ThePhysicist
07-26-2006, 04:48 PM
The Nature of Solids: The Crystalline Bonds
Quebec City, September 17, 1996
by Stephan Bourget, physicist
Effortless Physics Lessons (http://www.effortlessphysicslessons.com/)
Solid state physics is a very new science, developed primarily at the beginning of our century. It was given for goal the study of properties of solid materials, which can be classified in two categories: crystalline solids and amorphous solids. The latter can be regarded as liquids of very great viscosity and do not present this structural order particular to the crystalline solids. It is the case of glass and several plastics. But lets put our attention on crystalline solids. These solids are characterized by the regular repetition, in space, of structural units. More precisely, a crystal can be seen like a regular repetition of lattices (characterized by three vectors a, b, c) consisting of bases in a three-dimensional periodic network of nodes and having the property of symmetry. But what explains the great energy of cohesion of the crystalline solids? Which are the bonding strengths between the bases of the network? It is there the subject which we will tackle through the study of the ionic, covalent, metallic and molecular crystals.
* * *
Certain crystals known as ionic, like NaCl (to 94%, actually), KCl and MgO, consist of a network of ions bonded by an electrostatic force which we call force of Coulomb. Such ions are formed when atoms having one or more electrons slightly bonded transfer electrons of valence towards atoms whose external electron shell is almost complete, to acquire a stable electronic configuration. Their position depends on the balance between attractive forces of atoms of opposite charges and repelling forces of atoms of same charges, but especially on the Pauli exclusion principle preventing the overlap of the electronic clouds of two atoms of opposite charges. Indeed, no electron in the same system can be characterized by the same quantum state, and the energy necessary to place the electrons in surplus on higher energy levels would generate a force of lower cohesion due to an arrangement of higher energy. The binding energy is a few electron-volts (eV) and is higher than in all other types of crystals. The mechanical resistance of ionic crystals is strong and their melting point is high (qmelting = 808°C for NaCl). They are soluble in polar liquids.
Several molecules are formed by the sharing of pairs of valence electrons between their constitutive atoms. This sharing of electrons generates a bond known as covalent between the atoms, and this one is directional, because the binding energy depends on the relative orientation of that bond. It is also saturable, because the number of covalent bonds cannot generally exceed the number of valence electrons. This kind of bond is very stable (a few electron-volts), and thus even generates very hard substances of very high melting point when it is responsible for the cohesion of certain crystalline solids, of which solubility is very rare. It is the case of diamond (qmelting = 3500°C), of Si and Ge, but the purely covalent crystals are very rare. When the involved atoms are not identical, the pairs of electrons are not equally shared, those being more attracted by atoms of higher electronegativity. It results an intermediate bond between the pure covalent and the pure ionic bonds, and generates a dipole moment for the molecules.
In the metallic crystals like Fe or Ni, the whole of atoms bathes in a sea of free electrons acting like an electrostatic glue. It is this particular structure which confers to metals their great thermal and electric conductivity, compared to other crystals where the electrons are bonded. This type of bond is a little less strong than ionic and covalent bonds, but more than those which we will consider below.
There are additional weaker bonds (about 0.1 eV, at most) which appear in molecular crystals; they are Van der Waals and hydrogen bonds, appearing sometimes simultaneously.
The attraction of Van der Waals draws its origin from the permanent, induced or instantaneous electric dipoles. Water H2O is an example of a dipolar molecule illustrating an effective separation of charges. But dipoles can be induced by a polar molecule close to another which is non polar. Or instantaneous dipoles can appear in non polar or neutral molecules consequently to the random movement of electrons whose distribution, statistically symmetrical, is not necessarily thus at a given moment. In all cases, dipoles tend to agglomerate themselves more strongly as thermal agitation is weaker. The Pauli exclusion principle will prevent the overlapping of electronic clouds once again. Van der Waals binding energy corresponds to approximately 0.01 times the energy of the ionic or covalent bonds. Such molecular crystals have a low mechanical resistance, have low vaporization and melting points (qvap = -186°C for Ar, -161°C for CH 4 ) and are soluble in covalent liquids.
The hydrogen bond, on the other hand, plays a prevalent role in a solid such as ice, where the pairs of electrons in the two unbounded orbitals of the water molecule are attracted by the hydrogen cores of the adjacent molecules. This type of bond can also play a role in other crystal lattices like HF or NH 3 . The hydrogen cores being very small, that enables them to play a single role in its compounds by forming very directional bonds.
* * *
All things considered, although we briefly studied various types of bonds in crystalline solids, all these bonds can be regarded as a consequence of the same electrostatic interaction between the core and the electrons, and certain arrangements can in addition coexist in the same solid. These bonds account for the cohesion of these solids, which gets stronger as the binding energy is higher. And while pushing a little further, these bonds can give an account for their behaviors and thus help us better understand the world which surrounds us.
References
André Arès, Jules Marcoux, Physique: Structure de la matière, Montréal, Lidec, [c.1971], pp. 289-297.
Arthur Beiser, Physics (http://www.amazon.com/exec/obidos/ASIN/0201168677/stephanshomepage), 4th edition, Menlo Park, The Benjamin / Cummings Publishing Company, [c.1986], pp. 766-775.
G. H. Wannier, "The Nature of Solids", in Scientific American, December 1952, pp. 39- 48.
Joseph Kane, Morton Sternheim, Physique (http://www.amazon.com/exec/obidos/ASIN/0471801240/stephanshomepage), Paris, InterEditions, [c.1986], pp.658-669.
J. R. Hook, H. E. Hall, Solid State Physics (http://www.amazon.com/exec/obidos/ASIN/0471928054/stephanshomepage), 2nd edition, Chichester, John Wiley & Sons, 1991, pp. 1-9, 28-31.
Paul R. O'Connor, Joseph E. Davis Jr., et alii., La Chimie: Expériences et principes, Montréal, Centre Éducatif et Culturel, [c.1974], pp. 94-95, 333-351.
Quebec City, September 17, 1996
by Stephan Bourget, physicist
Effortless Physics Lessons (http://www.effortlessphysicslessons.com/)
Solid state physics is a very new science, developed primarily at the beginning of our century. It was given for goal the study of properties of solid materials, which can be classified in two categories: crystalline solids and amorphous solids. The latter can be regarded as liquids of very great viscosity and do not present this structural order particular to the crystalline solids. It is the case of glass and several plastics. But lets put our attention on crystalline solids. These solids are characterized by the regular repetition, in space, of structural units. More precisely, a crystal can be seen like a regular repetition of lattices (characterized by three vectors a, b, c) consisting of bases in a three-dimensional periodic network of nodes and having the property of symmetry. But what explains the great energy of cohesion of the crystalline solids? Which are the bonding strengths between the bases of the network? It is there the subject which we will tackle through the study of the ionic, covalent, metallic and molecular crystals.
* * *
Certain crystals known as ionic, like NaCl (to 94%, actually), KCl and MgO, consist of a network of ions bonded by an electrostatic force which we call force of Coulomb. Such ions are formed when atoms having one or more electrons slightly bonded transfer electrons of valence towards atoms whose external electron shell is almost complete, to acquire a stable electronic configuration. Their position depends on the balance between attractive forces of atoms of opposite charges and repelling forces of atoms of same charges, but especially on the Pauli exclusion principle preventing the overlap of the electronic clouds of two atoms of opposite charges. Indeed, no electron in the same system can be characterized by the same quantum state, and the energy necessary to place the electrons in surplus on higher energy levels would generate a force of lower cohesion due to an arrangement of higher energy. The binding energy is a few electron-volts (eV) and is higher than in all other types of crystals. The mechanical resistance of ionic crystals is strong and their melting point is high (qmelting = 808°C for NaCl). They are soluble in polar liquids.
Several molecules are formed by the sharing of pairs of valence electrons between their constitutive atoms. This sharing of electrons generates a bond known as covalent between the atoms, and this one is directional, because the binding energy depends on the relative orientation of that bond. It is also saturable, because the number of covalent bonds cannot generally exceed the number of valence electrons. This kind of bond is very stable (a few electron-volts), and thus even generates very hard substances of very high melting point when it is responsible for the cohesion of certain crystalline solids, of which solubility is very rare. It is the case of diamond (qmelting = 3500°C), of Si and Ge, but the purely covalent crystals are very rare. When the involved atoms are not identical, the pairs of electrons are not equally shared, those being more attracted by atoms of higher electronegativity. It results an intermediate bond between the pure covalent and the pure ionic bonds, and generates a dipole moment for the molecules.
In the metallic crystals like Fe or Ni, the whole of atoms bathes in a sea of free electrons acting like an electrostatic glue. It is this particular structure which confers to metals their great thermal and electric conductivity, compared to other crystals where the electrons are bonded. This type of bond is a little less strong than ionic and covalent bonds, but more than those which we will consider below.
There are additional weaker bonds (about 0.1 eV, at most) which appear in molecular crystals; they are Van der Waals and hydrogen bonds, appearing sometimes simultaneously.
The attraction of Van der Waals draws its origin from the permanent, induced or instantaneous electric dipoles. Water H2O is an example of a dipolar molecule illustrating an effective separation of charges. But dipoles can be induced by a polar molecule close to another which is non polar. Or instantaneous dipoles can appear in non polar or neutral molecules consequently to the random movement of electrons whose distribution, statistically symmetrical, is not necessarily thus at a given moment. In all cases, dipoles tend to agglomerate themselves more strongly as thermal agitation is weaker. The Pauli exclusion principle will prevent the overlapping of electronic clouds once again. Van der Waals binding energy corresponds to approximately 0.01 times the energy of the ionic or covalent bonds. Such molecular crystals have a low mechanical resistance, have low vaporization and melting points (qvap = -186°C for Ar, -161°C for CH 4 ) and are soluble in covalent liquids.
The hydrogen bond, on the other hand, plays a prevalent role in a solid such as ice, where the pairs of electrons in the two unbounded orbitals of the water molecule are attracted by the hydrogen cores of the adjacent molecules. This type of bond can also play a role in other crystal lattices like HF or NH 3 . The hydrogen cores being very small, that enables them to play a single role in its compounds by forming very directional bonds.
* * *
All things considered, although we briefly studied various types of bonds in crystalline solids, all these bonds can be regarded as a consequence of the same electrostatic interaction between the core and the electrons, and certain arrangements can in addition coexist in the same solid. These bonds account for the cohesion of these solids, which gets stronger as the binding energy is higher. And while pushing a little further, these bonds can give an account for their behaviors and thus help us better understand the world which surrounds us.
References
André Arès, Jules Marcoux, Physique: Structure de la matière, Montréal, Lidec, [c.1971], pp. 289-297.
Arthur Beiser, Physics (http://www.amazon.com/exec/obidos/ASIN/0201168677/stephanshomepage), 4th edition, Menlo Park, The Benjamin / Cummings Publishing Company, [c.1986], pp. 766-775.
G. H. Wannier, "The Nature of Solids", in Scientific American, December 1952, pp. 39- 48.
Joseph Kane, Morton Sternheim, Physique (http://www.amazon.com/exec/obidos/ASIN/0471801240/stephanshomepage), Paris, InterEditions, [c.1986], pp.658-669.
J. R. Hook, H. E. Hall, Solid State Physics (http://www.amazon.com/exec/obidos/ASIN/0471928054/stephanshomepage), 2nd edition, Chichester, John Wiley & Sons, 1991, pp. 1-9, 28-31.
Paul R. O'Connor, Joseph E. Davis Jr., et alii., La Chimie: Expériences et principes, Montréal, Centre Éducatif et Culturel, [c.1974], pp. 94-95, 333-351.