ATOMIC BONDING Primary Bonds
Ionic (e.g., salts, metal oxides)
Covalent (e.g., within polymer molecules) Metallic (e.g., metals)
CORROSION
A table listing the standard electromotive potentials of metals is shown on the previous page.
For corrosion to occur, there must be an anode and a cathode in electrical contact in the presence of an electrolyte.
Anode Reaction (Oxidation) of a Typical Metal, M Mo→ Mn++ ne–
Possible Cathode Reactions (Reduction)
½ O2 + 2 e–+ H2O → 2 OH–
½ O2 + 2 e–+ 2 H3O+→ 3 H2O 2 e–+ 2 H3O+→ 2 H2O + H2 When dissimilar metals are in contact, the more
electropositive one becomes the anode in a corrosion cell.
Different regions of carbon steel can also result in a corrosion reaction: e.g., cold-worked regions are anodic to noncold-worked; different oxygen concentrations can cause oxygen-deficient regions to become cathodic to oxygen-rich regions; grain boundary regions are anodic to bulk grain; in multiphase alloys, various phases may not have the same galvanic potential.
DIFFUSION Diffusion Coefficient D = Do e−Q/(RT), where D = diffusion coefficient Do = proportionality constant Q = activation energy
R = gas constant [8.314 J/(mol•K)]
T = absolute temperature
THERMAL AND MECHANICAL PROCESSING Cold working (plastically deforming) a metal increases strength and lowers ductility.
Raising temperature causes (1) recovery (stress relief), (2) recrystallization, and (3) grain growth. Hot working allows these processes to occur simultaneously with deformation.
Quenching is rapid cooling from elevated temperature, preventing the formation of equilibrium phases.
In steels, quenching austenite [FCC (γ) iron] can result in martensite instead of equilibrium phases—ferrite [BCC (α) iron] and cementite (iron carbide).
PROPERTIES OF MATERIALS Electrical
Capacitance: The charge-carrying capacity of an insulating material
Charge held by a capacitor q = CV
q = charge C = capacitance V = voltage
Capacitance of a parallel plate capacitor C fdA
= C = capacitance
ε = permittivity of material
A = cross-sectional area of the plates d = distance between the plates
ε is also expressed as the product of the dielectric constant (κ) and the permittivity of free space (ε0 = 8.85 × 10−12 F/m) Resistivity: The material property that determines the resistance of a resistor
Resistivity of a material within a resistor L
= RA t
ρ = resistivity of the material R = resistance of the resistor
A = cross-sectional area of the resistor L = length of the resistor
Conductivity is the reciprocal of the resistivity
Photoelectric effect−electrons are emitted from matter (metals and nonmetallic solids, liquids or gases) as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength and high frequency.
Piezoelectric effect−the electromechanical and the electrical state in crystalline materials.
Mechanical
Strain is defined as change in length per unit length; for pure tension the following apply:
Engineering strain L
L
0
= D f
ε = engineering strain
∆L = change in length L0 = initial length True strain
L
T= dL f εT = true strain
dL = differential change in length L = initial length
εT = ln(1 + ε)
61 MATERIALS SCIENCE/STRUCTURE OF MATTER Aluminum
Antimony Arsenic Barium Beryllium Bismuth Cadmium Caesium Calcium Cerium Chromium Cobalt Copper Gallium Gold Indium Iridium Iron Lead Lithium Magnesium Manganese Mercury Molybendum Nickel Niobium Osmium Palladium Platinum Potassium Rhodium Rubidium Ruthenium Silver Sodium Strontium Tantalum Thallium Thorium Tin Titanium Tungsten Uranium Vanadium Zinc Zirconium
Al Sb As Ba Be Bi Cd Cs Ca Ce Cr Co Cu Ga Au In Ir Fe Pb Li Mg Mn Hg Mo Ni Nb Os Pd Pt K Rh Rb Ru Ag Na Sr Ta Tl Th Sn Ti W U V Zn Zr
26.98 121.75
74.92 137.33
9.012 208.98 112.41 132.91 40.08 140.12
52 58.93 63.54 69.72 196.97 114.82 192.22 55.85 207.2 6.94 24.31 54.94 200.59
95.94 58.69 92.91 190.2 106.4 195.08
39.09 102.91
85.47 101.07 107.87 22.989 87.62 180.95 204.38 232.04 118.69 47.88 183.85 238.03 50.94 65.38 91.22 Atomic Weight
2,698 6,692 5,776 3,594 1,846 9,803 8,647 1,900 1,530 6,711 7,194 8,800 8,933 5,905 19,281
7,290 22,550
7,873 11,343
533 1,738 7,473 13,547 10,222 8,907 8,578 22,580 11,995 21,450 862 12,420
1,533 12,360 10,500 966 2,583 16,670 11,871 11,725 7,285 4,508 19,254 19,050 6,090 7,135 6,507 Density ρ (kg/m3) Water = 1000
660 630 subl. 613
710 1,285
271 321 29 840 800 1,860 1,494 1,084 30 1,064
156 2,447 1,540 327 180 650 1,250
−39 2,620 1,455 2,425 3,030 1,554 1,772 63 1,963
38.8 2,310
961 97.8 770 3,000
304 1,700
232 1,670 3,387 1,135 1,920 419 1,850 Melting Point (°C)
895.9 209.3 347.5 284.7 2,051.5
125.6 234.5 217.7 636.4 188.4 406.5 431.2 389.4 330.7 129.8 238.6 138.2 456.4 129.8 4,576.2 1,046.7 502.4 142.3 272.1 439.6 267.9 129.8 230.3 134 753.6 242.8 330.7 255.4 234.5 1,235.1
− 150.7 138.2 117.2 230.3 527.5 142.8 117.2 481.5 393.5 284.7 Specific Heat
[J/(kg˙K)]
2.5 39 26 36 2.8 107 6.8 18.8
3.2 7.3 12.7
5.6 1.55 13.6 2.05 8 4.7 8.9 19.2 8.55 3.94 138 94.1 5 6.2 15.2
8.1 10 9.81
6.1 4.3 11 7.1 1.47
4.2 20 12.3
10 14.7 11.5 39 4.9 28 18.2
5.5 40 Electrical Resistivity (10−8 Ω˙m) at 0°C (273.2 K)
236 25.5
−
− 218
8.2 97 36
− 11 96.5
105 403 41 319
84 147 83.5 36 86 157
8 7.8 139 94 53 88 72 72 104 151 58 117 428 142
− 57 10 54 68 22 177
27 31 117
23 Heat Conductivity
λ[W/(m˙K)]
at 0°C (273.2 K) 1,220
1,166 subl. 1,135
1,310 2,345 519 609 84 1,544 1,472 3,380 2,721 1,983 86 1,947
312 4,436 2,804 620 356 1,202 2,282
−38 4,748 2,651 4,397 5,486 2,829 3,221 145 3,565
102 4,190 1,760 208 1,418 5,432 579 3,092
449 3,038 6,128 2,075 3,488 786 3,362 Melting Point (°F)
Metal Symbol
Properties of Metals
62 MATERIALS SCIENCE/STRUCTURE OF MATTER
The elastic modulus (also called modulus, modulus of elasticity, Young's modulus) describes the relationship between engineering stress and engineering strain during elastic loading. Hooke's Law applies in such a case.
σ = Eε where E is the elastic modulus.
Key mechanical properties obtained from a tensile test curve:
• Elastic modulus
• Ductility (also called percent elongation): Permanent engineering strain after failure
• Ultimate tensile strength (also called tensile strength):
Maximum engineering stress
• Yield strength: Engineering stress at which permanent deformation is first observed, calculated by 0.2% offset method.
Other mechanical properties:
• Creep: Time-dependent deformation under load. Usually measured by strain rate. For steady-state creep this is:
dt
d A ne RT f= v -Q
A = pre-exponential constant n = stress sensitivity
Q = activation energy for creep R = ideal gas law constant T = absolute temperature
• Fatigue: Time-dependent failure under cyclic load. Fatigue life is the number of cycles to failure. The endurance limit is the stress below which fatigue failure is unlikely.
• Fracture toughness: The combination of applied stress and the crack length in a brittle material. It is the stress intensity when the material will fail.
KIC=Yv ra KIC = fracture toughness σ = applied engineering stress a = crack length
Y = geometrical factor
a 2a
EXTERIOR CRACK (Y = 1.1) INTERIOR CRACK (Y = 1)
The critical value of stress intensity at which catastrophic crack propagation occurs, KIc, is a material property.
♦ W.R. Runyan and S.B. Watelski, in Handbook of Materials and Processes for Electronics, C.A. Harper, ed., McGraw-Hill, 1970.
♦
Some Extrinsic, Elemental Semiconductors
B AI Ga P As Sb Al Ga In As Sb
Periodic table group of dopant
III A III A III A V A V A V A III A III A III A V A V A
Maximum solid solubility of dopant (atoms/m3)
600 × 1024 20 × 1024 40 × 1024 1,000 × 1024 2,000 × 1024 70 × 1024 400 × 1024 500 × 1024 4 × 1024 80 × 1024 10 × 1024 Si
Ge
Element Dopant
♦
Impurity Energy Levels for Extrinsic Semiconductors Eg − Ed
(eV) 0.044 0.049 0.039 0.069
−−
−−
− 0.012 0.013 0.096
−−
−−
− 0.005 0.003
−
− Si
Ge
GaAs Semiconductor
P As Sb Bi B Al Ga In Tl P As Sb B Al Ga In Tl Se Te Zn Cd
Dopant Ea
(eV)
−−
−− 0.045 0.057 0.065 0.160 0.260
−− 0.010− 0.010 0.010 0.011 0.01
−− 0.024 0.021
Stress is defined as force per unit area; for pure tension the following apply:
Engineering stress A F v= 0
σ = engineering stress F = applied force
A0 = initial cross-sectional area True stress
A
T F v = σT = true stress F = applied force
A = actual cross-sectional area
63 MATERIALS SCIENCE/STRUCTURE OF MATTER
Representative Values of Fracture Toughness Material KIc (MPa•m1/2) KIc (ksi•in1/2)
A1 2014-T651 24.2 22
A1 2024-T3 44 40
52100 Steel 14.3 13
4340 Steel 46 42
Alumina 4.5 4.1
Silicon Carbide 3.5 3.2
RELATIONSHIP BETWEEN HARDNESS AND TENSILE STRENGTH
For plain carbon steels, there is a general relationship between Brinell hardness and tensile strength as follows:
TS psi 500 BHN
TS MPa 3.5 BHN
-_
^ i
h
ASTM GRAIN SIZE
. ,
S P
N
N N
2
2
0 0645
Actual Area mm where
.
V L
n 0 0645
1
2 mm
actual
2
=
=
=
-_
_ ^
i
i h
SV = grain-boundary surface per unit volume
PL = number of points of intersection per unit length between the line and the boundaries
N = number of grains observed in a area of 0.0645 mm2 n = grain size (nearest integer > 1)
COMPOSITE MATERIALS f
C fc
E
f E fE
f
1
c i i
c i i
i i
c i i
c i i
# #
t t
v v
R R
R R
R
=
=
=
−
= G
ρc = density of composite
Cc = heat capacity of composite per unit volume Ec = Young's modulus of composite
fi = volume fraction of individual material
ci = heat capacity of individual material per unit volume Ei = Young's modulus of individual material
σc = strength parallel to fiber direction
Also, for axially oriented, long, fiber-reinforced composites, the strains of the two components are equal.
(∆L/L)1 = (∆L/L)2
∆L = change in length of the composite L = original length of the composite
Hardness: Resistance to penetration. Measured by denting a material under known load and measuring the size of the dent.
Hardenability: The "ease" with which hardness can be obtained.
JOMINY HARDENABILITY CURVES FOR SIX STEELS
(#2) and (#8) indicate grain size
in.
Van Vlack, L., Elements of Materials Science & Engineering, Addison-Wesley, 1989.
64 MATERIALS SCIENCE/STRUCTURE OF MATTER
The following two graphs show cooling curves for four different positions in the bar.
C = Center
M-R = Halfway between center and surface
3/4-R = 75% of the distance between the center and the surface
S = Surface
These positions are shown in the following figure.
C M-R 3/4-R S
♦
COOLING RATES FOR BARS QUENCHED IN AGITATED WATER
♦
COOLING RATES FOR BARS QUENCHED IN AGITATED OIL
Impact Test
The Charpy Impact Test is used to find energy required to fracture and to identify ductile to brittle transition.
Impact tests determine the amount of energy required to cause failure in standardized test samples. The tests are repeated over a range of temperatures to determine the ductile to brittle transition temperature.
♦ Van Vlack, L., Elements of Materials Science & Engineering, Addison-Wesley, 1989.
65 MATERIALS SCIENCE/STRUCTURE OF MATTER
Concrete
♦
8,000 6,000 4,000 2,000
1,000
W/C BY WEIGHT 0.40 0.60 0.80 1.00 RECOMMENDED
PERCENT ENTRAINED AIR
NO ADDED AIR
AVERAGE 28-DAY COMPRESSIVE STRENGTH, PSI
Concrete strength decreases with increases in water-cement ratio for concrete with and without entrained air.
Water-cement (W/C) ratio is the primary factor affecting the strength of concrete. The figure above shows how W/C expressed as a ratio of weight of water and cement by weight of concrete mix affects the compressive strength of both air-entrained and non-air-air-entrained concrete.
•
6,000
4,000
3,000
2,000 5,000
1,000
COMPRESSIVE STRENGTH, PSI
AGE, DAYS
0 8 1 0
9 8
2 4 1 7 3 0
STORED CONTINUOUSLY IN LABORATORY AIR IN AIR AFTER 28 DAYS
IN AIR AFTER 14 DAYS IN AIR AFTER 3 DAYS
CONTINUOUSLY MOIST CURED
Concrete compressive strength varies with moist-curing conditions. Mixes tested had a water-cement ratio of 0.50, a slump of 3.5 in., cement content of 556 lb/yd3, sand content of 36%, and air content of 4%.
IN AIR AFTER 7 DAYS
Water content affects workability. However, an increase in water without a corresponding increase in cement reduces the concrete strength. Superplasticizers are the most typical way to increase workability. Air entrainment is used to improve durability.
Amorphous Materials
Amorphous materials such as glass are non-crystalline solids.
Thermoplastic polymers are either semicrystalline or amorphous.
Below the glass transition temperature (Tg) the amorphous material will be a brittle solid.
TEMPERATURE
VOLUME
Tg Tm
GLASS
LIQUID
CRYSTAL
The volume temperature curve as shown above is often used to show the difference between amorphous and crystalline solids.
Polymers
Polymers are classified asthermoplastics that can be melted and reformed. Thermosets cannot be melted and reformed.
Tg Tm
LOG E or LOG σ
TEMPERATURE
The above curve shows the temperature dependent strength (σ) or modulus (E) for a thermoplastic polymer.
Polymer Additives
Chemicals and compounds are added to polymers to improve properties for commercial use. These substances, such as plasticizers, improve formability during processing, while others increase strength or durability.
Examples of common additives are:
Plasticizers: vegetable oils, low molecular weight polymers or monomers
Fillers: talc, chopped glass fibers
Flame retardants: halogenated paraffins, zinc borate, chlorinated phosphates
Ultraviolet or visible light resistance: carbon black Oxidation resistance: phenols, aldehydes
Thermal Properties
The thermal expansion coefficient is the ratio of engineering strain to the change in temperature.
= T
a f
D
α = thermal expansion coefficient ε = engineering strain
∆T = change in temperature
Specific heat (also called heat capacity) is the amount of heat required to raise the temperature of something or an amount of something by 1 degree.
At constant pressure the amount of heat (Q) required to increase the temperature of something by ∆T is Cp∆T, where Cp is the constant pressure heat capacity.
At constant volume the amount of heat (Q) required to increase the temperature of something by ∆T is Cv∆T, where Cv is the constant volume heat capacity.
An object can have a heat capacity that would be expressed as energy/degree.
The heat capacity of a material can be reported as energy/
degree per unit mass or per unit volume.
♦ Concrete Manual, 8th ed., U.S. Bureau of Reclamation, 1975.
• Merritt, Frederick S., Standard Handbook for Civil Engineers, 3rd ed., McGraw-Hill, 1983.
66 MATERIALS SCIENCE/STRUCTURE OF MATTER
BINARY PHASE DIAGRAMS
Allows determination of (1) what phases are present at equilibrium at any temperature and average composition, (2) the compositions of those phases, and (3) the fractions of those phases.
Eutectic reaction (liquid → two solid phases) Eutectoid reaction (solid → two solid phases) Peritectic reaction (liquid + solid → solid) Peritectoid reaction (two solid phases → solid) Lever Rule
The following phase diagram and equations illustrate how the weight of each phase in a two-phase system can be determined:
COMPOSITION, WT%
0% B
100% A 100% B
0% A B A
L
β + L α + L
α + β α β
xα x xβ
TEMPERATURE, °C TEMPERATURE, °F
(In diagram, L = liquid.) If x = the average composition at temperature T, then
x xx xx xx
%
%
100 100 wt x
wt
#
#
=
= a b
-b a
b
b a
a
Iron-Iron Carbide Phase Diagram
♦
♦ Van Vlack, L., Elements of Materials Science & Engineering, Addison-Wesley, Boston, 1989.
67 STATICS FORCE
A force is a vector quantity. It is defined when its (1) magnitude, (2) point of application, and (3) direction are known.
The vector form of a force is F = Fx i + Fy j
RESULTANT (TWO DIMENSIONS)
The resultant, F, of n forces with components Fx,i and Fy,i has the magnitude of
F Fx i, F,
i n
i y i n 1
2
1
21 2
= +
= =
d n d n
> ! ! H
The resultant direction with respect to the x-axis is arctan Fy i, F,
i n
x i i
n
1 1
i =
= =
e ! ! o
RESOLUTION OF A FORCE Fx = F cos θx; Fy = F cos θy; Fz = F cos θz
cos θx = Fx /F; cos θy = Fy /F; cos θz = Fz /F
Separating a force into components when the geometry of force is known and R= x2+ y2+ z2
Fx = (x/R)F; Fy = (y/R)F; Fz = (z/R)F MOMENTS (COUPLES)
A system of two forces that are equal in magnitude, opposite in direction, and parallel to each other is called a couple. A moment M is defined as the cross product of the radius vector r and the force F from a point to the line of action of the force.
M = r × F; Mx = yFz – zFy, My = zFx – xFz, and Mz = xFy – yFx. SYSTEMS OF FORCES
F = Σ Fn
M = Σ (rn × Fn) Equilibrium Requirements
Σ Fn = 0 Σ Mn = 0