Wilfried B. Holzapfel - Modern Alchemy and the Philosopher's Stone

“How can we do that?” Marie asked incredulously.

Professor Wood explained. “Well, by definition, the boundary between the outer liquid and inner solid core of Earth occurs right at the point where the pressure crosses the melting curve of the corresponding iron-nickel alloy. In the hypothetical phase diagram that we looked at earlier ( Figure 14), the melting curve indicated that the melting temperature increases with increasing pressure. This is typical of most materials. It is also what we expect for the materials in Earth's core. From the models on the composition of Earth we know that the pressure at this depth is about 330 GPa. The melting curve of pure iron has been measured in the laboratory at pressures up to 220 GPa. By extrapolating the melting curve to 330 GPa, my friends have estimated 11,12 that the melting temperature at that depth in Earth should be about 4700° C.

Helen was amazed. “That is fantastic!” she exclaimed.

“Not bad, right?” The professor smiled broadly. Then he added, “But to obtain a more accurate model of all the processes inside Earth, we would still like to know how reliable this estimate of temperature really is. The uncertainty in measuring the melting temperature of pure iron based on laboratory data is approximately plus or minus 300°C. The precise amount of nickel present in the alloy should not increase this uncertainty significantly. But adding oxygen, sulfur, and perhaps also magnesium to the iron-nickel alloy could cause the melting temperature of Earth's core to be lower by several hundred degrees!

“You see, if scientists measure something, they have to think about the accuracy or uncertainty of their measurement results.”

Marie was quite pleased by this whole discussion, but Helen was perplexed. “But what about the quintessence ?” Helen asked. “Have you forgotten about that?”

“No, I have not,” Professor Wood replied. “But I felt that I needed the example of the wide range of pressures and temperatures inside Earth to be able explain the larger map of states for the universe to you. You might wonder how large the ranges on such a map might be compared with the conditions on our Earth!”

Professor Wood produced another chart from his stack. He first drew attention to the vertical and horizontal axes on this new chart ( Figure 19).

“Following the layout of the hypothetical phase diagram that I showed you earlier ( Figure 14), my map of states for the universe depicts the landscape with respect to the pressures on the horizontal axis and temperature on the vertical axis. The scales for these axes also use powers of ten the same way that we did for the maps of the microcosm, but I have extended them to cover the unfathomable depths of space in the universe.

“In this map, unlike the phase diagram that we discussed earlier, I have labeled several areas, but I have shown no sharp boundaries. I have used different colors and symbols here to highlight different areas of special interest to us. Do you see these curves that are shaped like hockey sticks in the range of 10 10Pa, or 10 GPa? The brown curve shows the range of pressure and temperature that we experience on Earth. The red one corresponds to those of the sun. I have included several other regions marked with names that may be unfamiliar to you. The brown curve for Earth shows us that the pressure at the surface starts with the air pressure of one atmosphere or 10 5Pa. Inside Earth, at a depth of 30 km, the pressure increases to about one gigapascal (1 GPa) and then further to 366 GPa in the center of Earth as we have just discussed. The upper end of the brown curve in this figure corresponds to nearly 10 12Pa.

“The temperature scale is in degrees Kelvin and the lower end of it is close to absolute zero at 1 K. As you probably know, 0 K is equal to minus 273.24 °C. That, of course, is a very low temperature. The boiling point of water is correspondingly +373.24 K. I chose these units because 0 K corresponds to the lowest conceivable temperature. In physics, there are many advantages to the use of this absolute temperature as a reference.

Figure 19: Map of states for the world

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