MSE 201 Test 1

Intro to Materials Science and Engineering at UTK

Atomic Number

The number of protons in the nucleus of an atom, which determines the element's identity and its position in the periodic table.

Atomic Mass

The weighted average mass of an atom's isotopes, reflecting both the number of protons and neutrons in the nucleus.

Isotope

Atoms of the same element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses.

Atomic Weight

The average mass of an atom of an element, measured in atomic mass units (amu), taking into account the relative abundance of its isotopes. (Weighted Average of all occuring isotopes)

Two atomic models cited in text and their major differences

Bohr atomic model and wave-mechanical model. The major difference is that in the Bohr Model, the electrons orbit the nucleus in a specific orbit, but in the wave-mechanical model there is no way to pinpoint the exact location of an electron, rather electron locations are given by an electron cloud. This electron cloud is the probability of an electron being there.

Bohr atomic model

A model of the atom where electrons orbit the nucleus in defined paths or orbits, each with a fixed energy level.

Wave-Mechanical model

A modern model of the atom that describes electrons as wave functions, where their position is defined by probabilities rather than fixed orbits, resulting in an electron cloud representation.

Four quantum numbers which all electrons are characterized by in an atom

• Principle (n) describes the energy and distance from the nucleus - the shell

• Angular momentum (l) describes the shape of the subshell and its orbitals

• Magnetic (m) defines the orientation of the orbitals within the subshell

• Spin (s) indicates the direction of the electron's spin. (+1/2 or -1/2)

What are the trends in relative energies of electrons from the various shells and subshells?

The trends indicate that energy levels increase with increasing principal quantum number (n) and that within a given shell, subshells with higher angular momentum quantum numbers (l) have increasing energy. Generally, the order of energy levels is s < p < d < f within the same principal energy level.

What is meant by “electron configurations” and how are the shells filled?

Electron configurations refer to the distribution of electrons in an atom's orbitals, following the Aufbau principle, Pauli exclusion principle, and Hund's rule. Shells are filled in order of increasing energy, typically from lowest to highest, with electrons occupying available orbitals until each is filled before moving to the next.

What are valence electrons and why are they important?

Valence electrons are the outermost electrons of an atom that are involved in chemical bonding. They determine an atom's reactivity and ability to form bonds with other atoms.

What common numbers are included on the periodic table, and what is the importance of each?

• atomic number, which indicates the number of protons in an atom

• atomic mass, which represents the average mass of an atom's isotopes

• group and period numbers, which help categorize elements based on their properties and electron configurations.

What are groups in the periodic table?

Groups in the periodic table are vertical columns that categorize elements with similar chemical properties and similar valence electron configurations.

What are periods in the periodic table?

Periods are the horizontal rows which represent elements that have the same number of electron shells with atomic number increasing along a period.

What is an electronegative element?

An electronegative element is one that has a strong tendency to attract electrons in a chemical bond, resulting in a partial negative charge.

What is an electropositive element?

An electropositive element is one that has a strong tendency to lose electrons in a chemical bond, resulting in a partial positive charge.

What is the periodic trend for electronegativity?

Increases across a period from left to right.

Decreases down a group from top to bottom.

What are the periodic trends of elements on the periodic table for the physical properties of elements, including conductivity and ductility?

Conductivity generally increases with metallic character, while ductility tends to decrease down a group and increase across a period. Ductility is higher for metals, while nonmetals are more brittle.

Why are the bonding forces and energies important?

The interatomic forces which bind atoms together affect the physical properties of the material.

What are the two types of forces between two atoms, what causes each forces, and what variables do the forces depend on?

• The two types of forces between atoms are attractive and repulsive forces.

• The magnitude of these forces is dependent upon the interatomic distance between the two atoms.

• Attractive forces originate from the type of bonding between the two atoms. It is caused by orbital polarization and bonding. Repulsive forces originate from the interactions between the electron clouds of the two elements and are only important at small interatomic separations.

What does the area under the Force-Interatomic separation curve represent?

It represents the potential energy between the two atoms.

What is bonding energy?

It is the energy to separate two atoms from r0 to infinity. Calculated by integrating the area under the force vs distance curve.

Metallic bonds

• Mechanism: sharing electrons between all atoms in an electron sea, delocalized electrons float through metal lattice

• Relative Strength: weaker than covalent and ionic

• Types of elements that form these bonds: formed between to metallic atoms

• Non-directional: bonding force is equal in all directions

• high thermal and electrical conductivity

• commonly forms metallic alloys

Covalent Bonds

• Mechanism: sharing electrons between adjacent atoms; requires similar electronegativities; usually involves s and p orbitals

• Relative Strength: stronger than metallic, weaker than ionic

• Types of elements that form these bonds: non-metals

• Directional: bonding force directed between the atoms that share the electron

• commonly form ceramics, allotropes of carbon, spines of polymers

• typically makes good electrical insulators

Ionic bonds

• Mechanism: donating electrons (one cation and one anion bonded together) Requires an electron transfer and large differences in electronegativity

• Relative Strength: strongest bonds

• Types of elements that form these bonds: one metal with one nonmetal

• Non-directional: bonding force equal in all directions

• commonly form ceramics

What is covalent bond hybridization?

It is the mixing of atomic orbitals. As electrons are shared, orbitals deform and energy levels redistribute —> formation fo “molecular orbitals”

• example: sp3 hybrid orbital molecules containing carbon

What is the name for secondary bonding and what are its main characteristics?

Van der Waals Bonds

• Mechanism: formation of “intermolecular” bonds due to the coulombic attraction between electric dipoles (not electron exchanges)

• Relative Strength: very weak

• Types of elements/materials that form these bonds: polymers, hydrogen

• Directional

• commonly forms adhesives, surfactants, emulsifiers, desiccants

What is mixed bonding?

When materials are made up of multiple types of atomic bonds

• example: covalent-ionic mixed bonds

Covalent-ionic is the most common

Ionic character is determined by comparing the electronegativities of the two elements and tells you how much of the material is made up of ionic bonds as a percentage.

What type of bonds are typical for the following?

• Polymers

• Ceramics

• Metals

Polymers:

• Covalent and secondary bonds

• weak bond energy

• secondary bonding is responsible for many of its physical properties such as low melting temperature, small modulus of eleasticity, large value of thermal expansion

Ceramics:

• Ionic and covalent

• strong bond energy

• high melting temp, large modulus of elasticity, small value of thermal expansion

Metals:

• Metallic bonding

• variable bond energy

• moderate values for melting temp, modulus of elasticity, and thermal expansion

Dipoles

an electric dipole occurs when there is some separation of positive and negative charge in an atom or molecule

Primary Bond

Interatomic bonds that are relatively strong and for which bonding energies are relative large. Includes ionic, covalent, and metallic bonds

Secondary Bond

interatomic and intermolecular bonds that are relatively weak and for which bonding energies are relatively small. Normally involves atomic or molecular dipoles. Includes Van der Waals forces and hydrogen bonds

crystalline materials

atoms are arranged in periodic, 3-D arrays; an ordered, repeating pattern

• common of metals, ceramics, and few polymers

noncrystalline materials

atoms have no periodic arrangement

• typical of glass, most polymers

• occurs for complex structures and if materials cool rapidly

Amorphous materials

same as noncrystalline

Crystal Structure

the manner in which atoms are arranged in a crystalline material

Lattice of a crystal structure

3-D array of points describing the regular geometric arrangement of points in crystal space

Unit cell

basic structural unit of a crystal structure, defined in terms of atom (or ion) positions within a parallelepiped volume

BCC

Body Centered Cubic

• appearance: atoms located at each of the cube’s 8 corners and on located at the cetner of the cube

• atoms per unit cell: 2

• coordination number: 8

• APF: 0.68

FCC

Front Centered Cubic

• appearance: atoms located at 8 cube corners and at the center of all 6 faces

• atoms per unit cell: 4

• coordination number: 12

• APF: 0.74 (max achievable)

HCP

Hexagonal Close Packed

• appearance: A-Site: atoms at each corner of hexagon with one at center of hexagon. B-Site: 3 atoms arranged in a triangle. Follows stacking sequence of ABAB…

• atoms per unit cell: 6

• coordination number: 12

• APF: 0.74

SC

Simple Cubic

• appearance: cube with atoms located at each of the 8 corners

• atoms per unit cell: 1

• coordination number: 6

• APF: 0.52

What’s the difference between theoretical and bulk density?

Bulk density: mass of the many particles of a material divided by the total volume they occupy

• rho=total mass/total volume

Theoretical density: mass of atoms in a unit cell divided by the total volume of the unit cell

• rho=mass of atoms in unit cell/volume of unit cell

Polymorphism

ability of a material to exist in more than one form or crystal structure

Allotropy

the possibility of the existence of two or more different crystal structure for a substance (generally an elemental solid)

• example: carbon (diamonds and graphite)

Crystal system

Scheme by which crystal structures are classified according to unit cell geometry

Seven systems and how they differ?

Each system differs in the relation between the lengths of each side of the structure and the relation between the angles that are between the faces of the structures

• cubic

• tetragonal

• rhombohedral (trigonal)

• triclinic

• orthorhombic

• monoclinic

• hexagonal

What coordinate system is used to define lattice position in a unit cell?

Cartesian coordinate system, coordinates are determined as fractional multiples of a, b, and c unit cell edge lengths given as a sequence of three numbers in the format ###

What is linear density and why is it important?

The number of atoms centered on a direction vector divided by the length of the direction vector

• higher linear densities tend to occur along diagonals

• important to determine physical properties such as material strength and predict where it is most likely to break or deform

What is planar density and why is it important?

number of atoms centered on a plane divided by the area of the plane

• important to determine physical properties such as material strength and predict where it is most likely to break or deform

Close packed crystal structures

• Includes FCC and HCP (APF = 0.74)

• Maximizes attraction between atoms

• Minimizes total intermolecular energy

• Affects multiple physical properties including density

Single crystalline materials

occurs when periodic arrangement of atoms (the crystal structure) extends without interruption throughout the entire specimen

• have easily predicted material properties and behaviors

Polycrystalline materials

many small single crystals arranged together

• cystral grains are usually around 1 nm to 2 cm in size

Grains

an individual crystal in a polycrystalline metal or ceramic

Grain boundaries

the interface separating two adjoining grains having different crystallographic orientations

Anisotropic materials

a material which exhibits different values of a property in different crystallographic directions

• example: BCC iron has a different modulus of elasticity across its edge vs its diagonal when you look at a unit cell or a crystal

What properties are affected by anisotropy?

• absorbance

• refractive index

• thermal and electrical conductivity

• tensile and mechanical strength

• magnetic properties

• ability to absorb light

Isotropic material

having identical values of a property in all crystallographic directions

• undeformed polycrystals tend to be isotropic

• beneficial for when you need to design something with constant properties or strengths

Noncrystalline solid

solid state in which there is no long range atomic order

Amorphous solid

having a noncrystalline structure

What is a crystalline defect? What are the 3 types and how are they different?

lattice irregularities with dimensions on the order of an atomic diameter

they are responsible for atomic motion, plastic deformation, catalysis, processing failures

• point: includes vacancies, interstitial atoms, substitutional impurites

• linear: dislocations

• interfacial: grain boundaries, twin boundaries

What is the simplest type of point defect?

vacancy

Self-interstitial defect

host atoms are positioned in interstitional between atoms

• not considered common due to the large lattice distortions they cause

Alloy

metallic substance that is composed of two or more elements

• example: carbon and iron make steel

Solid solution

homogeneous crystalline phase that contains two or more chemical species

• Interstitial: impurity atoms fill the voids or interstices among host atoms

• Substitutional: impurity atoms replace or substitute for the host atoms

Given a binary solid solution, which is the solute and which is the solvent?

solute: the component or element present in a minor concentraton. it is dissovled into the solvent

solvent: the component that is present in the greatest amount. it dissolves the solute

Hume-Rothery Rules

Rules that are the widely accepted conditions for the formation of complete substitutional solid solutions

1. atomic radii within 15% (otherwise there is phase separation)

2. Crystal structures are the same

3. similar electronegativities

4. similar valence values (within two)

Main criteria for interstitial solid solution to form

atomic radii are different enough (60-80% difference or greater)

What are the two ways to measure the concentration (composition) of an alloy?

Weight percent and atom percent

Edge dislocations

• extra half plane of atoms inserted into a crystal structure

• burger’s vector perpendicular to dislocation line

• requires a lot of energy

• can occur due to applied stress during plastic deformation, like during mechanical processing or when a crystal is being subjected to external forces.

Screw dislocations

• spiral planar ramp resulting from shear deformation

• burger’s vector parallel to dislocation line

What does a Burger’s vector give with regard to linear dislocations?

a vector that denotes the magnitude and direction of lattice distortion associated with a dislocation

Interfacial defect

occurs in 2 dimensions

• Grain boundaries: between individual grains

• Phase boundaries

• Twin boundaries: mirror reflections of atom positions on one side of twin plane to another

• Stacking faults: issues in the planar stacking sequence

Volume defects

• 3-D; may contain pores, cracks, foreign inclusions

• typically introduced during processing or fabrication

Why is it important to know avg grain size of polycrystalline materials?

smaller grains typically result in stronger materials, so this is important when you need to make materials stronger or weaker to suit specific uses

Microstructure

the structural features of an alloy (e.g. grain and phase structure) subject to observation under a microscope

Interstitial solid solution

a solid solution in which relatively small solute atoms occupy interstitial positions between the solvent or host atoms

Substitutional solid solution

a solid solution in which the solute atoms replace or substitute for the host atoms

Diffusion

mass transport by atomic motion

Interdiffusion

diffusion of atoms of one material into another material (impurity diffusion)

Self-diffusion

atomic migration in a pure metal

Two conditions for diffusion to occur

1. there must be an empty adjacent site

2. the atom must have sufficient energy to break exisiting bonds with its neighbor atoms and then cause some lattice distortion during the deplacement

Mechanisms that occur in vacancy diffusion

• atoms and vacancies exchange positions

• applies to host and substitutional impurity atoms

• rate of diffusion depends on number of vacancies and activation energy to exchange

Mechanisms that occur in interstitial diffusion

• small, interstitial atoms move from one interstitial position to an adjacent one

• more rapid than vacancy diffusion

Which type of diffusion typically occurs at a faster rate?

interstitial

Steady state diffusion

diffusion condition for which there is no net accumulation or depletion of diffusing species. Diffusion flux is indepenedent of time

How is diffusion flux influenced by diffusivity, concentration, and distance into the solid? (Fick’s Law)

• flux is directly proportional to diffusivity

• flux is directly proportional to concentration gradient

• flux is inversely proportional to distance into the solid (increasing distance into solid decreases flux)

Nonsteady state (transient) diffusion

the diffusion condition for which there is some net accumulation or depletion of diffusing species, flux is dependent on time

Two main things that influence the rate of diffusion

• the mass of the diffused species (directly related to flux)

• the area over which diffusion occurs (indirectly related to flux)

Carburizing

exposing the lower carbon steel to a carbon rich atmosphere at an elevated temperature which results in the diffusion of carbon atoms into the steel