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Solid State

Condensed matter encompasses both liquid and solid (Figure 13-03f). Solid state physics is the study of rigid matter or solids. It is
Conidensed Matter Phase Diagram the major branch of condensed matter physics including both crystalline solids such as insulator, metal, semiconductor as mentioned above; and non-crystalline solids (Soft Matter) such as amorphous solid, granular matter, quasi-crystal, and polymer. Solid materials are formed from densely-packed atoms, with strong interacting forces between them. For example, sodium chloride (NaCl) is held together by ionic bonds, it is the covalent bonds responsible for metallic bonding, and the van der Waals forces provide the bonding to the noble gases (in solid form).

Figure 13-03f Condensed Matter
[view large image]

Figure 13-03g Phase Diagram [view large image]

These interactions are responsible for the mechanical, thermal, electrical, magnetic and optical properties of solids.

Theoretically, such system of atoms or molecules is described by :

where the sum and interaction V include all the constituents in the system. There are usually about 1023 particles in the system making solution of these equations impracticable. Approximations to alleviate the problem are introduced such that the energy scale under consideration is below 1 ev, while the interacting distance smaller than 10-8 cm is ignored. This is appropriate for ordinary solids which are insensitive to the details outside these scales. Under these assumptions it is possible to introduce macroscopic quantity such as density by averaging over the individual behavior of the particles. Actually many properties in solids are emergent resulting from interactions among large numbers of particles. For example, water and ice are governed by the same equation but exhibit completely different properties. Such phenomena have something to do with the phase (Figure 13-03g) rather than the basic equation, which is highly symmetrical. Water exhibits the translational and rotational symmetry of the basic laws, while ice is only invariant under the discrete translational and rotational group of its crystalline lattice. In other words, the translational and rotational symmetries of the microscopic equations have been spontaneously broken in solid phase.

    Some experimental methods to measure the macroscopic properties of solids:

  1. Scattering - Use neutrons or X-rays to discover the structure of the solid (see X-ray Diffraction).
  2. NMR - Apply static magnetic field B and measure the absorption or emission frequency of electromagnetic radiation = geB/m to calculate the charge to mass ratio e/m, where g 2 is the electron spin correction.
  3. Thermodynamics - Measure the response of macroscopic variables (energy, volume, etc.) to variations of temperature, pressure, etc. to derive quantities such as specific heat (Cv = U/T) etc.
  4. Transport - Measure the gradient of heat or electrical current to determine the thermal or electrical conductivity.

Table 13-02 below lists some macroscopic properties of solid at 293oK and 1 atm 101 kpa (1 pa = 1 kg/m-s2). Examples are given for the high and low limits.

Property Definition Unit Example (High) Example (Low)
Density Amount of Mass within a volume gm/cm3 Platinum (21.45) Kapok (0.050)
Melting Point Temperature for solid turning into Liquid oK Graphite (3800) Ice (273)
Heat of Fusion Heat/mass to completely convert solid to liquid (107) ergs/gm Quartz (~830) Lead (25)
Specific Heat Amount of heat to raise 1oK in unit mass (104) ergs/gm-K Concrete (3350) Iron, Pure (106)
Thermal Conductivity Rate of heat flow through temperature gradient (104) ergs/sec-cm-K Diamond (900) Kapok (0.03)
Electrical Resistivity Resistance of Current flow (10-6) ohms-cm Paraffin (3x1018) Silver (1.6)
Linear Expansivity Linear expansion (%) at the raise of 1oK (10-6) 1/K Plastic (250) Diamond (~0)
Tensile Strength Maximum stress before yielding Mpa Steel (3000) Concrete (~4)
Elongation Deformation/original-length before fracture % Plastic (800) Iron, cast (~0)
Young's Modulus Ratio of stress to strain Gpa Diamond (1200) Rubber (0.02)

Table 13-02 Some Macroscopic Properties of Solid

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