Materials Science

Materials Science is a Division C event which tests knowledge of the properties and characteristics of metals, ceramics, polymers and composite materials, with a focus on material characterization techniques, intermolecular forces, and surface chemistry. The event typically consists of a test with one or more accompanying lab portions.

Event Format

Teams are allowed to bring two non-camera calculators, writing utensils, and five two-sided pages of notes.

Event supervisors will provide any needed materials and constants.

Students must wear closed-toed shoes, chemical splash goggles, full length pants or skirts, and a lab coat or chemical apron & long-sleeved shirt. Gloves are optional.

The Material Performance section and the Intermolecular Forces section will both be weighted 50% in this event.

The Basics

Materials Science

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. This scientific field investigates the relationship between the structure of materials at atomic or molecular scales and their macroscopic properties. It incorporates elements of applied physics and chemistry.

• Metals -
• Ceramics -
• Polymers -
• Composites -

Basic Terms

Stress - Force per unit area. Represented by $\sigma$

Strain - The amount of deformation an object experiences compared to its original size and shape. Represented by $\epsilon$

Young's Modulus - A measure of the stiffness of an elastic material.It is equal to the stress over the strain.

Plastic Deformation- Irreversible deformation, as opposed to the reversible elastic deformation.

Yield Strength - The stress at which a material begins to deform plastically.

Creep Rate - The slow permanent deformation under the influence of stresses. It occurs as a result of long term exposure to high levels of stress that are below the yield strength of the material.

Viscosity - A measure of a fluid's resistance to gradual deformation by stress.

Surface Tension - The tendency of liquids to resist external force, caused by cohesion.

Contact Angle - The angle where a liquid/vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation.

Ionic Bond - The bonding between a non-metal and a metal that occurs when charged atoms (ions) attract after one loses one or more of its electrons.

Covalent Bond - The chemical bond that involves the sharing of pairs of electrons between atoms.

Crystalline - A solid material whose constituent atoms, molecules, or ions are arranged in an ordered pattern extending in all three spatial dimensions.

Semi-Crystalline - A material composed partially of crystalline and partially of amorphous matter.

Amorphous - Also known as a non-crystalline solid, they lack the long-range order characteristic of a crystalline material.

Atomic Packing Factor - The fraction of volume in a crystal structure that is occupied by atoms.

Material Characterization Techniques

Young's Modulus

Young's modulus describes a materials resistance to liner strain, like pulling a wire or placing a weight on a column.

$E=\frac{\sigma}{\epsilon}=\frac{FL_0}{A_0 \Delta L}$

• $E$ is the Young's modulus (modulus of elasticity)
• $F$ is the force exerted on an object under tension (a compressive force is represented by a negative value)
• $A_0$ is the original cross-sectional area through which the force is applied;
• $\Delta L$ is the amount by which the length of the object changes;
• $L_0$ is the original length of the object.

The force may be found using Hooke's Law, $F=-kx$ where

• $x$ is the displacement of the spring's end from its equilibrium position.
• $k$ is a constant called the rate or spring constant.
• $F$ is the restoring force exerted by the spring on that end.

Yield Strength

The Yield Strength of a material is the force at which the material begins to deform plastically, or the force at which changes are not fully reversible.It is determined through a Stress-Strain curve, such as the one below.

1. True elastic limit
2. Proportionality limit
3. Elastic limit(yield strength)
4. Offset yield strength

For some materials (e.g., metals and plastics), change from elastic to plastic cannot be easily identified. Therefore, an offset method to determine the yield strength of the material tested is used. An offset is specified as a % of strain (for metals, usually 0.2%, for plastics, usually a value of 2%). The stress that is determined from the intersection point when the line of the linear elastic region (with slope equal to the Young's Modulus) is drawn from the offset becomes the Yield Strength by the offset method. For example, in the above image, an ofset of 0.2% is used for the yield strength.

Surface Area/Volume Ratio

As simple as it sounds, The ratio can be found by dividing the Surface area of an object by its volume, both of which can be determined by simple geometry. Typically, as a shape gets bigger, its surface area to volume ratio tends to decrease.

Creep Rate

Creep Rate is "the permanent deformation of material under constant load."

To test the creep rate of a material, a sample put under a constant stress and constant temperature, for which the strain is measured over time.

There are three stages of creep. The first stage is characterized by a high initial strain rate, which slows with time due to work hardening. This leads it to the second stage of creep, in which the strain rate remains almost constant as work hardening and thermal softening remain about equal. In the third and final stage, the strain rate exponentially increases. In the above graph, $\epsilon 0$ represents the initial strain value known as the elastic strain.

Viscosity

Viscosity is "the resistance to flow."

Viscosity is caused by friction between molecules that move at different velocities. When in a tube, for example, the adhesion to the walls causes the outer material to move slower, while the material in the center moves faster. This means that some stress is required for the liquid to move. The more viscous the material, the more stress is needed.

A simple test of viscosity is to simply fill a graduated cylinder with the test liquid, and time how long a steel ball(or some other heavy object) takes to reach the bottom. While not giving an "accurate" measure of viscosity, or a number in terms of viscosity's actual units(which is in Pascals times seconds, $Pa$·$s$), it does provide a good comparison between liquids, and is a test you may find in the lab portion of the event.

State and National Topics

The following are advanced topics that should only be found on state and national tests.

Fracture toughness

Fracture toughness is the ability of a material containing a crack to resist fracture.

The linear-elastic fracture toughness of a material is determined from the stress intensity factor ($K$). It is measured in $Pa$·$\sqrt{m}$.

There are three types of tests for fracture toughness, diagrams of which can be found below.

Mode I is the most common, and the following equation can be used to determine the stress intensity factor.

$K_I$ can be found by using the following:

$K_I=\sigma\sqrt{\pi a \beta}$

• Where $K_I$ is the fracture toughness,
• $\sigma$ is the applied stress (in $Pa$)
• $a$ is the crack length (in meters)
• $\beta$ is a crack length and component geometry factor that is different for each specimen and is dimensionless.

Fatigue Limit

The fatigue limit is the amplitude of cyclic stress required to cause failure. Some metals are able to withstand small stresses for a seemingly infinite number of cycles, while others fail even with small stresses with enough cycles.

The following is an example of a Fatigue Limit test.

The X-axis is a log scale of the number of cycles(of the stress). The Y axis is the amount of stress. The lines show the number of cycles at a given stress for failure to occur. For example, at about 45 ksi, the aluminium fails after 10000 cycles.

At the endurance limit, the steel does not break under even large number of cycles at low stress, while the aluminium does not show this property.

Shear Modulus

The shear modulus is equal to the shear stress over the shear strain, and is a measure of rigidity. It describes a materials resistance to shearing strains, like that of dull scissors.

$G=\frac{{F}{L}}{A \Delta x}$

• Where $G$ is the Shear Modulus,
• $F$ is the force,
• $L$ is the original length of the object,
• $A$ is the area on which the force acts
• $\Delta x$ is the transverse displacement.

This diagram shows where those factors are.

Poisson's Ratio

Poisson's Ratio is the measure of how much a material expands(or contracts) when stretched or squeezed. Most objects have a positive Poisson's ratio, meaning they expand when squeezed and contract when stretched. However, some materials do exist with a negative ratio. The value of the ratio is $-1.0<\nu <0.5$ due to the requirement for the Young's, shear, and bulk modulus to be positive.

$\nu=-\frac{d\epsilon_y }{d\epsilon_x }$

• Where $\nu$ is Poisson's ratio,
• $d\epsilon_y$ is transverse or lateral strain (negative for (stretching), positive for compression)
• $d\epsilon_x$ is axial strain (positive for tension, negative for compression).

Intermolecular Forces

Chemical Tests

Surface Chemistry

Surface Tension

The contractive tendency of the surface of a liquid that allows it to resist an external force. It is caused by the cohesion of liquid molecules. This cohesion draws atoms towards each other. At the surface however, there are no atoms pulling down. This means all the forces are pointing up, which cause objects to float.

Surface tension is represented by $\gamma$ and has the units of force along a unit length, where the force is parallel with the surface but perpendicular with the line (meaning the force is directed towards the liquid). For example, water has a surface tension of around 72 dynes/cm (at 25° C). The SI unit is newtons per meter, the cgs unit is dynes per cm. One dyn/cm corresponds to 0.001 N/m.

Contact Angle

The angle, conventionally measured through the liquid, where a liquid/vapor interface meets a solid surface, and is used to determine the "wettability" of a substance (such as a non-stick pan or waterproof fabric). The angle is the measure between a line tangent to the point of contact between the liquid and solid, and the surface of a material, $\theta$ in the following picture.

The static sessile drop method uses a profile picture of the drop to determine this angle. This type of picture will be similar to the one above.

Contact angles are sensitive to contamination, with values reproducible to better than a few degrees only obtainable under laboratory conditions. For bare metal or ceramic surfaces, a contact angle of 0° is common. In general, surfaces with a contact angle of greater than 90° are considered hydrophobic, under 90° considered hydrophilic.

There are actually two types of contact angles. If a small amount of liquid is added, the contact angle will increase without changing the radius of the drop. This contact angle is called the advancing contact angle, $\theta_A$. If a small amount of liquid is removed, the contact angle will decrease. This is called the receding contact angle, $\theta_R$. This is the dynamic sessile drop method.

The difference between the two angles, $\theta _A - \theta_R$ is the contact angle hysteresis

Crystal Structures

Crystal Types

Ionic

Ionic bonds are bonds between two charged atoms. Most crystals made from ionic bonds are alkali halides, meaning they have atoms the alkali group, and atoms from the halide group. Salt, such as NaCl is a good example of an ionic crystal.

Ionic crystal structures can have different ratios of each ion. NaCl, shown below, has a 1:1 ratio. Furthermore, as each atom touches 6 other atoms, this structure is 6:6-co-ordinated, meaning any one atom touches 6 other atoms.

Other compounds, such as caesium chloride, are 8:8-co-ordinated, meaning each atom touches eight others. For atoms with a 1:1 ratio, if the radius of the positive ion is bigger than 73% of that of the negative ion, then 8:8-co-ordination is possible. Less than that (down to 41%) then you get 6:6-co-ordination. Lower than 41%, 4:4-co-ordination occurs.

Ionic compounds usually have similar properties. They have high melting and boiling points due to the strength of their bonds, they are hard and brittle, they conduct electricity when dissolved in water(as the free ions can conduct charges), and they make good insulators(as the ions are bound tightly to each other when solid).

Covalent

Covalent crystals (also known as Network Solids) are formed by the sharing of electrons between atoms. They form some of the hardest crystals, including diamonds. Graphite is another example of a covalent crystal.

Strong bonding in a layer with weak bonding between layers makes its strength anisotropic, meaning its structure is largely direction dependent.

In general, covalent compounds have a lower melting and boiling point than ionic compounds, more flexible than ionic compounds, aren't soluble in water, and thus don't conduct electricity in water. They are also poor conductors of heat, making them good insulators.

Crystallinity

Crystallinity refers to the degree of structural order in a solid. There are three degrees of crystallinity.

The three types are shown in the following picture, and explained below.

Crystalline

A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an ordered pattern extending in all three spatial dimensions. Large crystals are usually identifiable by their macroscopic geometrical shape, consisting of flat faces with specific, characteristic orientations. Crystal structures are repeats of a Unit Cell.

Semi-Crystalline A structure that has both Crystalline and Amorphuos properties. they are also known as polycrystalline structures. These structures have true crystal portions with mixed size and orientation.

Almost all metals, and many ceramics, are polycrystalline.

Amorphous

A structure with little to no crystal properties. Common types of amorphous solids include gels, thin films, and glass.

Common Atomic Packing

FCC

FCC stands for Face-Centered Cubic, which has the same structure as Cubic Close-Packed. The Unit Cell, or repeatable unit, of FCC is a cube with an atom at each corner of the unit cell and an atom situated in the middle of each face of the unit cell.

FCC has an Atomic Packing Factor of 0.74. The Atomic Packing Factor, or APF, is equal to the volume of the atoms in a unit cell over the volume of the unit cell. A packing factor of 0.74 means 74% of the volume can be thought of as containing an atom.

BCC

BCC stands for Body Centered Cubic. The unit cell of BCC is a cube with an atom at each corner and a single atom in the center.

BCC has an APF of 0.68, meaning it is less dense than FCC or HCP.

HCP

HCP stands for Hexagonal Close-Packed. Its structure is the most complex of the three. Its structure is most easily explained through a picture.

HCP has an APF of 0.74, the same as FCC

Simple Cubic

A simple cubic unit cell's structure is as simple as the name. It has one atom at each corner

Simple Cubic has an APF of 0.52, the least dense of the covered crystal structures. (The only structure less dense is diamond cubic, APF of 0.34, which is not covered by the rules)

Material Classes

Metals

Metals use metallic bonds to form their structures. Metallic bonds constitute positively charged metal ions in a "sea" of delocalized electrons.In metallic bonds, electrons are free to move around the structure of metal ions, meaning that electrons belonging to molecules are not attached to a specific atom in that molecule. This allows metals to have unique properties.

Properties:

• Low Hardness - Metallic bonds give the metal ions freedom to move around. This means that the metal can change shape without breaking any bonds, due to the free nature of metallic bonding.
• High Elastic Modulus -
• Low Thermal Expansion - When placed in a high-heat environment, metals will typically expand very little. The exact change can be determined by the equation $\Delta L = \alpha T L_i$, where $\alpha$ is the coefficient of linear thermal expansion, $T$ is the temperature of the surroundings (in Celsius), and $L_i$ is the initial length of the bar.
• High Ductility - The freedom of movement of electrons in metallic bonding also allows for free movement of ions. This means that the metal can be pulled into wires without breaking any bonds, meaning it does not take large amounts of energy to do.
• Low Corrosion Resistance - All the free electrons in metallic bonds tempt outside elements, usually oxygen, to steal pieces of the metal. Rust is a well known byproduct of corrosion of iron. It is done through the chemical process of oxidation. It usually forms either oxides or salts of the metal.
• High Electrical Conductivity - The freedom of electrons in metallic bonds allow them to travel across molecules without difficulty, which allows them to carry a charge across the metal.
• High Density - Many metals assume a BCC, FCC, or HCP arrangement in the crystalline state. See Common Atom Packing [1] for more information.
• High Thermal Conductivity - Metals have high thermal conductivity for the same reason they have high electrical conductivity. Not only do the free electrons have the ability to transfer charge, they also make it easy to transfer heat along the metal.
• High Boiling Point - The strength of metallic bonds require a lot of energy to break. This means that most metals have high boiling points. Except for a few notable cases, all metals have high boiling points. Even Gallium, which melts in the hand, has a boiling point close to that of copper due to the strength of the bonds.

Appearance

 This is an image of copper, sanded down to show texture. Metals are identified by their grain, having long strands that all point in the same direction. Metals can also be in foams, which look almost like a sponge, yet still have the grain structures visible. This is a magnified image of metal foams, in which metal is filled with air pockets.

Ceramics

Ceramics have a combination of both ionic bonds (between metal and nonmetal atoms) and covalent bonds (between two nonmetals).

Properties:

• High Hardness -
• High Elastic Modulus -
• High Thermal Expansion -
• Low Ductility -
• High Corrosion Resistance -
• Varying Electrical Conductivity -
• Low Density -
• Varying Thermal Conductivity -

Appearance

Ceramics appear to be composed of tiny building blocks glued together, although sometimes these individual grains can be difficult to see.

Polymers

Polymers consist mostly of covalent bonds, as they consist of mostly nonmetal atoms.

Properties:

• Low Hardness-
• Low Elastic Modulus-
• Low Thermal Expansion-
• High Ductility-
• Low Corrosion Resistance-
• Low Electrical Conductivity-
• Low Density-
• Low Thermal Conductivity-

Appearance