Download Multielectron Atoms * The Independent Particle Approximation

Physics 471: Solid State Physics
Professor Micky Holcomb
Office: 437 White Hall
[email protected]
http://community.wvu.edu/~miholcomb/
Today: Introduction to me, you, class structure and topic
About Your
Professor
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Went to school at Vanderbilt and Berkeley
Did graduate work at a national lab
Did internship at IBM on quantum computing
Toyed with a non-scientific internet startup
Decided I liked teaching, so I’m here now
My Work: Surface & Interface Physics
Magnetic
Dead
Layers
Exchange Bias
Delafossites
Topological Insulators
Definition of a Multiferroic
Ferromagnetic
Ferroelectric
field
Before field
After field
Spontaneous magnetization whose Spontaneous polarization whose
direction can be changed with an direction can be changed with an
applied electric field (voltage)
applied magnetic field
Multiferroic
Electric Control of Magnetism
Coupling at interfaces is not
well understood
Review paper, Holcomb et al., IJMPB (2012)
INDIRECT COUPLING
http://www.helmholtz-berlin.de/forschung/magma/mdynamik/forschungsbereiche/multiferroicity_en.html
Measurement Techniques
WVU: Nonlinear Optics
San Francisco
Focused on Second Harmonic
Generation and MOKE
Synchrotron Techniques At National Labs:
X-ray Absorption Spectroscopy
Provides information on
Photoemission Electron
symmetry and interfacial time
Microscopy (PEEM)
dynamics
Beyond the standard techniques (XRD, VSM, TEM, etc.), we focus
on unique interfacial measurement techniques.
As we are about to spend a lot of
time together,
please introduce yourself.
-Name and Year
- Taken or in quantum mechanics yet?
-Planned career path (or possibilities, if debating)
-Why are you taking this course?
Important Class Issues
• Text: Understanding Solid State Physics by
by Holgate (in stock on Amazon, $22 - 85)
• Strongly recommended: Intro. to Solid State
Physics by Kittel ($1-178)
Others
• Lecture PPTs will be available online shortly
after class. (additional material, not tested)
• I expect you to do the Holgate reading (and
ideally skim Kittel) before coming to class so
that we can focus on details/applications.
There is another reason.
Why cramming
does not work for
the long run
How
Do We
Learn?
Through Repetition: the more times (and more ways) we
repeat something, the more important our brains think it is,
and the more likely we are to remember it
Another good reason to read multiple books
How Do We Learn?
Amygdala:
Hippocampus:
Prefrontal Cortex:
Fight or Flight
Memory
Executive Function
My
Goal
Why Cramming Doesn’t Work
Learning
Assessment
• There are many different physics skills (problem
solving, written and oral communication, etc). My
assignments reflect this variety.
• Homework: Late assignments arriving in my hands
will be counted 20% for each day late.
• Feel free to work together on HW, but do not copy.
Copying of anyone else’s work is an honor code violation.
Oral Communication
of Science
Is one of the more difficult skills to master and
grade. Your skill will be evaluated in 2 ways:
•In class discussion (with both a
partner and to the entire class)
on in-class problems
Discussion Questions
• Some of these questions will be easy to make sure
you have important background. If everyone thinks
it’s easy, we’ll move through these fast. Otherwise,
vital to cover.
• Some of the questions will be harder. My goal is to
coach you through these problems, not just do
them for you. You learn more this way.
Oral Communication
of Science
Is one of the more difficult skills to master and
grade. Your skill will be evaluated in 2 ways:
•In class discussion (with both a
partner and to the entire class)
on in-class problems
•You will teach through a
presentation. Pick a topic and
get it approved.
Course Grading
Course Grade: Homework 25%, Midterm 30%, Final
30%, In-class Discussion 4%, Show & Tell 1%,
Presentation 10%
Grading scale: A (>85), B (70 - 84), C (60% - 69%), D
(50% - 59%), F (<49%)
Teaching: A student receiving an A on their
presentation will at least 1) make and share
organized powerpoint slides, 2) make eye contact
with classmates, 3) discuss applications of physics,
4) motivate why topic is interesting, 5) identify key
points and 6) stay close to the allotted time. (See
syllabus for more)
My Teaching Philosophy Regarding Slides
•If you become a professor, you will be
instructed to (regarding teaching) “beg, borrow
and steal.” Preparing a good lecture is hard! So,
if someone manages to, then reuse it!
• Therefore, many of my slides are adaptations. I pick what I
deem to be the most instructive slides.
• I find this to work out pretty well, accept that there are
many different notations for the same things are used. (e.g.
lattice vectors)
• In reality, papers use different notation, so it is a useful
practice to get used to multiple forms of terminology.
Please ask if you are confused about any terminology.
Physics 471: Solid State Physics (SSP)
Office: 437 White Hall
Office hour: Tuesdays 2:30-3:30PM or by
appointment
[email protected]
http://community.wvu.edu/~miholcomb/
Today’s Plan:
Take ungraded pre-test. When finished, read over
syllabus. If time remains, I will introduce SSP.
What is solid state physics?
• Solid state physics (SSP) explains the properties of
solid materials which follow from Schrödinger’s
equation for a collection of atomic nuclei and
electrons interacting with electrostatic forces.
• SSP, also known as condensed matter physics, is the
study of the behavior of atoms when they are
placed in close proximity to one another. Many of
the concepts relevant to liquids too.
What is the point?
• Understanding the electrical properties of solids
is right at the heart of modern society and
technology.
• The entire computer and electronics industry
relies on tuning of a special class of material, the
semiconductor, which lies right at the metalinsulator boundary. Solid state physics provide a
background to understand what goes on in
semiconductors.
schedule
Why is Solid State Physics Important?
Electronic Properties
- Transistors (the heart of electronics)
Electron/Photon Interactions
- Laser Diodes, Photodiodes, CCDS
Electron/Phonon Interactions
- Piezoelectric materials
Electron Spin/Charge Interactions
- Spintronics, Quantum Computing
Highly Correlated Electronics Systems
- Superconductors, Magnets
New technology for the future will involve developing and understanding new classes
of materials. By the end of this course we will see why this is a non-trivial task.
What do pencil lead and diamond
have in common?
What property are they complete
opposites?
Electrical resistivity of three states of
solid matter
They are all just carbon!
How can this be? After all, they each contain a system
of atoms and especially electrons of similar density.
Graphite is a metal, diamond is an insulator and
buckminster-fullerene is a superconductor.
With the remaining time today:
Let’s remind ourselves of how we deal with
individual atoms
In the remainder of the semester we’ll focus on
the effects of bringing lots of atoms together
What is the simplest atom?
What can you tell me about it?
Potential energy felt by an electron?
ke
U (r )  
r
2
Reminder: k=1/4o
Multielectron Atoms
(i.e., atoms other than hydrogen)
• Because electrostatic forces between electrons are strong, we need to take
them into account
• We approximate this by treating the force on each electron independently,
which includes force from nucleus + force from all other electrons
• In this case, inner electrons can shield the nuclear charge, called “screening”
Screening
electron
cloud
We write the effective potential energy felt by an electron as
+Ze
r
electron
ke 2
U (r )   Z eff (r )
r
Zeff is the effective charge that the electron feels and depends on r. Note that
Z eff  Z
when r is inside all other electrons
Z eff  1
when r is outside all other electrons
Reminder: k=1/4o
Energy Levels
• As in the hydrogen atom, quantum states of electrons in multielectron
atoms are specified by the quantum numbers n, l, m, mS
• In hydrogen atom, all states of a given n are degenerate (in zero magnetic
field and neglecting the fine structure)
• In multielectron atoms the dependence of the potential energy on r due
to screening lifts the degeneracy between these states:
ke 2
U (r )   Z eff (r )
r
Why does the effective radius look like this?
In hydrogen, all n orbital (ns,np,nd) states have the same energy
I won’t always have time to get to all
of the slides. You won’t be tested on
them in this case, but it’s not a bad
idea to look through them if you have
time.
Electron distribution
• For a multielectron atom, how are the electrons distributed
among the different energy levels and orbitals?
• Electrons would all crowd the ground state (lowest energy) if it
wasn’t for the:
Pauli Exclusion Principle: No two electrons
(fermions) in a quantum system can occupy the
same state (i.e., have the same quantum numbers)
Would ground state helium or lithium be easier to ionize (remove
an electron)?
Helium ground state
Helium excited state
Lithium ground state
How does the number of electrons
determine the properties of the
elements?
The Periodic Table
Properties of Helium
2He:
Use notation ZE: e.g. 1H, 2He
• Ground state: two electrons in 1s state (spin up/down)
• Screening of each electron by the other
• This results on a relatively large ionization energy
(energy to remove an electron from a neutral atom) of 24.6 eV
• Also large excitation energy (E2s-E1s) = 19.8 eV vs. 10.2
eV for H
• Chemically inactive as a result of the large excitation
and ionization energies – will not solidify unless low
temperatures (4.2 K) and high pressures are used
• Chemically inert gases are called noble or inert
Helium ground state
Helium excited state
In groups, consider (for ~3 minutes):
Compare ionization energies and effective radius
of the elements Z=3 Lithium & Z=4 Beryllium
Draw the ground state and excited states
Properties of Lithium
3Li:
• Ground state: two electrons in 1s state + one electron in
2s state
• Ionization energy significantly smaller than He: expect
Zeff ~1 with n=2, resulting in 5.4 eV
• Large effective radius due to occupancy of n=2 level
• Reactive as a result of the small ionization energy – can
form compounds such as LiF
Properties of First Ten Elements
4Be:
• Ground state: two electrons in 1s state + two electrons in 2s state
• Larger Z means larger ionization energy than Li (9.3 eV vs. 5.4 eV)
• Excitation energy to 2p state is relatively low (2.7 eV) which makes Be
chemically active and allows it to bond to other atoms (forms a solid)
• Smaller effective radius due to larger Z than Li
Lowest excited
state for Be:
Properties of First Ten Elements
Other elements
• Increasing Z causes electrons to be more tightly bound (causing greater ionization
energies), however, when the quantum number changes higher energy states are
occupied, meaning they are less tightly bound (causing lower ionization energies)
• For Z=5 (B) electron goes to 2p state, slightly higher in energy (due to screening)
causing binding energy to drop slightly (8.3 eV vs. 9.3 eV for Be). Very pure isolated
boron is produced with difficulty, as boron tends to form refractory materials
containing small amounts of carbon or other elements.
• For Z=6 (Be) to Z=10 (Ne) electrons go into 2p state causing steady increase in
ionization energy and decrease in radius due to increase in Z (all electrons go into
n=2 level)
• In going from Z=10 (Ne) (full n=2 shell) to Z=11 (Na, one electron in 3s) level
ionization energy suddenly drops due to large increase in occupation energy of n=3
state (Zeff ~1, similar to Li)
In Groups: Rank the Ionization Energies
For each of the following sets of atoms, decide
which has the highest and lowest ionization
energies and why.
a. Mg, Si, S
b. Mg, Ca, Ba
c. F, Cl, Br
d. Ba, Cu, Ne
e. Si, P, N