Column
Penetration depth (effective thickness)
The following formula gives the ratio
G
x
between the intensity of diffracted x-rays from a sample of infinite
thickness and the intensity of diffracted x-rays from a sample with a specific finite thickness of x cm.
⎟
⎠
⎞
⎜
⎝
⎛ −
−
=
=
∫
∫
∞
θ
μ
sin
2
exp
1
0
0
x
dI
dI
G
D
x
D
x
Substitute the values for angle
θ
of the incident x-ray beam and x-ray absorption coefficient
μ
(/cm) in the following
formula to obtain
x
cm, the effective thickness.
μ
θ
μ
θ
2
sin
2
sin
)
1
ln(
x
x
K
G
x
=
−
−
=
where,
(
)
x
x
G
K
−
−
=
1
ln
Diffracted x-ray
utilization rate
G
x
(%)
50
75
90
95
99
99.5
K
x
0.69
1.39
2.30
3.00
4.61
6.91
The following table shows the results of calculations of the sample thicknesses x cm that give a diffracted x-ray
usage rate of 90% when
K
x
= 2.30 and
θ
= 90
°
.
密度ρ
(g/cm
3
)
MoKα
CuKα
CoKα
CrKα
MoKα
CuKα
CoKα
CrKα
α‐Al
2
O
3
3.97/2
3.34
31.1
48.0
97.6
1.74
0.187
0.121
0.060
Si
2.42/2
6.44
60.6
93.3
189
1.48
0.157
0.102
0.050
α‐SiO
2
2.65/2
3.71
34.5
53.1
108
2.34
0.252
0.164
0.080
CaCO
3
2.71/2
8.02
70.9
107
205
1.06
0.120
0.079
0.041
α‐Fe
2
O
3
5.26/2
27.3
216
42.7
86.5
0.160
0.020
0.103
0.051
ZnO
5.60/2
44.7
50.7
78.2
159
0.092
0.081
0.053
0.026
Ag
2
O
7.22/2
24.1
204
300
548
0.132
0.016
0.011
0.0058
PbO I(正方)
9.53/2
112
216
311
540
0.022
0.011
0.0078
0.0089
Al
2.70
5.16
48.6
74.8
152
0.826
0.088
0.057
0.028
α‐Fe
7.86
38.5
308
52.8
108
0.038
0.0048
0.028
0.014
SUS(18-8)
7.93
37.9
278
110
106
0.038
0.0052
0.013
0.014
Cu
8.92
50.9
52.9
81.6
166
0.025
0.024
0.016
0.0078
Pb
11.34
120
232
334
579
0.0085
0.0044
0.0030
0.0018
ポリエチレン
0.93
0.59
4.0
6.1
12.5
21.0
3.09
2.02
0.989
塩化ビニール
1.41
6.73
62.0
94.2
186.2
1.21
0.132
0.086
0.044
Si
2.42
6.44
60.6
93.3
189
0.738
0.079
0.051
0.025
α‐SiO
2
2.65
3.71
34.5
53.1
108
1.17
0.126
0.082
0.040
質量吸収係数μ/ρ(cm
2
/g)
90%利用率の厚さ(mm)
物質
粉末
金属
ポリマー
単結晶
Substance
Powder
(tetragonal)
Metal
Density
ρ
Mass absorption coefficient
μ
/
ρ
(cm
2
/g)
Thickness for 90% utilization rate (mm)
Polymer Polyethylene
Vinyl chloride
Single crystal
substance
Содержание 2080A211
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