chargeability and the polarizable volume fraction
DESCRIPTION
CHARGEABILITY AND THE POLARIZABLE VOLUME FRACTION. J.B.Merriam University of Saskatchewan. CHARGEABILITY DEPENDS ON HOST RESISTIVITY, ELECTROCHEMICAL SURFACE IMPEDANCE, GRAIN SIZE AND VOLUME FRACTION OF POLARIZABLE MATERIAL. BUT. - PowerPoint PPT PresentationTRANSCRIPT
CHARGEABILITY AND THE POLARIZABLE VOLUME FRACTION
J.B.MerriamUniversity of Saskatchewan
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
VOLUME FRACTION
CH
AR
GEA
BIL
ITY
m o (V/V
)DATA FROM MAHAN REDMAN AND STRANGWAY
volume fraction 0.006 - 0.06volume fraction 0.006 - 0.09 grain size 28 - 450
grain size 30 - 500
resistivity 15 m - 105 m
10-2
10-1
100
101
102
10310
-3
10-2
10-1
100
FREQUENCY (Hz)
|Z| (
M) o
r PH
ASE
(rad
)
CR
ITIC
AL
FRE
QU
EN
CY
CHARGEABILITY m = 1-RHF/RLF
HIGH FREQUENCY LIMIT RHF=2440
LOW FREQUENCY LIMIT RLF=7300
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
2
4
6
8
10
12
14
16
18
20
VOLUME FRACTION OF INCLUSIONS
bulk/
host
Hashin-ShtrikmanMaxwellStatistical theoryBruggemannWong and Strangway
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110
-3
10-2
10-1
100
101
102
103
VOLUME FRACTION
bulk/
host
HASHIN-SHTRIKMAN RESISTIVITY
CONDUCTIVE INCLUSIONS
grain=1000host
100
10
0.1
0.01
grain=0.001host
RESISTIVE INCLUSIONS
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
VOLUME FRACTION
CH
AR
GEA
BIL
ITY
m o (V/V
)DATA FROM MAHAN REDMAN AND STRANGWAY
volume fraction 0.006 - 0.06volume fraction 0.006 - 0.09 grain size 28 - 450
grain size 30 - 500
resistivity 15 m - 105 m
9m = --------------- (2+5+22)
-4-2
02
46 0
0.20.4
0.60.8
10
0.2
0.4
0.6
0.8
1
VOLUME FRACTION LOG(hosthg/2RS)
CH
AR
GEA
BIL
ITY
(V/V
)
host/
grain=1000
00.2
0.40.6
0.81
-5
0
5
100
0.2
0.4
0.6
0.8
1
VOLUME FRACTION LOG(host/
grain)
CH
AR
GEA
BIL
ITY
(V/V
)
hosthg/2RS = 0.1
-4-2
02
46-5
0
5
100
0.1
0.2
0.3
0.4
LOG(hosthg/2RS)
host/
grain
CH
AR
GEA
BIL
ITY
(V/V
)
= 0.1
10-2
10-1
100
101
102
10310
-3
10-2
10-1
100
101
FREQUENCY (Hz)
|Z| (
MO
hm) o
r PH
ASE
(deg
) LEAD #5 IN SILICA SAND AND WATER
2 4 6 8
x 10-3
0
0.5
1
1.5x 10
-3
real Z (M)
-imag
Z (M
)
NYQUIST
10-2
10-1
100
101
102
10310
-3
10-2
10-1
100
101
FREQUENCY (Hz)
|Z| (
MO
hm) o
r PH
ASE
(deg
) ALUMINIUM IN SILICA SAND AND WATER
7 8 9
x 10-3
0
0.5
1
1.5x 10
-3
real Z (M)
-imag
Z (M
)
NYQUIST
0 0.1 0.2 0.3 0.4 0.5 0.60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
VOLUME FRACTION
CH
AR
GEA
BIL
ITY
(V/V
)
#5 STEEL#5 RUSTED#5 PbBB Cu
10-4
10-3
10-2
10-1
100
101
102
10310
-3
10-2
10-1
100
101
FREQUENCY (Hz)
|Z| (
M
) or P
HA
SE (d
eg)
STEEL, RUSTED STEEL, COPPER AND LEAD AT 13%
fc=0.005 Hz
c= -3.6 deg
fc=0.003 Hz
c= -6.0 deg
STEEL
RUSTED STEEL
fc=3.5 Hz
c=-5.7 deg
COPPER
fc=63 Hz
c=-7 deg
LEAD
0 0.05 0.1 0.15 0.2 0.250
0.1
0.2
0.3
0.4
0.5
0.6
0.7
VOLUME FRACTION
CH
AR
GEA
BIL
ITY
(V/V
)SINGLE CRYSTALS IN WATER
PYRITEARSENOPYRITEMAGNETITEGALENAMARCASITEILMENITEPYRRHOTITERUTILEHEMATITESPHALERITE
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110
-3
10-2
10-1
100
101
102
103
VOLUME FRACTION
bulk/
host
HASHIN-SHTRIKMAN RESISTIVITY
CONDUCTIVE INCLUSIONS
grain=1000host
100
10
0.1
0.01
grain=0.001host
RESISTIVE INCLUSIONS
0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.150.2
0.25
0.3
0.35
0.4
0.45
0.5
VOLUME FRACTION
CH
AR
GEA
BIL
ITY
(V/V
)GRAIN SIZE IS NOT IMPORTANT
1.44cm dia.0.79 cm dia.0.60 cm dia.0.45cm dia.0.29 cm dia.0.27 cm dia.0.21 cm dia.0.16 cm dia.0.10 cm dia.
1 2 3 4 5 6 70.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.3
NORMALIZED SURFACE AREA
CH
AR
GEA
BIL
ITY
(V/V
)SURFACE AREA IS NOT IMPORTANT
0.1 cm dia.0.16 cm dia.0.21 cm dia.0.27 cm dia.0.29 cm dia0.45 cm dia.0.60 cm dia
0 0.05 0.1 0.150
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
VOLUME FRACTION
CH
AR
GEA
BIL
ITY
(V/V
)GRAIN DISTRIBUTION IS NOT IMPORTANT
Pb #5 ALL IN FIRST HALFPb #5 ALL IN MIDDLEUNIFORM
0 0.5 1 1.5 2 2.5 30
0.05
0.1
0.15
0.2
0.25
0.3
0.35
ASPECT RATIO (radius/length)
CH
AR
GEA
BIL
ITY
(V/V
)GRAIN SHAPE IS IMPORTANT
AXIAL Cu CYLINDERSORTHOGONAL CU CYLINDERSAXIAL CYLINDERS (FINITE ELEMENTS)ORTHOGONAL CYLINDERS (FINITE ELEMENTS)SPHERES
CHARGEABILITY DEPENDS ON HOST RESISTIVITY, ELECTROCHEMICAL SURFACE IMPEDANCE, GRAIN SIZE AND VOLUME FRACTION OF POLARIZABLE MATERIAL
BUT
IN MOST CIRCUMSTANCES ONLY THE VOLUME FRACTION OF POLARIZABLE MATERIAL IS IMPORTANT
EXCEPTIONAL CIRCUMSTANCES INCLUDE LARGE GRAIN SIZE, HIGH HOST RESISTIVITY, HIGH GRAIN RESISTIVITY AND LOW SURFACE IMPEDANCE