The Hypsometric Law and Its Significance for Solving the Problem of Magma Formation
Abstract Generated abstract
This paper develops the author’s application of the hypsometric law of physicochemistry to the problem of magmatic differentiation and magma formation. Using published average chemical analyses and densities for intrusive rock types, it converts oxide weight percentages into partial molecular numbers and gram-molecular component shares, then compares their distribution from granites through diorites and gabbros to peridotites. The resulting tables and diagrams are presented as evidence of regular vertical variation in magma composition under gravity, with silica and alkali components increasing toward lower-density acidic rocks and ferromagnesian components increasing toward denser ultrabasic rocks. The study argues that these molecular recalculations clarify the position of rock types in gravitational differentiation schemes and provide a basis for comparing individual rock analyses with average intrusive compositions.
Full Text
THE HYPSOMETRIC LAW AND ITS SIGNIFICANCE FOR SOLVING THE PROBLEM OF MAGMA FORMATION.
II. CONVERSION OF THE ORDINARY CHEMICAL COMPOSITION OF INTRUSIVE ROCKS TO GRAM-MOLECULAR
A. M. Kuzmin
In the author’s work, published in the journal Geology and Geophysics, on the basis of the hypsometric law of physicochemistry and of concrete materials testifying that the chemical composition—and, consequently, the mineralogical composition as well—in the magmatic body of intrusive formations situated in the field of the earth’s gravity must change regularly from top to bottom. This is also essentially indicated by the successively formed rocks of the vein facies of intrusions, from aplite-granitic to diorite-gabbroic composition, arriving from different depths of a magmatic chamber that is in the stage of formation.
In the aforementioned work of the author it is shown graphically (Fig. 1) that, in accordance with the law just indicated, in the magmatic mass at the stage of magmatic differentiation there should occur, as it were, a stratification of the liquid magma, the overall chemical composition of which from one layer to another gradually changes from a liquid melt close to granites to a liquid melt close to gabbro-peridotites; i.e., in accordance with what has been said, it follows that the magmatic rocks subsequently formed as a result of crystallizational differentiation must change their qualitative and quantitative composition from granites through diorites to gabbro-peridotites.
Fig. 1, illustrating the general propositions stated above, is constructed on the following basis. As is known, the average density of the earth’s crust increases from top to bottom. For this reason the values of the average density of rocks from 2.5 to 3.4 g/cm³ are plotted on the ordinate line. The abscissa lines are divided into one hundred parts, and their sum is taken to be 100%. In G. Rosenbusch’s Descriptive Petrography [4], for intrusive rocks, average chemical analyses and their average density values in g/cm³ are given. In this case, on the density ordinate we plot the average values of the specific gravities of intrusive rocks from granites to peridotites, equal to 2.6, 2.64, 2.75, 2.85, 2.92, and 3.32 g/cm³. If the chemical composition of the rocks is expressed in the form of oxides SiO₂, TiO₂, Al₂O₃, Fe₂O₃, FeO, MnO, MgO, CaO, Na₂O, K₂O, H₂O, P₂O₅, then at the level of rocks of a definite density—for example, at the level of 2.85 g/cm³, corresponding to the average density of diorites—we shall plot in the form of line segments corresponding to the percentage content of one or another oxide of the rock, in the order adopted for expressing the general character of the chemical composition of a rock. The ends of the segments of the corresponding oxides are connected
lines, moving from one level to another. As a result, the same diagram is obtained as that presented in Fig. 1.
From analysis of this diagram there clearly follows the necessary regularity in the change of the chemical composition of magmatic rocks with depth, indicating that at the stage of magmatic differentiation a stratification of the liquid magma must, as it were, occur in the magma, and this stratification must correspondingly affect the formation
Fig. 1. Diagram of the regular distribution of the principal components in the most important types of intrusive rocks as a function of the specific gravities of the latter.
later of the corresponding intrusive formations, i.e., in the literal sense their regular character will correspond to Fig. 1.
Let us next try to express the average figures for the weight percentages of the oxides composing one or another intrusive rock as a quantity in fractions of a gram-molecule. Comparing the magnitude of the content of components in moles, taking one as the unit, will make it possible to reveal a number of new regularities.
According to V. I. Kireev [2], the mean molecular weight of a solution is determined by the following formula:
\[ M = m_1N_1 + m_2N_2 + m_3N_3 + m_4N_4 + m_5N_5 + m_6N_6 + \ldots , \]
in which \(m_1, m_2, m_3, \ldots m_x\) are the molecular weights of the components of the solution, and \(N_1, N_2, N_3, N_4, N_5, \ldots N_x\) are the molecular fractions, which in sum
\[ N_1 + N_2 + N_3 + N_4 + N_x = N = 6.023 \cdot 10^{23} \]
are equal to Avogadro’s number.
Next, we assume that the formula just given will also be valid for solids similar to magmatic rocks. In order to make use of this formula, in Table 1 we present tabular data from the appropriate reference works for the principal components of intrusive rocks: the atomic weight of the molecule, its density in \(\mathrm{g/cm^3}\), the specific (molecular) volume, and quantities characterizing the mass of the molecule in grams \((m_x \cdot 10^{-23})\).
If we know the percentage content of a component in a rock, then we can determine the partial values of the number of molecules of one or another substance that enters into the gram-molecule of the given rock.
For example, \(\mathrm{SiO_2}\) in gabbro constitutes 47.36% of the rock; then \(N_x\)—the number of silica molecules in a mole—will be equal to (Table 3)
\[ N_5^1 = \frac{6.023 \cdot 10^{23} \cdot 47.39}{100} = 2.854 \cdot 10^{23}; \]
\(\mathrm{Al_2O_3}\) in gabbro constitutes 18.52% of the rock; then the number of alumina molecules in a mole will be equal to
\[ N_5^3 = \frac{6.023 \cdot 10^{23} \cdot 18.52}{100} = 1.115 \cdot 10^{23}. \]
Table 1
| Components | Molecular weight | Specific gravity of components | Specific (molecular) volume | Mass of molecule in grams \(m_x \cdot 10^{-23}\) |
|---|---|---|---|---|
| \(\mathrm{SiO_2}\) | 60 | 2.67 | 22.5 | \(9.96 \cdot 10^{-23}\) |
| \(\mathrm{TiO_2}\) | 80 | 4.2 | 19.0 | \(13.20 \cdot 10^{-23}\) |
| \(\mathrm{Al_2O_3}\) | 102 | 3.96 | 25.8 | \(16.93 \cdot 10^{-23}\) |
| \(\mathrm{Fe_2O_3}\) | 160 | 5.1 | 31.3 | \(26.56 \cdot 10^{-23}\) |
| \(\mathrm{FeO}\) | 72 | 5.97 | 12.0 | \(11.95 \cdot 10^{-23}\) |
| \(\mathrm{MnO}\) | 71 | 5.4 | 13.1 | \(11.79 \cdot 10^{-23}\) |
| \(\mathrm{MgO}\) | 40 | 3.6 | 11.1 | \(6.60 \cdot 10^{-23}\) |
| \(\mathrm{CaO}\) | 56 | 3.3 | 17.0 | \(9.30 \cdot 10^{-23}\) |
| \(\mathrm{Na_2O}\) | 62 | 2.27 | 27.4 | \(10.29 \cdot 10^{-23}\) |
| \(\mathrm{K_2O}\) | 94 | 2.32 | 40.5 | \(15.61 \cdot 10^{-23}\) |
| \(\mathrm{P_2O_5}\) | 142 | 2.39 | 59.4 | \(23.58 \cdot 10^{-23}\) |
| \(\mathrm{H_2O}\) | 18 | 1.0 | 18.0 | \(2.99 \cdot 10^{-23}\) |
The sum of the partial numbers of molecules of one or another substance for one and the same rock must be equal to \(N = 6.023 \cdot 10^{23}\):
\[ N_5^1 + N_5^2 + N_5^3 + N_5^4 + \ldots + N_5^{12} = N = 6.023 \cdot 10^{23} \]
\[ N_3^1 + N_3^2 + N_3^3 + N_3^4 + \ldots + N_3^{12} = N = 6.023 \cdot 10^{23}. \]
If, for each component, its molecular mass \(m_x \cdot 10^{-23}\) grams and the number of molecules of this substance in a mole are known, then we can determine, in grams, the share of each component in the gram-molecule.
For example, for \(\mathrm{SiO_2}\) in peridotites \(N_6^1 = 2.579 \cdot 10^{23}\) (Table 2), and its molecular mass is \(m_1 \cdot 10^{-23} = 9.96 \cdot 10^{-23}\) grams. The share of silica in a mole of the rock is equal to
\(m_1 \cdot 10^{-23} \cdot N_6^1 = 9.96 \cdot 10^{-23} \cdot 2.579 \cdot 10^{23} = 25.69\) grams.
For \(\mathrm{Al_2O_3}\) in the same rocks, \(N_6^3 = 0.322 \cdot 10^{23}\), and its molecular mass is \(m_3 \cdot 16.93 \cdot 10^{-23}\) grams. The share of alumina in a mole of the rock is equal to
\(m_3 \cdot 10^{-23} \cdot N_6^3 = 16.93 \cdot 10^{-23} \times 0.322 \cdot 10^{23} = 5.45\) grams.
The author may be reproached on the grounds that, in the composition of magma, chemical elements take an essential part in the form of various chemical compounds, and not in the form of oxides, and that it would be more correct to carry out all calculations in terms of the molecules of rock-forming minerals. In this connection it may be noted that such a conversion to mineral molecules has no special fundamental significance1 for the general solution of the problem posed by the author. Carrying out such a conversion would not only considerably complicate the entire work, but at the same time would require concrete data on the quantitative content of the corresponding minerals in the rocks whose chemical analyses are used in the present work. Such data are absent in Rosenbusch [4] and R. Daly [1].
On the basis of the foregoing, for peridotites and pyroxenites (21 analyses) with an average specific gravity of \(3.32 \dfrac{\text{grams}}{\text{cu. cm}}\) [4, p. 223], we have the following data (Table 2).
Table 2
| Components | Average composition of the rock, in weight % | \(N_6^x\)—partial number for each component: level designation | \(N_6^x\)—partial number for each component: \(N_6^x = a \cdot 10^{23}\) | Share of each component in the gram-molecule, \(m_x \cdot 10^{-23} N_6^x\) |
|---|---|---|---|---|
| \(\mathrm{SiO_2}\) | 42.82 | \(N_6^1\) | \(2.579 \cdot 10^{23}\) | 25.69 |
| \(\mathrm{TiO_2}\) | 1.45 | \(N_6^2\) | \(0.087 \cdot 10^{23}\) | 1.14 |
| \(\mathrm{Al_2O_3}\) | 5.34 | \(N_6^3\) | \(0.322 \cdot 10^{23}\) | 5.45 |
| \(\mathrm{Fe_2O_3}\) | 3.18 | \(N_6^4\) | \(0.191 \cdot 10^{23}\) | 5.07 |
| \(\mathrm{FeO}\) | 11.73 | \(N_6^5\) | \(0.706 \cdot 10^{23}\) | 8.44 |
| \(\mathrm{MnO}\) | 0.18 | \(N_6^6\) | \(0.011 \cdot 10^{23}\) | 0.13 |
| \(\mathrm{MgO}\) | 25.87 | \(N_6^7\) | \(1.560 \cdot 10^{23}\) | 10.30 |
| \(\mathrm{CaO}\) | 5.79 | \(N_6^8\) | \(0.349 \cdot 10^{23}\) | 3.25 |
| \(\mathrm{Na_2O}\) | 0.77 | \(N_6^9\) | \(0.046 \cdot 10^{23}\) | 0.47 |
| \(\mathrm{K_2O}\) | 0.78 | \(N_6^{10}\) | \(0.047 \cdot 10^{23}\) | 0.73 |
| \(\mathrm{H_2O}\) | 1.92 | \(N_6^{11}\) | \(0.115 \cdot 10^{23}\) | 0.33 |
| \(\mathrm{P_2O_5}\) | 0.17 | \(N_6^{12}\) | \(0.010 \cdot 10^{23}\) | 0.24 |
| 100.00 | \(N\) | \(6.023 \cdot 10^{23}\) | 61.25 |
For gabbro, characterized by 21 analyses, with an average specific gravity of 2.92 $\frac{\text{grams}}{\text{cu. cm}}$, the partial numbers for each component of the rock and the share of participation of each component in the gram-molecule of the rock may be presented in the following Table 3 [4, p. 185].
Table 3
| Components | Average composition of the rock, wt. % | $N_5^x$—partial numbers for each component: designation of the level | $N_5^x = a \cdot 10^{23}$ | Share for each component in the gram-molecule of the rock, $m_x \cdot 10^{-23} N_5^x$ |
|---|---|---|---|---|
| SiO$_2$ | 47.36 | $N_5^1$ | $2.854 \cdot 10^{23}$ | 28.43 |
| TiO$_2$ | 1.45 | $N_5^2$ | $0.049 \cdot 10^{23}$ | 0.65 |
| Al$_2$O$_3$ | 18.52 | $N_5^3$ | $1.115 \cdot 10^{23}$ | 18.88 |
| Fe$_2$O$_3$ | 3.29 | $N_5^4$ | $0.198 \cdot 10^{23}$ | 5.25 |
| FeO | 7.32 | $N_5^5$ | $0.441 \cdot 10^{23}$ | 5.27 |
| MnO | 0.15 | $N_5^6$ | $0.009 \cdot 10^{23}$ | 0.4 |
| MgO | 6.85 | $N_5^7$ | $0.413 \cdot 10^{23}$ | 2.73 |
| CaO | 10.95 | $N_5^8$ | $0.550 \cdot 10^{23}$ | 6.14 |
| Na$_2$O | 2.44 | $N_5^9$ | $0.147 \cdot 10^{23}$ | 1.51 |
| K$_2$O | 0.73 | $N_5^{10}$ | $0.044 \cdot 10^{23}$ | 0.69 |
| H$_2$O | 1.29 | $N_5^{11}$ | $0.073 \cdot 10^{23}$ | 0.23 |
| P$_2$O$_5$ | 0.25 | $N_5^{12}$ | $0.015 \cdot 10^{23}$ | 0.35 |
| 100.00 | $N$ | $6.023 \cdot 10^{23}$ | 70.44 |
For the average composition of diorites, characterized by 14 analyses and having an average specific gravity equal to 2.85 $\frac{\text{grams}}{\text{cu. cm}}$ [4, p. 172], the partial numbers of particles of the given substance and the share of each component in the gram-molecule of the rock may be illustrated by the following table [4].
The partial numbers of particles of the corresponding components in granodiorites, the average composition of which was obtained from 18 analyses of similar rocks with an average specific gravity equal to 4.75 $\frac{\text{grams}}{\text{cu. cm}}$ [4, p. 170], and the shares of these components in the group of rocks under consideration may be presented in the following Table 5.
The partial numbers of particles of the corresponding components in granites, the average composition of which was obtained from 20 analyses of rocks with an average specific gravity equal to 2.64 $\frac{\text{grams}}{\text{cu. cm}}$ [4, p. 104], and the share of each component in the gram-molecule of the rock is characterized by the following Table 6.
And, finally, for alkaline granite of average composition, obtained from 13 analyses, with an average specific gravity of 2.64 $\frac{\text{grams}}{\text{cu. cm}}$
Table 4
| Components | Average composition of the rock, wt. % | \(N_4^x\)-partial numbers for each component: designation of the level and component | \(N_4^x = a \cdot 10^{23}\) | Fraction of each component in a gram-molecule of the rock \(m_x \cdot 10^{-23}\cdot N_4^x\) |
|---|---|---|---|---|
| SiO\(_2\) | 55,46 | \(N_4^1\) | \(3,340 \cdot 10^{23}\) | 33,27 |
| TiO\(_2\) | 0,94 | \(N_4^2\) | \(0,057 \cdot 10^{23}\) | 0,75 |
| Al\(_2\)O\(_3\) | 16,92 | \(N_4^3\) | \(1,020 \cdot 10^{23}\) | 17,27 |
| Fe\(_2\)O\(_3\) | 2,73 | \(N_4^4\) | \(0,164 \cdot 10^{23}\) | 4,36 |
| FeO | 4,80 | \(N_4^5\) | \(0,289 \cdot 10^{23}\) | 3,45 |
| MnO | 0,13 | \(N_4^6\) | \(0,008 \cdot 10^{23}\) | 0,09 |
| MgO | 4,44 | \(N_4^7\) | \(0,267 \cdot 10^{23}\) | 1,76 |
| CaO | 7,33 | \(N_4^8\) | \(0,441 \cdot 10^{23}\) | 4,10 |
| Na\(_2\)O | 3,63 | \(N_4^9\) | \(0,219 \cdot 10^{23}\) | 2,25 |
| K\(_2\)O | 2,41 | \(N_4^{10}\) | \(0,145 \cdot 10^{23}\) | 2,26 |
| H\(_2\)O | 0,89 | \(N_4^{11}\) | \(0,054 \cdot 10^{23}\) | 0,16 |
| P\(_2\)O\(_5\) | 0,32 | \(N_4^{12}\) | \(0,019 \cdot 10^{23}\) | 0,85 |
| 100,00 | \(N\) | \(6,023 \cdot 10^{23}\) | 70,17 |
Table 5
| Components | Composition of the rock, wt. % | \(N_3^x\)-partial numbers for each component: designation of the level and component | \(N_3^x = a \cdot 10^{23}\) | For each component in the gram-molecule \(m_x \cdot 10^{-23}\cdot N_3^x\) |
|---|---|---|---|---|
| SiO\(_2\) | 67,00 | \(N_3^1\) | \(4,035 \cdot 10^{23}\) | 40,18 |
| TiO\(_2\) | 0,51 | \(N_3^2\) | \(0,031 \cdot 10^{23}\) | 0,41 |
| Al\(_2\)O\(_3\) | 15,96 | \(N_3^3\) | \(0,915 \cdot 10^{23}\) | 25,49 |
| Fe\(_2\)O\(_3\) | 1,98 | \(N_3^4\) | \(0,119 \cdot 10^{23}\) | 3,16 |
| FeO | 2,17 | \(N_3^5\) | \(0,131 \cdot 10^{23}\) | 1,56 |
| MnO | 0,07 | \(N_3^6\) | \(0,005 \cdot 10^{23}\) | 0,05 |
| MgO | 1,76 | \(N_3^7\) | \(0,106 \cdot 10^{23}\) | 0,70 |
| CaO | 3,55 | \(N_3^8\) | \(0,214 \cdot 10^{23}\) | 3,20 |
| Na\(_2\)O | 3,88 | \(N_3^9\) | \(0,233 \cdot 10^{23}\) | 2,40 |
| K\(_2\)O | 2,99 | \(N_3^{10}\) | \(0,180 \cdot 10^{23}\) | 2,80 |
| H\(_2\)O | 0,77 | \(N_3^{11}\) | \(0,046 \cdot 10^{23}\) | 0,14 |
| P\(_2\)O\(_5\) | 0,13 | \(N_3^{12}\) | \(0,008 \cdot 10^{23}\) | 0,21 |
| 100,00 | \(N\) | \(6,023 \cdot 10^{23}\) | 70,30 |
Table 6
| Components | Rock composition, wt. % | \(N_2^x\)-partial numbers for each component: notation of equations and components | \(N_2^x = a \cdot 10^{23}\) | Fraction of each component in the gram-molecule of the rock \(m_x \cdot 10^{-23} N_2^x\) |
|---|---|---|---|---|
| SiO\(_2\) | 72,02 | \(N_2^1\) | \(4,338 \cdot 10^{23}\) | 43,21 |
| TiO\(_2\) | 0,34 | \(N_2^2\) | \(0,020 \cdot 10^{23}\) | 0,26 |
| Al\(_2\)O\(_3\) | 13,13 | \(N_2^3\) | \(0,791 \cdot 10^{23}\) | 13,39 |
| Fe\(_2\)O\(_3\) | 1,46 | \(N_2^4\) | \(0,088 \cdot 10^{23}\) | 2,33 |
| FeO | 1,77 | \(N_2^5\) | \(0,107 \cdot 10^{23}\) | 1,28 |
| MnO | 0,11 | \(N_2^6\) | \(0,007 \cdot 10^{23}\) | 0,08 |
| MgO | 0,55 | \(N_2^7\) | \(0,033 \cdot 10^{23}\) | 0,22 |
| CaO | 1,48 | \(N_2^8\) | \(0,089 \cdot 10^{23}\) | 0,82 |
| Na\(_2\)O | 3,50 | \(N_2^9\) | \(0,211 \cdot 10^{23}\) | 2,17 |
| K\(_2\)O | 4,77 | \(N_2^{10}\) | \(0,287 \cdot 10^{23}\) | 4,68 |
| H\(_2\)O | 0,72 | \(N_2^{11}\) | \(0,068 \cdot 10^{23}\) | 0,13 |
| P\(_2\)O\(_5\) | 0,15 | \(N_2^{12}\) | \(0,009 \cdot 10^{23}\) | 0,21 |
| 100,00 | \(N\) | \(6,023 \cdot 10^{23}\) | 68,78 |
Table 7
| Components | Rock composition, wt. % | \(N_1^x\)-partial numbers for each component: notation of equations and components | \(N_1^x = a \cdot 10^{23}\) | Fraction of each component in the gram-molecule of the rock \(m_x \cdot 10^{-23} N_1^x\) |
|---|---|---|---|---|
| SiO\(_2\) | 73,22 | \(N_1^1\) | \(4,410 \cdot 10^{23}\) | 43,92 |
| TiO\(_2\) | 0,20 | \(N_1^2\) | \(0,012 \cdot 10^{23}\) | 0,16 |
| Al\(_2\)O\(_3\) | 12,47 | \(N_1^3\) | \(0,751 \cdot 10^{23}\) | 12,71 |
| Fe\(_2\)O\(_3\) | 1,92 | \(N_1^4\) | \(0,116 \cdot 10^{23}\) | 3,18 |
| FeO | 1,30 | \(N_1^5\) | \(0,078 \cdot 10^{23}\) | 0,93 |
| MnO | 0,07 | \(N_1^6\) | \(0,005 \cdot 10^{23}\) | 0,06 |
| MgO | 0,21 | \(N_1^7\) | \(0,013 \cdot 10^{23}\) | 0,08 |
| CaO | 0,49 | \(N_1^8\) | \(0,029 \cdot 10^{23}\) | 0,27 |
| Na\(_2\)O | 4,62 | \(N_1^9\) | \(0,279 \cdot 10^{23}\) | 2,87 |
| K\(_2\)O | 4,86 | \(N_1^{10}\) | \(0,293 \cdot 10^{23}\) | 4,57 |
| H\(_2\)O | 0,59 | \(N_1^{11}\) | \(0,035 \cdot 10^{23}\) | 0,10 |
| P\(_2\)O\(_5\) | 0,04 | \(N_1^{12}\) | \(0,002 \cdot 10^{23}\) | 0,05 |
| 100,00 | \(N\) | \(6,023 \cdot 10^{23}\) | 68,90 |
[4, p. 104], the partial numbers of particles of a given substance and the share of each component in the gram-molecule of the rock may be illustrated by Table 7 below.
Table 8 is a summary of the results of calculations of the role of a component in the gram-molecule of each rock (of averaged composition), which is characterized by its specific gravity and molecular volume. The first six analyses in the table are taken as the final results of the calculations from Tables 2—7. The next five analyses, 7—11, represent the partial shares of the components of such rocks as dunite [4, p. 223, analysis 19], lherzolite [1,5, average of 13 analyses], gabbro [1, average of 41 analyses], quartz diorite [1,5, average of 55 analyses], and granite [5, average of 546 analyses].
From this table the following conclusions may be drawn: with increasing specific gravity of an intrusive rock, the molecular volume of its gram-molecule decreases, whereas the weight of the gram-molecule remains approximately one and the same, although there are some deviations and fluctuations that require further investigation. As for the behavior of the principal components of the composition of rocks, their share, or percentage, in the gram-molecule changes more strictly and regularly from one level to another. Finally, both Fig. 1 and Fig. 2 indicate that the share of gabbro-peridotites in the structure of the Earth’s crust is much greater than the share of rocks of the gabbro-granite series.
The additional data of the following analyses (7—11), presented in Table 8, make it possible to solve a number of other practical problems. Thus, for example, fresh dunite (analysis 7), with a specific gravity of 3.29, should in Fig. 1 lie above the 3.3 level, but the partial share of magnesium oxide in dunite differs sharply in magnitude from that of magnesium oxide in the rock lying at the 3.29 level. Determination of the molecular volume of dunite shows that this latter rock should lie at a level lower than the peridotites with a specific gravity of 3.32, if the diagram is constructed on the basis of the molecular volumes.
Fig. 2. Diagram of the average contents of the principal components in the chief types of intrusive rocks, constructed according to the molecular volumes and the share of each component in the gram-molecule.
Granites, corresponding to the average composition of 546 analyses, with a molecular volume of 25.9 and a density of 2.66 g/cm³, fall exactly in the interval between the figures of the second and third rows of analyses. Thus, the molecular volumes calculated for lherzolites, gabbros, quartz diorites, and granites, and the shares of each component in the gram-
Table 8
| Specific gravity of rock | Molecular volume of gram-molecule of rock | Weight of gram-molecule of rock | Share of components in gram-molecule of rock: SiO₂ | Share of components in gram-molecule of rock: TiO₂ | Share of components in gram-molecule of rock: Al₂O₃ | Share of components in gram-molecule of rock: Fe₂O₃ | Share of components in gram-molecule of rock: FeO | Share of components in gram-molecule of rock: MnO | Share of components in gram-molecule of rock: MgO | Share of components in gram-molecule of rock: CaO | Share of components in gram-molecule of rock: Na₂O | Share of components in gram-molecule of rock: K₂O | Share of components in gram-molecule of rock: H₂O | Share of components in gram-molecule of rock: P₂O₅ | Name of rocks and number of analyses |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2,6 | 27,0 | 68,90 | 43,92 | 0,16 | 12,71 | 3,18 | 0,93 | 0,06 | 0,08 | 0,27 | 2,87 | 4,57 | 0,10 | 0,05 | Alkaline granites (13) |
| 2,64 | 26,0 | 68,78 | 43,21 | 0,264 | 13,39 | 2,33 | 1,28 | 0,08 | 0,22 | 0,82 | 2,17 | 4,68 | 0,13 | 0,21 | Granites (20) |
| 2,75 | 25,56 | 70,30 | 40,18 | 0,41 | 15,49 | 3,16 | 1,56 | 0,05 | 0,70 | 3,20 | 2,40 | 2,80 | 0,14 | 0,21 | Granodiorites (18) |
| 2,85 | 24,6 | 70,17 | 33,27 | 0,75 | 17,27 | 4,36 | 3,45 | 0,09 | 1,76 | 4,10 | 2,25 | 2,26 | 0,16 | 0,75 | Diorites (14) |
| 2,92 | 24,1 | 70,44 | 28,43 | 0,65 | 18,88 | 5,25 | 5,27 | 0,11 | 2,73 | 5,14 | 0,69 | 0,69 | 0,23 | 0,35 | Gabbro (21) |
| 3,32 | 18,45 | 61,25 | 25,69 | 1,14 | 5,45 | 5,07 | 8,44 | 0,13 | 10,30 | 3,25 | 0,47 | 0,73 | 0,33 | 0,24 | Peridotites (21) |
| 3,29 | 16 | 52,76 | 23,90 | 0,08 | 0,66 | — | 9,32 | — | 17,91 | 0,56 | 0,11 | 9,08 | — | — | Lunar fresh |
| 3,33 | 17,18 | 57,11 | 26,36 | 0,08 | 4,92 | 3,51 | 4,56 | 0,13 | 14,63 | 2,00 | 0,31 | 0,20 | 0,19 | 0,14 | Leucolite (13) |
| 2,98 | 23,73 | 70,73 | 28,94 | 0,77 | 18,23 | 5,05 | 4,28 | 0,09 | 2,18 | 6,16 | 2,18 | 1,39 | 0,26 | 0,40 | Gabbro (41) |
| 2,81 | 24,78 | 69,63 | 36,95 | 0,53 | 16,51 | 4,06 | 2,71 | 0,07 | 1,15 | 3,01 | 2,69 | 1,97 | 0,22 | 0,38 | Quartz diorite (55) |
| 2,66 | 25,9 | 67,94 | 42,10 | 0,30 | 14,76 | 2,52 | 1,28 | 0,08 | 0,35 | 1,12 | 2,15 | 3,87 | 0,15 | 0,26 | Granites (55–66) |
molecule of the rock make it possible to determine more precisely the position of these rocks in gravitational schemes of magmatic differentiation.
Finally, comparison of chemical analyses of any magmatic rocks for which density has been determined with the data presented in the diagram of Fig. 1 will make it possible to say how close a given rock, in its chemical composition, is to the average type of rocks, or how sharply it deviates from it.
On the basis solely of the partial values, given in Table 8, for the participation of each component in the gram-molecule (mole) of the rock, one can construct diagrams or, for clarity, express graphically\(^2\) the role of each component in the transition from peridotites to granites (Fig. 2).
In studying the graphical forms of the quantitative distribution in rocks of each component separately, shown in Fig. 2, what first attracts attention is the strict spatial regularity in the increase or decrease of the role of one or another component in the composition of the corresponding magmatic rocks, from ultrabasic to acid rocks, from rocks with a density of \(3.3 \ \frac{\text{grams}}{\text{cu. cm}}\) to rocks with a density of \(2.6 \ \frac{\text{grams}}{\text{cu. cm}}\). In fact, the data given for the graphical representation of the quantitative distribution of components in the corresponding rocks are so clear and obvious that there is no need to dwell on them.
However, it should be said that the data of Fig. 2 are astonishingly similar to the theoretical diagram (Fig. 3) constructed for an aggregate consisting of five components \(A, B, C, D, E\), for which the density of the substance of each component increases successively from \(A\) to \(E\),
Fig. 3. Diagram of a theoretically possible regular distribution by density of substances \(A, B, C, D, E\) with different specific gravities in a multicomponent solution or melt situated in a gravitational field and obeying the hypsometric law of physico-chemistry.
\(^2\) We shall consider the construction of the diagrams in Fig. 2 using silica as an example. From the mean vertical line dividing the field into two symmetrical parts, the numbers corresponding to the specific gravity and expressing the proportions of each component in the gram-molecule of the rock are plotted, at the corresponding level, on one side and the other. As is evident from the diagrams, the points determining the proportions of each component in the gram-molecule of the rock fall strictly along regular lines.
i.e., \(d_A < d_B < d_C < d_D < d_E\). The fractions \(N_2^{I}, N_2^{II}, N_2^{III}, N_2^{IV}, N_2^{V}, \ldots\) of each component in the magma (rock) at one level or another, the sum of which is equal to \(N = 6.023 \cdot 10^{23}\), Avogadro’s number. The densities of the magma change from level to level: \(d_1 < d_2 < d_3 < d_4 < d_5 < d_6\). In the diagram of Fig. 3, substance \(A\) behaves like \(\mathrm{SiO_2}\). Substance \(C\) behaves like \(\mathrm{Al_2O_3}\) and \(\mathrm{CaO}\); substance \(E\) behaves like \(\mathrm{MgO}\), \(\mathrm{FeO}\), \(\mathrm{TiO_2}\), etc.
If we turn to the well-known diagrams given in textbook literature, illustrating the distribution of the principal rock-forming minerals in intrusive rocks, from peridotites to alkaline granites and syenites, then in this case as well we see the same pattern of regularities as above, but in a different expression. Namely: the ferromagnesian minerals, as follows from Fig. 1, as a rule decrease quantitatively from peridotites to granites. At the same time, a qualitative change takes place in the ferromagnesian minerals themselves: their molecular volumes increase upward from olivine to biotite. This regularity in the distribution of olivines, pyroxenes, hornblendes, and biotites reveals the interdependence of the entire mineral composition both horizontally and, especially, vertically. Plagioclases, changing from basic to acidic, reach a relative maximum in gabbro-diorites and decrease quantitatively in the direction of granites and syenites. Alkaline feldspars, beginning with diorites, increase rapidly in quantity toward the syenites, in which their content reaches a relative maximum. Quartz reaches a maximum in granites and decreases quantitatively both toward syenites and toward diorites.
Thus, the diagrams just considered in Figs. 1, 2, and 3 once again clearly show that the mineral composition of magmatic rocks is, in the main, in full accord with the quantitative-qualitative distribution of components by rock types and is very close in character to our theoretical diagram (Fig. 3).
REFERENCES
- R. O. Daly. Igneous Rocks and the Depths of the Earth. ONTI, Moscow, 1936.
- V. A. Kireev. A Short Course in Physical Chemistry. 1963.
- F. Yu. Levinson-Lessing. Petrography. Gosizdat, Moscow–Leningrad, 1940.
- G. Rosenbusch. Descriptive Petrography. Gosgeolizdat, 1934.
- F. Birch, D. Scherer, G. Spicer. Handbook for Geologists on Physical Constants. IL, Moscow, 1949.
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This is easily verified if similar conversions are made, for example, for olivine \(\mathrm{Mg_2SiO_4}\) with specific gravity 3.15 and for orthoclase—\(\mathrm{KAlSi_3O_8}\). The discrepancy in the figures thus obtained will depend on the accuracy of measuring specific gravities. ↩