Index |

X

The Melting Point - Relation to Pressure

Attached herewith is paper number ten in my liquid series which shows that the melting points under pressure can be accurately computed by means of a very simple equation. This paper makes a highly significant contribution to the work as a whole, as the melting point equation is not only a purely theoretical expression derived directly from the basic postulates of the work, but it is also the same equation that was used to calculate solid compressibilities in previous papers. It is difficult to visualize the possibility that such an equation could successfully reproduce the full range of experimental values in either field unless it were an essentially correct representation of the physical facts; the possibility that an incorrect expression could accomplish these results in both fields is wholly inconceivable.

It appears to me that this occasion, on which I am submitting some striking new evidence of the validity of the fundamental postulates on which my work is based, is an appropriate time to make some comments regarding those aspects of currently accepted physical theory with which my findings are in conflict. It is true; of course, that these conflicts are quite numerous, and there is a very understandable reluctance to believe that accepted theory can be wrong in so many important respects. But it is not difficult to prove this point. It is quite a task to prove that any of the current theories are wrong, because long years of effort on the part of the theorists have enabled them to adjust their theories to fit the facts in most cases and to devise means of evading most of the many contradictions that still remain, but it is quite simple to show that the particular theories in question are lacking in factual support and therefore can be wrong. As long as this is true, it is clearly in order to consider conflicting theories.

The case in favor of my new theoretical structure rests primarily on the contention that not a single one of the thousands of necessary and unavoidable consequences of my fundamental postulates is inconsistent with any positively established fact. It becomes very important, therefore, to distinguish clearly between items that are definitely known to be factual and those, which do not qualify. The enclosed memorandum is a discussion of this situation as it applies to the points of conflict. The memorandum does not attempt to discuss all of the points at issue, nor to make an exhaustive analysis of any case; nothing short of a book-length presentation could cover that much ground. However, the various categories of pseudo-facts commonly encountered are described and illustrated by examples, and it should not be difficult to see that every one of the accepted ideas with which my findings are in conflict is one of these pseudo facts: a hypothesis, assumption, or extrapolation masquerading in the guise of an established fact.

Perhaps it will be regarded as presumptuous for me to suggest that the strict and critical tests which will be applied to my new theory be applied to the conflicting parts of currently accepted theory as well, but I believe that by this time the new developments which I have covered in the liquid papers add up to an impressive enough total to justify a full and comprehensive examination of the underlying theories, including a careful consideration of this question as to the true status of conflicting ideas.

D. B. Larson


 

Strictly speaking, the melting point is a phenomenon of the solid state rather than of the liquid state and in general its behavior follows the solid state pattern, but since this temperature constitutes the point of transition between the two physical states it has some close relations with various liquid properties which justify giving it some consideration in this survey of the liquid state,

If the melting point were actually a property of the liquid, we could expect that it would be linearly related to the pressure, just as the true liquid component of the volume and other liquid properties are so related. Solid state properties, however, are directly or inversely related to the square root of the pressure, rather than to the first power, for reasons that are explained in the author's book "The Structure of the Physical Universe", which develops the general physical theories underlying the liquid principles that form the basis for this series of papers. It has already been brought out in a paper which preceded this liquid series5 that the solid state equivalent of Bole's Law, PV = k, is PV2 = k, from which we obtain the relation V/V0 = P01/2(P +P0)1/2. In terms of density this becomes

d  =

(P +P0)1/2

d0

 

P01/2

The previous solid compressibility paper showed that this equation is able to reproduce the experimental values of the compression, within the existing margin of uncertainty, over the entire range of temperatures, pressures and substances for which data are available.

According to the basic theory, this is a characteristic relationship applying to solid state properties in general, rather than merely a volume relation, and we may therefore rewrite the equation, substituting Tm, the normal melting point, for d0, and Tp, the melting point under an externally applied pressure P, for d. We then have

Tp  =

(P +P0)1/2

Tm

(16)

P01/2

It will be noted that this expression is identical with the well-known Simon melting point equation, except for the substitution of a constant for one of the two variables of the Simon equation, which the originator expresses as

P

=  (

 T

)C  -  1

 

a

 T0

Simon's factor a corresponds to the initial pressure, as is generally recognized, His factor c (unexplained theoretically) has usually been assigned a value somewhere between 1.5 and 2 in application to organic compounds and other low melting point substances, and replacing this variable factor by the constant value 2 is not a major modification of the equation, so far as the effect on the calculated values is concerned, as these values are not very sensitive to changes in c if accompanied by corresponding changes in a. The situation with respect to the high melting point elements, which are often assigned considerably higher values of the factor c. will be discussed later.

No satisfactory theoretical explanation has thus far been discovered for the Simon equation, but this expression agrees with the experimental results over a wide range of pressures and substances, and it is generally conceded that such a theoretical explanation must exist. Strong and Bundy state the case in these words, "Simon's fusion equation has now endured a considerable amount of experimental and theoretical examination. Because it applies in so many cases... it must contain fundamentally correct concepts concerning some of the properties of matter".50

In the areas previously covered by this series of papers, the new equations, which have been developed, are to a large degree filling a vacuum, as no generally applicable mathematical representations of these properties have hitherto been available. It is therefore quite significant that when we reach an area where an equation of recognized standing does already exist, the new development does not produce something totally new; the general liquid principles on which the work is based lead to a melting point expression which is essentially a modified form of the previously existing equation. Here, as in so many places outside the liquid field, genuine knowledge already in existence coincides with the products of the development of the postulates of this work, and can simply be incorporated into the new theoretical structure with nothing more than minor modifications. What the new development actually does, in essence, is to establish the exact nature of those "fundamentally correct concepts" to which Strong and Bundy refer.

But even though the required modification of the Simon equation is minor, it does not necessarily follow that it is unimportant. As brought out in paper IX of this series, the more restrictive the mathematical expression of a physical property can be made, the more likely it is to be a correct representation of the true physical facts, providing, of course, that it produces results which agree with the experimental values within the margin of uncertainty of the latter. Replacement of one of the two adjustable factors in the Simon equation by the constant value 2 as required by the new theory is an important move in this direction.

Now that this value has been fixed, the only additional requirement for a complete and unequivocal definition of the pressure-melting point relation for each substance is a means of calculating the initial pressure applicable in each case. In the solid compressibility paper previously mentioned, the following equation for the initial pressure applicable to compression of solids was developed:

P0  =

16649 abc

  atm.

 

s03

The initial pressure applicable to liquid compressibility is considerably lower and paper IV in this series expressed this relation as

P0  =  415.84  n/ V0

atm.

 

   

Since the melting point is at the boundary between the liquid and solid states, it is to be expected that the initial pressure applicable to this property will lie somewhere between the true liquid and true solid values, and a study of this situation leads to an equation of an intermediate type:

P0  =  664.28

   abc   

atm.

 

nV02/3

The symbols in this equation have the same significance as in the expressions for the true liquid and true solid initial pressures. The factors a, b, and c are the effective displacements in the three dimensions of space, a concept that is explained in the author's book previously mentioned. V0 is the initial specific volume of the liquid as defined in paper II of this series, and n is the number of independent units in the molecule at the melting temperature.

The values of n applicable to the solid-liquid transition are usually less than those applicable to liquid compressibility, as would be expected since the number of effective units per molecule is normally less in the solid, particularly at low temperatures, than it is in the liquid, and an intermediate value is appropriate for the boundary state. There is also a marked tendency toward a constant value in each of the various homologous series of compounds, at least in those portions of these series for which experimental data are available. Thus the value for most of the aliphatic acids is 4, and for the normal alcohols it is 3. Most elements have n = 1, the principal exceptions being such elements as sulfur and phosphorus which have quite complex liquid structures.

In the majority of substances on which experimental results are available for comparison including most of the common organic compounds, the a and c factors take the theoretical maximum values 4 and 8 respectively. The factor b is usually 1 at low pressures, except for the elements in the middle of each periodic group, which have the same tendency toward higher values that was noted in the case of solid compressibility.

Some of the low melting point elements have a-c-b values at or near the theoretical minimum, a point which is of particular interest; first, because it provides a definite reference point for these factors which helps to demonstrate that they have a real physical significance, and second, because the wide spread between the possible values of the factors at the lower end of the scale makes identification of the applicable factors a very simple matter. Helium, for example, takes the minimum values, 1-1-1. The next higher combination that is theoretically possible 1-1-1 would result in a reduction of more than 20 percent in the melting temperature at the upper end of the experimental temperature range. This is, of course, far outside the margin of experimental uncertainty, which is normally in the neighborhood of one or two percent and the 1-1-1 factors are therefore definitely the ones that are applicable.

The situation with respect to the other elements of very low melting point is similar, and the theoretical melting point pattern for these substances is therefore positively established. It does not necessarily follow, however, that the divergence between the experimental melting points and the values thus calculated is always chargeable to experimental error. The theoretical values are those which would result from the application of pressure only, without any "second order" effects such as those due to the presence of impurities, to consolidation of molecules under pressure, to polymorphic transitions, etc, and they will not necessarily coincide exactly with the results of accurate measurements made on a substance which is subject to extraneous influences of this kind.

It should also be recognized that correlation of the theoretical and experimental values is not as simple a matter in the melting point field as it is for a property such as surface tension, on which we have a large volume of reasonably accurate experimental data. Only a comparatively small amount of work has been done on the melting curves, and most of that has been confined to the range below 1000 atm. Outside of the recent work with the metallic elements and the elements of very low melting point, Bridgman's investigations are practically the only source of information at the higher pressures. This, of course, introduces some serious uncertainties into any correlations that we may attempt. If the calculated and experimental values agree, each serves to some extent as a corroboration for the other, but where there is a divergence it is not immediately apparent which of the two is in error.

The correlations of theory against experiment in the areas covered by previous papers in this series have been of the, massive type, Calculations have been carried out for hundreds of substances of many different classes and, although it has not been possible to show all of these data in the tabulations accompanying the papers, a reasonably good sample has been included in each case. Where the experimental data are scarce and to a large degree unconfirmed 2 as in the present instance) it will be necessary to use a more selective technique, and to examine the evidence of the validity of each phase of the theoretical relationship separately, rather than verifying the entire development in one operation by a massive demonstration of agreement with the results of observation.

The first point, which we will want to consider, is the validity of the square root relationship. For this purpose the most significant experimental results are those in which the percentage increase in the melting point is the greatest. Where the ratio of the melting point at the upper end of the experimental pressure range to the normal melting point is less than 2, the difference between a square root curve and some other possible exponential curve, or a linear curve, is small, and unless the experimental values are extremely accurate it is difficult to determine which relation these values actually follow. The divergence of the curves increases rapidly, however, as the ratio rises, and if this ratio is 4 or more the nature of the curve is readily ascertained.

For this particular purpose, therefore, the work at the highest pressures is of no particular value. Even where pressures in the neighborhood of 150,000 atm. have been reached in the study of the metallic elements, the corresponding melting point ratio is only about 1.2. In the range from 1.0 to 1.2 the difference due to even a fairly large change in the exponent of the melting point expression is negligible. It is not surprising, therefore, that there is much difference of opinion as to just what this exponent should be. In the case of iron, for example, Gilvarry arrives at an exponent of 1.9 for the Simon formula, Simon himself selects 4, and Strong gives us the value 8 (which corresponds to 1/8 on the basis of equation 16).51 On first consideration this seems to be an extreme case of disagreement, but if the value of Simon's constant a is adjusted empirically (as is always done, of course), the differences between these various exponential curves in this range are so much less than the experimental uncertainty that the curves are for all practical purposes coincident. For example, the square root of 1.1 is 1.0488 and the square root of 1.2 is 1.0954. If the curve from 1.0 to 1.2 were linear, the value at 1.1 would be 1.0477, which differs from 1.0448, the value on the square root basis, by only one-tenth of one percent. A similar calculation using an exponent of 1/8 (equivalent to Strong's value 8) shows that the deviation from the linear curve is still less, only about 0 of one percent. Where the normal melting point is in the vicinity of 20000, a change from Gilvarry's exponent 1.9 to Strong's exponent 8 changes the position of the midpoint of the curve only about one degree if the value of a is fitted to the maximum experimental value of the melting temperature. It is therefore clear that within the experimental pressure range all of the exponents selected by previous investigators are in agreement with each other and with the exponent of equation 16, But where the experimental data fit everything they prove nothing.

The definite verification of the square root relationship is furnished by the elements of very law melting point, the most conclusive demonstration coming from helium and hydrogen. Helium does not melt at all except under pressure, and its melting curve cannot be referred to the normal melting point in the usual manner, but a study of the situation indicates that the melting point of this element can be calculated from equation 16 by the use of a pseudo-melting point which has been evaluated empirically as 11.1 K. We first calculate the melting point under pressure just as if 11.1 were the normal melting point, and then we subtract 11.1 from the result. At 5000 atm. for example, we find that the quantity (P +P0)1/2/P01/2 amounts to 4.516. Multiplying by 11.1 we obtain 50.13, and subtracting 11.1 we arrive at a theoretical melting point of 39.03 K. A measurement at this pressure is reported as 39 K. If the value of the expression

 

(P +P0)1/2

-  1

 

P01/2

is less than 1.0 (that is, if the true melting point is below the pseudo-melting point), the true melting point is proportional to the 2/3 power of the foregoing expression instead of the first power. The reasons for this behavior are not clear, although it is not surprising to find that the values below the reference temperature, which correspond in some degree to negative temperatures, are abnormal, Table X-1 compares the calculated and experimental melting points of helium. Here we see that although the maximum pressure of observation is only 7270 atm, the melting point ratio (designated as R in this and the following tables) at this pressure is 4.4, which is well above the minimum requirement for positive identification of the nature of the melting curve.

Also included in this table are the values for He3 which are computed in the same manner, except that the pseudo-melting point is slightly higher, 11.5 K, and the 5/6 power is substituted for the 2/3 power below the pseudo-melting point. It will be noted that for both isotopes the differences between the theoretical and experimental values are abnormally high in the vicinity of the pseudo-melting point. This is a mathematical effect of the distribution of molecular velocities in the neighborhood of a transition point, similar to the effect on the fluidity values discussed in paper VIII, page 3, and rough calculations indicate that when the transition is studied in detail so that the proper corrections for this effect can be determined, the agreement at these temperatures will be found just as close in this range as it is where the transition effect is absent.

Aside from hydrogen, which will be discussed later, there is no other substance on which the melting curve has been followed farther than a ratio of about 2.5. In the range from around 2.0 to 2.5 we find such substances as nitrogen, which shows an agreement within 1 over the full experimental pressure range (if we use Bridgman's values up to his pressure limit); carbon tetrachloride, which agrees within 1 to 6000 kg/cm, with somewhat larger deviations above this pressure ethyl bromide, which agrees within 2 to 25,000 kg/cm and shows a deviation of 5 at 30,000 kg/cm, beyond what appears to be a transition of some kind; chloroform, which agrees with the results of one set of measurements by Bridgman to within 2 but differs substantially from another set of results; and two of the normal alcohols, ethyl and butyl, for which the agreement is within 4 and 3 respectively up to 25,000 kg/cm, beyond which the values diverge. It is not clear whether this divergence is due to experimental error or to a transition to a new value of P0 similar to the transitions, which were found in the study of compressibility.

The calculated and experimental melting points for these substances are listed in Table X-2,. Also included in this table are values for a few other substances which have been observed up to 11,000 kg/cm or higher) but only to melting point ratios between 1.25 and 2.0, Even though the information available within the range of significant melting point ratios is quite limited, the comparisons in this table should be sufficient to add considerable weight to the conclusions reached on the basis of the helium values

The melting curves of a large number of substances have been determined with precision to pressures in the neighborhood of 1000 atm. For reasons previously discussed, these determinations are of no value from the standpoint of verifying the square root relation, but now that the validity of this relation has been confirmed by other means, the values in the lower pressure range can be utilized as a test of equation 17, and a number of comparisons of melting points in this range are given in Table X - 3. Since all other factors that enter into the determination of the melting points of the common organic compounds are definitely fixed, identity of the values of n applicable to related compounds) or obvious regularities in the values for such compounds, are strong evidence of the validity of equations 16 and 17 and of the theoretical principles from which these equations were derived. For example, melting points for the first seven of the aliphatic acids computed on the basis of n = 4 agree with the experimental results within 1 in four cases, and in only one of these compounds (propionic acid) is there any deviation as large as 3

Benzene and some of its simple derivatives contribute additional evidence of the same kind. Benzene itself has n = 5, and a large percentage of the closely related compounds for which melting curves are available take the same values of this factor. Among these are toluene, two of the xylenes, naphthalene, benzophenone, nitrobenzene, and two of the nitrobenzene. Representative examples of both the benzenes and the aliphatic acids are included in Table X-3.

The data for water, Table X - 4, are particularly interesting. The a-c-b values are 4-8-1 as usual, except that there is a transition to 4-8-2 between 8000 and 9000 kg/cm affecting ice VI only. Disregarding the abnormal forms of ice that exist below 2000 kg/cm, we find that the entire melting point pattern of water, complex as it is, can be reproduced simply on the assumption that the factor n, the number of effective units in the molecule, increases step by step as we pass from one form of ice to the next: ice III - 1, ice V - 2. ice VI - 3, ice VII - 4. (The status of ice IV is questionable; it may not even exist). Except in the range from 20,000 to 28,000 kg/cm, where the effects of a polymorphic transition that takes place at 22,400 kg/cm are in evidence, the agreement between the calculated and experimental values is within 2 in all cases.

The increase in the factor b from 1 to 2 which was found at a pressure of approximately 9000 kg/cm in ice VI is one of the very few instances where the existence of a transition of this kind, involving an increase in the initial pressure, appears to be definitely confirmed. The pattern of increase in this factor found in the study of solid compressibility suggests, however, that such transitions may be normal, and that their infrequent appearance in melting phenomena is merely due to the relatively narrow pressure range that has thus far been covered experimentally.

A similar transition in the opposite direction occurs in hydrogen and the inert gases above helium. Here we find that the initial a-c-b values are 1-1-1, but subsequently these factors drop to the minimum level 1-1-1, What we may regard as the normal pattern for this transition is illustrated by krypton and xenon, Table X-5. In these elements the 1-1-1 factors prevail up to 170 K (one-third of the liquid temperature unit, 510). From 170 to 340 (two-thirds of the temperature unit) there is a linear transition to 1-1-1, and above 340 the effective factors remain at this minimum level. The experimental results on argon are erratic and inconclusive, but not inconsistent with values calculated on the same basis. Neon and hydrogen follow the same general pattern, but the transition temperatures are fractional values of those normally applicable. In the case of hydrogen, the transition begins at 28.3 K, one-sixth of the normal 170, and is completed in 113.3, two-thirds of the normal interval. Table X-6 compares the hydrogen melting points calculated on this basis with a set of values compiled from experimental data. As the table shows, the two sets of values agree within 1/4 degree up to the two highest pressures of observation, and even in these cases the difference is less than degree.

Table X-7 lists the values of the various factors entering into the calculation of initial pressures and melting points for all of the substances included in the preceding tabulations.

TABLE X - 1
Melting Points - Helium
He4 P0 = 266.4 kg/cm (52)
P R Tm Obs.
37.3 .068 1.85 1.91
238.7 .377 5.79 5.70
482.2 .676 8.55 8.75
750.8 .954 10.76 12.54
1018.9 1.197 13.29 13.88
1280.3 1.409 15.64 16.01
1539.2 1.603 17.79 18.01
1746.8 1.749 19.41 19.52
2032.8 1.938 21.51 21.52
2251.5 2.074 23.02 23.01
2480.1 2.211 24.54 24.46
2813.3 2.400 26.64 26.48
2986.4 2.494 27.68 27.50
3323.9 2.671 29.65 29.47
3496.0 2.758 30.61 30.47

TABLE X - 1
Melting Points - Helium
He4 atm. (53)
P R Tm Obs.
3280 2.704 30.01 30
4170 3.144 34.90 35
5140 3.576 39.69 40
6170 3.993 44.32 45

TABLE X - 1
Melting Points - Helium
He3 P0 = 294.1 kg/cm (52)
P R Tm Obs.
75.9 .173 1.99 1.94
232.0 .405 4.66 4.68
322.3 .512 5.89 5.86
535.3 .724 8.33 8.42
729.9 .887 10.20 10.45
1010.9 1.106 12.72 13.00
1251.2 1.292 14.86 15.03
1505.1 1.473 16.94 17.00
1776.0 1.653 19.01 19.00
2054.9 1.826 21.00 21.00
2281.2 1.959 22.53 22.51
2518.3 2.092 24.66 24.02
2759.6 2.222 25.55 25.51
3008.3 2.351 27.04 27.01
3262.3 2.478 28.50 28.50
3253.7 2.603 29.93 30.01

TABLE X - 2
Melting Points
Nitrogen (54)
P
M kg/cm
R Tm Obs.
0 1.000 63 63
1 1.324 83 82
2 1.582 100 99
3 1.806 114 113
4 2.003 126 126
5 2.183 138 138
6 2.350 148 149
M atm. (55)
7 2.540 160 157.5
8 2.689 169 169
9 2.830 178 178.5

TABLE X - 2
Melting Points
Carbon Dioxide
P
M kg/cm
R Tm Obs.
(54)
0 1.000 217 217
1 1.078 234 236
2 1.151 250 253
3 1.219 265 268
4 1.283 278 282
5 1.345 292 295
6 1.404 205 306
7 1.461 317 317
8 1.514 329 328
9 1.567 340 339
10 1.618 351 349
12 1.715 372 367

TABLE X - 2
Melting Points
Lead
P
M kg/cm
R Tm Obs.
(56)
0 1.000 600 600
3 1.036 622 622
6 1.071 643 643
9 1.105 663 663
12 1.138 683 682
15 1.171 703 701
18 1.202 721 719
21 1.232 739 737
24 1.262 757 754
27 1.291 775 770
30 1.320 792 785
33 1.347 808 800

TABLE X - 2
Melting Points
Mercury
P
M kg/cm
R Tm Obs.
0 1.000 234 234
2 1.047 245 245
4 1.092 256 255
6 1.135 266 265
8 1.176 275 275
10 1.216 285 285
12 1.255 294 295

TABLE X - 2
Melting Points
Chloroform
P
M kg/cm
R Tm Obs.
0 1.000 210 212
1 1.090 229 228
2 1.173 246 245
3 1.250 263 261
4 1.323 278 277
5 1.392 292 291
6 1.458 306 306
7 1.521 319 319
8 1.581 332 332
9 1.640 344 345
10 1.696 356 357
11 1.750 368 369
12 1.803 379 381

TABLE X - 2
Melting Points
Ethyl Bromide
P
M kg/cm
R Tm Obs.
0 1.000 154 154
5 1.318 203 203
10 1.572 242 244
15 1.791 276 278
20 1.986 306 307
25 2.164 333 331
30 2.327 358 353

TABLE X - 2
Melting Points
Aniline
P
M kg/cm
R Tm Obs.
0 1.000 267 267
1 1.070 286 286
2 1.136 303 305
3 1.198 320 322
4 1.257 336 338
5 1.313 351 352
6 1.368 365 366
7 1.420 379 380
8 1.470 392 392
9 1.518 405 405
12 1.655 442 439

TABLE X - 2
Melting Points
Chlorobenzene
P
M kg/cm
R Tm Obs.
0 1.000 228 228
1 1.071 244 245
2 1.138 259 261
3 1.201 274 276
4 1.261 288 290
5 1.318 301 303
6 1.373 313 315
7 1.426 325 327
8 1.476 337 337
9 1.525 348 348
10 1.573 359 358
11 1.619 369 367
12 1.664 379 377

TABLE X - 2
Melting Points
Nitrobenzene
P
M kg/cm
R Tm Obs.
0 1.000 279 279
1 1.080 301 300
2 1.155 322 321
3 1.225 342 342
4 1.291 360 361
5 1.354 378 379
6 1.414 395 396
7 1.472 411 411
8 1.528 426 427
9 1.581 441 443
10 1.633 456 458
11 1.683 470 472

TABLE X - 2
Melting Points
Bromobenzene
P
M kg/cm
R Tm Obs.
0 1.000 242 242
1 1.071 259 261
2 1.139 276 279
3 1.202 291 295
4 1.262 305 309
5 1.320 319 323
6 1.375 333 335
7 1.428 346 347
8 1.479 358 359
9 1.528 370 370
10 1.576 381 381
11 1.623 393 391
12 1.668 404 401

TABLE X - 2
Melting Points
Carbon Tetrachloride
P
M kg/cm
R Tm Obs.
0 1.000 250 251
1 1.145 286 287
2 1.274 319 319
3 1.391 348 349
4 1.498 375 376
5 1.599 400 400
6 1.694 424 423
7 1.783 446 444
8 1.868 467 465
9 1.950 488 485

TABLE X - 2
Melting Points
Bromoform
P
M kg/cm
R Tm Obs.
0 1.000 281 281
1 1.086 305 305
2 1.166 328 327
3 1.241 349 348
4 1.311 368 368
5 1.378 387 387
6 1.442 405 404
7 1.502 422 421
8 1.561 439 436
9 1.618 455 452
10 1.672 470 467
11 1.725 485 482

TABLE X - 2
Melting Points
Ethyl Alcohol
P
M kg/cm
R Tm Obs.
0 1.000 156 156
5 1.290 201 197
10 1.525 236 234
15 1.729 270 268
20 1.911 298 298
25 2.078 324 327
30 2.232 348 355
35 2.375 371 382

TABLE X - 2
Melting Points
Butyl Alcohol
P
M kg/cm
R Tm Obs.
0 1.000 188 183
5 1.278 240 240
10 1.505 283 285
15 1.703 320 322
20 1.880 353 353
25 2.041 384 381
30 2.191 412 405
35 2.331 438 428

TABLE X - 3
Melting Points
Benzene
P
M kg/cm
R Tm Obs.
(57)
0 1.000 279 279
166 1.015 283 283
349 1.033 288 288
538 1.050 293 293
728 1.066 297 298
993 1.090 304 305

TABLE X - 3
Melting Points
p-Nitrotoluene
P
M kg/cm
R Tm Obs.
(57)
0 1.000 325 325
112 1.009 328 328
297 1.024 333 333
483 1.039 338 338
671 1.054 343 343
857 1.068 347 348
972 1.077 350 351

TABLE X - 3
Melting Points
Rutures Acid
P
M kg/cm
R Tm Obs.
(57)
0 1.000 268 268
290 1.021 274 213
567 1.041 279 278
837 1.060 284 283
986 1.071 287 286

TABLE X - 3
Melting Points
o-Xylene
P
M kg/cm
R Tm Obs.
(57)
0 1.000 248 248
220 1.021 253 253
437 1.042 258 258
654 1.063 264 263
865 1.082 268 268
1080 1.101 273 273

TABLE X - 3
Melting Points
m-Nitrotoluene
P
M kg/cm
R Tm Obs.
(57)
0 1.000 289 289
164 1.013 293 293
372 1.031 298 298
578 1.047 303 303
781 1.063 307 308
982 1.079 312 313

TABLE X - 3
Melting Points
Caproic Acid
P
M kg/cm
R Tm Obs.
(57)
0 1.000 269 269
218 1.016 273 273
487 1.036 279 278
760 1.056 284 283
890 1.065 286 286
996 1.073 289 288

TABLE X - 3
Melting Points
p-Xylene
P
M kg/cm
R Tm Obs.
(57)
0 1.000 286 286
49 1.006 288 288
197 1.024 293 293
343 1.041 298 298
495 1.058 303 303
647 1.075 307 308
803 1.093 313 313
957 1.110 317 318

TABLE X - 3
Melting Points
Acetic Acid
P
M kg/cm
R Tm Obs.
(57)
0 1.000 290 290
168 1.011 293 293
415 1.029 298 298
663 1.045 303 303
957 1.064 309 309

TABLE X - 3
Melting Points
Caprylic Acid
P
M kg/cm
R Tm Obs.
(57)
0 1.000 289 289
190 1.014 293 293
434 1.033 299 298
669 1.050 303 303
922 1.068 309 308

TABLE X - 5
Melting Points
Krypton
P
M kg/cm
R1 R2 2% Tm Obs.
(58)
0 1.000 1.000 0.0 116 116
2 1.414 1.581 2.4 164 165
4 1.732 2.000 27.1 209 209
6 2.000 2.345 48.2 251 252
8 2.236 2.646 66.5 291 293
10 2.449 2.915 82.9 329 332
12 2.646 3.162 100.0 367 370

TABLE X - 5
Melting Points
Xenon
P
M kg/cm
R1 R2 2% Tm Obs.
(58)
0 1.000 1.000 0.0 166 161
1 1.183 1.265 19.4 199 198
2 1.342 1.484 37.6 232 231
3 1.483 1.674 54.1 263 262
4 1.612 1.844 68.8 294 292
5 1.732 2.000 82.3 324 322
6 1.844 2.146 94.7 353 351
7 1.949 2.281 100.0 379 379
8 2.049 2.409 100.0 400 406

TABLE X - 4
Melting Points
Water (54) Ice III
P
M kg/cm
R Tm Obs.
(57)
0 1.000 241  
2 1.038 250 251
2.5 1.048 253 253
3 1.057 255 255
3.5 1.066 257 256

TABLE X - 4
Melting Points
Water (54) Ice VI (4-8-1)
P
M kg/cm
R Tm Obs.
(57)
0 1.000 206  
4.5 1.237 255 255
5 1.261 260 260
5.5 1.283 264 266
6 1.306 269 270
6.5 1.329 274 274
7 1.351 278 278
8 1.394 287 286

TABLE X - 4
Melting Points
Water (54) Ice V
P
M kg/cm
R Tm Obs.
(57)
0 1.000 226  
3.5 1.129 255 256
4 1.146 259 260
4.5 1.163 263 263
5 1.180 267 266
5.5 1.197 271 269
6 1.213 274 272

TABLE X - 4
Melting Points
Water (54) Ice VI (4-8-2)
P
M kg/cm
R Tm Obs.
(57)
0 1.000 237  
9 l.237 293 293
10 1.261 299 299
15 1.372 325 326
16 1.394 330 330
18 1.435 340 339
20 1.476 350 347
22 1.515 359 354

TABLE X - 4
Melting Points
Water (54) Ice VII
P
M kg/cm
R Tm Obs.
(57)
0 1.000 172.5  
22.4 2.125 367 355
24 2.183 377 369
26 2.254 389 384
28 2.323 401 397
30 2.389 412 410
32 2.454 423 423
34 2.517 434 434
36 2.579 445 445
38 2.639 455 456
40 2.690 465 466

TABLE X - 6
Melting Points
Hdrogen (59)
P
M kg/cm
R Tm Obs.
(57)
0 l.000 14.00 14
33.2 1.077 15.08 15
67.3 1 150 16.10 16
103.5 1:223 17.12 17
142.3 1.297 18.16 18
183.6 1.371 19.19 19
227.1 1.445 20.23 20
272.3 1.518 21.25 21
318.6 1.589 22.25 22
366.0 1.659 23.23 23
415.0 1.729 24.20 24
465.6 1.797 25.16 25
518 1.866 26.12 26

TABLE X - 6
Melting Points
Xenon
P
M kg/cm
R1 R2 2% Tm Obs.
(58)
572 1.934 2.261 0.7 27.11 27
628 2.002 2.348 1.5 28.10 28
685 2.069 2.434 2.2 29.08 29
744 2.136 2.519 3.0 30.06 30
867 2.270 2.689 4.5 32.04 32
996 2.402 2.856 6.0 34.01 34
1131 2.534 3.021 7.4 35.97 36
1274 2.605 3.186 8.9 37.96 38
1422 2.795 3.350 10.4 39.94 40
1821 3.118 3.753 14.0 44.89 45
2258 3.438 4.150 17.5 49.87 50
2735 3.755 4.544 21.0 54.89 55
3249 4.070 4.935 24.5 59.95 60
3801 4.382 5.321 27.9 65.02 65
4389 4.693 5.704 31.4 70.14 70
5014 5.002 6.085 34.8 75.30 75
5674 5.308 6.463 38.2 80.48 s0

TABLE X - 7
Initial Pressures
  a-c-b n V0 P0
Hydrogen 1-1-1 1 9.318 208.8
  1-1-1 1 9.318 139.2
Helium (He4) 1-1-1 1 3.519 266.4
(He3) 1-1-1 1 6.256 294.1
Nitrogen 2-1-1 1 1.0048 1327
Krypton 1-1-1 1 .3359 2066
  1-1-1 1 .3359 1378
Xenon 1-1-1 1 .2407 2581
  1-1-1 1 .2407 1720
Mercury 2-4-1 1 .0702 20859
Lead 4-6-1 2 .0876 40510
C02 4-8-1 5 .5722 6180
C014 4-4-1 6 .4108 3212
Ice III 4-8-1 1 .7640 25486
Ice V 4-8-1 2 .7640 12743
Ice VI 4-8-1 3 .7640 8495
  4-8-2 3 .7640 16990
Ice III 4-8-1 4 .7640 6371
Ethyl alcohol 4-8-1 3 .9145 7537
Butyl alcohol 4-8-1 3 .8526 7897
Acetic acid 4-8-1 4 .6346 7211
Butyric acid 4-8-1 4 .7043 6727
Caproic acid 4-8-1 4 .7254 6596
Caprylic acid 4-8-1 4 .7304 6566
Benzene 4-8-1 5 .7208 5299
o-Xylene 4-8-1 5 .7721 5061
p-Xylene 4-8-1 6 .7937 4141
Nitrobenzene 4-8-1 5 .5989 5996
m-Nitrotoluene 4-8-1 5 .5977 6004
p-Nitrotoluerie 4-8-1 5 .5893 6061
Aniline 4-8-1 4 .6786 6895
Chlorobenzene 4-8-1 4 .5827 6784
Bromobenzene 4-8-1 5 .4360 6735
Chloroform 4-8-1 7 .4315 5328
Bromoform 4-8-1 10 .2364 5567
Ethyl bromide 4-8-1 5 .4305 6792

REFERENCES

5. Larson, D. B., Compressibility of Solids, privately circulated paper available from the author on request.

50. Strong, H. M., and Bundy, F. P., Phys. Rev., 115-278.

51. See discussion by Strong in Nature, 183-1381.

52. MiIls, R. L., and Frilly, E. R., Phys. Rev., 99-480. Numerical values supplied by Dr, Mills in private communication.

53. Holland, Huggill and Jones, Proc. Roy, Soc. (London), A 207-268.

54. Bridgman, P. W., various, For a bibliography of Bridgman's reports see his book "The Physics of High Pressure". 0. Bell & Sons., London, 1958. All values in Table X-2 are from Bridgman unless otherwise specified.

55. Robinson., D. W., Proc. Roy. Soc. (London), A 225-393. Butuzov, V. P., Doklady Akad. Nauk, S.S.S.R., 91-1083

57. Deffet, Ll, Bull, Soc. Chim. Belg., 44-41.

58. Lahr, P. H. and Eversolet W. 0., J. Chem. Engr. Data, 7-42.

59. Compiled from original sources by Wooley, Scott and Brickwedde, J. Res. N.B.S., 41-3790


Index |