ens 205 materials science i chapter 2: atomic bonding

1

ENS 205Materials Science I

Chapter 2: Atomic Bonding

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

2

ObjectivesAt the end of this chapter:• Know the quantum number of elements and apply them.• Know the periodic table of elements• Know the 4 methods by which atoms bond to each other• Understand the energy/force relationship between atoms

making atomic bonds.

3

Material Infrastructure• What makes their materials behavior, mechanical for

instance, different?

– Microstructure- major properties result from mechanisms occurring at either atomic or the microscopic level

– Chemical or Atomic Bonding

• Strong bonding of ceramics: high strength and stiffness, and resistance to temperature and corrosion, but brittle

• Weakly bonding of chain molecules in polymers: low strength and stiffness, creep deformation

4

Atom• Atoms = nucleus (protons

and neutrons) + electrons

• Protons and Neutrons have the same mass, and determines the weight of the atom

• Mass of an electron is much smaller than mass of proton/neutron, and can be neglected in calculation of atomic mass.

electron

neutron

proton

5

Atom

A brief review of the building block of materials: Solid atoms, ions, molecules nucleus + electrons Protons and neutrons Properties of materials atoms of the material Nucleus Electrons Electronic magnetic Thermal mechanical Optic thermal

electron

neutron

proton

6

Atom: Definitions• Consider the number of protons and neutrons

in the nucleus as the basis of the chemical identification periodic table (placed by the number of protons)

• Atomic Mass Unit (amu) =mass of proton or neutron ~ 1.66x10-24 gr

Nucleus most of the weight (np+nn) 1.66 10-24 g But a small portion of the space 1.3 10-6 nm

Electrons almost no weight 0.911 10-27 g But occupy > 99% of the volume 0.059 nm Influence most of the properties

7

Atom: Definitions• Atomic number = the number of protons in

the nucleus

• Avogadro’s number, Nav : 6.023x1023 # of protons or neutrons necessary to produce a mass of 1 gr. Avogadro’s number (Nav )of atoms of a given element termed as gram-atom

amu=1/ Nav

1.66x10-24 = 1/6.023x1023

8

Atom: definitions• A mole is the amount of matter that has a mass

in grams equal to the atomic mass in amu of the atoms (A mole of carbon has a mass of 12 grams).

Example: C12 carbon isotope1 C12 atom 6 protons+6 neutrons 12 amu Nav many C12 atom1 mole C12 atom 12 gr

– Mole of a compound contains Avogadro’s number of each constituent atom

– E.g. 1 mole of NaCl, 6.023x1023 of Na atoms + 6.023x1023 Cl atoms

9

Atomic number

Atomic mass (in amu)

10

Quantum NumbersElectronic energy levels in atoms are specified by using

quantum numbersThe principal quantum is “n”.• n indicates the primary electron shell in an atom where the

shells are represented by K=1, L=2, M=3, etc.

11

The atomic structure of sodium, atomic number 11, showing the electrons in the K, L, and M quantum shells.

the most inner K-shell can accommodate only two electrons, called s-electrons; the next L-shell two s-electrons and six p-electrons; the M-shell can host two s-electrons, six p-electrons, and ten d-electrons; and so on.

The electronic configuration of the different energy levels fill in a relatively straight forward pattern in a shorthand notation. 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 … .eg., for Carbon, which has an atomic number of 6, it has 6 protons and 6 electrons. It’s electronic configuration in shorthand notation is 1s2 2s2 2p2 .

Planetary atomic model

13

Electron (Atomic) Orbitals

14

Electron (Atomic) Orbitals

• The electron volt (eV) – energy unit convenient for description of atomic bonding

• Electron volt - the energy lost / gained by an electron after it has moved through a potential difference of 1 volt .

E = q × V• For q = 1.6 x 10-19 Coulombs V = 1 volt

1 eV = 1.6 x 10-19 J

15

Identification of the ElementsWe can identify the elements using their florescence energy when a material

is irradiated by an x-ray, electron or gamma ray.

16

Identification of the ElementsThe energy of an x-ray emitted from a K, L or M shell

electron can be used to identify the atomic number of the element present in a material.

17

Atomic Bonding• Classification of engineering materials may be based on the nature of atomic

bonding. Understanding the atomic bonding requires the understanding of the structure of the individual atoms

• Chemical bonds: hold atoms and molecules together in solids. – Most of the materials not composed of just a single specie of atoms. They

are compounds, composed of molecules made up of atoms from two or more elements.

– When two or more atoms combine to form molecules of a compound, they form atomic bonds between them through chemical bonding.

• Chemical bonding is essentially the interaction of electrons from one atom with the electrons of another atom. The bonding of adjacent atoms is essentially an electronic process– Primary Bonding– Secondary Bonding

18

Atomic Bonding

• When atoms are combined into solids, there are several bonding mechanisms that can occur, which result in properties that may differ substantially from those of the atom alone. Hence, it is necessary to understand the types of bonding that can occur In the Solid Sphere Model, there are three primary or strong bonds and one weaker or secondary (but important!) type of bond between atoms or ions.

• 1) Ionic bonds• 2) Covalent bonds• 3) Metallic bonds• 4) Van der Waals bonds

19

Atomic or ionic radius

• An atomic or ionic radius refers to the radius corresponding to the average electron density

20

Valence Electrons

• Valence electrons are those electrons in the outer shells that are easily removed or added to form either a positive or negative charge for the purpose of combinations with other atoms.

• These then form ions, which we shall see, are important for ceramics and semiconductors.

• Valence electrons are the single most important structure of an atom or ion as they determine the physical (mechanical), electrical, photonic and magnetic properties of materials.

21

Valence ElectronsWhat is the valence of an atom?• The valence is the ability of the atom to enter into chemical combination

with other elements and is often determined by the number of outermost combined s, p, and /or d levels.

• Examples are:• Mg: 1s2 2s2 2p6 3s2 valence = 2• Al: 1s2 2s2 2p6 3s2 3p1 valence = 3• Ge: 1s2 2s2 2p6 3s2 3p1 3d10 4s2 4p2 valence = 4

Valence electrons determine all of the properties of the material!




22

Valence Electrons(cont’d)There are exceptions to the filling order of the electronic shells • e.g., Iron, Fe – atomic no. = 26; 1s2 2s2 2p6 3s2 3p6 3d8 [3d6 4s2 ]; instead of

completely filling the 3d orbital with 8 electrons, Fe first fills the 4s orbital.

Electron Configuration of Nickel

http://www.webelements.com/webelements/elements/text/Fe/econ.html

23

Exceptions in 3d, 4d, 5d

• A d subshell that is half-filled or full (ie 5 or 10 electrons) is more stable than the s subshell of the next shell. This is the case because it takes less energy to maintain an electron in a half-filled d subshell than a filled s subshell.

• For instance, copper (atomic number 29) has a configuration of [Ar]4s1 3d10, not [Ar]4s2 3d9

• Likewise, chromium (atomic number 24) has a configuration of [Ar]4s1 3d5, not [Ar]4s2 3d4 where [Ar] represents the configuration for argon.

http://en.wikipedia.org/wiki/Copper

http://en.wikipedia.org/wiki/Chromium

24

Valence Electrons

25

Atomic Structure• Filled outermost shells are the most stable (non-reactive)

configurations. The atoms with unfilled valence shells strive to reach the stable configuration by gaining or loosing electrons or sharing electrons with other atoms. This transference/sharing of electrons result in a strong bonding among atoms,

26

ElectronegativitySome properties of elements include:• Electronegativity is the tendency of an atom to gain an

electron. High electronegativity atoms tend to be on the right side of the Periodic Table and low electronegativity atoms are on the left side. What is the most electronegative element?

• Electropositivity is the tendency of an atom to loss electrons.• High electronegative atoms tend to react with high

electropositive atoms to form ionic molecules and ceramic materials.

• The sharing of electrons tends to make very strong atomic bonds. In the case of ceramics these bonds may break abruptly making the ceramic brittle.

27

The electronegativities of selected elements relative to the position of the elements in the periodic table.

28http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

29

Periodic Table

The atomic number, atomic mass, density and crystal structure are given.

30

Atomic Bonding• Primary Bonds are formed when outer orbital electrons are

transferred or shared between atoms. strong and stiff, hard to melt, metals and ceramics,– Ionic– Covalent– Metalic

http://hyperphysics.phy-astr.gsu.edu/hbase/Chemical/eleorb.html

31

Secondary bonds

• Secondary bonds: relatively weak, behavior of liquids, bonds between carbon-chain molecules in polymers, due to subtle attraction between positive and negative charges (no transfer or sharing) – Van der Waals– Hydrogen

32

• An ionic bond is created between two unlike atoms with different electronegativities. When sodium donates its valence electron to chlorine, each becomes an ion; attraction occurs due to their opposite electrostatic charges, and the ionic bond is formed.

• The size of the Cl ion is big compared to its elemental size whereas the size of Na ion is small compared to its elemental size.

•eg. Na and Cl form NaCl where the properties of the resultant material (salt) is very different from either of the atoms. Cl and Na are both highly corrosive where Cl is associated with acids and Na is associated with bases.

Primary Chemical Bonds: Ionic Bonding

33


• A collection of such charged ions, form and electrically neutral solid by arranging themselves into regular crystalline array

• Makes material hard and brittle

• Non-directional: A cation (Na+) will attract any adjacent anion (Cl-) equally in all directions

34

When a voltage is applied to an ionic material, entire ions must move to cause a current to flow. Ion movement is slow and the electrical conductivity is poor. Thus ionic materials like SiO2 and Al2O3 make good insulators of electricity.

35


CCmVk

qZqZkKaKFc

1890

210

2

1016.0,/.109

))((

Nature of the bonding force for the ionic bond coulombic attractions force Fc

With small a, Fc gets large, then a ideally be equal to zero?

36

With small a, FC gets large, then a ideally be equal to zero?

Oppositely charged ions gets closer, leads to increase in FC, but it is counteracted by an opposing repulsive force FR due to - overlapping of the similarly charged electric fields from each ions- the attempt to bring the two positively charged nuclei closer together

where λ and ρ are experimentally determined constants for a given ion pair

/aR eF

Primary Chemical Bonds Ionic Bonding

37

Bonding Force, Net force F=FR+FC

Equilibrium bond length where F=0

Interatomic spacingThe equilibrium distance between atoms is caused by a balance between repulsive and attractive forces. Equilibrium separation occurs where the total-atomic energy of the pair of atoms is at a minimum, or when no net force is acting to either attract or repel the atoms. The interatomic spacing is approximately equal to the atomic diameter or, for ionic materials, the sum of the two different ionic radii.


38


• Bonding energy, E is related to bonding force through the differential expression

Equilibrium bond length a0 corresponds to- F = 0 and - A minimum in the energy curve stable ions

positions

dadEF

39

0

0aada

dEF


A material that has a high binding energy will also have a high strength and high melting temperature.

40

Bonding Energy• How does bonding energy relate to melting point?• Modulus of Elasticity?• Coefficient of Thermal Expansion?• Hint: The higher the bonding energy the more tightly the atoms are

held together.

41

• Coordination number is the number of adjacent ions (or atoms) surrounding a reference ion (or atom)

• Depends directly on the relative sizes of the oppositely charged ions– Radius ratio r/R (smaller ion to the larger ion)


Coordination number

42

Larger ions overlap: instability because of high repulsive forces

Coordination number

43

MORE TO COME IN Ch 3…

Coordination number

44

Coordination Number

As r/R→1, a coordination number as high as 12 is possible

45

Questions to think on ?

• Why don’t we have a coordination Why don’t we have a coordination number greater than unity. number greater than unity.

• Why coordination numbers of 5, 7, 10, Why coordination numbers of 5, 7, 10, 11 are absent? 11 are absent?

46

Covalent BondsMaterials with covalent bonds tend to occur among atoms with small differences

in electronegativity and therefore the elements are close to one another in the periodic table.

• Two or more atoms share two or more electrons.

• The atoms most commonly share their outer s and p electrons so that each atom can tend to approach an inert gas structure.

• Example, Si; Z = 14; 1s2 2s2 2p6 3s2 3p2 or 1s2 2s2 2p6 3s1 3p3 are possible with the second configuration being more stable.

47

Electron orbitals are represented as particles orbiting at a fixed radius. In reality, electrons charge is found in a range of radii. Representation of the actual electron density

Highly directional due to sharing of electrons with specific neighboring atoms

48

Primary Chemical Bonds: Covalent Bonding

• While ionic bonds are non-directional, covalent bonds are very directional so atoms can best share their electrons.

• Covalent bonds are very strong.– They tend to be brittle with poor electrical conductivity. Why then is Why then is

Silicon and other like materials used in the electronics industry?Silicon and other like materials used in the electronics industry?– Many hydrocarbons, eg., C2 H4 , are covalently bonded. Many polymeric

materials such as polyvinyl chloride (PVC), used as molded plastic on cars, have primarily covalent bonds.

49


• A continuous covalent bond arrangement to form a 3D network of a solid

• Diamond is a cubic crystal structure of carbon (formed at a temperature of 1325°C, a pressure of 50000 kg/cm2 is required to grow diamond) – Highest melting temperature– Highest hardness– Highest elastic modulus

50

Carbons’s electronic configuration in shorthand notation is 1s2 2s2 2p2

Double bond covalent sharing of two pairs of valence electrons

When energy providedBonding of adjacent molecules, double bondsingle bond between each adjacent molecule pair

51

Spaghetti-like structure of solid polyethylene

52


• The bonding force and energy curves are similar to ionic bonding

• But the nature of the bonding is different leading to different force equations

54

Primary Chemical Bonds: Covalent Bonding• Bond Angle

– An important characteristic as the bonding is of directional nature of valence electron sharing

Carbon atom tends to form four equally spaced bonds, resulting tetrahedral configuration.

tetragonal: having four corners or angles

55

Ionic-Covalent Bonds• Many materials have properties, which can best be described as a

mixture of ionic and covalent bonding.

– Example 1, Silica (SiO2), a group IV-VI compound from the periodic table. Each Si atom bonds with 4 O atoms and each O atom binds with 2 Si atoms to give 8 electrons to each (see next slide).

Oxygen ’s electronic configuration (8 electrons) : 1s2 2s2 2p4

Silicon’s electronic configuration (14 electrons): 1s2 2s2 2p6 3s2 3p2

– Example 2, Gallium Arsenide (GaAs), a group III-V compound from the periodic table, used for lasers.

– – Example 3, Indium Phosphide (InP), a group II-VI compound

from the periodic table, used for Light Emitting Diodes (LEDs).– These materials are are very important as electronic and photonic

materials.

56

Atomic Bonding of Silicon Dioxide

Both the outer shells of Si and O are filled with electrons making SiO2 a very stable material.

Each Si atom bonds with 4 O atoms and each O atom binds with 2 Si atoms to give 8 electrons to each

57

Ionic-Covalent Bonds• As the electronegativity difference between the

atoms increases, the bonding becomes more ionic.

• The fraction of bonding that is covalent can be estimated from the following equation:

)exp(-25 covalent Fraction 2E

where E is the difference in electronegativities.

58

Metallic BondsMetallic bonds occurs in Metallic elements, which tend to

have a low electronegativity.• A metallic bond is non-directional• The outer (valence) electrons are given up to form a “sea

of mobile electrons”, which are attracted by a set of fixed positive ion cores.– These mobile electrons are called “conduction” electrons

and they form the “glue” to bond the metal atoms together.

– The sharing of electrons produces a lower energy state than when the individual atoms are collected separately

59

Metallic Bonding– Less than half full shell of

electrons, each atom donates its outer shell electrons to a “cloud” of electrons

– Shared by all the (metal) atoms

– Atoms to become positively charged ions as they all give up electrons to for the “cloud”

– Ions are attracted by the electron cloud and held together

– Nondirectional

– The mobility of the electrons electrical conductivity

60

When voltage is applied to a metal, the electrons in the electron sea can easily move and carry a current.

61

• Atomic bonding without electron transfer or sharing much less bonding energy

• Attraction of opposite charges (somewhat similar to ionic bonding) that are asymmetrically distributed-dipoles-within each atom or molecular unit being bonded

Secondary bonding

A dipole (Greek: dyo = two and polos = pivot) is a pair of electric charges, separated by some (usually small) distance. Dipoles can be characterized by their dipole moment, a vector quantity with a magnitude equal to the product of the charge and the distance separating the two poles

62

Secondary bonding : Van der Waals Bonding

• These bonds are much weaker than the three primary bonds but are very prevalent in materials, and thus very important.

• These bonds are formed by electrostatic attraction between groups of atoms or molecules that are either permanently polarized or dynamically polarized (i.e., changing as in a chemical process).

• • They possess an electric dipole moment

– eg., H2O where the oxygen is more strongly electronegative than H so O shares H2‘s electrons giving oxygen a negative potential and H a positive potential.

• Many organic molecules, polymers, and ceramics exhibit this type of bonding, often referred to as “hydrogen” bonding” with permanent polarization on an atomic level.

– These weak bonds enable life’s processes to occur such as photosynthesis and the “Hydrogen Cycle”.

63

When two neutral argon atoms (perfectly symmetric) brought nearby, slight shift from symmetry (induced dipole) weak attraction force between the two Ar.

Argon (a noble gas) does not tend to form a primary bond because it has stable, filled outer orbital shell

Secondary bonding

64

Secondary bonding• Externally electrically neutral chemical molecules can have a dipole inside.

– water is a triangular molecule, H2O– The internal charge distribution is such that the hydrogen side has a

slight excess of positive charge and the oxygen end is correspondingly negative.

65

Van der Waals Bonding• Van der Waals bonding can change the properties of a material substantially.• eg., for long chained carbon molecules, for long chained carbon molecules, polymers are covalently bonded polymers are covalently bonded

and hence might be expected to be brittleand hence might be expected to be brittle. The long chain molecules are . The long chain molecules are bonded together between the chains by Van der Waals bonds so ductility bonded together between the chains by Van der Waals bonds so ductility is obtained by the distortion of the weak bonds rather than between the is obtained by the distortion of the weak bonds rather than between the strong covalent bonds along the chain itself.strong covalent bonds along the chain itself.

In Polyvinyl Chloride (PVC), the chloride atoms attached to the polymer chain have a negative charge and the hydrogen atoms are positively charged enabling van der Waals bonding.

66

Chemical Bonding

69

Sample Problems

• The number of atoms per cm3, n, for material of density d (g/cm3) and atomic mass M (g/mol):

n = Nav × d / M– Diamond (carbon): d = 3.5 g/cm3, M = 12

g/moln = 6×1023 atoms/mol × 3.5 g/cm3 / 12 g/mol = 17.5 × 1022 atoms/cm3

ens 205 materials science i chapter 2: atomic bonding

Documents