These poles and zone-lines, whilst inducing fluctuations in data density in the reconstructed datasets, which can prove problematic during post-analysis, are critical for determining information such as angular magnification, as the crystallographic relationships between features are typically well known.

When new minerals are discovered, a standard procedure of scientific analysis is followed, including measures to identify a mineral's formula, its crystallographic data, its optical data, as well as the general physical attributes determined and listed.

The repetitive technique of crystallographic data collection and the often high symmetry of crystalline materials cause the diffractometer to record many symmetry-equivalent reflections multiple times.

Another participant at that meeting, Richard Garwin of IBM, recognized the potential of the method and put Tukey in touch with Cooley, who implemented it for a different ( and less-classified ) problem: analyzing 3d crystallographic data ( see also: multidimensional FFTs ).

In 1929, in order to remove confusion from the proliferation of crystallographic data, Ewald proposed review and collection of the best data into a single publication.

Although never given much credence, these alternative models were finally disproved when Frederick Sanger successfully sequenced insulin and by the crystallographic determination of myoglobin and hemoglobin by Max Perutz and John Kendrew.

This leads to Bragg's law, which describes the condition for constructive interference from successive crystallographic planes ( h, k, and l, as given in Miller Notation )< ref >

The full 3D representation of crystallographic texture is given by the orientation distribution function () which can be achieved through evaluation of a set of pole figures or diffraction spectra.

A few examples of crystallographic defects include vacancy defects ( an empty space where an atom should fit ), interstitial defects ( an extra atom squeezed in where it does not fit ), and dislocations ( see figure at right ).

* Microstructure: scattering centers include internal surfaces such as grain boundaries, crystallographic defects and microscopic pores.

Reflection groups also include Weyl groups and crystallographic Coxeter groups.

This involves measuring the angles of crystal faces relative to theoretical reference axes ( crystallographic axes ), and establishing the symmetry of the crystal in question.

Over the following decade Klug used methods from X-ray diffraction, microscopy and structural modelling to develop crystallographic electron microscopy in which a sequence of two-dimensional images of crystals taken from different angles are combined to produce three-dimensional images of the target.

The electron beam suffers diffraction by the regular crystal lattice planes of the metal atoms and the differing relative angles between the beam and the lattice planes of each grain in the metal's microstructure result in image contrast ( between grains of different crystallographic orientation ).

* parallel cut to one of the octahedron faces ( cutting all 3 cubic axes at the same distance from the crystallographic centre ): three sets of bands running at 60 ° angles each other

The Euler angles then describe the transition from the sample ’ s reference frame into the crystallographic reference frame of each individual grain of the polycrystal.

The dipole density or polarization ( dimensionality ) may easily be calculated for crystals by summing up the dipole moments per volume of the crystallographic unit cell.

The two phases have a tetragonal structure which consists of two sheared crystallographic unit cells.

Within the unit cell is the asymmetric unit, smallest unit the crystal can be divided into using the crystallographic symmetry operations of the space group.

It is therefore questioned whether Crick's colleague, Dr. Max Perutz, acted unethically by allowing Crick access to Dr. Franklin's MRC report about the crystallographic unit of the B-DNA and A-DNA structures.

The space groups in three dimensions are made from combinations of the 32 crystallographic point groups with the 14 Bravais lattices, each of the latter belonging to one of 7 lattice systems.

Discrete point groups in more than one dimension come in infinite families, but from the crystallographic restriction theorem and one of Bieberbach's theorems, each number of dimensions has only a finite number of point groups that are symmetric over some lattice or grid with that number.

Accepted crystallographic symbolism has been used ; ;

A petrographic microscope, which is a optical microscope fitted with cross-Polarizer | polarizing lenses, a conoscopy | conoscopic lens, and compensators ( plates of anisotropic materials ; gypsum plates and quartz wedges are common ), for crystallographic analysis.

Cleavage is not a universal property among minerals ; for example, quartz, consisting of extensively interconnected silica tetrahedra, does not have a crystallographic weakness which would allow it to cleavage, whereas micas — which have perfect basal cleavage — consist of sheets of silica tetrahedra which are very weakly held together.

The distance between two bonded atoms is a sensitive measure of the bond strength and its bond order ; thus, X-ray crystallographic studies have led to the discovery of even more exotic types of bonding in inorganic chemistry, such as metal-metal double bonds ,< ref > metal-metal quadruple bonds ,< ref > and three-center, two-electron bonds.

However, x-ray crystallographic studies of both types of enzymes reveal that, other than containing a critical Mg2 + ion at the catalytic site, they are virtually unrelated to each other ; indeed template-dependent nucleotide polymerizing enzymes seem to have arisen independently twice during the early evolution of cells.

* ( 3, 1 ): Three-dimensional line groups ; with the 3D crystallographic point groups, the rod groups

The substrate preparation includes choosing an appropriate material and its crystallographic orientation ; cleaning it, often with a diamond powder to abrade a non-diamond substrate ; and optimizing the substrate temperature ( about ) during the growth through a series of test runs.

In a crystal lattice, certain crystallographic directions are preferred directions, or easy axes, for the magnetization ; the crystal is easier to magnetize in these directions and requires more energy to magnetize in other directions.

There are infinitely many three-dimensional point groups ; However, the crystallographic restriction of the infinite families of general point groups results in there being only 32 crystallographic point groups.

tensor quantities ; the superscript denotes the crystallographic direction

Data on such comparisons together with data on the effect of light intensity are given in Table 1.

A summary of meteorite data, prepared by Whipple ( 1958 ) on the basis of photographic, visual, and radar evidence, is given in Table 5-1.

The data given in Table 2, show the routine operation of the aerator.

The BOD data are given in Table 4.

References to the data sources are given in the crystal descriptions.

Much emphasis was given to quantitative data, seen as the key to unlocking all of social history.

In the 1990s, Jürgen Schmidhuber described an algorithmic theory of beauty which takes the subjectivity of the observer into account and postulates: among several observations classified as comparable by a given subjective observer, the aesthetically most pleasing one is the one with the shortest description, given the observer ’ s previous knowledge and his particular method for encoding the data.

This value also indicates the meaning of a data element for a given object ( or record ) type.

At any given time, data can be transferred between the master and one other device ( except for the little-used broadcast mode ).

A character encoding system consists of a code that pairs each character from a given repertoire with something else — such as a bit pattern, sequence of natural numbers, octets, or electrical pulses — in order to facilitate the transmission of data ( generally numbers or text ) through telecommunication networks or for data storage.

Similarly, changes in the collection and / or calculation of data on crime may affect the public perceptions of the extent of any given " crime problem ".

Some drives use special techniques, such as Plextor's GigaRec or Sanyo's HD-BURN, to write more data onto a given disc ; these techniques are inherently deviations from the Compact Disc ( Red, Yellow, and / or Orange Book ) standards, making the recorded discs proprietary-formatted and not fully compatible with standard CD players and drives.

Other advantages are that one can easily find the first or last elements on the list ( most likely to be useful in the case of numerically sorted data ), or elements in a given range ( useful again in the case of numerical data, and also with alphabetically ordered data when one may be sure of only the first few letters of the sought item or items ).

There is a close connection between machine learning and compression: a system that predicts the posterior probabilities of a sequence given its entire history can be used for optimal data compression ( by using arithmetic coding on the output distribution ), while an optimal compressor can be used for prediction ( by finding the symbol that compresses best, given the previous history ).

Data compression can be viewed as a special case of data differencing: Data differencing consists of producing a difference given a source and a target, with patching producing a target given a source and a difference, while data compression consists of producing a compressed file given a target, and decompression consists of producing a target given only a compressed file.