Crystallography and Law of Interfacial Angles
Law of the Constancy of Interfacial Angles
Since the internal structure of any mineral is always constant, and since the possible crystal faces of that mineral have a definite relationship to that structure, it follows that mineral have a definite relationship to that structure, it follows that the faces must have also a definite relationship to each other. This fact may be stated as follows: The angles between two similar faces on the same substance are always the same. Figure 3 will also illustrate this point. The face which cuts the network along the line A-C must make an angle of 45 degrees with the face which cuts along the line A-B, etc. This law is the most fundamental and important in the science of crystallography. It frequently enables one to identify a mineral by the measurement of the interfacial angles on its crystals. A mineral may be found in crystals of widely varying shapes and sizes, but the angle between two similar faces will always be the same.
And important part of the study of crystallography consists in the measuring and classifying of the interfacial angles on the crystals of all minerals. These measurements are accomplished by means of instruments know as goniometry. For accurate work, particularly in the case of small crystals, a type of instrument known as a reflection goniometer is used. This is an instrument upon which the crystal to be measured is mounted so as to reflect beams of light from its faces through a telescope to the eye. The size of the angle through which a crystal has to be turned in order to throw successive beams of light from two adjacent faces into tie telescope determines the angle existing between the faces. A simpler instrument used for approximate work and with larger crystals is known as a contact goniometer.
The regular internal structure of crystals requires that the ultimate individual mineral units must be at least physically alike. A physical likeness between these units necessitates that they should also be the same chemically, or at least closely similar. Consequently we can state that in general a crystal must be made up of a regular assemblage of units which are chemically the same, and therefore that a crystallized mineral must have a definite and uniform chemical composition. This statement is a general one and will suffice for the present; certain modifications will be found stated on page 84 under isomorphism. A crystal is a guaranty of the chemical homogeneity of a mineral. From this it follows that only definite chemical compounds are capable of crystallization.
To sum up the conclusions of the preceding paragraphs: A crystal is a solid with definite chemical composition which possesses a definite internal arrangement of its mineral units. These internal characteristic are expressed outwardly in a definite external form. And since the internal structure of the same substance is always constant, the angles between the similar bounding planes of the crystals of that substance are also constant.