Question: What does it mean when atoms are sticking to each other?
About the article "Chemistry", section "Bonding".

Candidate passages:
The key to understanding the mechanism behind hardness is understanding the metallic microstructure, or the structure and arrangement of the atoms at the atomic level.
In fact, most important metallic properties critical to the manufacturing of today’s goods are determined by the microstructure of a material.
At the atomic level, the atoms in a metal are arranged in an orderly three-dimensional array called a crystal lattice.
In reality, however, a given specimen of a metal likely never contains a consistent single crystal lattice.
A given sample of metal will contain many grains, with each grain having a fairly consistent array pattern.
At an even smaller scale, each grain contains irregularities.
There are two types of irregularities at the grain level of the microstructure that are responsible for the hardness of the material.
These irregularities are point defects and line defects.
A point defect is an irregularity located at a single lattice site inside of the overall three-dimensional lattice of the grain.
There are three main point defects.
If there is an atom missing from the array, a vacancy defect is formed.
If there is a different type of atom at the lattice site that should normally be occupied by a metal atom, a substitutional defect is formed.
If there exists an atom in a site where there should normally not be, an interstitial defect is formed.
This is possible because space exists between atoms in a crystal lattice.
While point defects are irregularities at a single site in the crystal lattice, line defects are irregularities on a plane of atoms.
Dislocations are a type of line defect involving the misalignment of these planes.
In the case of an edge dislocation, a half plane of atoms is wedged between two planes of atoms.
In the case of a screw dislocation two planes of atoms are offset with a helical array running between them.
In glasses, hardness seems to depend linearly on the number of topological constraints acting between the atoms of the network.
Hence, the rigidity theory has allowed predicting hardness values with respect to composition.
Dislocations provide a mechanism for planes of atoms to slip and thus a method for plastic or permanent deformation.
Planes of atoms can flip from one side of the dislocation to the other effectively allowing the dislocation to traverse through the material and the material to deform permanently.
The movement allowed by these dislocations causes a decrease in the material's hardness.
The way to inhibit the movement of planes of atoms, and thus make them harder, involves the interaction of dislocations with each other and interstitial atoms.
When a dislocation intersects with a second dislocation, it can no longer traverse through the crystal lattice.
The intersection of dislocations creates an anchor point and does not allow the planes of atoms to continue to slip over one another A dislocation can also be anchored by the interaction with interstitial atoms.
If a dislocation comes in contact with two or more interstitial atoms, the slip of the planes will again be disrupted.
The interstitial atoms create anchor points, or pinning points, in the same manner as intersecting dislocations.
By varying the presence of interstitial atoms and the density of dislocations, a particular metal's hardness can be controlled.
Although seemingly counter-intuitive, as the density of dislocations increases, there are more intersections created and consequently more anchor points.
Similarly, as more interstitial atoms are added, more pinning points that impede the movements of dislocations are formed.
As a result, the more anchor points added, the harder the material will become. 
Valence bond theory now complements molecular orbital (MO) theory, which does not adhere to the VB idea that electron pairs are localized between two specific atoms in a molecule but that they are distributed in sets of molecular orbitals which can extend over the entire molecule.
MO theory can predict magnetic and ionization properties in a straightforward manner, while valence bond theory gives similar results but is more complicated.
Valence bond theory views aromatic properties of molecules as due to spin coupling of the π orbitals, while molecular orbital theory views it as delocalization of the π-electrons.
The underlying mathematics are also more complicated, limiting VB treatment to relatively small molecules.
On the other hand, VB theory provides a much more accurate picture of the reorganization of electronic charge that takes place when bonds are broken and formed during the course of a chemical reaction.
In particular, valence bond theory correctly predicts the dissociation of homonuclear diatomic molecules into separate atoms, while simple molecular orbital theory predicts dissociation into a mixture of atoms and ions.
More recently, several groups have developed what is often called modern valence bond theory.
This replaces the overlapping atomic orbitals by overlapping valence bond orbitals that are expanded over a large number of basis functions, either centered each on one atom to give a classical valence bond picture, or centered on all atoms in the molecule.
The resulting energies are more competitive, with energies from calculations where electron correlation is introduced based on a Hartree–Fock reference wavefunction.
The most recent text is by Shaik and Hiberty. 
The Hill system (or Hill notation) is a system of writing chemical formulas such that the number of carbon atoms in a molecule is indicated first, the number of hydrogen atoms next, and then the number of all other chemical elements subsequently, in alphabetical order.
When the formula contains no carbon, all the elements, including hydrogen, are listed alphabetically.
By sorting formulas according to the number of atoms of each element present in the formula according to these rules, with differences in earlier elements or numbers being treated as more significant than differences in any later element or number — like sorting text strings into lexicographical order — it is possible to collate chemical formulas into what is known as Hill system order.
The Hill system was first published by Edwin A. Hill of the United States Patent and Trademark Office in 1900.
It is the most commonly used system in chemical databases and printed indexes to sort lists of compounds. 
Similar to these views, in 1803 John Dalton took the atomic weight of hydrogen, the lightest element, as unity, and determined, for example, that the ratio for nitrous anhydride was 2 to 3 which gives the formula N2O3.
Interestingly, Dalton incorrectly imagined that atoms “hooked” together to form molecules.
Later, in 1808, Dalton published his famous diagram of combined "atoms":In Amedeo Avogadro's famous 1811 paper "Essay on Determining the Relative Masses of the Elementary Molecules of Bodies", he essentially states, i.e.
according to Partington's "A Short History of Chemistry", that:Note that this quote is not a literal translation.
Avogadro uses the name "molecule" for both atoms and molecules.
Specifically, he uses the name "elementary molecule" when referring to atoms and to complicate the matter also speaks of "compound molecules" and "composite molecules".
During his stay in Vercelli, Avogadro wrote a concise note ("memoria") in which he declared the hypothesis of what we now call Avogadro's law: "equal volumes of gases, at the same temperature and pressure, contain the same number of molecules".
This law implies that the relationship occurring between the weights of same volumes of different gases, at the same temperature and pressure, corresponds to the relationship between respective molecular weights.
Hence, relative molecular masses could now be calculated from the masses of gas samples.
Avogadro developed this hypothesis in order to reconcile Joseph Louis Gay-Lussac's 1808 law on volumes and combining gases with Dalton's 1803 atomic theory.
The greatest difficulty Avogadro had to resolve was the huge confusion at that time regarding atoms and molecules—one of the most important contributions of Avogadro's work was clearly distinguishing one from the other, admitting that simple particles too could be composed of molecules, and that these are composed of atoms.
Dalton, by contrast, did not consider this possibility.
Curiously, Avogadro considers only molecules containing even numbers of atoms; he does not say why odd numbers are left out.
In 1826, building on the work of Avogadro, the French chemist Jean-Baptiste Dumas states:In coordination with these concepts, in 1833 the French chemist Marc Antoine Auguste Gaudin presented a clear account of Avogadro's hypothesis, regarding atomic weights, by making use of “volume diagrams”, which clearly show both semi-correct molecular geometries, such as a linear water molecule, and correct molecular formulas, such as H2O:In two papers outlining his "theory of atomicity of the elements" (1857–58), Friedrich August Kekulé was the first to offer a theory of how every atom in an organic molecule was bonded to every other atom.
He proposed that carbon atoms were tetravalent, and could bond to themselves to form the carbon skeletons of organic molecules.
In 1856, Scottish chemist Archibald Couper began research on the bromination of benzene at the laboratory of Charles Wurtz in Paris.
One month after Kekulé's second paper appeared, Couper's independent and largely identical theory of molecular structure was published.
He offered a very concrete idea of molecular structure, proposing that atoms joined to each other like modern-day Tinkertoys in specific three-dimensional structures.
Couper was the first to use lines between atoms, in conjunction with the older method of using brackets, to represent bonds, and also postulated straight chains of atoms as the structures of some molecules, ring-shaped molecules of others, such as in tartaric acid and cyanuric acid In later publications, Couper’s bonds were represented using straight dotted lines (although it is not known if this is the typesetter’s preference) such as with alcohol and oxalic acid below:In 1861, an unknown Vienna high-school teacher named Joseph Loschmidt published, at his own expense, a booklet entitled "Chemische Studien I", containing pioneering molecular images which showed both "ringed" structures as well as double-bonded structures, such as:Loschmidt also suggested a possible formula for benzene, but left the issue open.
The first proposal of the modern structure for benzene was due to Kekulé, in 1865.
The cyclic nature of benzene was finally confirmed by the crystallographer Kathleen Lonsdale.
Benzene presents a special problem in that, to account for all the bonds, there must be alternating double carbon bonds:In 1865, German chemist August Wilhelm von Hofmann was the first to make stick-and-ball molecular models, which he used in lecture at the Royal Institution of Great Britain, such as methane shown below:The basis of this model followed the earlier 1855 suggestion by his colleague William Odling that carbon is tetravalent.
Hofmann's color scheme, to note, is still used to this day: nitrogen = blue, oxygen = red, chlorine = green, sulfur = yellow, hydrogen = white.
The deficiencies in Hofmann's model were essentially geometric: carbon bonding was shown as planar, rather than tetrahedral, and the atoms were out of proportion, e.g.
carbon was smaller in size than the hydrogen.
In 1864, Scottish organic chemist Alexander Crum Brown began to draw pictures of molecules, in which he enclosed the symbols for atoms in circles, and used broken lines to connect the atoms together in a way that satisfied each atom's valence.
The year 1873, by many accounts, was a seminal point in the history of the development of the concept of the "molecule".
In this year, the renowned Scottish physicist James Clerk Maxwell published his famous thirteen page article 'Molecules' in the September issue of "Nature".
In the opening section to this article, Maxwell clearly states:After speaking about the atomic theory of Democritus, Maxwell goes on to tell us that the word 'molecule' is a modern word.
He states, "it does not occur in "Johnson's Dictionary".
The ideas it embodies are those belonging to modern chemistry."
We are told that an 'atom' is a material point, invested and surrounded by 'potential forces' and that when 'flying molecules' strike against a solid body in constant succession it causes what is called pressure of air and other gases.
At this point, however, Maxwell notes that no one has ever seen or handled a molecule.
In 1874, Jacobus Henricus van 't Hoff and Joseph Achille Le Bel independently proposed that the phenomenon of optical activity could be explained by assuming that the chemical bonds between carbon atoms and their neighbors were directed towards the corners of a regular tetrahedron.
This led to a better understanding of the three-dimensional nature of molecules.
Emil Fischer developed the Fischer projection technique for viewing 3-D molecules on a 2-D sheet of paper:In 1898, Ludwig Boltzmann, in his "Lectures on Gas Theory", used the theory of valence to explain the phenomenon of gas phase molecular dissociation, and in doing so drew one of the first rudimentary yet detailed atomic orbital overlap drawings.
Noting first the known fact that molecular iodine vapor dissociates into atoms at higher temperatures, Boltzmann states that we must explain the existence of molecules composed of two atoms, the “double atom” as Boltzmann calls it, by an attractive force acting between the two atoms.
Boltzmann states that this chemical attraction, owing to certain facts of chemical valence, must be associated with a relatively small region on the surface of the atom called the "sensitive region".
Boltzmann states that this "sensitive region" will lie on the surface of the atom, or may partially lie inside the atom, and will firmly be connected to it.
Specifically, he states “only when two atoms are situated so that their sensitive regions are in contact, or partly overlap, will there be a chemical attraction between them.
We then say that they are chemically bound to each other.” This picture is detailed below, showing the "α-sensitive region" of atom-A overlapping with the "β-sensitive region" of atom-B: 
A half-life usually describes the decay of discrete entities, such as radioactive atoms.
In that case, it does not work to use the definition "half-life is the time required for exactly half of the entities to decay".
For example, if there are 3 radioactive atoms with a half-life of one second, there will not be "1.5 atoms" left after one second.
Instead, the half-life is defined in terms of probability: "Half-life is the time required for exactly half of the entities to decay "on average"".
In other words, the "probability" of a radioactive atom decaying within its half-life is 50%.
For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay.
Note that after one half-life there are not "exactly" one-half of the atoms remaining, only "approximately", because of the random variation in the process.
Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a "very good approximation" to say that half of the atoms remain after one half-life.
There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.