Quantized atomic vibrations
Main article: Einstein solid While the assumption that a solid has independent oscillations is very accurate, these oscillations are sound waves, collective modes involving many atoms. In the Einstein model, each atom oscillates independently. Einstein was aware that the frequency of the actual oscillations would be different, but he nevertheless proposed this theory becauseEinstein continued his work on quantum mechanics in 1906, by explaining the specific heat anomaly in solids. This was the first application of quantum theory to a mechanical system. Since Planck's distribution for light oscillators had no problem with infinite specific heats, the same idea could be applied to solids to fix the specific heat problem there. Einstein showed in a simple model While the assumption that a solid has independent oscillations is very accurate, these oscillations are sound waves, collective modes involving many atoms. In the Einstein model, each atom oscillates independently. Einstein was aware that the frequency of the actual oscillations would be different, but he nevertheless proposed this theory because that the hypothesis that solid motion is quantized explains why the specific heat of a solid goes to zero at zero temperature.
Einstein's model treats each atom as connected to a single spring. Instead of connecting all the atoms to each other, which leads to standing waves with all sorts of different frequencies, Einstein imagined that each atom was attached to a fixed point in space by a spring. This is not physically correct, but it still predicts that the specific heat is 3NkB, since the number of independent oscillations stays the same.
Einstein then assumes that the motion in this model are quantized, according to the Planck law, so that each independent spring motion has energy which is an integer multiple of hf, where f is the frequency of oscillation. With this assumption, he applied Boltzmann's statistical method to calculate the average energy of the spring. The result was the same as the one that Planck had derived for light: for temperatures where kBT is much smaller than hf, the motion is frozen, and the specific heat goes to zero.
So Einstein concluded that quantum mechanics would solve the main problem of classical physics, the specific heat anomaly. The particles of sound implied by this formulation are now called phonons In physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's thermal and electrical conductivities. In. Because all of Einstein's springs have the same stiffness, they all freeze out at the same temperature, and this leads to a prediction that the specific heat should go to zero exponentially fast when the temperature is low. The solution to this problem is to solve for the independent normal modes A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency. The frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge or molecule, has a set of normal modes that depend on individually, and to quantize those. Then each normal mode has a different frequency, and long wavelength vibration modes freeze out at colder temperatures than short wavelength ones. This was done by Debye The debye is a CGS unit (a non-SI metric unit) of electric dipole moment[note 1] named in honor of the physicist Peter J. W. Debye. It is defined as 1 × 10−18 statcoulomb-centimeter.[note 2] Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of 10-10 statcoulomb[note 3] (, and after this modification, Einstein's quantization method reproduced quantitatively the behavior of the specific heats of solids at low temperatures.
<<Table of Contents Albert Einstein was an ethnically Jewish, German-born theoretical physicist. He is best known for his theories of special relativity and general relativity. Einstein received the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.". He is often | Next>> | Show All>>
