Superconductivity and PCA

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15 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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Superconductivity and PCA
(a)The Villars map (or quantum structural diagram) for 67 high Tc
(>10K)
binary/ternary superconductors
(b) Matthias profiles
Identification of Superconductivity RegionUsing Structure Map
From P. Villars and J.C. Phillips, Phys. Rev. B, 37, 2345 (1988).
In 2001,
Nagamatsuet al. encouraged materials scientists to study AlB
2
type
compounds again by finding the superconductivity of the AlB
2
type MgB2
that have a critical temperature T
c
of 39K.
(J. Nagamatsuet al., Nature410, 63, 2001)
Motivation of Research
Property-structure envelope
MgB2
-Where is it on the Pettifor’s AB2 type structure map?
MgB2 (Tc~39K)
From D.G. Pettifor, Intermetallic Compounds: Principles and Practice,
J.H. Westbrook and R.L. Fleischer, Eds., 1, 419, Chichester: John Wiley & Sons (1995).
Data fusion (Villars Map + Matthias rule) through the PCA
Note.
Linearly weighted Ionization energy and Cohesive energy were also included.
PCA with Superconductivity Data
Scoring
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-4
-2
0
2
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6
P
C
3

(
1
2
.
6
5
%
)
P
C
2

(
2
1
.
8
6
%
)
P
C
1

(
4
6
.
4
7
%
)
-3-2-10123
-4
-3
-2
-1
0
1
2
3
4
5
PC2
PC1
-4-3-2-1012345
-2
-1
0
1
2
3
PC3
PC2
Score Plots: Visualization of multivariate data
-3-2-10123
-2
-1
0
1
2
3
PC3
PC1
Projection on PC2-PC3
Projection on PC1-PC3
Projection on PC1-PC2
Black data points
are real 3D feature of
Superconducting data Set
-0.2
0
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0.4
0.6
0.8
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0
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1
Loadings on PC 2 (21.86%)
Loadings on PC 3 (12.65%)
-3
-2
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0
1
2
3
-6-4-20246
A15
AlB
2
Cupric Oxide
Mo6PbS
8
NaCl
Pr2Rh
2Sn13
CrFe
C15
AuCu
3
AsNi
Co4S5Si10
Miscellaneous
PC3
PC2
Interesting Score Plot and Loading Plot
MgB2
T
h
e
s
e

p
a
t
t
e
r
n
s

c
a
me

f
r
o
m
t
h
e

e
f
f
e
c
t

o
f

V
a
l
e
n
c
y
Valency
Electronegativity
Cohesive Energy
Ionization Energy
Pseudopotential radii sums
Other discriminant
method can be applied
to identify the spatial feature
of MgB2.
Scores Plot
•Plotting PCA values
PC2= 0.89Nv+0.01X-0.39R+0.03C+0.22I
PC3= 0.41Nv+0.41X+0.75R-0.06C-0.29I
•Every data point represents a material /
compound with all attributes embedded
Loadings Plot
•Plotting latent variable on PCA projections
PC2= 0.89Nv+0.01X-0.39R+0.03C+0.22I
PC3= 0.41Nv+0.41X+0.75R-0.06C-0.29I
•Every data point is an attribute
•Relative correlations between attributes across
the data set of the study ….
i.e. materials chemistry
-4-3-2-1012345
-2
-1
0
1
2
3
PC3
PC2
Visualization of multivariate data
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1
Loadings on PC 2 (21.86%)
Loadings on PC 3 (12.65%)
Valency (Nv)
Electronegativity (X)
Cohesive Energy (C)
Ionization Energy (I)
Pseudopotential radii sums ®