Systems and methods for determining a packing fraction of a substance
View Patent ↗A method for determining a type of a substance is described. The method includes determining a packing fraction of the substance from a molecular interference function.
1. A method for determining a type of a substance, said method comprising:
determining a molecular interference function as a ratio of a measured diffraction profile of the substance and a theoretical total free atom scatter cross-section; and
determining a packing fraction of the substance from the molecular interference function.
2. A method in accordance with claim 1 further comprising removing a plurality of cryslalline interference peaks from a diffraction profile of the substance before said determining the packing fraction of the substance.
3. A method in accordance with claim 1 wherein the diffraction profile is obtained by receiving scattered x-rays from the substance.
4. A method in accordance with claim 1 further comprising
generating the theoretical total free atom scatter cross-section based on an effective atomic number of the substance.
5. A method in accordance with claim 1 further comprising calculating a second moment from the molecular interference function.
6. A method in accordance with claim 1 further comprising:
calculating a second moment from the molecular interference function; and
generating a packing fraction from the second moment.
7. A processor for determining a type of a substance, said processor configured to:
determine a molecular interference function as a ratio of a measured diffraction profile of the substance and a theoretical total free atom scatter cross-section; and
determine a packing fraction of the substance from the molecular interference function.
8. A processor in accordance with claim 7 wherein said processor further configured to remove a plurality of crystalline interference peaks from a diffraction profile of the substance before determining the packing fraction of the substance.
9. A processor in accordance with claim 7 wherein the diffraction profile is obtained by receiving scattered x-rays from the substance.
10. A processor in accordance with claim 7 wherein said processor further configured to
generate the theoretical total free atom scatter cross-section based on an effective atomic number of the substance.
11. A processor in accordance with claim 7 wherein said processor further configured to calculate a second moment from the molecular interference function.
12. A processor in accordance with claim 7 wherein said processor further configured to:
calculate a second moment from the molecular interference function; and
generate a packing fraction from the second moment.
13. A processor in accordance with claim 7 wherein said processor further configured to calculate a second moment from the molecular interference function by applying
X
2
S
=
∫
0
∞
x
2
I
min
(
x
)
ⅆ
x
∫
0
∞
I
min
(
x
)
ⅆ
x
,
where X2S is the second moment, x is a momentum transfer, and I min (X) is an iteration cycle amplitude determined from the molecular interference function.
14. A processor in accordance with claim 7 wherein said processor further configured to:
calculate a second moment from the molecular interference function; and
generate a packing fraction from the second moment by applying η=a(X2S) where η is the packing fraction, X2S is the second moment and a is a coefficient received by the processor.
15. A system for determining a type of substance, said system comprising:
an x-ray source configured to generate x-rays;
a detector configured to receive primary and scattered radiation after the x-rays pass through the substance; and
a processor configured to determine a molecular interference function as a ratio of a measured diffraction profile of the substance and a theoretical total free atom scatter cross-section and determine a packing fraction of the substance from the molecular interference function.
16. A system in accordance with claim 15 wherein said processor further configured to remove a plurality of crystalline interference peaks from a diffraction profile of the substance before determining the packing fraction of the substance.
17. A system in accordance with claim 15 wherein the diffraction profile is obtained by receiving scattered x-rays from the substance.
18. A system in accordance with claim 15 wherein said processor further configured to
generate the theoretical total free atom scatter cross-section based on an effective atomic number of the substance.
19. A system in accordance with claim 15 wherein said processor further configured to calculate a second moment from the molecular interference function.