goniometer

goniometer, instrument for measuring angles, particularly used in the study of crystals. Nicolaus Steno in 1669 determined the interfacial angles of quartz crystals by cutting sections perpendicular to the edges, the plane angles of the sections being the angles between the faces which were perpendicular to the sections. The earliest instrument used to measure these angles was the contact goniometer devised by Arnould Carangeot in 1783.

Contact goniometers

A contact goniometer consists of two metal rules pivoted together at the centre of a graduated semicircle. The instrument is placed with its plane perpendicular to an edge between two faces of the crystal to be measured, and the rules are brought into contact with the faces. The angle between the rules, as read on the graduated semicircle, then gives the angle between the two faces. The rules are slotted, so that they may be shortened and their tips applied to a crystal partly embedded in its matrix. The instrument illustrated is employed for the approximate measurement of large crystals.

Reflecting goniometers

The reflecting goniometer is an instrument of far greater precision and is used for the accurate measurement of the angles when small crystals with smooth faces are available. Such faces reflect sharply defined images of a bright object. By turning the crystal about an axis parallel to the edge between two faces, the image reflected from a second face may be brought into the same position as that formerly occupied by the image reflected from the first face. The angle through which the crystal has been rotated, as determined by a graduated circle to which the crystal is fixed, is the angle between the normals to the two faces.

Several forms of instruments depending on this principle have been devised. The earliest type consisted of a vertical graduated circle reading degrees and minutes, which turned about a horizontal axis. A great improvement was effected by placing the graduated circle in a horizontal position. Many forms of the horizontal-circle goniometer have been constructed: they are used on telescopes and collimators, and in construction they are essentially the same as a spectrometer, with the addition of arrangements for adjusting and centring the crystal on a stage on the horizontal circle. Light from any convenient source is passed through the slit of the collimator and the image reflected from the crystal face is viewed in the telescope. The crystal holder can be adjusted to bring the image exactly on the cross wires of the telescope. The circle can then be rotated until the image from a second crystal face is brought on the cross wires of the telescope. The angle through which it has been turned is the angle between the two face normals.

However, with a horizontal-circle goniometer, it is necessary to mount and readjust the crystal for the measurement of each zone of faces (i.e., each set of faces intersecting in parallel edges). Further, in certain cases, it is not possible to measure the angles between zones. These difficulties have been overcome by the use of a two-circle goniometer. The crystal is set up and adjusted with the axis of a prominent zone parallel to the axis of either the horizontal or the vertical circle. The positions of the faces are fixed by the simultaneous readings of the two circles. Some disadvantages are overcome by adding still another graduated circle to the instrument, with its axis perpendicular to the axis of the vertical circle, thus forming a three-circle goniometer. With such an instrument measurements may be made in any zone or between any two faces without readjusting the crystal. Goniometers have been devised for measuring crystals during their growth in the mother liquor and for cutting section plates and prisms from crystals (precious stones) accurately in any desired direction. An ordinary microscope fitted with cross wires and a rotating graduated stage serves the purpose of a goniometer for measuring the plane angles of a crystal face or section.

Weissenberg X-ray goniometers

The Weissenberg X-ray goniometer is used in recording X-ray reflections from crystals. The crystal oscillates through about 200° around an edge, as a cylindrical camera is translated back and forth parallel to the crystal rotation axis. In Martin Julian Buerger’s design the angle which the rotation axis makes with the X-ray beam is variable.