# The refractometer.

The index of refraction is a fundamental property of a substance, and its determination may provide valuable diagnostic information about minerals and crystals. Over a period of four centuries, widely varying devices and experimental arrangements for measuring indices of refraction have been developed. These instruments are generally called refractometers, or-if the physical phenomenon of total reflection is used--also total reflectometers. These range from the precursor of Kepler's refractometer (1611) to the primitive but ingenious instrument of Wollaston (1802) to modern, ultra-precise total reflectometers.

INTRODUCTION

Light is an electromagnetic radiation which is generated by a source and travels at a constant speed. The speed of light in vacuum was first determined in 1676 by the Dane Olaf Romer (1644-1710), from astronomical observations of the moons of Jupiter. It has the unimaginably high value of approximately 300,000 kilometers per second (186,000 miles per second): a light ray from the Sun takes only 8 minutes to reach the Earth. The speed of light is retarded to varying degrees in all media except a vacuum. The ratio of the speed of light while passing through a material to the speed of light in a vacuum is given as the refractive index (n) for the material; the simple relationship is:

n = [[c.sub.0]/[c.sub.1]]

n = refractive index

[c.sub.0] = speed of light in a vacuum (300,000 km/sec)

[c.sub.1] = speed of light in the material

From this formula it is clear that the index of refraction is a pure number with a value greater than 1.

The index of refraction is an important physical constant. It is distinctive for any given substance and can therefore be employed diagnostically. It is considerably influenced by physical and chemical variations; thus its value will alter with changes in temperature, pressure or composition. For example, it is possible, by measuring the index of refraction, to ascertain the purity of solutions, the chemical composition of mixed crystals, and even the water content of butter or the Brix degree of wine.

The measurement of indices of refraction is generally of great importance, and is employed in--aside from mineralogy--routine optical procedures, petrochemistry, analytical testing of foodstuffs and beverages, and medicine. Devices used to measure indices of refraction are called refractometers.

The index of refraction may be thought of as "optical density," since it depends directly on the kinds of atoms in the medium, as well as on their stacking and arrangement. For each chemical element there is an empirically determined constant which describes the influence of the element on the refractive index of the whole substance: if one knows the chemical composition of a compound, it is possible to calculate what the compound's theoretical index of refraction should be. The comparison of this with the value actually measured furnishes a criterion for the quality of the data, called the "compatibility index"; as an empirical formula it is called the Gladstone-Dale Relation (Mandarino, 1976, 1981). When a new mineral species is described, the international IMA CNMMN (International Mineralogical Association; Commission of New Minerals and Mineral Names) requires a determination of its compatibility index--indicating the importance given to this value.

In mineralogy, the determination of refractive index is very important, but also somewhat problematical. That is because (except in the case of isometric crystals) the propagation of light is anisotropic, i.e., the speed of light within the crystal varies in different directions. Light propagating from an imaginary source in the center of a crystal does not travel uniformly in all directions, so as to make the shape of a hollow sphere, but rather it forms more complex three-dimensional figures.

To better imagine optical relationships, the model of the indicatrix has proven very useful. Described by Fletcher in 1892, this is an imaginary three-dimensional surface in which all axial lengths represent the value of the refractive index in a given direction.

The indicatrix for an isometric crystal is a sphere (see Fig. 1); the refractive index, which is the same in all directions, corresponds to the radius of the sphere. In tetragonal, trigonal and hexagonal crystals, the indicatrix is an ellipsoid (elongated, somewhat like a lemon, or in some cases flattened, like a tangerine). This indicatrix has two "principal" refractive indices, one parallel to the rotational (c) axis, the other perpendicular to it. In orthorhombic, monoclinic and triclinic crystals the indicatrix is an ellipsoid with three axes, the indicatrix being extended from the three mutually perpendicular "principal" indices of refraction: this shape is somewhat like that of a potato or a kiwi fruit. Depending on the symmetry of the crystal, either one, two, or three principal indices of refraction have to be measured, and in order to do that, the crystal must correspondingly be oriented.

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Methods for the Determination of Refractive Indices

There are two basic methods for determining refractive indices: by measuring the speed of the light, and by determining the angle formed by light rays at the boundary between two substances (refraction).

Direct measurement of the speed of light in a medium which retards the speed by a relatively small amount runs up against nearly insurmountable technical difficulties. In practice, therefore, one measures the speed of light by measuring the difference between the time a light beam takes to pass through a sample and the time a parallel beam takes to go through a medium with known refractive index. The difference between the two beams is rendered both visible and measurable through interference, i.e. superpositioning of the light. Since these methods are practically insignificant for mineralogy, they will not be elaborated upon here.

In contrast, all methods which are important for mineralogy depend on the phenomenon of light refraction. The fact that a beam of light is bent at an angle when passing from one medium into another was grasped intuitively by early humans, who, when fishing, knew that the prey was not where it seemed to be, but instead was nearer to the hunter. The physical explanation for this phenomenon is given by Snell's Law, named after the Dutch mathematician Willebrord van Roijen Snell (1580-1629) of Leiden, who formulated the law in 1618. This discovery remained unknown until its posthumous publication in the famous book Dioptrica (1703) of his countryman Christiaan Huygens (1629-1695).

Snell's Law implies that a beam of light, when passing from an optically less dense (faster) medium into an optically denser (slower) medium, is deflected towards the perpendicular of incidence (Fig. 2).

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The formula is:

[[c.sub.1]/[c.sub.2]] = [[n.sub.2]/[n.sub.2]] = [sin [alpha]/sin [beta]]

Snell's Law is exemplified clearly when a light beam passes through a prism. In this case, refraction takes place at both boundaries between glass and air, i.e., the beam is bent twice. Another important phenomenon is also observed. The original beam of white light is differentiated into spectral colors, and the blue light (of shorter wavelength) is bent more strongly than the red light (of longer wavelength). This signifies that the speed of the blue light through the glass is less than the speed of the red light, i.e. the refractive index for the blue light is accordingly greater. This relationship between refractive index and wavelength is termed dispersion (see Fig. 3).

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The magnitude of the dispersion is yet another physical constant for any substance. It is determined by measurement of refractive indices for different wavelengths, and it can be of major diagnostic and technical significance. In the optics industry, for example, a precise knowledge of the dispersion of different glasses is indispensable for the production of high-grade systems of lenses. Dispersion is also the cause of the glittering color-play in faceted gems, especially diamonds.

The dispersion curve of a substance is shown in Fig. 4. Usually the values given in determination tables are for the [n.sub.D]-spectral line, which is the bright-yellow line for sodium vapor, with a wavelength of 589.3 nm (5893[Angstrom]). There are historical reasons for this, since this particular "monochromatic" light (light of a single wavelength) can be generated very easily when kitchen salt (NaCl, halite) is scattered into the flame of a Bunsen burner. There have been unsuccessful attempts to generally replace this value by the one for the green mercury line at 546 nm ([n.sub.e]), since the human eye is more sensitive to this light, and its wavelength lies in about the middle of the visible spectrum.

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A straightforward method of measuring refractive indices by utilizing Snell's Law was described in 1611 by the famous "natural philosopher" and astronomer Johannes Kepler (1571-1630), in his Dioptrik. It is simple as it is intelligent, being based on the differences between shadows thrown in oblique sunlight through bodies with different refractive indices. The principle is illustrated in Fig. 5. In an opaque trough lies a small block of glass with height equal to that of the wall of the trough. In the empty area inside the trough, the projected shadow corresponds to the surface BCHK, but inside the glass block it corresponds to the surface BDGI.

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Today the measurement with a prism is carried out with the aid of goniometers or spectrometers. This principle will be described in greater detail under the heading "The Prism Method."

A further important phenomenon follows as a consequence of Snell's Law: as the angle [beta] increases from the ray path given by the green line in Figure 6, angle [alpha] also increases proportionately until it finally reaches 90[degrees]. A ray of light (red line in Fig. 6) originating from an optically denser medium ([n.sub.2]) then travels exactly along the boundary plane. When angle [beta] increases further, past that of [[beta].sub.crit], no more light can pass out of the denser medium into the less dense one, and all light will be reflected from the boundary surface back into the denser medium (yellow line). The angle [[beta].sub.crit] for the grazing light (red line) is also called the "critical angle of total reflection," and from it, the difference between the indices of refraction of the two media can be calculated conveniently and accurately. The critical angle is determined with a refractometer, by adjusting the light/shadow demarcation using a telescope with crosshairs. The generation of this light/shadow boundary is easily understandable when one allows light to impinge from the right (Fig. 6) at a nearly flat angle ([alpha] close to 90[degrees]) onto the boundary surface from the optically thinner medium. Light can then attain the critical angle of total reflection in the range [beta] [less than or equal to] [[beta].sub.crit], but never in the dark gray area. By far the majority of refraetometers are based on this physical phenomenon; they may be also called total reflectometers.

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In 1611 the phenomenon of total reflection was also described by Johannes Kepler, and in 1802 it was first used by Wollaston for the determination of refractive indices. In principle, all total reflectometers derive from the instrument of Wollaston, which was both ingenious and simple; it will be described below.

Practicing mineralogists often face the problem of determining refractive indices of very small samples. In these cases the methods described above are not practicable, and the investigator must revert to microscopic examination by the so-called "immersion method." The principle underlying this method is very simple. There will be no refraction or diffraction phenomena along the surfaces of a colorless substance provided the refractive index of the sample exactly matches its surrounding fluid. The sample will be invisible.

In practice, the test sample is surrounded by an immersion liquid, whose composition and temperature (hence its refractive index) are manipulated so that the sample becomes invisible. Then the refractive index of the liquid is measured with a refractometer. Because the dispersion curve for a liquid is always much steeper than for a solid body (see Fig. 4, dotted line), the refractive index is identical only for one given wavelength (i.e. color of light): in Fig. 7 the immersion is matched for green light (Fig. 4, [n.sub.c] = [n.sub.i]), whereas in the blue (Fig. 4, [n.sub.c] < [n.sub.i]) and red regions (Fig. 4, [n.sub.c] > [n.sub.i]) of the spectrum the grain is clearly visible.

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Precision of Measurement of Refractive Indices

Whatever the method employed, measurements of refractive index can be carried out with a high degree of precision with some care. Accuracy to the third decimal place can be attained mostly without difficulties--it was even arrived at by Wollaston (1802) with his simple set-up. Routine measurements to identify a mineral species are carried out with a margin of error around [+ or -]0.002. With somewhat more care and appropriate apparatus, measurements to an error margin of [+ or -] 0.0001 may be attained. For precision measurements in optics and food-quality control, etc., however, an accuracy better than [+ or -] 0.00001 is necessary. This requires considerable expenditure and very closely controlled conditions. One of the essential factors is constancy of temperature. Usually, the refractive indices of liquids vary by about 0.0005 per degree Celsius; for solid bodies this value is clearly smaller, but still can easily reach 0.00005/[degrees]C.

I. THE PRISM METHOD

With the prism method, any optical goniometer (Burchard, 1998) or spectrometer may be employed as a refractometer, simply because the refraction angle of the prism edge ([omega]) and that between the incident and the deviated light rays ([delta]) is to be measured. The one-circle goniometer is the most sensible choice, since the complex construction of the two-circle goniometer unnecessarily increases possible sources of error. The prism of the substance to be measured is located on the goniometer head or the adjustable central disc of the spectrometer, its edge aligned exactly parallel to the instrument's axis of rotation, and the prism angle [omega] is measured by standard goniometer methods. Subsequently [delta] is determined for a beam penetrating the prism. The light path for such a beam, which is exactly symmetrical with respect to the prism edge, is shown for green light in Fig. 8. For this beam [delta] becomes a minimum, and the formula for calculation, following Snell's Law, is especially simple.

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This method thus is designated as minimum deviation method. It is characterized by high accuracy, assuming that the prism has been prepared perfectly. In the case of anisotropic crystals, principal indices of refraction to be measured must be parallel to the edge or in the symmetry plane of the prism. In addition, the faces of the prism have to be perfectly polished and exactly plane. In order to meet this requirement, elaborate crystal grinding apparatus such as "grinding tripods," shown in Figure 9, have been developed.

To determine the three principal refractive indices of a biaxial crystal one needs at a minimum two prisms in different orientations. In especially favorable cases one can use natural crystal faces, of course, if their quality and orientation are appropriate (for example, the prism faces of a hexagonal or orthorhombic crystal).

If, instead of a crystal, a hollow prism with plane and parallel glass walls is used, an easy and precise measurement of fluids will be possible. A few micro-refractometers for the determination of small volumes of fluids, which are usually employed in connection with the microscopic immersion method, are based on this hollow prism technique (e.g. the Jelley-Refractometer by Leitz/Wetzlar, the Microscope Refractometer by Zeiss/Oberkochen, and the Wilke-Refractometer by Hofmann/Clausthal). The detailed description of these devices is beyond the scope of this publication.

For a thorough description of the prism method, see Groth (1905) and Tutton (1911).

II. METHOD OF TOTAL REFLECTION

As shown above, total reflection can occur only when a light beam passes from an optically denser medium to an optically less dense one. With most total reflectometers, the sample is aligned with a plane face against a body of highly light-refracting glass, which may be in the form of a hemisphere, half-cylinder, or prism. In this case, the space necessarily present between the sample and the glass body must be filled with a liquid of high refraction--higher than the one of the sample, otherwise one will only be measuring the boundary angle for the interstitial air. To calculate the index of refraction of the unknown sample, one needs a very exact knowledge of the index of the glass body.

In principle, of course, only samples with indices smaller than those of the glass body and the contact liquid can be measured, which limits the range of measurement to n [less than or equal to] 1.9. Particularly for gemstone refractometers, there have been attempts to increase this range by using materials with a higher refractive index (such as zirconia, with n = 2.26), but the attempts have been problematic, as almost no contact liquids with comparably high indices are available.

Until the middle of the 20th century, the total reflectometer was the instrument that mineralogists chiefly used to measure the indices of refraction. Besides the capacity of the instrument for high accuracy, this was more importantly due to the fact that only a single, arbitrarily oriented, polished face suffices for the measurement of all three of the principal refractive indices of an anisotropic crystal. In these birefringent substances, two bright/dark demarcations are visible rather than one, and the locus (and thus the critical angle) for both lines changes with rotation about an axis perpendicular to the plane of contact between crystal and glass body. The maximum and minimum values of these lines define the principal refractive indices [n.sub.x] and [n.sub.z], and one of the two inflection points of them defines [n.sub.y] (for further details see Hurlbut, 1984). An axis of rotation with a divided circle for either the crystal alone (e.g., the Liebisch refractometer) or both crystal and glass body combined (e.g. the Pulfrich and the Abbe hemisphere-refractometers) is therefore an essential feature of such instruments for mineralogical use.

Today, total reflectometers are still used primarily in gemology. Hurlbut (1984) describes very clearly the principles, the methods of measurement, and the applications of this instrument.

The nomenclature of total reflectometers is not consistent throughout the literature. The same instrument may be called a refractometer or total reflectometer by different authors or even by the same author in different descriptions. Refractometer is the more general term since the critical angle of total reflection is a peculiar aspect of reflection, thus all total reflectometers are also refractometers. In this publication the term total reflectometer is consistently used for all refractometers which are based on the measurement of the critical angle of total reflection for the determination of the index of refraction.

A. Total Reflectometers with Glass Bodies

Wollaston 's Apparatus

Wollaston's method relies on the congruency of triangles (see Fig. 11); it is elucidated by Danker (1885).

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In principle, all total reflectometers derive from a simple but ingenious apparatus described in 1802 by William Hyde Wollaston (1766-1828). Wollaston's experimental setup was almost primitive; it can be duplicated by any competent handyman. It consists simply of a board, a number of thin wooden planks connected with hinges, and a glass cube of known refractive index with at least two polished faces. The glass cube (P) (see Fig. 10) rests on the board cd, in which there is a small depression that holds the substance to be measured. This substance has to be in close contact with the bottom face of the cube, and even at this early date Wollaston realized that an immersion liquid had to be applied when a solid is measured--for this he used oil of the sassafras laurel tree. The light is incident from the right. The board de has a randomly determined length; in Wollaston's case it is 10 inches, and the board ef has a length which agrees exactly with the product of the refractive index of the glass cube and the length de--in Wollaston's case this is 15.83 inches, since the glass cube had a refractive index of n = 1.583. The board ig is a pointer of half the length of ef, thus is also the radius of a circle with the diameter ef. Thanks to gravity its pointed end always lies perpendicularly underneath e, and the sine of angle [beta] is directly readable on a graduated scale along fg. With this measurement the critical angle of total reflection is determined with a sighting arrangement (small marks along de). Since, when the experiment is performed in daylight, dispersion effects cause colors to fan out on the boundary surface, Wollaston focused on the yellow part of the spectrum.

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The Abbe Double Prism Total Reflectometer

In his fundamental book of 1874 "neue Apparate zur Bestimmung des Brechungs- und Zerstreuungsvermbgens fester und flussiger Korper" (New Devices for the Determination of the Refractive and Dispersive Capabilities of Solid and Fluid Bodies), Ernst Abbe presented design drawings of a total reflectometer (see Fig. 12) that is primarily useful for measuring fluids.

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On a round metal base a tiltable mirror is mounted, microscope-style, for better illumination of the viewing field. A vertical L-shaped column holds the sector of a graduated circle along with a vernier that is rotatable about a horizontal axis. Firmly attached to the graduated circle is a telescope by means of which the critical angle of total reflection may be observed.

Also firmly attached with the horizontal swivel pin is a right-angled, 60-degree glass prism such that its edge is perpendicular to both the plane of the divided circle and the axis of the telescope. By means of a guiding groove and a spring-tensioned locking screw, a second prism of the same form and size is brought adjacent to the hypotenuse face of the first prism, creating an N-shaped cross-section (see Fig. 12 top left). The fluid to be measured is introduced as a thin film between the hypotenuse faces of the two prisms. Ideally the testing is carried out in monochromatic light. The reading of the position of the critical angle appears directly on the scale (using a small magnifying lens) and is accurate to the fourth decimal place.

In 1898, Pulfrich altered Abbe's double-prism total reflectometer to make it usable also for solid substances. For this purpose the second prism was removed and a small triangular auxiliary prism was mounted on the remaining prism. This made it possible to illuminate the solid substance in reflected light, whose plane face is in contact with the prism.

In order to eliminate the influence of temperature, later models of the Abbe double-prism total reflectometer were fitted with a system of internal passages and external tubes for circulating water. For convenience the second prism was hinged. This type of total reflectometer was manufactured in quantity by Carl Zeiss of Jena, Bausch & Lomb of the USA, and Adam Hilger of London. It should again be pointed out here that this device is of merely minor importance in mineralogical research except for the fact that it was often used for calibrating index liquids.

The Liebisch Total Reflectometer

In 1884 Liebisch described two "Neuere Apparate fur die Wollaston'sche Methode zur Bestimmung von Lichtbrechungs-verhaltnissen" (New devices for applying the Wollaston method for determining the relations between indices of refraction). The principle of the method is shown in Figure 13 and an engraving in Figure 14. The equal sided glass prism ABC with a high index of refraction has two polished faces (AB and BC); AC can either be polished or frosted. The crystal (shown in yellow) is placed with its polished surface onto the prism face AB, of course again with a high index immersion liquid for optical contact in-between. It is held in place by gentle pressure of a special spring-loaded device described in more detail later. A diffuse light enters the prism via the face AC, is reflected on the crystal's polished face, and leaves the prism through BC. Observation of the reflected light is facilitated by a telescope (e.g. the telescope of a goniometer), and the critical angle is visible by a sharp demarcation between a bright and a feebly illuminated portion of the image. For measuring anisotropic crystals, the sample must be rotated about an axis perpendicular to the reflecting face, and both the angle of rotation about this axis and the corresponding value of the critical angle have to be monitored. It is essential that the crystal's polished face lies always exactly parallel to the prism face AB. Therefore, Liebisch designed a special delicate device: the crystal is mounted with beeswax onto a small disc which is suspended within a pair of gimbaled rings similar to the attachment of a gyrocompass. This arrangement assures a gentle and proper contact between crystal and prism for all settings. The amount of rotation of the crystal can be read out by a divided circle and a vernier to 5 minutes.

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Theodor Liebisch (1852-1922) distinguished himself by his experimental inquiries into the properties of minerals and rocks. From 1908 to 1921 he was the director of the Humboldt University in Berlin, noteworthy for its famous mineral collection.

Liebisch's total reflectometer was produced by the Fuess Company in Berlin/Steglitz. In the 1909 price list, Fuess offered several different designs: Model 1 (for 115 Marks), a small instrument to be used as an accessory to all goniometers (e.g. No. II as shown in Fig. 16), a larger device with important improvements for the adjustment and a larger divided circle for higher precision (Model II for 230 Marks) exclusively for the No. I goniometer, and a so-called "Selbststandiges Totalrefraktometer"--an autonomous instrument for 250 Marks.

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The range of measurements is limited by the index of the glass prism, but high refractive glasses have two major drawbacks: 1) they are very soft and will be scratched during intensive use, and 2) they show a yellow tint which reduces the transparency in blue light and thus make measurements in this portion of light more difficult. Therefore all instruments were delivered with a second interchangeable prism of lower index for routine measurements in a lower range. Figure 15 shows the device and both prisms in a fitted case, and also illustrates the complexity and delicacy of the mechanical parts of this accessory.

The Pulfrich (Wolz) Total Reflectometer

Carl Pulfrich (1858-1927) was employed after 1883 as an assistant professor at the University of Bonn. He experimented with the refractive indices of crystals, glasses and liquids. At this time he came into contact with the firm of Max Wolz, a resident in Bonn. In 1890 Ernst Abbe called Pulfrich to Jena to be the first head of the "optical measuring instruments" department of the Carl Zeiss Company. Above all, Pulfrich became famous for his success in optimizing refractometers; less well known are his pioneering achievements in the field of stereo-photogrammetry--all the more amazing since he was blind in one eye.

In 1887 and 1888, still in Bonn, Pulfrich introduced his "new total reflectometer," as well as "a new refractometer." The instruments resemble each other, but the first is more technically elaborate (see Fig. 17). The central part of his total reflectometer consisted of a glass cylinder with a height of 31 mm and a diameter of 38 mm on a vertical, rotatable axis, with a small horizontal circle on which the degree of rotation may be monitored. A centering device enables exact adjustment of the glass cylinder. The flat upper face of this cylinder has a frosted bevel on its circumference and a planepoliched center. The refractive index of the glass was 1.7151, and thus sufficient for the measurement of most mineral species.

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Fig. 17 shows a cross section of the cylinder on its centering device, and the ray paths from a light source on the left to the observer's eye. [[mu].sub.1] is the glass cylinder of the total reflectometer, [mu] is the sample (ideally also a cylinder with its polished face in contact with [[mu].sub.1], but any other shape of the sample would do as well as long as a polished face is present).

The critical angle of total reflection is observed, through a telescope with crosshairs, as a sharp bright/dark boundary, and its value is read out on a large divided circle. Because of the elbow-type design of the telescope, all settings and readings can be made from the front side of the instrument.

As already mentioned above, this type of total reflectometer is useful to measure all three principal refractive indices of anisotropic crystals on just one polished face. In the advanced Pulfrich total reflectometer, the whole unit of glass cylinder and crystal can be rotated about a vertical axis by means of a large spoked wheel on the lower end of the instrument.

The "new refractometer equipped particularly for use by chemists" (1888) is--in comparison to the elaborate total reflectometer--a simplified model without a vertical rotation axis and was widely distributed in the laboratories of its day to measure the refractive index of fluids (Fig. 18). Its most important distinguishing feature is a 90[degrees] prism as a glass body onto whose horizontal face a trough for holding liquids is cemented, rather than the vertical glass cylinder of the large total reflectometer. The delicate prism is protected on both sides by glass plates, and only two polished faces--the vertical face for the exiting light beam, and the horizontal face which holds the trough--are visible. The dark cement which was used for assembling these parts makes any false reflection impossible. A mechanical axis of rotation is missing; therefore this apparatus is only of limited use for mineralogical measurements.

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The first such Pulfrich instruments were fabricated by the mechanical workshop of Max Wolz of Bonn. This company was founded in 1883, and exhibited these devices as late as the World Exhibition in Paris in 1900. Wolz instruments may be recognized by their dark green lacquer, which clearly distinguishes them from the products of other manufacturers.

With Zeiss in Jena, Pulfrich further developed the "refractometer for use in chemistry" after 1890. In 1895 he described his "universal device for refractometric and spectroscopic examination." The most important new features were a Geissler tube as a monochromatic light source and an ingenious heating system; the latter enabled the testing of liquids at differing temperatures.

The Abbe Hemispherical Total Reflectometer

Ernst Abbe (1840-1905) was a mathematician, physicist, optician, entrepreneur and social reformer. He investigated the theoretical fundamentals for improving microscopes. For example, he solved the problem of distortions of color in microscope objectives and developed achromatic systems of lenses. Abbe invented many new optical instruments. From 1866 he was a friend of Carl Zeiss (1816-1888) of Jena; he joined the Zeiss firm (founded in 1846), and in 1889 he took over its proprietorship and leadership. Ernst Abbe was also well known as a socio-political reformer; he introduced many groundbreaking and exemplary reforms of welfare for the factory workers. In 1891 he signed over all his assets to a foundation that still exists today.

After 1885, when Bertrand had first devised a small reference scale total reflectometer with a glass hemisphere (cf. Fig. 27), Abbe and his associates picked up the idea. At Zeiss's establishment in Jena a perfect instrument was developed which lent itself especially to precise measurement of indices of refraction of solids.

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Siegfried Czapski (1861-1907) became Abbe's assistant in 1885; his hemisphere total reflectometer was first introduced on September 20, 1889, at the Natural Science Convention in Heidelberg. In principle its mechanical construction was the same as that of the Pulfrich-Wolz total reflectometers. However, instead of a glass cylinder, a hemisphere (n = 1.8904) with a diameter of 4 cm and a plane face on top was utilized. This change offered a technical and economic advantage, as a perfect hemisphere is easier to manufacture than a cylinder. By applying an optical trick, Abbe was able to decisively improve on the sharpness of the demarcation curve of total reflection. The front lens of the objective of the observation telescope is a concave lens of the same glass and of the same radius of curvature as was used for the hemisphere (Fig. 19): this compensates for inaccuracies in the image which otherwise would occur when the light rays leave through the curved surface of the hemisphere.

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The mechanical construction of the Zeiss total reflectometer resembles that of the Pulfrich-Wolz instruments. The hemisphere is mounted with bearings on a complicated adjustable support resting on a small horizontal graduated circle. The larger vertical circle, with a diameter of 13.5 cm, is furnished with a locking and tangential fine-movement device. The exact value of the angle may be read with a micrometer screw. To facilitate observation, the light beam enters the telescope at an angle and, in the original model, is directed through a tube within the axis of the vertical circle. The light is reflected from a mirror and proceeds either across the plane face, or through the hemisphere from below. The telescope is arranged in the form of an elbow, and rotated by an arm about the axis of the main graduated circle; it may be positioned on either side of the hemisphere. The axes of rotation of both graduated circles intersect each other at right angles in the center of the sphere of which the hemisphere is half.

From 1895, at the Zeiss workshop, Pulfrich perfected the Abbe hemispherical total reflectometer. He gave full consideration to making the instrument employable for the smallest crystal faces. He introduced the instrument--which in this highly developed form would find wide application--on September 22, 1897, at the Natural Science Convention in Braunschweig, and in 1899 he published a paper about it. The most important improvement was the introduction of a darkening mechanism in order to limit the illumination to the crystal face being measured. Pulfrich chose a rotatable metal plate with apertures of different diameters; alternatively, an iris-like diaphragm mounted on a carriage with perpendicular sliders would have the same effect. Additionally Pulfrich attached an additional lens in front of the eyepiece of the telescope to convert this into a low-powered microscope in which the crystal could be viewed for orientation and adjusting. Thanks to this optical trick it was now possible to measure small polished faces down to 1.33 mm.

Later Zeiss models are characterized by the fact that the axis of the telescope no longer coincides with the axis of the main vertical circle but lies on its outer edge. Most of the other mechanical and optical components were retained unchanged (see Fig. 20).

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The Zeiss instrument came with a separate box for accessories; in it were two telescope oculars, providing respectively 2X and 3X magnifications, and a third objective which, in combination with one of the oculars, comprised a low-powered microscope.

While sodium light was used to illuminate small crystal plates, sunlight also could be used for larger crystals, and the refractive index for different colors of the spectrum (based on the position of well-known Fraunhofer lines), and thus the dispersion of the crystals, could be measured. Employed for this purpose was a direct vision ocular spectroscope, which also came in the accessories box.

Also made available was a small box with 10 standard reference samples (see Fig. 20) of isosceles glass prisms with different refractive indices. Viola (1899) described his "differential method" as follows: "if the refracting capacity of a mineral is measured with complete accuracy, one can choose for comparison, from among the available glass samples, one whose refractive capacity is near that of the mineral. For example, if one wants to measure the refractive capacity of albite, one chooses a glass sample whose refractive index approaches 1.52157. This sample is placed on the hemisphere of the Abbe instrument, and the telescope is adjusted to the demarcation line as produced through the glass sample. The position of the telescope is then locked to the graduated circle. Thereupon the glass sample is removed without changing anything in the apparatus, and the albite sample is put in its place. Since the telescope has not been moved, the demarcation line as produced by the albite is adjusted with the aid of the fine movement micrometer screw. In this way the angular difference (between the glass and the albite) may be read off, or rather calculated, with great precision." The main graduated circle is rendered dispensable using this method.

In 1905 the Abbe hemisphere total reflectometer, with the features described above, cost 550 Marks, including the glass samples and the carrying case. All of the instruments were signed and numbered.

The design and improvements which originated with Abbe, Czap ski and Pulfrich of the Zeiss workshop were adopted by C. Leiss, the head of the contemporary firm of R. Fuess, Berlin Steglitz. After 1900 the firm of Fuess also offered a variety of hemisphere total reflectometers built almost exactly like that of Zeiss.

Total reflectometer Model I (see Fig. 21) was introduced in 1902 by C. Leiss and by C. Klein. It was mounted on a horseshoe-shaped base. One major feature distinguishing it from the Zeiss instruments is the fact that instead of interchangeable tubes for objective lenses, a hinged magnifying lens in front of the eyepiece was used, affording rapid crossover between telescopic enlargement (1.25-X) and microscopic enlargement (10X).

The trailblazing innovation of the Fuess hemisphere total reflectometer lies in the fact that, if the observing tube is put into a vertical position (see Fig. 22), the instrument can be transformed into a weakly magnifying polarization microscope. To enable this the support of the hemisphere has a central bore through it. Underneath there is installed a polarizing unit and an illuminating mirror. The analyzing unit may be inserted by a slider directly into the ocular. By this means, the index of refraction of single grains in polished thin sections without cover slips may be measured: the thin section is laid on the hemisphere with its polished side downwards, a grain is selected in the "microscope position," the telescope tube is loosened, and in a "total reflectometer position" (see Fig. 21) the demarcation curve of total reflection is determined. Thus the Fuess Model 1, at a price of 500 Marks, was the perfect instrument for mineralogists!

The Fuess Model II (Fig. 38), mounted on a solid tripod base, was developed well before 1900 and was of about the same overall size as Model I. The number of optical fittings for the telescope was reduced as compared to Model I. A device to reduce light intensity, in the form of a sleeve with adjustable slits, was also a new feature. This could be inverted above the hemisphere, and its use permitted examinations of samples without the need to darken the room. The Model II cost 340 Marks.

Model III (see Fig. 23), priced at 170 Marks, was described by C. Leiss in 1908. The dimensions of the instrument, the hemisphere and the graduated circle are smaller than for the models already mentioned. The optical system is mounted on a round base plate that could be adjusted for height. This model was developed above all for demonstrational uses; refractive index can be determined only to the second decimal place.

[FIGURE OMITTED]

The Wallerant Microscope Total Reflectometer

Around the turn of the 20th century, Frederic Wallerant (1859-1936) modified the instrumental set up. The observation telescope remained in a fixed position and was no longer rotated simultaneously with the graduated circle it could be locked with. In this new arrangement the glass prism and the sample attached could be rotated around the sector of a vertical divided circle.

Wallerant was professor for mineralogy at the Sorbonne in Paris. His main field of research was polymorphism and liquid crystals. In 1897 Wallerant suggested a method to determine the refractive indices of minerals in thin sections by means of total reflection. He commissioned the Paris firm of Phillipe Pellin to build a microscope accessory to be fitted on the stage of a Zeiss petrographic microscope. This attachment, firmly screwed onto the stage, has a ring-shaped base plate to allow light to pass from the optical system below the stage (see Fig. 24). It could be rotated horizontally with the stage. A thin section (without coverslip but with a perfectly polished surface) is placed on the slightly truncated edge of an equilateral glass prism of high refractive index (n = 1,89). This setup could be tilted by a graduated vertical circle with a sector of 50 degrees until the critical angle appears, manifested by the boundary between a bright and a dark field. Klein in 1902 augmented the Wallerant device by improving the optical system of the microscope, mainly the centerable iris diaphragm which was essential to focus on a small area of the thin section.

In 1902 Wallerant published details concerning another new total reflectometer, probably built by Pellin in Paris. Its turning apparatus was very similar to the one above. However, it was an autonomous instrument by itself with an observation telescope fixed rigidly at an inclination of 45 degrees. Its glass prism had a very peculiar shape--on the outside it was bounded by eight isosceles triangles with an acute angle of 45 degrees. All of these are inclined towards the ninth face--the base--at 60 degrees, thus forming an eight-cornered pyramid. The prism is attached to a vertical graduated sector. It also could be rotated horizontally analogous to the movement of the stage in the model described above. The advantage of this oddly shaped prism is the fact that the refractive indices of the crystal could be determined successively through two opposing prism faces. This minimized errors resulting from nonparallelism of crystal and basal prism planes. It would appear that these microscope total reflectometers were not widely distributed. A comparable instrument incorporating a glass hemisphere (see Fig. 25) originates from the same period.

[FIGURE OMITTED]

All these ideas and proposals of Wallerant and Klein influenced the construction of the Model I hemispherical total reflectometer of Fuess. The optical system suggested by both authors was fully maintained.

Hand-held Reference Scale Total Reflectometers

The small reference scale total reflectometer lends itself chiefly for quick approximate determinations of refractive indices in various fields of application. The hand-held instruments are very compact. There are no mechanical rotational parts, as a graduated reference scale within the field of vision permits direct read-off to the second decimal. This type of instrument is frequently used in the gemstone trade and for instructional purposes. The invention is owed to Emile Bertrand (1844-1909) who published an article in 1885, unfortunately without a diagram or any mention of the maker. Bertrand, who described a great number of new mineral species, was called in an obituary by Wyroubuff (1910) "un veritable genie de l' appraeil" (a true genius of apparatus). Bertrand became immortalized by his invention of the lens inserted between the ocular and the objective into the tube of a petrographic microscope for the conoscopic investigation of interference figures of crystals.

The Bertrand total reflectometer (Fig. 26) consists of a brass tube R, 5 cm in length and 2.5 cm in diameter. Within, there were two additional short sliding tubes for focussing. The innermost one was fitted with a magnifying lens L on its outer side. The central tube had at its inner end a scale S divided into tenths of a millimeter. The main outer tube is slanted at an angle of 30 degrees at the side opposite the lens. There it is covered by a metal plate holding a glass hemisphere H of high refractive index of about 1.8 with a diameter of 1cm. The plane of the cover plate coincides with that of the hemisphere. Light is admitted by a small section of frosted glass G arranged on top of the hemisphere, thus illuminating its plane surface and any test sample placed on it. The reference scale has to be calibrated with substances of known refractive indices before the instrument can be used. The only instrument of this type known to the authors was built by Wehrlein of Paris (Fig. 27).

It is interesting to note that these small total reflectometers, equipped with a prism rather than a hemisphere, are manufactured today in quantity. These low-priced instruments with specially calibrated scales are employed in a great variety of applications. For instance, the concentration of sugar in wine grapes, anti-freeze detergent in automobile radiators or in solar panels or of serum protein in urine may be determined quickly and conveniently.

The gemstone expert of the British Museum of Natural History in London, G. F. Herbert Smith (1872-1953), improved and amended the Bertrand instrument maintaining its dominating features. A corrective convex glass lens was arranged in proximity to the hemisphere compensating for the spherical curvature of the focal plane and effecting a sharp demarcation line between the bright and dark field. For convenient viewing the setting of the read out lens was bent at a 90-degree angle (see Fig. 28). The firm of J. H. Steward produced two similar models of the Herbert Smith pocket total reflectometer. The larger one, in its wooden case and a printed reference card listing the refractive indices of the major gemstones, was priced at 9 Pounds 10 Shillings, or 130 Marks.

[FIGURE 28 OMITTED]

In 1904 C. Leiss introduced the Model IV total reflectometer of the Fuess, Berlin firm (see Fig. 23). The hemisphere (n = 1.7938) was rotatable around its vertical axis for the examination of doubly refractive crystals. It was in a metal casing for protection. For testing in reflected light, the casing was furnished with a narrow slit that could be shut for experiments with "grazing" light. The Model IV, priced at 90 Marks, was detachable and came with both a wooden handle and a base plate and column.

B. Total Reflectometers with Liquids

The principle of all immersion total reflectometers is identical with that of total reflectometers with glass prisms or hemispheres in that total reflection appears on the boundary between different optical media. In the immersion total reflectometers, the crystal with a polished face or a perfect natural growth face is immersed in a fluid with higher index of refraction, and the critical angle is likewise defined as a line of demarcation between a brightly and a feebly illuminated field. In order to increase accuracy of the measurement, these instruments allow the determination of this line twice, once by tilting the telescope to the right and once by tilting it to the left. Half the angle between the two settings equals the required angle and the refractive index may be calculated accordingly. Also, in case of doubly refractive crystals, there are two demarcations to be distinguished as fields of differing grades of shadings.

Kohlrausch Total Reflectometer

The renowned experimental physicist Friedrich Kohlrausch (1840-1910) conducted research in electrical conductivity, among other fields. In 1878 he published the results obtained with his new instrument, which he called a total reflectometer. The original instrument was built in the university town of Gottingen by the mechanic Wilhelm Apel (?-1898). It was suitable only for observations in a darkened room.

The Kohlrausch total reflectometer (Fig. 29) is mounted on a heavy base plate supporting a triangular column approximately 30 cm in height. At its upper end it carries a divided circle (10 cm diameter) including two verniers and read out lenses. On its underside there is a detachable pear-shaped glass flask with a flat bottom to house the liquid. This vessel has a plane-polished window where it faces the observation telescope. The crystal with its polished face is mounted on a cork plate which is suspended on a holder into the flask. The latter rests on a very complicated adjusting apparatus allowing recordable three-dimensional manipulations from outside the glass cell. A clamping screw can lock the axis of the graduated circle and the crystal holder for either independent or simultaneous rotation. The observation telescope is arranged horizontally either on an outside slide or, in later models, in a collar of the main column as in the device shown in figure 30. The axis of the telescope is perpendicular to the axis of the divided circle. In order to view and to facilitate adjustment of the polished crystal face, the telescope may be converted into a low-powered microscope by simply replacing lenses. A simple sketch (Fig. 31) was provided by Tutton (1911) illustrating the Kohlrausch principle in a horizontal section. Diffuse light enters from one side (s) onto the crystal (c). It is reflected and observed by the telescope (T) through the window (P) of the flask (F) filled with liquid (L).

[FIGURE 29 OMITTED]

[FIGURE 31 OMITTED]

Wilhelm Apel in Gottingen offered the original Kohlrausch total reflectometer with articulated adjusting device for 160 Marks; the company also provided abundant accessories for this instrument. In 1891 the firm of Georg Barthels, also from Gottingen, asked between 100 and 150 Marks "depending on size and accessories." A slightly modified version, lacking the sophisticated adjustment device, was offered by Fuess, Berlin in 1909 for 175 Marks (Fig. 30).

[FIGURE 30 OMITTED]

Suspended Goniometers used as Total Reflectometers

It was M. Bauer of Konigsberg (Kaliningrad) who first recognized (1881) that optic axis angle goniometers originally devised by Des Cloizeaux (1817-1897) and improved in 1871 by Groth (1843-1927) were suitable also for the Kohlrausch method. These instruments include a horizontal graduated circle with a centering and adjusting crystal holder suspended below instead of being positioned above (Fig. 33). The other prerequisite for Kohlrausch studies is a parallelsided glass trough to be filled with a liquid with a high refractive index into which the sample is immersed. This cell is supported by a rectangular small table adjustable for height. The axial angle goniometer also comprises an observation telescope modifiable for a diminishing image. Bauer summarized all the necessary conversions from a goniometer to a total reflectometer.

[FIGURE 33 OMITTED]

During the first two decades of the 20th century these inverse axial angle apparatuses were improved, supplemented and equipped with additional innovations including small heating units. The resulting "universal mineralogical instruments" could be conveniently used as goniometers, for instance for the study of growing crystals in solutions, and for studies in polarized light as well as in reflectometry.

In 1899 Leiss published a description of an "improved total reflectometer" built by the famous firm of Fuess, Berlin and priced at 430 Marks. In this context the "crystal polymeter," also built by Fuess and priced at 2250 Marks, should be mentioned (see Fig. 90 of Burchard 1998). This three-circle goniometer--the largest ever constructed--likewise had a suspended crystal holder and was suitable for Kohlrausch studies. Fairly similar inverse universal apparatus were devised by Henry A. Miers (1858-1942) and were built by the London firm of Troughton & Simms. The model of 1904 still had two supporting columns for the optical system, thus limiting the effective operational are of traverse of the observation telescope. The 1910 (?) model took care of this problem by employing only one broad column (see Fig. 32). Miers took great care to control the temperature of the liquid, demonstrated by elaborate regulation devices. A stream of water flowing through a perforated metal ring pipe at the edge of the cylindrical glass trough, and a stirring arrangement inside the trough driven by an electrical motor guaranteed temperature constancy, which is monitored by a thermometer. A "universal goniometer" by A. Hutchison (1913) and also built by Troughton & Simms, London, costing 30 Pounds, was very similar to the one of Miers. For both the Fuess and the Troughton & Simms suspended goniometers, a direct-vision spectroscope could be fitted to employ the method of Soret (see later heading).

[FIGURE 9 OMITTED]

[FIGURE 32 OMITTED]

Supplementary Glass Vessels for Fuess Goniometers

Most Kohlrausch total reflectometers were rather expensive, and it is not surprising that for economic reasons several supplementary devices were developed by Fuess, Berlin. All of these were suitable for use on goniometer Models 1 to 3 by Fuess. Especially the standard Models 2 and 2a were omnipresent at most mineralogical institutions of that time. The cylindrical glass vessels with appropriate crystal holders were designed to be filled with highly refractive liquids like monobromonaphthalene or methylene iodide. In 1896 two Munich mineralogists, A. J. Moses and E. Weinschenk (1865-1921), commissioned a three-part accessory from the local firm of Bohm & Wiedemann, priced at 25 Marks. The glass vessel was connected to the tube of the observation telescope by means of a rigid arm. The complexly constructed crystal holder replaced the small button that usually rests on top of the goniometer head and permitted unlimited manipulations of the crystal. Following the suggestions of Soret (see next heading) there was a second crystal holder nearby where a reference sample (fluorite) could be attached. A cylindrical cardboard casing could be inverted from above. It was covered by asbestos, and openings were cut in where adjoining the collimator and telescope lenses. This casing functioned as an air-bath and served as an insulator against temperature fluctuations.

A similar arrangement was proposed in 1908 by the Portuguese mineralogist V. Souza Brandao and was marketed by Fuess, Berlin for 90 Marks. It consisted of two parts: the simple C-shaped crystal holder was connected directly onto the top of the goniometer head. The arm for the glass cell was attached to the telescope tube by numerous articulations. It could be pushed aside but the original position with respect to the axis of the telescope was easily reproduced. There was no casing for temperature constancy present.

In 1898 Carl Klein (1842-1907) published a photograph of an "observation instrument following the Kohlrausch principle." Carl Klein gained recognition as a crystallographer at several German universities and was an inventor of a great many crystal rotating devices mainly to be employed with petrographic microscopes. Klein stated that C. Leiss of Fuess, Berlin looked after the construction of the 1898 instrument with "patience and devotion." This instrument remains somewhat enigmatic as there was no graduated circle, and it cannot be found in any of the Fuess catalogues; possibly it was one of a kind. A rectangular base plate supported two columns. One supported a rigidly mounted horizontal observation telescope. The other carried a cylindrical glass vessel with an inverted two-circle Klein rotating device that permitted rotation and recording of both the vertical and horizontal axis of the crystal holder.

In the final pages of his monumental book "Physikalische Krystallogrphie" (1905) Groth catalogued listings of mineralogical instruments by various German manufacturers. Included in this listing, under the heading of Fuess, is a "large total reflectometer suitable for goniometer No. I" priced at 270 Marks. This entry is somewhat puzzling since usually Groth described almost all instruments in his text, and there is no reference in any of the Fuess catalogues. However, there exists one "goniometer supplementary glass vessel" to be attached directly onto the goniometer head by means of two screws. It dates circa 1920 as is indicated by the nickel-plated parts (see Fig. 34). The cylindrical glass flask has a diameter of 10 cm and is adaptable exclusively to the large No. I Model goniometer. A rotational crystal holder may be suspended from above. Only the rotation within the plane of the crystal holder can be recorded. The critical angle corresponding to the total reflection is determined with great accuracy using the divided circle of the No. I goniometer. In front of the collimator tube of the goniometer a small monochromator may be inserted, enabling measurements of dispersion.

[FIGURE 34 OMITTED]

The Total Reflectometer of Soret

Measurements with Kohlrausch total reflectometers are hampered by some intrinsic disadvantages. For one, the refractive index is influenced by the temperature of the surrounding fluid. Secondly, measurements of dispersion require monochromatic light and thus different light sources (e.g. Geissler tubes). In order to overcome these shortcomings Charles Soret (1834-1904) of Geneva conceived an advanced instrument in 1883. This fairly complex apparatus (see Fig. 35) was built by the famous company SIP--Societe Genevoise pour la construction d'instruments de physique et de mecanique--headed by its then-director Theodore Turrettini (1845-1916).

[FIGURE 35 OMITTED]

[FIGURE 36 OMITTED]

III. MICROSCOPIC IMMERSION METHOD

In mineralogical practice this is the most frequently used technique for samples for which a smooth plane surface is difficult to obtain because of the grain size, hardness, internal cracking, or other unfavorable circumstances. It is also the simplest, quickest, and most expedient of all the methods, requiring no elaborate grinding or other sample preparation; only a mortar & pestle and a set of calibrated immersion liquids are needed. For the immersion method one generally employs a standard polarizing microscope and a grain mount of the crystals to be measured. The accuracy depends on the precision with which the match between the refractive index of the immersion and that of the crystal can be set. Suitable methods of finding this match are the Becke-line (a line of light which results from diffraction at the boundary face between two media of different refractive index, and which disappears at the point of match; an accuracy of [+ or -]0.002 is attainable by this method), phase contrast (an optical method which otherwise finds its use chiefly in medicine and biology--Piller, 1952), or "dispersion staining" (an optical staining based on refraction at the boundary between media of different dispersion--Dodge, 1948; Laskowski et al., 1979). The measuring process and its accuracy can be further enhanced considerably through the [lambda]-T-variation method of Emmons (1929). By this method the immersion liquid is first roughly adjusted to the grain to be measured, e.g. by mixing two liquids with different indices of refraction. The fine-tuning and precise match is subsequently set by variation of both temperature and wavelength of light.

Problems with this method are: (1) obtaining an appropriate orientation of anisotropic grains for measuring principal refractive indices, and (2) determining the refractive index of the immersion liquid at the moment of the match. The selection of crystals in suitable orientation can be made from microscopic observations using interference figures, or, much more elegant and precise, through the use of rotation apparatuses as accessories to the microscope (e.g. the universal-stage, also known as a U-stage, and the spindle-stage). With the universal-stage there are flow-through cells for heating by temperature controlled liquids, and the spindle-stage can also be furnished with heating cells for this purpose.

Of course it is imperative that the refractive index of the fluid at the moment of match with the crystal is known or quickly determinable. To this end, Emmons (1929) used an external Abbe total reflectometer, whose prism is circulated around by the same fluid as the cell which holds crystal and immersion, and thus is at the same temperature.

For high precision measurements by the immersion method, two special devices with in situ refractometers were designed: the universal stage total reflectometer and the micro-refractometer spindle-stage.

The Universal-Stage Total Reflectometer

The universal-stage total reflectometer is a special attachment for the Leitz universal-stage; it consists of an upper hemisphere with a small central hemispherical well that holds an immersion liquid that is chosen to have a slightly higher index of refraction than the crystal. This is placed onto a special glass slide forming the flat lower cover of the immersion cell. Orientation of the sample for determining the principal refractive indices proceeds by the standard universal-stage method. Subsequently the temperature is raised by a special resistance heating device, whereby the refractive index of the immersion liquid is lowered until the match is reached. At the point of match the universal stage is tilted about its horizontal axis until total reflection occurs on the interface between the glass slide which holds the crystal, and the immersion liquid. The angle of the tilt yields the exact refractive index value for the immersion liquid, and therefore also for the crystal. In principle the universal-stage total reflectometer resembles a classical hemispherical total reflectometer, though combined with the universal adjustability of a universal-stage. Berger (1942) showed that with this equipment a precision of better than [+ or -]0.001 is attainable.

[FIGURE 37 OMITTED]

[FIGURE 38 OMITTED]

The universal-stage total reflectometer is not very easy to use, and thus it has never been widely adopted. Therefore these instruments are rather scarce.

The Spindle Stage

In principle the spindle stage is a modern version of earlier rotation devices with immersion cells (e.g., Klein's trough devices) which were widespread around 1900 (Medenbach et al., 1998; Kile, 2003). Through a computer-supported interpretive process the spindle-stage can be used to quickly and precisely orient a single crystal for measurement of indices of refraction, and subsequently to determine the values by the immersion method (Bloss, 1981; Dyar et al., 2008). In 1965, Feklichev und Florinsky suggested an internal refractometer for such devices. The refractometer is a second crystal with perfectly known optical data and orientation, which is placed in the same drop of liquid as the unknown. This refractometer crystal is mounted on a second spindle, and, during rotation, its index of refraction varies with the angle. In practice, the unknown is oriented first by the spindle-stage method, then the index of the immersion liquid is varied until a match is achieved (e.g. based on observation of the Becke line or dispersion staining); the refractometer crystal is then rotated until it also matches the index of the immersion liquid. The value calculated from the angle of the refractometer crystal is thus identical to the one for the immersion liquid and the unknown. An improved micro-refractometer spindle stage employing this method was described in 1985 by Medenbach (Fig. 37). With this instrument it is possible to measure even the smallest grains with an accuracy of [+ or -]0.0003.

ACKNOWLEDGEMENTS

The authors are grateful to Tom Moore who provided an initial English translation of the German manuscript. The final version was improved considerably by a careful review and numerous comments by Dan Kile.

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Ulrich Burchard

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ulrich.burchard@t-online.de

Olaf Medenbach

Ruhr-Universitat Bochum

olaf.medenbach@rub.de