The energy required to change some body(mole, gram, cm^3) by some delta T. start learning





A model for heat capacity 1. Treat each atom as an isolated harmonic oscillator and all atoms vibrate at the same frequency (w0) [this is wrong] 2. is population distribution. (phonos act like boson) 3. C=dU/dT 4. High T limit, right, Low limit, wrong start learning


Heat capacity of Einstein model



A model for heat capacity 1. an atom is a harmonic oscillator 2. linear and isotropic dispersion of frequency of phonons 3. High T limit 3kb, Low limit T T^3 start learning


Heat capacity of Debye Model



1. Solid is period 2. traveling was solution has peridic boundary condition start learning





Periodic boundary condition which impose the restrictiin that a wave function must be periodic on a certain Bravais latticr start learning


Bornvon Karman boundary condition



The trial wavefunction will always give an expectation value larger than or equal to the groundenergy. start learning


Ritz variational medthpd, Ritz principal



start learning





start learning





start learning





start learning





start learning





start learning





start learning





start learning





cristallographic restriction theorem start learning


cristallographic restriction theorem



start learning





start learning





start learning





start learning





Born Oppenheimer approximation start learning


Born Oppenheimer approximation



start learning





start learning





Those transitions are those that involve a latent heat. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. start learning


First order phase transitions



Those phase transitions are also called "continuous phase transitions". They are characterized by a divergent susceptibility, an infinite correlation length, and a power law decay of correlations near criticality. start learning


Second order phase transition



This magnetism refers to materials that are not affected by a magnetic field. start learning





This magnetism refers to materials like aluminum or platinum which become magnetized in a magnetic field but their magnetism disappears when the field is removed. start learning





This magnetism refers to materials (such as iron and nickel) that can retain their magnetic properties when the magnetic field is removed. start learning





start learning




