Midterm 1
biomaterials
- used for implants in the body - must be biocompatible (not produce adverse reactions in the body) - all types of materials may be used biomedically
interplanar spacing
magnitude of the distance between two adjacent and parallel planes of atoms BCC: h, k, l must be even for scattering FCC: all even or all odd
shape-memory alloys
metals that, after having been deformed, revert to their original shape after temperature change
hybridization
mixing (or combining) of two or more atomic orbitals with the result that more orbital overlap during bonding results (sp3 in diamond, sp2 in carbon)
unstable electron configurations
most electrons have unstable configurations because valence shell is usually not filled
polymorphism (allotropy)
two or more distinct crystals for the same material (composition and stoichiometry) i.e. C (diamond, graphite, graphene, C60)
copolymers
two or more kinds of repeat units
hexagonal close-packed (HCP)
N = 6 coordination number = 12 APF = 0.74 ABABABAB... close-packed plane {0001}
hydrogen bonding
N, O, F
Arrhenius equation
Nv = (N)e^[(-Qv)/(k)(T)] N = total number of atomic sites Qv = activation energy required for formation of a vacancy T = absolute temperature in Kelvins k = gas or Boltzmann's constant
strength
ability to withstand an applied stress without failure; metals usually have highest strength
energy levels or states
adjacent states separated by finite energies
isotactic (stereoisomers)
all R groups on same side of chain
TEM
an image is formed from an electron beam that, although passing through the specimen, is scattered and/or diffracted
diffractometer
apparatus used to determine the angles at which diffraction occurs for powdered specimens
point defects
associated with one or two atomic positions - vacancy atoms - interstitial atoms - substitutional atoms
polar
asymmetric charge distribution
fluctuating dipoles
asymmetric electron clouds
thermal expansion
captures increase in average distance between the atoms - smaller if E0 is steeper
Frenkel defect
cation vacancy -- cation interstitial pair
deteriorative characteristics
chemical reactivity of materials
Schrodinger's equation
defines a wave function that can be used to determine the probability of finding an electron at a certain location
mixed ionic-covalent bonding
degree of either bond depends on difference in EN of the constituent atoms 50% ionic character => delta x ~= 1.7
magnetic properties
demonstrate the response of a material to the application of the magnetic field
energy and packing relationship
dense, ordered packed structures tend to have lower energies
bottom-up approach
design and build new structures from their atomic-level constituents, one atom or molecule at a time
materials engineering
designing or engineering the structure of a material to produce a predetermined set of properties on the basis of structure-property correlations
piezoelectric ceramics
expand and contract in response to an applied electrical field (or voltage), also generate an electric field when their dimensions are altered
Bragg's Law
expression relating the x-ray wavelength and interatomic spacing to the angle of the diffracted beam
Pauling
if two atomic orbitals each containing a single electron can overlap, a bond is formed
linear structures
long flexible chains
branched structures
lower density
saturated hydrocarbons
- each carbon singly bonded to four other atoms - all covalent bonds are single bonds
group IA elements
(alkali metals) have one electron greater than a filled shell
energy well
(bond strength = E0 = energy released to form bond) - deep well = strong bond - shallow well = weak bond - more asymmetric the well = larger thermal expansion coefficient - higher the curvature of the well = larger the stiffness
polycrystals
(each grain is a single crystal) most engineering materials are polycrystals (simpler processing, relatively cheap) properties may/may not vary with direction if grains randomly oriented, isotropic if grains are textured, anisotropic
group 0 elements
(inert gasses) have filled electron shells
ml
(magnetic) describes specific orbital within subshell (-l to l)
Madelung Rule
(neutral atoms)
n
(principal energy shell) describes electron shell or energy level (1, 2, 3, etc.)
ms
(spin) describes intrinsic angular momentum of electron (1/2 spin up, -1/2 spin down)
dislocations
- 1D defects around which atoms are misaligned - dislocation motion is the primary mechanism by which plastic (permanent) deformation occurs and are central to mechanical properties of metals
bifunctional monomers
- 2D chainlike structure results from a monomer that has 2 active bonds
trifunctional monomers
- 3 active bonds, from which 3D network structures form
lattice parameters
- 3 edge lengths: a, b, c - 3 interaxial angles: alpha, beta, Y - cubic system (FCC and BCC): a = b = c; alpha = beta = Y = 90 (greatest degree of symmetry) - hexagonal (HCP): a = b, not = c; alpha = beta = 90, Y = 120
smart materials
- able to sense changes in their environment and then respond to these changes in predetermined manners--traits that are also found in living organisms - comprised of sensor (which detects an input signal) and an actuator (which performs a responsive and adaptive function) - actuators: shape-memory alloys, piezoelectric, magnetostrictive materials
ceramics point defects
- anion and cation vacancies can exist - cations interstitials more observed than anion - must be electrically neutral
grain boundaries
- boundary region separating two grains where there is some atomic mismatch - transition from lattice of one region to that of another - slightly disordered - low density in grain boundaries; high mobility, high diffusivity, high chemical reactivity
disadvantages for ceramics for automobile engines
- brittle - difficult to remove internal voids (that weaken structures) - ceramic parts are difficult to form and machine
synthetic polymers
- cheap to produce - properties can be controlled or desired - environmental concerns (recycling, resource usage, sustainability, toxicity)
ceramics
- compounds between metallic and nonmetallic elements (at least 2 elements) - ionic bonding (refractory), large bond energy - cations (usually fit in interstitial space) smaller than anions (crystals much be electrically neutral overall) - usually oxides, nitrides, and carbides - relatively stiff and strong - brittle and hard - insulators (non conducting), except high-Tc superconductors - more resistant to high temperatures and harsh environments than metals and polymers - low thermal conductivity - low melting/boiling points - larger molecules have higher boiling points - can be transparent, translucent, or opaque - i.e. cookware, cutlery, brick, tile, etc.
silicate ceramics
- comprised of Si and O (most abundant elements on earth) - structure is more conveniently represented in terms of interconnecting SiO^4− 4 tetrahedra (forms in tetrahedral networks) - relatively complex structures may result when other cations (e.g.,Ca2+, Mg2+, Al3+) and anions (e.g., OH−) are added - possesses some covalent character (bonds are somewhat directional and strong)
polymers and plastics
- covalent, van der waals, and hydrogren bonding - long hydrocarbons and other non-metallic bonded molecules - many are organic compounds chemically based on carbon, hydrogen, and other nonmetallic elements - soft, ductile, high flexibility, low strength, low density - thermal and electrical insulators, nonmagnetic - i.e. rubbers, plastics, etc. - with either rising temperature or decreasing strain rate, modulus of elasticity diminishes, tensile strength decreases, and ductility increases
thermosets
- crosslinked with 3 links/mer or network polymers - rigid 3D molecules due to covalent bonds - cannot be reshaped - do not soften upon heating - difficult to recycle - i.e. vulcanized rubber
nanomaterials
- distinguished by size < 100 nm - size leads to changes in variety of material properties - can be metals, ceramics, polymers, or composites - uses bottom-up approach
secondary bonding
- dominated by van der Waals forces - exists between all atoms and molecules (weak electrostatic attraction between polar molecules or atoms) - secondary bonding forces arise from atomic or molecular dipoles - inter-chain (POLYMER) and inter-molecular
Bohr atomic model
- early attempt to describe electrons in atoms in terms of position (electron orbitals) and energy (quantized energy levels) - electrons assumed to revolve around nucleus in discrete orbitals - only certain energies allowed (quantized and not continuous) - significant limitations because of inability to explain various electron phenomena
semiconductors
- electrical properties intermediate between those of electrical conductors (i.e. metals and metal alloys) and insulators (i.e. ceramics and polymers) - properties extremely sensitive to small concentrations of impurity atoms
edge dislocation
- extra half plane of atoms inserted in a crystal structure; one part under compression, other under tension - b (Burgers vector) perpendicular to dislocation line - extra energy due to unsatisfied bonds along dislocation line - shear stress leads to movement of dislocation line ("slip" implies ductility) - impurity atoms like to segregate to edge dislocation cores because it minimizes strain energy
metallic bonding
- found in metals and their alloys - valence e- are delocalized to form an "electron cloud/sea/gas" or Fermi liquid--these are the conduction electrons - non-directional bonding - cations held by negatively-charged electron "glue" - extreme case of bonding where e- are shared by all atoms of the crystal--responsible for ductility, electrical conduction, and shininess/opacity
area defects
- free surfaces - grain boundaries - twins - stacking faults
volume defects
- inclusions - precipitates - pores - cracks
polymer orgo summary
- intramolecular covalent bonds between C, H, N, O, S, Cl, F - similar EN - C: 4 bonds - N: 3 bonds - O and S: 2 bonds - H, C, F: 1 bond - intermolecular bonds: weaker hydrogen and van der Waals
thermoplastics
- linear polymers with 2 links/mer - branched with flexible chains - can be softened or melted repeatedly by raising the temperature - weak secondary bonds between chains - strong bonds within chains - relatively soft - can be recycled - i.e. PE, PVC
equilibrium vacancy concentrations
- low at low temperature - high at high temperature (atoms migrate from bulk to surface island increasing its size)
ionic bonding
- metal donates electrons (cation), nonmetal accepts electrons (anion) - requires large difference electronegativity values - for stability, nearest neighbors must have opposite charges (NaCl = Na+Cl-) => leads to brittle nature of ionicly bonded materials - found in most CERAMICS
periodic table trends
- metals (electropositive elements): readily give up electrons to become + ions - nonmetals (electronegative elements): readily acquire electrons to become - ions
impurities in solids
- no such thing as a pure metal (impurities, foreign atoms ALWAYS present) - most metals are alloys (impurity atoms DELIBERATELY ADDED to modify properties) - adding impurity atoms results in solid solution or second phase formation
OLED: Organic Light-emitting Diodes
- non-brittle - flexible and lightweight - lower cost/impact - degrade over time - poor color balance - sensitive to water (used in experimental flexible smartphones)
ground state configuration
- number of electrons = Z (neutral atom) - electrons occupy lowest energy states
metals
- one or more metallic elements, nonmetallic elements in small amounts - metallic or ultimate covalent bonding, varying bond energy - strong, ductile (malleable) - relatively dense - high thermal and electrical conductivity - opaque, reflect light - some magnetic properties - i.e. aluminum, copper, steel, etc.
advantages of ceramics for automobile engines
- operate at high temperatures - low frictional losses - operate without a cooling system - lower weights than current engines
simplified atomic bonding in solids
- primary bonds (usually strong): ionic, covalent, metallic - secondary bonds (usually much weaker): van der waals (or induced dipoles), hydrogen bond (or permanent dipoles) - atoms achieve full orbitals by transferring or sharing valence electrons with other atoms (bonding minimizes overall energy of the system)
electronegativity
- ranges from 0.7 to 4.0 - larger values: tendency to accept electrons
Miller indices (hkl)
- reciprocals of the (three) axial intercepts for a plane - always cleared of fractions and common multiples - all parallel planes have same Miller indices - read off intercepts of plane with axes in terms of a, b, c - take reciprocals of intercepts - reduce to smallest integer values - enclose in parentheses, no commas (h k l)
unsaturated hydrocarbons
- share 2 or 3 pairs of electrons - double and triple bonds somewhat unstable
amorphous
- short-range order but no long range order (no periodic packing) - exhibit no diffraction (Bragg) peaks - glass is most common - though more challenging, metals can be made amorphous by rapid solid techniques (no long range order, no grain boundaries) (excellent corrosion resistance, good ductility, high strength)
covalent bonding
- similar EN and share electrons to minimize energy - bonds determined by valence--s and p orbitals dominate bonding - C has 4 valence and needs 4 more, H has 1 and needs 1 - bonds are directional and occur between specific atoms participating in electron sharing - common in NON-METALLIC compounds (right side of periodic table excluding noble gases) - hugely varying properties (cannot determine on basis of bonding characteristics)
solid solutions
- solute atoms added to host (solvent) material - compositionally homogenous (impurity atoms are randomly and uniformly dispersed throughout the solid)
semicrystalline polymers
- some form spherulite structures
screw dislocation
- spiral planar ramp resulting from shear deformation - b is parallel to deformation line - direction of step movement is perpendicular to applied stress - possess extra energy due to non-ideal bonding configurations
point coordinates
- used to define positions of atoms (point particles) or centroid of a void - unit cell: a, b, c lattice constants - point coordinates: q, r, s - pc for unit cell center: a/2, b/2, c/2 - pc for unit cell corner: 1 1 1 (and 0 0 0, 1 0 0, 0 1 0, 0 0 1, 1 1 0, 1 0 1, 0 1 1) - integer multiple of lattice constants => identical position in another unit cell - qa = lattice position referred to the x-axis - rb = lattice position referred to the y-axis - sc = lattice position referred to the z-axis
Hume-Rothery rules
1) atomic size factor: difference in atomic radii between two atom types must be less than about +-15% 2) crystal structure: must be same 3) EN factor: similar EN 4) valences: should be similar
atomic mass unit (amu)
1/12 mass of 12C; atomic mass of specific atom in amu ~ Z + N 1 amu = 1 g/mol
oxygen electron configuration
1s^2 2s^2 2p^4
number of atoms per unit cell (N)
FCC = 4 BCC = 2 SC = 1
atomic packing factor (APF)
FCC, HCP = 0.74 (max packing possible for spheres all having same diameter) BCC = 0.68 SC = 0.52
octahedral sites
FCC: 4 coordination number: 6 produced by joining 6 sphere centers
tetrahedral sites
FCC: 8 coordination number: 4 straight lines drawn from the centers of surrounding host atoms form a four-sided tetrahedron
stacking faults
FCC: error in ABCABC packing sequence (i.e. ABCABABC)
net force between two atoms
FN = FA (force of attraction) + FR (force of repulsion
trans-isoprene (geometrical isomer)
H atom and CH3 group on opposite sides of chain (packs more tightly)
cis-isoprene (geometical isomer)
H atom and CH3 group on same side of chain (easily bends one way)
syndiotactic (stereoisomers)
R groups alternate sides
atactic (stereoisomers)
R groups randomly positioned
melting temperature (Tm)
Tm is larger if E0 is larger
plastic deformation
[permanent, nonrecoverable] mode of materials failure important in various industries (control of dislocations are a MAIN STRENGTHENING MECHANISM in metals)
toughness
ability to contain a crack and resist fracture; metals usually toughest
grain boundary energy
atomic bonding is less regular along grain boundary - impurity atoms tend to segregate here due to open structure - crystallographic misalignment exists
body centered cubic (BCC)
atoms located at all eight corners and in center a = 4R/sqrt(3) N = 2 coordination number = 8 APF = 0.68
face centered cubic (FCC)
atoms located at corners and centers of all cube faces a = 2Rsqrt(2) (a = cube length edge) (R = atomic radius) N = 4 coordination number = 12 APF = 0.74 volume = a^3 = 16(R^3)(sqrt2) ABCABCABC... close-packed plane {111} - 4 octahedral sites, 8 tetrahedral sites (number of atoms = number of octahedral sites; number of tetrahedral sites = 2*number of atoms)
isotopes
atoms of same element with different atomic masses
simple cubic (SC)
atoms only at corners of cube no metals have this because of low APF, only element is polonium (metalloid or semi-metal) N = 1 coordination number = 6 APF = 0.52
crystalline materials
atoms pack in periodic 3D arrays (typical for metals, many ceramics, some polymers)
l
azimuthal or angular (orbitals) describe subshell and orbital shape s (l=0), p (l=1), d (l=2), f (l=3) (0, 1, 2, 3,...,n-1)
weighted average (MW)
based on weight fraction of molecules within a given range
unit cells
basic structural unit or building block of the crystal structure and defines the crystal structure by virtue of its geometry and the atom positions within
phase [grain] boundaries
between two different phases (compositions) in an alloy
number averaged (MN)
bin the chains into a set of ranges and determine the number fraction in each range
Heisenberg Uncertainty Principle
both particle momentum and position cannot be determined simultaneously
polymer stress-strain
brittle (curve A), plastic (curve B), highly elastic (curve C)
dislocations & crystal structures
close-packed planes and directions are preferred directions for Burgers vectors in metals FCC: many close-packed planes/directions HCP: only one plane, 3 directions BCC: none
composites
composed of 2 or more dissimilar materials in order to get ideal combination of properties i.e. fiberglass, wood, concrete
spherulite
consists of a collection of ribbon-like chain-folded lamellar crystallites that radiate outward from its center
cross-linked structures
covalent bonds
materials engineer
creates new products or systems using existing materials and/or develops techniques for processing materials
materials scientist
develops or synthesizes new materials; explore how material properties arise from composition and structure
high technology
device or product that operates or functions using relatively intricate and sophisticated principles, including electronic equipment (camcorders, DVD players), computers, fiber-optic systems, spacecraft, aircraft, and military rocketry; built using advanced materials
anisotropy
directionality dependence of properties
quantized
electron may change energy but must make quantum jump either to allowed higher energy (with absorption of energy) or lower energy (emission of energy)
subatomic structure
electrons within individual atoms and interactions with their nuclei
SEM
employs an electron beam that raster-scans the specimen surface; an image is produced from back-scattered or reflected electrons
bonding energy (E0)
energy at minimum point, energy required to separate two atoms to infinite separation - materials with large bonding energies typically also have high melting temperatures - graph: depth of energy well to r0 (sum of ionic radii)
Fermi energy
energy corresponding to highest filled state at 0 K
Coulomb's Law
energy of interaction between two charges Epot = [(Z1)(Z2)(e^2)]/[4pi(E0)r] Z1 and Z2 = net charges (valences) of ions e = charge on electron E0 = permittivity of free space r = distance between ions (m) if Z1/Z2 are of same sign Epot = + (meaning repulsive) if Z1/Z2 are different signs Epot = - (attractive) describes negative potential energy which is attractive, but as ions come closer e- repel each other due to Pauli repulsion
self-interstitial
extra atoms positioned between atomic sites - self-interstitial atoms are large relative to available interstitial space and are LESS likely to occur than a vacancy
network structures
form 3D networks
tilt [grain] boundaries
form at low angles when edge dislocations stack up (low energy)
highly polar molecules
form when hydrogen covalently bonds to a nonmetal like flourine
crystal system
geometry of unit cell (cubic, hexagonal, monoclinic, etc.)
surfaces of single crystals present low energy planes
greater planar densities have low surface energies
x-ray diffraction
helps determine crystal structures
isomerism
polymers have same chemical formula but have different atomic arrangements
catalyst
increases rate of chemical reaction without being consumed - active sites on catalysts are normally surface defects
materials science
investigating the relationships that exist between the structures and properties of materials
crystalline defect
lattice irregularity having one or more of its dimensions on the order of an atomic diameter
mixed dislocations
lead to curved dislocation line - burgers vector is unchanged even though nature and direction of the dislocation line changes
crystallographic direction
line between two points (vector) - vector repositioned (if necessary) to pass through origin - read off projections in terms of unit cell dimensions a, b, c - adjust to smallest integer values - enclose in [square brackets], no commas: [u w v] - overbar = negative index - i.e. 1, 0, 1/2 => 2, 0, 1=> [2 0 1]
dislocation line
line in the crystal around which some of the atoms are misaligned
Pauli Exclusion Principle
no two electrons can have the same quantum numbers; each electron state can hold no more than 2 electrons with opposite spins
elastic deformation
nonpermanent (when applied load is released, the piece returns to its original shape)
planar density
number of atoms per unit are that are centered on a particular crystallographic plane
linear density
number of atoms per unit length whose centers lie on the direction vector for a specific crystallographic direction
surfaces
number of dangling bonds (open sides of atoms) increases reactivity => atom fully surrounded on all four sides is least reactive
atom percent (at%)
number of moles of an element in relation to total moles of the elements in the alloy C'1 = nm1/(nm1 + nm2) * 100% nm1 = number of moles of component 1
degree of polymerization (DP)
number of monomers per polymer chain
coordination number
number of nearest neighbors FCC and HCP = 12 BCC = 8 SC = 6
8-N' rule
number of possible covalent bonds for an atom = 8 -N' N' is the number of valence e-
atomic number (Z)
number of protons in nucleus (equal to number of electrons in neutral species)
permanent dipoles
occur in polar molecules
molecular entanglements
occur when the chains assume twisted, coiled, and kinked
linear defects
one-dimensional - dislocations
attractive force formula
only applies for two isolated ions that have opposite charges
wave-mechanical model
orbitals are not discrete, position of electrons defined by probability of electron at various locations around the nucleus
density (p)
p = nA/(Vc)(NA) n = number of atoms within unit cell A = atomic weight Vc = volume of unit cell NA = Avogadro's number (6.022*10^23 atoms/mol) p(metals) > p(ceramics) > p(polymers)
Shottky defect
paired set of cation and anion vacancies
bonding types/material classes
polymers: covalent metals: metallic ceramics: ionic/mixed ioniccovalent molecular solids: van der Waals semi-metals: mixed covalentmetallic intermetallics: mixed metallicionic
four mat sci principles
processing -> structure -> properties -> performance
single crystals
properties vary with direction, anisotropic - atomic order extends uninterrupted over the entirety of the specimen; under some circumstances, single crystals may have flat faces and regular geometric shapes - can be obtained only for slow and carefully controlled growth rates
surface phenomena
proportion of atoms located on surface sites of a particle increases dramatically as its size decreases
equilibrium
r = r0 (FN = 0 and energy is minimized)
twin [grain] boundary
reflection of atom positions along the twin plane (lowest energy)
mechanical properties
relate deformation to an applied load or force (i.e. stiffness, strength, toughness)
structure
relates to the arrangement of its internal components
thermal behavior
represented in terms of heat capacity and thermal conductivity
magnetostrictive materials
responsive to magnetic field
solidification
result of casting a molten material - nuclei form - nuclei grow to form crystals--grain structure - crystals grow until they meet each other
stereoisomerism
same molecular formula but position of atoms in space is different (mirror images)
homopolymers
same repeat units
crystallography
science that helps understand and to some extent rationalize the atomic-scale structure of crystalline materials
quantum numbers
size, shape, spacial orientation, number of states within each subshell
substitutional solid solution
solute or impurity atoms replace or substitute for host atoms
family of directions <uwv>
spacing of atoms along each direction is the same
electrical properties
stimulus is an electric field
optical properties
stimulus is electromagnetic or light radiation (i.e. index of refraction and reflectivity)
elastic modulus
stress/strain - force/displacement (slope of F(r) at r = r0)
average atomic weight formula
sum of amu values (multiplied by corresponding percentages)
atomic mass (A)
sum of the masses of protons (Z) and neutrons (N) within the nucleus; mass of proton is similar to mass of neutron, but much larger than mass of electron
percent crystallinity
tensile strength and modulus (E) increase with % crystallinity
vacancies
vacant atomic site in a crystalline structure - all crystalline solids contain vacancies - presence of vacancies increases entropy (disorder) of the crystal - equilibrium number of vacancies depends on and increases with temperature (see Arrhenius equation)
atomic weight
weight of 6.022*10^23 molecules or atoms (Avogadro's constant = amu/g) (not integers because weighted average of atomic masses of the atom's naturally occurring isotopes)
weight percent (wt%)
weight of particular element relative to total alloy weight
natural polymers
wood, rubber, wool, cotton, silk, leather