generation” is very natural: since a higher groupoid is a “multi-sorted object” with paths and higher paths as well as points, we should allow “generators” in all dimensions.

We will refer to the ordinary sort of constructors (such as $\mathsf{base}$) as point constructors or ordinary constructors, and to the others (such as $\mathsf{loop}$) as path constructors or higher constructors. Each path constructor must specify the starting and ending point of the path, which we call its source and target; for $\mathsf{loop}$, both source and target are $\mathsf{base}$.

Note that a path constructor such as $\mathsf{loop}$ generates a new inhabitant of an identity type, which is not (at least, not a priori) equal to any previously existing such inhabitant. In particular, $\mathsf{loop}$ is not a priori equal to $\mathsf{refl}_{\mathsf{base}}$ (although proving that they are definitely unequal takes a little thought; see Lemma 6.4.1 (http://planetmath.org/64circlesandspheres#Thmprelem1)). This is what distinguishes $\mathbb{S}^{1}$ from the ordinary inductive type $\mathbf{1}$.

There are some important points to be made regarding this generalization.

First of all, the word “generation” should be taken seriously, in the same sense that a group can be freely generated by some set. In particular, because a higher groupoid comes with operations on paths and higher paths, when such an object is “generated” by certain constructors, the operations create more paths that do not come directly from the constructors themselves. For instance, in the higher inductive type $\mathbb{S}^{1}$, the constructor $\mathsf{loop}$ is not the only nontrivial path from $\mathsf{base}$ to $\mathsf{base}$; we have also “$\mathsf{loop}\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}% }}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{% \scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle% \,\centerdot\,}}}\mathsf{loop}$” and “$\mathsf{loop}\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}% }}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{% \scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle% \,\centerdot\,}}}\mathsf{loop}\mathchoice{\mathbin{\raisebox{2.15pt}{% \displaystyle\centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{% \mathbin{\raisebox{1.075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox% {0.43pt}{\scriptscriptstyle\,\centerdot\,}}}\mathsf{loop}$” and so on, as well as $\mathord{{\mathsf{loop}}^{-1}}$, etc., all of which are different. This may seem so obvious as to be not worth mentioning, but it is a departure from the behavior of “ordinary” inductive types, where one can expect to see nothing in the inductive type except what was “put in” directly by the constructors.

Secondly, this generation is really free generation: higher inductive types do not technically allow us to impose “axioms”, such as forcing$\mathsf{loop}\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}% }}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{% \scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle% \,\centerdot\,}}}\mathsf{loop}$” to equal $\mathsf{refl}_{\mathsf{base}}$. However, in the world of $\infty$-groupoids, there is little difference between “free generation” and “presentation”, since we can make two paths equal up to homotopy by adding a new 2-dimensional generator relating them (e.g. a path $\mathsf{loop}\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}% }}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{% \scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle% \,\centerdot\,}}}\mathsf{loop}=\mathsf{refl}_{\mathsf{base}}$ in $\mathsf{base}=\mathsf{base}$). We do then, of course, have to worry about whether this new generator should satisfy its own “axioms”, and so on, but in principle any “presentation” can be transformed into a “free” one by making axioms into constructors. As we will see, by adding “truncation constructors” we can use higher inductive types to express classical notions such as group presentations as well.

Thirdly, even though a higher inductive type contains “constructors” which generate paths in that type, it is still an inductive definition of a single type. In particular, as we will see, it is the higher inductive type itself which is given a universal property (expressed, as usual, by an induction principle), and not its identity types. The identity type of a higher inductive type retains the usual induction principle of any identity type (i.e. path induction), and does not acquire any new induction principle.

Thus, it may be nontrivial to identify the identity types of a higher inductive type in a concrete way, in contrast to how in http://planetmath.org/node/87569Chapter 2 we were able to give explicit descriptions of the behavior of identity types under all the traditional type forming operations. For instance, are there any paths from $\mathsf{base}$ to $\mathsf{base}$ in $\mathbb{S}^{1}$ which are not simply composites of copies of $\mathsf{loop}$ and its inverse? Intuitively, it seems that the answer should be no (and it is), but proving this is not trivial. Indeed, such questions bring us rapidly to problems such as calculating the homotopy groups of spheres, a long-standing problem in algebraic topology for which no simple formula is known. Homotopy type theory brings a new and powerful viewpoint to bear on such questions, but it also requires type theory to become as complex as the answers to these questions.

Fourthly, the “dimension” of the constructors (i.e. whether they output points, paths, paths between paths, etc.) does not have a direct connection to which dimensions the resulting type has nontrivial homotopy in. As a simple example, if an inductive type $B$ has a constructor of type $A\to B$, then any paths and higher paths in $A$ result in paths and higher paths in $B$, even though the constructor is not a “higher” constructor at all. The same thing happens with higher constructors too: having a constructor of type $A\to(x=_{B}y)$ means not only that points of $A$ yield paths from $x$ to $y$ in $B$, but that paths in $A$ yield paths between these paths, and so on. As we will see, this possibility is responsible for much of the power of higher inductive types.

On the other hand, it is even possible for constructors without higher types in their inputs to generate “unexpected” higher paths. For instance, in the 2-dimensional sphere $\mathbb{S}^{2}$ generated by

• A point $\mathsf{base}:\mathbb{S}^{2}$, and

• A 2-dimensional path $\mathsf{surf}:\mathsf{refl}_{\mathsf{base}}=\mathsf{refl}_{\mathsf{base}}$ in ${\mathsf{base}=\mathsf{base}}$,

there is a nontrivial 3-dimensional path from $\mathsf{refl}_{\mathsf{refl}_{\mathsf{base}}}$ to itself. Topologists will recognize this path as an incarnation of the Hopf fibration. From a category-theoretic point of view, this is the same sort of phenomenon as the fact mentioned above that $\mathbb{S}^{1}$ contains not only $\mathsf{loop}$ but also $\mathsf{loop}\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}% }}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{% \scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle% \,\centerdot\,}}}\mathsf{loop}$ and so on: it’s just that in a higher groupoid, there are operations which raise dimension. Indeed, we saw many of these operations back in §2.1 (http://planetmath.org/21typesarehighergroupoids): the associativity and unit laws are not just properties, but operations, whose inputs are 1-paths and whose outputs are 2-paths.

Title 6.1 Introduction
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# Total Ordering on Field of Quotients is Unique

## Theorem

Let $\struct {K, +, \circ}$ be a field of quotients of an ordered integral domain $\struct {D, +, \circ, \le}$.

Then there is one and only one total ordering $\le'$ on $K$ which is compatible with its ring structure and induces on $D$ its given total ordering $\le$.

That ordering is the one defined by:

$P = \set {\dfrac x y \in K: x \in D_+, y \in D_+^*}$

## Proof

First, note that from Divided by Positive Element of Field of Quotients:

$\forall z \in K: \exists x, y \in R: z = \dfrac x y, y \in R_+^*$

Now we show that $P$ satistfies conditions $(1)$ to $(4)$ of Positive Elements of Ordered Ring.

From Addition of Division Products and Product of Division Products, it is clear that $P$ satisfies $(1)$ and $(3)$.

$\Box$

Next we establish $(2)$.

Let $z \in P \cap \paren {-P}$.

Then $z \in P$ and $z \in \paren {-P}$. Thus:

$\exists x_1, x_2 \in D_+, y_1, y_2 \in D_+^*: z = x_1 / y_1, -z = x_2 / y_2$

So:

$x_1 / y_1 = -\paren {x_2 / y_2} \implies x_1 \circ y_2 = -\paren {x_2 \circ y_1}$

But $0 \le x_1 \circ y_2$ and $-\paren {x_2 \circ y_1} \le 0$.

So $x_1 \circ y_2 = 0$.

As $0 < y_2$, this means $x = 0$ and therefore $z = 0$.

Thus $(2)$ has been established.

$\Box$

Now to show that $(4)$ holds.

Let $z = x / y$ where $x \in D, y \in D_+$.

Suppose $0 \le x$. Then $z \in P$.

However, suppose $x < 0$. Then $0 < \paren {-x}$ so $-z = \paren {-x} / y \in P$.

Thus:

$z = -\paren {-z} \in -P$

So:

$P \cup \paren {-P} = K$

So by Positive Elements of Ordered Ring, the relation $\le'$ on $K$ defined by $P$ is a total ordering on $K$ compatible with its ring structure.

$\Box$

Now we need to show that the ordering induced on $D$ by $\le'$ is indeed $\le$.

Let $z \in D_+$. Then $z = z / 1_D \in P$, as $1_D \in D_+^*$.

Thus $D_+ \subseteq P$ and $D_+ \subseteq D$ so $D_+ \subseteq D \cap P$ from Intersection is Largest Subset.

Conversely, let $z \in D \cap P$. Then:

$\exists x \in D_+, y \in D_+^*: z = x / y$

If $x = 0$ then $z = 0$, and if $0 < x$ then as $z \circ y = x$ and $0 < y$, it follows that $0 < z$ by item 1 of Properties of a Totally Ordered Ring.

So $\forall z \in D: 0 \le z \iff z \in P$.

Thus it follows that $z \in D \cap P \implies z \in D_+$, i.e. $D \cap P \subseteq D_+$.

Thus $D_+ = D \cap P$.

By item $(2)$ of Properties of Ordered Ring, we have:

$x \le y \iff 0 \le y + \left({-x}\right)$

and thus it follows that the ordering induced on $D$ by $\le'$ is $\le$.

$\Box$

Now we need to show uniqueness.

Let $\preceq$ be a total ordering on $K$ which is compatible with its ring structure and induces on $D$ the ordering $\le$.

Let $Q = \set {z \in K: 0 \preceq z}$.

We now show that $Q = P$.

Let $x \in D_+, y \in D_+^*$.

Then $0 \preceq x$ and $0 \prec 1 / y$ from item 4 of Properties of a Totally Ordered Ring.

Thus by compatibility with ring structure, $0 \preceq x / y$.

Hence $P \subseteq Q$.

Conversely, let $z \in Q$.

Let $z = x / y$ where $x \in D, y \in D_+^*$.

Then $x = z \circ y$ and by compatibility with ring structure, $0 \preceq x$.

Thus $0 \le x$ and hence $z \in P$, and so $Q \subseteq P$.

So $Q = P$.

Therefore, by item $(2)$ of Properties of Ordered Ring, it follows that $\preceq$ is the same as $\le$.

$\blacksquare$


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# zbMATH — the first resource for mathematics

Trigonometric integrals over one-dimensional quasilattices of arbitrary codimension. (English. Russian original) Zbl 1359.11071
Math. Notes 99, No. 4, 590-597 (2016); translation from Mat. Zametki 99, No. 4, 603-612 (2016).
The author of this paper studies the one-dimensional quasilattices $$Q=Q(\alpha, l_{1}, l_{2})$$ defined as the set of points $$\{x_{n}\}_{n=-\infty}^{\infty}$$ under the conditions $$x_{-1}=0$$, $$x_{n+1}=\{_{x_{n}+l_{2}, {n\alpha}\geq 1-\alpha.} ^{x_{n}+l_{1}, {n\alpha} <1-\alpha,}$$, where $$l_{1}, l_{2}$$ are arbitrary distinct positive numbers, $$\alpha$$ is irrational number. This paper is a continuation and generalization of the previous paper [the author, Math. Notes 97, No. 5, 791–802 (2015; Zbl 1331.11062); translation from Mat. Zametki 97, No. 5, 781–793 (2015)]. The author studies trigonometric integrals of the form $$I_{n,d}=\int_{\mathbb{T}^{d}}\int_{0}^{1}|f_{n}(\alpha, \lambda)|d\lambda d\alpha$$, where $$\mathbb{T}^{d}$$ is, as in the previous paper, exchanged tiling of the $$d$$-dimensional torus $$\mathbb{T}^{d}=T_{0}\bigsqcup T_{1}\bigsqcup \cdots \bigsqcup T_{d}$$. The main result is the following theorem: Let $$\varphi$$ be a monotone increasing function such that $$\varphi>0$$ for all positive integer $$n$$ and the series $$\Sigma_{n=1}^{\infty}1/\varphi(n)$$ converges. Then the following estimate holds: $$I_{n,d}=O(\ln^{d+1}n \varphi(\ln \ln n))$$. The paper ends with a posed problem about an inequality in the theory of Diophantine approximations.
##### MSC:
 11L03 Trigonometric and exponential sums, general 11H31 Lattice packing and covering (number-theoretic aspects)
Full Text:
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