A matter is defined as anything that has mass, which occupies space and may be perceived by senses. There are three states of matter, viz. (a) solid, (b) liquid, and (c) gaseous states. Whatever may be the state of matter, it is composed of particles. In this article, we shall study the particle model of matter.

Particle and Kinetic Model of Matter:

The particle model is also known as a dynamic particle model. On the basis of the particle model, different states of matter can be explained easily. Some assumptions of this model are as follows.

• All matter is made of tiny particles. However, the arrangement and the distribution of particles are different in the three states of matter.
• Empty spaces exist between these particles. These empty spaces are called voids.
• The particles exert force attraction on one another but the magnitude of these interparticle forces is different in the three states of matter.
• The particles are not stationary and have a tendency to acquire motion. In solids, they are fixed at a position and only vibrate about their mean position. In liquids and solids besides vibrational motion, the particles have translatory motion.
• With the increase in the temperature the kinetic energy of the particles hence the thermal energy increases.

Evidence of Particle Nature of Matter:

If we add potassium permanganate in water kept in a glass jar. We can observe the purple coloured particles separate from the crystals of potassium permanganate and spread in water. Ultimately whole water turns purple.

If we add crystals of salt in water, they settle at the bottom. Gradually their size starts reducing and ultimately the crystal disappear but whole water gets a uniform salty taste. Besides the volume of water does not increase. it indicates salt particles occupy inter-particulate spaces.

When a scent bottle is opened at one corner of a room the fragrance can be smelt at any corner of the room. The molecules of scent occupy the inter-particulate space.

Evidence of Kinetic Nature of the Particles of Matter:

The English Botanist Robert Brown, in 1927 observed that colloidal particles exhibit continuous random motion in all directions in a straight line.  He found such movement when pollen grains were suspended in water. 

The phenomenon of continuous zig-zag movement of colloidal particles in straight-line paths in a random direction is known as a Brownian movement. A pollen grain is placed on the surface of water taken in a beaker. It shows the Brownian movement. The pollen grain is surrounded by a large number of water molecules that constantly bombard the pollen grain. On unequal bombardment, the pollen grain gets pushed in certain directions. This experiment proves the kinetic nature of particles of matter.

Characteristics of Particles of the matter:

Particles of matter are very small.

All matter is made up of very small particles that are not visible to naked eye. It can be proved by the following experiment. Take two or three crystals of potassium permanganate and add them in 100ml of water. The solution formed is deep purple in colour. Now take 10ml of this solution and add it to another beaker containing 00ml of fresh water, again you will observe that the colour of the water will change but the solution will be faint compared to that in the first case. Repeat this procedure four or more time. In every step, we observe that the colour of the water changes but it will become fainter and fainter.

The solution remains coloured even at a very high dilution. Which shows that potassium permanganate added is broken into very very small particles exhibiting their characteristic properties. Hence we can conclude that particles of matter are very very small.

Particles have spaces between them.

If we add crystals of salt in water, they settle at the bottom. Gradually their size starts reducing and ultimately the crystal disappear but whole water gets a uniform salty taste. Besides the volume of water does not increase. it indicates salt particles occupy inter-particle spaces present between water particles.

Particles are constantly moving.

A pollen grain is placed on the surface of water taken in a beaker. It shows Brownian movement. The pollen grain is surrounded by a large number of water molecules which constantly bombard the pollen grain. On unequal bombardment, the pollen grain gets pushed in certain directions. This experiment shows that the particles of matter are constantly moving. Thus they possess kinetic energy. As the temperature rises, particles move faster. Hence with the increase in temperature the kinetic energy of the particles also increase.

Particles Attract each other.

Particles of matter have a force acting on them. This force keeps the particles together. The strength of this force of attraction varies from one kind of matter to another.  This force of attraction varies from substance to substance it can be verified by the fact that some forces can be powdered by applying small force, while some break into crystals, while some do not break. This force of attraction between the particles of the same substance is called cohesion. The attractive forces between the particles are maximum in solids and minimum or negligible in case of gases.

States of Matter on the Basis of Particle and Kinetic Model:

Solid State:

At room temperature, the particles of solids occupy definite positions. They can vibrate about their mean positions, but they cannot move from one position to another. The particles are bound to one another strongly. Hence solids have definite shape and definite volume.

Liquid State:

The particles of liquid do not have fixed positions, and they slide over one another within the bulk of the liquid. Thus particles can move from one position to another, but cannot leave the bulk. The particles are bound loosely. Hence liquids have definite volume but don’t have a definite shape. They take shape of the container in which they are kept.

Gaseous State:

In gases, the particles lie far apart and exert a very weak force of attraction on one another. Actually, the particles of gas are in random motion can change position continuously, and can move away from each other. They occupy the whole space available. Only walls of containers restrict their movement. Hence gases have neither definite shape nor definite volume.

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In this article, we shall study a change in the state of a substance.

Melting (Solid → Liquid):

The process of change of solid substance into its liquid state is called melting or fusion. The constant temperature at which the solid becomes liquid upon absorption of heat at constant pressure is called the melting point of that solid at that pressure.

Generally melting point increases with the increase in pressure. Ice is the exception to this because its melting point decreases with the increase in the pressure. Melting point at standard pressure is a characteristic property of a substance. The melting point decreases with the addition of the impurity. Hence melting point can be considered as criteria for purity.

Melting points of some important substances are ice (0 °C), iron (1535 °C), aluminium (660 °C), gold (1064 °C), silver (961 °C), aluminium (660 °C), tin (232 °C), zinc (419.5 °C), copper (1084°C), etc.

Explanation on the Basis of Kinetic Model: 

When solids are heated the thermal energy of particles increases. Thus the cohesive forces between the particles weaken to such extent that the particles can have relative motion with respect to each other but cannot move out of the bulk.  Thus solid gets converted into liquid (melts).

Applications of Melting:

• Melting is very important in the production of alloys. If a binary alloy is to be produced. The element with a higher melting point is melted in a crucible and an element with a lower melting point is added to the molten metal. The second element also melts forming almost a homogeneous solution called alloy. Alloys have many applications in everyday life. Some examples of alloys are

• Substances with a high melting point are used to make high-temperature devices. For example, tungsten is used in an incandescent bulb.
• Metals are melted and they are cast (moulded) to give the solids required shape.

Factors Affecting Melting Point:

Internal factors:

• Inter-Molecular (Particle) Forces: If the attractive forces between the molecules of solid are weaker and then the solid has a low melting point. The attraction between the molecules of covalent compounds is weaker than that in ionic solids and hence covalent compounds have a lower melting point than that of the ionic compounds.
• The shape of molecules: If the shape of the molecule is such that it can have a closed packing of the molecules, then the substance has a higher melting point.
• Size of the molecule: The smaller size of molecules can have a closed packing (less void space) of the molecules, then the substance has a higher melting point.

External Factors: 

• Impurity: The melting point of a substance decreases with the presence of impurities in it, The phenomenon is called melting point depression. The particles of impurity disrupt the repeating pattern of forces that hold the solid together. Hence less energy is required to melt the part of the solid surrounding the impurity. Salt is spread on the frozen street so that the melting point decreases and the ice melt fast.
• Pressure: For the solids, those expand on heating, the melting point increases with increase in the pressure. It is due to the fact that the pressure opposes the increase in the distance between molecules (expansion). e.g. silver, gold, copper, paraffin wax, etc. For the solids, those contract on heating, the melting point decreases with increase in the pressure. It is due to the fact that the pressure supports the decrease in the distance between molecules (contraction). e.g. ice, cast iron, bismuth, brass, etc.

When two ice cubes are pressed together they form a single block of ice. The phenomenon is called regelation. When the two cubes are pressed against each other. the ice at the interface melts due to lowering of melting point. When the pressure is released the melted ice (water) at the interface solidifies again and a single block of ice is obtained.

Sublimation (Solid ⇔ Gas):

Sublimation is the process by which a heated solid directly changes into its gaseous state i.e. vapour state. These vapours on cooling directly give solid. Such substances are called sublimates. Examples are ammonium chloride, ammonia, naphthalene balls, camphor, etc.

Explanation on the Basis of Kinetic Model: 

Certain solids are heated the thermal energy of molecules increases so that the interparticle forces become negligible and the particles can move freely.  Thus such solids on heating get converted directly into gases. This phenomenon is known as sublimation. The cohesive forces between the particles in such substances are weak.

Freezing (Liquid → Solid):

The process of change of matter from a liquid state to a solid state is called freezing or solidification. The constant temperature at which a liquid changes into solid by giving out heat energy (or cooling) is called the freezing point of the liquid. The freezing point of a liquid is a characteristic property of the liquid. Hence can be considered as criteria of purity.

Freezing points of some important substances are water (0 °C), benzene (5.5 °C), mercury (- 38.87 °C), etc.

Explanation on the Basis of Kinetic Model: 

When liquids are cooled the thermal energy of particles decreases. Thus the cohesive forces between the particles strengthen to such extent that the particles can not have relative motion with each other and they occupy the fixed positions.  Thus liquid gets converted into solid (freezes).

Applications of Freezing:

• It is used for the preparation of ice creams.
• The lowering of the freezing point on the addition of solute to the solution is used to find molecular mass of the solute.

Factors Affecting Freezing Point:

For the same substance, the freezing point of the liquid is equal to the melting point of the solid. Therefore the factors those affect melting point of solid obviously affect the freezing point of the liquid.

Freezing Mixtures: 

a mixture of two or more substances (e.g. ice water and salt, or dry ice and alcohol) which can be used to produce temperatures below the freezing point of water.

A freezing mixture of 3 parts of ice and 1 part of NaCl produces a temperature of – 21 °C. A freezing mixture of 2 parts of ice and 3 parts of K₂CO₃ produces a temperature of  – 46 °C.  A freezing mixture of dry ice and alcohol or ethers can produce a temperature of – 60 °C.

In a freezing mixture, a soluble salt is added. The heat required to dissolve one mole of soluble solute in a solvent is called heat of solvation. This heat required for dissolution of solid is taken from the mixture itself and thus the freezing point decreases in steps.

Freezing mixtures ate used to preserve perishable foodstuff like meat and fishes. They are used for producing sub-zero temperatures in laboratories and industrial units.

Evaporation or Vaporization (Liquid → Gas):

The process of conversion of a substance from the liquid state to its vapour state at any temperature below boiling point is called evaporation or vaporization.

Explanation on the Basis of Kinetic Model: 

Some particles from liquid surface possess kinetic energy sufficient to overcome the attractive forces from remaining particles of the liquid and become completely free and escape out as a gas particle in the surroundings. This phenomenon is called evaporation or vaporization.

The rate of evaporation is directly proportional to the surface area and the temperature of the liquid.

During evaporation, the temperature of liquid falls. To maintain temperature balance the liquid particles absorb heat from the surroundings making the surrounding cooler. We have already seen that the molecules with higher kinetic energy leave the surface of the liquid, thus there is an overall decrease in the kinetic energy of liquid. This is one of the reasons for the decrease in the temperature of the liquid.

To increase the rate of evaporation we should increase the surface area, the temperature and the wind speed and should decrease the humidity.

Characteristics of Evaporation:

• It is a surface phenomenon as it takes place on the surface of the liquid.
• It takes place at all temperatures.
• It is a slow process
• The temperature of liquid falls.

Applications of Evaporation:

• During hot day sweat is formed on the body which evaporates. The necessary heat required for the evaporation of the sweat is taken from the body and thus the body temperature is maintained.
• Common salts are produced in shallow lagoons. The water from creek or sea is collected. Water evaporates leaving common salt behind.
• Water gets cooled in an earthen pot (matka). Water seeps through the porous earthen pot and gets on the surface of the pot. It evaporates and the necessary heat required for the evaporation of the water is taken from the water inside the pot and thus the temperature of the water inside the pot decreases.
• Drying of clothes is due to evaporation of water. We have to spread the clothes (increase in surface area), under the sun (increasing temperature) at a windy place.
• In refrigerator the cooling gas (freon) gets evaporator in tubes surrounding freezer region, The necessary heat required for the evaporation of the water is taken from the freezer region and thus the temperature of the freezer region decreases.

Boiling (Liquid → Gas):

Boiling process of change of a liquid into a vapour at a particular temperature and pressure from all part of the liquid. Boiling is a bulk process and takes place throughout the liquid.

When we supply heat energy to liquid the particles start moving faster. At a certain temperature, a point is reached when the particles have enough energy to break free from the forces of attraction of each other. At this temperature, the liquid starts changing into a gas (vapours). The temperature at which a liquid starts boiling at the atmospheric pressure is known as its boiling point. Pure liquids have fixed boiling points. It can be considered as the criteria of purity.

The constant temperature at which a liquid changes to vapour under normal atmospheric pressure is called the boiling point of the liquid. Boiling points of some important liquids are water (100 °C), Ethyl alcohol (78.3 °C), benzene (80.2 °C), chloroform (62 °C), sulphuric acid (280 °C), diethyl ether (35 °C), etc.

Explanation on the Basis of Kinetic Model: 

During boiling, not only the particles on the surface of the liquid but those near walls of the container also start leaving the liquid. It can be seen that small vapour bubbles are formed inside the liquid on walls of the container. As temperature increases the pressure of vapours in bubble increases. The bubbles start growing in size. A point is reached when the vapour pressure inside the bubble is equal to that of atmospheric pressure. At that instant, the bubble detaches from the walls of the container and rise upward. Reaching the surface it bursts giving vapours to the surroundings. Thus there is continuous agitation of the mass of liquid and we say liquid is boiling.

As the pressure increases the boiling point increases. Soluble impurities increase boiling point.

Characteristics of Boiling:

• It is a bulk phenomenon as it takes place throughout the liquid.
• It takes place at fixed temperatures.
• It is a fast process
• The temperature of liquid remains constant.

Factors Affecting Boiling Point:

• Pressure: As the external (atmospheric) pressure decreases boiling point decreases. Hence at higher altitude water boils below 100 °C. Hence higher altitude, food is not cooked properly. To avoid this problem pressure cooker is used for cooking food.

Working of Pressure Cooker:

The basic principle of a pressure cooker is that the boiling point of water increases with the increase in pressure. A pressure cooker is a steel or aluminum vessel with a lid which is airtight. There is a safety valve to release steam to decrease the excess pressure above certain designated pressure. The steam is formed from water in the pressure cooker which has no escape route gets collected in the vessel which put extra pressure on water, which leads to increase in the boiling point of water above 100 °C. Thus gradually the boiling point of water goes on increasing. When the required pressure is reached, the safety valve lifts due to steam pressure and excess of steam is blown out. The safety wall closes and the process restarts. The pressure of steam is even throughout the vessel and hence the food is cooked fast and evenly. The pressure cooker saves a lot of fuel required for cooking.

• Impurity: When a solid is dissolved in liquid the boiling point increases beyond the normal boiling point. Hence during steaming of food, some salt is added to water, so that the food cooks well.

Liquefaction or Condensation:

Liquefaction is the process in which the gaseous substance changes into a liquid state at a particular temperature.

Explanation on the Basis of Kinetic Model:

On cooling the particles of gas lose their kinetic energy and their speed decreases. The decrease in their speed reduces interparticle space and the particles come so close so that the attractive forces between them increase and the gas gets converted into a liquid.

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A matter is defined as anything that has mass, which occupies space and may be perceived by senses. There are three states of matter, viz. (a) solid, (b) liquid, and (c) gaseous states.

Historical Perspective of States of Matter:

Ancient Indian philosophers suggested that all the forms of matter are made up of five basic elements (they called it tatva) they called these five basic elements as ‘panch maha bhoota’. These elements are the sky (Akash), air (vayu), fire (teja), water (aap) and earth (soil). Ancient Greek philosophers considered that all for of matter are made of fire, water, air and the earth. Thales (640-546 BC) suggested that all things arose from the water.

The properties which decide the state of matter are the interparticle space, the force of attraction between particles, and the kinetic energy of particles due to their motion. Thus different states of matter can be explained on the basis of particle and kinetic model.

Solid State:

It has a definite shape and definite volume at a given temperature and pressure. A substance is said to be in the solid state if its melting point is above the room temperature at the atmospheric pressure e.g. Chair, chalk, desk, salt, silver, etc.

Characteristics of Solid State:

• Solids have a definite shape and volume.
• There are strong cohesive forces between the molecules of solid.
• The molecules of solid are fixed at one point.
• The melting point of the solid is above room temperature at atmospheric pressure.
• Solids have high densities.

Particle Model:

According to the particle model, in the solid state, the constituent particles are very close to each other. Hence voids between them are very small. There are strong cohesive forces between the particles of solid.

Due to small voids and strong cohesive forces, the particles are not free to change their position and thus can’t have relative motion w.r.t. each other. Thus the particles of solid are fixed at one point. Hence solids have a definite shape and definite volume at given temperature and pressure.

Kinetic Model:

Due to small interparticle space and strong cohesive forces, the particles are fixed in one position. They can only vibrate about their mean position. Hence solids have low thermal energy and thus particles cannot break away from each other by overcoming inter-particles attractive forces. Thus they have a definite spatial arrangement. Hence solids have a definite shape and definite volume at a given temperature and pressure.  When the average distance between the particles increases beyond 10-9 m, the solid melts into a liquid.

Liquid State:

It has a definite volume but has indefinite shape. It will take the shape of the container containing it. A substance is said to be in the liquid state if its boiling point is above the room temperature and melting point is above the room temperature at the atmospheric pressure e.g. water, alcohol, milk etc.

Characteristics of Liquid State:

• Liquids do not have a definite shape but have a definite volume
• In liquids, the cohesive forces are weaker compared to solid and stronger compared to gases.
• Molecules of liquid move freely anywhere but can’t leave the bulk.
• The boiling point of a liquid is above and its freezing point (melting point) is below the room temperature at the atmospheric pressure.
• Liquids have comparatively low densities compared to solids but have higher densities than gases.

Particle Model:

According to the particle model, in the liquid state, the distance between constituent particles is more compared to that between solid particles and less than that between gaseous particles. Thus voids are more compared to that in solids but less compared to that in gases. The cohesive forces between the particles of a liquid are weaker than that between solid particles and stronger than that between gaseous particles.

Hence the cohesive forces are weak enough so that the particles of liquid can have relative motion w.r.t. each other but these cohesive forces are strong enough to stop the particles of a liquid to go out of the bulk. Hence liquids have a definite volume but have indefinite shape.

Kinetic Model:

The interparticle distance between the particles is more than that in the solid state. Hence the attractive forces are weaker than that in the solid state. There is larger void space among the particles. Hence the particles can vibrate with a higher amplitude. At the same time, the particles can move in the bulk. Hence they have translational motion.

Thus particles in the solid state have more thermal energy than that in the solid state. Thus liquids can flow and have a definite volume. Due to their fluidity, they acquire the shape of the container in which they are kept.

Gaseous State:

Gas has neither a definite shape nor a definite volume. It takes the shape and volume of the container. Thus it occupies the whole available volume. A substance is said to be in the gaseous state if its boiling point is below room temperature at atmospheric pressure. e.g. air, oxygen, nitrogen, carbon dioxide.

Characteristics of Gaseous State:

• Gases have neither definite shape nor a definite volume.
• In gases, the intermolecular forces of attraction are very weak i.e. almost zero.
• Molecules of gases move freely anywhere.
• The condensation point (boiling point) of gas is below the room temperature at atmospheric pressure.
• Gases have very low densities.

Particle Model:

According to the particle model, iIn the gaseous state, the distance between constituent particles is very large compared to that between solid particles of the liquid. Voids are very large. The cohesive forces between the particles of a gas are negligible. Hence the particles of a gas can move away freely from the bulk and occupy any space available. Hence, gases have neither a definite shape nor a definite volume.

Kinetic Model:

In the gaseous state, the distance between constituent particles is very large compared to that between solid particles of the liquid. The cohesive forces between the particles of a gas are negligible. Hence the particles are free to move and free to vibrate. Hence they have the highest kinetic energy (hence thermal energy) in this state compared to the solid and liquid state.

On cooling the gas the kinetic energy of the gas particles decreases and the molecules come near to each other resulting in an increase in the cohesive forces and thus the gas condenses to form a liquid.

Notes:

• By changing the temperature or pressure or both, the state of the substance can be changed.
• Besides these three standard states of matter, there are two more states called plasma state (Exists at very high temperature) and Bose-Einstein condensate (Exists at the very very cold condition).

Comparative Study of States of Matter:

Plasma State:

This state exists at superheated gaseous state consisting of a mixture of electrons and positively charged ions with unusual properties. These particles are super energetic and are at super excited state. It is found at extremely high temperatures such as interiors of suns and stars or intense electric fields as a discharge tube. Astronomers reveal that 99% of all matter in the universe exists in the plasma state.

Bose-Einstein Condensate (1924):

This state was predicted by Einstein and proved by Satyendra Nath Bose in 1920.  It is super cooled solid in which atoms lose their separate identity. They get condensed and behave like a single super atom. This state is very useful for the modern concept of superconductivity.

Bulk Properties of Matter:

The bulk properties of matter depict the collective behaviour of a large number of particles taken together. These properties are not exhibited by the particle individually.

Volume, pressure, temperature, melting point, boiling point, vapour pressure, density, surface tension, viscosity etc. are the bulk properties of matter.

Bulk properties of matter are dependent on the state of the matter and they change with the change in the state of the matter. Similarly, these bulk properties depend on the energy of constituent particles and electrostatic attraction between them. The change in the physical state and the bulk properties of matter depend on the energy of constituent molecules and intermolecular attraction between them.

It is to be noted that the chemical properties of a substance do not change with the change in the state of the substance

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On the basis of electrical conductivity, substances can be classified into three types conductors, insulators, and semiconductors. In this article, we shall have a brief idea of semiconductors.

Semiconductors are the substances whose conductivity lies between the conductors and insulators e.g. Germanium, Silicon, etc. They are covalent solids. These elements are members of the fourth group of the periodic table with outer orbit configuration ns² np² and valency 4. There are no free electrons for conduction in semiconductors at low temperature (absolute zero). Thus germanium crystal acts as an insulator at absolute zero. As the temperature increases, the energy gap reduces and some electrons jump to the conduction band. Thus the conductivity of semiconductors increases with the increase in the temperature. Such semiconductors are also called as extrinsic or pure semiconductors. The conductivity of semiconductors can be increased by purposely adding pentavalent or trivalent impurity (doping) to their crystal in small traces.

The structure of Pure Silicon (Semiconductor) Crystal:

We can see that each silicon atom share its four valence electrons with neighbouring 4 silicon atoms to form four covalent bonds. Thus at absolute zero, all the electrons are localized and not available for conduction. Thus at absolute zero silicon behaves as an insulator.

Types of Semiconductors:

Depending upon the working semiconductors are classified into two types.

Intrinsic semiconductors:

A semiconductor which is in extremely pure form is called intrinsic semiconductor e.g. Germanium, Silicon. The crystal structure of these elements consists of regular repetition in three dimensions of a unit cell having the form of a tetrahedron, with one atom at each vertex. 3. The two-dimensional representation is as shown below.

Consider a semiconductor like germanium having valency four. Germanium atom has four electrons in its outermost shell. Germanium has a crystalline structure in which each atom of germanium shares its valence electrons with four neighboring atoms forming four covalent bonds. The covalent bonds are strong bonds. Thus there is no free electron for conduction in germanium at low temperature (absolute zero). Thus germanium crystal acts as an insulator at absolute zero.

At room temperature, the thermal energy of some electrons increases and they are set free. These free electrons get delocalized and are available for conduction. When these electrons get delocalized, a hole is created at their position. Thus the crystal shows a small conductivity.

Extrinsic semiconductors:

The crystal of intrinsic semiconductors shows a small conductivity. The conductivity of semiconductors can be increased by adding a small quantity of some impurity in the pure crystal of the semiconductor. This process is called doping. The ratio of impurity is very low i.e. 1 atom of impurity for every 10⁶ to 10¹⁰ atoms of semiconductors. These atoms of impurities are so less that they do not affect the crystal structure of the semiconductor. Generally, trivalent or tetravalent elements are added as impurities to semiconductor crystal. Depending upon the impurity the semiconductors are classified into two types a) p-type semiconductor and b) n-type semiconductor

p-type Semiconductor:

Let us suppose the germanium is doped with an element from the third group say boron (trivalent impurity). Boron has three Valency electrons. Therefore, boron can form only three covalent bonds with neighboring germanium atoms. One of the covalent bonds around each boron atom has an electron missing. The absence of an electron is called a hole. This impurity is called acceptor impurity.

Under the action of an electric field, an electron from a neighboring completely filled covalent bond jumps into this hole creating a hole in the bond from which electron has moved. The process is repeated continuously. Thus the hole appears to move through the crystal from a positive end to a negative end. Thus the conductivity of doped germanium increases. The absence of an electron in the hole means the presence of a positive charge. Hence the doped material is called p-type semiconductor.

Characteristics of p-type Semiconductors:

• In p-type semiconductors, doping is done with trivalent impurity i.e. impurity from the third group of the periodic table.
• The impurity in the p-type semiconductor is called the acceptor impurity.
• Each atom of impurity creates a hole in the crystal.
• The electrical conductivity is due to the hole.
• When a potential difference is applied across the p-type of semiconductor, the holes appear to move from a positive end to a negative end.
• In p-type semiconductors, holes are the major charge carriers.

n-type Semiconductors:

Let us suppose the germanium is doped with an element from the fifth group say phosphorous (pentavalent impurity). Phosphorus has five valence electrons. Therefore, phosphorus can form four covalent bonds leaving one free electron unbonded. Due to pentavalent doping the number of free electrons increases. This impurity is called the donor impurity.

Under the action of an electric field, free-electron around phosphorous moves through the crystal from the negative end to a positive end. Thus the conductivity of doped germanium increases. The presence of an electron means the presence of a negative charge. Hence the doped material is called an n-type semiconductor.

Characteristics of n-type Semiconductors:

• In n-type semiconductors, doping is done with pentavalent impurity i.e. impurity from the fifth group of the periodic table.
• The impurity in the n-type semiconductor is called the donor impurity.
• Each atom of impurity leaves one free electron in the crystal.
• The electrical conductivity is due to electron set free by the electron.
• When a potential difference is applied across n-type of semiconductor, the electrons move from a negative end to a positive end.
• In n-type semiconductors, electrons are the major charge carriers.

Uses of Semiconductors:

• Various combinations of n-type and p-type semiconductors are used for making electronic components.
• A diode is a combination of n-type and p-type semiconductors and is used as a rectifier.
• Transistors are made by sandwiching a layer of one type of semiconductor between two layers of the other type of semiconductor. NPN and PNP types of transistors are used to detect or amplify radio or audio signals.
• The solar cell is an efficient photodiode used for the conversion of light energy into electrical energy. It consists of both p-type and n-type semiconductors.

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In the last article, we have studied the dielectric properties of solids. In this article, we shall study the electrical properties of solids.

Electrical Conductivity:

The electrical conductivity of solids is due to the motion of electron or positive holes. The conductivity due to the motion of electron or positive holes is called electronic conductivity. The electrical conductivity may be due to the motion of ions. The conductivity due to the motion of ions is called ionic conductivity. Conductivity due to electrons is called n-type conductivity while that due to holes is called p-type conductivity.

In metals, electrical conductivity is due to the motion of electrons and the electrical conductivity increases with the increase in the electrons available for conduction, the electrical conductivity increases. In pure ionic solids, ions are not available for conduction hence in the pure solid state they are insulators. Due to the presence of defects in the crystal electrical conductivity increases.

Solids exhibit a varying range of electrical conductivities, extending of magnitude ranging from 10^–20 to 10⁷ ohm^–1 m^–1. Solids can be classified into three types on the basis of their conductivities. The difference in conductivities of conductors, insulators, and semiconductors can be explained on the basis of band theory.

Electrical Conductivity on the Basis of Energy Bands:

The group of discrete but closely spaced energy levels for the orbital electrons in a particular orbit is called energy band. Inside the crystal, each electron has a unique position and no two electrons see exactly the same pattern of surrounding charges. Because of this, each electron will have a different energy level. These different energy levels with continuous energy variation form what are called energy bands.

The energy band which includes the energy levels of the valence electrons is called the valence band. The energy band above the valence band is called the conduction band. With no external energy, all the valence electrons will reside in the valence band.

On the basis of energy bands and electrical conductivity, solids can be classified as:

Conductors:

The solids with conductivities ranging between 10⁴ to 10⁷ ohm^–1 m^–1 are called conductors. Metals have conductivities in the order of 10⁷ ohm^–1 m^–1 are good conductors. In conductors, the lowest level in the conduction band happens to be lower than the highest level of the valence band and hence the conduction band and the valence band overlap. Hence the electron in the valence band can migrate very easily into the conduction band. Thus at room temperature, a large number of electrons are available for conduction. Examples: Copper, Aluminium, Silver, Gold, All metals

Characteristics of Conductors:

• The substances which conduct electricity through them to a greater extent are called conductors.
• In conductors, the conduction band and valence band overlap with each other or the gap between them is very small.
• There are free electrons in the conduction band.
• Due to increase in temperature conductance decreases.
• There is no effect of the addition of impurities on the conductivity of conductors.
• Their conductivity ranges between 10⁴ to 10⁷ ohm^–1 m^–1.

Conduction in Metallic Solids:

A metal conductor conducts electricity through the movement of free electrons. Metals conduct electricity in solid as well as a molten state. The conduction of electricity is due to the transfer of electrons and not due to the transfer of matter. The conductivity of metals depends upon the number of valence electrons available per atom. It is nearly independent of the presence of impurity and lattice defects. Conductivity decreases with the increase in the temperature. It can be explained as follows

M → Mⁿ⁺_kernel + ne^–  free electrons

The kernels are fixed. Due to the increase in temperature, the amplitude of vibration of kernels increases. Hence the obstruction to the flow of electron increases.

Insulators :

These are the solids with very low conductivities ranging between 10^–20 to 10^–10 ohm^–1 m^–1. The conduction band and valence band are widely spaced. Thus forbidden energy gap between the valence band and conduction band is large (greater than 3 eV). Hence the electron in the valence band cannot migrate into the conduction band. Hence no electrons are available for conduction. But at a higher temperature, some of the electrons from the valence band may gain external energy to cross the gap between the conduction band and the valence band. Then these electrons will move into the conduction band. At the same time, they will create vacant energy levels in the valence band where other valence electrons can move. Thus the process creates the possibility of conduction due to electrons in conduction band as well as due to vacancies in the valence band. Examples: Glass, wood, paper, plastic, mica.

Characteristics of Insulators:

• In Insulators the conduction band and valence band are widely separated.
• There are no free electrons in the conduction band.
• There is an energy gap between the conduction band and the valence band which is more than 3 eV.
• There is no effect of change of temperature on the conductivity of insulators.
• There is no effect of the addition of impurities on the conductivity of insulator.
• They have very low conductivities ranging between 10^–20 to 10^–10 ohm^–1 m^–1.

Semiconductors :

These are the solids with conductivities in the intermediate range from 10^–6 to 10⁴ ohm^–1 m^–1.

The forbidden energy gap between the valence band and conduction band is less than 3 eV. Thus energy gap between the valence band and conduction band is small. At absolute zero, no electrons are available for conduction.

As the temperature increases, many electrons from the valence band may gain external energy to cross the gap between the conduction band and the valence band. Then these electrons will move into the conduction band. At the same time, they will create vacant energy levels in the valence band where other valence electrons can move. Thus the process creates the possibility of conduction due to electrons in conduction band as well as due to vacancies in the valence band. Examples: Silicon, Germanium

Characteristics of Semiconductors:

• In semiconductors, the conduction band and valence band are very close to each other or the forbidden energy gap between them is very small.
• The electrons of the valence bond can easily be excited to the conduction band.
• There is an energy gap between the conduction band and valence band which is less than 3 eV.
• Due to increase in temperature conductance increases.
• There is an effect of the addition of impurities on the conductivity of semiconductors.
• Their conductivity ranges from 10^–6 to 10⁴ ohm^–1 m^–1.

Science > Chemistry > Solid State > Electrical Properties of Solids

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In the last article, we have studied the magnetic properties of solids. In this article, we shall study the dielectric properties of solids.

Source of Dielectric Properties of Solids:

In insulators, electrons in the individual atom or ion are bound to corresponding nuclei. Hence they are not able to migrate. Thus they are localized. Due to this localization, no electrons are available for conduction and insulators do not conduct electricity to them. If the external electric field is applied these atoms or ions undergo polarization due to the formation of dipoles.

Now the dipoles produced can behave in two ways. They may align themselves in such a way that there is a net dipole moment of the crystal or they may align themselves in such a manner that they cancel each other’s dipole moment and the net dipole moment of the crystal is zero.

Dielectric Properties of Solids:

Due to polarization, the solid show some interesting properties as discussed below.

Piezoelectricity:

The crystal in which the individual dipoles formed due to polarization align themselves in such a way that there is a net dipole moment of the crystal shows piezoelectricity.

When mechanical stress (pressure) is applied to such crystal, the atoms or ions in the crystal are displaced and the crystal produces electricity. Conversely, when an electric field is applied to such crystal, there is displacement 0f the ions or atoms (anti piezoelectricity). Due to these properties, they are used as mechanical-electrical transducers.

They are used in a pickup of record players, pressure sensors, engine knock sensors, etc.

Pyroelectricity:

Some piezoelectric crystals on heating produce electricity. Electricity produced by this method is called pyroelectricity. The phenomenon is called the pyroelectric effect.

They are used in passive infrared (PIR) sensors. They are a common type of motion detector thermal sensors, which can detect the movement of human beings, animals, objects, etc., They are used in infrared non-contact thermometers.

Ferroelectricity:

In some piezoelectric crystals, the dipoles are permanently aligned even in the absence of the electric field. In such crystals, the direction of polarization can be shifted by applying an external electrical field. This phenomenon is known as ferroelectricity.

They are used in capacitors as a dielectric, in non-volatile memory, in ultrasound imaging and actuators, for making thermistors, oscillators, filters, light deflectors, modulators, and displays.

Examples of such materials are Barium Titanate (BaTiO₃), Lead Titanate (PbTiO₃), sodium potassium tartarate (Rochelle salt), Potassium dihydrogen phosphate (KH₂PO₄), etc.

Anti-ferroelectricity:

When the dipole in alternate polyhedra point up and down, the net dipole moment of the crystal is zero. Such a crystal is called antiferroelectric.

Example – Lead zirconate (PbZrO₃)

Science > Chemistry > Solid State > Magnetic Properties of Solids

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In this article, we shall study the magnetic properties of solids, classification of solids on the basis of their magnetic properties.

Every substance has some magnetic properties associated with it. The origin of these properties lies in the magnetic moments associated with the electrons. The magnetic moment of electron originates from two types of motions (i) its orbital motion around the nucleus and (ii) its spin around its own axis. Thus electrons behave like tiny magnets. Thus, each electron has a permanent spin and an orbital magnetic moment associated with it.

The magnitude of this magnetic moment is very small and is measured in the unit called Bohr magneton μ_B. It is equal to 9.27 × 10^–24 A m². The magnitude of the magnetic moment due to spin is ± μ_B and is directed along the axis of the spin. The magnitude of orbital motion is equal to m_lμ_B and is directed along the axis of rotation. Where m_l is the spin quantum number of the electron.

Types of Magnetic Material:

On the basis of their magnetic properties, substances can be classified into five categories:
(i) paramagnetic (ii) diamagnetic (iii) ferromagnetic (iv) antiferromagnetic and (v) ferrimagnetic.

Diamagnetic Substances:

Diamagnetic substances are weakly repelled by a magnetic field. The magnetism exhibited by such substance is called diamagnetism. Examples: H₂O, TiO₂, V₂O₅, NaCl and C₆H₆

They are weakly magnetized in a magnetic field in opposite direction. Diamagnetism is shown by those substances in which all the electrons are paired and there are no unpaired electrons. The pairing of electrons cancels their magnetic moments and they lose their magnetic character.

Paramagnetic Substances:

Paramagnetic substances are weakly attracted by a magnetic field. Examples: O₂, Cu²⁺, Fe³⁺, Cr³⁺, TiO, Ti₂O₃, VO, VO₂, and CuO

They are magnetized in a magnetic field in the same direction. They lose their magnetism in the absence of a magnetic field. They are temporary magnets. Paramagnetism is due to the presence of one or more unpaired electrons which are attracted by the magnetic field.

Ferromagnetic Substances:

The substances which are attracted very strongly by a magnetic field are called ferromagnetic substances. Examples: iron, cobalt, nickel, gadolinium, and CrO₂

Besides strong attractions, these substances can be permanently magnetized. In the solid-state, the metal ions of ferromagnetic substances are grouped together into small regions called domains. Thus, each domain acts as a tiny magnet. In an unmagnetized piece of a ferromagnetic substance, the domains are randomly oriented and their magnetic moments get canceled. When the substance is placed in a magnetic field all the domains get oriented in the direction of the magnetic field and a strong magnetic effect is produced. The alignments of domains persist even when the magnetic field is removed and the ferromagnetic substance becomes a permanent magnet.

Antiferromagnetism:

Substances like MnO showing antiferromagnetism have domain structure similar to ferromagnetic substance, but their domains are oppositely oriented and cancel out each other’s magnetic moment. Examples: V₂O₃, Cr₂O₃, MnO, Mn₂O₃, FeO, Fe₂O₃, CoO, Co₂O₃, NiO

Ferrimagnetism:

Ferrimagnetism is observed when the magnetic moments of the domains in the substance are aligned in parallel and anti-parallel directions in unequal numbers. Examples: Fe₃O₄ (magnetite) and ferrites like MgFe₂O₄ and ZnFe₂O₄.

They are weakly attracted by a magnetic field as compared to ferromagnetic substances. These substances also lose ferrimagnetism on heating and become paramagnetic.

Iron is strongly ferromagnetic:

Iron shows strong magnetic properties. It is a ferromagnetic substance and it can be magnetized permanently. The atomic number of iron is 28. Its electronic configuration is [Ar] 3d6 4s2. The box diagram of its electronic configuration is

There are four unpaired electrons. i.e. their spins are not neutralized. Hence they show strong magnetic properties. Hence iron is strongly magnetic.

Guoy’s Method of Studying Magnetic Properties of Solids:

The method consists of weighing the substances in an out of the magnetic field. If the substance is diamagnetic it weighs less in the magnetic field due to the opposite direction of the magnetic field set in the diamagnetic substance (repulsion). If the substance is paramagnetic it weighs more in the magnetic field due to the same direction of magnetic field set in paramagnetic substance (attraction). If the substance is ferromagnetic, then the effect is the same as that in the case of paramagnetic substance but the extent of pull is more than that in the case of paramagnetic substance.

Science > Chemistry > Solid State > Magnetic Properties of Solids

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In this article, we shall study defects in the crystal structure, sources of defects and their types.

Source of Defects in Crystal Structure:

At absolute zero, crystals tend to have a tendency to have a perfectly ordered arrangement. This arrangement at absolute zero represents the lowest energy state of the crystal. As the temperature increases, there is a change in the orderly arrangement of constituents in the crystal. The defects in crystal structure are basically irregularities in the arrangement of constituent particles. Any deviation from the perfectly ordered arrangement constitutes a defect or imperfection. Such defects which are due to temperature change are referred as thermodynamic defects. The imperfection also may be due to impurities present in solid.

The defects in the crystal due to the irregularities in the arrangement of atoms or ions are called atomic imperfections. They are due to missing or misplaced ions. Such defects are referred as point defects. Point defects are the irregularities or deviations from ideal arrangement around a point or an atom in a crystalline substance

If the deviation from periodicity extends over microscopic regions of crystal then they are called lattice imperfections. If lattice imperfections extend along the line they are called line defects. The line defects are the irregularities or deviations from an ideal arrangement in entire rows of lattice points. They are also called dislocations. If the defects extend along a plane they are called plane defects. These imperfections in crystal lead to modification of some properties of the solid or may give rise to new properties.

Usually a solid consists of an aggregate of a large number of small crystals. These small crystals have defects in them. This happens when the crystallization process occurs at the fast or moderate rate. Single crystals are formed when the process of crystallization occurs at an extremely slow rate. Even these crystals are not free of defects.

Point Defects in Crystal Structure:

Point defects are the irregularities or deviations from ideal arrangement around a point or an atom in a crystalline substance. Point defects can be classified into three types:

Stoichiometric Defects in Crystal Structure:

The compound in which the number of positive and negative ions are exactly in the ratios indicated by their chemical formulae are called stoichiometric compounds. The point defects that do not disturb the stoichiometry of the solid are called stoichiometric defects. They are intrinsic or thermodynamic defects. The electrical conductivity of crystal increases due to this defect. These defects are of two types, vacancy defects and interstitial defects.

Vacancy Defects or Schottky Defects:

When some of the lattice sites are vacant, the crystal is said to have vacancy defect. The defect produced due to vacancies caused by an absence of anions and cations in the crystal lattice of ionic solid is called a Schottky defect. Thus in such defect, one positive ion and one negative ion are missing from their respective positions leaving behind a pair of holes. This defect can also develop when a substance is heated.

Due to this defect, the observed density of crystal is found to be lower than the expected density. This defect is observed in ionic compounds with high coordination number, high radius and with cations and anions have almost equal size. like NaCl, KCl, CsCl, AgBr, KBr, etc.

Vacancy defects increase with the increase in temperature. It can be observed w.r.t. NaCl crystal as given in the table

Interstitial Defects or Frenkel Defects:

When cation and anion from ionic solid leave its regular site and moves to occupy a place between the lattice site (interstitial sites) is called an interstitial defect. This defect associated with the ionic compound is called Frenkel defect or dislocation defect. The ions occupying interstitial sites are called interstitials. The formation of this defect depends on the size of interstitials.

This defect is observed in case of an ionic compound having low coordination number and relatively smaller cations which can fit into interstitial space. This defect is common when the difference in ionic radii of two participating ions is large.

The presence of this defect does not alter the density of the solid. The presence of ions in interstitial sites increases the dielectric constant of the crystal.

Example: In AgCl the defect is observed due to Ag⁺ ions. In ZnS the defect is observed due to Zn⁺⁺ ions. AgBr, AgI

Non-Stoichiometric Defects in Crystal Structure:

There are many compounds in which the ratio of positive and negative ions present in the compound differs from that required by the ideal chemical formula of the compound. Such defects are termed as non-stoichiometric or Berthollide compounds. For example, vanadium oxide is represented as VO_x. The value of x in the crystal of the oxide varies from 0.6 to 1.3. Similarly, iron oxide is represented as Fe_xO. The value of x in the crystal of the oxide varies from 0.93 to 0.95. The balance of positive and negative charge in such compounds is maintained by having extra electrons or extra positive charges. Such defects are called non-stoichiometric defects.

These defects are of two types: (i) metal excess defect and (ii) metal deficiency defect.

Metal Excess Defect:

A metal excess defect due to anionic vacancies:

This defect is likely to be shown by a crystal which shows Schottky defects. A compound may have excess metal ion if the negative ion is absent from its lattice site, leaving a hole which is occupied by an electron to maintain electrical neutrality.

Alkali halides like NaCl and KCl show this type of defect. When crystals of NaCl are heated in an atmosphere of sodium vapour, the sodium atoms are deposited on the surface of the crystal. The Cl^– ions diffuse to the surface of the crystal and combine with Na atoms to give NaCl. This happens with the loss of an electron by sodium atoms to form Na⁺ ions. The released electrons diffuse into the crystal and occupy anionic sites. As a result, the crystal now has an excess of sodium. The anionic sites occupied by unpaired electrons are called F-centres (from the German word Farbenzenter for the colour centre). They impart a yellow colour to the crystals of NaCl. The colour results by excitation of these electrons when they absorb energy from the visible light falling on the crystals. Greater the number of F-centres, greater is the intensity of the colour.

Similarly, the excess of lithium makes LiCl crystals pink and excess of potassium makes KCl crystals violet (or lilac).

Such solids having F- centres are paramagnetic due to the presence of unpaired electrons in the hole.

A Metal excess defect due to the presence of extra cations at interstitial sites:

This defect is due to the presence of extra positive ion at the interstitial site. Electrical neutrality is maintained by the presence of electron at the interstitial site. This defect is likely to be shown by a crystal which shows Frenkel defects.

Zinc oxide is white in colour at room temperature. On heating, it loses oxygen and turns yellow. Now there is an excess of zinc in the crystal and its formula becomes Zn_1+xO. The excess Zn²⁺ ions move to interstitial sites and the electrons to neighbouring interstitial sites. Due to the presence of an electron in interstitial space, the electrical conductivity of ZnO increases on heating.

Metal Deficiency Defect Due to Cationic Vacancies: 

The non-stoichiometric compounds may have metal deficiency due to the absence of the metal ion from its lattice site. The electrical neutrality is maintained by acquiring a higher positive charge by the adjacent ion.

There are many solids which are difficult to prepare in the stoichiometric composition and contain less amount of the metal as compared to the stoichiometric proportion.

This type of defect is mainly shown by transition elements. A typical example of this type is FeO which is mostly found with a composition of Fe_0.95O. It may actually range from Fe_0.93O to Fe_0.96O. In crystals of FeO some Fe²⁺ cations are missing and the loss of positive charge is made up by the presence of the required number of Fe³⁺ ions.

Note:

Both metal excess compounds and metal-deficient compounds act as semiconductors. Due to the presence of electron metal excess compounds work as n-type semiconductors. While metal deficient compounds conduct electricity through positive hole conduction work as p-type semiconductors.

Point Defects due to Presence of Foreign Atoms or Impurity Defects:

This defect occurs when regular cation of a crystal is replaced by some different cation. The different cation may occupy a regular lattice site or interstitial site.

If the impurity cation is substituted in place of regular cation then the defect is known as substitution impurity defect. If the impurity cation occupies interstitial space then the defect is called interstitial impurity defect.

Interstitial impurity in Stainless Steel:

Substitutional impurity in Brass

Substitutional impurity in NaCl

If molten NaCl containing a little amount of SrCl₂ is crystallised, some of the sites of Na+ ions are occupied by Sr²⁺. Each Sr²⁺ replaces two Na+ ions. It occupies the site of one ion and the other site remains vacant. The cationic vacancies thus produced are equal in number to that of Sr²⁺ ions.

Another similar example is the solid solution of CdCl₂ and AgCl.

Science > Chemistry > Solid State > Defects in Crystal Structure

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The ratio of the radius of cations (r⁺) to the radius of the anion (r^–) is known as the radius ratio of the ionic solid.

The significance of radius ratio:

• It is useful in predicting the structure of ionic solids.
• The structure of an ionic compound depends upon stoichiometry and the size of ions.
• In crystals, cations tend to get surrounded by the largest possible number of anions around it.
• Greater the radius ratio, greater is the coordination number of cations and anions.
• If cations are extremely small and anions are extremely large, then the radius ratio is very small. In such case packing of anions is very close to each other and due to repulsion between anions, the system becomes unstable. Hence the structure changes to some suitable stable arrangement.
• The radius ratio at which anions just touch each other, as well as central cation, is called the critical radius ratio.

Effect of Radius Ratio on Coordination Number:

A cation would fit exactly into the octahedral void and would have a coordination number of six if the radius ratio were exactly 0.414. Similarly, a cation would fit exactly into the tetrahedral void and would have a coordination number of four, if the radius ratio were exactly 0.225.

Let us consider a case in which a cation is fitting exactly into the octahedral void of close pack anions and have the coordination number of six, in this case, the radius ratio is exactly 0.414.

When the radius ratio is greater than this, then the anions move apart to accommodate larger cation. This situation is relatively unstable. If the radius ratio is further increased the anions will move farther and farther apart till to reach a stage at which more anions can be accommodated. Now, the bigger cation moves to bigger void i.e. octahedral void whose coordination number is 8. This happens when the radius ratio exceeds 0.732.

In case of radius ratio becomes less than 0.414, the six anions will not be able to touch the smaller cation. To touch the cation, the anions starts overlapping with each other, which is an unstable situation. Hence smaller cation moves to smaller void i.e. tetrahedral void and coordination number decreases from 6 to 4.

Note: Although a large number of ionic substances obey this rule, there are many exceptions to it.

Radius Ratio of Interstitial Voids:

The vacant space left in the closest pack arrangement of constituent particles is called an interstitial void or interstitial site.

Tetrahedral Voids:

Locating Tetrahedral Voids:

Let us consider a unit cell of ccp or fcc lattice [Fig. (a)]. The unit cell is divided into eight small cubes. Each small cube has atoms at alternate corners as shown. Each small cube has 4 atoms. When joined to each other, they make a regular tetrahedron as shown in the figure. Thus, there is one tetrahedral void in each small cube and eight tetrahedral voids in total in the unit cell. Each of the eight small cubes has one void in one unit cell of ccp structure. The ccp structure has 4 atoms per unit cell. Thus, the number of tetrahedral voids is twice the number of atoms.

Radius Ratio of Tetrahedral Void:

A tetrahedral site in a cube having a tetrahedral void of radius ‘r’ is as shown at the centre of the cube. Let ‘R’ be the radius of the constituent particle of the unit cell. Let ‘a’ be each side of the cube.

Consider face diagonal AB (Right-angled triangle ABC). We have,

AB² = a² + a²

∴  AB² = 2 a²

∴  AB² = √2 a

Now the two-sphere touch each other along face diagonal AB

∴  2R = √2 a

∴  R = √2 a/2

∴  R =  a/√2  ……. (1)

Consider body diagonal AD (Right-angled triangle ABD). We have,

AD² = AB² + BD²

∴  AD² = (√2 a)² + a²

∴  AD² = 2 a² + a² = 3 a²

∴  AD = √3 a

Now the two spheres at the diagonals touch the tetrahedral void sphere along body diagonal AD

∴  2 R + 2r  = √3 a

∴  R + r  = (√3/2)a  ……..  (2)

Dividing equation (2) by (1)

Thus the radius ratio for the tetrahedral void is 0.225

Octahedral Voids:

Locating Octahedral Voids:

Let us consider a unit cell of ccp or fcc lattice [Fig. (a)]. The body centre of the cube, C is not occupied but it is surrounded by six atoms on face centres. If these face centres are joined, an octahedron is generated. Thus, this unit cell has one octahedral void at the body centre of the cube.

Besides the body centre, there is one octahedral void at the centre of each of the 12 edges. [Fig. (b)]. It is surrounded by six atoms, four belonging to the same unit cell (2 on the corners and 2 on face centre) and two belonging to two adjacent unit cells.

Since each edge of the cube is shared between four adjacent unit cells, so is the octahedral void located on it. Only 1/4 th of each void belongs to a particular unit cell.

For cubic close-packed structure:
Number of octahedral void at the body-centre of the cube = 1
12 octahedral voids located at each edge and shared between four unit cells

Thus number of octahedral valve at 12 edges =12 x 1/4 = 3
Thus, the total number of octahedral voids in unit cell = 1 + 3 = 4

In the ccp structure, each unit cell has 4 atoms. Thus, the number of octahedral voids is equal to this number of atoms.

Radius Ratio of Octahedral Void:

A octahedral site in a cube having octahedral void of radius r is as shown at the centre of the cube. Let R be the radius of the constituent particle of the unit cell. Let a be each side of the cube. In this case we can see that a = 2R

Consider Right angled triangle ABC. We have,

AB² = AC² + CB²

∴  (2R + 2r)² = a² + a²

∴  (2R + 2r)² = 2 a²

∴  2R + 2r = √2 a

But from figure a = 2R

∴  2R + 2r = √2 x 2R

∴   R +  r = √2  R

∴   r = √2  R – R

∴   r = (√2  – 1)R

∴   r = (1.414  – 1)R

∴   r = 0.414R

Thus radius ratio for the octahedral void is 0.414

Science > Chemistry > Solid State > Radius Ratio and its Significance

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In this article, we shall study two types of voids formed during hexagonal closed packing namely, a) Tetrahedral voids and b) octahedral voids.

Let us consider a closed pack hexagonal packing in the first layer as shown. There are empty spaces between the particles (sphere) are called voids.

All the voids are equivalent in the first layer they have marked alternately as ‘a’ and ‘b’. The spheres of the second layer can be either placed on voids which are marked ‘a’ or ‘b’ but it is impossible to place spheres on both types of voids simultaneously. When spheres of the new layer are placed on voids marked ‘a’ then voids marked as ‘b; remain unoccupied.

Thus there is no void above ‘a’ in the second layer but there is void above ‘b’ even in the second layer. The void between the first layer and second layer at ‘a’ is tetrahedral void, while the void between the first layer and the second layer at ‘b’ is octahedral void.

T = Tetrahedral void and O = Octahedral void

Tetrahedral Voids:

Wherever a sphere of the second layer is above the void of the first layer (or vice versa) a tetrahedral void is formed. These voids are called tetrahedral voids because a tetrahedron is formed when the centres of these four spheres are joined. These voids have been marked as ‘T’ in the figure.

Octahedral Voids:

At other places, the triangular voids in the second layer are above the triangular voids in the first layer, and the triangular shapes of these do not overlap then the octahedral void is formed. One of them has the apex of the triangle pointing upwards and the other downwards. These voids have been marked as ‘O’ in the figure.

Number of Voids:

The number of these two types of voids depends upon the number of close-packed spheres.

Let the number of close-packed spheres be N, then, the number of octahedral voids generated = N and the number of tetrahedral voids generated = 2N

Characteristics of Tetrahedral Voids:

• The vacant space or void is surrounded by four atomic spheres. Hence co-ordination number of the tetrahedral void is 4.
• The atom in the tetrahedral void is in contact with four atoms placed at four corners of a tetrahedron.
• This void is formed when a triangular void made coplanar atoms (first layer) is in contact with the fourth atom above or below it (second layer).
• The volume of the void is much smaller than that of the spherical particle.
• If R is the radius of the constituent spherical particle, then the radius of the tetrahedral void is 0.225 R.
• If the number of close-packed spheres is N, then the number of tetrahedral voids is 2N.

Characteristics of Octahedral Voids:

• The vacant space or void is surrounded by six atomic spheres. Hence, the coordination number of the tetrahedral void is 6.
• The atom in the octahedral void is in contact with six atoms placed at six corners of an octahedron.
• This void is formed when two sets of equilateral triangles pointing in the opposite direction with six spheres.
• The volume of the void is small.
• If R is the radius of the constituent spherical particle, then the radius of the octahedral void is 0.414 R.
• If the number of close-packed spheres is N, then the number of octahedral voids is N.Characteristics of Voids

Packing Voids in Ionic Solids

We have already seen that when particles are close-packed resulting in either cubic closed packing (ccp) or hexagonal close packing (hcp) structure, two types of voids are generated. The number of octahedral voids present in a lattice is equal to the number of close-packed particles, the number of tetrahedral voids generated is twice this number.

Ionic solids are formed from cations and anions. The charge is balanced by an appropriate number of both types of ions so that net charge on solid is zero (neutral).

In ionic solids, the bigger ions (usually, anions) form the close-packed structure and the smaller ions (usually, cations) occupy the voids. If the smaller ion is small enough then tetrahedral voids are occupied, if bigger, then octahedral voids are occupied.

Not all octahedral or tetrahedral voids are occupied. In a given compound, the fraction of octahedral or tetrahedral voids that are occupied, depends upon the chemical formula of the compound, as can be seen from the following examples.

Example 1:

A compound is formed by two elements X and Y. Atoms of the element Y (as anions) make cubic closed packing (ccp) and those of the element X (as cations) occupy all the octahedral voids. Obtain the formula of the compound.

Solution:

Given that the cubic closed packing (ccp) lattice is formed by the element Y.

The number of octahedral voids generated would be equal to the number of atoms of Y present in it.

Since all the octahedral voids are occupied by the atoms of X, their number would also be equal to that of the element Y. Thus, the atoms of elements X and Y are present in equal numbers or 1:1 ratio.

Therefore, the formula of the compound is XY.

Example 2:

Atoms of element B form hexagonal close packing (hcp) lattice and those of element A occupy 2/3rd of tetrahedral voids. Obtain the formula of the compound formed by the elements A and B.

Solution:

The number of tetrahedral voids formed is equal to twice the number of atoms of element B

Only 2/3rd of these are occupied by the atoms of element A. Hence the ratio of the number of atoms of A and B is 2 × (2/3):1 or 4:3

Hence the formula of the compound is A₄B₃.

Science > Chemistry > Solid State > Tetrahedral Voids and Octahedral Voids

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