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After postulating a direct correlation between electron concentration and crystal structure in beta-phase alloys, Hume-Rothery analyzed the trends in melting points, compressibilities and bond lengths as a function of group number in the periodic table in order to establish a system of valencies of the transition elements in the metallic state.
Similar to the ideal hcp structure, the perfect dhcp structure should have a lattice parameter ratio of = In the real dhcp structures of 5 lanthanides (including β-Ce) / variates between 1.596 (Pm) and 1.6128 (Nd). For the four known actinides dhcp lattices the corresponding number vary between 1.620 (Bk) and 1.625 (Cf).
The Widmanstätten structures form due to the growth of new phases within the grain boundaries of the parent metals, generally increasing the hardness and brittleness of the metal. The structures form due to the precipitation of a single crystal phase into two separate phases.
The scientific definition of a "crystal" is based on the microscopic arrangement of atoms inside it, called the crystal structure. A crystal is a solid where the atoms form a periodic arrangement. (Quasicrystals are an exception, see below). Not all solids are crystals.
Metallic bonding is not the only type of chemical bonding a metal can exhibit, even as a pure substance. For example, elemental gallium consists of covalently-bound pairs of atoms in both liquid and solid-state—these pairs form a crystal structure with metallic bonding between them.
A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system (see table in Crystal system#Crystal classes). The trigonal crystal system consists of the 5 point groups that have a single three-fold rotation axis, which includes space groups 143 to 167.
An amorphous metal (also known as metallic glass, glassy metal, or shiny metal) is a solid metallic material, usually an alloy, with disordered atomic-scale structure. Most metals are crystalline in their solid state, which means they have a highly ordered arrangement of atoms .
The atoms of simple metallic substances are often in one of three common crystal structures, namely body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal close-packed (hcp). In bcc, each atom is positioned at the center of a cube of eight others.