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UNIT-I Paper Code: PHY 521 WKB approximation Quantisation rule Tunnelling through a barrier Qualitative discussion on α-decay Time dependent perturbation theory and transition probability. UNIT-II Laboratory and centre of mass frames Differential and total scattering cross section Scattering amplitude Scattering by spherically symmetric potentials Partial wave analysis and phase shifts Scattering by a rigid sphere and square well Coulomb scattering Formal theory of scattering – Green function in scattering theory Lippman- Schwinger equation Born Approximation. UNIT-III Meaning of identity and consequences Symmetric and anti symmetric wave functions Slater determinant Symmetric and antisymmetric spin wavefunctions of two identical particles Collision of identical particles UNIT-IV Ladder operators Eigen values and Eigenfunctions of L2 and Lz PHYSICS CHE521: QUANTUM MECHANICM PG SEMESTER:- II, PAPER: - V Using spherical harmonics Angular momentum and rotations Total angular momentum J L-S coupling; eigenvalues of J2 and Jz Addition of angular momentum Clebsch- Gordan coefficients for j1= j2=1/2 and j1=1, j2=1/2 Coupled and uncoupled representation of eigenfunctions Angular momentum matrices Pauli spin matrices Spin eigenfunctions Free particle wavefunctions including spin Addition of two spins. UNIT-V Klein – Gordon equation Feynman-Stuckelberg interpretation of negative energy states and concept of antiparticles Dirac equation Covariant form Adjoint equation Plane wave solution and momentum space spinors Spin and magnetic moment of the electron Non relativistic reduction. Helicity and chirality Properties of γ matrices Charge conjugation Normalisation andcompleteness of spinors.
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red clay pottery
Unit 1 Red clay pottery 1. Pre-historic background In red clay pottery, various prehistoric figures indicate a high degree of artistry and excellent conceptions of designs. a. Assumption The primitive races of the society must have taken some clays, as they found on the surface of the ground, or by some river bed, then picking up the rocky fragments, beating it with hand or with stones etc. to prepare a mix for shaping by hand, the shapes as needed or fancy dictated. At first this simple handmade pottery would have been hardened by drying in sun or by some accidental fire on unbaked clay articles should have brought out the fact that the baked clay articles becomes hard in different colors- buff, brown, red, smoked etc. on firing. b. Mythological There are many legends in mythology about the discovery of clay for pottery purpose. 1. The first may at that at the beginning of human civilization, when the god “Brahma”, the creator of the universe, had made use of clay to prepare a model man into which he breathed life. Then named those assistants as “PRAJAPATHI” meaning the creator of “man”. Who helped him to prepare models of man. That is why, this section of primitive race, which used to work with clay in India is called “Prajapathi”. 2. Secondly, when lord Shiva intended to marry the daughter of Hemwants kumhar, a Brahmin, made a kulalka (water pot) with the help of Sudarshan Chakra of lord Vishnu to be used as a wheel and the mountain of Mandra to be used as a pivot beneath to hold it up and thus carried out marriage ceremony. Ever since his descendants have been known as Kumbhars or makers of water jars. It is also said that lord Shiva took two beads from his necklace and created a man and a women for making water pots of khubhas. Thus the cast of kumhars or potters started. Also in Ramayana age, it is said that when Sita faced the problem of carrying water on big leaves from Nandakani River to her ashram. She had to procure a matka these legends. 3. Archeological If we study the pre-historic civilizations based on excavations and frequents found of terracotta wares. In one or two instances fragments of that has been described as pottery have been found, estimated to be 10000 years or early, but no finished articles have been unearthed of that period, these fragments show a crude attempt of decoration generally made with a piece of stick or impresses of the figure. While the potteries of later times are hard fired and the decoration included both engraved and painted designed vessels and often given a striking and beautiful effects. These fragments of terracotta wares of low quality and with crude attempts of decoration seems to be period of earlier stage human civilization i.e. pre historic period, but it has been studied that these pre-historic periods may not have begin at the same times at two places as it depends on the start of human civilization at those places and keeping in view only the pre-historical background based on excavations so far carried out may be specifically looked on- a. Western pottery • Ancient Fareast and Egypt • Ancient Aegean and Greek • Etruscan and Roman • Fes Islamic • European: to the end of 18th century b. Eastern and South East Asian Pottery • China • Korea • Japan • Thailand and Annam c. American Indian Pottery • North America • Central America • South America As per archaeological studies so far conducted, the places of earliest the main centers of ancient civilization to be- • Nile • Mesopotamia • Indus-Valley • Yellow River basin Ancient Far East & Egypt (Western Pottery) In the early 1960, excavations revealed that in Egypt, the handmade pottery was made in great variety in the predynastic period and hard fired wares of good quality ware attained in later period, most common variety has decoration with dull white pigment fired on pale clay in dark ferruginous earth fused with alkaline flux. But as early as the first dynast figures, vases and tiles of the material were covered with the fired glass (frit), and then were colored turquoise and green with copper oxide. The pottery of ancient Greek, prehistoric and historical is distinguished from all other fictile wares of same ages by its free development of naturalistic painted decoration and the excavations revealed that handmade pottery with highly polished surface was developed during the period 6000 to 3000 B.C. and the main centers of production ware Thessaly and Crete. Though, the painted pottery was developed in pre historic Mesopotamia and Egypt long before its appearance in Aegean Lands. In India, Initially the excavations in the region of Indus-valley at Harappa in Punjab and Mohenjo-Daro in Sind were started and have revealed that the potters, around 2700 B.C were working with well burnt bricks, sculptures in terracotta etc. All the sculptures were round in shape i.e. wheel made and mostly painted/incised, the shapes were varied, but types with handles are rare. The painted designs are usually in black on a dark slip and consist of advanced geometrical patterns, foliar motifs and occasional animal figures. The dark red and black ware has been found abundantly at Nal in Baluchistan, also on Waziristan frontiers. Secondly, when the Indian culture was flourishing, the development of human civilization was more in provincial forms and thus skilled potters settle down or extended their art on migration to other parts of northern India at different provinces. Specially, overall area reaching from Baluchistan to Kathiawar and through rajputana to Ganges valley, Islamic potters since 1000 A.D, and the skilled potters were brought from these Muslim countries. These Islamic potters were given full support in all respects of life and settled down in alluvial plains along with Muslim Empherous as the clay of that area was better than other fields but they used to keep their skills in their families. Just after the downfall of Mughal Empire, some of the Islamic potter to earn more living hood, setting down in villages nearby Gangetic bell viz. Chunar, Roorkee around Gorakhpur, Jhansi, Ajamgarh and Lucknow etc. in Uttar Pradesh. The potter had the skill and knew the technique for making the red and black terracotta but these potters did not changed the items of production to get better price then the products of daily needs. But since the downfall of Mughal Empire in India had due to strong competition with metal items of artifacts nature, the skilled potters also started facing competition due to poor sales network and exploitation by the middle man in their trade. These potters also started making the products of daily need to encash their products immediately viz. milk kulhar, water pots, surahi, bowls etc. and encashed them by selling, while flower vases, astray, bonsai and ekabana pots etc. were produced in very limited quantity against specific order. As the products were low valued, they were forced to work under financial crises, which resulted in low quality products using low grade clays and firing at lower temperature to reduce the fuel cost. 2. Raw materials The oldest ceramic raw material is clay, which is the most abundantly and cheaply available. It can be defined as an earthy material that forms a coherent, sticky mass which is readily moldable when wet but if it dries, it becomes hard, brittle and retains its shape. Moreover, if heated to redness, it becomes still harder and is no longer susceptible to action of water. These common clays are the weathering product of igneous, sedimentary and metamorphic rocks. Due to different climatic conditions prevailing in India, the available clays can be divided broadly into seven groups. Generally, the alluvial, black cotton and red clays are the clays of potter’s interest. a. Alluvial clay – are the secondary clays, being carried and deposited by rivers and are found in deltas and river valleys. These clays are grey coloured and consists of sand and silt in association with hard Kankar and are of fairly slagging nature. The plasticity of these clays varies from poor to very high depending upon the nature of weathering. The chemical and rational analysis show that high content of fluxy material makes the soil low fusible and the presence of calcite and magnesite deteriorates the fired colour of clay developed due to coloring elements. Chemical analysis Wt % Rational Analysis Wt % SiO2 55.52 Muscovite 12.08 Al2O3 15.00 Haematite 7.63 Fe2O 3.61 Calcite 11.93 TiO2 0.84 Anatase 0.84 MgO 1.83 Magnesite 3.81 CaO 6.69 Free quartz 24.76 Na2O 3.39 K2O 1.64 L.O.I 7.24 b. Black cotton soil- is grayish and is clayey to loamy, composed largely of clay material. It is generally black and contains high alumina, lime and magnesia. It swells considerably on addition of water and dries up with conspicuous cracks by losing the moisture. The swelling property is due to high content of montmorillonite and badyellite group of clay minerals. Chemical analysis Wt % Rational analysis Wt % SiO2 72.21 Kalomite 19.73 Al2O3 8.75 Quartz 5.22 Fe2O3 7.90 Feldspar 59.68 TiO2 0.25 Haematite 7.90 CaO 3.40 Rutile 0.25 MgO 0.40 Calcite 3.40 Na2O 0.52 Magnesite 0.40 K2O 0.36 L.O.I 6.11 c. Red soil- consists mainly of kaolinite. However, the association of montmorillonite and illite group are also frequent. The presence of highly silicious and ferruginous impurities and other stony materials have an adverse effect on the vitrification behavior and fired properties of the clay. These clays are not used directly and are generally admix with non-plastic materials/additives (10-40%). These additives impart strength and reduce water absorption. With the advancements of science and technology, the rural artisian can utilize all other types of clays i.e. mountainous clay, desert clay and laterite clay as well. However, the percentage of utilization is limited to 40% with some additives, like low grade fire clays, ball clay etc. These additives are essential to enhance the firing temperature and getting the desired properties. Chemical analysis Wt % Rational analysis Wt % SiO2 64.16 Feldspar 28.90 TiO2 0.78 Kaolin 31.06 Al2O3 16.94 Quartz 30.82 Fe2O3 5.38 Calcite 1.97 CaO 1.14 Magnesite 1.09 Na2O 1.46 Haematite 5.37 K2O 2.82 Rutile 0.79 L.O.I 6.35 d. Mountainous soil The grit content I the mountainous soil must be as low as possible, otherwise extra labour cost will be required for its processing. Higher percentage of residue is responsible for low plasticity. Atterberg no. and dry strength, whereas, higher percentage of final particles is responsible for better plasticity and dry strength, though increasing dry shrinkage. The even distribution of particles also enhances the dry strength. Chemical analysis Wt % SiO2 62.12 TiO2 1.07 Al2O3 12.27 Fe2O3 8.99 CaO 4.54 MgO 0.99 Na2O 1.70 K2O 2.28 L.O.I 5.69 e. Desert Soil In order to utilize the desert soil economically in pottery, it has to be admixed with other additives in definite proportions and crushed in ball mills to a certain mesh size. The additives are very specific to result in a tri-axial body along with common clays after being fired which are mainly sand, rice husk ash, grog and other feldspathic materials if required. The texture and shrinkage of the body is dependent on the fineness and grain size distribution. Chemical analysis Wt % Rational analysis Wt % SiO2 63.82 Feldspar 40.52 TiO2 0.98 Kaolin 18.87 Al2O3 15.31 Quartz 27.28 Fe2O3 4.97 Calcite 4.36 CaO 2.47 Magnesite 4.98 MgO 1.48 Haematite 4.92 K2O 3.02 L.O.I 5.22 f. Laterite clay Laterite is associated with the black hard kankar. Its moderate slaking nature indicates moderate cohesion between the clay particles. Grit content is substantial. Higher percentage of finer particles reveals good plasticity of clay. The dry M.O.R value is high due to even distribution of the grains of different sizes. Presence of bentonitic minerals is also impart higher Atterberg no., dry liner shrinkage and dry M.O.R and low apparent volume porosity. The fired colour varies from brownish red to blackish red. Presence of bentonitic mineral can also produce cracks while firing. Rational analysis show substantial quantity of free quartz along with feldspathic and micaceous materials. Coloring oxides are deteriorated by the presence of calcite and magnesite as thay are adequate enough to bleach the colour while firing. Chemical analysis Wt % Rational analysis Wt % SiO2 69.70 kaolinite 14.45 TiO2 0.79 Feldspar 36.89 Al2O3 12.22 Quartz 40.80 Fe2O3 4.31 Rutile 0.82 CaO 1.10 Haematite 4.45 Na2O 1.80 Magnesite 0.57 K2O 3.46 L.O.I 6.64 Formation of soil The earth crust is composed of three types of rocks viz. igneous, sedimentary and metamorphic. Igneous rock is the source of all other kind of rocks. Igneous rock is formed by the effect of volcanic eruption and subsequent solidification of the lava. These rocks are subjected to the variation of temperature, pressure, water, salinity, composition and as a result are weathered and disintegrated and still further divided into tiny pieces by friction. Under suitable conditions, these are carried and deposited by flowing water and air into undisturbed basins and thus sedimentary rocks are formed. Igneous and sedimentary rocks may again be transformed into different rocks without changing their overall compositions, these are called metamorphic rocks. Of these rocks, sedimentary rocks are the chief source of clay. The sedimentary rocks are easily weathered and disintegrated and are deposited by combination of several weathering and depositing agents through centuries. Mineralogy The basic rocks from which the rocks are formed are complex alumino-silicates. During weathering, these are hydrolyzed, alkali and alkaline earth ions form soluble salts and are leached out and the remainder is hydrated alumino-silicates of varying composition and structure and free silica. The hydrated silicates of Al are the clay substances • Extremely small/ fine flake like particles. • Controls the physico-chemical properties. Kaolinite group Basic structure consists of O atoms arranged to give alternate layers of tetrahedral holes and octahedral holes. • Si in tetrahedral sites and Al in 2/3rd of octahedral sites form Kaolinite, rarely dickkite and nacrite. • Si replaces Al in octahedral sites, a continuous series- anuaxite- thin hexagonal plates. • Basal spacing – 7.2 Ao , tend to become stacked on top of each other and loosely cemented into aggregates. • Adjacent O layers are able to take up a unimolecular H2O layer, making basal spacing 10 Ao Halloysite. • A continuous series between Kaolinite and halloysite, intermediate- livesite Montmorilonite group • Two layers of tetrahedral sites to every octahedral site. • These minerals absorb large quantities of water between adjacent layers, changing basal spacing from 10 to 20 Ao • O lattice can accommodate different atoms. • Octahedral site- Al, Mg, Fe+2, Zn • Tetrahedral sites- Si or Al. Illite group • These minerals resemble mica. • Have large space to contain cations. • Finely divided, makes accessible to exchange of cation Additives Additives are fillers used in the clay mix to improve the properties before and firing. The generally used additives are silica sand, rice husk ash, red clay and white clay grog, quartz, feldspar, ball clays and talc etc. 1. China clay/Fire clay/Ball clay – These clays having molecular formula (Al2O3.2Sio2.2H2O) are the principle constituents of kaolin or china clay. Plasticity of these clays is a very important factor which depends upon the shape, size and the distribution of clay particles. They are basically used to improve the whiteness and the maturing temperature of the body mix as well as the firing range. These white clays basically differ from red clays in respect of higher percentage of Al2O3 and very low percentage of Fe2O3 which effects in increasing the maturing temp. China clay plays an important role in ceramic bodies in both unfired and fired states. It is necessary to know their characteristics before their implementation into the body. The following tests are conducted to know the characteristics of the clays to judge their stability for a particular body. • Colour • Residue • Dry shrinkage • Dry strength • Particle size distribution • Water of Plasticity • Rheological properties • Fired colour • Fired shrinkage • Fired strength • Water absorption • Chemical analysis • DTA/ TG etc. Ball clay is plastic sedimentary clay. It imparts high green strength and good workability to pottery bodies. The primary mineral phase is Kaolinite. Micaceous minerals and quartz are the dominant minerals present as impurities along with the minor impurities feldspar, chlorite, titanium compound, pyrites, haematite etc. Ball clays also contain varying amounts of carbonaceous matter. The carbonaceous matter in colloidal form influences the physical properties of the clays. Ball clays are much finer than the china clays. Finer particle size imparts high shrinkage as well as high strength. In internal practice, ball clays are used in the range of 10-40% in various traditional bodies. Fireclay mainly consists of mineral kaolinite with minor amounts of other clay minerals, quartzite, iron and titania bearing materials. Mineralogical studies reveal a disorder in the structure of kaolinite present in the fireclays. The fireclays are used in the manufacturing of refractories, and are capable of withstanding temperatures around 1700oC. Fireclays have two modes of occurrences (1) fairly well defined beds associated with coal seam and (2) lenticular beds associated with other coarser sediments. The colour and other characteristics usually vary depending on the mode of formation. Their chemical parameters determine their suitability in refractory industry which include 60-62% SiO2, 24-36% or above Al2O3 and < 5% total fluxes of which the alkalies and iron should be particularly low. Fireclays include both plastic and non plastic varities. Non-plastic fireclays are generally used in making grogs. A good quality fireclay must have 24-26% water of plasticity and shrinkage and after firing it should be within 6-8%. 2. Quartz/Quartzite/Silica sand- • Mineralogical name of silica is quartz or quartzite. • Chemical formula is SiO2 • Specific gravity- 2.65 to 2.66 • Hardness on Moh’s scale- 6 • Silica sand is another form of SiO2 which does not required calcinations before use. • Quartz and quartzite is used after calcination as well. • It melts at 1730OC and form high viscous glass. • The free quartz undergoes phase transformation during thermal change and consequently volume changed takes place which leads to the development of stresses in the structure. • It is widely used as inexpensive hard and chemically stable filler. • Controls both drying and firing shrinkage. • Remains almost non-reactive during firing but dissolves partly in the feldspar melt to form a highly viscous liquid. • Aids in resistance to the corrosive action of acids. • Helps to develop strength and hardness. 3. Feldspar • It is mostly of three varieties- Potash feldspar (K2O.Al2O3.6SiO2), soda feldspar (Na2O.Al2O3.6SiO2) and lime feldspar (Cao.Al2O3.2SiO2). • Potash feldspar is suitable for the body mix due to the formation of high viscous liquid during firing. • Soda feldspar is suitable for glazes due to formation of low viscous liquid during firing. • Lime feldspar is suitable for glass industry. • It acts as a flux. • Fluxing action depends on the type of alkalies present. • Permissible limit of iron oxide in feldspar is 0.07 to 0.15%. 4. Red clay grogs and white clay grogs • Small grains of any type of fired clay are known as grog • Grains of fired red clay bricks or lump are known as red clay grog • Grains of fired white burning clays are called fireclay grogs. • Grog works as an anti shrinkage agent in the body mixes. • Grog should be of various sizes to give better interlocking of grains. • It also improves mechanical and thermal shock properties. 5. Rice husk ash Rice husk ash (RHA) contains an active form of silica (87-97% of SiO2) with small amount of alkalies and other trace elements and is available in large quantities in India. Presently about 30 million tons of rice husk is produced in India per annum. Rice husk contains ash from 13 to 29% by weight depending on the variety, climate and geographic location. About 6 million tons of rice husk ash is produced in India, which is mostly thrown away as waste. The silica in rice husk is in hydrated amorphous form either opal or silica gel. The use of rice husk ash in the form of silica in the ceramic field reported by some scientists. Rice husk ash which contains active silica in large amounts also contains high proportion of carbon in the composition and hence is presently disposed off by the rice mill industry as waste. Due to the substantial carbon content, it has so far not been used in whiteware manufacture. Rice husk ash with minor or negligible amount of carbon, if incorporated in a whiteware composition, could be used to make an improvement in the properties and might be beneficial in many ways for the development of technical ceramics. It has been found that complete replacement of quartz by RHA drastically reduces both the maturing temperature and the percentage of thermal expansion, and increases the strength marginally in whiteware bodies.
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Handbook on Refractory
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