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GY 302: Crystallography & Mineralogy
GY 302: Crystallography & Mineralogy
UNIVERSITY OF SOUTH ALABAMA
Lecture 1: Introduction to Crystallography
Lecture 1: Introduction to Lecture 1: Introduction to CrystallographyCrystallography
Todays Agenda1. Basics of Crystallography
2. Symmetry Operations
What is Crystallography?
What is Crystallography?
The science of crystallization, crystal form, structure The science of crystallization, crystal form, structure and symmetry.and symmetry.
What is Crystallography?
Math + Chemistry + Physics =Math + Chemistry + Physics =
The science of crystallization, crystal form, structure The science of crystallization, crystal form, structure and symmetry.and symmetry.
Why do Crystallography?
At last count, there are well over 4000 distinct At last count, there are well over 4000 distinct mineralsminerals in our solar systemin our solar system
Why do Crystallography?
At last count, there are well over 4000 distinct At last count, there are well over 4000 distinct mineralsminerals in our solar systemin our solar system
They are composed of 90+ elements, as well as more They are composed of 90+ elements, as well as more complex ions like COcomplex ions like CO3322--, SO, SO4422--, PO, PO4433-- etc.etc.
Why do Crystallography?
At last count, there are well over 4000 distinct At last count, there are well over 4000 distinct mineralsminerals in our solar systemin our solar system
They are composed of 90+ elements, as well as more They are composed of 90+ elements, as well as more complex ions like COcomplex ions like CO3322--, SO, SO4422--, PO, PO4433-- etc.etc.
Minerals are assembled according to exact chemical Minerals are assembled according to exact chemical blueprintsblueprints
Why do Crystallography?
At last count, there are well over 4000 distinct At last count, there are well over 4000 distinct mineralsminerals in our solar systemin our solar system
They are composed of 90+ elements, as well as more They are composed of 90+ elements, as well as more complex ions like COcomplex ions like CO3322--, SO, SO4422--, PO, PO4433-- etc.etc.
Minerals are assembled according to exact chemical Minerals are assembled according to exact chemical blueprintsblueprints
and those blue prints are controlled by and those blue prints are controlled by mathematical and physical laws.mathematical and physical laws.
As a bare minimum, this class requires you to understand basic bonding principles (CH 100/131 level) e.g., how electrons fill shells and sub-shells according to quantum mechanics.
20
2
4 reV =
Chemical Considerations:
22+00SS00KK11 -
-
++1+1-
+00- 66+--11PP11- 22+00SS00LL22
Number of electrons
msm1subshelllShelln
Spin Quantum Number
Magnetic Quantum #
Angular Momentum Quantum Number
Principle Quantum Number
Orbital Orientation
s (1 lobe) p (2 lobes)
d (4 lobes)
Chemical Considerations:
Chemical Considerations:
Hydrogen: 1S1Helium: 1S2
Uranium: [Rn] 5f3 6d1 7s2
-- weak bondsweak bonds-- low to high melting pointslow to high melting points-- metallic metallic lusterslusters--electrically conductiveelectrically conductive
MetallicMetallic
-- strong bondsstrong bonds-- hard minerals hard minerals -- very high melting pointsvery high melting points-- vitreous vitreous adamantine adamantine lusterslusters
CovalentCovalent
--strong bondstrong bond--high melting pointshigh melting points--vitreous vitreous lusterslusters--higher solubility higher solubility
IonicIonic
Mineral propertiesMineral propertiesBondBond
Na+ Cl-
Chemical Considerations:
So
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c
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:
w
w
w
.
w
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b
c
h
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m
.
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Crystallography:
Crystal Structure
S
o
u
r
c
e
:
h
t
t
p
:
\
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s
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a
f
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a
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Crystallography:
Crystal Systems
Crystal Systems
Crystals are classified according to the lengths and angles between crystallographic axes
Crystal Systems
Crystals are classified according to the lengths and angles between crystallographic axes
3 axis are the same length
All axes are at 90 to one another
a=b=c;=== 90
Crystal Systems
Crystals are classified according to the lengths and angles between crystallographic axes
3 axis are the same length
All axes are at 90 to one another
a=b=c;=== 90
This defines the Cubic or Isometric Crystal System
Crystal SystemsThe 6 (or 7) Crystal Systems.
Plagioclase" $ ( 90a b cTriclinic6Gypsum, Orthoclase" =$ =90 , ( 90a b cMonoclinic5Aragonite, Staurolite" =$ =( =90a b cOrthorhombic4Quartz, Calcite" =$ =120 , ( =90a= a1=b cTrigonal3bApatite" =$ =120 , ( =90a1= a2=a3 cHexagonal3aZircon" =$ =( =90a = b cTetragonal2Halite, Galena, Pyrite" =$ =( =90a = b = cCubic1
Mineral examplesAngles between axesAxesCrystal System
Crystal Systems
There are also subdivisions of
each system that we will get to in
time
Crystal Systems
First Lab next week
Symmetry
Symmetry
is the hardest thing for students to appreciate, understand or visualize.
Symmetry
1) Reflection symmetry (mirror planes)
Symmetry
1) Reflection symmetry (mirror planes)
Symmetry
1) Reflection symmetry (mirror planes)
Symmetry
1) Reflection symmetry (mirror planes)Isometric crystals have up to 9 mirror planes
Symmetry
1) Reflection symmetry (mirror planes)
Symmetry
2) Rotational symmetry
Symmetry
2) Rotational symmetry
Symmetry
2) Rotational symmetry
4 fold rotational axis
Symmetry
2) Rotational symmetry
Symmetry
2) Rotational symmetry: usually three 4 fold rotational axes defines the isometric system (highest order)
Symmetry
2) Rotational symmetry: but there are also 4 x 3-fold rotational axes at the corners*
* there is more to the 3-fold axis story to be revealed in an upcoming lecture
Symmetry
2) Rotational symmetry and 6 x 2-fold rotational axes at the edges
Symmetry
2) Rotational symmetry
Crystal Systems
Symmetry operations:
1) Reflection (mirror planes)
Crystal Systems
Symmetry operations:
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)
Crystal Systems
Symmetry operations:
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion
Crystal Systems
Symmetry operations:
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion
Crystal Systems
Symmetry operations:
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion
Crystal Systems
Symmetry operations:
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion
Crystal Systems
Symmetry operations:
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion
Center of Inversion
Crystal Systems
Symmetry operations:
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion
Crystal Systems
Symmetry operations:
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion
Crystal Systems
Symmetry operations:
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion4) Translation (We will consider this next time)
Crystal Systems
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion4) Translation
Basic symmetry operations
Crystal Systems
1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion4) Translation
5) Screw Rotation6) Glide Rotation7) Rotoinversion
Basic symmetry operations
Compound symmetry operations
Todays Lecture Homework1.1. Purchase a hand lens, the GY 302 Mineral notebook and Purchase a hand lens, the GY 302 Mineral notebook and
one big 3 ring binder* and decent art supplies (pencil, one big 3 ring binder* and decent art supplies (pencil, eraser, ink pens)eraser, ink pens)
*for your notes, syllabus, assignments, quizzes etc.*for your notes, syllabus, assignments, quizzes etc.
Next Time1.1. Plane and Plane and BravaisBravais latticelattice
Your First Lab AssignmentExamine 4 wooden models from the isometric and hexagonal Examine 4 wooden models from the isometric and hexagonal crystal systemscrystal systems (2 from each group)(2 from each group)
A) sketch the crystalA) sketch the crystalB) identify all mirror planesB) identify all mirror planesC) Identify the highest rotational symmetryC) Identify the highest rotational symmetryD) identify all other rotational axesD) identify all other rotational axesE) Identify the point group of the mineral (starting next week)E) Identify the point group of the mineral (starting next week)
Due Date1.1. Sept 7Sept 7thth by 1:00 pm (followed by a quiz)by 1:00 pm (followed by a quiz)