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File 128927742991.gif - (161.40KB , 631x472 , aerogel_1.gif )
971 No. 971 [Edit]
Part 1: Structure of materials

You can imagine materials being composed of atoms with springs attached to one another. A force is needed to pull the atoms apart and compress them closer together. The way these atoms are stuck together determine many properties of the material. Part 1 will deal with atomic structure of materials, including packing, the categories of structures and bond energy (how much energy needed to alter the structure).
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>> No. 972 [Edit]
Part 1(a): Packing

Packing refers to the way atoms are arranged.

A great number of bonds per unit area implies shorter bond lengths, and hence higher densities.

The angle of these bonds affects how atoms are stacked. The bond angle is responsible for what kind of crystal* structure the material has.

*A crystal in this context refers to a chunk of material where everything inside is arranged in orderly pattern.
>> No. 973 [Edit]
Part 1(b): Primary bonds

When atoms are chemically connected to each other via the sharing or donating of electrons, the bond is called a primary bond. These bonds are strong compared to secondary bonds. There are several main types of primary bonds.

Ionic bonds: occurs between two elements which have a high disparity in electron charge. The difference in charge makes one species strongly electronegative and the other strongly electropositive, and the effect of this is that one species completely donates all its valence electrons to the other. Ionic bonds are non-directional, meaning rotating the direction of the bond doesn't affect anything. Physical characteristics: high melting point, high elastic modulus (inelastic), high hardness, poor electrical conductivity. Some ionic substances include alumina, cement and magnesia.

Covalent bonds: bonding between two elements with fairly similar charge tends to create covalent bonds, where the electrons are shared, rather than completely given to one species. Covalent bonds are highly directional, meaning the directions of the bonds between atoms are very strict and dislike change. Physical properties: extremely high elastic modulus (inelastic), high strength, high melting point, low electrical conductivity. Some covalent substances include diamond, glass (silicon dioxide).

Metallic bonding: these are characterised by delocalised electrons. Electrons are free to move between all the atoms in the substance, and ions are held together by the electron cloud surrounding them. As such, the bonds are non-directional. Physical properties: high elastic modulus, good electrical conductivity, good ductility (because atoms can slide past each other without permanently deforming the crystal structure).
>> No. 974 [Edit]
Part 1(c): Secondary bonds

Secondary bonds are attractions between atoms caused by temporary dipoles from electrons swirling around. They exist in all materials, but are usually overshadowed by the stronger effects of primary bonds. Such attractions are called Van der Waals attractions, except in certain cases involving hydrogen atoms.

Hydrogen bonding: is a notable case of Van der Waals attraction. Hydrogen is a lot more electropositive than other elements, and forms especially strong secondary bonds with nitrogen, oxygen and fluorine atoms.
>> No. 975 [Edit]
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Part 1(d): Bond energy

Consider the previous analogy of bonds being like springs between atoms. Pulling atoms apart requires energy because the atoms are attracted to each other. Conversely, pushing atoms closer requires energy because it causes the electron fields of each atom to overlap and creates repulsion. The energy needed to do this at varying distances from atom center is depicted in the graph.

In nature, systems tend to move towards a configuration of the least energy. Atoms will tend to space themselves out at a specific distance corresponding to the lowest point on the dip in the graph.

It is from this graph that we will create our definition of bond stiffness. Let us define the Force needed to change bond length to a specific length as F=dU/dr, where dU stands for change in bond energy and dr stands for change in bond length (in other words, the graph of F against r is the derivative function of the graph U against r.).

Bond stiffness will be the amount of force needed to cause a certain change in bond length. We define bond stiffness as s=dF/dr, where dF stands for change in force.
>> No. 976 [Edit]
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Here is a diagram comparing the elastic/young's modulus of different materials. Note that elastic modulus is not the same as stiffness, although they are related. A high elastic modulus means the material is hard and inelastic.

Ceramics are often composed of either ionic and covalent substances or a mixture of those two. Metals have metalic bonding. Polymers (i.e 'plastics') have covalent bonding within their long molecular chains and Van der Waals or Hydrogen bonds between the chains.

Now that we've explain a bit about bonding, we can explain various properties of materials. For instance, glass is very hard because of its rigid, directional covalent lattice structure. However, provide enough force, and it will shatter because those directional bonds cannot reattach themselves. Metals like iron are also strong, but applying enough force to them will cause them to simply bend because the bonds are not as picky and can reattach themselves easily.

Tomorrow we will talk more about stiffness and Young's modulus.
>> No. 977 [Edit]
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>> No. 978 [Edit]
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>> No. 979 [Edit]
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Looks like gen chem for materials engineering.
>> No. 980 [Edit]
Nah, its an intro to materials science for first year materials students. You will see that it gets less 'chemically' later on.

Also, anyone is welcome to ask questions.
>> No. 981 [Edit]
Part 1(e): Crystal structures (or lack thereof)

A final word on the structure of materials. The atoms in most engineering materials stack themselves in an orderly way. Atoms stack to create grains, and grains stack together to make a whole solid. The exact way atoms stack depends on factors such as bond angle, size of atoms, types of elements present, etc. We will not go into detail about this.

Metal crystal Structures include:
-Body-centered cubic (e.g Iron)
-Face centered cubic (E.g Aluminium, copper)
-Close packed hexagonal (e.g Titanium, zinc)
I can't be bothered to find diagrams.

Ceramic crystal structures: these are far more complex than metallic crystal structures because usually more than one element is present. I will not go into detail about the myriads of complex structures here.

Amorphous structures: not all substances stack their atoms in a orderly, structured way. Such stacking styles are called amorphous, or non-crystalline. For instance, polymers have long spaghetti-like chains which are randomly stacked on top of each other. The atoms which compose glass do not have a fixed pattern in which they arrange themselves.
>> No. 982 [Edit]
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Part 2: Modulus and stress-strain curve.

Modulus and the stress-strain curve are important ways in which to describe the mechanical properties of a material.

A stress-strain curve relates the amount of force per unit area needed to cause a sample to elongate a certain amount. The stress-strain curve for any material is found by submitting a standardised size of sample to a 'tensile test' inside a tensile testing machine.

Stress is defined by force per unit (cross-sectional) area. It is usually measured in GPa (1x10^9 Newtons per square metre) because one pascal is an extremely small pressure. Strain is defined as the ratio of the change in elongation to initial elongation. Strain does not have units: it is purely a number.
>> No. 983 [Edit]
Part 2(b): Features of the stress-strain curve

(See graph above for this post)

Remember that these curves describe the behaviour of the material as it undergoes increasing strain during a tensile test. The curve depicted is a general curve used to illustrate generic features of the stress-strain curve. Other materials may look different.

Initially, the relationship between stress and strain is linear. We call this is ELASTIC region, because if you release the load on the sample anywhere inside this region, the sample will spring back to its original length like an elastic band. The gradient of this linear section is the value of Young's modulus for this material (more on this later). The point where the linear region stops is called the yield point. Yield point will not always be distinct (e.g in the case of iron), and instead of a point there is a region of transition form linear to non-linear. In this case, sometimes we instead pick a general point inside that region to be the 'yield point', which we call the offset yield point (see end of this post). Regardless, the value of stress at this point is called the yield strength. Atomically, this region is where the atoms are being pulled apart, but can still pull themselves together again after the load is removed.

After the elastic region comes the plastic region. Any further elongations at this point are permanent, and the sample will not spring back to shape. At some point in the plastic region, the graph will stop increasing, and begin to dip. The value of stress at this point is called the Ultimate Strength. The region after Ultimate Strength is called the 'necking region', and in reality is when the material begins to get narrow at a concentrated segment. Most of the stress gets concentrated at this point, and the result of this is that the average stress throughout the sample decreases. Atomically, this region is where atoms are pulled apart to such a distance that their charges are not strong enough to pull each other back together again.

The point at which the graph abruptly ends is when the sample has snapped. We call this the point of failure.

Offset yield point: In situations where the transition from elastic to inelastic deformation is not abrupt, we use an offset yield point. We take a point on the x-axis with a certain percentage of the maximum strain (usually the percentage is 0.1% or 0.2%) and draw a line parallel to the linear region of the graph. The intersection of that line and the graph is the offset yield point.
>> No. 984 [Edit]
Part2(c): Elastic/Young's Modulus

Basically, Young's modulus is a measure of how much force you need to cause some amount of change in length in a material. As we have stated before, elastic modulus is the gradient of the elastic region on a stress-strain curve. Formally it is defined as E=(stress)/(strain).

A high Young's modulus means the substance is stiff. You will need a lot of force to cause a small change in length. Conversely, a low Young's modulus means the substance is elastic, and you only need a small force to cause a large change in length.

Some materials with high modulus include metals and ceramics. Materials with a low modulus include polymers. Note that polymers have fairly flat stress-strain graphs.
>> No. 985 [Edit]
Part 2(d): Energy for deformation

Remember in Part 1, we said that bond stiffness was the derivative function of energy needed to rip bonds apart against the distance. By corollary, the integral function of the stress-strain curve is in fact the function of the amount of energy needed to deform a material to a certain length. This simply means that the area under the graph on a stress-strain graph is the energy.
>> No. 986 [Edit]
Part 2(e): Strength

In materials science, strength refers to the ability of a material to withstand applied stress without failure. Strength is a very important consideration, because we often want to know how much force a material can take before it breaks, or we want to choose suitable materials for building structures. Again, the stress-strain curve, made from data from a tensile testing machine, is where we find our reading for strength.

Other material properties for consideration are hardness and toughness. Hardness can be quickly and cheaply tested by subjecting a material to a known force under a diamond shaped 'indentor' and looking at the hole created. Toughness is a comparison of the amount of energy a material can take as opposed to the force it can take, before yielding.

As a final word on this topic, not all stress strain curves have a similar pattern to the ones depicted. For instance, the stress strain curve of a ceramic ends abruptly after a very short elastic region because a ceramic snaps at fairly low tensile strengths. Polymers can have very widely varying graphs, and their elastic region of deformation may not even be linear.

The next few parts will deal with theory about dislocations, which goes a long way in explaining how cracks and imperfections in materials form.
>> No. 987 [Edit]
Part 3: Dislocations and ways to make metals stronger

Part 3(a): What dislocations are

Dislocations are essentially 'imperfections in the crystal structure'. The atoms in a crystal do not always line up perfectly, and there may be some abnormalities such as a missing atom or an extra atom which distorts the pattern of the lattice. Dislocations can travel through the crystal along 'slip planes' using a caterpillar-like motion. Diagrammatically, we use a perpendicular symbol to depict a dislocation. A typical engineering alloy will contain 100,000km worth of dislocations per centimetre cubed.

Dislocations may or may not be wanted in a material, depending on circumstances. Introducing more dislocations into a material tends to set up a 'forest of dislocations' which causes dislocations to get tied up in one another, stopping them (and the slip plane) from moving. This makes a material hard, but at the same time makes it more brittle and inflexible. Hardness might be desirable in a bridge girder which you don't want to wobble, but undesirable for steel used in springs.
>> No. 988 [Edit]
Part 3(b): Intrinsic lattice resistance to dislocations

For a dislocation to move, it needs to break and reform a bond between two atoms. This requires a force, and this resistive force is called the intrinsic lattice resistance, symbol Fi. Dislocations move when the slip planes slide over each other.

In metals, Fi is low because of the non-directional nature of the bonding which means that the atoms don't give a fuck that they're sliding. In contrast, ceramics have a high Fi because bonds between atoms are highly directional, and breaking one bond to move a dislocation implies breaking fifty million other bonds on the slip plane too.
>> No. 989 [Edit]
Part 3(c): Making metals stronger

In this section I will describe some techniques used to increase the overall lattice resistance of metals, and hence stop dislocations from moving. The movement of dislocations is the mechanism by which slip planes move, and on a macroscopic scale is 'bending' which is often undesirable.

Solid solution strengthening: Is basically 'alloying'. Consider this: with water, you can dissolve sugar into it and get a solution of water with sugar molecules interspersed through it. With metals, the same is true: you can 'dissolve' molten zinc into molten copper and receive a 'solution' of both.

How does this inhibit the movement of dislocations? Solid solution strengthening introduces impurity atoms into the crystal lattice. These impurities have different atom size compared other atoms, and so they distort the crystal lattice. Dislocations need more force/energy to move past these distortions. Two main factors are responsible for the increase in intrinsic lattice resistance: difference is atom size and the amount of impurities added. Copper and zinc have fairly similar atom size, so there needs to be a mixture of about 30% Zinc to 70% copper. Carbon and iron have a huge difference in atom size, so only 0.3% of carbon needs to be added to the Iron to get the same effect.

Precipitation hardening: Let us carry our analogy with sugar and water further. If you add lots of sugar to hot water and dissolve it all, you may find out that some of the sugar recrystallises out of the solution when it cools down. The same thing occurs with metal alloys. Some impurity atoms will 'precipitate', forming small particles of impurities inside the matrix of the alloy.

These precipitate particles impede dislocation movement. Dislocations are forced to either go around, or cut through these particles. If they go around the particle, the dislocation tends to leave traces of itself around the particle called 'Orowan loops', which themselves impede dislocation movement and get bigger and bigger with each passing dislocation.

Work hardening: This is basically working the metal to deliberately introduce more dislocations, and create a forest of dislocations to stop dislocation motion. The metal can be hammered, rolled, bent, drawn, etc. The basic idea is to plastically deform the metal to create more dislocations.

Grain size strengthening: This is one of the only techniques which increases hardness without making the metal brittle in the process. Remember that materials are composed of crystals, each of which are 'grains' which are stuck together. The orientation of the lattice in adjacent grains are different, so dislocations have trouble travelling from grain to grain because they have to switch direction. As a result, the dislocations get stuck and pile up at the grain boundaries. The trick is to make grains very small, so that there are lots of boundaries which impede dislocation movement. Grain boundary strengthening is described by the Hall-Petch equation, which is very important and will be in the exam.

There are numerous other niche strengthening techniques. Also note that introduced dislocations can only be removed by annealing, i.e heating the metal to recrystallisation temperature.
>> No. 990 [Edit]
Part 4: Fast fracture

Fast fracture is when cracks in a material expand rapidly, causing a catastropic failure of the material, even if its below yield point stress. For a crack to grow, there needs to be sufficient stress on the crack. To calculate this critical stress, we consider the work needed for the crack to grow. The work done by the load needs to be greater than the difference between change in elastic energy and energy absorbed at the crack tip (this crap doesn't make no sense.) Equation:

δW ≥ δUel - Gc.t.δa

Gc is the energy absorbed per unit area of crack, with t(delta)a being the new crack area. Gc is the measure of the materials 'toughness', and is how much energy is needed to propagate a crack. A high Gc means the material is tough and cracks have a hard time getting bigger (e.g copper), a low one implies the opposite (e.g ceramics).

Honestly I don't know what i'm talking about in this section.

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