Stability of lattice structure

Every junction in a stable latticework structure is made up of four quanta of matter each. Each quantum of matter tends to remain angularly equidistant from its neighbors. Each latticework square has four quanta of matter as its sides. Apparent repulsion between their bodies (as a result of adhesion between quanta of matter in contact at common junction point) tends to maintain shape of latticework square. Deformation of a latticework square changes its shape. One or more sides of the latticework square may tend to elongate. Since the quanta in the lattice structure are already under compression and their lengths are controlled by the compression, lengths of sides of a deformed latticework square will be automatically adjusted to suit the required shape. Similarly, if it is required to reduce lengths of latticework square’s sides, excess pressure from ends of quanta of matter will be able to reduce their lengths to suit the shape of latticework square. A reduction in length of a quantum of matter will be compensated by increase in its width. An increase in its length will be accompanied by a reduction in its width. At a stable junction point, with four quanta of matter, each quantum of matter is under stress to move in line with its neighbor and form quanta-chain. Such motion is prevented by presence of four quanta of matter at the junction. Stress between neighboring quanta of matter tends to keep angle between neighboring quanta of matter at equal value. If left free, a latticework square will automatically seek its most stable state in the shape of a perfect square. This is possible only if all sides of a latticework square are formed by quanta of matter of somewhat equal matter-content. If deformation of latticework square is too great, number of quanta of matter at its junctions may be increased to accommodate more quanta of matter or reduced to have lesser number of quanta of matter. In these cases, geometrical shape of latticework squares may be altered temporarily. In this state, the lattice structure remains under stress as long as the deformation remains in the lattice structure. Tendency of latticework squares and hence that of lattice structure to strive towards stable state, endows a lattice structure with its inherent property to strive towards isotropic, homogeneous and serene state. All deformations are opposed by equal and opposite stabilizing efforts.

Formation of lattice structure

If there are more than two quanta of matter in contact with each other (in the same spatial dimension, at a place), interactions due to adhesion between their matter-contents at points of direct contacts between them, may move all quanta of matter so that their ends meet at a point in space to form a junction. Inter-quanta adhesion will further move the quanta of matter angularly in common plane, so that all quanta of matter meeting at a junction settle at equal angular difference between adjacent quanta of matter. Each quantum of matter at every junction is capable to join another junction at its other end. Only stipulation is that all quanta of matter, joined by junctions are in the same spatial plane. Once, any two quanta of matter form a junction, all further additions to the junction will be in the same spatial plane. First two quanta of matter, which initiates build up of quanta-chain, determine spatial plane of all associated structures. Numerous junctions, formed at both ends of associated quanta of matter, form a latticework structure in its plane. Junctions in a regular latticework have to have equal numbers of quanta of matter and they should be of equal lengths. Geometrically, each junction may have three, four or six quanta of matter each. Sections of latticework structure formed by junctions with three quanta of matter each appear in the shape of series of hexagons. They are structurally very unstable and flaccid. This structure is easily destroyed during deformations of latticework structure. Sections of latticework structure formed by junctions with four quanta of matter each appear in the shape series of of squares. They are structurally stable and yielding. This structure can withstand reasonable deformation and return to its stable state easily. Sections of latticework structure formed by junctions with six quanta of matter each appear in the shape of series of triangles. They are structurally very stable and rigid. This structure prevents all reasonable deforming efforts. Nature chooses latticework structure that is stable and yielding. Latticework structure with four quanta of matter, to every stable junction, is superior construction. Each section of this latticework structure, which may be called a latticework square, has one quantum of matter as its side. In its stable and homogeneous state, sides of a latticework square are of equal length. During deformations, sides of latticework squares may change their lengths and the square may change its shape accordingly.