Chemistry Reference
In-Depth Information
1. Calculate the cofactors of the determinant on the elements of the first row:
¼ðs
22
s
p
Þðs
33
s
p
Þs
23
a ¼
ðs
22
s
p
Þ
s
23
s
23
ðs
33
s
p
Þ
¼ s
13
s
23
s
12
ðs
33
s
p
Þ
s
12
s
23
b ¼
s
13
ðs
33
s
p
Þ
¼ s
12
s
23
s
13
ðs
22
s
p
Þ
s
12
ðs
22
s
p
Þ
c ¼
s
13
s
23
2. Calculate the factor k
1
a
2
k ¼
p
þb
2
þ c
2
3. Calculate the direction cosines or eigenvectors:
l
p
¼ ak m
p
¼ bk n
p
¼ ck
Repeat steps 1-3 for all three principal stresses, and then obtain the eigenvector by
2
4
3
5
l
1
m
1
n
1
l
2
m
2
n
2
l
3
m
3
n
3
or in angles
2
3
cos
1
l
1
cos
1
m
1
cos
1
n
1
4
5
cos
1
m
2
cos
1
n
2
cos
1
l
2
cos
1
m
3
cos
1
n
3
cos
1
l
3
APPENDIX 9.B PARAMETERS FOR STRESS MEASUREMENT
The parameters required for X-ray stress determination are the crystal lattice
parameter, d-spacing, Miller index, X-ray wavelength (target material), stress-free
2u
0
, Young's modulus E, Poisson's ratio n, and the anisotropic factor A
RX
. Among
these parameters, the most important parameters are the Young's modulus E and
Poisson's ratio n. In principle, stress and strain values can be determined from any
measured diffraction rings in either transmission mode or reflection mode using the
2Dmethodwith givenE and n. In order to have a higher angular resolution and enough
sample rotation range, diffraction rings with 2u
0
in the range of 110
-160
are
preferred, but not absolutely necessary with XRD
2
. The following table lists the
parameters for most commonly used materials. These parameters are supplied only
for the user's convenience. Since the parameters, especially E and n, are different with
different material conditions, different experimental methods, or even different
theoretical assumptions, users are encouraged to determine the parameters based
on their experiments and references.
