Elementary Solids

The basic concept of modification of a shape by form features is volume adding and removing. The shape is then adjusted by fillet and other treatment features. While solid primitives are geometric oriented shapes, form features can be application orientated. In other words, form features can be defined according to their purpose and function in the modeled part and use in a part model. At the same time, form features are often defined as pure geometry. 

Modeling by form features requires three different sets of information about the application of the modeled shape object, the shape itself, and the representation of the shape. The Form Feature Information Model (FFIM) of the STEP product model standard of the ISO describes the above sets of information on three levels. 

It was recognized that instances of the same shape carry different information on different parts for different products. For that reason, on level one the application information of the shape is described in the form of attributes. This description is called an application feature. The form feature is described on level two as a general-purpose shape aspect. The shape of a part can be defined by different sets of form features from different aspects of the shape. The form feature is defined according to its shape modification 

Solid sweep described by unified topology and geometry 

The purpose of reference elements is not a shape modification but the assistance of the construction of feature based part models. 

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An elementary solid, such as silver, is regarded as composed of atoms oscillating about fixed centres. The total energy content is therefore partly kinetic and partly potential. Since the solid has a finite compressibility, the atoms may be supposed to be maintained at small distances apart by forces they exert upon one another, and these may be resolved into two sets, one of which opposes a closer approximation of the atoms, and the other tends to draw the latter together. Both are functions of the distance between the atoms, and for a given distance are equal, since the form of the body is altered by external forces alone. 

C Kittel, Elementary Solid State Physics, Wiley, New York, 1962, Chap 5... 

This rule conforms with the principle of equipartition of energy, first enunciated by Maxwell, that the heat capacity of an elementary solid, which reflected the vibrational energy of a three-dimensional solid, should be equal to 3RJK-1 mol-1. The anomaly that the free electron theory of metals described a metal as having a three-dimensional structure of ion-cores with a three-dimensional gas of free electrons required that the electron gas should add another (3/2)R to the heat capacity if the electrons behaved like a normal gas as described in Maxwell s kinetic theory, whereas the quantum theory of free electrons shows that these quantum particles do not contribute to the heat capacity to the classical extent, and only add a very small component to the heat capacity. 

Fig. 5.6. The fraction of molecules whose absorption and emission transition moments are parallel and oriented in a direction within the elementary solid angle. This direction is defined by angles 8 and .

M. Ali Omar, Elementary Solid State Physics, Addison-Wesley, Reading, MA (1975). Fermi s law, etc. 

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