Dr. P. Lucas
U of A
MSE 110
Miller indices
SUMMARY FROM LAST CLASS
•
A set of atomic planes entirely defines a crystal structure and we can identify these
planes based on their orientation in the unit cell using the
Miller indices
.
•
The plane orientation is specified by the intercept with each axes of the unit cell.
•
This defines a set of Miller indices
(hkl)
determined as follow:
•
Find an origin for which the plane intercepts all axes. Except for parallel axes.
•
Find the intercepts on the three axes in fraction of the cell parameter. Except
for parallel axes where intercept is
∞
.
•
Determine the reciprocal of these numbers.
•
Reduce the reciprocals to the smallest integers having the same ratio.
•
Cite the three integers in parenthesis placing bars over negative indices.
•
Using Bragg’s equation
λ
= 2d sin
θ
a set of dspacings is obtained from the
θ
values on the XRD pattern. Each
d
correspond to a plane of orientation
(hkl)
.
2
2
2
)
(
l
k
h
a
d
hkl
+
+
=
•
For a cubic cell, the geometric relationship
between
a
,
d
and
(hkl)
is
•
By inspection, we can calculate
a
and obtain the set of
(hkl)
for each dspacing.
This determines the structure entirely.
•
a
,
d
and
(hkl)
from all known minerals are compiled in a database.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Dr. P. Lucas
U of A
MSE 110
Thermodynamics:
INTRO TO THERMODYNAMICS
•
What characterizes a system (a solid, a liquid, a gas or a mixture)
when it is at equilibrium (when it doesn’t evolve anymore).
•
Thermodynamics is the study of equilibrium states.
•
It is powerful because it allows you to predict if a reaction or a
process will take place, the direction of the process or the reaction,
and the amount of energy transferred.
•
Processes: melting, vaporization… Reactions: Na + Cl
2
Æ
NaCl
•
In order to characterize the thermodynamic state of a system we will
need to introduce new variables:
•
The
enthalpy H
: characterize the heat transferred during a process.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Lucas
 Thermodynamics, Energy, Dr. P. Lucas U, Dr. P. Lucas

Click to edit the document details