Atomic Bonding and Materials Properties

MME131: Lecture 5 Atomic Bonding and Materials Properties A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics What promote bonding? Classification and characteristics of atomic bond Summary of bonding in materials Properties from bonding Energy diagram and properties of materials References: 1. Callister. Materials Science and Engineering: An Introduction. 2. Askeland. The Science and Engineering of Materials. Lec 05, Page 1/26

Why Review Bonding? Atoms form the fundamental building blocks from which all matter is made. The properties of a solid depend exquisitely on the types of atoms from which it is made. It makes sense to begin any study of materials with a review of the chemistry and physics of atoms Bonding in Solids Chemical bonds between atoms occur when the valence electrons in the atoms interact with each other in such a way that the overall energy is more favorable than when the atoms are separated The energy is most favorable when each atom can obtain eight outershell electrons (an octet), which gives it a noble gas configuration Three primary ways for atoms to achieve an octet in the outer shell: give or take valence electrons (ionic bonding) share valence electrons with neighboring atoms (covalent bonding) share valence electrons with all atoms (metallic bonding) Lec 05, Page 2/26

Primary Bonds Electrons are transferred or shared Strong (100-1000 KJ/mol, or 1-10 ev/atom) Metallic: atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place. Covalent: electrons are shared between the molecules, to saturate the valence band. Example - H 2 Ionic: strong Coulombic interaction among negative atoms (have an extra electron each) and positive atoms (lost an electron). Example - Na + Cl - Metallic Bonding Occurs in materials composed of electropositive atoms (metals), which would prefer to give up their valence electrons, but no electronegative atoms are available to accept them So, valence electrons are delocalized and shared by all atoms in the material Model of a metallic solid Each atom donates its valence electrons to the whole. Atom therefore becomes a cation (here called an ion core) Donated electrons form an electron cloud surrounding all the ion cores Electron cloud binds all the ion cores together by Coulombic forces, thus producing the strong unidirectional metallic bond Lec 05, Page 3/26

Example: Calculating the Conductivity of Silver Calculate the number of electrons capable of conducting an electrical charge in 10 cm 3 of silver. The density and the atomic mass of silver are 10.49 g/cm 3 and silver 107.868 g/mol, respectively. ANSWER The valence of silver is one, and only the valence electrons are expected to conduct the electrical charges one. Then Mass of 10 cm 3 = (10 cm 3 ) (10.49 g/cm 3 ) = 104.9 g No. of atoms = (104.9 g) (6.023x10 23 atoms/mol) 107.868 g/mol = 5.85x10 23 atoms No. of electrons = (5.85x10 23 atoms) (1 valence electron/atom) = 5.85x10 23 valence electron/atom per 10 cm 3 Covalent Bonding Covalent bonding occurs by a sharing of valence electrons between two atoms so that an octet is effectively formed around each atom Bonding occurs between electronegative atoms (right side of periodic table) since no electropositive atoms available to donate electrons Electronegativity measures how strongly the atoms attract electrons in a bond. The bigger the electronegativity difference the more polar the bond. 0.0-0.3 = covalent non-polar ; 0.3-1.67 = covalent polar ; >1.67 = ionic Electron density distributions Non-polar Covalent Bond Polar Covalent Bond Lec 05, Page 4/26

Covalent bonds are highly directional. In silicon, a tetrahedral structure is formed, with angles of 109.5 required between each covalent bond. The tetrahedral structure of silica (Si0 2 ), which contains covalent bonds between silicon and oxygen atoms O O Si O O Example: Design of a Thermistor A thermistor is a device used to measure temperature by taking advantage of the change in electrical conductivity when the temperature changes. Select a material that might serve as a thermistor in the 500 to 1000 o C temperature range. SOLUTION Photograph of a commercially available thermistor (Courtesy of Vishay Intertechnology, Inc.) The resistance of a thermistor can be made to increase or decrease with increasing temperature. These are known as positive temperature coefficient of resistance (PTCR) or negative temperature coefficient of resistance (NTCR) thermistors, respectively. The fact that a thermistor changes its resistance in response to a temperature change is used to control temperature or switch the operation of an electrical circuit (turn on and off ) when a particular device (i.e., a refrigerator, hairdryer, furnace, oven, or reactor) reaches a certain temperature. Lec 05, Page 5/26

Two design requirements must be satisfied: a material with a high melting point must be selected. the electrical conductivity of the material must show a systematic and reproducible change as a function of temperature. Covalently bonded materials might be suitable. They often have high melting temperatures, and, as more covalent bonds are broken when the temperature increases, increasing numbers of electrons become available to transfer electrical charge. We will have to make sure the changes in conductivity in the temperature range are actually acceptable. The semiconductor silicon is one choice. Silicon melts at 1410 o C and is covalently bonded. Silicon will have to be protected though against oxidation. A number of ceramics also have high melting points and behave as semiconducting materials. Many make use of barium titanate (BaTiO 3 ) based formulations. Polymers would not be suitable, even though the major bonding is covalent, because of their relatively low melting, or decomposition, temperatures. Ionic Bonding Ionic bonding occurs in a solid that contains more than one types of atoms (one is highly electronegative and the other is highly electropositive). Mutual ionization by electrons transfer from one atom to another (here ion means charged atom). The tendency for charge transfer between atoms increases as the electronegativity difference (DZ) increases between the dissimilar atoms. Their opposite charge attracts the cations to the anions by Coulombic forces. The coulombic forces that bind cations and anions is called ionic bonding. Lec 05, Page 6/26

Secondary Bonding No transfer or share of electrons Interaction of atomic/molecular dipoles Weak (< 100 KJ/mol or < 1 ev/atom) Exists between virtually all atoms or molecules Evidenced for inert gases, between molecules of covalently bonded structures. Coulombic attraction between opposite charges Very weak bonding energy, typically of the order of only 10 kj/mol (0.1 ev) No electron sharing/transfer Asymmetric charge distribution Formation of atomic or molecular dipole (permanent, or temporary) Fluctuating Induced Dipole Bonding same - ve and + ve charge centre Illustration of London forces, a type of a van der Waals force, between atoms An instantaneous and short-lived electric dipole is created due to the separation (d) of +ve and -ve charge centres Example: Liquefaction / solidification of inert gases and other gases e.g., H 2, Cl 2. Very small bond energy (~1.0 kj/mol) due to small dipole moment (q x d) Reasons: constant vibrational motion of atoms Lec 05, Page 7/26

Permanent Dipole Bonding Weak bonding forces among covalent bonded molecules, if they contain permanent dipole Example: Hydrogen bonding in water molecules Directional covalent bonds between H and O Two H on one side of O H side net positive charge O side net negative charge Results much higher polarisation because of larger displacement between the centres of negative and positive charges. H O H Dipole Higher bond energy (~21 kj/mol for water) Dipole Bonding Mixed Bonding A very few compounds exhibit pure ionic or covalent bonding. Iron, for example, is bonded by a combination of metallic and covalent bonding Compounds formed from two or more metals (intermetallic compounds) may be bonded by a mixture of metallic and ionic bonds (particularly when there is a large electronegativity difference between the elements. Ceramics and semiconducting compounds having metallic and nonmetallic elements have a mixture of covalent and ionic bonds. Most polymeric materials have a mixture of covalent and secondary bonds. Lec 05, Page 8/26

(a) Within each chain, bonding between carbon is covalent. The individual chains are weakly bonded to one another (between chlorine and hydrogen atoms) by van der Waals bonds. This additional bonding makes PVC stiffer. (b) When a force is applied to the polymer, the van der Waals bonds are broken and the chains slide past one another. Mixed bonding in polyvinyl chloride (PVC) Example: Determine if Silica and Diamond are Ionically or Covalently Bonded For elements A and B with electronegativities X A and X B, the fraction ionic character of bonding can be determined as - 0.25 (X A -X B ) F = 1 - e 2 As difference in electronegativity increases, ionic character of the bond is increased. X Si = 1.8 X O = 3.5 XC = 2.5 F Silica = 1 - exp [- 0.25(1.8-3.5) 2 ] = 0.486 F Diamond = 1 - exp [- 0.25(2.5-2.5) 2 ] = 0 So, diamond is purely a covalent ceramic, while silica possesses only about 50% of covalent character. Lec 05, Page 9/26

Summary: Properties of bonding Type Bond energy Properties of bonding Ionic Large! Non-directional (ceramics) Covalent Variable Directional Large Diamond Small Bismuth (semiconductor, ceramics, polymer chains) Metallic Variable Non-directional Large Tungsten Small Mercury (metals) Secondary Smallest Directional Inter-chain (polymers) Intermolecular Bonding in Materials covalent semiconductors polymers Examples of bonding in materials: metallic metals Metals : Metallic ionic Ceramics : Ionic / covalent Polymers : Covalent and secondary Semiconductors : Covalent / covalent and ionic secondary ceramics and glasses Lec 05, Page 10/26

Properties from metallic bonding Atoms joined by metallic bond can shift their relative positions (without breaking) when the metal is deformed, permitting metals to have good ductility. Properties from metallic bonding Atoms joined by metallic bond can shift their relative positions (without breaking) when the metal is deformed, permitting metals to have good ductility. Lec 05, Page 11/26

When voltage is applied to a metal, the electrons in the electron cloud can easily move and carry a current. Applied Voltage Properties from covalent bonding When a silicon rod is bent, the bonds must break if the silicon atoms are to permanently change their relationships to one another. For an electron to move and carry a current, the covalent bond must be broken, requiring high temperatures or voltage. Thus covalent materials are brittle rather than ductile, and behave as electrical insulators instead of conductors. Many ceramics, semiconductors, and polymers are fully or partially bonded by covalent bonds, explaining why glass shatters when dropped and why bricks are good insulating materials. Lec 05, Page 12/26

Properties from ionic bonding Solids that exhibit considerable ionic bonding are also often mechanically strong because of the strength of the bonds. Electrical conductivity of ionically bonded solids is very limited. A large fraction of the electrical current is transferred via the movement of ions and cause ionic conductivity. When voltage is applied to an ionic material, entire ions must move to cause a current to flow. Owing to their size, ions typically do not move as easily as electrons. Ions move slowly and, thus, the ionic conductivities of these material are poor. However, in many technological applications we make use of the electrical conduction that can occur via movement of ions as a result of increased temperature, chemical potential gradient, or an electrochemical driving force. Examples of these include: lithium ion batteries that make use of lithium cobalt oxide conductive indium tin oxide coatings on glass for touch sensitive screens for displays, and solid oxide fuel cells based on compositions based on zirconia (ZrO 2 ) Lec 05, Page 13/26

Properties from secondary bonding When a force is applied to the polymer, the van der Waals bonds are broken easily and the chains slide past one another. Thus is why polymers are soft and ductile. When heat is applied, the secondary bonds melts easily, thus making polymers as lowmelting materials. Mixed bonding in polyvinyl chloride (PVC) Binding Energy Interatomic spacing is the equilibrium spacing between the centers of two atoms. Binding energy is the energy required to separate two atoms from their equilibrium spacing to an infinite distance apart. Modulus of elasticity (E) is the ratio of stress and strain in the elastic region, which indicates the degree of stiffness of the material Yield strength (YS) is the level of stress above which a material begins to show permanent deformation. Coefficient of thermal expansion (CTE) is the amount by which a material changes its dimensions when the temperature changes. Lec 05, Page 14/26

Atoms or ions are separated by an equilibrium spacing that corresponds to the minimum inter-atomic energy (aka the binding energy) for a pair of atoms or ions (or when zero force is acting to repel or attract the atoms or ions) A steep df/da slope gives a higher binding energy Force - distance curve for two materials Lec 05, Page 15/26

Binding energy and the melting point Energy, E bond length, r Bond energy, E 0 Equilibrium spacing between atoms, r 0 Distance between atoms, r energy distance diagram r 0 Melting temperature, T m, is larger, if the bond energy, E 0, at r 0 is larger, and E 0 smaller T m the radius of curvature of the energy-distance curve is smaller. larger T m Lec 05, Page 16/26

Binding energy and the modulus of elasticity length, L 0 UNDEFORMED cross-sectional area, A 0 Elastic Modulus DEFORMED DL F F A 0 = E DL L 0 r 0 Elastic modulus, E, is larger, if E 0 smaller E larger E the bond energy, E 0, at r 0 is larger, and the radius of curvature of the energy-distance curve is smaller. Binding energy and the coefficient of thermal expansion Coef. of Thermal Expansion DL L 0 = a (T 2 T 1 ) DL length, L 0 UNHEATED HEATED Equilibrium spacing between atoms Increase in spacing between atoms due to increase in energy DE by heating for weakly bonded materials Increase in spacing between atoms due to the same increase in energy DE by heating for strongly bonded materials DE DE Materials that display a steep curve with a deep trough have low linear coefficients of thermal expansion Lec 05, Page 17/26

Summary Ceramics (Ionic and covalent bonding) Metals (Metallic bonding) Polymers (Covalent and secondary) Large bond energy Large T m Large E Small a Intermediate/Variable bond energy Moderate T m Moderate E Moderate a Directional properties (bond energy) Small T m Small E Large a Next Class MME131: Lecture 6 Packing of Atoms in Solids Lec 05, Page 18/26

Additional Reading 7.1.1 Structure of Individual Atom orbital electrons principal quantum number, n = 3 2 1 Bohr Atom Very few material properties are influenced significantly by the atomic nucleus Some exceptions are: density atomic mass ability to scatter neutrons nucleus (Z+N) Z = no. of protons N = no. of neutrons Almost all material properties are profoundly influenced by the electrons around the nucleus Lec 05, Page 19/26

The atomic number of an element is equal to the number of electrons or protons in each atom. The atomic mass of an element is equal to the average number of protons and neutrons in the atom. The Avogadro number of an element is the number of atoms or molecules in a mole. The atomic mass unit of an element is the mass of an atom expressed as 1/12 the mass of a carbon atom. Example 7.1 Dopant Concentration in Silicon Crystal Silicon single crystals are used extensively to make computer chips. Calculate the concentration of silicon atoms in silicon, or the number of silicon atoms per unit volume of silicon. During the growth of silicon single crystals it is often desirable to deliberately introduce atoms of other elements (known as dopants) to control and change the electrical conductivity and other electrical properties of silicon. Phosphorus (P) is one such dopant that is added to make silicon crystals n-type semiconductors. Assume that the concentration of P atoms required in a silicon crystal is 10 17 atoms/cm 3. Compare the concentrations of atoms in silicon and the concentration of P atoms. What is the significance of these numbers from a technological viewpoint? Assume that density of silicon is 2.33 g/cm 3. Lec 05, Page 20/26

SOLUTION Atomic mass of silicon = 28.09 g/mol. So, 28.09 g of silicon contain 6.02310 23 atoms. Now, the mass of one cm 3 of Si is 2.33 g. So, 2.33 g of silicon will contain (2.33 6.02310 23 / 28.09) atoms = 4.9910 22 atoms. So, the concentration of silicon atoms in pure silicon is 510 22 atoms/cm 3. Significance of comparing dopant and Si atom concentrations If we were to add phosphorus into this crystal, such that the concentration of P is 10 17 atoms/cm 3, the ratio of concentration of atoms in silicon to that of P will be (510 22 ) / (10 17 ) = 510 5 This says that only 1 out of 500,000 atoms of the doped crystal will be that of phosphorus (P). This explains why the single crystals of silicon must have exceptional purity and at the same time very small and uniform levels of dopants. 7.1.2 Electronic Structure of an Atom Quantum numbers are the numbers that assign electrons in an atom to discrete energy levels. A quantum shell is a set of fixed energy levels to which electrons belong. Pauli exclusion principle specifies that no more than two electrons in a material can have the same energy. The two electrons have opposite magnetic spins. The valence of an atom is the number of electrons in an atom that participate in bonding or chemical reactions. Electronegativity describes the tendency of an atom to gain an electron. Lec 05, Page 21/26

The Electron The behavior of electrons can be correctly described only by the theory of quantum mechanics For most of you, quantum mechanics will be covered in an upcoming physics course For this class, we will simply borrow some of the major results of the theory so that we can adequately understand the behavior of electrons Major Results from Quantum Mechanics Electrons sometimes behave like particles (Bohr s model) they can scatter off objects they have momentum But sometimes they can also behave like waves (Schrodinger's model) they don't exist uniquely at any given location, but are spread out in space they can interfere with each other they can form standing waves in a cavity their energy and momentum depend on their wavelength Lec 05, Page 22/26

Energy When orbiting an atomic nucleus, electrons are best described by energy waves with a specific amplitude and wavelength The wave motion, wavelength, and amplitude of electrons are found by solving the Schrodinger's equation For an electron surrounding an atomic nucleus, only certain wavelengths, energies, and amplitudes satisfy Schrodinger's equation The valid solutions of Schrodinger's equation can be catalogued in terms of three integers, plus a fourth number that is either 1/2 or -1/2. These four numbers taken together are called the quantum numbers of the electron. The first three quantum numbers are n, l, and m, and the fourth quantum number is called the spin. Electron Energy State f f d f d p s d p s Electrons have discrete energy states tend to occupy lowest available energy state d p s s p s d p s p s 1 2 3 4 5 6 7 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p Principal Quantum Number, n Lec 05, Page 23/26

Survey of Elements have complete s and p subshells Most elements: Electron configuration is not stable. Why? Valence (outer) shell not completely filled Valence Electrons For a given atom, electrons having energy greater than or equal to those in the outermost shell are called valence electrons Valence electrons are those that interact most strongly with the outside world Ionization involves addition or subtraction of valence electrons Bonding between atoms occurs by interactions between their valence electrons Conductivity (both electrical and thermal) in metals occurs by migration of valence electrons Lec 05, Page 24/26

Electronegativity A measure of how willing an atom to accept an electron to achieve stable configuration The most stable configuration of electrons is completely filled valence shells Sub-shells with one or two electron: low electronegativity Sub-shells with one or two missing electron: high electronegativity Example 7-2 Comparing Electronegativities Using the electronic structures, compare electronegativities of calcium and bromine. Ca (20): 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 Br (35): 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 5 ANSWER Calcium has 2 electrons in its outer 4s orbital and bromine has 7 electrons in its outer 4s4p orbital. Calcium tends to give up electrons and is strongly electropositive, but bromine tends to accepts electrons and is strongly electronegative. Lec 05, Page 25/26

Electronegativity controls how elements combine (bond) with each other Lec 05, Page 26/26