The Solid State

As we know matter exists in mainly three states – solid, liquid and gas. These three physical states differ in terms of many properties. They differ in terms of their intermolecular interaction, the kinetic energy of individual particles, interatomic distances, electrical conductivity, etc. Solids are found on a large scale in the form of objects we witness every day. Along with the two other significant physical states, solids make up the universe that we inhabit. But as students, we must be aware of the fact that there are states of matter other than solid, liquid and gas. Students will come across these ideas in higher classes. But, for convenience, we are limiting our study to the basic three states. Here we are discussing the solid state of matter in detail. 

Characteristics of Solid-State 

• In solids, particles are tightly packed. 

• Solids have a  definite mass and  shape. 

• The  intermolecular distances are short and intermolecular forces are strong in solids..

• They have fixed volumes.

• They have definite boundaries and r constituent particles have fixed positions and oscillate about their mean positions. 

• They are rigid and have negligible  compressibility.

What makes Solids have Properties Different From that of Liquids and Gases?

Liquids and gasses are together known as fluids but solids do not fit into this group. 

Fluids are substances that can flow. This happens because of low intermolecular forces in liquids and gasses. Due to this property, the fluids can flow by overcoming their chemical bonds. Solids can not undergo this process and hence they are very rigid.

Solid particles, unlike fluid particles, can not take the shape of the container in which they are kept. This phenomenon is again explained by the nature of bonds present in solids. Solid particles are very closely bound and have a low distance between them. This also makes them very hard to compress, unlike fluids which can be compressed easily as they have large intermolecular distances.

Fluid particles are in constant motion. The speed differs in liquids and gases and particles are faster in the gaseous state due to the presence of high kinetic energy. But liquid particles do move even though they do not separate from each other. This phenomenon is not observed in solids and they are different in this regard.

Solids also possess lustre due to which they can shine and reflect light. This feature is demonstrated through solids like gold and silver which glimmer and shine. The fluids do not possess lustre.

Dielectric Properties of Solids

Dielectric property studies relate to the storage and dissipation of electrical and magnetic energy in materials. Some dielectric properties of solids are: 

• Piezoelectricity 

• Pyroelectricity 

• Ferroelectric 

• Anti-ferroelectric 

Piezoelectricity-A

Solid in which individual dipoles are formed and the net dipole moment of the solid (crystal) is oriented to exhibit piezoelectricity. When pressure is applied to such a solid, those atoms or ions move to generate electricity. Piezoelectricity is the charge that accumulates in some crystals due to mechanical stress. This means that piezoelectricity is the electricity that results from pressure and latent heat. The word piezoelectric comes from the Greek words piezein, which means "push or push," and elecktron, which means "amber" (ancient source of  charge). Piezoelectricity was discovered in 1880 by the French physicists Jack and Pierre Curie. This dielectric property of solids is used in medicine, the  automotive industry, information technology, and telecommunications. 

Pyroelectricity

The word "pyroelectricity" comes from  two Greek words, pyrr, which means "fire" and elecktron, which means "amber" (ancient source of  charge) or "electricity". increase. 

Pyroelectricity is the ability  to generate a temporary voltage when a particular crystal is heated or cooled. Some piezoelectric crystals generate electricity when heated, so the generated electricity is called pyroelectricity, and this phenomenon is called the pyroelectric effect. Pyroelectric crystals are generally  electrically polarized and therefore contain a  large electric field. Changes in temperature change the position of  atoms  in the crystal structure. Due to the change in crystal structure, the polarization of the crystal changes and the voltage across the crystal rises. If the temperature remains constant at the new value, the pyroelectric voltage will disappear due to the leakage current. 

Used for heat sensors, power generation and  fusion. These can be used with PIR (Passive Infrared) sensors, non-contact infrared thermometers, and motion detectors. Motion detection heat sensors are used to detect the motion of people, animals, objects, etc. 

Ferroelectricity

For some crystals, the dipoles are permanently aligned  in the absence of an electric field. They have spontaneous electric polarization. When an external electric field is applied to such a crystal, its electric polarization is reversed. Discovered by Valasek in 1920 with potassium sodium tartrate. The word ferroelectricity consists of two words: iron and ferro, which means  electricity. All ferroelectric materials are also pyroelectric. 

They are used in the following materials:

• Ferroelectric capacitors, 

• Ferroelectric RAM, 

• High quality infrared cameras, 

• Fire sensors, sonars, 

• Vibration sensors, and 

• Diesel engine fuel injectors. 

It is also used in ferroelectric tunnel junctions (FTJs). Ferroelectrics exhibit catalytic properties. Therefore, they can also be used for catalysis. It also functions as an energy harvester. Materials with both ferroelectric and ferromagnetic properties are called multiferroics. There are many types of research  on  multiferroics. 

Anti - Ferroelectricity

As the name implies, it is the opposite of ferroelectricity. The relationship between antiferromagnetism and ferroelectricity is similar to the relationship between ferromagnetism and antiferromagnetism. Crystals with the antiferromagnetic properties of dipoles are composed of a regular arrangement of electric dipoles, with adjacent dipoles oriented in opposite (antiparallel) directions. This creates a Netzerodipole moment. Spontaneous electric polarization is zero because the adjacent dipoles cancel each other out. This property of crystals can appear and disappear depending on temperature, pressure, growth method, external electric field, etc. The temperature at which the antiferroelectricity disappears is called the Néel or Curie point.

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• When an electric field is applied there is a dipole e array of antiferroelectric material. 

•  It is mainly used for supercapacitors, integration with ferromagnets, high energy storage, etc. 

• There are  Amorphous and crystalline solids.

• They can be  divided into two types based on  their component placement- that is Crystalline solids and  Amorphous solids.

• Crystalline solids have the arrangement that particles can be seen in an orderly manner which means that they have the  regular pattern of constituent particles and are repeated  throughout the  crystal. 

• Amorphous solid have the  irregularly shaped constituent particles and the  particles are only seen at short distances and the  patterns are  scattered in the solid and the  arrangement of  particles between them are chaotically seen.  crystalline solids can be classified into the following four types based on the type of intramolecular force between them. 

• Molecular Solid are made up of molecules and are of three types. 

• Non-polar molecular solids that have the  non-polar covalent bonds between  atoms are called non-polar molecular solids. B. H₂, Br₂, etc. 

• Polar  molecular solids have polar covalent bonds between  atoms and are known as the  polar molecular solids. In this type of solids the molecules are held together by dipole-dipole interactions. For example, HCl, SO₂. 

• Hydrogen-bonded molecular solids Molecular solids consist of  polar covalent bonds between  atoms and  molecules and are bonded by hydrogen bonds which are known as hydrogen-bonded molecular solids.

• For example, we can say that the  three-dimensional space is created by a series of individual transformation operations which was named after the  French physicist Auguste Bravais.

• He is well known in the field of  crystallography. He gave the concept of Brave lattice and formulated the Brave method. 

• There are  14 Bravais lattices that can classify the constituent particles of a crystal. These grids  are obtained by combining a grid system and a centering type. 

• The  lattice  system is a class of lattices which has the same set of lattice points that are a subset of the crystal system arithmetic class. The grid can be  divided into 7 grid systems- that are  Cubic,  Tetragonal,  Orthorhombic,  Hexagonal,  Rhidron,  Monoclinic,  Triclinic.

• The centering type gives the identification of the  location of grid points within the unit cell. 

• Primitive Unit Cell (P)-In this grid are the  points at the  corners of the cell and are called  a simple unit cell and constituent  particles are  at the corners of the grid of the unit cell and there are no particles anywhere else in the cell.

• The  primitive cell has only one grid point. 

• Non-Primitive Unit Cells have  particles at other positions and corners of the grid and are divided as  Body Mind where the  grid points are in the corners of the cell and there is an additional grid point in the center of the cell and has  particles in the corners and centers of the body or cells. 

•  Area Center (F) has a point in the corner of the cell and there is an additional grid point in the center of each area of ​​the cell. Base Center grid point is at the corner of the cell, and there is an additional grid point in the center of each face of the  pair of parallel faces in the cell and known as the end center. Hence  there are particles in the corners  of each face and particles in the center.

Not all combinations of lattice systems and centring types give rise to new possible lattices. After a combination of them, several lattices we get are equivalent to each other. 

Amorphous and Crystalline Solids 

Solids can be classified into two types on the basis of arrangement of their constituent particles –

• Crystalline solids 

• Amorphous solids 

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Crystalline Solids – In crystalline solids, the arrangement of constituent particles is found in an ordered manner. It means in crystalline solids a regular pattern of the constituent particles is found which repeats itself periodically over the entire crystal. 

Amorphous Solids – In amorphous solids constituent particles are found in irregular shape. In these solids regular arrangement of constituent particles is found over short distances only. These patterns are found scattered in the solid and in between the arrangement of the particles is found disordered. 

Classification of Crystalline Solids 

Crystalline solids can be classified into following four types on the basis of different types of intermolecular forces between them –

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• Molecular Solids – Those crystalline solids whose constituent particles are molecules are called molecular solids. They can be divided into following three types –

• Non - Polar Molecular Solids – Those molecular solids which have non - polar covalent bonds between the atoms are called non - polar molecular solids. Example, H2, Br2 etc.  

• Polar Molecular Solids - Those molecular solids which have polar covalent bonds between the atoms are called polar molecular solids. In such molecular solids, molecules are held together by dipole – dipole interactions. Example - HCl, SO2 etc.  

• Hydrogen Bonded Molecular Solids - Those molecular solids which have polar covalent bonds between the atoms and the molecules are held together by hydrogen bonding are called hydrogen bonded molecular solids. Example – water molecules are held together by hydrogen bonding. 

• Ionic Solids - Those crystalline solids whose constituent particles are ions are called ionic solids. In these solids cations and anions are bonded together by strong electrostatic forces. Examples – NaCl, ZnS etc. 

• Metallic Solids - Those crystalline solids whose constituent particles are positive metal ions and electrons, are called metallic solids. In such solids a collection of orderly arranged positive metal ions are surrounded by or held together by free electrons. Example – Fe, Au, Ag etc. 

• Covalent Solids – In these crystalline solids, atoms of non – metals are joined to their adjacent atoms by a covalent bond. For example, in diamonds and graphite etc. As covalent bonds are strong, they hold all the atoms in their position firmly. That’s why these solids are hard and brittle. These solids are also known as network solids or giant molecules. 

Crystal Lattice and Unit Cell

Crystal Lattice - A lattice is a geometric arrangement of the points in space at which the atoms, molecules, ions or constituent particles of a crystal occur. It describes the arrangement of particles in the crystal.

Unit Cell - Unit cell of a crystal is defined by a lattice. Lattice point is the point or position in the unit cell or on the lattice in a crystal where the probability of finding an atom or ion is the highest.

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Bravais Lattice - Bravais Lattice is an infinite array of discrete points in three - dimensional space generated by a set of discrete translation operations. It is named after French physicist Auguste Bravais. He is known for his work in crystallography. He gave the concept of Bravais lattice and formulated Bravais Law. 

In three – dimensional space, 14 Bravais lattices are there into which constituent particles of the crystal can be arranged. These 14 Bravais lattices are obtained by combining lattice systems with centering types. 

A Lattice system is a class of lattices with the same set of lattice point groups, which are subgroups of the arithmetic crystal classes. 14 Bravais lattices can be divided into 7 lattice systems –

• Cubic 

• Tetragonal 

• Orthorhombic 

• Hexagonal 

• Rhombohedral 

• Monoclinic 

• Triclinic 

Centering types identify the locations of the lattice points in the unit cell. 

Primitive Unit Cell (P) – In this lattice points are found on the cell corners only. It is also sometimes called a simple unit cell. In these constituent particles are found at the corners of the lattice in the unit cell, no particles are located at any other position in the cell. Thus, a primitive cell has only one lattice point. 

Non – Primitive Unit Cells – In these unit cells particles are found in other positions of the lattices as well with corners. These can be divided into following types –

• Body Centered (I) - In this lattice points are found on the cell corners with one additional lattice point at the center of the cell. Thus, it has particles at the corners and center of the body or cell. 

• Face Centered (F) - In this lattice points are found on the cell corners with one additional lattice point at the center of each face of the cell. Thus, it has particles at the corners and center of each face.

• Base Centered (C) - In this lattice points are found on the cell corners with one additional lattice point at the center of each face of one pair of parallel faces of the cell. It is also called end centered. Thus, it has particles at the corners and one particle at the center of each opposite face. 

Not all combinations of lattice systems and centering types give rise to new possible lattices. After combining them, several lattices we get are equivalent to each other.

14 - Types of Bravais Lattice

All 14 Bravais Lattices show a similarity 

• Each lattice point has one particle of the crystal.

• This constituent particle of the crystal can be anything like an atom, ion, or molecule.

• These points are joined by straight lines. 

• When we join the  lattice point of the crystal, we get the geometrical shape of the crystal.

• Each one of the 14 Bravais lattices possesses a special  geometry. After combining the lattice system and centring types we can see that the lattices were equivalent and have been already excluded. 

List of 14 – Types of Bravais Lattices

For description, we are using a, b and c to denote the dimensions of the unit cells and α, β, γ to denote corresponding angles in the unit cells. 

• Cubic – Cubic system shows three types of Bravais lattices – Primitive, base centred and face-centred. For cubic systems –

a = b = c

α = β = γ = 90°

• Tetragonal – Tetragonal system shows two types of Bravais lattices – Primitive, body centred. For tetragonal systems –

a = b ≠ c

α = β = γ = 90°

• Orthorhombic – Orthorhombic system shows four types of Bravais lattices – Primitive, body centred, base centred and face-centred. For orthorhombic systems –

a ≠ b ≠ c

α= β=γ=90°

• Hexagonal - The Hexagonal system shows one type of Bravais lattice which is Primitive. For hexagonal systems –

a = b ≠ c

α =120°, β = γ = 90°

• Rhombohedral - Rhombohedral system shows one type of Bravais lattice which is Primitive. For rhombohedral systems –

a = b = c

α = β = γ ≠  90°

• Monoclinic - Monoclinic system shows two types of Bravais lattices – Primitive, base centred. For Monoclinic systems –

a = b ≠ c

α ≠ 90°, β = γ = 90°

• Triclinic – Triclinic system shows one type of Bravais lattice which is Primitive. For triclinic systems

a ≠ b ≠ c

α ≠ β ≠ γ ≠ 90°

Thus, from the cubic system – two, from tetragonal – two, from orthorhombic – four, from hexagonal – one, from rhombohedral – one, from monoclinic two and triclinic one Bravais lattices are found. If you add all these Bravais lattices, you get a total of 14 Bravais lattices. 

Number of Atoms in a Unit Cell

Close–Packed Structures 

• Solids have always a dense structure. This means that the components are very close and the void place is very less. They also have  a three-dimensional dense structure. 

• One-dimensional high-density packing has the  constituent particles as rigid spheres. Here is a one-dimensional, dense structure- 

• Two-dimensional high-density packing-contains  constituent particles as rigid spheres. 

• Three-dimensional dense of the  constituent particles as a rigid sphere are less than as it is specified

Packing Efficiency 

In any way solids  will always have some vacant space between them which is called a void. The quantitative aspect of the solid crystal structure can be well understood with the  help of packing efficiency. 

Packing efficiency is the percentage of total space filled by the particles. Mathematically, it can be expressed by the following formula –

Packing Efficiency = \[\frac{\text{Volume Occupied By All Constitutent Particles in Unit Cell}}{\text{Volume of The Unit Cell}} \times 100 \]

 Following Factors Affect The Packing Efficiency of The Crystalline Solids

• The volume of the unit cell

• Number of atoms in the unit cell

• Volume of atoms present in the unit cell 

Importance of Packing Efficiency 

• It helps to know the structure of the solid.

• By packing efficiency one can  know the density and consistency of the crystalline solid. 

• Various attributes of the crystalline solid can be seen  efficiently. 

Calculations Involving Unit Cell Dimensions 

Density of the Unit Cell = \[\frac{\text{Mass of Unit Cell}}{\text{Volume of Unit Cell}}\].............(1)

Mass of unit cell = mass of each constituent particle x number of particles in the unit cell .............(2)

Mass of a constituent particle = \[\frac{\text{Molar mass of the solid}}{\text{Avogadro’s number}}\]

Mass of a constituent particle = \[\frac{M}{N_A}\]--------(3)

The number of particles in a unit cell will depend on the type of unit cell. Let us suppose the number of particles in the unit cell is n. Now, let’s put the values in the equation (2) from (3) –

Mass of unit cell = \[(\frac{M}{N_A}) n\] -------------------(4)

Put the values of equation (4) in equation (1), we get

 Density of the unit cell =  \[\frac{nM}{N_A a^{3}} \]

Relation between the radius of an atom and edge length of the unit cell –

For simple cubic unit cell (scc) –  a = 2r 

For body-centred cubic cell (bcc) – a = (\[\frac{4r}{\sqrt{3}}\])

For face-centred cubic cell (fcc) – a = \[2\sqrt{2}r\]

Imperfections in Solids 

The meaning of defect is shortcomings or imperfections. Solid crystals also show some kinds of defects which we study in solid-state chemistry. Some units of the crystals may have one or more atoms lesser than other ideal units of crystals. These imperfections of crystals are called defects in crystals. In other words, the interruptions in regular patterns in crystalline solids are called crystallographic defects. There are many types of crystallographic defects such as point defects, line defects, planar defects etc. Frenkel defects are point defects. These defects in the crystals make them interesting to study. As said by Colin Humphreys –

“Crystals are like people, it is the defects in them which tend to make them interesting!”

What are Point Defects? 

Those defects in the crystals which occur around an atom or particle are called point defects. These defects occur only at or around a single lattice point. They do not extend in space in any dimension. That’s why they are also called zero-dimensional solid-state interstitial positions in the crystal.

• Foreign atoms occupy the interstitial position in the crystal lattice.

• The original atom of the crystal is replaced by a foreign atom. 

Types of Point Defects 

Point defects can be further divided into the following types –

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Stoichiometric Defects – The compounds which obey the law of definite proportions, the law of constant composition and the law of conservation of mass are called stoichiometric compounds. The defects in crystals that do not disturb the stoichiometry of the compound or crystal are called stoichiometric defects. 

Stoichiometric Defects Can Be Divided Into Following Types 

• Vacancy Defect – The point defect which is produced when an atom goes missing from its original lattice site is called a vacancy defect. It creates a vacancy in the lattice site as shown in the diagram below –

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It results in a decrease in the density of the substance. Several vacancy defects depend on the temperature of the crystal. It occurred due to imperfect packing during crystallization. 

• Interstitial Defect – The point defect which occurs when an atom takes the interstitial position of the lattice structure is called an interstitial defect. The atom can be of the same crystal or foreign crystal/material. If the atom is of the same crystal, then the defect is called a self-interstitial defect. It is shown below through the diagram –

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This Defect Increases The Density of The Crystal. It Causes Atomic Distortion. 

• Schottky Defect - Schottky defect is also a point defect that is observed in various crystals. Named after a German physicist, Walter H. Schottky, this defect occurs commonly in ionic crystals where the size of cation and anion is similar. The point defect which occurs when cation and anion leave their corresponding lattice sites and create a pair of vacancy defects is called the Schottky defect. Take, for example, KCl. Potassium (K) has an atomic number of 17 and Chlorine (Cl) has an atomic number of 19. Both the ions are of similar size, and hence it is a good candidate for showing Schottky defects. 

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The Nature of Schottky Defects 

Schottky defects usually occur when heat is applied to the crystals of an ionic compound. Heat raises the temperature and thus the thermal vibrations in the crystal. This creates a gap in the crystal pattern. Gap is created by stoichiometric ratio H. Depending on the availability of ions in the compound. For example, in a common ionic compound with the formula XnYm, "n" ions from X and "m" ions from Y are left to create vacancies. Such groups of  vacancies are sometimes referred to as  Schottky clusters. Schottky defects reduce the density of ionic compounds and reduce the total mass of the same crystal volume as some of the ions leave the crystal.

Concentration of Defects

As explained previously, Schottky defects are formed by applying heat. At any given temperature, there is a concentration of defects (i.e. Schottky defects per unit volume) given by the following formula:

\[n_s \thickapprox N e^{\frac{- \triangle H_s}{2kT}}\]

Where, 

ns = number of Schottky defects per unit volume at temperature T (in Kelvins) in a crystal with N anion and N cations per unit volume, and ∆Hs is the enthalpy for creating one defect.

• Frenkel Defect - When an atom or smaller ion (generally a cation) leaves its place in the lattice, creating a vacancy and becomes an interstitial by lodging in a nearby location. Thus, a vacancy is created in the lattice. This type of defect is called Frenkel defect. It was discovered by soviet physicist Yakov Frenkel. It is a type of point defect which is also known as dislocation defect. 

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Frenkel Defect in NaCl Crystal 

Frenkel Defect Examples  

Following are examples of Frenkel Defect –

• NaCl (Sodium Chloride) (Frenkel Defect is shown in NaCl in the image above)

• Zinc sulphide 

• Silver (I) Chloride 

• Silver (I) Bromide 

• Silver (I) Iodide 

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Frenkel Defect in Silver Chloride 

Reason for Frenkel Defect 

When the ionic compound size of anions is much larger than cations then Frenkel Defect occurs. Due to the size difference in ions, ions occupy an interstitial position in the lattice. Ionic crystals having Frenkel defects also remain neutral in nature. As the number of cations and anions remain equal. Thus, it can be said that Frenkel defects are shown by those ionic solids which have large size differences between the cation and anion. 

Frenkel defect doesn’t have any impact on density, mass or volume of the crystal as in this defect migration of ions takes place within the crystal. So, the density, mass and volume of the ionic crystal remain the same even after having a Frenkel defect.

Calculation of Number of Frenkel Defects 

The number of Frenkel Defects can be calculated by the following formula – 

\[\sqrt{NN^{’}} e^{\frac{- \triangle H}{2kT}}\]

Where N = normally occupied positions 

N’ = Number of available positions

∆H = Enthalpy released by 1 Frenkel defect 

R = Gas constant 

T = Temperature 

Difference Between Schottky and Frenkel Defect

Like the Frenkel defect, the Schottky defect is also a point defect in crystalline solids. Even a few crystalline ionic compounds such as silver bromide exhibit both Schottky and Frenkel defects as well. 

• Non- Stoichiometric Defects – The defects in crystals that disturb the stoichiometry of the compound or crystal are called stoichiometric defects. Non – Stoichiometric defects can be divided into the following two types –

• Metal Excess Defects – As the name suggests in this defect metal ions occur in excess in the lattice of the crystal. It can take place by following two ways –

1. Anionic Vacancy – Anion goes missing from its corresponding lattice site and creates a vacancy. This vacancy is occupied by an electron to maintain the overall electric charge zero or neutral. It is called the F -centre electron that gives colour to the compound. 

2. Extra Cations – Sometimes in some crystals extra cations fit into the interstitial site on heating the crystal. An equal number of electrons do the same to maintain the electrical neutrality of the crystal. 

• Metal Deficiency Defects – In some compounds there is a deficiency of metal than their ideal stoichiometric proportions. It is normally found in transition elements as they possess multiple valencies.

Electrical Properties of Solids

The crystalline solids can be classified into three types based on their electrical properties –

• Conductors – Conductors are those solids that conduct electricity efficiently. Metals like silver, aluminum, copper are good conductors of electricity. In these solids, the valence band and conduction band overlap each other. 

• Insulators –Insulators are those solids that do not conduct electricity. As rubber, wood and plastics are insulators of electricity. In these solids valence band and conduction band have a large energy gap which is called the forbidden gap. Due to the large energy gap, electrons cannot jump from the valence band to the conduction band.  

• Semiconductors- Semiconductors are  solids that conduct electricity more than conductors, but conduct electricity more than insulators. Their conductivity can be increased by adding a small amount of suitable impurities. Metalloids such as silicon and germanium are electrical semiconductors. In these solids, the energy gap between the valence band and the conduction band is small. 

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Positions of  valence bands and conduction bands of conductors, semiconductors and insulators