Expansion of Solids

The expansion of solid bodies. All solid bodies expand when their temperature is raised. If is the length of a rod of the substance at the temperature and the length at the temperature 2, then the quantity 

For many substances this quantity is very nearly independent of the temperature and of the magnitude of the interval 

In many cases, the expansion does not follow this simple law. We must then have recourse to the more general equation 

The expansion on heating is not confined merely to the length of the solid body, but increases all the dimensions (of an isotropic body) uniformly. In the simplest case, w e have for the length I, the breadth 6, and the height c of a rectangular parallelepiped the equations l = l l+at), 

As a is always a very small quantity, we may neglect higher pow ers of a than the first, and obtain as a first approximation to the volume of the solid body 

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Coefficients of Cubical Expansion of Solids, in Lange s Handbook of Chemistry, 12 th ed., ed. John A. Dean (New York, McGraw-Hill 1979), Table 10-43. 

Because of its low and regular thermal expansion, vitreous silica is employed in apparatus used to measure the thermal expansion of solids. A detailed account of the different methods used for this purpose has been published (227). The most common form of dilatometer utilizes a vitreous silica tube closed at the bottom and containing the test sample. A movable rod of vitreous silica, resting on the sample, actuates a dial indicator resting on the top of the rod. The assembly containing the sample is placed in a furnace, bath, or cooling chamber to attain the desired temperature. 

W. Souder, ".Thermal Expansion of Solids , USNadBurStandards Circular No 486, US-GovtPrintingOffice, Washington, DC (1950)... 

H. Billet, the coeff. of cubical expansion of solid iodine is 0 0002350, and according to J. Dewar 0 0002510 between —38 85° and 17° the coeff. of thermal expansion for liquid iodine is 0-000856 according to H. Billet. 

J. Dewar gives 0-0000787 for the coefficient of expansion of solid dodecahydrated disodium hydrophosphate, and H. Kopp, between 5° and 35°, gives for the volume v at 0° when iq is the volume at 0°, v=u1(l+0-0000830890—O Oe47O9902 +O O91797403), and for the molten salt between —37° and 68°, v=v (l +0-0004350). C. Porch gives for a soln. of dipotassium hydrophosphate the coeff. of expansion XlO6 between ... 

G. Ruffino, C.A. Swenson and G.K. White, 1998, Thermal expansion of solids, CINDAS Data Series on Material Properties, vol. 1-4, ed. C.Y. Ho (ASM International). 

Dulqko and Anaoo s experiments on elasticity of hlgh-pressurs steam, 28. ebullition and evaporation. 20-22, eleotriolty, heat produced by, 2, estimation of hosting power of different kin da of fuel, 1O6-II8. expansion of solids, 4-6. 

Expansion of Solids.—The rate of expansion in solid bodies is greatly dependent on their state of aggregation hence it will be evident that the same amount of caloric will operate differently on different solids, but the effect is more visible in the metals than upon other solid non-metallic substances. 

ASTM E831, 2003. Standard test method for linear thermal expansion of solid materials by thermomechanical analysis. 

Further developments in the field of insoluble polymer-supported organotin compounds will be accompanied by the expansion of solid state tin NMR data and the development of new NMR techniques. In Table 8, some representative examples of 117Sn and 119Sn NMR chemical shifts of polymer-supported organotin compounds are given. 

An interferometer can be used to very accurately measure the thermal expansion of solids. Although not utilized commercially to the level of dilatometry, NIST standard materials, which are in turn used to calibrate dilatometers, have had their expansion characteristics determined using interferometry. In fact, the formal definition of the meter is based on interferometric measurements. The operation of the device is based on the principle of interference of monochromatic light. The fundamental relations between wavelength and distance will first... 

Glass expands as it gets hot. The effects of expansion of solid materials are well demonstrated with the ring-and-ball demonstration. In this demonstration, a ring is unable to get past a ball on the end of a rod. If the ring is heated just a small amount, it expands sufficiently to easily slide past the ball. In a similar fashion, a warm glass container holds more liquid than a cool glass container. 

Hence the coefficient of expansion of solid phosphorus at ordinary temperatures is 0-0037 c.c. per degree Centigrade. The solid expands... 

Also, changes in reaction mixture porosity, e, during the process were accounted for by the volumetric expansion of solids due to chemical reaction. 

S.I. Novikova. Thermal Expansion of Solids (Moscow, Nauka, 1974). 

Thermal and Defects-lnduced (Chemical) Expansion of Solids... 

The thermal expansion of solids depends on their structure symmetry, and may be either isotropic or anisotropic. For example, graphite has a layered structure, and its expansion in the direction perpendicular to the layers is quite different from that in the layers. For isotropic materials, ay w 3 a . However, in anisotropic solid materials the total volume expansion is distributed unequally among the three crystallographic axes and, as a rule, cannot be correctly measured by most dilatometric techniques. The true thermal expansion in such case should be studied using in situ X-ray diffraction (XRD) to determine any temperature dependence of the lattice parameters. 

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