Scattering Length Density - Revision history

KevinYager at 19:09, 21 January 2015

2015-01-21T19:09:19Z

KevinYager: /* X-ray scattering lengths */

2015-01-21T19:08:09Z

‎X-ray scattering lengths

66.249.83.102 at 19:41, 14 June 2014

2014-06-14T19:41:15Z

KevinYager: /* Calculating */

2014-06-07T15:26:25Z

‎Calculating

KevinYager: /* Neutron scattering lengths */

2014-06-06T04:50:14Z

‎Neutron scattering lengths

KevinYager: /* Energy dependence */

2014-06-06T04:46:21Z

‎Energy dependence

KevinYager: /* See Also */

2014-06-05T21:27:49Z

‎See Also

130.199.3.165: /* Calculating */

2014-06-05T13:06:32Z

‎Calculating

68.194.136.6 at 00:27, 5 June 2014

2014-06-05T00:27:10Z

KevinYager: /* Calculating */

2014-06-04T18:28:56Z

‎Calculating

← Older revision		Revision as of 19:09, 21 January 2015
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−	The '''Scattering Length Density''' ('''SLD''', sometimes denoted ''N<sub>b</sub>'') is a measure of the scattering power of a material. It increases with the physical density (how tightly packed the scattering entities are), as well as the intrinsic scattering power of the 'scattering entities'. For [[x-rays]], the scattering arises from the electron density, whereas for neutrons, the scattering arises from the nuclear scattering lengths.	+	The '''Scattering Length Density''' ('''SLD''', sometimes denoted ''N<sub>b</sub>'') is a measure of the scattering power of a material. It increases with the physical density (how tightly packed the scattering entities are), as well as the intrinsic scattering power of the 'scattering entities'. For [[x-rays]], the scattering arises from the electron density, whereas for [[neutrons]], the scattering arises from the nuclear scattering lengths.

	==Calculating==		==Calculating==

@@ Line 15: / Line 15: @@
 ===X-ray scattering lengths===
-For x-rays, the scattering arises from the interaction between the incident wave and the electron clouds of the atoms in the material. Thus, the scattering power scales with electron density in the material (with corrections for additional effects, such as [[resonant scattering]], a.k.a. absorption lines). In practice, one can look up tabulated values of the [[atomic scattering factor]] for the atom in question. From this, one can compute the scattering length using:
+For x-rays, the scattering arises from the interaction between the incident wave and the [[electron cloud]]s of the [[Atomic Form Factor|atoms]] in the material. Thus, the scattering power scales with electron density in the [[material]] (with corrections for additional effects, such as [[resonant scattering]], a.k.a. absorption lines). In practice, one can look up tabulated values of the [[atomic scattering factor]] for the atom in question. From this, one can compute the scattering length using:
 :<math>
 \begin{alignat}{2}

← Older revision		Revision as of 19:41, 14 June 2014
Line 1:		Line 1:
−	The '''Scattering Length Density''' ('''SLD''', sometimes denoted ''N<sub>b</sub>'') is a measure of the scattering power of a material. It increases with the physical density (how tightly packed the scattering entities are), as well as the intrinsic scattering power of the 'scattering entities'. For x-rays, the scattering arises from the electron density, whereas for neutrons, the scattering arises from the nuclear scattering lengths.	+	The '''Scattering Length Density''' ('''SLD''', sometimes denoted ''N<sub>b</sub>'') is a measure of the scattering power of a material. It increases with the physical density (how tightly packed the scattering entities are), as well as the intrinsic scattering power of the 'scattering entities'. For [[x-rays]], the scattering arises from the electron density, whereas for neutrons, the scattering arises from the nuclear scattering lengths.

	==Calculating==		==Calculating==

@@ Line 4: / Line 4: @@
 SLD can be computed from the scattering lengths and material densities. Specifically:
 :<math>\mathrm{SLD} = \frac{\sum_{i=1}^{N}b_i}{V_m}</math>
-where we sum the scattering length contributions (''b<sub>i</sub>'') from the ''N'' atoms within the [[unit cell]], and divide by the volume, ''V<sub>m</sub>'' of this 'unit cell'. Note that the 'unit cell' need not be a crystallographic unit cell: it is simply a representative volume of the material in question: the atoms within it may be arranged randomly (e.g. amorphous material) or in a crystalline way. For instance for a single molecule, ''V<sub>m</sub>'' is simply the molecular volume, and the sum includes all the atoms in the molecule. In general we don't know what the appropriate 'molecular volume' should be, but we can compute it from the known bulk density of the material (<math>\rho</math>) and the molecular weight (''MW''):
+where we sum the scattering length contributions (''b<sub>i</sub>'') from the ''N'' atoms within the [[unit cell]], and divide by the volume, ''V<sub>m</sub>'' of this 'unit cell'. Note that the 'unit cell' need not be a crystallographic unit cell: it is simply a representative volume of the material in question: the atoms within it may be arranged randomly (e.g. amorphous material) or in a crystalline way. For instance for a single molecule, ''V<sub>m</sub>'' is simply the molecular volume, and the sum includes all the atoms in the molecule. In general we don't know what the appropriate 'molecular volume' should be, but we can compute it from the known bulk density of the material (<math>\rho</math>) and the molecular weight (''M''):
-::<math>V_m = \frac{ \mathrm{MW} }{\rho N_a}</math>
+::<math>V_m = \frac{ M }{\rho N_a}</math>
 Where ''N<sub>a</sub>'' is the Avogadro constant. Thus:
-:<math>\mathrm{SLD} = \frac{\sum_{i=1}^{N}b_i}{V_m} = \frac{\rho N_a \sum_{i=1}^{N}b_i}{\sum_{i=1}^{N}\mathrm{M}_i} </math>
+:<math>\mathrm{SLD} = \frac{\sum_{i=1}^{N}b_i}{V_m} = \frac{\rho N_a \sum_{i=1}^{N}b_i}{\sum_{i=1}^{N}M_i} </math>
-where M<sub>''i''</sub> is the atomic molar mass for each element. Note that the above sum is over ''every atom'' in the representative volume (i.e. a particular atom repeated twice should be added twice). The equation can be recast in terms of weighting factors (stoichiometric numbers in a chemical formula, or concentrations in a mixture) to yield:
+where ''M<sub>i</sub>'' is the atomic molar mass for each element. Note that the above sum is over ''every atom'' in the representative volume (i.e. a particular atom repeated twice should be added twice). The equation can be recast in terms of weighting factors (stoichiometric numbers in a chemical formula, or concentrations in a mixture) to yield:
-:<math>\mathrm{SLD} = \frac{\rho N_a \sum_{i=1}^{N} c_i b_i}{\sum_{i=1}^{N} c_i \mathrm{M}_i} </math>
+:<math>\mathrm{SLD} = \frac{\rho N_a \sum_{i=1}^{N} c_i b_i}{\sum_{i=1}^{N} c_i M_i} </math>
 ===[[Neutron scattering lengths]]===

@@ Line 11: / Line 11: @@
 :<math>\mathrm{SLD} = \frac{\rho N_a \sum_{i=1}^{N} c_i b_i}{\sum_{i=1}^{N} c_i \mathrm{M}_i} </math>
-===Neutron scattering lengths===
+===[[Neutron scattering lengths]]===
-For neutrons, the ''b<sub>i</sub>'' in the above equation are the neutron scattering lengths for the atoms in question. This value depends on the strength of the interaction between a neutron and a given nucleus. It is in general not easy to predict this quantity theoretically; instead experiments are performed to tabulate the scattering lengths. Refer to the [http://www.ill.eu/quick-links/publications/ neutron data booklet] (starting on page 1.1-8) for tables of ''b<sub>i</sub>'' for known isotopes.
+For neutrons, the ''b<sub>i</sub>'' in the above equation are the [[neutron scattering lengths]] for the atoms in question. This value depends on the strength of the interaction between a neutron and a given nucleus. It is in general not easy to predict this quantity theoretically; instead experiments are performed to tabulate the scattering lengths. Refer to the [http://www.ill.eu/quick-links/publications/ neutron data booklet] (starting on page 1.1-8) for tables of ''b<sub>i</sub>'' for known isotopes.
 ===X-ray scattering lengths===

@@ Line 51: / Line 51: @@
 [[Image:Gold-SLD.png|400px]]
 ==See Also==
 * [[Critical angle]]
 * [http://www.ncnr.nist.gov/resources/activation/ SLD calculator]: NIST Center for Neutron Research calculator for predicting SLD.