Why are metals malleable and ductile? These two properties seem to be related. Is there a microscopic understanding of these properties possible?
Let's draw a comparison with ceramics, which—just as metals are generally ductile—are generally brittle.
First, note that crystals (and metals and ceramics are both generally polycrystalline) can deform through dislocation motion. A dislocation is a line defect that carries plasticity through a crystal. The classic analogy is moving a rug by kicking a wrinkle down its length. You don't need to deform the entire crystal at once; you just need to sweep one (or many) dislocations through the material, breaking a relatively small number of bonds at a time.
Here's a simple illustration of a curved dislocation carrying shear through a crystal; the passage of the dislocation leaves a new permanent step:
So this is a very convenient way to achieve permanent deformation. However, it's much easier to break these bonds in metals than in ceramics because the metallic bonds in the former are weaker than the ionic/covalent bonds in the latter (as evidenced by the fact that ceramics are generally refractory, i.e., they have high melting temperatures). In particular, the delocalized nature of the electrons in metals allows dislocation to slip by easily. This equates to ductility/malleability. (The two terms are identical for this discussion; they differ only in the type of loading conditions that result in easy deformation.)
Additionally, in metals with a face-centered-cubic crystalline structure (think gold or copper, for example), the structural symmetry provides many possible slip planes along which dislocations can easily propagate. This equates to even greater ductility/malleability.
Here's an illustration of a face-centered-cubic structure; the close packing of atoms on multiple planes allows dislocations to hop only short distances, greatly easing their passage:
In contrast, dislocation motion is so strongly hindered in ceramics (because the bonds are directional and the charges are rigidly fixed) that it may take less energy to simply break all the bonds at once, corresponding to bulk fracture and brittleness.
One consequence of these microscopic differences between metals and ceramics is the way that they respond to cracks or flaws. A sharp crack produces a stress concentration, essentially because the stress field has to twist sharply around it. In a metal, this stress concentration isn't much of a problem—some dislocations will move, resulting in plastic deformation and blunting of the crack tip. This option is much less likely in a ceramic because of the impediments to dislocation motion. It may just be easier to break the bonds permanently and form a new open surface at the formerly high-stress area. This is the mechanism of crack propagation, and if the crack continues to propagate, you get bulk fracture.
Metals are malleable and Ductile because of metallic bonding. Metallic bonding is different from ionic and covalent bonding. Metallic bonding is it's own type of bond. Metallic bonds are described with the modern theory of bonds by applying the schrodinger equation to each atom and bringing the atoms closer and closer to form as many wave functions as the number of atoms. There are bonds and antibond wave formations describing the possible wave functions. All of these form the possible band energies. Bonds within a crystal structure only hold the structure together if the average bonded energy state is lower than isolated states. Metals have an average bonded energy stucture lower than isolated atoms. The fermi level has to be known to kind of figure out what happens next to the valence electrons within a metal. Tables for this energy level of different metals of interest can be looked up. The fermi energy level is the top energy state of all the paired electrons at absolute zero. At absolute zero all the electrons within are paired and sequentially fill the occupyable states from the bottom energy to the Fermi energy. When a metal is heated the electrons can move to higher energy states all the way to the vacuum level which is the highest antibond possible within the structure. Past the vacuum level an electron is ejected from the metal. The fermi-energy is important because it is miraculously the average electron energy within the metallic structure above absolute zero. There is a conduction band in metals made possible because all the orbitals overlap and the outer electron has a very low ionization level. The conduction band is very close to the fermi energy level. Very little heat or potential difference is needed to bump the electrons up to the higher conduction states of energy to move around within its structure. The difference between the fermi energy and the conduction band is loosely known as the Band Gap. In conductors the Band Gap doesn't really exist because of the orbitals overlapping and sharing a moveable electron. The orbital overlapping and moveable electron creates continuous energy spectrum. The electrons are continuously allowed to occupy higher energy states. Basically the bonded state between two metal atoms is lower than a single atom and a single atom has to ionize it's electron to form the bond. If you are familiar with the work function of a metal(Fermi energy level + Photon energy to eject electron). the conduction band is between this point and the fermi level but on the order of something small enough that enables the electron to move around the structure very easily and never belong to a particular atom. However, the conduction band might be right at the fermi level. Quantum mechanically the electrons within a metallic structure are represented as travelling waves. They are know to form a sort of electron cloud within the structure glueing the atoms together with the coulombic attraction between the atoms ionized positive ion charge. You can visualize balls neatly stacked with perfect layers and cubic form with a type of cloud holding it together. As electrons move the they create a hole and this is a new location for a different electron. The electrons move randomly or by imput energy. On the average there is always enough electron charge to stick things together because randomly there is a certain average to want to fill the hole or the an external energy the electrons have a direction into the hole from a source further back. The malleability and Ductability is a result of the metallic bonding. Because the electrons can move around easily enough, the metallic atoms can be manipulated to get shifted in the desired way and nothing restricts the electron cloud from moving back around the shifted atoms. Malleability and Ductability seem to be possible because of this phenomenom. The strength of the material has to do with the alignment of the crystal like formations. i.e. A metal wants to start off in one whole crystal like formation. Which is why a softened metel gets soft during the slow cooling process. The atoms try to form into a perfect crystal. But as it is heated and cooled fast enough this crystal structure will break up into sub-crystal structures(a structure formed by more than one smaller crystal structure). Probably because of thermal dynamic principles. Perhaps the surges of the electron cloud from hotter to cooler regions happen in intrinsic ways to create enough force along certain spots to shift things around proportional to the sub crystals collective strength? Regardless this process gives the whole metal a stronger more brittle effect. Afterwards the electrons can drift around the hardened steel as before but the pathways have changed. For malleability and ductability, the state of the crystal structure is probably averaged to keep the same original crystal formation but the levels squish in (i.e. the lower/upper/adjaceant levels). The electrons just flow into around the squished structure like nothing is any different during and after the the process. But pressure creates heat and this heat forces the atom to stay in higher energy states(on the average). The higher states are anti bonded states so there is no glue holding the atom to it's neighbours until the force is removed. When a metal is heated the number of anti-bonded electron energy increases and is easier to manipulate the steel into a desired shape because the electrons are wanting to drift into cooler regions. So the amount of glue holdind the heated structure decreases proportionally to the amount of heat. Malleability and Ductability sound very much the same because they involve the same amounts of heating or cooling.