The document outlines the scientific research method and provides guidance on developing mathematical models and completing a thesis. It describes the four main steps of the scientific method as observation, hypothesis, experimental testing, and predictions. Observation involves recognizing facts or occurrences, which are then used to form a hypothesis. The hypothesis is then tested experimentally, and if proven true, predictions can be made. Mathematical models, such as using equations to fit experimental data, can help test hypotheses and predictions. Following the scientific method and reporting iterations that include publishable results are keys to completing a successful thesis.

2. Outline
• Scientific Research Method
• Development of Mathematical Models
• Applying these methods to completing a Thesis
Scientific Research – 1: investigation or experimentation aimed at the discovery and interpretation of
facts, revision of accepted theories or laws in the light of new facts, or practical application of such new
or revised theories or laws
2 : the collecting of information about a particular subject

3. Scientific Method of Research
Four Steps:
• If the experiments prove the hypothesis to be true, it becomes a theory or law of nature. If the experiments prove the
hypothesis to be false, the hypothesis must be rejected or modified. The scientific method used properly should give us
predictive power (to understand phenomena which have not been tested).
Further reading found at http://teacher.nsrl.rochester.edu/phy_labs/AppendixE/AppendixE.html
2. Hypothesis
3. Testing4. Predictions
1. Observation
False
True
TestH
ypothesis

4. •Observation –
an act of recognizing and noting a fact or occurrence often involving
measurement with instruments
• Experiments performed in the laboratory.
• Experiments gained from knowledge of the
literature.
Keys to Implementation in your Research:
Sorting Observations (from Literature Searches):
Useful Not Useful (Yet!)
Contains unanswered
questions which you think you
have means of addressing
Proclaims research has
explained everything (does not
contain unanswered questions)
Note Results (in report format- optional) for
future use in confirming/denying your
hypothesis (once your hypothesis is found)!
Formulate Hypothesis!

5. •Hypothesis –
tentative assumption made in order to draw out and test its logical or empirical
consequences
Example,
• Hypothesis of author Anton (UTRC paper) : Ionic radius of Ti4+ enhances desorption kinetics.
• Observation in Paper by Anton et al.: NaAlH4 doped with Ti4+, Ti3+ and Ti2+ have different ionic radii, but the same
rate of enhanced H2 desorption kinetics.
• New Hypothesis in Paper by Anton (not tested by Anton, et al.): Ti2+, Ti3+ and Ti4+ adopt the same oxidation state
after entering the NaAlH4 structure.
Keys to Implementation in your Research:
• Good Hypothesis can be TESTED with Experiment or Calculation.
• This requires A LOT of thought and reading--- leap from observation to
hypothesis. It is worth the effort because after thinking this through, you are
ready to go into the laboratory (which is the FUN part of research)!
Suggestions (no one can tell you HOW to do this, you have to develop this skill):
1. Couple archival journal reading with your in-class theory.
2. Couple archival journal reading with your ‘common sense’ or intuition about the
way things should be in the system that you are studying.
3. Follow a logical reasoning about what you are reading with scientific and/or
mathematical basis (use drawings and diagrams to help your understanding).
4. Write up your thoughts and opinions either in report format (or in a way which
you can follow within one notebook).

6. •Experimental Testing –
to be assigned a standing or evaluation on the basis of tests 2 : to apply a test
as a means of analysis or diagnosis
Example,
• New Hypothesis: Ti2+, Ti3+ and Ti4+ adopt the same oxidation state after entering the NaAlH4 structure.
• Test: EXAFS Absorption spectroscopy can measure bond length and # of bonds. We may dope NaAlH4 with
Ti2+, Ti3+ and Ti4+ and measure bond length of each. If they are the same, then they have all assumed one
oxidation state after entering the structure (and we can measure this oxidation state also using EXAFS by
determining the # of bonds).
Keys to Implementation in your Research:
• Good TESTS will prove or disprove your hypothesis.
• Experimental Tests can be performed within the realm of computing. (e.g. Coventor
model with calculations and predictions can serve as experiment and model).
• Consider all alternatives. Experiment may not disprove all (but may disprove only
parts) of your hypothesis. That is still alright to perform. Carefully note which aspects
of your hypothesis this experiment will test.
• Consider the availability of instrumentation to perform your tests.
Suggestions:
• See IfM website for list of available equipment.
• If you do not know (or have never heard of it), learn about that equipment, what it measures,
what it can fabricate, what is does, etc. (For nearly ALL Characterization Techniques, see
Metals Handbook, Volume 10 (LATECH call #: REFERENCE-- TA459 .A5)
• Ask questions! Schedule meetings with appropriate people in charge of equipment to inquire
about capabilities and terms/conditions for use.

7. •Predictions–
to declare or indicate in advance; especially : foretell on the basis of
observation, experience, or scientific reason
Example,
Test: EXAFS Absorption spectroscopy can measure bond length and # of bonds. We may dope NaAlH4 with Ti2+,
Ti3+ and Ti4+ and measure bond length of each. If they are the same, then they have all assumed one
oxidation state after entering the structure (and we can measure this oxidation state also using EXAFS by
determining the # of bonds).
Prediction 1: If Ti2+, Ti3+ and Ti4+ gain equivalent oxidation states after entering the structure, then the same should
be true for Co2+, Co3+, and Co4+ (or any other metal dopant).
or
Prediction 2: If Ti2+, Ti3+ and Ti4+ gain equivalent oxidation states after entering the structure via ball-milling, then
the same should be true for Ti2+, Ti3+, and Ti4+ after entering the structure via chemical precipitation from
Na+, Al3+, and Ti?+ salt solutions.
Keys to Implementation in your Research:
• Good Predictions can also be tested against your hypothesis.
• Consider going back to the basics (textbook theory) to development of a
mathematical model/construct which will help to make predictions about more
systems than you can reasonably test.
Suggestions:
• You may begin thinking about predictions as soon as you have a hypothesis,
however, if your hypothesis is proven false, your prediction will also fail!
• Use mathematical model to test your prediction.

8. •Mathematical Models–
Empirical vs. Deterministic
Examples,
Test: EXAFS Absorption spectroscopy data is in hand. Prediction 1: If Ti2+, Ti3+ and Ti4+ gain equivalent oxidation
states after entering the structure, then the same should be true for Co2+, Co3+, and Co4+ (or any other metal
dopant).
Model: We use FEFF8.0, WINXAFS to fit the XAFS equation to measured data --- varying types of neighboring
species (e.g. neighbors may be 2 Na atoms and 1 Al atom or 3 Al atoms and 1 Na atom). bond length and # of
bonds (coordination number) until we have a good fit. We did not know what environment our Ti atom was in
prior to model fitting, now, we have modeled our system to match our data. Our model is then made up of the
XAFS equation, bond lengths, and # of bonds.
Keys to Implementation in your Research:
• All thesis experiments should have empirical models (at least).
• If do not have a mathematical model--- only data, then we need to find an equation for
which we can perform least squares fitting your data.
• My suggestion: If you run into an interesting hypothesis which can be tested via
deterministic models (first principles approach), meet with IfM modeling faculty
(Mainerdi, Paun, Hegab or DeRosa) to discuss the hypothesis and modeling.
Empirical Deterministic
Based on experimental
observation (e.g. least squares
curve fitting, coventor MEMS
calculations, XAFS FEFF8.0
Analysis)
Based on first principles approach!
(e.g. Monte Carlo calculations,
Density Functional Theory,
Molecular Dynamics, Computational
Fluid Dynamics)

9. Further Suggestion:
• Know what has been done by others. Do not reinvent the wheel
unnecessarily!!!
• Understand your field. This qualifies you to make reasonable hypothesis
about fundamental advances in the field.
• Do not strive to solve all problems in the field, look for small advances in
your field.
• Small advancements lead to critical developments.
• Prepare to report results even if hypothesis fails. False hypothesis are
also advancements in science (and will save others time and money on
repeating these experiments). Failed hypothesis should also be used to
make suggestions for future directions (making you and EXPERT since
you can suggest new directions in your field!!!).

10. What do I need to do to Complete a
Thesis Option???
• Perform 1 iteration of the Scientific Method!!!
• Observation
• Hypothesis
• Experimental Test
• Prediction --- then you may STOP (You do not need to test
predictions in order to successfully write your thesis). Your
thesis should, however, include a reporting of your
predictions under the heading…’ Suggestions for Future
Work’. If you complete one iteration within 5 weeks, then
you should go further….
• Thesis should have publishable results from iterations
of the Scientific Method!!!
Good Luck and Happy Researching!!!