5b. sistem kristal

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?


The science of crystallization, crystal form, structure The science of crystallization, crystal form, structure and symmetry.and symmetry.


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



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




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)



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-


So

u

r

c

e

:

w

w

w

.

w

e

b

c

h

e

m

.

n

e

t

\

c

s

m

.

j

m

u

.

e

d

u

Crystallography:

Crystal Structure

S

o

u

r

c

e

:

h

t

t

p

:

\

\

s

t

a

f

f

.

a

i

s

t

.

g

o

.

j

p

Crystallography:

Crystal Systems

Crystal Systems

Crystals are classified according to the lengths and angles between crystallographic axes

Crystal Systems


3 axis are the same length

All axes are at 90 to one another

a=b=c;=== 90

Crystal Systems


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)Isometric crystals have up to 9 mirror planes

Symmetry

1) Reflection symmetry (mirror planes)

Symmetry

2) Rotational symmetry

Symmetry


4 fold rotational axis

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


Crystal Systems

Symmetry operations:

1) Reflection (mirror planes)

Crystal Systems


1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)

Crystal Systems


1) Reflection (mirror planes) 2) Rotation (2, 3, 4, 6 fold axes)3) Inversion

Crystal Systems



Center of Inversion

Crystal Systems



Crystal Systems


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)

5b. sistem kristal

Documents