The symmetry of the Patterson Function (the symmetry of Patterson space) is higher than the one of the electron density function (the crystal), so that if the crystal symmetry can be represented by one of the 230 space groups, the corresponding Patterson symmetry will be represented by only 24 space groups..
What is the Patterson function in crystallography?
He defined a function, called the Patterson function (symbolized by P(uvw)), which is the self-convolution of the electron density and displays a set of interatomic vectors. The Fourier transform of this function results in the intensities. where u, v, and w are the coordinates of a vector..
What is the Patterson method of crystallography?
The Patterson method, due to Arthur Lindo Patterson in 1935, is an important technique for obtaining a model structure without knowing the phases. A Fourier map is constructed using the intensities (to be more correct, the squares of the moduli of the structure factors) with all contributions given the same phase..
What is the Patterson method of phase problem?
The Patterson function is obtained by calculating a map using the squared structure factor magnitudes, and all the phases set to zero. Instead of peaks at the atomic positions, the Patterson map shows peaks at every position that corresponds to an interatomic vector in the structure..
In physics, the phase problem is the problem of loss of information concerning the phase that can occur when making a physical measurement. The name comes from the field of X-ray crystallography, where the phase problem has to be solved for the determination of a structure from diffraction data.
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. It is essentially the Fourier transform of the intensities rather than the structure factors.
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. Wikipedia
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
How is Patterson function derived from a crystal with 3 atoms?
Projection of the Patterson functionderived from a crystal with three atoms
To obtain this functiongraphically from the known structure of a crystal (left figure)all interatomic vectors are plotted (central figure) andmoved parallel to themselves to the origin of the unit cell ofthePatterson space (right figure)
What is the difference between a real crystal cell and a Patterson cell?
Vectors in a Patterson correspond to vectors in the real crystal cell, translated to the Patterson origin
Their weights are proportional to the product of electron densities at the tips of the vectors in the real cell
The Patterson unit cell has the same size as the real crystal cell
What is the Patterson method?
The Patterson method, due to Arthur Lindo Patterson in 1935, is an important technique for obtaining a model structure without knowing the phases
A Fourier map is constructed using the intensities (to be more correct, the squares of the moduli of the structure factors) with all contributions given the same phase
The Patterson function is important in crystallography because it can be computed without phase information. We can also compute a Patterson from a trial atomic model and compare it to the observed Patterson. When the model is oriented correctly and placed in the correct position in the unit cell, the two Pattersons should be similar.
British crystallographer (1902–1966)
Arthur Lindo Patterson was a pioneering British X-ray crystallographer. Patterson was born to British parents in New Zealand in 1902. Shortly afterwards the family moved to Montreal, Canada and later to London, England. In 1920 Patterson moved to Canada for college at McGill University, Montreal. Firstly he concentrated on Mathematics and but then changed his major to Physics. He received his bachelor's degree in 1923 and a master's in 1924. His master's thesis was on the production of hard X-rays by interaction of radium β rays with solids.
Patterson crystallography
Topics referred to by the same term
Patterson may refer to:
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.
