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Diamond's cubic structure is in the Fd 3 m space group (space group 227), which follows the face-centered cubic Bravais lattice. The lattice describes the repeat pattern; for diamond cubic crystals this lattice is "decorated" with a motif of two tetrahedrally bonded atoms in each primitive cell , separated by 1 / 4 of the width of the ...
Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances, the weak diamagnetic force is overcome by the attractive force of magnetic dipoles in the material.
A space vehicle's flight is determined by application of Newton's second law of motion: =, where F is the vector sum of all forces exerted on the vehicle, m is its current mass, and a is the acceleration vector, the instantaneous rate of change of velocity (v), which in turn is the instantaneous rate of change of displacement.
Propositions 70 and 71 consider the force acting on a particle from a hollow sphere with an infinitesimally thin surface, whose mass density is constant over the surface. The force on the particle from a small area of the surface of the sphere is proportional to the mass of the area and inversely as the square of its distance from the particle.
Celestial motion, without additional forces such as drag forces or the thrust of a rocket, is governed by the reciprocal gravitational acceleration between masses. A generalization is the n -body problem , [ 3 ] where a number n of masses are mutually interacting via the gravitational force.
An example comes from considering a scalar field in D-dimensional Minkowski space.Consider a Lagrangian density given by (,).The action is = (,). The Euler–Lagrange equation for this action can be found by varying the field and its derivative and setting the variation to zero, and is:
Diamond is the hardest material on the qualitative Mohs scale. To conduct the quantitative Vickers hardness test, samples of materials are struck with a pyramid of standardized dimensions using a known force – a diamond crystal is used for the pyramid to permit a wide range of materials to be tested. From the size of the resulting indentation ...
Diamonds crystallize in the diamond cubic crystal system (space group Fd 3 m) and consist of tetrahedrally, covalently bonded carbon atoms. A second form called lonsdaleite, with hexagonal symmetry, has also been found, but it is extremely rare and forms only in meteorites or in laboratory synthesis. The local environment of each atom is ...