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Physical Properties of Ice
When the temperature of pure ice is gradually raised under the ordinary atmospheric pressure, melting always commences sharply at a certain invariable temperature, which remains constant until fusion is complete, this is one of the most remarkable Physical Properties of Ice. On account of the ease with which this constant temperature can be attained it has been chosen as the standard zero for the Celsius (Centigrade) and Reaumur thermometric scales. The melting-point is slightly affected by pressure, each increase of one atmosphere lowering the transition temperature of ice to water by approximately 0.0075.
That such ought to be the case was first realised by James Thomson who, in 1849, showed that from theoretical considerations a connection must exist between the melting-point of a solid and the pressure. The following year this was experimentally demonstrated by his brother W. Thomson (Lord Kelvin), who found that under a pressure of 8.1 atmospheres the melting-point of ice was lowered by 0.059° C., equivalent to a fall of 0.0073° per atmosphere. In the table are given the more accurate determinations of Tammann, the third column giving the results calculated in terms of atmospheres.
These data are represented in the pressure-temperature diagram (fig.) by the fusion curve AB, which is steep, but curved towards the abscissa, as the results in the last column of the above table clearly demand. This curve represents the equilibrium between ordinary ice or ice I and water, the triple point A representing the condition of equilibrium of water-vapour, liquid water, and ice I. Under a pressure of 2200 kilograms, corresponding to the point B in the figure, there is a break in the fusion curve, a new form of ice appearing, known as ice III, the melting-point of which, in contradistinction to ice I, rises with the pressure, as indicated by BC which slopes away from the ordinate.
Depression of the Melting-Point of Ice under Pressure
Physical Properties of Ice are related with water triple point. At the triple point B, therefore, liquid water, ice I and ice III are in equilibrium, the temperature being -22° C. Tammann found that up to pressures of 2500 kilograms, the solid produced by the spontaneous crystallisation of water is invariably ice I, even in the ice III region. Above this pressure, however, ice III forms, and it is interesting to note that under these conditions the ice has a smaller volume than the liquid water, so that a vessel in which the pressure is greater than 2500 kilograms per sq. cm. cannot be employed to demonstrate the expansive force of ice formation.
Returning to the triple point, B, let us assume a slight increase of pressure, accompanied by a fall in temperature. Liquid water disappears and we move in the direction BD, which represents equilibrium between ice I and ice III. At D another discontinuity occurs, this new triple point representing the equilibrium point of the three solid phases ice I, ice III, and ice II. If now the pressure is slightly reduced and the temperature lowered, the solid phase ice III disappears and we pass along a line not shown in the figure representing the conditions of equilibrium between ice I and ice II. Owing to the slow rate of transformation of ice III, it is possible to travel in the direction BD beyond the point D along a line, which represents the metastable condition of equilibrium between ice I and ice III.
If, on the other hand, on reaching the point D, the temperature and pressure are both raised, instead of lowered, as previously, we pass along DG, which gives the conditions of equilibrium ice II and ice III. At G, ice V appears, this being the triple point at which ice II, ice III, and ice V can co-exist. By again raising the temperature and by a slight increase in pressure, the triple point C is reached, which could also be attained from B by a considerable rise in pressure and a slight rise in temperature.
At C liquid water appears, and is in equilibrium with ice III and ice V.
Increase of pressure, accompanied by rise of temperature, enables us to pass along the curve CH to the triple point H, at which point ice VI appears. This point represents the conditions of equilibrium of ice V, ice VI, and liquid water, and lies above 0° C, namely at +0.16° C. By increasing the pressure and raising the temperature still higher, ice V disappears, HK representing the equilibrium ice VI - liquid water. The remarkable feature of ice VI lies in the fact that it is stable only at temperatures above 0° C., increase of pressure serving to raise its melting- point. Indeed, it is possible to have solid water in the form of ice VI even at 80° C. The foregoing conditions of equilibrium are summarised in the following table:
Equilibrium pressures and temperatures
The position of ice II is interesting, for it is surrounded by solid phases, and hence can never be in equilibrium with liquid water.
It will be observed that no mention has been made of ice IV, the existence of which is uncertain. Tammann obtained certain indications of the possibility of its existence, but Bridgman was unable to confirm, so the term has been left in order that the nomenclature shall not require alteration in the event of the possible existence of this particular form of ice being substantiated.
Ice I is the lightest variety of ice known, having a density less than unity, all the other forms being more dense than water. It is the ordinary ice which is always obtained during the normal crystallisation of water under atmospheric pressure.
Numerous attempts have been made to determine accurately the specific gravity of ice at 0° C. with reference to that of water at 0° C.
The density of ice at -188.7° C. is given as 0.9300. The approximate densities of the polymorphic forms of ice are as follows:
It will be observed that these are all greater than unity.
It will be noticed that Bunsen's value for the density of ice I differs only by about 0-1 per cent, from that of Leduc, and the latter author suggests that the difference is mainly due to the fact that Bunsen had not removed every trace of air from his water. Compared with all the results, however, Leduc's value appears somewhat high, and Roth, in a critical survey, recommends the mean value 0-9168 as probably most nearly correct.
This being granted, the volume of 1 gram of ice at 0° C. is 1.09075 c.c., and the contraction on melting is 0.09062 c.c. (1 gram of water at 0° C. has a volume of 1.00013 c.c.) - that is about 8.2 per cent. The magnitude of this change in volume is evident from a consideration of the following data, which give the percentage volume changes - in most of these instances, expansions - when certain solid elements melt.
It is interesting to note that the density of natural ice is slightly different from artificial, as made by cooling water in a freezing mixture. This was first observed by Dufour in 1862, and confirmed by Nichols in 1899. Possibly this is a question of age, the ice undergoing slight change on standing; although Barnes found no appreciable difference between old and new ice. In any case the variation is extremely small. The expansion of water upon solidification plays an important part in the natural disintegration of rocks. It may be experimentally demonstrated in the case of water by filling a cast-iron cylinder with air-free water and tightly closing it with a well-fitting screw. On allowing it to lie in a mixture of ice and salt the water freezes and bursts the cylinder. This is simply a modification of the experiment apparently first carried out by Hughens in 1667. The experiment was repeated by Boussingault in 1871, a temperature of -24° C. being attained without congelation, as was proved by the fact that an enclosed steel ball still rattled when the cylinder was shaken.
The hardness of ice is 1.5 (Mohs' scale).
At low temperatures ice is exceedingly hard and very resistant to shock. Above -12° C. it begins to soften appreciably. Bishop Watson states that, at the marriage of Prince Gallitzin in 1739, the Russians fired ice cannon in honour of the event, the cannorl withstanding the shock more than once without bursting.
Ice exerts a definite vapour pressure which, at 0° C., is identical with that of water, so that at this point the three phases - solid, liquid, vapour - can co-exist. This is not the real triple point, because pressure lowers the melting-point of ice, and by definition 0° C. is the melting-point of ice under a pressure of one atmosphere. The true triple point therefore lies at +0.0076° C., and in the absence of air, OB, which represents the vapour pressure of ice at various temperatures, is termed the sublimation curve.
Another very important Physical Properties of Ice, is the vapour pressure of ice at various temperatures below 0° C. has been determined by several investigators, the results of Scheel and Heuse being given in the following table:
Vapour Pressure of Ice
The vapour pressure, p, of ice at any temperature t° C. may be calculated from either of the following equations:
Judging by the results of Dewar and Vincent the temperature coefficient is high, the expansion coefficient covering the lower temperature being only about half of that over the range -10° to 0° C. The results of Struve (1850) closely agree with the more modern work of Vincent (1902).
Ice, when free from air bubbles, is colourless and transparent, except in thick masses, when it appears slightly blue. When formed from water at temperatures of -1.5° to 0° C. the ice is usually clear, and possesses a maximum density and cohesion. If produced at temperatures below -3° C., minute bubbles of air render the ice milky.
Ice crystals usually belong to the hexagonal system, the axial ratio being:
A:C = 1:1,617.
According to Hartmann, the crystallites separating from various undercooled aqueous solutions are of three kinds, according to the concentration and extent of undercooling. Hexagonal crystal skeletons, consisting either of hexagonal plates with six rays or rectangular plates with four rays, are produced when the degree of undercooling is small. Spherulites are formed when the undercooling exceeds a certain limit, whilst feathery growths only occur with very dilute solutions. That the different forms are identical is shown by the fact that undercooled, pure water freezes at the same temperature when inoculated with any one of them.
Prendel has concluded that ice is dimorphous, crystallising in both the hexagonal and cubic systems. Ice crystals are brittle, and their viscosity varies with the direction of shear.
The refractive index for sodium light is 1.310. In conductivity of heat ice resembles ordinary water, except that the value varies slightly with the direction in the ice crystal. Its coefficient of compressibility between 100 and 500 megabars at -7° C. is 0.000,0120, as determined experimentally by Richards and Speyers, a value only about one-fourth of that of liquid water at neighbouring temperatures, about five times that of glass, and somewhat less than that of metallic sodium. It appears to have an abnormally high temperature coefficient, as the following computations indicate:
Compressibility of Ice
It will be observed, however, that the computed compressibility at -7° C. is appreciably higher than that actually found, and the authors quoted suggest that in part this "may possibly be due to a considerable softening of the ice just before melting."
When rubbed by liquid water, ice becomes positively electrified, a fact of considerable meteorological interest.
The specific heat of ice is approximately half that of water, namely, 0.5057 at 0° C., and expressed in 20° calories. Its heat capacity when pure varies but little with the temperature, and the following equation is given as representing the specific heat, Qt, at various temperatures, t:
Qt = 0.5057 + 0.001,863t.
At low temperatures the specific heat falls considerably, as is evident from Dewar's researches, the results of which are given in the following table:
Specific heat of Ice at low temperatures
The latent heat of fusion of ice has been the subject of much research. The most noteworthy determinations are given in the table.
Under atmospheric pressure, the value 79.7 would appear to be a fair mean, accurate to about 0-1 per cent., employing the 15° calorie. Increase of pressure reduces both the melting-point and latent heat of fusion, as the following data show:
The latent heats of fusion of the polymorphic varieties approximate to that of ice I, and but little exchange takes place during transformation from one variety to another.
The heat of formation of ice from gaseous hydrogen and oxygen at 0° C. is 69.96 Calories.
Pure ice, free from air bubbles, cavities, and suspended material, frequently exhibits a beautiful blue colour when seen in bulk. This is regarded as an absorption effect, due to the tendency of large molecular aggregates to absorb the long rays of light. The blocks of ice lose their colour upon prolonged exposure to light, and more rapidly upon exposure to direct sunlight.
That such ought to be the case was first realised by James Thomson who, in 1849, showed that from theoretical considerations a connection must exist between the melting-point of a solid and the pressure. The following year this was experimentally demonstrated by his brother W. Thomson (Lord Kelvin), who found that under a pressure of 8.1 atmospheres the melting-point of ice was lowered by 0.059° C., equivalent to a fall of 0.0073° per atmosphere. In the table are given the more accurate determinations of Tammann, the third column giving the results calculated in terms of atmospheres.
 |
| The pressure-temperature diagram for water, ice, and water-vapour. |
Depression of the Melting-Point of Ice under Pressure
| Melting-point, ° C. | Pressure in kilograms per sq. cm. | Pressure in Atmospheres. | Depression in Melting-point per Atmosphere. |
| 0 | 1 | 0.968 | . . . |
| -2.5 | 336 | 325 | 0.0077 |
| -5 | 615 | 595 | 0.0084 |
| -7.5 | 890 | 861.5 | 0.0087 |
| -10.0 | 1155 | 1118 | 0.0089 |
| -12.5 | 1410 | 1365 | 0.0091 |
| -15.0 | 1625 | 1573 | 0.0095 |
| -17.5 | 1835 | 1776 | 0.0099 |
| -20.0 | 2042 | 1977 | 0.0100 |
| -22.1 | 2200 | 2130 | 0.0104 |
Physical Properties of Ice are related with water triple point. At the triple point B, therefore, liquid water, ice I and ice III are in equilibrium, the temperature being -22° C. Tammann found that up to pressures of 2500 kilograms, the solid produced by the spontaneous crystallisation of water is invariably ice I, even in the ice III region. Above this pressure, however, ice III forms, and it is interesting to note that under these conditions the ice has a smaller volume than the liquid water, so that a vessel in which the pressure is greater than 2500 kilograms per sq. cm. cannot be employed to demonstrate the expansive force of ice formation.
Returning to the triple point, B, let us assume a slight increase of pressure, accompanied by a fall in temperature. Liquid water disappears and we move in the direction BD, which represents equilibrium between ice I and ice III. At D another discontinuity occurs, this new triple point representing the equilibrium point of the three solid phases ice I, ice III, and ice II. If now the pressure is slightly reduced and the temperature lowered, the solid phase ice III disappears and we pass along a line not shown in the figure representing the conditions of equilibrium between ice I and ice II. Owing to the slow rate of transformation of ice III, it is possible to travel in the direction BD beyond the point D along a line, which represents the metastable condition of equilibrium between ice I and ice III.
If, on the other hand, on reaching the point D, the temperature and pressure are both raised, instead of lowered, as previously, we pass along DG, which gives the conditions of equilibrium ice II and ice III. At G, ice V appears, this being the triple point at which ice II, ice III, and ice V can co-exist. By again raising the temperature and by a slight increase in pressure, the triple point C is reached, which could also be attained from B by a considerable rise in pressure and a slight rise in temperature.
At C liquid water appears, and is in equilibrium with ice III and ice V.
Increase of pressure, accompanied by rise of temperature, enables us to pass along the curve CH to the triple point H, at which point ice VI appears. This point represents the conditions of equilibrium of ice V, ice VI, and liquid water, and lies above 0° C, namely at +0.16° C. By increasing the pressure and raising the temperature still higher, ice V disappears, HK representing the equilibrium ice VI - liquid water. The remarkable feature of ice VI lies in the fact that it is stable only at temperatures above 0° C., increase of pressure serving to raise its melting- point. Indeed, it is possible to have solid water in the form of ice VI even at 80° C. The foregoing conditions of equilibrium are summarised in the following table:
Equilibrium pressures and temperatures
| Point in fig. | Phases in Equilibrium. | Pressure. | Temperature, °C |
| A | Water-vapour - liquid water - ice I | 4.579 mm.Hg. | +0.0076 |
| B | Liquid water - ice I - ice III | 2115 kilos/cm2 | -22 |
| D | Ice I - ice II - ice III | 2170 kilos/cm2 | -34.7 |
| G | Ice II - ice III - ice V | 3510 kilos/cm2 | -24.3 |
| C | Liquid water - ice III - ice V | 3530 kilos/cm2 | -17 |
| H | Liquid water - ice V - ice VI | 6380 kilos/cm2 | +0.16 |
The position of ice II is interesting, for it is surrounded by solid phases, and hence can never be in equilibrium with liquid water.
It will be observed that no mention has been made of ice IV, the existence of which is uncertain. Tammann obtained certain indications of the possibility of its existence, but Bridgman was unable to confirm, so the term has been left in order that the nomenclature shall not require alteration in the event of the possible existence of this particular form of ice being substantiated.
Ice I is the lightest variety of ice known, having a density less than unity, all the other forms being more dense than water. It is the ordinary ice which is always obtained during the normal crystallisation of water under atmospheric pressure.
Numerous attempts have been made to determine accurately the specific gravity of ice at 0° C. with reference to that of water at 0° C.
The density of ice at -188.7° C. is given as 0.9300. The approximate densities of the polymorphic forms of ice are as follows:
| Ice II | 1.03 |
| Ice III | 1.04 |
| Ice V | 1.09 |
| Ice VI | 1.06 |
It will be observed that these are all greater than unity.
It will be noticed that Bunsen's value for the density of ice I differs only by about 0-1 per cent, from that of Leduc, and the latter author suggests that the difference is mainly due to the fact that Bunsen had not removed every trace of air from his water. Compared with all the results, however, Leduc's value appears somewhat high, and Roth, in a critical survey, recommends the mean value 0-9168 as probably most nearly correct.
This being granted, the volume of 1 gram of ice at 0° C. is 1.09075 c.c., and the contraction on melting is 0.09062 c.c. (1 gram of water at 0° C. has a volume of 1.00013 c.c.) - that is about 8.2 per cent. The magnitude of this change in volume is evident from a consideration of the following data, which give the percentage volume changes - in most of these instances, expansions - when certain solid elements melt.
| Element | Cd | Hg | K | Na | P | Pb | Sn | Bi |
| Volume change per cent | 4.72 | 3.67 | 2.6 | 2.5 | 3.5 | 3.39 | 2.80 | -3.31 |
It is interesting to note that the density of natural ice is slightly different from artificial, as made by cooling water in a freezing mixture. This was first observed by Dufour in 1862, and confirmed by Nichols in 1899. Possibly this is a question of age, the ice undergoing slight change on standing; although Barnes found no appreciable difference between old and new ice. In any case the variation is extremely small. The expansion of water upon solidification plays an important part in the natural disintegration of rocks. It may be experimentally demonstrated in the case of water by filling a cast-iron cylinder with air-free water and tightly closing it with a well-fitting screw. On allowing it to lie in a mixture of ice and salt the water freezes and bursts the cylinder. This is simply a modification of the experiment apparently first carried out by Hughens in 1667. The experiment was repeated by Boussingault in 1871, a temperature of -24° C. being attained without congelation, as was proved by the fact that an enclosed steel ball still rattled when the cylinder was shaken.
The hardness of ice is 1.5 (Mohs' scale).
At low temperatures ice is exceedingly hard and very resistant to shock. Above -12° C. it begins to soften appreciably. Bishop Watson states that, at the marriage of Prince Gallitzin in 1739, the Russians fired ice cannon in honour of the event, the cannorl withstanding the shock more than once without bursting.
Ice exerts a definite vapour pressure which, at 0° C., is identical with that of water, so that at this point the three phases - solid, liquid, vapour - can co-exist. This is not the real triple point, because pressure lowers the melting-point of ice, and by definition 0° C. is the melting-point of ice under a pressure of one atmosphere. The true triple point therefore lies at +0.0076° C., and in the absence of air, OB, which represents the vapour pressure of ice at various temperatures, is termed the sublimation curve.
Another very important Physical Properties of Ice, is the vapour pressure of ice at various temperatures below 0° C. has been determined by several investigators, the results of Scheel and Heuse being given in the following table:
Vapour Pressure of Ice
| Temperature, ° C. | Vapour Pressure, mm. Hg. |
| 0 | 4.579 |
| -1 | 4.219 |
| -2 | 3.885 |
| -3 | 3.575 |
| -4 | 3.288 |
| -5 | 3.022 |
| -6 | 2.776 |
| -7 | 2.548 |
| -8 | 2.337 |
| -9 | 2.143 |
| -10 | 1.963 |
| -15 | 1.253 |
| -20 | 0.784 |
| -25 | 0.480 |
| -30 | 0.288 |
| -35 | 0.168 |
| -40 | 0.096 |
| -45 | 0.053 |
| -50 | 0.0296 |
| -55 | 0.0156 |
| -60 | 0.0073 |
| -65 | 0.0023 |
The vapour pressure, p, of ice at any temperature t° C. may be calculated from either of the following equations:
Judging by the results of Dewar and Vincent the temperature coefficient is high, the expansion coefficient covering the lower temperature being only about half of that over the range -10° to 0° C. The results of Struve (1850) closely agree with the more modern work of Vincent (1902).
Ice, when free from air bubbles, is colourless and transparent, except in thick masses, when it appears slightly blue. When formed from water at temperatures of -1.5° to 0° C. the ice is usually clear, and possesses a maximum density and cohesion. If produced at temperatures below -3° C., minute bubbles of air render the ice milky.
Ice crystals usually belong to the hexagonal system, the axial ratio being:
A:C = 1:1,617.
According to Hartmann, the crystallites separating from various undercooled aqueous solutions are of three kinds, according to the concentration and extent of undercooling. Hexagonal crystal skeletons, consisting either of hexagonal plates with six rays or rectangular plates with four rays, are produced when the degree of undercooling is small. Spherulites are formed when the undercooling exceeds a certain limit, whilst feathery growths only occur with very dilute solutions. That the different forms are identical is shown by the fact that undercooled, pure water freezes at the same temperature when inoculated with any one of them.
Prendel has concluded that ice is dimorphous, crystallising in both the hexagonal and cubic systems. Ice crystals are brittle, and their viscosity varies with the direction of shear.
The refractive index for sodium light is 1.310. In conductivity of heat ice resembles ordinary water, except that the value varies slightly with the direction in the ice crystal. Its coefficient of compressibility between 100 and 500 megabars at -7° C. is 0.000,0120, as determined experimentally by Richards and Speyers, a value only about one-fourth of that of liquid water at neighbouring temperatures, about five times that of glass, and somewhat less than that of metallic sodium. It appears to have an abnormally high temperature coefficient, as the following computations indicate:
Compressibility of Ice
| Temperature, ° C. | Average Compressibility of Ice between Zero Pressure and the Melting Pressure. (Megabars.) |
| 0 | 0.000,033 |
| -5 | 0.000,023 |
| -7 | 0.000,021 |
| -10 | 0.000,019 |
| -15 | 0.000,018 |
It will be observed, however, that the computed compressibility at -7° C. is appreciably higher than that actually found, and the authors quoted suggest that in part this "may possibly be due to a considerable softening of the ice just before melting."
When rubbed by liquid water, ice becomes positively electrified, a fact of considerable meteorological interest.
The specific heat of ice is approximately half that of water, namely, 0.5057 at 0° C., and expressed in 20° calories. Its heat capacity when pure varies but little with the temperature, and the following equation is given as representing the specific heat, Qt, at various temperatures, t:
Qt = 0.5057 + 0.001,863t.
At low temperatures the specific heat falls considerably, as is evident from Dewar's researches, the results of which are given in the following table:
Specific heat of Ice at low temperatures
| Temperature Range, ° C. | Specific Heat of Ice. |
| 18 to -78 | 0.463 |
| -78 to -188 | 0.285 |
| -188 to –252.5 | 0.146 |
The latent heat of fusion of ice has been the subject of much research. The most noteworthy determinations are given in the table.
Under atmospheric pressure, the value 79.7 would appear to be a fair mean, accurate to about 0-1 per cent., employing the 15° calorie. Increase of pressure reduces both the melting-point and latent heat of fusion, as the following data show:
| Temperature, ° C. | 0 | -5 | -10 | -15 | -20 |
| Latent heat (calories) | 79.8 | 73.7 | 68.0 | 62.5 | 57.7 |
The latent heats of fusion of the polymorphic varieties approximate to that of ice I, and but little exchange takes place during transformation from one variety to another.
The heat of formation of ice from gaseous hydrogen and oxygen at 0° C. is 69.96 Calories.
Pure ice, free from air bubbles, cavities, and suspended material, frequently exhibits a beautiful blue colour when seen in bulk. This is regarded as an absorption effect, due to the tendency of large molecular aggregates to absorb the long rays of light. The blocks of ice lose their colour upon prolonged exposure to light, and more rapidly upon exposure to direct sunlight.
Colloidal Ice
Colloidal Ice can readily be obtained as an organosol by rapidly cooling saturated solutions of water in organic media. When, for example, chloroform, saturated with water, is rapidly cooled to - 30° C., the ice separates out in particles of colloid dimensions, and the sol may be passed unchanged through filter paper.
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