Atomic scattering factors - Revision history

KevinYager: /* Related forms */

2015-01-28T19:43:09Z

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2015-01-28T19:39:12Z

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2015-01-28T19:36:20Z

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2015-01-20T17:20:23Z

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2015-01-20T17:20:12Z

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2014-06-07T15:54:16Z

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2014-06-07T15:51:03Z

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2014-06-07T15:42:31Z

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2014-06-07T15:21:01Z

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@@ Line 40: / Line 40: @@
 | <math>f_1 = \frac{2 \pi M_a}{ \rho N_a r_e \lambda^2 } \delta</math>
 | <math>f_1 = \frac{M_a}{\rho N_a r_e} \mathrm{Re}(\mathrm{SLD}) </math>
-| <math> f_1 = \rho_e</math>
+| <math> f_1 = \frac{M_a}{\rho N_a} \rho_e</math>
 |-
 | <math>\theta_c = \sqrt{ \frac{ \rho N_a r_e \lambda^2 }{ \pi M_a} f_1 }</math>
@@ Line 47: / Line 47: @@
 | <math>\theta_c = \sqrt{ 2 \delta }</math>
 | <math>\theta_c\approx \sqrt{\frac{\lambda^2 \mathrm{SLD} }{\pi}}</math>
-| <math>\theta_c = \rho_e</math>
+| <math>\theta_c = \sqrt{ \frac{r_e \lambda^2}{\pi} \rho_e }</math>
 |-
 | <math>q_c = \sqrt{ \frac{ 16 \pi \rho N_a r_e  }{ M_a} f_1 }</math>
@@ Line 54: / Line 54: @@
 | <math>q_c \approx \frac{4\pi}{\lambda}\sqrt{ 2\delta }</math>
 | <math>q_c = \sqrt{ 16 \pi \mathrm{SLD} }</math>
-| <math>q_c = \rho_e</math>
+| <math>q_c = 4 \sqrt{ \pi r_e \rho_e}</math>
 |-
 | <math>\delta = \frac{ \rho N_a r_e \lambda^2 }{2 \pi M_a} f_1</math>

@@ Line 40: / Line 40: @@
 | <math>f_1 = \frac{2 \pi M_a}{ \rho N_a r_e \lambda^2 } \delta</math>
 | <math>f_1 = \frac{M_a}{\rho N_a r_e} \mathrm{Re}(\mathrm{SLD}) </math>
 |-
 | <math>\theta_c = \sqrt{ \frac{ \rho N_a r_e \lambda^2 }{ \pi M_a} f_1 }</math>
@@ Line 46: / Line 47: @@
 | <math>\theta_c = \sqrt{ 2 \delta }</math>
 | <math>\theta_c\approx \sqrt{\frac{\lambda^2 \mathrm{SLD} }{\pi}}</math>
 |-
 | <math>q_c = \sqrt{ \frac{ 16 \pi \rho N_a r_e  }{ M_a} f_1 }</math>
@@ Line 52: / Line 54: @@
 | <math>q_c \approx \frac{4\pi}{\lambda}\sqrt{ 2\delta }</math>
 | <math>q_c = \sqrt{ 16 \pi \mathrm{SLD} }</math>
 |-
 | <math>\delta = \frac{ \rho N_a r_e \lambda^2 }{2 \pi M_a} f_1</math>
@@ Line 58: / Line 61: @@
 | <math>\delta</math>
 | <math>\delta \approx \frac{\lambda^2}{2 \pi}\mathrm{Re}(\mathrm{SLD})</math>
 |-
 | <math>\mathrm{Re}(\mathrm{SLD}) = \frac{\rho N_a r_e}{M_a} f_1</math>
@@ Line 64: / Line 68: @@
 | <math>\mathrm{Re}(\mathrm{SLD}) \approx \frac{2 \pi}{\lambda^2}\delta</math>
 | <math>\mathrm{Re}(\mathrm{SLD})</math>
 |-
 | <math>\rho_e = \frac{\rho N_a}{M_a} f_1</math>
@@ Line 70: / Line 75: @@
 | <math>\rho_e = \frac{2 \pi}{r_e \lambda^2} \delta</math>
 | <math>\rho_e = \frac{ \mathrm{Re}(\mathrm{SLD}) }{r_e}</math>
 |}

@@ Line 31: / Line 31: @@
 * '''Real [[refractive index]]''' <math>\delta</math>, the refractive component of the refractive index.
 * '''Real [[Scattering Length Density]]''' <math>\mathrm{Re}(\mathrm{SLD})</math>, the primary (non-absorptive) component of the scattering contrast.
 {| class="wikitable"
@@ Line 63: / Line 64: @@
 | <math>\mathrm{Re}(\mathrm{SLD}) \approx \frac{2 \pi}{\lambda^2}\delta</math>
 | <math>\mathrm{Re}(\mathrm{SLD})</math>
 |}

@@ Line 69: / Line 69: @@
 ==See Also==
-* [[Atomic form factor]]
+* [[Atomic Form Factor]]
 * [http://henke.lbl.gov/optical_constants/asf.html Periodic table of atomic scattering factors]: Useful tool for looking up the values for any element.
 * [https://subversion.xor.aps.anl.gov/trac/pyFprime/ APS Python code for calculating ''f'']
 * [http://reference.iucr.org/dictionary/Atomic_scattering_factor Online Dictionary of Crystallography: Atomic scattering factor]

@@ Line 69: / Line 69: @@
 ==See Also==
 * [http://henke.lbl.gov/optical_constants/asf.html Periodic table of atomic scattering factors]: Useful tool for looking up the values for any element.
 * [https://subversion.xor.aps.anl.gov/trac/pyFprime/ APS Python code for calculating ''f'']
 * [http://reference.iucr.org/dictionary/Atomic_scattering_factor Online Dictionary of Crystallography: Atomic scattering factor]

@@ Line 38: / Line 38: @@
 | <math>f_1 = \frac{ M_a}{ 16 \pi \rho N_a r_e  } q_c^2</math>
 | <math>f_1 = \frac{2 \pi M_a}{ \rho N_a r_e \lambda^2 } \delta</math>
-| <math>f_1 \approx \frac{M_a}{\rho N_a r_e} \mathrm{Re}(\mathrm{SLD}) </math>
+| <math>f_1 = \frac{M_a}{\rho N_a r_e} \mathrm{Re}(\mathrm{SLD}) </math>
 |-
 | <math>\theta_c = \sqrt{ \frac{ \rho N_a r_e \lambda^2 }{ \pi M_a} f_1 }</math>
@@ Line 49: / Line 49: @@
 | <math>q_c = \frac{4 \pi}{\lambda}\sin\theta_c</math>
 | <math>q_c</math>
-| <math>q_c = \frac{4\pi}{\lambda}\sqrt{ 2\delta }</math>
+| <math>q_c \approx \frac{4\pi}{\lambda}\sqrt{ 2\delta }</math>
 | <math>q_c = \sqrt{ 16 \pi \mathrm{SLD} }</math>
 |-
 | <math>\delta = \frac{ \rho N_a r_e \lambda^2 }{2 \pi M_a} f_1</math>
 | <math>\delta = \frac{\theta_c^2}{2}</math>
-| <math>\delta = \frac{\lambda^2}{32 \pi^2}q_c^2</math>
+| <math>\delta \approx \frac{\lambda^2}{32 \pi^2}q_c^2</math>
 | <math>\delta</math>
 | <math>\delta \approx \frac{\lambda^2}{2 \pi}\mathrm{Re}(\mathrm{SLD})</math>
 |-
-| <math>\mathrm{Re}(\mathrm{SLD}) \approx \frac{\rho N_a r_e}{M_a} f_1</math>
+| <math>\mathrm{Re}(\mathrm{SLD}) = \frac{\rho N_a r_e}{M_a} f_1</math>
 | <math>\mathrm{Re}(\mathrm{SLD}) \approx \frac{\pi}{\lambda^2}\theta_c^2</math>
 | <math>\mathrm{Re}(\mathrm{SLD}) = \frac{q_c^2}{16\pi}</math>

@@ Line 35: / Line 35: @@
 |-
 | <math>f_1</math>
-| <math>f_1 = \frac{ \pi}{ n_a r_e \lambda^2 } \theta_c^2</math>
+| <math>f_1 = \frac{ \pi M_a}{ \rho N_a r_e \lambda^2 } \theta_c^2</math>
+|
 |-
-| <math>\theta_c = \sqrt{ \frac{ n_a r_e \lambda^2 }{ \pi} f_1 }</math>
+| <math>\theta_c = \sqrt{ \frac{ \rho N_a r_e \lambda^2 }{ \pi M_a} f_1 }</math>
 | <math>\theta_c</math>
 | <math>\theta_c \approx \frac{\lambda}{4 \pi} q_c </math>
@@ Line 52: / Line 52: @@
 | <math>q_c = \sqrt{ 16 \pi \mathrm{SLD} }</math>
 |-
-| <math>\delta = \frac{ n_a r_e \lambda^2 }{2 \pi} f_1</math>
+| <math>\delta = \frac{ \rho N_a r_e \lambda^2 }{2 \pi M_a} f_1</math>
 | <math>\delta = \frac{\theta_c^2}{2}</math>
+|
@@ Line 58: / Line 58: @@
+|
 |-
-| <math>\mathrm{Re}(\mathrm{SLD}) \approx n_a r_e f_1</math>
+| <math>\mathrm{Re}(\mathrm{SLD}) \approx \frac{\rho N_a r_e}{M_a} f_1</math>
 | <math>\mathrm{Re}(\mathrm{SLD}) \approx \frac{\pi}{\lambda^2}\theta_c^2</math>
 | <math>\mathrm{Re}(\mathrm{SLD}) = \frac{q_c^2}{16\pi}</math>