Rigaku SmartLab - Page 26

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
exp1
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)1ln(
xx
KG
x =
−−
=
where,
(
)
xx
GK
−
−
=
1ln
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 absor
p
tion coefficient
μ
/
ρ
(
cm
2
/g)
Thickness for 90% utilization rate (mm)
Polymer
Pol
y
eth
y
lene
Vin
y
l chloride
Single crystal
substance