The following article is a simplified, less formal presentation of an earlier unpublished article by me dated 8-14-1995, but now some illustrations, some additional data and speculation have been added.
Approach to Metal Tensile Strength Using Concepts of Guericke and Venturi
This article attempts to simplify the subject of metal tensile strength and metal behavior, by making meaningful conceptual comparisons.It uses some concepts which Guericke and Venturi used, to explain and demonstrate relative pressure differentials, (i.e. so called "attraction"). This article does not predict or explain all details of all metals, but rather addresses the subject in a general way, (an "overview"). ((It attempts to relate the ultra-high hardness of special diamonds (i.e. made with isotopes of carbon) to the Venturi concept.))
In 1654 Otto von Guericke demonstrated how removing air, (i.e. air with kinetic energy) from two touching, hollow ("Magdelburg") hemispheres, caused "suction" to occur. And thus, how the hemispheres clung together so strongly that even horses could not pull them apart.
In the 18th century, Daniel Bernoulli and Giovanni Venturi explained how a suction-like effect arises when an orderly fluid flows through a narrowed channel (i.e. Bernoulli's equation and the related Venturi effect).
However, Guericke would have achieved no "attraction" between his metal hemispheres without real external air (i.e. air pressure). Similarly, the Venturi's effect would suck no air into a carburetor, due to relative suction, unless there were real surrounding air (i.e. air pressure or the like). Thus, in my "treatment" of metal tensile strength" to follow, one might initially imagine that some medium, (old "aether", a photon gas, or something) pressurizes our metal surface, and also, equally, the interior of the metal, (i.e. including the surfaces of the atoms and/or particles in the metal's interior).
Discussion: (the "Guericke" Concept, and the Tensile Strength of Tungsten, etc.)
We start by using, as an example, the ultimate tensile strength of tungsten. Among the metals of great usefulness, and for which data is readily available, tungsten seems to have the highest ultimate tensile strength:
Let us imagine a hot liquid drop of tungsten shortly before some energy is removed (or "sucked" out of it), causing it to solidify. It is somewhat analogous to Guericke's hollow hemispheres just before he pumped out the air (i.e. the kinetic energy of air). We will make an "order of magnitude" comparison between Guericke's hemisphere "suction" strength and tungsten's tensile strength, when an equal amount of energy per volume is removed from both.
tungsten's "heat of fusion" is 25.4x104 joule/kgm.
tungsten's density is 19.3x103 kgm/meter3,
so that the heat per volume of tungsten, that we must remove, to solidify it, is given by the product: 25.4x104 joule/kgm times 19.3x103 kgm/meter3, which gives:
(Heat/Vol.)to solidify tungsten = 48.2x108 joule/meter3.
But this (energy per volume), i.e. joule/meter3, has the same dimension as pressure (or "suction"), so we also have:
(Heat/Vol)to solidify tungsten = 48.2x108 newton/meter2.
It is interesting to note that the ultimate tensile strength of tungsten:
is "of the same order of magnitude" as the energy per volume which we had to remove from tungsten in order to solidify it, which was:
48.2x108 joule/meter3 or (newton/meter2), whichever "dimensions" you prefer.
Thus, let us "coin" a new term, "potential recovery ratio", (PRR), which we will define as the ratio: PRR =
ultimate tensile strength possible / energy per volume removed during solidification.
For tungsten, (W), it is about 85%. For Guerike's hemispheres, it is about 66.7%. ((In the case of the hemispheres, we are referring to the resulting "suction" (pressure) divided by just the kinetic ("translation") energy per volume of the air removed. Thus, it is actually an approximation and a simplification based on an "ideal gas")). For molybdenum, (Mo), the ratio, i.e. "PRR", is 65%, about the same as for the case of the hemispheres and ideal gas. (In the periodic table, both "Mo" and "W" belong to group VI.)
Other descriptive details and limitations:
We have shown that metal's ultimate tensile strength seems to never exceed the energy per volume released during solidification. We will further note that in most cases, the ultimate tensile strength obtainable is moderately less, or much less, than the energy per volume released during solidification, ( i.e. less than "Guerike's 66.7%"). Some examples ("PRR's") are: Zr, 58%; Ti, 55%; Fe, 41%; Ni, 40%; Mg, 38%; Ag, 33%; Al, 26%; Zn, 26%; Au, 20%; Pb, 9%; all values approximate. (See Ref. 1, 2, 3) Generally, metals which release the greatest energy per volume during solidification also have greater "PRR" values, (i.e. "efficiencies"). (Although the "lowest" of the above values is comparatively low, I would not consider it to be trivial).
Regarding the above-simplified approach, we must remember
that metals, while still very hot (immediately after solidification)
not have much strength. They must be cooled down considerably
(i.e. Presumably as if we created some "suction" between the atoms or
nuclei during solidification, but still need to greatly reduce the excessive
vibration of the atoms before the potential strength can manifest itself.)
This generally involves further removal of heat, i.e. an amount comparable
in magnitude to that given off during solidification. (Miscellaneous
Of course, during a phase change from a gaseous to a liquid metal state,
a "heat of condensation" is also given off. Although the liquid has
"strength," it does not suddenly become all gaseous again. To avoid
addressing too many topics now,
I address that separately in my later article: "Elementary Human
General Discussion: (the VENTURI Concept and Metal Tensile Strength, etc.)
In what follows, we will make comparisons and draw analogies between metal behavior and the Venturi effect. It is also interesting to keep in mind these factors: There is a limit to how fast a fluid can flow in a narrowing channel before turbulence occurs, and the "venturi suction" is lost. There are somewhat similarly limits to an airplane wing's "angle of attack" and the associated rate of climb before turbulence sets in and the plane stalls and is lost. And there are limits to the hardening of metal before "brittleness" sets in, it cracks or breaks, and it usefulness is lost. Let that be the first set of analogies. (Let us also mention that some "annealing" after hardening may relieve metal brittleness and stress, with a small compromise of hardness. Analogously, less extension of an airplane's flap will decrease the throw of air downward, increase smoothness, but with some compromise of comparative lift.)
More Detailed Discussion: (with special theory, facts, and predictions)
(When this article was first written, it was difficult for me to find data on the tensile strengths of the various pure isotopes of metals, and it still is. It is possible, that if and when such data comes to my attention, I will have to retract part of this article.) In the detailed discussion that follows, we use the following abbreviations:
H2 denotes a hydrogen molecule, with two nuclei, each consisting of one proton.
H-D denotes a "heavy" hydrogen molecule, consisting of two nuclei, the first nucleus with just one proton, and the second nucleus with a proton and neutron ( i.e. the "D" standing for "deuterium").
D2 denotes a "deuterium" molecule, (a still heavier form of a hydrogen molecule than H-D).
T2 denotes a "very heavy" hydrogen molecule, with two nuclei, each consisting of one proton and two neutrons. (i.e. the "T" stands for "tritium", a radioactive atom with a half-life of about 12.5 years).
The following asserted facts are very important when considered together:
1. All the above, H2 , H-D, D2 , and T 2 , are a form of a hydrogen molecule, each with just 2 positively charged protons, and just 2 negatively charged electrons. Based on Coulomb's law, and electro-magnetism, one would expect hardly any differences in strength of bond when comparing pure solids of the same element, but with different numbers of neutrons
2. But there are, instead, (in my view) "wildly", great and significant "measured" "molecular" bond strength differences, and an indication of this is their unusual, great so-called physical differences between isotopes of the same element! I think this occurs because the "topography" is very different at the nuclei, when comparing H2 , H-D, D2 , T2 . Let us use our extremely useful Venturi analogy to analyze this. As the neutrons are added, the mass of each nucleus, its radius, and its cross sectional area greatly change. (See Ref. 4) A narrowing of the open area (or open channel) between nuclei thus occurs. While it is true that the channels remain still quite open, yet, let us consider the amount of very relevant "incremental" constriction, (the cause of the venturi effect). Perhaps the effect tends to approximately double with the doubling or tripling of the nuclear cross section. (I can not predict the detailed results of flow deflections and other changes caused by increased nuclear cross section and other changes, but significant changes in results seem likely.)
3. The above reasoning seem to invite us to compare the increase of nuclear neutrons (and expected increase in the venturi suction) with an expected increase in the tensile strength, triple point, or melting point in crystals, which ever data we can find. The triple point of H2 , H-D, D2 , and T2 are 13.96 deg.K, 16.60deg. K, 18.73deg.K, and 20.62deg.K, respectively. (See Ref. 5) (For H2O, D2O, and T2O, melting points also increase, respectively.) We also gather from summaries of research articles that "neutron irradiation" can increase so-called "TZM and Mo-5% Re alloys" tensile strength. (See Ref. 6) Also, the following has just come to my attention: We are accustomed to the "Mohs Hardness Scale" starting at 1 and ending with a diamond at 10, but diamonds created with isotopes of carbon have exceeded the mark of 10 on the hardness scale. (See Ref. 7) Nothing else does.
When Guericke pumped out air from between his hemispheres, it was the removal of the kinetic energy of the enclosed air and the continued pressure of the external air, that caused them to "suction attract" each other. Their "suction strength" was approximately equal to 66.7% of the "kinetic energy" per volume of the gas removed. We compared this with the tensile strength which very strong metals can potentially develop per the energy per volume removed from them during solidification, i.e. 85% and 65%, for "W" and "Mo", respectively, as compared to the 66.7% "Guericke case". We "coined" and defined a term, to compare the ultimate tensile strength which might be recovered, to the heat per volume removed during solidification. We noted that most metals have less percent "recovery efficiency" than the strongest metals, and that such "efficiency" generally goes down in cases where metals release less energy per volume during solidification. It appears that a metal's ultimate tensile strength never exceeds the energy per volume released during its solidification.
We then considered Venturi's concept, and noted that altering the alignments, width, obstacles, flow, and possible occurrence of turbulence, can greatly affect the relative suction arising in a channel. By analogy, we noted that such metallurgical operations as annealing, drawing (squeezing) through dies, and quenching can greatly affect metals' tensile strength and brittleness or other features. We predicted significant tensile strength differences in different isotopes of the same light metal (i.e. metals with the same number of protons in the nucleus, and the same number of electrons outside of the nucleus; but different numbers of neutrons in the nucleus). (This is because the added neutrons increase the nuclear cross-section and Venturi action.) That prediction may be surprising to people who believe that the electric and/or electromagnetic "attraction" (or actions), between charged particles at a distance, should overwhelmingly determine the metal bond strength. (Ref. 8) (It appears recently that diamonds have been created, using isotopes of carbon, with a hardness exceeding the mark of 10 on Mohs Hardness Scale.)
Historically, Schrodinger's "wave mechanics" has been applied to a crystal lattice. The term, "wave mechanics," seems to invite a hydrodynamics or flow analogy. Perhaps inviting some "Venturi analogy," as was presented in my article. ((Miscellaneous, speculative, note: Something like Schrodinger's wave equation, itself, may have been envisioned by Chief Crazy Horse in his dream, if one analyzes the dream using Spinoza's concept of prophecy, (See Illustration 2 and associated Ref 9.10, 11).))
2-20-2003 Speculative ADDENDUM: I believe I read that for single GAS molecules (say H-H or D-D), bond energies change very little with added neutrons. Thus, the contrasting behavior of SOLID isotopes seems rather unique!
Ref. 1. Handbook of Chemistry
and Physics, 43rd ed.; Chemical Rubber Publishing Co.:
Cleveland, Oh. 1962, "Elastic Constants for Solids", pp 2164-2168, and
"Tensile Strength of Metals", p 2188. (Note, statement that values considered
Below are references dealing with speculative philosophical and historical issues, which I think are interesting, but not directly related to the scientific propositions in my article:
Ref. 9. Neihardt, J. G.; Black Elk Speaks,
12th ed.; University of Nebraska Press, Lincoln. 1961, Chapter
VII, p 85; lower part of page describes Crazy Horse's dream.
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Carl R. Littmann
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