#mse45l

Prof L. M. [#mse45 lm], fall 2021 [#fall2021]

hw1: 1, 3, 4, 5, 6, 7 /7 [#mse45 hw1, #mse45 lm hw1]

hw2: i basically bombed hw2 w a 61/100 so,,

hw3: 3, 5, 6 /6 [#mse45 hw3, #mse45 lm hw3]

hw4: 3, 4, 5, 6 /6 [#mse45 hw4, #mse45 lm hw4]

hw5: 1, 2, 3, 4, 5, 6 /7 [#mse45 hw5, #mse45 lm hw5]

hw6: all 7 qns [#mse45 hw6, #mse45 lm hw6]

hw7: all 7 qns [#mse45 hw7, #mse45 lm hw7]

hw8: all 7 qns [#mse45 hw8, #mse45 lm hw8]

hw9: all 8 qns [#mse45 hw9, #mse45 lm hw9]

hw10: all 7 qns [#mse45 hw10, #mse45 lm hw10]

MSE 45L [#mse45L]

lab 2 : Recovery, Recrystallization, & Grain Growth intro, disc [#mse45 lab2, #mse45L lab2]

lab 3 : Binary Alloy Phase Diagrams abstract, intro, disc [#mse45 lab3, #mse45L lab3]

lab 4 : Heat Treatment of Steel abstract, disc [#mse45 lab4, #mse45L lab4]

lab 5 : Uniaxial Tensile Test intro [#mse45 lab5, #mse45L lab5]

lab 6 : Electronic Properties of Materials abstract, intro, disc [#mse45 lab6, #mse45L lab6]

Electronic Properties of Materials

DISCLAIMER: i post this in hope it is a helpful guide/for desperate times when you need some guidance. remember our honor code. remember this trust i put in you.

if you wanna see my full report just drop me a dm. ill share it gladly one surviving bear to another.

Graded: 27/30

Comments: Great work! Metals: Melting would increase resistance due to scattering. Semi: Nice, close! Ionic: Nice. Would be nice to see a final sentence on applications/implications

Part I (Metals/Conductors)

Question 1

Rank the five (5) specimens in order of purity, and specify ρr for each specimen in micro-ohm-cm.

<table of sample no, α, ꭓ and ρr>

Impurity is directly correlated with the (residual) resistivity in the sample. Since sample 17 has the smallest ρr, it has the least impurities followed by 16, 18, 19 then 20 (most impurities, least pure).

Question 2

To what precision can you verify Matthiessen's rule? To answer this question, consider how the resistivity changes with temperature for a fixed concentration of impurities, then how the resistivity changes with impurity concentration when the temperature is fixed.

Matthiessen's rule is usually used with data at liquid helium temperature (4.2 K), where the thermal component is effectively zero. Since the lowest temperature we could achieve in this lab was 77K, this was set as a baseline temperature for our calculation of resistivity by Matthiessen's rule, and resistance measured at this temperature was assumed to have no thermal resistivity component. Because resistivity increases as temperature/impurity concentration increases, our calculation with Matthiessen's rule is not the most accurate.

Question 3

Would you expect ρ to increase or decrease as T is increased through the melting point? Why?

Resistivity should decrease slightly as T is increased through the melting point. Past the melting point, in liquid state, the electrons are able to move more freely without having to navigate the uniform solid structure. However, there is still a very large thermal component to the resistivity at such high temperatures, and the change in state will not affect the overall resistivity by a lot.

Question 4

If you dope a metal A with another metal B where ρB < ρA, do you expect the resistivity of the alloy to increase or decrease? Why?

Doping is the introduction of a very small concentration of another substance. If a metal A was doped with another metal B where ρB < ρA, the resistivity would increase. Since the concentration is very small, metal B would still be considered an impurity and would increase the measured resistance. Unless metal B was introduced in significant quantities, it would not decrease the resistivity even though ρB < ρA.

Part II (Semiconductors)

Question 5

Plot ln (G) versus 1/T for the semiconducting sample studied in this lab.

Question 6

Over what temperature range, if any, does your sample behave as an intrinsic semiconductor?

When fitted with a best fit line, the R2 value of the line is very close to 1, with less than a 5 percent margin, indicating that the data can be fitted into almost a straight line. Temperatures above room temperature (range: 25˚C to 100˚C) where thermally generated carriers are numerous enough to dominate carrier concentration, were tested. However the graph does not exhibit an exhaustion range where the graph plateaus out and starts exhibiting extrinsic behaviour after. Along with the assumption that the germanium sample is sufficiently pure, we conclude that the semiconductor behaves intrinsically when between 25˚C to 100˚C.

Question 7

What is the energy gap for your sample? Compare with published literature values and cite your sources.

With the understanding that the graph displays intrinsic behaviour, the slope of the best fit line then represents -Eg/2k, equating to -3810.3. Solving for Eg (taking k as 8.617e−5 eV/K) the energy gap of the sample is 0.657 eV. This compares well with the known band gap energy for germanium⁴, 0.67eV.

Question 8

Predict the resistance at 150°C of your sample.

Assuming that the semiconductor continues to behave as an intrinsic semiconductor, the data can be extrapolated and resistance is predicted to be 37.42 Ohms at 150˚C.

Part III (Insulators)

Question 9

Plot ln (G) versus 1/T for the insulator sample studied in this lab.

Question 10

What is the temperature corresponding to the change in slope of the ln (G) vs 1/T plot? If you don't observe any change in slope, what does that mean?

A jump followed by a change in slope of the ln (G) vs 1/T plot is observed when the temperature is 529.9˚C. Below this temperature, the number of vacancies is due to impurities in the sample and is temperature independent. The conductivity is hence controlled by the migration energy, Em. Above the 529.9˚C, the steeper slope observed is due to the increase in anion-cation vacancy pairs (Schottky defects) and its effect on conductivity dominates that of vacancies due to impurities. The conductivity for this segment depends on the formation energy of Schottky pairs, W. If no change in slope is observed, it would suggest that there is an incredibly high amount of impurities in the sample and a large amount of thermal energy would be needed for conductivity due to thermally induced Schottky defects to dominate that of vacancies due to impurities.

Question 11

From your plot determine both Em and W in eV.

The slope for the portion 1, at temperatures above 529.9˚C would equal to -(Em + W/2)/k, and the slope for portion 2 would be -Em/k. With the gradient of the best fit lines for the two graphs, we can solve these equations (taking k as 8.617e−5 eV/K) to get Em = 0.775 eV and W = 1.629 eV

Question 12

Do you think that conductivity measurements could be used as an index of purity in ionic crystals? Discuss.

Conductivity measurements could be useful in determining the purity of ionic crystals for a given crystal lattice. For a known ionic compound, the impurity level can be determined relatively by comparing the critical temperature where the slope of the ln (G) vs 1/T plot changes, with that of the same compound with a known/different purity. However this cannot be done across different compounds and crystal structures as conductivity is different and cannot be attributed solely to differences in purity.

Electronic Properties of Materials

DISCLAIMER: i post this in hope it is a helpful guide/for desperate times when you need some guidance. remember our honor code. remember this trust i put in you.

if you wanna see my full report just drop me a dm. ill share it gladly one surviving bear to another.

Graded: 10/10

Comments: Excellent abstract!

Electronic Properties of Materials

DISCLAIMER: i post this in hope it is a helpful guide/for desperate times when you need some guidance. remember our honor code. remember this trust i put in you.

if you wanna see my full report just drop me a dm. ill share it gladly one surviving bear to another.

Graded: 13.5/15

Comments: Good introduction! References are helpful. Maybe a diagram of bandgap/conduction comparisons would make it even better. Also AIP citation has numbers behind punctuation.

Electronic properties of materials are dependent on the electronic structure of materials. In solids (high concentration of atoms), atomic orbitals overlap to produce continuous bands of energy instead of discrete levels as seen in individual molecules. The electronic band structure describes the range of energy levels electrons can exist in, and the band structures of conductors, semiconductors and insulators have distinct differences that explains their conductivity. The most prominent difference is the band gap – the minimum amount of energy required for an electron to move from its ground state (valence band) to the next available energy level (usually in the conduction band if the valence band is filled). For conductors, the valence band is partially filled, so there are open states within the valence band for electrons to move into without requiring significant energy to traverse a band gap¹. For semiconductors and insulators, this is not the case, and the conductivity is directly related to the band gap. Semiconductors have a narrow band gap of less than 2 to 3 eV, while insulators have wide band gaps larger than 3 eV, a threshold that is hard to cross at normal voltages leading to little or no conductivity.

When an energy input (such as thermal) promotes electrons to a higher energy band, it leaves behind a hole in the valence band. Both holes and electrons can work as charge carriers. Holes and electrons can further differentiate semiconductors into two types. Intrinsic semiconductors have a close hole to electron concentration, whereas one of the charge carriers dominates in extrinsic semiconductors. This can be due to the input of substitutional impurity atoms with higher or lower valence than the lattice atoms, known as n-type and p-type doping respectively.

The conductivity of a material is directly affected by its resistivity. Ideally, in perfect crystals, electrons are able to move about freely without resistance. In real crystals, electrons often face resistance due to lattice imperfections and impurities. This is known as residual resistivity. Overall resistivity of a material is the sum of residual resistivity and the thermal contributions from lattice/molecular vibrations², known as Matthiessen’s rule³. For ionic solid insulators, electrical conductivity arises due to the migration of ions when an electric field is applied. The nature of ionic solids disfavors the movement of charged ions within the lattice, so conductivity of ionic solids is directly related to lattice defects, particularly vacancies.

In this experiment, materials of varying conductivity were explored to investigate how temperature change and the presence of impurities affects electrical resistivity, and better understand the nature of electrical conductivity in materials.

<prof>, Chapter 18: Electrical Properties (2021)

<prof>, MSE 45L Laboratory 6: Electronic Properties of Materials (2021).

Uniaxial Tensile Test

DISCLAIMER: i post this in hope it is a helpful guide/for desperate times when you need some guidance. remember our honor code. remember this trust i put in you.

if you wanna see my full report just drop me a dm. ill share it gladly one surviving bear to another.

Graded: 13/15

Comments: Great intro and description of features/regions of stress-strain curves. This could be made a lot more clear by including a figure!

Uniaxial tensile tests are a common way to observe and test the elastic and plastic deformation of materials. These tests are often carried out with a (hydraulic) machine that applies an increasing amount of load to a sample while simultaneously elongating the sample, holding one end stationary1. The applied load and change in length of the sample are monitored. Usually, the sample is destructively tested until failure to better understand the limits of the material tested.

Data from uniaxial tensile tests are incredibly useful to understanding the material, and can be manipulated to provide various information. With the knowledge of the sample’s initial length and initial cross sectional area (or diameter), the engineering stress and engineering strain can be computed by dividing the force applied by the initial cross sectional area and the change in length by the initial length respectively2. From the stress-strain graph of the material, we are able to view how the sample changes elastically (non-permanent) and then plastically. Based on the initial linear change associated with the stress-strain graph, the gradient of the slope, the Young’s Modulus (E) of the material, can be calculated. The Poisson's ratio (v), the relative ratio between the strain in two perpendicular directions, can also be calculated. The ultimate tensile strength of the material, the highest point in the stress-strain graph, can also be determined, and is important in acknowledging the maximum stress/strain the material can take before necking and fracture occurs. Charpy impact testing is also another way to test materials by measuring notch toughness, and is most commonly used to observe the ductile-to-brittle transition in materials. The ductile-to-brittle transition is the sudden change in a material’s ductile property below a certain temperature.

heat treatment of steel

DISCLAIMER: i post this in hope it is a helpful guide/for desperate times when you need some guidance. remember our honor code. remember this trust i put in you.

if you wanna see my full report just drop me a dm. ill share it gladly one surviving bear to another.

Graded: 10/10

Binary Alloy Phase Diagrams

DISCLAIMER: i post this in hope it is a helpful guide/for desperate times when you need some guidance. remember our honor code. remember this trust i put in you.

if you wanna see my full report just drop me a dm. ill share it gladly one surviving bear to another.

Graded: 15/15

Comments: Excellent introduction!

Phases are sections of a system with homogenous structure and the same chemical and physical properties. Phase diagrams are used to present the phases of a multicomponent system at equilibrium, often depicted as a function of changing temperature. Phase diagrams for non-pure samples, such as alloys and mixtures, can also be presented as a function of composition, and they do not have well defined single melting temperatures and melt over a range of temperatures. ^1,2 For alloys, cooling curves tell a portion of the phase diagram and has a shape very different from that of pure elements. Cooling an alloy to liquidus (a phase boundary below the stable liquid phase in a binary phase diagram), first causes some sections in the alloy to solidify, releasing some heat (heat of fusion), causing the cooling rate of the alloy to decrease. At different compositions, the starting temperature at which the alloy starts and ends solidifying The solid particles within the alloy then grow, until the entire sample solidifies or until a reaction isotherm is reached. Cooling curves are very useful in determining the composition of an alloy, as the rate of cooling changes at different phase field boundary temperatures, depending on the composition of the alloy.

In this experiment, an unknown alloy of lead-antimony with either 5%, 11.2% or 15% (weight percent) antimony was given. The alloy was heated to 300 ̊C and allowed to cool to 200 ̊C. Cooling curves were generated for the unknown alloy of lead-antimony to determine phase field boundary temperatures and the sample was then imaged under an optical microscope to observe its microstructure. Comparing our data with the provided published cooling curves and microstructural images for known Pb-Sb compositions, the composition of the unknown lead-antimony sample could be determined.

<prof>, MSE 45L Laboratory 3: Binary Alloy Phase Diagrams (2021).

Binary Alloy Phase Diagrams

DISCLAIMER: i post this in hope it is a helpful guide/for desperate times when you need some guidance. remember our honor code. remember this trust i put in you.

if you wanna see my full report just drop me a dm. ill share it gladly one surviving bear to another.

Graded: 10/10

Comments: Excellent abstract! [sorry 4 flex 😩]