MME 2001 MATERIALS SCIENCE 1 13.10.2015

outline ● overview of last lecture periodic table / electronegativity Classification of elements / interatomic bonding

● Structure of solids: crystaline vs noncrystalline Crystal systems; BCC, FCC, HCP atomic packing crystallographic directions, planes ● QUIZ (will start at 14:50 p.m. !)

The Periodic Law Mendeleev realized that: When arranged by increasing atomic number, the chemical elements display a regular and repeating pattern of chemical and physical properties.

what are these properties?  Metallic vs nonmetallic character  Atomic radius

 Ionization energies (energy necessary to remove the outermost electron from the atom)  Electron affinities (energy change when an

electron is added to a neutral atom)  Reactivity

 Electronegativity

Organisation of the periodic table The vertical columns: groups from 1 to 18. Elements in the same group have similar valence electron structures and hence similar chemical and physical properties.

groups

Organisation of the periodic table elements are situated, with increasing atomic number, in seven horizontal rows called periods. Each contains elements with electrons in the Same outer shell.

periods

Periodic table

nonmetallic character İonization energy Negative electron affinity

İonization energy

nonmetallic character

metallic character Atomic radii

metallic character Atomic radii

Negative electron affinity

Periodic Table

Ionization Energy IE = energy required to remove an electron from an atom in the gas phase.

Mg (g) + 738 kJ ---> Mg+ (g) + e-

Electronegativity ● the tendency of an atom to attract electrons towards itself. ● Atoms are more likely to accept electrons if their outer shells are almost full, and if they are less “shielded” from (i.e., closer to) the nucleus.

electronegativity increases!

Electronegativity

Electronegativity

Metals, Nonmetals & Metalloids 1

Nonmetals

2 3

4 5

Metals

6 7

Metalloids

Metals 88 elements are metals or metal like element Physical properties:  good conductors of heat and electricity  shiny  ductile (can be stretched into thin wires)  malleable (can be pounded into thin sheets)  High density (heavy for their size)  High melting point chemical properties:  Easily lose electrons  Form positive (+) ions  Corrode easily

Non-metals Their characteristics are opposite to those of metals.

Physical Properties of Nonmetals:  No luster (dull appearance)  Poor conductor of heat and electricity  Brittle (breaks easily)  Not ductile  Not malleable  Low density  Low melting point  Many non-metals are gases.

Non-metals Chemical Properties of Non-metals:  Tend to gain electrons  metals that tend to lose electrons but nonmetals that tend to gain electrons, to form compounds with each other.  These compounds are called ionic compounds.  When two or more

nonmetals bond with each other, they form a covalent compound.

Metalloids  Metalloids (metal-like) have properties of both metals and non-metals.  They are solids  can be shiny or dull  They conduct heat

and electricity better than non-metals but not as well as metals  They are ductile and malleable

interatomic bonding ● the bonding involves the valence electrons

● the nature of the bond depends on the electron structures of the constituent atoms. ● There are three types of bonding: each bonding type arises from the tendency of the atoms to assume stable electron structures.

● Secondary or physical forces and energies are weaker than the primary ones, but nonetheless influence the physical properties of some materials.

interatomic bonding  Ionic  Metal (cation) with non-metal (anion)

Transfer of electron(s)  Strong bond  high melting point  Covalent  Non-metal with non-metal  Sharing of electron(s)  Non-polar (equal distribution of electrons)  Polar (uneven electron distribution)  Weak bonds…low melting points  Metallic (nuclei in a “sea” of shared electrons) 

ionic bonding ● Forms between metallic and nonmetallic elements; elements at the horizontal extremities of the periodic table. ● a metallic atom easily gives up its valence electrons to the nonmetallic atoms. ● In the process all the atoms acquire stable configurations and become ions. ● Ionic bonding is non-directional (magnitude of the bond is equal in all directions around the ion) ● Ceramic materials exhibit ionic bonding

Ionic Bonding • Occurs between + and - ions. • Requires electron transfer. • Large difference in electronegativity required. Na (metal) Unstable 11 electrons

electron

Cl (nonmetal) Unstable 17 electrons

Na (cation) + Cl (anion) stable stable Coulombic Attraction positive and negative ions, by virtue of their net electrical charge, attract one another

Ionic Bonding - examples • Predominant bonding in Ceramics NaCl MgO CaF 2 CsCl

Give up electrons

Acquire electrons

Ion Sizes + Li,152 pm 3e and 3p

Li + , 78 pm  e  2e and 3 p

Forming a cation.

 CATIONS are SMALLER than the atoms from

which they come.  The electron/proton attraction has gone UP and so size DECREASES.

Ion Sizes F, 71 pm 9e and 9p

F- , 133 pm + e  10 e and 9 p

Forming an anion.

 ANIONS are LARGER than the atoms from

which they come.  The electron/proton attraction has gone DOWN and so size INCREASES.  Trends in ion sizes are the same as atom sizes.

ionic bonding ● The predominant bonding in ceramic materials is ionic. ● Ionic materials are characteristically hard and brittle and, electrically and thermally insulative. ● These properties are directly related to electron configurations and/or the nature of the ionic bond.

covalent bonding ● stable electron configurations are assumed by the sharing of electrons between adjacent atoms. ● Two atoms that are covalently bonded will each contribute at least one electron to the bond, and the shared electrons may be considered to belong to both atoms. ● The covalent bond is directional; it is between specific atoms and may exist only in the direction between one atom and another that participates in the electron sharing.

Covalent Bonding similar electronegativity  share electrons bonds are determined by valence – s & p orbitals dominate bonding shared electrons Example: CH4 H of carbon atom CH 4 H C: has 4 valence e-, ∙∙ needs 4 more H: C : H H H C ∙∙ H: has 1 valence e-, H needs 1 more H shared electrons Electronegativities of hydrogen atom are comparable.

● ● ● ●

covalent bonding ● Covalent bonds may be very strong, as in diamond, which is very hard and has a very high melting temperature, 3550 C, or they may be very weak, as with bismuth, which melts at about 270 C. ● Polymeric materials typify this bond, the basic molecular structure often being a long chain of carbon atoms that are covalently bonded together with two of their available four bonds per atom. ● The remaining two bonds normally are shared with other atoms, which also covalently bond.

covalent bonding ● interatomic bonds may be partially ionic and partially covalent. ● very few compounds exhibit pure ionic or covalent bonding. ● the degree of either bond type depends on the relative positions of the components in the periodic table or the difference in their electronegativities. ● The wider the separation (the greater the difference in electronegativity), the more ionic the bond. ● the closer they are (the smaller the difference in electronegativity), the greater the degree of covalency.

interatomic bonding No electronegativity difference between two atoms leads to a purely non-polar covalent bond. A

B

A small electronegativity difference leads to a polar covalent bond. A

B

A large electronegativity difference leads to an ionic bond.

metallic bonding ● Metallic materials have one, two, or at most, three valence electrons. ● these valence electrons are more or less free to drift throughout the entire metal and form a “sea of electrons”. ● the metallic bond is nondirectional in character. The free electrons act as a “glue” to hold the ion cores together. ● Bonding may be weak or strong; bonding energy 68 kJ/mol (0.7 eV/atom) for mercury and 849 kJ/mol (8.8 eV/atom) for tungsten. Their respective melting temperatures are 39 and 3410 C.

metallic bonding

Secondary-van der waals-bonding Secondary, van der Waals, or physical bonds are weak in comparison to the primary or chemical ones; bonding energies are typically on the order of only 10 kJ/mol (0.1 eV/atom). Secondary bonding exists between virtually all atoms or molecules, but its presence may be obscured if any of the three primary bonding types is present. Secondary bonding is evidenced for the inert gases, which have stable electron structures, and, in addition, between molecules in molecular structures that are covalently bonded.

Properties linked with bonding if the bond energy is higher, ● Melting point is higher ● Thermal expansion coefficient is smaller ● Elastic modulus is higher

Energy

ro

r

Primary Bonds Large bond energy Ceramics high Tm (Ionic & covalent bonding): high E small  Variable bond energy Metals moderate Tm (Metallic bonding): moderate E moderate  Polymers (Covalent & Secondary):

Directional Properties Secondary bonding dominates small Tm small E high 

structure of solids

Energy and Packing Non dense, random packing

Energy typical neighbour bond length

typical neighbour bond energy

Dense, ordered packing

r

Energy typical neighbour bond length

typical neighbour bond energy

Dense, ordered packed structures tend to have lower energies!

r

Materials and Packing Crystalline materials: atoms are situated in a repeating array over large atomic distances; long-range order exists.. each atom is bonded to its nearest-neighbor atoms. typical of: metals many ceramics some polymers

crystalline SiO2 Si Oxygen

noncrystalline solids noncrystalline materials: no periodic packing of atoms occurs in the case of complex structures rapid solidification amorphous = noncrystalline many polymers some ceramics ? metallic glasses

noncrystalline SiO2 Si Oxygen

Materials and Packing crystalline SiO2

Si

Oxygen

noncrystalline SiO2

noncrystalline solids ● crystalline vs amorphous solid depends on the ease with which a random atomic structure in the liquid can transform to an ordered state during solidification. ● Therefore, amorphous materials are characterized by atomic or molecular structures that are relatively complex and become ordered only with some difficulty.

noncrystalline solids ● rapid cooling through the freezing temperature  noncrystalline solid / no time for ordering! ● metals normally form crystalline solids ● some ceramic materials are crystalline, whereas others, the inorganic glasses, are amorphous.

● polymers may be completely noncrystalline and semicrystalline consisting of varying degrees of crystallinity.

noncrystalline solids T

metals crystalline

dT/dt  noncrystalline

t

noncrystalline solids T

ceramics

crystalline

dT/dt  noncrystalline t

Structure of solids issues of interest ● How do atoms assemble into solid structures? (we shall focus on metals for the time being!) ● How does the density of a material depend on its structure? ● When do material properties vary with the sample (i.e., part) orientation?

Structures of crystalline solids ● properties of crystalline solids depend on the crystal structure of the material, the manner in which atoms are spatially arranged.

● For example, magnesium, having one crystal structure, is much more brittle (i.e., fracture at lower degrees of deformation) than aluminium that has yet another crystal structure.

Structure – mechanical properties

aluminium

magnesium

structure – physical properties ● significant property differences exist between crystalline and noncrystalline materials having the same composition. ● For example, noncrystalline ceramics and polymers normally are optically transparent; the same materials in crystalline form tend to be opaque or, at best, translucent. Alumina Single crystal Polycrystal-low porosity high porosity

structure of crystalline solids ● atomic hard-sphere model: atoms (or ions) are thought of as being solid spheres having welldefined diameters. These spheres touch one another. ● the unit cell is the basic structural unit or building block of the crystal structure and defines the crystal structure by virtue of its geometry and the atom positions.

metallic crystal structures ● metallic bonding ● nondirectional: minimal restrictions as to the number and position of nearest-neighbor atoms ● hence, relatively large numbers of nearest neighbors ● three relatively simple crystal structures are found for most of the common metals:

face centered cubic body-centered cubic hexagonal close-packed

(FCC) (BCC) (HCP)

metallic crystal structures tend to be densely packed. Reasons for dense packing: ● Typically, only one element is present, so all atomic radii are the same. ● bonding is not directional. ● nearest neighbor distances tend to be small in order to reduce bond energy (energy minimization). ● electron cloud shields cores from each other ● have the simplest crystal structures.

metallic crystal structures

crystal systems Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal. The unit cell geometry is completely defined in terms of six lattice parameters

edge lengths: a, b, and c (lattice constants) interaxial angles: , , and  (lattice angles) There are seven different possible combinations of a, b, and c, and ,  and 

crystal systems 7 distinct crystal systems cubic tetragonal hexagonal orthorhombic rhombohedral monoclinic triclinic 14 crystal lattices

crystal systems cubic: a=b=c, ===90

simple cubic

body-centered cubic (BCC)

face-centered cubic (FCC)

tetragonal: a=bc, ===90 simple tetragonal

body-centered tetragonal (BCT)

crystal systems orthorombic: abc, ===90

simple

body-centered base-centered face-centered

monoclinic: abc, ==90 simple monoclinic

base-centered monoclinic

crystal systems

rhombohedral a=b=c, ==90

hexagonal a=bc, ==90 =120

Total of 14 Bravais lattices!

triclinic abc, 90

crystal systems

cubic a=b=c ===90

triclinic abc 90

maximum symmetry

minimum symmetry

metallic crystal structures How can we stack metal atoms to minimize empty space? 2-dimensions

vs

cube 6 faces 8 corners 12 edges

metallic crystal structures F.C.C. Crystal structure:

hard-sphere unit cell reduced-sphere unit cell aggregate of many atoms

simple cubic structure (SC) • Rare due to low packing density (only Po has this structure) • Close-packed directions are cube edges.

• Coordination # = 6 (# nearest neighbors)

simple cubic (SC) structure ● Atoms touch each other along cube edges. ● each of 8 corner atoms is shared by eight unit cells: 8 x (1/8) = 1 atom/unit cell R

a = 2R unit cell volume = a3 = 8R3

BCC crystal structure ● unit cell has cubic geometry ● atoms are located at the corners of the cube. ● Some of the materials that have a bcc structure include lithium, sodium, potassium, chromium, barium, vanadium, alpha-iron and tungsten. ● Metals which have a BCC structure are usually harder and less malleable than close-packed metals such as copper and gold. ● When the metal is deformed, the planes of atoms must slip over each other, and this is more difficult in the bcc structure.

Body Centered Cubic Structure (BCC) 8 5

6

4 1

2

7 3

Coordination # = 8 Atomic packing of an BCC (110) plane.

body centred cubic (BCC) structure ● Atoms touch each other along cube diagonals. ● each of 8 corner atoms is shared by eight unit cells; single center atom is wholly owned: 8 x (1/8) + 1 = 1 + 1 = 2 atoms/unit cell ● each center atom touches eight corner atoms: 8 nearest neighbors

a 2.a

3.a = 4R

FCC crystal structure ● unit cell has cubic geometry ● atoms are located at the corners and the centers of all the cube faces. ● familiar metals with FCC crystal structure copper aluminium silver gold

Atomic arrangements - FCC Reduced sphere FCC unit cell with the (110) plane. Atomic packing of an FCC (110) plane.

Atoms touch each other along face diagonals.

Face Centered Cubic Structure (FCC) The face-centered atom in the front face is in contact with four corner atoms and four other face-centered atoms behind it (two sides, top and bottom) and is also touching four face-centered atoms of the unit cell in front of it. Coordination # = 12

FCC crystal structure atoms touch one another across a face diagonal; cube edge length a and the atomic radius R

a2 + a2 = (R+2R+R)2 2a2 = (4R)2 = 16R2

a2 = 8R2 a = 2R2

R = a /(22)

a

2R R

R

FCC crystal structure each of 8 corner atoms is shared by eight unit cells; each of 6 face-centered atoms belongs to only two. 8 x (1/8) + 6 x (1/2) = 1 + 3 = 4 atoms/unit cell The volume of the unit cell, a3 = (2R2)3 = 16R32

4R=2.a (a = 2R2)

cubic crystal structures X’tal structure Coordination # Atoms/unit cell simple cubic 6 1 body centred 8 2 face centred 12 4

atomic packing factor (APF) APF is the sum of the sphere volumes of all atoms within a unit cell divided by the unit cell volume:

the maximum packing possible for spheres all having the same diameter.

Atomic Packing Factor (APF)-SC Volume of atoms in unit cell APF = Volume of unit cell atoms unit cell

a R=0.5a

APF =

volume atom 4  (0.5a) 3 1 3 a3

close-packed directions

volume unit cell

1 contains 8 x 1/8 = 1 atom/unit cell

APF for a simple cubic structure = 0.52

Atomic Packing Factor: BCC 4R

3a a

2a R

a

2a

Close-packed directions: length = 4R = 3 a

atoms volume 4 3 unit cell 2  ( 3a/4) atom 3 APF = APF(BCC)= 0.68 volume a3 unit cell

Atomic Packing Factor: FCC Close-packed directions: length = 4R = 2 a 2a

a

Unit cell contains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell

volume atoms 4 3 atom ) p ( 2 a/4 4 unit cell 3 maximum APF = = 0.74 achievable APF a3 volume unit cell

Closed packed crystal structures A portion of a close-packed plane of atoms; A, B, and C positions are indicated. The AB stacking sequence for close packed atomic planes.

Hexagonal close packed (HCP) crystal structure Not all metals have unit cells with cubic symmetry; some common metals have a hexagonal structure

Closed packed crystal structures The real distinction between FCC and HCP lies in where the third close-packed layer is positioned. For HCP, the centers of this layer are aligned directly above the original A positions. stacking sequence, ABABAB ..., Atomic alignment repeats every other plane!

Closed packed crystal structures These planes are of the (111) type For FCC structure, the centers of the third plane are situated over the C sites of the first plane. This yields an ABCABCABC . . . stacking sequence; the atomic alignment repeats every third plane.

FCC Stacking Sequence • ABCABC... Stacking Sequence • 2D Projection B

A sites B sites C sites

A

B

C B

C B

B

C

B

B

A B C

FCC Unit Cell

Hexagonal close packed (HCP) crystal structure ● The HCP metals: Cd, Mg, Ti, and Zn. ● top and bottom faces consist of six atoms that form regular hexagons and surround a single atom in the center. ● Another plane that provides three additional atoms to the unit cell is situated between the top and bottom planes. The atoms in this mid-plane have as nearest neighbors atoms in both of the adjacent two planes.

Hexagonal close packed (HCP) crystal structure ● The equivalent of six atoms is contained in each unit cell ● one-sixth of each of the 12 top and bottom face corner atoms, one-half of each of the 2 center face atoms, and all 3 midplane interior atoms.: 12 x 1/6 + 2 x ½ + 3 = 2 +1 + 3 = 6 corner face midplane

Closed packed crystal structures ● both FCC and HCP crystal structures have atomic packing factors of 0.74, which is the most efficient packing of equal-sized spheres or atoms. ● these two crystal structures may be described in terms of close-packed planes of atoms (i.e., planes having a maximum atom or sphere packing density)

Hexagonal Close-Packed Structure (HCP) • ABAB... Stacking Sequence

• 3D Projection

c a

• 2D Projection

A sites

Top layer

B sites

Middle layer

A sites

• Coordination # = 12 • APF = 0.74 • c/a = 1.633

Bottom layer 6 atoms/unit cell

ex: Cd, Mg, Ti, Zn

Unit cell volume

Sin 60 = h /a h = a sin 60

Atomic packing factor

2R=a; R=a/2

ideal c/a ratio in HCP

a/2

h2= a2+(a/2)2 x=(2/3)h x2 + (c/2)2 = a2

see you next week!