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“In this diagram, the four elements of the alchemists, the four Essentia, are labeled using the modern names for the four possible states or phases of a single substance. Instead of the term Earth, I have written Solid. You can see that I have used the more general term Liquid in place of Water. Instead of Air, I have written Gas and in the field of Fire I have used the term Plasma. Are you familiar with this term?” The professor paused to see if the students were still with him on this picture.

“I remember that the word came up in my chemistry course, but perhaps you could remind us of exactly what you mean to infer by using this term to describe a fundamental state of matter,” Helen suggested.

“I can do that,” Professor Wood replied. “Generally we do not encounter materials in the plasma state unless they are separated from us by some sort of containment. For example, a plasma exists inside a fluorescent lamp tube, but we are not able to touch it. In a plasma, the gas is so hot that the molecules or atoms travel a high speed and undergo relatively violent collisions with each other. There is so much energy exchanged in the collisions that the valence electrons, the more loosely bound ones in the outer shells of the atoms or molecules, are simply knocked away from their home atoms. As a result, the atoms become ionized. Another example of molecules in the plasma state is a flash of lightning. As you might guess, coming in contact with such high-velocity ions would be very damaging to your skin.”

“So those little coils that we find inside those energy-saving light bulbs produce light in the form of a plasma?” Marie asked.

“Sort of,” the professor replied. “Fluorescent tubes contain mercury vapor and a filler noble gas.6 There is an electrical transformer in the lighting fixture that converts the normal AC voltage in our homes to a high voltage. In the presence of high voltage, the gases inside the glass tube form a plasma that radiates ultraviolet light. The inside of the fluorescent tube is coated with salts called phosphors that ‘fluoresce’ or produce visible light when they absorb ultraviolet light. So it is really the coating that provides the light that we see.

“On the other hand, the light that we see in the bright neon lights that are so common in night advertising is normally produced by collisions among the hot ions themselves. Most of the light that is produced by a fire or a candle actually arises mostly from glowing carbon particles. Otherwise, we might be able to see the plasma that exists in the vicinity of the wick or the wood.”

“I was not really aware of that,” Marie said. “I don’t recall ever hearing that a flame is an example of a plasma. I was vaguely aware that lightning and other electrical arcs conduct electricity by ionizing the air, but I hadn’t heard that the ionized air was an example of a material that is in its plasma state."

“It turns out that the hot, bright surface of the sun is also in such a plasma state. In fact, plasma is probably the predominant state of matter in the universe,” Professor Wood said.

“So it makes perfect sense to identify Plasma, along with Solid, Liquid and Gas, as the four basics states of matter that we can directly compare to the four elements that ancients had identified!”7 Helen was ecstatic with this realization.

“Great!” said Professor Wood. “We are all together on this concept. Now let’s look at the diagram more closely. In this illustration, the red balls represent atoms, just as we are used to thinking of them in materials that are in a solid, liquid or gaseous state. The purple stars with the squarish ring around them are meant to represent ions and free electrons that are dissociated from the ions. The black lines correspond to boundaries in pressure and temperature that separate the states of this hypothetical substance.

“For example, if you raise the temperature of a liquid or reduce the pressure on its surface, you can get the substance to evaporate and turn into a gas. That boundary is represented by this diagonal black line.” Professor pointed to the somewhat vertical straight line near the center of the diagram.

“We call that line the boiling curve. You can see that the boiling point of this hypothetical substance changes substantially if you heat it at a slightly different pressure. Similarly, if you cool the liquid form of the substance enough, you could get it to freeze. In that case the material would condense to a solid. Then, if you reheated the solid, the substance would melt and turn into a liquid again. That boundary corresponds to the curved line that we call the melting curve on the right-hand side of the diagram. The black curved line on the left is the boundary between solid and gas.

As you can see from this phase diagram, these processes depend directly on the pressure and temperature of their environment.

“Phase diagrams like this can be rather complex for molecular substances because the molecules can also react chemically or break down and disintegrate at higher temperatures,” he went on to say.

Professor Wood continued his explanation of the prototypical phase diagram. “If you compare the picture of the ancient alchemists with this modern view, the landscape is now divided by these specific boundaries. On ordinary geographical maps, North is towards the top of the page. To the right is East, South is toward the bottom of the page and West is to the left. Usually the maps show a scale that can be used to gauge distances in meters, kilometers, or miles between locations on the map.

In this phase diagram, the upward direction corresponds to increasing temperature and the horizontal direction to increasing pressure toward the right. In the study of materials science, the phase diagrams of all the pure substances are represented by such maps in a kind of atlas for the world of high pressure. Since physicists and chemists today always measure everything precisely, the scales on the side and bottom are normally neatly labeled with numerical values for temperature and pressure in appropriate units. The boundaries between the various phases are similar to the boundaries between different countries in the geographic maps.

“The three-state corner here, near the middle of the chart, is known as a triple point. Three boundaries and three phase regions meet at this point. As I have already mentioned, the melting curve shows that the melting temperature is dependent upon pressure. For example, liquid mercury becomes solid when it is compressed at normal room temperature. Perhaps you know that ice initially melts under pressure, but you probably also know that this unusual behavior is a very special feature of water in the world of high pressure!”

“Does this slightly curved line to left of the triple point represent the pressure at which sublimation and its reverse process is called deposition occur at different temperatures?” Helen asked, again feeling just a little self-satisfied at recalling the names of these transitions.

Professor Wood was impressed. “Very good, Helen!,” he said. “You can see from the portion of the line that is horizontal in this hypothetical substance that pressure plays a relatively minor role in those transitions. In other words, decreasing the pressure further does not change the temperature at which sublimation takes place. That is typical of most actual substances.”

Professor Wood continued his discussion of the prototypical phase diagram. “Note that the line that extends upward and separates the areas of gas and liquid has an endpoint. The location in temperature and pressure of this point varies considerably from substance to substance. This endpoint of the boiling curve is called the critical point with its characteristic values of the critical temperature and the critical pressure.”

“So how does this phase diagram compare with the ideas of the alchemists?” Helen asked.

“We can compare what is happening here to the old ideas of Democritus.” Professor Wood explained. “Democritus contended that the atoms move differently in all the substances. That is still the present view! In solids, the atoms or molecules are usually arranged at fixed locations but have small shaking vibrations. In liquids, the atoms move about in groups but maintain a kind of average distance from each other. Their vibrations about that average distance are stronger and faster than they were in the solid phase. The well-defined structure of a regular, solid crystal lattice breaks down into a dense irregular arrangement when the crystal melts.

“In a gas, the movements are wider and faster than in a normal liquid. Most atoms travel relatively long distances in free flight before they collide with another atom. As a result, the differences between a gas and a liquid on an atomic level reflect the frequency of the impacts, the range of the free flight and the average distance between the atoms. When a gas is compressed, the range of free flight and the average distance between the atoms all become smaller. The gas becomes denser and less compressible.”

Marie felt obliged to jump into the conversation at this point. “Engineers have made practical application of this fact in the design of the pneumatic and hydraulic devices that we commonly use in robotics and manufacturing processes. The pneumatic systems usually use air as the fluid that flows through the system and transfers energy among the various components. Hydraulic systems commonly use oil as the fluid because it simultaneously lubricates the internal surfaces of the system and that reduces wear. But there are plenty of other examples in which the particular application favors the choice of another liquid or gas.

“In refrigeration systems, for example, a compressor is used to pressurize a gas and convert it to a liquid. This is practical as long as the system insures that the temperature of the fluid stays below the critical temperature. That part of the system is usually designed to dissipate heat so that the fluid crosses the boiling curve from left to right and becomes liquid. In another part of the cooling system, the pressure is reduced by forcing the liquid through a small hole. The resulting liquid droplets are allowed to evaporate. The fluid then crosses the boiling curve from right to left. We know that evaporation causes cooling from the way that the natural evaporation of our perspirations helps to cool our bodies on a hot day.”

“Very nice, Marie!” The professor complimented her before continuing with his discussion of the hypothetical phase diagram. He was glad to see that the students were not only following his ideas, but contributing ideas of their own.

“It is also possible to cross the gas-liquid boundary without changing the pressure by cooling the gas below the boiling point of the substance. You have seen this phase transformation while watching water boil in a pot with a glass lid. The steam cools and precipitates into water droplets on the cooler pot lid. Normally, when water boils, the temperature is increased by an external heat source but the atmospheric pressure on the surface of the water remains constant. At constant pressure, you cross the boiling curve in the phase diagram from the bottom up while cooking and vice verse from the top down when water condenses. This process is obviously very important in the atmosphere and the condensation of water vapor to form dew or raindrops. The dew point that weatherman reports on the radio or TV is indicative of the temperature at which condensation will occur at constant barometric pressure on a particular day. That temperature varies from day to day, depending upon the relative humidity of the air.”

“I always wondered why they report the dew point on the TV,” Helen remarked. “What happens if the temperature is higher than the critical temperature in any of these systems?”

“Good question,” Professor Wood replied. “If the temperature is higher than the critical temperature, the motion of the particles becomes so strong that the attraction between the particles does not really matter anymore. Then there will be no more condensation of droplets. At that point, the system is represented in the phase diagram by this area above the end of the boiling curve.”

Professor Wood pointed to the area at the top-center of the chart (Figure 14). “In this supercritical range above the critical temperature, there is no qualitative or real structural difference between liquid and gas. The ancient Greeks and the alchemists did not know about this state. There has been a lot of research done in modern times on pure substances in the supercritical region of the chart. It turns out that for many substances, particularly for metals and quite a few salts, the critical temperatures are so high that the substance transforms to the plasma state by the time it reaches its critical temperature.

“You may also have noticed that, in this phase diagram, the transition to the plasma state has no clear boundary. Instead, there is a gradual increase in the number of ionized particles and it is not possible to draw another boundary line on the diagram. The transition is too smooth!”

“Now let me ask you a question, Helen,” the professor teased. “Do you agree now that a modern phase diagram is quite similar to those pictures of the ancient alchemists for their four elements, the four essentia?”

“Yes, thank you. Now that you have shown us that plasma is a fourth phase of the state of matter that all materials have, I can see the similarity,” Helen answered. “I also understand why we don’t talk about essential elements today. We simply refer to these four phases when we describe the differences among substances that the ancients had also observed. On the other hand, I still don’t see anything that corresponds to the fifth symbol, the six-pointed star in the middle of the four essentia, on that diagram that Marie has. That fifth essentia is the one that you described as having the properties of all the other four at the same time. Is there something on this diagram that corresponds to the quintessence?”

Professor Wood continued with a nod toward the phase diagram, “The ancient Greeks developed the idea of indivisible atoms, but the view that we are looking at here involves molecules, atoms, ions and electrons. Have you heard about radioactivity in your courses at school?

“Of course!” Helen replied. “During the Fukushima disaster the whole area was contaminated by radioactive debris! My chemistry course also touched lightly upon the subject of nuclear decay.”

“And where did the radiation come from?” asked the professor.

Helen’s high school chemistry teacher had delivered a special lecture to the class at the time of the disaster. Everyone in the class was aware that the disaster was serious and that many people were justifiably afraid of radioactivity. But they had been unclear about what was really going on. Helen responded to Professor Wood’s question with what she could remember of that lecture.

“In the case of the Fukushima disaster, radiation came from the radioactive materials that had been placed in the reactors to produce heat when their nuclei changed from one element to another. The nuclei emit alpha, beta, or gamma rays during their decay. When the tsunami destroyed the walls of the reactors, these materials were spread around the area. They were no longer contained but they continued to change and give off radiation. The heat that the changes made then was just lost to the atmosphere. That was not so dangerous.

“The danger to humans and other living things was that the gamma rays, which were really like very high-energy light waves, cause damage to the cells of living tissue – far worse than the damage that the ultra-violet light from the sun can cause to our skin. The main problem is that radioactive elements can be inhaled or ingested, and some of them are bioactive and become lodged in tissues, instead of being quickly excreted. Since the nuclei are inside of the body, the damaging radiation is alpha and beta radiation. Radioactive cesium and iodine are good examples of elements that increase the risk of bone and thyroid cancer.8 Gamma radiation from Cesium 137 inside the body poses a greater risk for cancer in humans than direct gamma radiation from outside the body.”

Professor Wood nodded to show his approval of Helen’s explanation. “When one chemical element changes to another without any help from an external source, we say that the nucleus has undergone radioactive decay. Your teacher probably also told you that Marie Curie, Pierre Curie and Henri Becquerel received the Nobel Prize in 1903 for their detailed investigations of this natural radioactivity, right?”

As Helen nodded in the affirmative, Professor Wood continued his explanation. “With their discoveries, they opened up a whole new field of science. They recognized that the atomic nuclei can decay, and that new and unknown particles are produced during the decay of the atomic nuclei. I don’t want to get into a detailed discussion right now of all the new elementary particles which were subsequently found. A whole ‘zoo,’ to use a popular expression, of elementary particles has been observed since then."

“So does this zoo of elementary particles have anything to do with the quintessence?” Helen asked. She was not about to give up asking him about that until she got a satisfactory answer.

“We’ll get to that,” the professor said. “But I guess that I can’t really explain the modern notion of quintessence to you without giving you at least a broad overview over the microcosm of the elementary particles after all.

“If you want to understand the modern world, if you want to know what we can discover in space and what happens out there, and if you want of get a feel of what holds the world together, I have to talk about the relationships between our microcosm and macrocosm. After that, we can discuss the quintessence and begin our journey through the world of high pressures. I think that you will be surprised by the exotic states of matter we will find there.”

“Then let us begin,” Marie said, anxious to learn some physics that was not going to be part of her introductory courses.

Professor Wood began slowly and carefully. “Most people are not aware of how much we already know today about the world around us. I’m sure that both of you know that humans and all living things are made up from a myriad of cells that are slightly larger than ten micrometers (10 μm = 10-5 meters). I ask you, what is smaller than that?”

“I know!” Helen exclaimed. “The viruses that cause many diseases are much smaller!”

“Indeed so! They are only about one-thousandth the size of bacteria. Typical diameters of the viruses are smaller than one micrometer. In other words, the dimensions of viruses are less than one millionth of a meter. In many respects, these viruses are not really cells, but are giant molecules. The more typical molecules that make up our cells are a thousand times smaller than that. I'm afraid that if I continue with these comparisons you will soon lose track of which things are the smallest!”

The professor again rummaged through his stack of drawings and figures. “This chart should help,” he said. “If you want to measure the length of very small things, you need scales of less than one millimeter with special nomenclature for even smaller lengths. I’m sure you know that we use scientific notation with negative exponents of ten to describe one thousandth, one millionth, and even smaller fractions of anything. You can see that notation here on the right side of the illustration (Figure 15).

Modern Alchemy and the Philosopher's Stone

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