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UNIT-1 THE SOLID STATE
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PART -1, , OUTLINE, , Characteristics of solids, Classification of solids, Classification of crystalline solids
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CLASSIFICATION OF SOLIDS, Types:1.Crystalline solid., , Crystalline(Quartz), , 2.Amorphous solid., , Amorphous(Glass)
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AMORPHOUS SOLIDS, The constituent particles have no regular, arrangement and have short range order., No sharp melting point and melt over a range, of temperature., Isotropic :- Physical properties are same in all, directions., Considered as pseudo solids or super cooled, liquids., Irregular cleavage., Amorphous solids on heating become, crystalline at some temperature., Ex: Glass objects of ancient civilization appear, milky . (Why……….), Amorphous solids have fluidity property., Ex: Glass windows in old buildings appear thick, at bottom . (Why……….)
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The constituent particles are orderly arranged ., Have long range order and sharp melting, points., Anisotropic :- some of the physical properties, like refractive index are different in different, directions., These are considered as true solids., They undergo a clean cleavage., Crystalline solids have definite heat of fusion., e.g. Diamond, Graphite, metals like Fe, Co, Cu, etc., Ionic compounds like NaCl, ZnS, KCl etc.
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CLASSIFICATION OF CRYSTALLINE SOLIDS, , MOLECULAR, SOLIDS, , NON POLAR SOLIDS, , IONIC, SOLIDS, , POLAR SOLIDS, , METALLIC, SOLIDS, , COVALENT (OR), NETWORK SOLIDS, , HYDROGEN BONDED, SOLIDS
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TYPES OF CRYSTALLINE SOLIDS, , 1.MOLECULAR CRYSTALLINE SOLIDS, Constituent particles are polar or non –, polar molecules or H-bonded molecules., , Iodine, , Force of attraction is dispersion force, or dipole- dipole interaction or hydrogen, bonding., Low melting and boiling point., Insulators, EX: Iodine, Iodine-unit-cell-3D-vdW, from wikimedia
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Constituent particles are ions., , Sodium, Chloride, , Force of attraction is ionic bond ., High melting and boiling points., Electrical insulators in the solid, state but conductors in aqueous, solution and molten state ., e.g: NaCl, LiF, MgO, ZnS, CaF2 etc., , Sodium-chloride-unit-cell-3D fro, wikimedia
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Constituent particles are +vely, charged metal ions (Kernels) and free, electrons., Force of attraction is metallic bond., High electrical and thermal, conductivity., Malleable and ductile., Sea of Free Electrons Theory, , High melting and boiling point., e.g.: Fe, Cu, Ag, Mg etc
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Constituent particles are, neutral atoms., Force of attraction is covalent, bond ., High melting point, Insulators, e.g.: Diamond, quartz, SiC,, AlN,, Conductor :- Graphite
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Graphite
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SUMMARY, Characteristics of solids, Classification of solids:-Crystalline and, amorphous, Classification of crystalline solids :Molecular , Ionic, Metallic and Covalent, solids .
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QUESTIONS, 1. Allotropy And Polymorphism, 2. Why is glass of window panes of very old buildings, found to be thicker at the bottom than at the top and, why is it milky?, 3.Glass is Amorphous whereas Quartz is Crytalline, but both are formed with SiO2 ; How?, 4. What type of interactions hold the molecules, together in a polar molecular solid?
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CRYSTAL LATTICE AND LATTICE POINT, , The, The regular arrangement of, the, constituent, particles, (atoms ,ions or molecules )of a, crystal in three dimensional, space is called crystal lattice or, space lattice, Each point in a crystal lattice, is called lattice point or lattice, site.
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UNIT CELL, , Unit, Unit cell is the smallest, portion of the crystal lattice, which , when repeated in, different directions generates, the entire lattice ., Unit cell is characterized by, following parameters., (i) Edges (a, b ,c), (ii)Angle between the edges .
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Types :Primitive or simple Unit cells, Centered unit cells, :, When constituent particles are, present only at the corners of a, unit cell, it is called primitive, unit cell.
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:, Constituent particles are present at and other, other centred positions., (i), :, Constituent particles at each corners and one, at the centre of the body., (ii), :, Constituent particles at each corners and, other at the centre of the faces., (iii), :, Constituent particles at each corners and, other at the centre of the alternate faces.
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NUMBER OF PARTICLES PER UNIT CELL
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VISUALIZATION OF UNIT CELL, , Courtesy – Next Education
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QUESTIONS, 1. What is the significance of lattice point?, 2. Explain how much portion of an atom, located at (i) corner and (ii) body centre of a, cubic unit cell is part of its neighbouring unit, cell.
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PART -3, , OUTLINE, , • Review of previous session, • Closed packing in solids, • Voids in solids
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REVIEW OF PREVIOUS SESSION, Characteristics of solids, Classification of solids:-Crystalline and amorphous, Classification of crystalline solids :- Molecular , Ionic,, Metallic and Covalent solids ., Crystal lattice and lattice points, Unit cell :- Primitive and Centred(bcc, fcc , ecc), Bravais lattices:- 14 types(7 Primitive and 7 Centred ), No. of atoms of unit cell :- For scc-1atom,, bcc-2 atoms and fcc-4 atoms.
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CLOSE PACKING IN SOLIDS, The constituent particles in solids are, close packed leaving minimum vacant, space ., The packing pattern follows in one, dimension , two dimension and three, dimension ., The no. of spheres neighbor to one, sphere, is called its co-ordination, number.
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CLOSE PACKING IN SOLIDS, , CLOSE PACKING IN ONE DIMENSION, , • In one dimensional close packing arrangement , each, sphere is in contact with two of its neighbours ., •, , Coordination number is 2 .
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CLOSE PACKING IN TWO DIMENSION, Square close packing in 2D(AAA….type ) : Second row is placed adjacent to the, first row and so on ., Co-ordination no. is 4 ., Hexagonal close packing in, 2D(ABAB….type) : second row is placed in the, depressions of spheres adjacent to first, row ., Co-ordination no. is 6 .
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PLACING OF SECOND LAYER ON FIRST LAYER, , • When the second layer of spheres is placed in, the depressions in first layer , two types of, voids get formed., Tetrahedral, voids, Octahedral, voids
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VOIDS IN SOLIDS, • The vacant space surrounded, by the spheres in the solids are, called voids., , Types:1. Tetrahedral voids :Holes surrounded by 4, spheres., 2. Octahedral voids :Holes surrounded by 6, spheres.
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NUMBER OF VOIDS IN SOLIDS, , , , Let the no. of close packed spheres = N, , Then the no. of octahedral voids = N, Then the no. of tetrahedral voids = 2N
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CLOSE PACKING IN THREE, DIMENSION(AAA…TYPE), , 3D close packing from 2D square, close packed layers :• Spheres of the second layer are, placed just above the first layer, and so on, as AAA…..type ., • The lattice generated in simple, cubic lattice ., • Unit cell is primitive ., • e.g. polonium
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CLOSE PACKING IN THREE DIMENSION, , 3D close packing from 2D, hexagonal close packed, layers :• Spheres of the second layer are, placed in the depression of first layer, ., • The third layer covers the tetrahedral, voids and forms ABAB…. Pattern and, forms hcp ., • Coordination no. is 12 .
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CLOSE PACKING IN THREE DIMENSION, 3D close packing from 2D, hexagonal close packed, layers :• Spheres of the second layer are, placed in the depression of first, layer ., • The third layer covers the, octahedral voids and forms, ABCABC…. Pattern and forms ccp, ., •, , Coordination no. is 12 .
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When Next 3rd layer is placed on T(Tetrahedral Void) Pattern is ABAB.. Type or, Hexagonal Close packing, e.g. Mo, Mg, Be, When Next 3rd layer is placed on O(Octahedral Void) Pattern is ABCABC.. Type or, Cubic Close packing, e.g. Fe, Ni, Cu, Ag, Au and Al, Both are equally efficient Have Packing Efficiency of 74%
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Size of T-Voids & O-Voids, , • Octahedral Void > Tetrahedral Void, • Should it Depend on the Size of Sphere/Particle?, • If R is the radius of the sphere in Closed packing, then;, – Radius (r) of the tetrahedral Void = 0.225R, – Radius (r) of the Octahedral Void = 0.414R
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SUMMARY, • Close packing pattern in one , two and three, dimension in solids., • Tetrahedral and octahedral void .The number, of tetrahedral voids are double the number of, spheres in the solid., • Size of Tetrahedral Void(0.225R) and, Octahedral Voids(0.414R).
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QUESTIONS, 1. Distinguish between, a)hexagonal close packing and cubic close, packing., b) Tetrahedral void and octahedral void
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PART -4 OUTLINE, , • Packing efficiency, • Calculation of packing efficiency in simple, cube ,bcc and fcc
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RELATION BETWEEN EDGE LENGTH(a) AND, RADIUS(r) OF ATOM, SCC, , FCC, , BCC
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PACKING EFFICIENCY, The fraction of the total volume of the crystal occupied by the, constituent particles is called packing efficiency ., Packing fraction=, , Volume of atoms per unit cell, Volume of unit cell, , Packing fraction=, , Number of atoms per unit cell Volume of one atom, Volume of unit cell, , n 43 r 3 3, Packing fraction =, , a = volume of cubic unit cell, 3, a, , a = edge length or side length of the unit cell, r = radius of atom, n = no of atoms per unit cell
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PACKING EFFICIENCY, Packing efficiency of simple cubic unit cell :a =2r, Volume of cubic unit cell = a3, PACKING EFFICIENCY, = volume occupied by One spheres x 100%, total volume of the unit cell, = 1 x (4/3)πr3 x 100%, (2r)3, , = π x 100, 6, , = 52.36% = 52.4%
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PACKING EFFICIENCY, Packing efficiency of face centred cubic unit cell :In ∆ABC, , AC2=BC2+AB2, b2=a2+a2, b= √2 a, , If r is the radius of the sphere, b= 4r= √2 a, a=4r/√2, PACKING EFFICIENCY = volume occupied by four spheres x 100%, total volume of the unit cell, = 4 x (4/3)πr3 %, (2 √2r)3, = (16/3)πr3 %, (16 √2r)3, = 74%
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COMPARISON OF PACKING EFFICIENCIES
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Summary, • Packing efficiency :- SCC - 52.4% , FCC – 74% ,, BCC – 68 % ., • packing efficiency is maximum in FCC unit, cell.
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DETERMINATION OF THE FORMULA OF THE, COMPOUND, , • A cubic solid is made of two elements X and Y., Atoms Y(anions) are at the corners of the cube, and X(cations) at present at face-centre of the, cubic lattice. What is the formula of the, compound?, Ans :Number of X atom per unit cell = 1/2 x 6 = 3, Number of Y atom per unit cell = 1/8 x 8 = 1, Formula of compound = X3Y
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DETERMINATION OF THE FORMULA OF THE, COMPOUND, , • A cubic solid is made of two elements X and Y., Atoms Y are at the corners of the cube and X, at the body centre. What is the formula of the, compound?, Ans :-, , Number of X atom per unit cell = 1, Number of Y atom per unit cell = 1/8 x 8 = 1, Formula of compound = XY
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CALCULATION OF THE DENSITY OF THE, UNIT CELL
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Silver crystallizes in FCC lattice. If edge length of the, cell is 4.07 × 10–8cm and density is 10.5 g cm–3,, calculate the atomic mass of silver, Ans:, Given:, Edge length, a = 4.077 × 10−8 cm, Density, d = 10.5 g cm−3, The given lattice is of FCC type,, Thus the number of atoms per unit cell, z = 4, We also know that NA = 6.022 × 1023 / mol, let M be the atomic mass of silver., We know,, , => M = da3Na / z, M = (10.5 x 4.077 × 10−8 x 6.022 × 1023 ) / 4 = 107.13 g /mol
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NUMERICALS, • 1.Chromium metal crystallizes with a body centred cubic lattice, The length of unit cell is found to be 287 pm. Calculate atomic, radius, the number of atoms per unit cell and density of, chromium. (Atomic mass of Cr = 52. g/ mol Avogadro No. = 6.02 x, 1023), • 2. Silver forms ccp lattice and X-ray studies of its crystals show, that the edge length of its unit cell is 408.6pm. Calculate the, density of silver( Atomic mass = 107.9 u), • 3. Niobium crystallizes in body centered cubic structure. If density is, 8.55 gm/cm3, calculate atomic radius of niobium using its atomic mass, 93u .
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Suppose the atoms N in the ccp = n, No. of tetrahedral voids = 2n, As 1/3 rd of the tetrahedral voids are occupied by atoms M, therefore,, No. of atoms M = 2 n /3, Ratio of M : N = 2 n / 3 : n = 2 : 3, Hence, the formula is M2 N3
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Questions, 1.Calculate the packing efficiency in case of, a metal crystal for body centred cubic ., 2.What is the packing efficiency of a simple, cube?, 3.Which unit cell has maximum packing, efficiency and what is the packing, efficiency percentage?
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PART 5, , OUTLINE, , • REVIEW OF PREVIOUS SESSION, , • IMPERFECTIONS IN SOLIDS, • TYPES OF POINT DEFECTS
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REVIEW OF PREVIOUS SESSION, • Close packing pattern in one , two and three, dimension in solids., • Tetrahedral and octahedral void ., , • Packing efficiency :- SCC - 52.4% , FCC –, 74% , BCC – 68 % .
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IMPERFECTION IN SOLIDS, Any deviation from perfectly ordered arrangement of, constituent particles In crystal lattice is called, imperfection in solids ., , Ideal crystal, , After imperfection
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Types of imperfections, There are 2 types of imperfections known in crystal, lattice., • Point defect :- Arises due to disorder in the, regular arrangement of constituent particles, around a point ., • Line defect :- Arises due to disorder in the regular, arrangement of constituent particles in entire, row .
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TYPES OF IMPERFECTIONS, Types of point defect :- 1.Stoichiometric defect, 2. Non- stoichiometric defect, 3. Impurity defect, STOICHIOMETRIC DEFECT, Vacancy defect, , Non Ionic, Compounds, , Interstitial defect, Frenkel defect, Schottky defect, , NON- STOICHIOMETRIC DEFECT, Metal excess defect, Metal deficiency defect, , Ionic, Compounds, , Non Stoichiometric compounds are known as Berthollides
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STOICHIOMETRIC DEFECT:, , VACANCY AND INTERSTITIAL DEFECT, • These are seen in non ionic compounds., • Vacancy defect :- Arises when some of, the lattice points are left vacant during, the crystal formation ., • Interstitial defect :- Arises when some of, the constituent particles accommodate, in the interstitial sites other than the, lattice points.
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STOICHIOMETRIC DEFECT:, , SCHOTTKY DEFECT, • It is seen in ionic compounds., , • Equal no of cations and anions are missing from their lattice sites generates, SCHOTTKY DEFECT., , •, , The vacancy defect(schottky) of ionic solids decreases the density of solid, , • Shown by the crystals with high coordination no. and similar size of cation and, anion ., • e.g.NaCl, KCl, NaBr, AgBr and CsCl
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STOICHIOMETRIC DEFECT:, , FRANKEL DEFECT, , • It is seen in ionic compounds., • In ionic solids in which the smaller ion i.e. cation is dislocated from its, normal site to an interstitial site generates Frenkel defect., , • In the interstitial defect (Frankel) of ionic solid ,density remains same., • Shown by the crystals with low coordination no. and large difference in the, size of cation and anion., •, , e.g. ZnS, AgCl, AgBr, AgI. (Not found in Alkali metal Halide)
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NON- STOICHIOMETRIC DEFECT:, , METAL EXCESS DEFECT, By Anion Vacancies, , By Presence of extra Cations at, interstitial sites., , By anion vacancies :It is seen in alkali halides., • An anion may be missing from the lattice sites, and the, hole is occupied by an electron that maintains electrical, neutrality is known as, F-centre. ( Farbenzenter), •, , The crystals become coloured due to excitation of these, unpaired electrons when they absorb energy from visible, light falling on the crystals ., , •, , Excess of Li-makes LiCl crystals pink , K -makes KCl, crystals violet and Na –makes NaCl crystals yellow .
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NON- STOICHIOMETRIC DEFECT:, , METAL EXCESS DEFECT, , By extra cations :• Arises due to the presence of extra cations in, the interstitial sites(Similar to Frenkel Defect) ., •, , Electrical neutrality is maintained by an, electron present in neighboring interstitial sites., , • ZnO is white in colour at room temp. When ZnO, is heated, it loses oxygen and turns yellow., ZnO, white, , Zn 2+ + 1/2 O2 + 2 eyellow
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NON- STOICHIOMETRIC DEFECT:, , METAL DEFICIENCY DEFECT, • Occurs when Metal shows Variable, Valency i.e. Transition metals, • Due to missing of cation from its, lattice site and presence of the, cation(of same metal) having, higher charge at adjacent site., • Examples: FeO, FeS, NiO., • Due to this reason it is difficult to, prepare FeO with Ideal, Composition. We actually obtain, FexO where x=0.93 to 0.96.
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IMPURITY DEFECT, • Arises when foreign atoms are present at the, lattice site in place of host atoms generates, impurity defect., • When a little amount of SrCl2 is added to, NaCl, then at some lattice sites Na+ ions are, substituted by Sr 2+ maintaining electrical, neutrality ., •, , The cationic vacancies produced are equal to, number of Sr 2+ ions added., , • Similar Type of Defect is Observed when, CdCl2 is added to NaCl., SrCl2 added to NaCl
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SEMICONDUCTORS, INTRINSIC SEMICONDUCTOR :Elements like Si and Ge, • Show too low electrical conductivity, which increases with temperature ., e.g. Si and Ge., Silicon, , •, , Conductivity can also be increased by, adding appropriate amount of suitable, impurity , process is called doping ., , • Impurity is of two types :Electron rich impurity and, Electron deficit impurity., , Germanium
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SEMICONDUCTORS, EXTRINSIC SEMICONDUCTOR :• A doped intrinsic semiconductor is called extrinsic semiconductor ., •, , Types :1. n-type semiconductor (Doped with electron rich impurities ), 2. p-type semi conductor (Doped with electron deficient impurities)
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Line Defect (Not is Syllabus)
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QUESTIONS, • Effect of Defects on Stability?, • Effect on Conductivity?, • Which is a Berthollide compound?, What type of stoichiometric defect is shown by AgCl?, What are F-centres?, Which crystal defect lowers the density of solid?, Which point defect in its crystal unit increases the, density of a solid?, • Why ZnO becomes yellow on heating ?, •, •, •, •
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SUMMARY, IMPERFECTIONS IN SOLIDS :, Line and point defects, TYPES OF POINT DEFECTS –, Vacancy defect, interstitial defect, Schottky, defect, Frenkel defect, • Impurity defect, stoichiometric defect, non, scoichiometric defect, •, •, •, •
