Under this assumption the space group must be Af and the following are the positions of the atoms in the unit cell.

The only effect of lack of a center would then be to release the hydrogen atoms to occupy general, rather than special, positions along the ( 111 ) axis.

If the Af bond is linear then there are three reasonable positions for the hydrogen atoms: ( 1 ) The hydrogen atoms are centered and hence all lie on a sheet midway between the oxygen sheets ; ;

Furthermore, in very small crystals a large fraction of the atoms are located at or near the surface of the crystal ; relaxation of the surface and interfacial effects distort the atomic positions, decreasing the structural order.

* Basis ( crystal structure ), the positions of the atoms inside the unit cell

A molecular structure depicts the bonds and relative positions of atoms in a molecule such as that in Paclitaxel shown here

Examples of such properties are structure ( i. e. the expected positions of the constituent atoms ), absolute and relative ( interaction ) energies, electronic charge distributions, dipoles and higher multipole moments, vibrational frequencies, reactivity or other spectroscopic quantities, and cross sections for collision with other particles.

* Antisite defects occur in an ordered alloy or compound when atoms of different type exchange positions.

The ability to determine the positions of atoms within materials has made the HRTEM an important tool for nano-technologies research and development.

Kekulé's idea of assigning certain atoms to certain positions within the molecule, and schematically connecting them using what he called their " Verwandtschaftseinheiten " (" affinity units ", now called " valences " or " bonds "), was based largely on evidence from chemical reactions, rather than on instrumental methods that could peer directly into the molecule, such as X-ray crystallography.

This process is self-regulating since the atoms that are at positions of high local curvature, such as adatoms or ledge atoms, are removed preferentially.

About 1902 Lewis started to use unpublished drawings of cubical atoms in his lecture notes, in which the corners of the cube represented possible electron positions.

Pyrimidine is a heterocyclic aromatic organic compound similar to benzene and pyridine, containing two nitrogen atoms at positions 1 and 3 of the six-member ring.

It is isomeric with two other forms of diazine: Pyridazine, with the nitrogen atoms in positions 1 and 2 ; and Pyrazine, with the nitrogen atoms in positions 1 and 4.

X-Ray diffraction studies on the hydrogen urate ion in crystals of ammomium hydrogen urate, formed in vivo as gouty deposits, reveal the keto-oxygen in the 2 position of a tautomer of the purine structure exists as a hydroxyl group and the two flanking nitrogen atoms at the 1 and 3 positions share the ionic charge in the six membered pi-resonance-stabilized ring.

From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder and various other information.

However, as computational and experimental methods improved over the next decades, it became feasible to deduce reliable atomic positions for more complicated two-and three-dimensional arrangements of atoms in the unit-cell.

Therefore, neutron scattering is very useful for observing the positions of light atoms with few electrons, especially hydrogen, which is essentially invisible in the X-ray diffraction.

The atoms in a crystal are not static, but oscillate about their mean positions, usually by less than a few tenths of an angstrom.

Random movement of all molecules occurs so that after a period molecules are found remote from their original positions.

Thus, the molecules are free to flow and their center of mass positions are randomly distributed as in a liquid, but still maintain their long-range directional order.

This is caused by forces that distort the positions, orientations, or shape of the molecules constituting the material.

For instance, a gas containing many molecules may require a separate dimension for each particle's x, y and z positions and momenta as well as any number of other properties.

In a hypothesized process of mechanosynthesis, reactive molecules would be attached to molecular mechanical systems, and their encounters would result from mechanical motions bringing them together in planned sequences, positions, and orientations.

where k = 1. 3806505 ( 24 ) × 10 < sup >− 23 </ sup > J K < sup >− 1 </ sup > is Boltzmann's constant, and the logarithm is taken to the natural base e. W is the Wahrscheinlichkeit, the frequency of occurrence of a macrostate or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system — number of ( unobservable ) " ways " in the ( observable ) thermodynamic state of a system can be realized by assigning different positions and momenta to the various molecules.

is the number of molecules which all have positions lying within a volume element d < sup > 3 </ sup > r about r and momenta lying within a momentum space element d < sup > 3 </ sup > p about p, at time t. Integrating over a region of position space and momentum space gives the total number of particles which have positions and momenta in that region:

However, linear molecules only have two rotations because rotations along the bond axis do not change the positions of the atoms in the molecule.

Fluctuations in temperature within a freezer also contribute to the onset of freezer burn because such fluctuations set up temperature gradients within the solid food and air in the freezer, which create additional impetus for water molecules to move from their original positions.

These enzymes are called restriction endonucleases or restriction enzymes, and they are able to cleave DNA molecules at the positions at which particular short sequences of bases are present

It has a peculiar crystal structure, whose cell spans 16 molecules in asymmetric positions and orientations.

In a gas, the relative positions of the atoms or molecules are completely random.

The perylene molecule consists of two naphthalene molecules connected by a carbon-carbon bond at the 1 and 8 positions on both molecules.

Hexameters also have a primary caesura — a break in sense, much like the function of a comma in prose — at one of several normal positions: After the first syllable in the third foot ( the " masculine " caesura ); after the second syllable in the third foot if the third foot is a dactyl ( the " feminine " caesura ); after the first syllable of the fourth foot ; or after the first syllable of the second foot ( the latter two often occur together in a line, breaking it into three separate units ).

In certain positions, English non-aspirated consonants can occur as variants of aspirated ones.

The fact that how fast reactions occur can often be specified with just a few concentrations and a temperature, instead of needing to know all the positions and speeds of every molecule in a mixture, is a special case of another key concept in physical chemistry, which is that to the extent an engineer needs to know, everything going on in a mixture of millions of billions of billions of particles can often be described by just a few variables like pressure, temperature, and concentration.

In most cases a game of Reversi reaches an end in which all 64 squares are filled, but positions in which the board is not full and neither player may make a legal move also occur with some frequency.

Code points with lower numerical values ( i. e. earlier code positions in the Unicode character set, which tend to occur more frequently in practice ) are encoded using fewer bytes.

They occur at specified positions in the frame, do not carry information, and are usually repetitive.

Note that the arguments of the binomial coefficient are decremented due to order: the last " failure " must occur last, and so the other events have one fewer positions available when counting possible orderings.

They did not show the polarization effect, suggesting that it does not necessarily occur when people simply hold opposing positions, but rather when they openly commit to them.

Schwa in English is limited to unstressed positions, but in some other languages it can occur as a stressed vowel.

Such positions can occur in the household of a non-member of a ruling family, such as a prince of the church:

* The Equivalence Constraint: code-switching can occur only in positions where " the order of any two sentence elements, one before and one after the switch, is not excluded in either language.

The transition between these two structures requires very little thermal activation energy because it is a diffusionless transformation, which results in the subtle but rapid rearrangement of atomic positions, and has been known to occur even at cryogenic temperatures.

* ILS Tutorial Animation Illustrates and describes how are ILS navigation signals displayed on board of an aircraft in various positions, which may occur during a safe approach for landing.

The order of these affixes is fixed, so we may view any given noun or verb as a stem followed by several inflectional slots, i. e. positions in which inflectional suffixes may occur.

However, while problems often present very artificial looking positions, studies often appear that they could occur in a game.

A power vacuum can also occur following a constitutional crisis in which large portions of the government resign or are removed, creating unclear issues regarding succession to positions of power.

There have been 50 to 100 reforms of the traditional Chinese calendar over 2500 years, most of which were intended to better fit the calendar months to astronomical lunations and to more accurately add the extra month so that the regular months maintain their proper seasonal positions, even though each seasonal marker can occur anywhere within its month.

The game tree is typically vastly larger than the state space because the same positions can occur in many games by making moves in a different order ( for example, in a tic-tac-toe game with two X and one O on the board, this position could have been reached in two different ways depending on where the first X was placed ).

Some occur in strategic positions in between provinces.

When the weather is fine, waterborne traffic jams frequently occur outside the grotto, as the rowboats jostle for positions to enter the cave in single file.

These occur at specific individual nucleotide positions within a gene.

They also occur in deeply embedded positions in English, as in " That's the girl that I don't know what < u > she </ u > did ", although this is sometimes considered non-standard.

# Bases that have been modified, especially by methylation, occur in several positions throughout the tRNA.