Definition of Solid State
Solid is the condensed state of matter in which particles (atom, molecules or ions) are closely arranged in fixed position with very little freedom of movement due to strong inter-particle forces and are nearly incompressible having very high density, rigid structure and mechanical strength.
Kinetic Description of Solids
1. According to kinetic molecular theory particles in solids have little space due to strong attractive forces.
2. The particles in solids are tightly packed together about their mean position.
3. Owing to restricted motion of particles, solids have fixed shape and volume.
4. when a solid is heated, the vibrational energy of particles increases and when a particular temperature is reached the vibrational energy of solid particles overcome the attractive forces, which results particles of solids lose their mean position as well as specific arrangement and change into liquid state.
Characteristic Properties of Solids
1. High density
2. Low compressibility
3. Rigidity
4. Definite shape and volume
5. High melting and boiling points
Compression/Compressibility
Solids are nearly and practically incompressible. The compressibility of solids is almost nearly zero due to absence of empty spaces. However, they are not absolutely incompressible, but the effect of pressure is negligible on solids and they cannot be compressed, instead the mass is deformed.
In term of kinetic theory,
The particles in solids are tightly bonded together due to strong attractive forces therefore only a very small unfilled space is left among them. Due to less empty spaces, solids are denser, rigid and hard and can withstand considerable external pressure.
Diffusion/Diffusibility
Solids diffuses very slowly as compared to liquids and gases due to close packing of their particles and restriction against the free movement of their particles. Diffusion is due to molecular motion. Although there is no translational movement among the molecules of solid, even though one solid diffuses into the another. However, rate of diffusion in solid is much slower than gas and liquid.
For example; if smoothly polished bars of Zinc and Copper are tied together, after very long time, one metal penetrates into the other and vice versa.
In terms of kinetic molecular theory, the limited diffusibility of solids can be explained as:-
The movement in solids particles is restricted and there is no translational movement among its particles but nevertheless particles are vibrating at their mean positions. This vibrational motion is responsible for diffusion in solids. Due to very limited vibratory movement, very small diffusion can take place.
Expansion
Solids expand on heating but this ability is very little as compared to liquids and gases. An increase in temperature weakens the attractive forces among particles of solids by producing slight gaps between their particles resulting in an increase in volume
Melting
Solid melt on heating at a particular temperature. In term of kinetic theory, on heating vibrational energy of particles of solids increases until at melting temperature the vibrational energy of the solid particles overcome the energy of existing bond among them resulting in the state change from solid to liquid state.
Sublimation
The process of direct conversion of solid to gaseous state (vapours) without passing through an intermediate liquid phase on heating is called Sublimation. Some solids directly change into vapours on heating without passing thorough liquid phase which is known as sublimation. The substances which change directly from solid state to vapours forms are called sublime substances. The rate of sublimation increases with the rise of temperature.
e.g. camphor, iodine, solid CO2 (dry ice), naphthalene, ammonium chloride etc.
In terms of kinetic molecular model, sublimation may be explained as:-
the attractive forces in sublime solids are quite weaker as compared with ordinary solids, thus on heating, high-energy surface particles of sublime solids overcome the attractive forces and directly pass into vapours.
Kinetic Energy and Molecular Motion
Particles of solid can only vibrate about their mean position. They do not possess translational and rational kinetic energy as liquids particles do. They have only vibrational kinetic energy.
Intermolecular forces
Particles in solid held together tightly in a fixed position due to strong intermolecular forces.
Deformity
Solids are almost incompressible, and they are deformed or shattered by high pressure.
In terms of kinetic molecular theory, deformation of solids can be explained as;
The particles of solids are so tightly bound together that there is slightly unfilled space between them. By applying external pressure, some particles are dislocated but the force of attraction is so strong that the rearranged atoms are held equally well to their neighbours. Hence deformity in mass occurs.
Melting
Melting is the characteristic property of solid by which they are converted into liquid state on heating.
In terms of kinetic molecular theory, melting may be explained as:
On increasing the temperature, the kinetic energy of solid particles is increased. Due to increased vibrational energy, their particles vibrate more vigorously thereby overcoming the forces holding them and solid particles do not remain on their mean position and becomes mobile i.e. move to and fro, showing properties of liquid.
Discoverer
Isomorphism was discovered by Eilhard Mitscherlich (1820).
Similar morphology (crystal forms)
Different chemical composition
The term “morphism” refers to the morphology i.e. the external appearance. Therefore, isomorphism and polymorphism are two terms used to describe the morphology of chemical substances. The existence of a substance in more than one crystalline form is known as polymorphism. If this substance is a single element, then it is called allotropy rather than polymorphism. If two or more different substances show the same morphology, then it is called isomorphism. The main difference between isomorphism and polymorphism is that isomorphism describes the presence of the same morphology in different substances whereas polymorphism describes the presence of different morphologies of the same substance.
Definition
Examples
Properties of isomorphous substances
Different physical and chemical properties
They have different physical and chemical properties. As isomorphous substances are composed of combinations of different atoms, the chemical and physical properties of isomorphous substances are different from each other. Such properties include mass, density, chemical reactivity, etc.
Mixed Crystals
The isomorphous substances can crystallize together to give mixed crystals.
Same atomic ratio or same empirical formula
They are comprised of the same atomic ratio i.e. they have same empirical formula i.e. isomorphous substances show that their atoms are usually found in the same ratio.
e.g.
NaF and MgO have same atomic ratios 1 : 1.
Other Examples of Isomorphs Crystal Pairs
Same polarizability and ratio of cation and anion radii
Isomorphs have usually same polarizability and ratio of cation and anion radii.
Isomorphism Vs Polymorphism
Discoverer
Polymorphism was discovered by Eilhard Mitscherlich (1821).
Different morphology; Same chemical composition, Depends on external conditions
Definition
Polymorphs or Polymorphous Substances
The substance (element or compound) which can exist in more than one crystalline form is called Polymorphous or Polymorphs i.e. it crystallizes in two or more different forms under different conditions having same chemical properties but different physical properties due to difference of structural arrangement of their particles.
Explanation
Polymorphism is a phenomenon in which a single substance (element or compound) occurs in more than one crystalline form having the same chemical properties but different physical properties. These different crystalline forms can be interconverted at its transition temperature. Different polymorphs have different transition temperature.
For example
CaCO3 is found as calcite in trigonal and aragonite in orthorhombic form.
CaCO3 Low pressure: Calcite – trigonal, High pressure: Aragonite – orthorhombic
AgNO3 is found in rhombohedral and orthorhombic system.
Examples
Properties of polymorphs
1. They have same chemical properties.
2. The have different physical properties due to difference of their structure.
Solids can be broadly classified on the basis of following parameters:
1. Based on various properties or geometrical shape (2 types)
2. Based on bonding present in its constituent particles of building blocks (4 types)
On the basis of the arrangement of constituent particles and shape, the solids have been classified into two categories, namely:
1. Crystalline solids or True Solids
2. Amorphous (Shapeless) solids (False or non-crystalline Solids)
Crystalline solids have a regular structure over the entire volume and sharp properties while amorphous solids have irregular structure over long distances and properties are not that sharp.
Comparison between crystalline and amorphous solids
Comparison between crystalline and amorphous solids
Comparison between crystalline and amorphous solids
Comparison between crystalline and amorphous solids
Definition
The solids which have well-defined regular three-dimensional geometrical order or shape due to highly ordered three-dimensional arrangement of particles (atoms, molecules or ions) are called Crystalline or True solids. Most of the solids occur in nature as crystalline solids. They have definite geometrical shape and sharp melting points.
When the constituent particles of a solid are arranged in a definite, regular and repeated geometric pattern throughout the entire three-dimensional network of the crystal then the solid is called crystalline or true solid. These are the solids in which three-dimensional arrangements of particles (atoms, molecules or ions) is regular (ordered) and repetitive having characteristic geometrical shape.
In crystalline solids, the structural unit is arranged in three dimension and this regular pattern throughout the crystal is called crystal lattice and the smallest fundamental portion or unit of crystal which repeats in all three dimensions to give the crystal structure is called unit cell.
Examples
metals, diamond, graphite, sulphur, Quartz, mica, ice, sucrose or sugar, alum, calcite, sodium chloride (rock salt), copper sulphate, ferrous sulphate, magnesium chloride, sodium carbonate, minerals etc.
Crystal lattice or crystal
They are composed of fundamental building blocks called unit cell which stacked or repeated in three dimensions to form crystal lattice or crystal.
True Solids
Crystalline Solids are also known as True Solids as they don’t tend to flow like pseudo solids.
Long and short range Order
Crystalline solids depict both long range and short range order.
Reason for Crystal formation
The reason for formation of regular pattern or crystal is that atoms, ions or molecules tend to arrange themselves in position of maximum attraction or in position of minimum energy.
Characteristic properties of crystalline solids
Following are the characteristic properties of crystalline solids:
1. Definite shape (regular structure and have definite geometrical shape)
2. Sharp melting point (long range and uniform attractive forces)
3. Symmetry (their appearance does not change on rotation)
4. Cleavage plane (breakage of a big crystal into small crystals of identical shape due to pressure)
5. Anisotropy (variations in physical properties along different molecular axes)
1. Definite Geometrical shape of crystals
Crystalline solids show regular structure and have definite geometrical shape. The constituent particles (atoms, ions or molecules) of crystalline solids are arranged in an orderly three-dimensional repeating pattern or network or layers called crystal lattice.
e.g.
the shape of unit cell of diamond is cubic and graphite is hexagonal.
Reason of Definite Shape
The atoms, molecules or ions in crystals are arranged in a definite regular geometrical pattern or shape. They have specific angles faces and axis. These angles and axis are present even if the crystals are broken down into small pieces. Hence, they possess a definite geometric shape. The potential energy of the configuration of constituent particles is minimum in the crystalline solid i.e. they are found in stable state.
They have long-range order. Periodicity in the arrangement of constituent particles extends over many million atomic diameters.
2. Sharp melting point
1. Crystalline solids are characterized by sharp melting point (i.e. whole solid melts at same time) which means they suddenly convert into liquid state at a definite temperature.
Reason of Sharp Melting Point
This is due to the fact that attractive forces between particles are long range and uniform. These forces breakdown at the same instant, at melting point.
The sharp melting point is because the distance between same atoms/molecules or ions is same and remains constant, unlikely from amorphous solids. (The heat of fusion is definite and fixed as the regularity in crystal lattice remains same and is ideal).When heated, all the particles eventually leave their fixed position at the same temperature and start movements. The temperature remains constant until all the solid change into liquid.
3. Cleavage and cleavage plane
Definition
The breakage of a big crystal into small crystals of identical shape due to external pressure is called Cleavage. The plane or line or point through which a crystal can be broken down into small identical crystals is called Cleavage Planes.
Crystalline solids have cleavage planes and exhibit the property of cleavage.
4. Anisotropy
Definition
Anisotropy is the property of molecules or substances to exhibit variations in physical properties along different molecular axes of the substance i.e. the variation of intensity of certain physical properties (such as electrical conductivity, refractive index etc.) in different directions is called anisotropy and the substance possessing this property is called Anisotrope.
The property of a crystalline substance in which its crystal shows variable intensity of physical properties (such as coefficient of thermal expansion, electrical and thermal conductivity, refractive index etc.) in different directions in the crystal lattice is called Anisotropy and the substance possessing this property is called Anisotrope.
Crystalline solids are usually anisotropic and exhibit the property of anisotropy i.e. they have certain physical properties that vary with direction. Crystalline solids show variable intensity of physical properties in different directions. Their physical properties like electrical conductivity, thermal conductivity, thermal expansion, refractive index, mechanical strength etc. are different in different directions.
Reason of Anisotropic Behaviour
The reason of anisotropic attitude is attributed to the fact that arrangement of particles is different in the different directions.
For example
(a) Graphite can conduct electricity parallel to its plane of layers but not perpendicular to plane because of electron movement is not allowed on perpendicular of the layer.
(b) A crystal has different values of refractive index because light passes with different velocities in different direction in a crystal.
5. Symmetry and Its Types
When crystalline solid or crystal is rotated about an axis by 360o (to a certain angle), a regular repetition of edges and faces is observed (and their appearance does not change) this is known as symmetry.
Crystalline solids possess symmetry and are symmetrical i.e. their appearance does not change when crystalline solids are rotated about an axis.
Elements of symmetry/symmetry elements
The symmetry of an individual crystal is determined by three elements called symmetry elements or elements of symmetry, which are plane of symmetry, axis of symmetry and centre of symmetry.
1. Plane of symmetry
2. Axis of symmetry
3. Center of symmetry
1. Plane of symmetry
It is an imaginary plane which divides the crystal into two equal parts in such a way that one is the image of other.
If a crystal can be divided by an imaginary plane into two equal halves such that one half is the exact mirror image of the other, it is said to have plane of symmetry.
2. Axis of symmetry
It is an imaginary line which the crystal can be rotated through 360o. It is an imaginary line drawn through the crystal such that rotating the crystal through 360o, the crystal present exactly the same appearance more than once.
It is the point at the center of the crystal which is equidistant from two opposite faces of a crystal.
3. Center of symmetry
It is a point in the crystal from which we can draw a line. This line intersects the surface of the crystal at equal distance on either side.
It is noted that a crystal may have a number of plane of symmetry or axis of symmetry, but it can have only one center of symmetry.
Elasticity
Different crystals have different degree of elasticity. They quickly recover their shape when deforming forces is removed.
Habit of Crystal
The shape in which a crystal grows is called habit of crystal
e.g. Habit of NaCl is cubic. NaCl has cubic habit means that during the crystallization of NaCl, it will adopt cubic geometry.
Crystal Growth
When a hot saturated solution of salt or molten solid is allowed to cool slowly, crystal are grown in various directions which is called crystal growth.
For example
a slow cooling of hot saturated solution of table salt give cubic crystals.
Definition
The Greek word amorphous means shapeless or without any form.
They are non-crystalline solids with no proper arrangement of atoms in the solid lattice. The particles in are arranged in a regular manner upto a small region only. In other words, amorphous solids don’t have certain organized arrangement of atoms and molecules.
Pseudo-solids or Super-cooled Liquids
They are not true solids. Due to short range order, small parts of amorphous solids may be crystalline and rest may be non-crystalline.
Amorphous Solids are also called Pseudo-solids or Super-cooled Liquids because they don’t form crystalline structure and has the ability to flow.
Amorphous solids are actually super-cooled liquid because they are formed when a substance in liquid state is cooled rapidly.
Polymeric solids and intermediate between solids and liquids
They are mostly polymeric solids.
They may be regarded as intermediate between solids and liquids.
Examples
Glass, plastics, rubber (polymeric solids), cement, polymers, talc powder, charcoal, tar, soot, resins, gel, amorphous silica (one of the best material for converting sunlight into electricity; photovoltaic cell), etc.
Characteristic properties of amorphous solids
Amorphous solids do not have long range of order of particles and assumed them closer to liquid. Thus on continuous heating, they gradually soften and finally convert into a flowing liquid. Amorphous solids do not have equally strong bonds
they do not have a definite shape due to random, non-repetitive three-dimensional pattern. They do not have sharp melting points and these solids first soften and then finally melt. Hence they melt over a wide range of temperatures. They are isotropic i.e. their physical properties are same in all directions. They do not give a clean surface after cleavage with a knife. Rather, they undergo an irregular breakage.
Following are the characteristic properties of amorphous solids:
1. No definite shape
2. Diffused melting point
3. Unsymmetry
4. Lack of cleavage plane
5. Isotropic and Isotropy
(i) No definite shape
1. Particles of amorphous solids are arranged in random, non-repetitive three dimensional pattern. Hence, they do not have a definite shape.
Reason
The constituent particles of matter inside amorphous solid are arranged in a random manner, that is, the position of atoms and molecules is not fixed and varies from one solid to another.
(ii) Diffused melting point
1. They are characterized by diffused melting point i.e. they do not have sharp melting point, which means that they melt over a wide range of temperatures.
Reason
This is because they variable intensity of intermolecular forces from place to place because of irregular packing of amorphous solids and have Short-range order.
(iii) Unsymmetrical
they are unsymmetrical i.e. their appearance change when these solids are rotated about an axis.
Reason
Amorphous solids are unsymmetrical in nature, due to irregular packing of atoms and molecules inside the solid lattice
(iv) Absence of cleavage plane
Amorphous solids lack cleavage planes i.e. they do not break down at fixed cleavage planes.
(v) Isotropy
They are isotropic i.e. their physical properties are same in all directions. [liquids and gases are also isotropic as their properties are independent of direction]. The amorphous solids is isotropic in nature i.e. the properties measured in all directions come out to be same,
for example refractive index of amorphous solids is same
Reason
The reason for isotropic in nature is that there is no long range order in them and arrangement is irregular along all the directions. Therefore, value of any physical property would be same along any direction.
Anisotropy is the variation in physical properties depending upon orientation/ direction of atoms, ions or molecules of a crystal.
Crystalline solids are anisotropic in nature, that is, some of their physical properties like electrical resistance or refractive index show different values when measured along different directions in the same crystals. This arises from different arrangement of particles in different directions. Since the arrangement of particles is different along different directions, the value of same physical property is found to be different along each direction.
On the basis of the nature of bonding or binding forces between the constituting particles (inter-particle attractive forces), crystals are classified into following four types:
Atomic/metallic crystals----------- strong binding forces; Metallic bond (80-1000 kJmol−1)
Ionic/ Electrovalent crystals ---Very strong binding forces, Ionic bond(400-4000kJmol−1)
Covalent Network crystals------ Weak binding forces, Covalent bond (150-500 kJmol−1)
Molecular crystals ----- Very weak forces, H-bond or van der Waal’s forces (1-40kJmol−1)
Summary of Atomic or Metallic Crystals
1. They consist of metal atoms packed and held together metallic bonding e.g. copper, iron, gold, etc.
2. They are characterized by luster, high melting point, high electrical and thermal conductivity, malleability and ductility.
Summary of Ionic Crystals or Electrovalent Crystals
1. They consist of positively and negatively charged ions, held together by electrostatic attraction (ionic bond) e.g. NaCl, CuSO4, KCl, MgF2 etc.
2. They are characterized by hard and brittle crystals, high melting point, High lattice energy, high electrical conductivity both in fused and solution form.
Summary of covalent network Crystals
1. They consist of non-metallic atoms held together by covalent bonds are called Covalent Crystals e.g. diamond, graphite, carbon, silicon, germanium, quartz (SiO2), carborundum or silicon carbide (SiC), BN, AlN, etc.
2. They are characterized by very hard and brittle crystals, high melting point, High lattice energy, poor electrical conductivity.
Summary of molecular Crystals
1. They consist of molecules held together either by hydrogen bonding or Vander Waal’s forces. For example; the polar and non-polar molecules such as Iodine, argon, S8, chlorine, ice, dry ice (solid CO2), sugar, glucose, methane, cholesterol, benzene, paraffin, ascorbic acid, hydroquinone, etc. form molecular crystals.
2.They are characterized by Soft to hard and brittle crystals with waxy texture, low melting point, low lattice energy, poor electrical conductivity.
Summary of Four Types of Solids According to Nature of Bonding
Summary of Four Types of Solids According to Nature of Bonding
Summary of Four Types of Solids According to Nature of Bonding
Summary of Four Types of Solids According to Nature of Bonding
Atomic or Metallic Crystals
Summary
Definition of Atomic Solids
The crystals which consist of metal atoms packed and held together by a special type of bonding i.e. metallic bonding are called Atomic or Metallic Crystals.
Examples
All metals like copper, iron, gold, silver, etc.
Explanation
[In metals, valence electrons are loosely held and free to move in crystal lattice. In this way electrons form a kind of negatively charged atmosphere called Electron Sea or Electron Gas in which positive ions of metal are immersed. The metallic bond is formed due to force of attraction between electron sea and positive ions of metal].
Metals are orderly collection of positive ions surrounded by and held together by a sea of free electrons. These electrons are mobile and are evenly spread out throughout the crystal. Each metal atom contributes one or more electrons towards this sea of mobile electrons.
These free and mobile electrons are responsible for high electrical and thermal conductivity of metals. When an electric field is applied, these electrons flow through the network of positive ions. Similarly, when heat is supplied to one portion of a metal, the thermal energy is uniformly spread throughout by free electrons.
Conductivity α 1/T
Another important characteristic of metals is their luster and colour in certain cases. This is also due to the presence of free electrons in them. Metals are highly malleable and ductile.
Constituent Particles
Kernels (atom without its valence shell i.e. nuclei with all the inner shell electrons) and electrons
Binding forces
Metallic bonds
Properties of Metallic Crystals
Metallic crystals are characterized by:
Electron Pool/Electron gas theory
1. Drude and Loren (1923)
2. Based on valecne bond theory
3. Metallic bond is purely covalent in nature
4. Electrons are delocalized not localized.
Ionic Crystals or Electrovalent Crystals
Summary
Definition
The crystals which consist of positively and negatively charged ions, held together by electrostatic attraction (ionic bond) arises due to transference of electrons are called Ionic Crystals. These are the solids consisting of oppositely charged ions i.e. positively charged cations and negativity charged anions held together by electrostatic forces or ionic bonds. Ionic bond is strong attractive force (600-4000 kJmol−1) and is non-directional.
For example
In the case of Table salt or sodium chloride (NaCl) ionic solid is composed of simple ions (Na+ and Cl−) held together by electrostatic forces of attraction whereas in the case of ammonium nitrate (NH4NO3), ionic solid comprises of polyatomic ions (NH4+ and NO3−) held together by electrostatic forces of attraction.
Examples
NaCl, CuSO4, KCl, MgF2 etc.
Explanation
Ions are the constituent particles of ionic solids. Such solids are formed by the three dimensional arrangements of cations and anions bound by strong coulombic (electrostatic) forces. They are not present in independent molecular forms, instead supposed to be present in formula unit form. These solids are hard and brittle in nature. They have high melting and boiling points. Since the ions are not free to move about, they are electrical insulators in the solid state. However, in the molten state or when dissolved in water, the ions become free to move about and they conduct electricity. Their shapes depend on ratio of cations and anions
They are hard and brittle because their stability depends upon the preservation of their geometric pattern.
Constituent Particles
Ions of opposite charges
Binding forces
Electrostatic forces
Properties of Ionic Crystals
Ionic crystals are characterized by:
Properties of Ionic Crystals
Ionic crystals are characterized by:
1. Brittle solids and easily shatter by hammering due to repulsion of ions of same charge
2. Very Hard solids due to the presence of strong electrostatic forces of attraction
3.High melting point (>1200oC) and boiling points and low volatility due to strong attractive force.
4. Conduction of electricity in fused state or in solution form due to free movement of ions.
5. Non-conductivity of electricity in solid state due to restricted vibration of ions because ions are rigidly held).
6. They are soluble in water and polar solvent.
7. have definite geometrical shape.
8. Do not exist in the form of molecules (rather shown by empirical formula, formula unit and formula mass).
9. High density due to close packing of ions
10. Soluble in in polar solvents
11. Do not exhibit isomerism due to non-rigid and non-directional nature of ionic bond but show isomorphism and polymorphism
Poor conductivity
Ionic compounds are good conductor electricity either in fused state or in aqueous solution due to free movement of ions towards respective electrode when a potential difference is applied.
However, ionic compound exhibit poor conductivity in the solid state due fixed and immobile position of ions in the ionic crystals.
Factors affecting the shape of an Ionic Crystal
Following factors affect the shape of ionic crystal
(i) Ionic Association
Due to electrostatic force of attraction in ionic solids, the oppositely charged ions are closely packed in specific order to form a particular shape. For example; in the crystal of common salt, each Na+ ion is surrounded by six Cl− ions and each Cl− ion is covered up with six Na+ ions, and this arrangement gives a cubic shape to it.
(ii) Radius Ratio (r+/r−)
In simple ionic crystals, the cations commonly occupy the voids or holes. The voids are empty spaces left between anionic spheres.
The structure of an ionic crystal depends upon the radius ratio of cation and anion. Radius ratio is the ratio of radius of cation to that of radius of anion (r+/r−) in the given ionic solid. It helps in predicting the shape of ionic solid.
Radius ratio = radius of cation/radius of anion
The critical radius ratio of the void (cation) and sphere (anion) is calculated by solid geometry.
Limiting radius Ratio for predicting the shape of Ionic Solids
Coordination number (CN)
The number of spheres (atoms, molecules or ions) directly surrounding a single sphere in a crystal is called coordination number.
For ionic compounds, the coordination number is the number of anions that are arranged about the cation in an organized structure. For example, NaCl has a coordination number of 6. In other words, 6 Cl- ions surround 1 Na+ ion. The number of anions that can surround a cation is dependent (but no entirely) on the relative sizes of the ions involved.
Taking NaCl, the radii of Na+ ion is 0.95Å and Cl− is 1.81Å, their ratio would be
forming the NaCl lattice with coordination number 6
Crystal structure of some elements and their coordination numbers
Steps of Drawing Unit Cell of NaCl
1. First draw a perfect cube. Draw a square:
2. Then draw an identical square, offset from the first one.
Getting the offset right is important. If you get it wrong, when you draw the ions, they will all end up in a muddle! The only way you are going to find this out is by trial and error. If you take the diagram above as a guide, you won't go far wrong.
3. Now join the two squares together to make a cube.
4. Divide the cube into 8 smaller cubes.
Start by drawing lines from the mid-points of each edge to the edge opposite on the same face of the cube. When you have done each face, it will look like this:
5. Finally, you have to draw three lines through the centre of the cube from the centre of each face to the centre of the opposite face.
Don't worry if, when you have finished, the lines don't meet exactly, or it looks a bit tatty. The sketches above are definitely flawed! We are doing chemistry, not technical drawing. All the flaws will get covered up when you add the ions.
6. Put the ions on.
Don't forget to add a key showing which ion is which.
Chloride ions have a diameter which is roughly twice the size of the sodium ions. The exact numbers don't matter - just show the chloride ions as bigger.
In the top layer of ions, it doesn't matter whether you start with sodium ions or chloride ions in the corners. All that matters is that you alternate the ions so that you never get two ions the same joined directly by one of the lattice lines.
To be sure you know exactly what you are doing, it would probably be a good idea to draw this twice - once with the chloride ions on the corners of the big cube, and once with sodium ions on those corners. That will force you to think rather than just copy.
When you have finished, always check that every lattice line has a sodium ion at one end and a chloride ion at the other. If you find two chloride or two sodium ions with a direct line joining them, you have done it wrong!
Alternate Way of Drawing Unit Cell of NaCl
Short Method of Unit Cell of NaCl Crystal
Independent molecules of NaCl do not exist in vapour phase as well as in solid state. That is why NaCl is said to be the formula unit of sodium chloride. Sodium chloride has giant ionic structure.
FCC structure
Coordination no. = 6
Na+ = 10e− (small size)
Cl− = 18e− (large size)
Calculation of Na+ and Cl− per unit Cell
Short Method
Detailed Note on Unit Cell of NaCl Crystal
Independent molecules of NaCl do not exist in vapour phase as well as in solid state. That is why NaCl is said to be the formula unit of sodium chloride. Sodium chloride has giant ionic structure.
Co-ordination Number
The number of ions of same kind that surround an oppositely charge ion is called coordination number. The structure of sodium chloride crystal is built up be repeating face centred cubic unit cells.
In crystallographic view point, in NaCl, each Na+ ion is surrounded by six Cl− ion and each Cl− ion is covered up with six Na+ ions. This ionic arrangement suggest that the coordination number of sodium chloride crystal is 6. The coordination number of Na+ is 6 and coordination number of Cl− is also 6.
Chloride (Cl−) Determination
the given figure shows that eight (8) chloride ions are located at the eight corners of cube while six (6) chloride (Cl−) ions at the centre of its six faces. On the basis of this information, we can determine the number of Cl− ions in each unit cell of sodium chloride crystal.
Since each chloride (Cl−) ion at the corner is shared between eight other unit cells, thus its share to each unit cell should be 1/8 therefore, no of Cl- at the corner is 1. On the other hand six faces have six chloride ions at their centre but each face share with two unit cells therefore no. of Cl− ion at the face is 3.
The unit cells shares one Cl− ion at one corner = 8
A unit cell gets a share of one Cl− ion at the corner = 1/8
A unit cell gets a total share of Cl− ions at eight corners = 1/8 x 8 = 1
A unit cell gets a share of one Cl− at one face = ½
A unit cell gets a total share of Cl− ions at six faces = ½ x 6 = 3
Total number of chloride ions in each unit cell = 1+3 = 4Cl−
Sodium (Na+) Ion Determination
There are 12 edges of cube, each contains one sodium (Na+) ion. Also each Na+ ion on the edge of cube is shared by four units cells therefore
No. of Na+ ions on each edge = ¼ x 12 = 3
No of Na+ ions on the centre of unit cell = 1
Total no. of Na+ ions in each unit cell = 3 + 1 = 4
Total sodium ion in unit cell = 4
Summary
Total ion pairs = 4
Total ions = 8
Total Cl− ion in unit cell = 4
Distance between same ions = 5.632Å
Distance between different ions = 2.815 Å
Ions at centre = 1
Macromolecular or Covalent Network Solids or covalent crystals (non-metallic crystals)
Definition
The crystals which consist of atoms held together by covalent bonds are called Covalent Crystals . These are the solids consisting of atoms of the same or different elements connected to each other by network of covalent bonds throughout the crystal forming a giant molecule.
Examples
diamond, graphite, carbon, silicon, germanium, quartz (SiO2), corborundum or silicon carbide (SiC), BN, AlN, etc.
Explanation
A wide variety of crystalline solids of non-metals result from the formation of covalent bonds between adjacent atoms throughout the crystal. They are also called giant molecules. Covalent bonds are strong and directional in nature, therefore atoms are held very strongly at their positions.
Such solids are very hard and brittle. They have extremely high melting points and may even decompose before melting.
Constituent Particles
Non-metallic Atoms
Binding forces
Covalent bond
Properties of Covalent Crystals
Covalent Crystals are characterized by:
Types of Covalent Crystals
1. Giant molecular covalent solids (e.g. diamond, carborundum, AlN etc.)
2. Layered molecular covalent solids (e.g. graphite, BN, CdI2 etc.)
Structure of diamond and graphite
In diamond each carbon atom is covalently bonded to four other carbon atoms at an angle of 109°.5 (called tetrahedral angle) to give crystal lattice of diamond. Due to close packing of atoms and large number of covalent bonds, diamond is very hard and has high melting point. Due to absence of free electron, diamond is bad conductor of electricity.
1. sp3 hybridization
2. Bond angle = 109.5°
3. Bond length = 154 pm
4. Hard = Close packing of atoms and large number of covalent bonds
5. High melting point (giant molecule)
6. Insulator or bad conductor (absence of free electrons)
In graphite each carbon atom is covalently bonded to three other carbon atoms at an angle of 120°, forming layers of hexagons. Adjacent layers of graphite are held together by weak Vander Waal’s forces. Due to space between layers graphite is soft and due to presence of weak Vander Waal’s forces, the layers easily slide over one another so graphite has greasy texture. Due to presence of free electron present on each carbon, graphite conducts electricity parallel to its plane of layers. In graphite along the layer there is more conduction but negligible in perpendicular direction. So conduction in graphite is anisotropic.
1. sp2 hybridization
2. bond angle = 120°
3. Bond length = 134 pm
4. Soft = Loose packing of atoms due to van deer Waal’s forces
5. High melting point less than diamond
6. Good conductor (due to delocalized pi-electrons)
7. Stability = thermodynamically more stable
Oil cannot be used as lubricating agent at high temperature but graphite can be used as lubricating agent at high temperature
Graphite is soft and a conductor of electricity. Its exceptional properties are due to its typical structure. Carbon atoms are arranged in different layers and each atom is covalently bonded to three of its neighbouring atoms in the same layer. The fourth valence electron of each atom is present between different layers and is free to move about. These free electrons make graphite a good conductor of electricity. Different layers can slide one over the other. This makes graphite a soft solid and a good solid lubricant.
Stability order
Graphite (∆Hf = 0) > diamond (∆Hf = 1.95) > Fullerene ( ∆Hf = 38 kJ)
Abnormal high pressure (15000-30000 atm) is required to convert graphite into diamond.
Molecular Crystals/ Covalent Molecular Solids
Definition
The crystals which consist of polar or non-polar molecules of a substance held together weak intermolecular forces either by hydrogen bonding or Vander Waal’s forces are called Molecular Crystals.
Examples
The polar and non-polar molecules such as Iodine, argon, S8, chlorine, ice, dry ice (solid CO2), sugar, glucose, methane, cholesterol, benzene, paraffin, ascorbic acid, hydroquinone, etc.
Constituent Particles
Molecules
Binding forces
van der Waal’s forces or Hydrogen bonding
Properties of Molecular Crystals
Molecular crystals are characterized by:
1. Soft to hard and brittle with waxy texture
2. Low melting point (usually below 400ºC)
3 Low lattice energy
4. Low heat of fusion and vapourization
5. Poor conductor of heat and electricity.
6. Crystal opaque (except diamond)
7. Polar molecular solids are soluble in water but non-polar molecular solids are insoluble in water
Volatility; Mostly volatile in nature
Melting/boiling points; Low due to weak forces of attraction
Density; low due to loose packing of particles
Compressibility; easily compressible due to weak forces
Conductivity; Bad conductors.
Solubility; Polar molecular solids are soluble in polar solvents like water while non-polar molecular solids are soluble in non-polar solvents like non-aqeuous solvent (CS2)
Types of Molecular Solids
(i) Polar molecular Solids
(ii) Non-polar molecular solids
(iii) Hydrogen bonded molecular solids
Polar molecular Solids
Their constituent particles are covalently bonded polar molecules. e.g. HCl, SO2 at low temperature and high pressure.
The molecules of substances like HCl, SO2, etc. are formed by polar covalent bonds. The molecules in such solids are held together by relatively stronger dipole-dipole interactions. These solids are soft and non-conductors of electricity. Their melting points are higher than those of non-polar molecular solids yet most of these are gases or liquids under room temperature and pressure. Solid SO2 and solid NH3 are some examples of such solids.
Non-polar molecular solids
Their constituent particles are covalently bonded non-polar or weakly polar molecules. e.g. H2, Cl2, CO2, CH4 at very low temperature.
They comprise of either atoms, for example, argon and helium or the molecules formed by non-polar covalent bonds for example H2, Cl2 and I2. In these solids, the atoms or molecules are held by weak dispersion forces or London forces. These solids are soft and non-conductors of electricity. They have low melting points and are usually in liquid or gaseous state at room temperature and pressure.
Hydrogen bonded molecular solids
Their constituent particles are covalently bonded polar molecules containing terminal polarized hydrogen. e.g. solid ice. The molecules of such solids contain polar covalent bonds between H and F, O or N atoms. Strong hydrogen bonding binds molecules of such solids like H2O (ice). They are non-conductors of electricity. Generally they are volatile liquids or soft solids under room temperature and pressure.
Definition
The temperature at which there is an equilibrium between solid and liquid phases of a solid is called melting point i.e. Melting point is the temperature at which both liquid and solid phases coexist at equilibrium.
Significance
Melting point is the criteria of purity of solids as pure substances have sharp melting point. It is also a measure of strength of intermolecular forces.
Factors affecting Melting point
1. Impurity
Impurities lower the melting point.
2. Pressure (effect of pressure on melting point or freezing point)
The substances which expand on melting (or contract on freezing), have a rise in melting point (or freezing point) with the increase in pressure.
e.g. wax
The substances which contract on melting (or expand on freezing), have fall in melting point (or freezing point) with the increase in pressure i.e. melting point (or freezing point) decreases with the increase in pressure. It is so because an increase in pressure helps contraction.
e.g. Ice.
Melting point of ice decreases on applying pressure because ice is the solid whose volume decreases on melting.
Definition
Sublimation is the process of direct conversion of solid to gaseous (vapour) state without passing through an intermediate liquid phase on heating. Some chemical substances in the solid state upon heating instead of changing into liquid state are sublimed directly in vapour state.
Sublime Solids
Sublime solids are the substances, which change directly from solid state to vapours forms. In sublime solids, intermolecular forces are less than ordinary solids. Following are the examples of sublime solids:
1. Ammonium chloride (NH4Cl)
2. Dry Ice (Solid CO2)
3. Naphthalene (C10H8)
4. Camphor (C10H16O)
5. Iodine (I2)
Explanation of Sublimation in terms of K.M.T.
According to KMT, in sublime solids, intermolecular forces are much less than ordinary solids. Hence on heating, high energy molecules at solid surface (having energy at the verge of two states) overcome the attractive forces holding them and directly pass into vapours.
The amount of heat energy required to completely melt 1 gram of a pure solid at its melting point is called Latent Heat of Fusion.
For example;
334 joules of heat is required to covert 1 gram ice to 1 g liquid water at 0°C. Thus latent heat of fusion of ice is 334 joules/g
Molar heat of fusion (DHfusion) is the amount of heat energy required to completely melt 1 mole of a pure solid at its melting point.
For example
molar heat of fusion of ice is 6 kJ/mol.
Latent heat as measure of strength of intermolecular forces
Latent heat values are a measure of strength of intermolecular forces. Stronger the intermolecular forces higher will be heat of fusion and vice versa. Heat of fusion increases in presence of hydrogen bonging.
Heat of fusion of a solid is always less than the heat of sublimation and heat of vaporization. [The heat of sublimation is always greater than the heat of fusion and heat of vapourization].
Transition temperature is the temperature at which two crystalline forms of the same substance can co-exist in equilibrium with each other. (It exists both for allotropes and polymorphs).
It has been noticed that the transition temperature of two different crystalline forms of a substance is always less than its melting point.
Definition
A crystal is formed by a large number of repetitions of basic building blocks called unit cells in space.
Examples
sugar, alum, metals, diamonds, graphite etc.
Reason for Crystal formation
The reason for formation of regular pattern or crystal is that atoms, ions or molecules tend to arrange themselves in position of maximum attraction or in position of minimum energy.
Lattice points or Lattice sites.
In crystals, the constituents particles are represented by points which are called Lattice points or Lattice sites.
Definition
A unit cell is formed by the arrangement of atoms, molecules or ions in three dimensional space and showing all the characteristics of actual crystal. These unit cells repeat itself in three dimensions in definite pattern to form the crystal.
For example
Unit cell of NaCl is cubic in shape, so its crystal will also be cubic in shape.
Unit cell contains three axes (a, b, c) and three angles (α, β, γ). These six parameters are called unit cell dimensions or crystallographic elements.
The shape of unit cell is described by length of its edges or sides (primitives or crystal axes or Axial distance or edge lengths) denoted by letters a, b, and c and angle between the edges (interfacial angles or Axial angle) represented by letters α, β and γ.
1. Length of its edges denoted by letters a, b and c (primitives/crystal axes/Axial distance/edge lengths)
2. Angle between the edges represented by letters α, β and γ (interfacial angles or Axial angle)
The length of the edges (primitives or crystal axes) and angles between the edges (interfacial angles) of a unit cell are collectively called cell dimensions or cell parameters or crystallographic elements.
The study of the structure and properties of crystals with the help of X-rays is called crystallography.
A crystal is formed by the arrangement of unit cells in a definite pattern, unit cells in turn are formed by the arrangement of atoms, ions or molecules in three dimensional space. If atoms, ions or molecules constituting a crystal are replaced by dots or points and placed at the same places as in a unit cell, then the resulting three dimensional arrays of points is called Crystal Lattice. In crystals, the constituents particles (atoms, molecules or ions) are represented by dots or points which are called lattice points or lattice sites and the arrangement of points in the crystal is called crystal lattice or space lattice or lattice array.
Crystal lattice is a regular repetitive three-dimensional pattern or arrangement of points which represents the positions of atoms, molecules or ions in space at different sites of the crystal.
The main characteristic of crystalline solids is a regular and repeating pattern of constituent particles. If the three dimensional arrangement of constituent particles in a crystal is represented diagrammatically, in which each particle is depicted as a point, the arrangement is called crystal lattice. Thus, a regular three dimensional arrangement is called crystal lattice. Thus, a regular three dimensional arrangement of points in space is called a crystal lattice. A portion of a crystal lattice is shown in fig.
Difference between Crystal Lattice and Unit cell
There are only 14 possible three dimensional lattices. These are called Bravais Lattices (after the French mathematician who first described them). The following are the characteristics of a crystal lattice:
(a) Each point in a lattice is called lattice point or lattice site.
(b) Each point in a crystal lattice represents one constituent particle which may be an atom, a molecule (group of atoms) or an ion.
(c) Lattice points are joined by straight lines to bring out the geometry of the lattice.
Unit cell is the smallest portion of a crystal lattice which, when repeated in different directions, generates the entire lattice.
In the formation of ionic solids, oppositely charged gaseous ions brought closer to each other and arranged three dimensionally in certain pattern releasing a high amount of energy known as lattice energy which is the energy associated with electrostatic interaction between the ions in a crystal.
A crystal may be made up of atoms, ions or molecules, held together by chemical bonds. To remove these atoms, ions or molecules from their fixed position in the crystal, a definite amount of energy is required called Lattice Energy.
Lattice energy is a measure of the stability of an ionic solid. Greater is the value of lattice energy of an ionic solid, more stable is the ionic solid.
Importance
Lattice energy value are helpful in predicting the solubility of ionic solids in water. Ionic compounds with smaller lattice energy and greater hydration energy are more soluble in water.
Method of determination
Lattice energy is indirectly determined by the use of Born-Haber cycle using Hess’s law.
Factors affecting lattice energy
1. Ionic size of Cation and Anion (Inversely proportional) (smaller ionic size, higher the lattice energy)
2. Nuclear charge or Charge of Ion (directly proportional) (greater nuclear charge, higher the LE)
Ionic size of Cation and Anion
The lattice energy decreases with the increase in the size of cation or anion. The smaller the size of cation or anion, the closer the packing of oppositely charged ion and thus require high energy to break the lattice and convert the solid into isolated gaseous ions.
Due to the electrostatic forces between them, the individual ions in an ionic lattice are attracted to each other. The strength of the electrostatic force of attraction is directly proportional to the magnitude of the charge held by the constituent ions, i.e. the greater the charge, the stronger the force of attraction, and the stronger the lattice.
For example
Lattice energy of naF (923 kJ/mol) is higher than KF (821 kJ/mol) because of smaller ionic radii of Na+ than K+ ion. The smaller ionic size of Na+ ion makes the packing more closely and thus need relatively high lattice energy for the separation of ions.
the lattice energy of calcium chloride is greater than that of potassium chloride despite the similarity in the crystal arrangements of these compounds. This is because the magnitude of the positive charge held by the calcium cation (+2) is greater than that held by the potassium cation (+1). As a consequence of this, the electrostatic forces of attraction are stronger in calcium chloride (than those in potassium chloride). Therefore, the lattice energy of CaCl2 is greater than that of KCl.
Nuclear charge or Charge of Ion
Lattice energy also affected by the charge of ion. The grater that charge of ion, the higher is the lattice energy.
For example
Lattice energy of BeF2 (3505 kJ/mol) is much higher than LiF (1036 kJ/mol) because lithium ion possess +1 charge in LiF whereas the charge of beryllium is +2 in BeF2.
Distance between the Ions
The lattice energy of an ionic compound is inversely proportional to the distance between the ions. The farther the distance between the ions in a lattice, the weaker the electrostatic forces holding them together, and the lower the lattice energy.
Smaller atoms feature smaller interatomic distances in the ionic lattice and stronger binding forces. Therefore, the smaller the size of the constituent ions, the greater the lattice energy of the ionic solid.
Lattice Energy of Some Ionic solids in kJ/mol
Decreasing order of lattice energy
LiCl > NaCl > KCl
The group of crystals, whose external shapes are built by only one kind of unit cell is called a Crystal System. All the known crystals have been classified into seven crystal systems.
The seven crystal systems are derived from decreasing symmetry (lifting degeneracies) of the cubic system by altering lengths and angles.
There are seven types of unit cells and there can be some sub types of unit cells. These seven unit cells are called primitive unit cells or crystal habits.
Unit cell
The smallest part of crystal lattice that has all the characteristic features of crystal is called a unit cell.
Unit cell contains three axes (a, b, c) and three angles (α, β, γ). These six parameters are called unit cell dimensions or crystallographic elements.
The study of the structure and properties of crystals with the help of X-rays is called crystallography.
Crystal and their classification
1. There are 230 different forms of crystals or space groups on the basis of symmetry of geometrical structures of crystals.
2. There are 32 crystal classes.
3. There are 14 types of Bravis lattices
4. There are 7 crystal systems.
5. The cubic system consist of three separate types of structure
(i) Simple (primitive)
(ii) Face centered
(iii) Body centered
6. The basic difference between Bravis lattice are
(i) Angles between the faces
(ii) Relative proportions of the sides
7. MOST ORDERED STRUCTURE: CUBIC
8. MOST DISORDERED: TRICLINIC
9. Structure resembling Matchbox: Orthorhombic
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