V. D. Kuznetsov.

The Effect of Temperature on the Internal Friction of Rock Salt.

§ 1. Purpose of the work. The question of the effect of temperature on the internal friction of rock salt is of great interest because: 1) its crystalline structure has been fully elucidated by the work of the Braggs (father and son),¹ and 2) its electrical conductivity has been studied by Curie² and Lukirsky.³ There is an undoubted connection between electrical conductivity and viscosity, and it is very important to establish the quantitative dependence between these quantities.

I determined the coefficient of internal friction of rock salt at various temperatures by the torsion method twice, with two different apparatuses. The first time, the torsion of salt was begun by me jointly with K. P. Grinakovskii in 1912, and was then continued by me alone in 1918.

The rock salt was supplied by B. P. Weinberg, who brought it from the Wieliczka mines (Austria).

§ 2. Basic formula. General remarks. If one end of a rod with a rectangular square cross section is fixed immovably, and to the other we apply a twisting moment \(M = Pd\), where \(P\) is the acting force and \(d\) the arm, then, after some time following the action of the force, the change in the angle of twist \(\Delta \varphi\) over equal intervals of time \(\Delta t\) becomes constant, i.e., a certain stationary regime is established, in which the angular velocity of twisting of one end relative to the other will be constant; then the coefficient of internal friction \(\eta\) may be calculated by the formula:

\[ \eta = \frac{6PdL}{a^4\left(\dfrac{\Delta \varphi}{\Delta t}\right)}, \]

where \(L\) is the length of the specimen being twisted and \(a\) is the side of the square of the cross section.

After the application of the twisting moment, the rate of deformation begins to decrease and, after a fairly long interval of time, becomes constant. If time is plotted along the abscissa axis and the magnitude of deformation along the ordinate axis, then the curve gradually rises, being concave toward the abscissa axis; but with the passage of time its concavity diminishes and the curve passes into a straight line with a definite inclination to the abscissa axis. The tangent of the angle of inclination is the measure of the angular velocity of twisting. To determine \(\eta\), the twisting must be carried out at constant force for so long a time that a stationary state is established. Throughout this interval of time it is necessary to maintain constancy of temperature.

§ 3. Instruments and apparatus. In Fig. 1 is shown the instrument which served in 1912 for twisting salt at \(405^\circ\). On board A were mounted the fixed stand B and the movable C, which moved along a guide and could be firmly fastened in any position by thumb screws. On the brass axle D (diam. 1.5 cm), rotating in iron double plate bearings E\(_1\) and E\(_2\), there were fastened a limbus G and a wheel F with a groove (diam. of the bottom of the groove 24.8 cm).

along the periphery. A rotating weight \(P\) was suspended from thread \(J\). At the end of the axle there was fastened a square, hollow, thick-walled, removable box \(K_1\), into which the end of the rock-salt specimen was cemented with plaster. To the sleeve \(L\), which could move along the upright \(C\), there was attached a rod with a box \(K_2\) for securing the second end. In the center of the bottom of each box conical points were made for the correct setting of the specimens.

The salt was surrounded by a brass cylindrical casing, divided into two parts along the generators, with slots for the axles. The casing, moreover, was wrapped in asbestos board. Heating was carried out by a Teclu gas burner with a regulator. Thermometer \(T\) was inserted into the tube of the casing. In front of limb \(G\) there was placed a measuring microscope with an ocular scale.

The specimen was fastened in the following manner. Small recesses were drilled in the middle of the bases of the specimen. Box \(K_1\) was removed from the axle and clamped in a lathe so that its conical point coincided with the center of the movable headstock of the lathe. The rock salt was clamped between the centers of the box and the headstock, and the gap between the salt and the walls of the box was filled with diluted plaster. After the plaster had dried, the box with the salt was removed from the lathe, screwed to the axle of the apparatus, and then the second end of the specimen was cemented in the same way.

Fig. 2 shows the apparatus constructed by me, with which I carried out torsion in 1918. On the wooden board \(AA\), two uprights \(B_1\) and \(B_2\) made of strip iron (\(1 \times 5\) cm) were fastened with bolts. In upright \(B_1\) a bicycle axle \(C\) was mounted on ball bearings. At one end of the axle an iron disk \(D\) (diam. \(17.5\) cm) was fastened, with iron overlays along the periphery to form a groove. A twisting weight \(P\) was suspended from thread \(F\). To the other end of the axle, which had been lengthened by means of a reducing coupling, there was attached a thick-walled brass square box \(F_1\) with four screws on its sides. Another similar box \(F_2\) was fastened to upright \(B_2\). The investigated bar of rock salt \(G\) was secured by its ends in the boxes, with metal plates placed between the screws and the salt across the whole width of the bar. Two small mirrors \(H_1\) and \(H_2\) were mounted on the salt. The rock salt together with the clamps \(F_1\) and \(F_2\) was placed in a double separable casing \(JK\). The inner part of the casing \(J\) was a box of red copper, and the outer \(K\)—a box of sheet iron, covered on all sides with asbestos board. The two half-boxes shown in Fig. 2 (the second parts have been removed for clarity) are joined to each other by two thick-walled tubes \(L_1\) and \(L_2\), whose inner diameter is slightly greater than the diameter of the axle. The casing stood on four screw legs, of which two, \(M_1\) and \(M_2\), are shown in the drawing. At first the casing was removed completely, and then, after the specimen had been fastened and the mirrors installed, it was put in place without contact with the rest of the apparatus and, consequently, without risk of disturbing the setting. After the first half of the casing had been installed, the second half of the inner box \(J\), to which the second halves of the tubes \(L_1\) and \(L_2\) were soldered, was first slid on, and, finally, the other half of the outer box \(K\) was put on.

In view of the fact that this arrangement of the casing proved in practice to be very convenient, it is shown separately in Fig. 3, from which it is evident how the very connection of the halves of the boxes is arranged. It should also be pointed out that the semicircular cutouts in the removable part \(K\) entered into grooves.

thicknesses \(L_1\) and \(L_2\). In the front side, both the inner and the outer boxes of the casing had polished glass plates (\(3.5 \times 10\) cm) \(N_1\) and \(N_2\) fitted into them. Between the two boxes, on the bottom of the casing, an electric heater \(O\) was placed, consisting of an iron frame on which a rheostat wire was wound with an asbestos gasket. Thermometer \(T\) served for measuring the temperature.

In Fig. 4 the mirror with the specimen is shown at natural size in three projections. The frames were cut from a sheet of tin. The mirrors were held on the specimen by three points 1, 2, and 3 and by an elastic bow.

§ 4. Methods. In 1912 the angle of rotation was determined directly from the limb, divided into half-degrees, through a measuring microscope whose magnification was chosen so that its scale served as a vernier. Readings were first taken at definite moments, and then the moments at which the zero of the microscope passed through definite divisions of the limb were noted.

The very method of determining the angle of torsion \(\varphi\) cannot be considered reliable, because it is impossible completely to eliminate the twisting of the ends in the clamps. Embedding in gypsum was proposed by B. P. Weinberg as the most reliable, since annealed and set gypsum changes little upon heating. With this method it is difficult to say what exactly constitutes the length \(L\) of the specimen. Can one take as \(L\) the length free from the clamps, or does the part of the specimen hidden in the clamps also take part in the torsion? I took as \(L\) the length free from the clamps, on the grounds that the bar of rock salt, which had been twisted in all by \(93^\circ\), had a helical line of edges only in the free part; the ends lying under the gypsum remained rectilinear.

Heating with a gas burner had the drawback that the gas pressure was uneven, and the screw had constantly to be regulated, which is rather inconvenient and fatiguing when the experiment is of long duration.

A common drawback of torsion methods is the friction in the bearings, which is especially large in an almost static state, i.e. at a very small angular velocity. To investigate the friction, a thread was passed over the wheel of the axle, and cups with equal loads \(P\) were suspended from its ends; then fine sand was poured in a thin stream into one of the cups, and the quantity \(p\) of sand necessary to set the axle into rotation was weighed. The investigation was carried out in 6 different azimuths, and the mean of 6 values of \(p\) was taken as the characteristic of the friction force. For loads \(2P\) from 0 to 4000 g it turned out that \(p\) is expressed by the formula:

\[ p = (14.3 + 0.0158 \cdot 2P)\ \text{g}. \]

The torsion of rock salt was carried out at \(P = 500\) g, and, consequently, the friction force \(p\), which at this load amounts to about 2–3%, could, in view of the accuracy of the experiments, have been neglected; but apparently this is not so. At a very small angular velocity the friction has a large influence and makes the very twisting nonuniform. Instead of a smooth increase of the angle \(\varphi\), the change occurs in jumps. Light taps on the axle, for example with a pencil, to a certain extent eliminate this drawback, and in more accurate experiments it would be necessary to arrange an automatically acting little mallet that could produce light blows on the axle.

The second method, which I used in 1918, is considerably more accurate: the apparatus had a more perfect construction; friction, owing to ball bearings, was reduced; the value of the length \(L\) was quite definite; the angle of torsion was determined by the mirror method and

scales, and heating by electric current maintained the temperature almost constant. The wire was heated by current from a large 70-volt storage battery, and the current was adjusted by a rheostat with a sliding contact.

§ 5. Description of the experiments. I. Experiments of May 19 and 20, 1912. At 9 a.m. on May 19 the burner was lit. Approximately by 1 p.m. the temperature had gradually been artificially raised to 395°, and at this temperature, under the action of a load of 500 grm., the rock salt was twisted until 5½ p.m.; then an asbestos cover was placed on the casing in order to raise the temperature still further, and by 7 o’clock the temperature had risen to 420°. Undergoing slight oscillations to one side and the other, this temperature was maintained until 11½ p.m. During the night of May 20 the temperature was again lowered to 397° and was maintained by me at this level all night. On the morning of May 20, from 7½ o’clock to 12¼ o’clock, the temperature was again raised to 418°, and then from 12¼ to 5 p.m. was kept constant at about 397°.5°.

Plotting along the abscissa axis the time from the beginning of twisting, and along the ordinate axis the angle of rotation, I obtained a sufficiently smooth curve, the tangent to which gradually inclined toward the abscissa axis. Beginning at 2 h. 50 m. at night and up to the end of the observations, i.e. until 5 p.m., the curve had the form of a straight line with slight breaks to one side and the other, depending on the change of temperature. This shows that a stationary regime during twisting had been reached. Over 14 h. 9 m. of uniform twisting the angle of rotation proved to be 15°.5, and over the entire duration of the experiment, 93°.

II. Experiments of March 15–19, 1918. At 6 h. 20 m. in the afternoon a load of 1000 grm. was suspended, and from that moment observations were begun at room temperature, which only on March 15 was 16°.3, while on March 17–19 it varied from 13°.5 to 14°.5. As the mean value of the temperature over the last three days one may take 14°.0. The observations were interrupted at 8 h. 25 m. in the morning on March 19. Two small mirrors were fixed on the salt at a distance \(L = 7.0\) cm. Two telescopes with vertical scales were mounted on one stand. The left scale was reflected from the left mirror and viewed in the right telescope, while the right scale, reflected from the right mirror, was observed in the left telescope. The mean distance \(D\) from the mirrors to those parts of the scales that were visible in the telescopes was 120 cm. Over the entire period the left small mirror turned from 35.70 cm to 36.20 cm, and the right from 34.83 to 35.08 cm. According to the curve, the regime may be considered stationary for 46 hours.

III. Experiments of March 30–31 and April 1–2, 1918. The apparatus was moved to a basement room. The arrangement was the same as in experiments II, but the mean distance \(D = 132.5\) cm. At 1 h. 50 m. on March 30 an electric current of 1 ampere was closed and was opened at 2 h. 25 m. on April 2. From the evening of March 31, the temperature recorded in the observations was at all times equal to 70.0°. The room temperature fluctuated within small limits around 13.5°. From 2 h. 30 m. on March 30 to the end of the observations, the left small mirror turned from 10.66 to 11.61 cm, and the right—from 29.71 to 30.16 cm.

IV. Experiments of April 5–6, 1918. An electric current of 1.5 amperes was closed at 11 h. 53 m. in the morning on the 5th and opened at 9 h. 10 m. on the 6th. From 12 h. 58 m. in the afternoon on the 5th to the end of the observations, the left small mirror turned from 14.51 to 15.52 cm, and the right—from 68.69 to 69.80 cm. The mean distance \(D\) could be taken as equal to 133 cm. The temperature fluctuated within the limits 131.8–131.0°, and in the last period was 131.0°.

Briefly by V. F. Kuznetsov: The Effect of Temperature on the Internal Friction of Rock Salt

Fig. 2.

Fig. 1.

Fig. 4.

Vertical axis: \(\log \delta\)

Horizontal axis: temperature.

Fig. 5.

Fig. 3.

§ 6. Results and conclusions. To calculate the mean temperature at which twisting took place, I took the products of the intervals of time during which the temperature remained constant by the corresponding temperature, and divided the sum of the products by the sum of the intervals of time.

In experiments I the length of the rock-salt specimen was equal to 6.1 cm. Both ends, over a length of 1.0 cm, were filled with gypsum. I assumed that no twisting occurred at the places of filling and took \(L = 4.0\) cm.

The length of the arm \(d\) in experiments I was 12.4 cm, and in experiments II—IV 8.75 cm. The twisting load was, in experiments I, 500 g, and in II—IV 1000 g. The angular velocity was expressed in radians and seconds. The mean value of the side \(a\) of the cross-section of the specimen in I was 1.024, and in II—IV 1.03 cm.

The results of the experiments are presented in the table.

Table.

Plotting temperature along the abscissa axis (Fig. 5), and \(\log \eta\) along the ordinate axis, we obtain a straight line; consequently, the dependence of \(\eta\) on temperature within the limits 14—405° for rock salt may be expressed by the formula

\[ \eta_\theta = \eta_{14} e^{-\alpha(\theta - 14)}, \]

where \(\alpha\) is a constant coefficient, and \(\eta_{14}\) is the value of \(\eta\) at 14°. Drawing the straight line through the two extreme points, we obtain \(\alpha = 0.024\).

A salt specimen, twisted over a length of 4 cm at 405° through an angle of 93°, was examined optically. It turned out that:

1. A bar that had been quite transparent became opaque and acquired a whitish appearance.

2. On examining a section about 3 mm thick in ordinary light, helical cracks were clearly visible; these apparently followed the direction of the cleavage planes.

3. On examining the same section in polarized light, interference coloration was observed, which testified to the transformation of the salt from an isotropic into an anisotropic body. It was impossible to determine the extinction angle of the coloration.

These observations show that during twisting rock salt becomes nonhomogeneous and, apparently, its crystalline lattice…

undergoes destruction. The residual deformation in the torsion of crystals may apparently be regarded as a displacement of elementary cubes from one position to another, separated from the first by an integral multiple of some number.

From the point of view of the structure of rock salt, considering the molecular forces acting between the elements of the lattice—the ions Na and Cl—as electrical forces, it is of great interest to investigate torsion at various temperatures of: 1) rock salt perpendicular to the cleavage plane and 2) molten salt.

(Completed in revision 18.6.23).

A. K. Ivanov.

Magnetic Observations in the Minusinsk Region in 1920

In the summer of 1920 an expedition from Tomsk University went to the Minusinsk region, consisting of representatives of the Cabinet of Geography and Anthropology, under the general direction of Prof. S. I. Rudenko. Carrying out the work assigned to me on the investigation of the lakes of the southwestern part of Achinsk District, at the end of July I undertook a trip through Minusinsk District in order to study its landscapes. At the same time, having an assignment from the Geographical Department of the Institute for the Study of Siberia, I incidentally made magnetic determinations at 16 points, listed in the following article by S. I. Shubin, who kindly agreed to compute the data of the observations made. The instrument with which the magnetic determinations were made was a simplified copy No. 3 of Bayer’s magnetic field theodolite (Carnegie Institute).

Even before the trip, I had encountered in the literature a statement by the soil scientist L. Prasolov that in the area west of the ulus Dzhirim—“8 versts from Bely Ius, Emel’ianov saw two conical hills, the rocks of which strongly affected the magnetic needle” (Proceedings of the Soil-Botanical Expeditions for the Investigation of Regions of Asiatic Russia. Part I. Soil Investigations of 1910, ed. K. D. Glinka. Issue 2. L. Prasolov. A Soil-Geographical Sketch of the Northwestern Part of Minusinsk District. St. Petersburg, 1914, p. 12). Prof. B. P. Weinberg, who made determinations here in 1915, also tentatively spoke of a magnetic anomaly in the Dzhirim area. With the intention of investigating this interesting region in detail, I scheduled it for the end of the route.

Unfortunately, the conditions of travel across the steppe proved unfavorable for the fragile instrument. Despite all precautions, after the very first trip on horseback the tube turned out to be damaged, and it was necessary to limit oneself only to observing the horizontal component. During the further journey, the stirrup for the magnet repeatedly slipped out from under the clamp, and the thread broke. It was necessary each time to unwind the thread again and determine its torsion, which slowed the work. Finally, already after the observations in the ulus Dzhirim, while traveling in its environs, the only spare thread broke, and there was then nothing with which to replace it. It was necessary to stop making observations precisely in this most interesting region.

My active assistant throughout the entire journey was the student of Tomsk University M. P. Gryaznov.

1. W. H. and W. L. Bragg. X-rays and Crystal Structure. Moscow, 1914. ↩

2. J. Curie, Ann. d. Ch. et de Phys. 18, 203 (1889). ↩

3. P. Lukirsky, Zh. R. F. O., 50, 26 (1918). ↩