Students should select minimum of 3 exams from the list below (total 6 exams are present in the list). The 4th exam can be taken from another program within FENS.

**MAT PhD qualifying exam: Topics and associated learning outcomes**

Each exam addresses all of the Learning Objectives for that topic. References as well as undergraduate and graduate level courses that are related to the topic are listed as starting points (ENS 205 contributes to all exams).

#### Thermodynamics

Students who pass the Thermodynamics Qualifying Written Exam are able to,

- Identify the restrictions imposed on complex engineering systems by the laws of thermodynamics and solve associated problems on model systems.
- Analyze heat engines using arguments related to thermodynamic cycles.
- Link thermodynamic potentials and related coefficient relations to experimentally measurable quantities.
- Construct and interpret phase diagrams for single component systems, displaying in-depth understanding of phase boundaries by applying the relevant stability relations.
- Analyze the thermodynamic equilibrium of a binary solution, displaying the difference between eutectics, spinodals and binodals; identify the microstructure in different regions of binary phase diagrams.
- Display a knowledge of the fundamental assumptions of ideal gas laws, ideal solutions, and regular solutions by applying them in thermodynamics problems.
- Analyze system equilibria at the interfaces and surfaces of micro to nanoscale materials —e.g., for bubbles, cavities, droplets, and precipitates--including the effect of curvature on solubility.

**References:**

H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, John Wiley & Sons.

D. V. Ragone, Thermodynamics of Materials Volume 1, Wiley.

P. Atkins and J. de Paula, Physical Chemistry, any Edition, W. H. Freeman.

**Related Courses:** ENS 202, ENS 205, MAT 308, MAT 501

#### Transport and Kinetics

Students who pass the Transport & Kinetics Qualifying Written Exam are able to,

- Apply the parallelism between heat, mass and momentum transfer principles to solve transport phenomena problems in simple geometries.
- Formulate nucleation and growth mechanisms in simple materials systems.
- Demonstrate a working knowledge of finite difference methods by solving simple computational transport phenomena problems
- Given a chemical reaction, set-up the rate equations and/or determine reaction order by analyzing tabulated data.
- Analyze the effect of diffusion and convection on solidification in binary systems.
- Analyze the effect of interfaces and curvature on phase transformations and solubility.
- Apply the principles of a time-temperature-transformation diagram to design material processing to achieve a desired microstructure.

**References:**

D.A. Porter, K.E. Easterling, Phase Transformations in Metals and Alloys, Chapman and Hall.

D.V. Ragone, Thermodynamics of Materials, Volume II, Wiley.

P. Shewmon, Diffusion in Solids, Springer.

**Related Courses:** CHEM 202, MAT 206, MAT 309

#### Synthesis and Processing

Students who pass the Synthesis & Processing Qualifying Written Exam are able to,

- Identify polymerization reactions to synthesize different types of polymers and explain initiation, propagation, termination, crosslinking, branching and gelation steps of polymerization/copolymerization synthesis reactions
- Calculate the average molecular weights of polymers, by displaying a working knowledge of the relationship between molecular weight and polymer properties (i.e. mechanical, thermal)
- Discuss various theories of polymer manufacturing processes
- Identify main components for composite materials and illustrate approaches for manufacturing and processing of composites
- Design ceramic powder synthesis using the basics of sol-gel processing and/or solution based techniques.
- Apply basic rules of glass formations, and express the basic principles for the workings of glass formers and modifiers.
- Apply microstructural control principles to identify its effects on properties of materials.

**References:**

G. Odian, Principles of Polymerization, Wiley-Interscience.

W.D. Kingery, H.K. Bowen, D.R. Uhlmann, Introduction to Ceramics, John Wiley & Sons.

T. W. Graham Solomons et al., Organic Chemistry, Wiley-Interscience.

**Related Courses:** NS 207, MAT 302, MAT 308, MAT 408, MAT 422, MAT 511, MAT 570

#### Mechanical Properties and Deformation

Students who pass the Mechanical Properties & Deformation Qualifying Written Exam are able to,

- Write stress-strain relationships in tensorial form and explain the symmetries emerging in these tensors.
- Formulate transformation of stresses and strains to determine principal stresses, strains and their directions.
- Illustrate tensile testing diagrams, and interpret the structural information these diagrams provide.
- Evaluate stress and strain based criteria to predict failure fate of a given material under different loading conditions.
- Predict mechanical properties of multi-phase/composite materials given the properties of constituents
- Set-up standard viscoelastic models to predict basic creep and stress relaxation behavior of materials systems and interpret experimental observations in relation to these models.
- Demonstrate knowledge of fatigue failure and S-N curves and discuss their implications for materials selection on specific problems.

**References:**

N. Dowling, Mechanical Behaviour of Materials, Pearson.

D. Roylance, Mechanical Properties of Materials, MIT.

E. Barbero, Introduction to Composite Materials Design, CRC Press.

**Related Courses:** MAT 307, MAT 314, MAT 505

#### Characterization and Modeling of Materials

Students are expected to understand the working principles of materials characterization equipment, particularly the underlying physics leading to the interpretation of data collected via,

- Spectrophotometry—UV-visible absorption, FTIR, Raman
- Thermal analysis—TG-DTA, DSC
- X-ray diffraction
- Microscopy—visible light microscopy, scanning electron microscopy
- Energy dispersive spectroscopy in the scanning electron microscope
- Atomic force microscopy
- Dynamic light scattering

Students who pass the Characterization and Modeling of Materials Qualifying Written Exam are then able to,

- Choose the appropriate characterization method for analyzing material structure—
*e.g.*microstructure, grain, crystal structure, electronic structure, molecular bonds - Describe the basic anatomy of the instrument
- Analyze the data—diffractogram, thermograms, spectra, images—and interpret probe-specimen interaction to elucidate material structure and physicochemical properties
- Write and provide a physics-based interpretation of the equations that describe pairwise interactions between covalently bonded and non-bonded atoms.
- Perform normal mode analysis on simple one dimensional systems of atoms connected by harmonic springs; interpret the resulting frequencies and eigenvectors to spectroscopic observations.

**References:**

J.I. Goldstein et al., Scanning Electron Microscopy and X‑Ray Microanalysis, Springer.

D.L. Pavia, et al., Introduction to Spectroscopy: a guide for students of organic chemistry, Harcourt College Publishers.

D. Brandon, W.D. Kaplan, Microstructural Characterization of Materials, Wiley.

A. R. Leach, Molecular Modelling, Prentice Hall (chapters 4 and 5).

**Related Courses:** MAT 306, MAT 312, MAT 405, MAT 571

#### Structure and Properties of Condensed Matter

Students who pass the Structure and Properties Qualifying Written Exam are able to,

- Identify different types of atomic bonds in compounds, alloys and other engineering materials based on elements of the periodic table (metals/nonmetals).
- Explain the band theory of crystals, its consequences and E-k band diagrams for metals, semiconductors and insulators.
- Describe the origin of electrical conduction by both classical and quantum mechanical means.
- Define the classical theory of optical properties and optical absorption, and relate optical absorption processes to the energy band diagrams of various materials; i.e. apply quantum mechanical description of optical processes.
- Explain the intrinsic/extrinsic semiconductors, the Hall effect in semiconductors, p-n junctions, metal-semiconductor interfaces using band theory.
- Interpret thermal properties of materials by applying both classical and quantum mechanical considerations, relating theories such as the Dulong-Petit law, Einstein model, and Debye model.
- Identify the link between electronic behaviour and optical measurements particularly by relating observations to the real and imaginary parts of the dielectric constant.

**References:**

J.D. Livingston, Electronic Properties of Engineering Materials, Wiley.

J. Salyom, Fundamentals of the Physics of Solids: Volume 1: Structure and Dynamics, Springer.

R. Bube, Electrons in Solids, Elsevier.

**Related Courses:** PHYS 302, MAT204, MAT408, MAT 509