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Physical Properties of Bismuth

It is possible that bismuth can exist in several allotropic forms, but the evidence at present available is not conclusive. Transition points have been reported, occurring at 75° C., 112° C. and 116° C. In addition, it has been suggested that a cubic modification of bismuth exists at temperatures just below the melting point, changing into the hexagonal form at a slightly lower temperature. No direct evidence has been obtained for the existence of cubic bismuth, but a transformation of this order might possibly afford an explanation of the cracks which are set up during the growth of a single bismuth crystal; evidence for the existence of such cracks is abundant, but it is more probable that they are due to impurities. A comparison of the electrical resistance of unannealed bismuth with that of the slowly-cooled metal indicates that a transformation occurs between 160° and 180° C. Investigation of the thermal and electrical properties of very pure bismuth, containing less than 0.01 per cent, of impurities (consisting of platinum, silver and iron), failed to reveal any transition point at 75° C. or near the melting point. The temperature-resistance curve shows no inflections between -190° and 271° C. Photomicrographs failed to show any difference in the structure of bismuth chilled at various temperatures. Evidence derived from the investigation of the thermal expansion of a bismuth single crystal has yielded interesting results with reference to the possible allotropic change at 75° C. When the thermal expansion is determined by ordinary methods there is a definite discontinuity on the temperature-expansion curve at 75° C. No such discontinuity was at first observed when measurements were made on the crystal lattice by X-rays, but a later investigation revealed a small but definite increase in the coefficient of expansion between 70° and 80° C. It is possible, therefore, that an allotropic change does occur at approximately 75° C., but the nature of the change, if it exists, has not been determined. It is probable that another modification of bismuth is obtained at the ordinary temperature by the application of pressure of the order of 25,000 kilograms per sq. cm. Since the transition to this new form is accompanied by a reduction in volume of about 9 per cent., it is deduced that this modification should be formed from the liquid with a contraction of the order of 4 per cent. This new form of bismuth appears to be analogous to the high-pressure modification of ice.

Bismuth is a white metal, having a slight reddish tinge and a brilliant metallic lustre. It is very brittle and can easily be powdered; it can, however, be worked to a very slight extent by very careful hammering. It crystallises in rhombohedra belonging to the hexagonal system

a:c = 1:1.3035; α = 87°34'

The examination of bismuth crystals by X-rays indicates that the metal crystallises in the di-hexagonal class of the hexagonal system; the structure is that of a face-centred lattice, the bismuth atoms lying on two interpenetrating face-centred rhombohedral lattices. The unit rhomb contains eight atoms, the length of the edge lying between 6.52×10-8 cm. and 6.57×10-8 cm. The length of the edge of unit structure is 3.28×10-8 cm. The three edges of the rhombohedron meet in the trigonal axis, and the angle between any two of the edges is 87°34'. The angles between the faces have been determined. The crystals have perfect cleavage parallel to the (111) plane and perpendicular to the trigonal axis, but the cleavage is not so good parallel to the (111) planes. The "atomic diameter," or closest approach of two atoms, is 3.11×10-8 cm. Bismuth crystallises from the melt in skeleton rhombohedra of the form indicated. The structures of spluttered and evaporated bismuth films and of electrolytic bismuth have also been described. Native bismuth probably has not preserved its primary structure. The spontaneous crystallising power of bismuth has been investigated. X-rays do not appear to alter the structure of bismuth during crystallisation. Investigation of the variation of certain physical properties of bismuth with crystal deformation has suggested that a secondary or "mosaic" structure is superimposed upon the lattice, and that this "mosaic" structure, which is perfectly regular, is capable of undergoing deformation without alteration of the crystal lattice itself.

Single crystals of bismuth have been prepared and their properties examined. On account of their anisotropic nature they have received considerable attention. The different values that have been obtained by different investigators for some of the properties may be due to imperfections in the crystal, for it is claimed that slight strains set up during the growth of a bismuth crystal have a great influence on the orientation of the trigonal axis of the crystal lattice; in addition, as has been mentioned previously, cracks may develop in the crystal at a temperature just below the melting point. The effect of a magnetic field upon the growth of a bismuth single crystal has been examined, and the results of these investigations lend support to the theory of "mosaic" structure.

The density of bismuth (D420) is 9.80. That of single crystals grown under normal conditions is 9.82 to 9.83; it is affected by the presence of a magnetic field during the growth of the crystal.

The coefficient of thermal expansion (linear) is 12.98×10-6 between -183° and 15° C., and 13.45×10-6 between 19° and 101° C. For a single crystal the coefficient at the ordinary temperature is 13.96×10-6 parallel to the trigonal axis, and 10.36×10-6 perpendicular to that axis, the mean coefficient between 20° and 240° C. being 16.6×10-6 parallel to the trigonal axis, and (12.0±0.2) ×10-6 perpendicular to that axis; between 240° C. and the melting point the coefficient falls off very markedly. The effect of a magnetic field upon the coefficient of thermal expansion (linear) of a single crystal has been determined. The coefficient of thermal expansion (cubical) is 39.6×10-6.

The mean compressibility is 3.0×10-6 for the pressure range between 100 and 500 megabars. This value decreases at very high pressures. The compressibility of single crystals has also been determined.

The hardness on Mohs' scale is 2.5; the Brinell hardness number (using a 6.35 mm. ball and a load of 40.3 kg. At 15.5° C.) is 7.3.

Temperature, ° C.2777127177227267272.7 (liq.)327.2 (liq.)371.1 (liq.)
Atomic Heat at Constant Pressure6.156.316.466.606.736.837.2177.1196.995
Atomic Heat at Constant Volume6.086.226.356.486.606.70. . .. . .. . .

Young's modulus is 0.32×106 kg. per sq. cm., and the tensile strength about 450 kg. per sq. cm.

The specific heat at the ordinary temperature lies between 0.03023 and 0.0303, and the variation with temperature is given approximately by

c = 0.030 + 0.000013t

(where t is the temperature in degrees Centigrade), but there is an anomalous increase when the temperature is 20° to 30° C. below the melting point. The atomic heats (in calories per gram-atom) at high temperatures are as in table. The atomic heats at low temperatures are:

Temp., ° C.Atomic Heat (calories per gram-atom).Temp., ° C.Atomic Heat (calories per gram-atom).Temp., ° C.Atomic Heat (calories per gram-atom).
-201.95.040-96.25.899 +12.36.139
-198.45.216-85.35.924 +22.26.089
-171.75.464-74.15.976 +25.26.104

The metal employed was very pure, and contained no lead, arsenic or antimony. The specific heat of bismuth is increased by chilling, and after exposure to X-rays.

The melting point is usually given as 271° C., but values as low as 269° C. have been recorded. The metal is very susceptible to supercooling, and it has been shown that the degree of supercooling at which the bismuth nuclei begin to reerystallise is definitely related to the degree of superheating to which the metal has been submitted; and also, that the crystal nuclei tend to persist after melting and are only slowly destroyed on superheating. If a single crystal of bismuth is heated to 10° C. above the melting point, and cooled slowly, the re-formed solid shows the same crystallographic orientation as the original crystal; when heated to a higher temperature, however, and then re-solidified, a random orientation results. The linear velocity of crystallisation reaches a maximum value of 2 cm. per minute with 2° of supercooling.

The latent heat of fusion is 13 calories per gram.

Bismuth contracts considerably on passing from the solid to the liquid state, the percentage contraction being 3.47. The metal further resembles water in that the liquid attains a maximum density at a temperature just above the melting point.1 It is probable, however, that at very high pressures a modification of bismuth exists whose density is greater than that of the corresponding liquid phase.

The density of liquid bismuth is given by

D = 10.07 – 0.00125(t - 269)

where t is the temperature in degrees Centigrade. Between 420° and 1100° C. the relationship between the specific volume, vt, and the temperature, t° C., is given by

vt = 0.1011 + (128×10-7)(t-420)

Between 420° and 271° C., however, this relationship does not hold, the specific volume decreasing less rapidly with fall of temperature below 420° C. From this, from a consideration of the effect of bismuth on the melting points of other metals, and from the surface tension, it is calculated that the molecular weight of bismuth is constant at approximately 209 between 420° and 1400° C., increasing sharply above that temperature and attaining a value of 334 at 1500° C. At 2100° C. bismuth again becomes monatomic.

The specific heat of the liquid at 369° C. is 0.019.

From his results, Birkumshaw deduces that liquid bismuth is associated. For the parachor, calculated from the results of Hogness and Birkumshaw, the values 92.0 and 94.4 have been obtained. The atomic parachor, determined by measurements on covalent compounds, is 80.0; there are thus positive anomalies of 12.0 and 14.4 respectively. Since, if a double bond joins two atoms, the parachor (calculated for one atom) will show a positive anomaly of 11.6, it is deduced that, for bismuth in liquid form, the molecule contains two atoms which share four electrons.

The viscosity of liquid bismuth decreases from about 0.0168 at 300° C. to about 0.01 at 600° C.

The boiling point lies between 1440° and 1500° C. It varies considerably with pressure, as the following data show:

Pressure (mm.)10225776047888892
Boiling point (° C.)12001310150018702100

From these data the latent heat of vaporisation of bismuth is found by calculation to be 42,700 gram-calories per mole. The variation of the vapour pressure of bismuth with temperature is given as follows:

Temperature (° C.)12101290138514101490
Pressure (mm.)63126300406760

Between 827° and 947° C. the vapour pressure of bismuth may be calculated from the expression

log10P = -52.23×195.26/T + 8.56

where P is the vapour pressure in millimetres and T the absolute temperature.

The vapour of bismuth at 2000° C. is monatomic, although at lower temperatures it is possible that both monatomic and diatomic molecules exist. It has been stated that the vapour at 851° C. contains 40 per cent, of Bi molecules and 60 per cent, of Bi2 molecules, while at 827° C. approximately 2 per cent, of Bi8 molecules were detected in addition to Bi and Bi2. No evidence has yet been obtained for the existence of molecules of different constitution, such as Bi3, Bi4 or Bi6. The heat of dissociation of diatomic molecules of bismuth is stated to be 77,100 ± 1200 gram-calories per mole.

Chiefly on account of the anisotropic nature of crystalline bismuth, the thermal, electrical and magnetic properties have received considerable attention.

Bismuth is a poor conductor of heat and of electricity; the relative thermal conductivity is 1.8, that of silver being 100. The variation of thermal conductivity with temperature of solid bismuth is as follows:

Temperature, ° C.1889160222233256
Thermal conductivity0.01940.01810.01700.01770.01770.0183

That of liquid bismuth is:

Temperature, ° C.286298376484584
Thermal conductivity0.04000.04180.03780.03720.0369

The conductivity in all the above cases is measured in gram-calories per cm. per sec. per degree Centigrade. It will be observed that the thermal conductivity of solid bismuth decreases to a minimum with rise of temperature, afterwards rising to the melting point; that of liquid bismuth is nearly constant above 300° C., whilst at the melting point there is a very considerable increase. Bismuth differs from most metals in this respect, although antimony also shows a slight increase in thermal conductivity on melting. The effects of pressure and of a magnetic field upon the thermal conductivity have been determined. The thermal conductivities of a single crystal of bismuth are:

Perpendicular to the trigonal axis0.0221 calories per cm. per sec. per ° C.
Parallel to the trigonal axis 0.0159 calories per cm. per sec. per ° C.
Mean value (assuming a random distribution of crystals)0.0195 calories per cm. per sec. per ° C.

The electrical resistance is 106.5×10-6 ohm-cm. at 0° C., and the variation with temperature is given by

R = 106.5[1 + 0.00391t + 0.0000058t2]×10-6 ohm-cm.

where t is the temperature in degrees Centigrade. The mean temperature coefficient of resistance between 0° and 100° C. is 446×10-5. At the melting point the resistance of solid bismuth is 267×10-6 ohm-cm.: that of liquid bismuth at the same temperature is 127.5×10-6 ohm-cm. Bismuth is not superconducting at -268.84° C. The resistance at low temperatures is as follows, being given as a ratio between that at the temperature stated (R) and that at 0° C. (R0).

Electrical resistance of Bismuth at low temperatures

Temperature, ° C.100R/R0Temperature, ° C.100R/R0

The effects on electrical resistance of pressure, of tension, and of a magnetic field have been investigated. The specific electrical resistance of a single crystal of bismuth is 1.38×10-4 ohm-cm. parallel to the trigonal axis, and 1.07×10-4 ohm-cm. perpendicular to that axis. At low temperatures the variation of electrical resistance of a single crystal with temperature is as follows (the value for the resistance is given as a ratio between the actual resistance at the temperature stated (R) and that at 0° C. (R0)).

Electrical resistance of single crystals of Bismuth at low temperatures

Parallel to Trigonal AxisPerpendicular to Trigonal Axis
Temperature, ° C.100R/R0Temperature, ° C.100R/R0

The influence of a magnetic field upon the electrical resistance of a single crystal has been investigated at low temperatures.

The thermal electromotive force of bismuth with respect to platinum is given (in microvolts) by

BiEPt = -61.95(t2-t1) + 0.0251(t2-t1)2 + 0.000262(t2-t1)3

between 0° and 268° C. Values have also been obtained for couples with copper, constantan and lead. The thermoelectric force between stressed and unstressed bismuth has been measured. Several investigators have drawn attention to a discontinuity in the thermoelectric power of bismuth at a temperature near the melting point. The effect of orientation on the thermal electromotive force of a single crystal of bismuth with reference to copper between 20° and 100° C. (expressed in microvolts) is as follows:

Effect of orientation on thermal E.M.F. Of single crystals of Bismuth with reference to Copper

Angle between Basal Cleavage Plane and Direction of Current.Thermal E.M.F.
0°0'-55(t2-t1) – 0.0312(t2-t1)2
5°5'-56.6(t2-t1) – 0.025(t2-t1)2
10°0'-61.4(t2-t1) - 0.10(t2-t1)2
17°7'-61.4(t2-t1) -0.0625(t2-t1)2
21°1'-61.1(t2-t1) – 0.0875(t2-t1)2

Bismuth is diamagnetic. The specific magnetic susceptibility is -1.346×10-6. The effect of temperature has been studied and the magnetic susceptibility of molten bismuth is found to be approximately one-hundredth that of solid bismuth just below the melting point.

The susceptibility is independent of the field strength at ordinary temperatures, but at temperatures of -250° C. or -260° C. it decreases at higher field strengths. It is also decreased by cold working. The magnetic properties of colloidal bismuth have been investigated with a view to determining the effect of particle size. Although the results of these investigations do not appear to be conclusive, it is suggested that the high diamagnetism of bismuth is a property of the crystal rather than of the atom. The magnetic susceptibility of a single crystal of bismuth in a direction perpendicular to the principal crystallographic axis is -(1.482 ± 0.014)×10-6, and in a direction parallel to this axis -(1.053±0.010)×10-6. The mean value is -1.340×10-6. From this it may be deduced that the magnetic susceptibility of a poly-crystalline aggregate is -(l.340±0.013)×10-6. The effect of temperature and of field strength on the magnetic susceptibility of single crystals has been investigated.

The various galvanometric and thermomagnetic effects in bismuth, such as the Hall effect, the Corbino effect, the Ettingshausen effect, the Nernst effect, the Righi-Leduc effect, etc., have been studied at great length. The Hall effect is negative and increases in a negative direction as the magnetic field increases, apparently approaching a limiting value; the Hall coefficient decreases as the temperature rises, becoming zero at the melting point; the crystalline structure and the orientation of the principal crystallographic axis to the primary current and to the magnetic field greatly influence the magnitude of the Hall effect; it is probably for this reason that many published results are discordant. The Hall effect in a single crystal has also been investigated. The Nernst effect is positive.

It is known that a substance may be caused to emit electrons when it is illuminated by light of sufficiently high frequency; the longest wavelength capable of producing this effect is called the photoelectric threshold. The value for poly crystalline bismuth lies between λ 2980 A and λ 3300 A; that for a single crystal between λ 2804 A and λ 2894 A.

The optical properties of bismuth in the massive condition, in the form of opaque films, in the molten condition and in the form of single crystals have been investigated.

Spectrum.—Bismuth compounds impart no characteristic coloration to the Bunsen flame. The wavelengths of the principal lines in the arc spectrum are as follows. (The numbers in parenthesis indicate the relative intensities of the lines, the lowest numbers indicating the weakest intensities.)

11711 (10), 9657.2 (10), 8210.8 (10), 6134.85 (5), 5742.55 (6), 5552.24 (8), 4722.7 (8), 4722.5 (10), 4722.2 (10), 4121.85 (6), 4121.52 (6), 3510.85 (6), 3397.21 (5), 3067.73 (9), 3024.64 (8), 2993.34 (9), 2989.04 (9), 2938.31 (10), 2897.98 (10), 2809.63 (8), 2780.52 (7), 2730.50 (5), 2696.76 (6), 2627.93 (8), 2524.52 (7), 2515.68 (6), 2489.4 (5), 2400.89 (8), 2276.57 (5), 2230.62 (8), 2228.25 (6), 2189.59 (6), 2177.3 (6), 2152.9 (7), 2134.4 (8), 2133.6 (7), 2110.3 (8), 2061.71 (8), 1533.7 (5).

The wavelengths of the most persistent lines in the arc spectrum, such as may be used for spectrochemical purposes, are as follows. (The expressions in parenthesis are the spectral terms allotted to the particular lines, adopting the usual notation.)

2061.71 (4S2-4P3), 2276.57 (4S2-4P2), 2780.52 (2D2), 2809.63 (2D3-2P2), 2897.98 (2D2-2P1), 2938.31 (2D3), 2989.04 (2D2), 3067.73 (4S2-4P1).

The " rale ultime," or most persistent line, has the wavelength 3067.73 A.

The wavelengths of the principal lines in the spark spectrum are as follows. (The numbers in parenthesis indicate the relative intensities of the lines.)

6809.1 (7), 6600.1 (7), 5209.28 (10), 5144.50 (6), 4722.7 (8), 4722.5 (8), 4722.2 (5), 4561.15 (8), 4302.13 (10), 4259.64 (10) 4079.22 (10), 3792.9 (8), 3695.53 (8), 3510.85 (5), 3067.73 (6), 2989.04 (5), 2938.3 (8), 2897.98 (5), 1346 (10), 1317 (15), 1306 (10), 1051 (10), 1045 (10).

The second and third order spectra have also been investigated, and it is indicated that the spectrum of singly ionised bismuth is that of the two-electron spectrum, and that of doubly ionised bismuth a simple one-electron doubled spectrum. The bismuth nucleus has a resultant moment of momentum

(h = Planck's constant)

The ionisation potential for singly ionised bismuth is about 14 volts, that for doubly ionised bismuth 25.4 volts and that for BiV 55.7 volts.

The arc and spark spectra in the ultra-violet region have been studied in some detail, and in the latter case the spectrum has been extended to a wavelength of λ 200 A. The Zeeman effect has been studied.

In the absorption spectrum of bismuth vapour both lines and bands are found, in addition to the " raie ultime " (λ 3067.73 A.). The bands appear in groups, occurring in the ultra-violet, and at higher temperatures, in the visible region. Each group consists of bands degraded towards the red. The approximate wavelengths of the bands in the ultra-violet region are (in A.) 2859.9, 2842.9, 2828.2, 2813.5, 2799.8, 2785.0, 2772.7, 2759.6, 2744.8, 2732.6, 2722.0, 2712.3, 2701.9, 2693.2, 2681.5, 2670.0. The lines 2276, 2230 and 2228 are also strongly absorbed, and there are other absorption lines of wavelength 2110, 2062 and 2021 A. At 800° C. fine absorption lines appear in the spectrum, the wavelengths of which do not appear to have been determined, while another banded structure is revealed at a lower wavelength. At about 1200° C. a banded structure is observed in the visible region extending from λ 4500 to λ 6500 A. The interval between the bands in this spectrum differs from about 35 A. at the violet end to about 90 A. at the red end. At higher temperatures the bands tend to merge into one continuous band.

The following are the wavelengths of absorption lines which are observed in the under-water spark spectrum; they correspond with those which are reversed in the arc spectrum:

3596.11, 3510.85, 3405.23, 3397.21, 3067.73, 3024.64, 2993.34, 2989.04, 2938.31, 2897.98, 2809.63, 2780.52, 2730.5, 2696.76, 2627.93, 2524.52, 2515.68, 2400.89, 2276.57, 2230.62, 2228.25, 2189.59, 2177.3, 2164.1, 2156.9, 2153.5, 2152.9, 2134.4, 2133.6, 2110.3, 2061.71.

At 1500° to 1600° C. bismuth vapour emits fluorescent radiation orange-yellow in colour. The fluorescence spectrum shows a banded structure which is more or less the exact complement of the absorption spectrum in the region examined. The wavelengths of bands that have been measured are:

6533.0, 6464.5, 6389.0, 6319.5, 6248.5, 6187.5, 6117.5, 6052.0, 5991.5, 5940.5, 5886.5, 5831.5, 5776.5, 5726.0, 5680.0, 5640.0.

It is convenient here to include a description of the spark spectrum of dilute solutions of bismuth trichloride. The wavelengths of the most persistent lines in this spectrum, and the minimum concentration of the solution in the spectrum of which they appear. These lines may be employed in quantitative analysis.

The X-ray spectrum of bismuth has been studied, and measurements obtained for the K, L, M and N series.

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