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1. Planck’s Constant and The Uncertainty Principal

         Marquise de Laplace’s theory of determinism that was an old-established belief of many scientists since early 19th century was dispelled in 1900 by Max Planck, a professor from Berlin University, who suggested that waves, such as light and x-rays, for example, can not be emitted at an arbitrary rate. He argued that the way they are emitted is restricted to certain “chunks” or “lumps,” that he named “quanta.”  The higher the frequency of the waves, the more energy each quantum would have, so at a high enough frequency of emission, a quantum would require more energy than there’s available. As a result, the radiation at high frequencies would be reduced and the rate at which the body lost energy would be finite. He called this theory the “Quantum Theory.”

          In 1926, another German scientist, Werner Heisenberg, incorporated his Uncertainty Principal into Planck’s Quantum Theory. First, Heisenberg argued, in order to predict future position of and velocity of a particle, its present velocity and position must be determined. If a light is shone on a particle, its position can be determined by observing the light that’s scattered by that particle, thus indicating its position. However, determination of precision of particle’s position would be restricted by the accuracy of the measurement of the light wave’s crest, so a short wave light must be used in order to measure position of the particle precisely. Further, using Planck’s hypothesis that at least one quantum of light must be used, since an arbitrary small amount of light can not be utilized, we can determine, that this quantum will sufficiently disturb the particle to change its velocity in an unpredictable way. The more precise reading of the particle we want, the shorter the light’s wavelength we’d need to use; this will increase the energy of a single quantum. This action will further increase the factor of disturbance upon the particle and, therefore, its velocity. This shows that the more precise you want to measure the position of a particle, the less accurate you can measure its velocity and vice versa.

Heisenberg proved that uncertainty in the position of the particle, times the uncertainty in its velocity, times the mass of the particle, can never be smaller than a certain quantity that he called The Planck’s Constant (h = (6.6260755 ± 0.00023)× 10-34 J* s). This applies to all types of particles and doesn’t depend on the way in which measurements are taken.

    To summarize two above observations, we can note that in Planck’s quantum hypothesis, light in some ways behaves as particles and Heisenberg’s uncertainty principal suggests that particles behave as waves, in some respect. Both particles and waves become “interchangeable” entities to an observer, depending how one wants to view them. Dimensional size of particles is therefore constrained by the dimensional wavelength and vise versa. As a result, particles will become waves (light, x-ray, etc.) at apparent velocities. They, however, may slow down, but deceleration may prove fatal to their previous state. Since energy will not disappear but merely change its state, upon deceleration, a particle may change its form. This form, however, will be constrained by the boundaries of its previous and unchanged physical properties (i.e. at less than extreme velocities atomic structure of a particle will either remain unchanged or will maintain close-to-original state, therefore not transforming itself to an absolute irrelevance to itself, but maintaining close-to-original-state form). Since electrons can be thought of as waves, by accelerating and decelerating atoms with subsequent wavelengths may very well change the length of each wave, producing new set of end-result material.


2. Hydrothermal process 

         Hydrothermal process, in theory, is a straightforward process. Many of us may remember from our school days the way we grew salt crystals. That was a simplified hydrothermal process, where room temperature was the “thermal” part (heat) and water was the “hydro” element in that process. Smaller salt particles fused with larger particles that did not fully dissolve in water solution. The larger the crystal, the stronger the attraction (gravity). Formation of a larger single crystal will accelerate until it comes close to reaching a critical mass point, then it will gradually decelerate and stop completely when that point is actually reached. However, since an absolute critical mass point will not be reached in practicality, the growth will never stop, but will slow to a point when it is not feasible to sustain the process. At that point more energy will be needed to sustain the growth than the proportional end-result to that amount of energy. Visually, we may not be able to observe any further growth of a crystal, since the growth will decelerate to extreme minimum. Another constrain will be the size of the vessel (or autoclave, in case of hydrothermal crystals that need higher than room temperature parameters). Even though further rapid growth can be achieved, it will be restricted by limitations of the inner size of the autoclave. Growing of hydrothermal gems, i.e. emeralds, is very much the same as growing salt crystals. The major difference being the chemicals used and parameters that are needed to start and sustain the process. There’re many elements that are required for the growth of a hydrothermal stone, depending on what material is involved. For example, to grow an emerald (green-colored beryl), you’d need a nutrient beryl (low grade emerald, either natural or already grown), this will act in the same manner as the dissolved salt particles in a water solution, acid (instead of water) and seeds of emeralds (instead of larger salt particles). Room temperature may be sufficient to start the process to grow salt crystals, but to grow a beryl a temperature of several hundred degrees C and pressure of thousands of PSI (pounds per square inch) is required. All the parameters and chemicals will change as you try to grow different materials, but the theory, in essence, remains the same.

    Now, let’s examine an outcome of a hydrothermal experiment. As an end-result, we may wonder, why is that those two crystals are never the same? Even though we used exactly the same chemicals, same amounts of acids, loading and heating parameters, we can’t find two identical crystals among our production. We even went to extreme length to prepare identical seeds, but, still, our end product differs from crystal to crystal. One crystal is noticeably thicker, the other one may have imperfections (inclusions), the surface of one crystal is noticeably smoother than the rest, etc. In other words, you will try to find two identical crystals and when you thought you did, they are different weight! Even in an optimal preparation-stage scenario, you will most probably never obtain exactly same end result.


3. Conclusion

       Now, that you’re familiar with the hydrothermal process and the dilemma facing crystal growers, we can unify it with the uncertainty principal and try to understand why we can’t get that coveted uniformed result.

         Since the particle movement is spontaneous and unpredictable, as shown in section 1, the position of a particle is left to chance, so its velocity. We’re talking, off course, about “blind,” utterly uncontrollable environment. Particles will interact in a chemical process that starts as a result of bringing conditions surrounding these particles to the state at which the process begins. Prior to that state, the solution (and therefore particles that it’s comprised of) will remain in a state of suspended animation, in other words the solution will not become active and will remain in its original state until the temperature rises and builds pressure up to activate the process. At “event horizon” point, particles will start to interact in a very peculiar manner – they will not “know” to either remain in their original state or “spill” out into a new state that eventually the process will drag them into. At that point, the particles will be dragged as into a black hole, with no pint of return, depositing themselves on the surface of the crystal that had strong enough gravity to attract them. The particles will start to interact in a non-predetermined way with multitude of different results. Since the Uncertainty Principal doesn’t allow us to predict future position of a particle and its velocity at the same time, and the rapid movement under extreme temperature and pressure in a Hydrothermal Process directly replicates and even emphasizes our visualization of the theory. We can safely say, that particle dispersion along the crystal is left to chance and, therefore, disposition of inclusions, cracks and other impurities.       

Implications of Uncertainty Principle on Spontaneous Growth of Hydrothermal Crystals


Written by Walter Barshai

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