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In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a critical tool in the interpretation of scattering patterns ( interference patterns ) obtained in X-ray , electron and neutron ...
The Patterson function is used to solve the phase problem in X-ray crystallography.It was introduced in 1935 by Arthur Lindo Patterson while he was a visiting researcher in the laboratory of Bertram Eugene Warren at MIT.
The structure function, like the fragmentation function, is a probability density function in physics. It is somewhat analogous to the structure factor in solid-state physics , and the form factor (quantum field theory) .
In condensed matter physics, the dynamic structure factor (or dynamical structure factor) is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization of the structure factor that considers correlations in both space and time.
Small molecules (up to ca. 1000 atoms) usually form better-ordered crystals than large molecules, and thus it is possible to attain lower R-factors. In the Cambridge Structural Database of small-molecule structures, more than 95% of the 500,000+ crystals have an R-factor lower than 0.15, and 9.5% have an R-factor lower than 0.03.
These normally indicate the presence of some medium range order corresponding to structure in the 2nd and higher coordination shells in g(r). At high-q the structure is typically a decaying sinusoidal oscillation, with a 2π/r 1 wavelength where r 1 is the 1st shell peak position in g(r). At very high-q the S(q) tends to 1, consistent with its ...
Eq. 2 is the cumulative Weibull distribution with scale parameter and shape parameter ; = [^ ()] = constant factor depending on the structure geometry, = structure volume; = relative (size-independent) coordinate vectors, ^ = dimensionless stress field (dependent on geometry), scaled so that the maximum stress be 1; = number of spatial ...
Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion.The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States Customary Units system).