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11.11.2011, Fri, 15:58, Moscow timeMost materials expand when heated, but there are a few unique substances that behave differently. Caltech engineers have discovered for the first time how one of these intriguing materials, scandium trifluoride (ScF3), shrinks when heated.
This discovery will lead to a deeper understanding of the behavior of all types of substances, and will also allow the creation of new materials with unique properties. Materials that don't expand when heated aren't just a scientific curiosity. They are useful in a variety of applications, such as high-precision mechanisms such as watches, which must remain highly accurate even when temperature fluctuates.
When solid materials are heated, most of the heat is lost to atomic vibrations. In ordinary materials, these vibrations push the atoms apart, causing the material to expand. However, some substances have unique crystal structures that cause them to shrink when heated. This property is called negative thermal expansion. Unfortunately, these crystal structures are very complex, and scientists have until now been unable to see how atomic vibrations cause the material to shrink in size.
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That changed with the 2010 discovery of negative thermal expansion in ScF3, a powdery substance with a relatively simple crystal structure. To figure out how its atoms vibrate when exposed to heat, American scientists used a computer to simulate the behavior of each atom. The properties of the material were also studied at the neutron laboratory of the ORNL complex in Tennessee.
The results of the study provided, for the first time, a clear picture of how the material compresses. In order to understand this process, you need to imagine scandium and fluorine atoms as balls connected to each other by springs. The lighter fluorine atom is bonded to two heavier scandium atoms. As the temperature increases, all the atoms begin to swing in several directions, but due to the linear arrangement of the fluorine atom and the two scandium atoms, the first vibrates more in directions perpendicular to the springs. With each vibration, fluorine attracts scandium atoms towards each other. As this occurs throughout the material, it shrinks in size.
The greatest surprise was the fact that during strong vibrations the energy of the fluorine atom is proportional to the fourth power of displacement (fourth power vibration or biquadratic vibration). Moreover, most materials are characterized by harmonic (quadratic) vibrations, such as the reciprocating motion of springs and pendulums.
According to the authors of the discovery, an almost pure fourth-degree quantum oscillator has never been recorded in crystals before. This means that studying ScF3 in the future will make it possible to create materials with unique thermal properties.
Most materials expand when heated, but there are a few unique substances that behave differently. Caltech engineers have discovered for the first time how one of these intriguing materials, scandium trifluoride (ScF3), shrinks when heated.
This discovery will lead to a deeper understanding of the behavior of all types of substances, and will also allow the creation of new materials with unique properties. Materials that don't expand when heated aren't just a scientific curiosity. They are useful in a variety of applications, such as high-precision mechanisms such as watches, which must remain highly accurate even when temperature fluctuates.
When solid materials are heated, most of the heat is lost to atomic vibrations. In ordinary materials, these vibrations push the atoms apart, causing the material to expand. However, some substances have unique crystal structures that cause them to shrink when heated. This property is called negative thermal expansion. Unfortunately, these crystal structures are very complex, and scientists have until now been unable to see how atomic vibrations cause the material to shrink in size.
That changed with the 2010 discovery of negative thermal expansion in ScF3, a powdery substance with a relatively simple crystal structure. To figure out how its atoms vibrate when exposed to heat, American scientists used a computer to simulate the behavior of each atom. The properties of the material were also studied at the neutron laboratory of the ORNL complex in Tennessee.
The results of the study provided, for the first time, a clear picture of how the material compresses. In order to understand this process, you need to imagine scandium and fluorine atoms as balls connected to each other by springs. The lighter fluorine atom is bonded to two heavier scandium atoms. As the temperature increases, all the atoms begin to swing in several directions, but due to the linear arrangement of the fluorine atom and the two scandium atoms, the first vibrates more in directions perpendicular to the springs. With each vibration, fluorine attracts scandium atoms towards each other. As this occurs throughout the material, it shrinks in size.
The greatest surprise was the fact that during strong vibrations the energy of the fluorine atom is proportional to the fourth power of displacement (fourth power vibration or biquadratic vibration). Moreover, most materials are characterized by harmonic (quadratic) vibrations, such as the reciprocating motion of springs and pendulums.
According to the authors of the discovery, an almost pure fourth-degree quantum oscillator has never been recorded in crystals before. This means that studying ScF3 in the future will make it possible to create materials with unique thermal properties.
Research by scientists from the United States has shown that the material, which tends to shrink when heated, is distinguished by a special type of atomic vibrations not observed in any other substances.Typically, heat causes substances to expand. But there are certain crystalline substances that tend to shrink when heated or, as they say in the scientific world, that have a negative coefficient of thermal expansion. Such materials are of great practical importance: they can be combined, for example, with today's traditional materials for the production of dental fillings, mirrors for telescopes and other objects that need to have fixed dimensions over a wide temperature range. A good example of such a substance is zirconium tungstate (ZrW 2 O 8), exhibiting a compression of 0.001% per degree Kelvin over a range of thousands of degrees. According to the geometric model of zirconium tungstate, the tetrahedra and octahedra from which the crystalline structure of the substance is formed remain rigid, but can rotate around their axis when heated, which reduces the volume of the material due to the formation of folds within its structure. These crystalline structures form so-called hard modes of vibration.
In one of the representatives of the class of substances with a negative coefficient of thermal expansion, scientists from the California Institute of Technology (USA) recently discovered previously unobserved vibrations of the crystal lattice. If we imagine these oscillations from the point of view of mechanics, then the stiffness of the “atomic spring”, which determines the parameters of the oscillations, in this case increases when the “spring” is stretched, in contrast to the classical case of atomic oscillations, where this “effective stiffness” remains constant. Detailed results of the work were published in the journal Physical Review Letters.
According to scientists, when modeling rigid vibration modes, the forces that control the movements of individual objects are usually not taken into account. This happens because in such crystals it is extremely difficult to calculate the forces within the complex. In the same zirconium tungstate, the unit cell, periodically repeating inside the crystal, includes 44 atoms. But recently, scientists have discovered that the compound scandium trifluoride (ScF 3) has comparable characteristics to zirconium tungstate in the temperature range from 10 to 1100 degrees Kelvin. There are only 4 atoms in the unit cell of a crystal of this substance, the interactions of which are much easier to analyze.
To assess the forces acting inside the unit cell of scandium trifluoride, the researchers assessed the vibration spectrum of the crystal lattice using neutron scattering. In particular, they were interested in the resonant frequency of various modes of vibration within the lattice. Measurements were taken in the range from 7 to 750 degrees Kelvin. As expected, most vibration modes practically did not change their resonance frequency with temperature changes. However, one of the modes surprisingly shifted its resonant frequency to the high frequency region, as if its stiffness increased with increasing temperature.
After calculating the identified phenomenon, scientists discovered that for most vibration modes, the potential energy increases in proportion to the square of the distance between the atoms. But for individual modes there is a dependence on the fourth power of distance. This assumption was fully confirmed by experimental facts revealed during neutron scattering.
The discovered fourth-order vibrations represent a huge and unexplored area of crystal physics, because higher modes of vibrations can also play a certain role in the properties of other substances, i.e. Potentially, research in this area could lead to the development of materials with new thermal properties. Moreover, scientists believe that their discovery may entail the need to modify existing theories of the behavior of substances that shrink when heated.
It is known that under the influence of heat, particles accelerate their chaotic movement. If you heat a gas, the molecules that make it up simply fly apart from each other. The heated liquid will first increase in volume and then begin to evaporate. What will happen to solids? Not each of them can change its state of aggregation.
Thermal Expansion: Definition
Thermal expansion is the change in size and shape of bodies with changes in temperature. Mathematically, it is possible to calculate the volumetric expansion coefficient, which allows us to predict the behavior of gases and liquids under changing external conditions. To obtain the same results for solids, it is necessary to take into account Physicists have allocated a whole section for this kind of research and called it dilatometry.
Engineers and architects need knowledge of the behavior of different materials under high and low temperatures to design buildings, roads and pipes.
Expansion of gases
The thermal expansion of gases is accompanied by an expansion of their volume in space. This was noticed by natural philosophers in ancient times, but only modern physicists were able to construct mathematical calculations.
First of all, scientists became interested in the expansion of air, since it seemed to them a feasible task. They got down to business so zealously that they got quite contradictory results. Naturally, the scientific community was not satisfied with this outcome. The accuracy of the measurement depended on the type of thermometer used, the pressure, and many other conditions. Some physicists even came to the conclusion that the expansion of gases does not depend on changes in temperature. Or is this dependence not complete...
Works by Dalton and Gay-Lussac
Physicists would have continued to argue until they were hoarse or would have abandoned measurements if He and another physicist, Gay-Lussac, had not been able to obtain the same measurement results at the same time independently of each other.
Lussac tried to find the reason for so many different results and noticed that there was water in some of the devices at the time of the experiment. Naturally, during the heating process it turned into steam and changed the amount and composition of the gases being studied. Therefore, the first thing the scientist did was to thoroughly dry all the instruments that he used to conduct the experiment, and eliminate even the minimum percentage of moisture from the gas under study. After all these manipulations, the first few experiments turned out to be more reliable.
Dalton worked on this issue longer than his colleague and published the results at the very beginning of the 19th century. He dried the air with sulfuric acid vapor and then heated it. After a series of experiments, John came to the conclusion that all gases and steam expand by a factor of 0.376. Lussac came up with a number of 0.375. This became the official result of the study.
Water vapor pressure
The thermal expansion of gases depends on their elasticity, that is, their ability to return to their original volume. Ziegler was the first to explore this issue in the mid-eighteenth century. But the results of his experiments varied too much. More reliable figures were obtained by using my father’s boiler for high temperatures, and a barometer for low temperatures.
At the end of the 18th century, the French physicist Prony attempted to derive a single formula that would describe the elasticity of gases, but it turned out to be too cumbersome and difficult to use. Dalton decided to empirically test all the calculations using a siphon barometer. Despite the fact that the temperature was not the same in all experiments, the results were very accurate. So he published them in table form in his physics textbook.
Evaporation theory
The thermal expansion of gases (as a physical theory) has undergone various changes. Scientists have tried to get to the bottom of the processes that produce steam. Here again the already well-known physicist Dalton distinguished himself. He hypothesized that any space is saturated with gas vapor, regardless of whether any other gas or vapor is present in this tank (room). Therefore, it can be concluded that the liquid will not evaporate simply by coming into contact with atmospheric air.
The pressure of the air column on the surface of the liquid increases the space between the atoms, tearing them apart and evaporating, that is, it promotes the formation of vapor. But the force of gravity continues to act on the vapor molecules, so scientists believed that atmospheric pressure has no effect on the evaporation of liquids.
Expansion of liquids
The thermal expansion of liquids was studied in parallel with the expansion of gases. The same scientists were engaged in scientific research. To do this, they used thermometers, aerometers, communicating vessels and other instruments.
All experiments together and each separately refuted Dalton's theory that homogeneous liquids expand in proportion to the square of the temperature to which they are heated. Of course, the higher the temperature, the greater the volume of liquid, but there was no direct relationship between it. And the expansion rate of all liquids was different.
The thermal expansion of water, for example, begins at zero degrees Celsius and continues as the temperature decreases. Previously, such experimental results were associated with the fact that it is not the water itself that expands, but the container in which it is located that narrows. But some time later, the physicist DeLuca finally came to the idea that the cause should be sought in the liquid itself. He decided to find the temperature of its greatest density. However, he failed due to neglect of some details. Rumfort, who studied this phenomenon, found that the maximum density of water is observed in the range from 4 to 5 degrees Celsius.
Thermal expansion of bodies
In solids, the main expansion mechanism is a change in the vibration amplitude of the crystal lattice. In simple words, the atoms that make up the material and are rigidly linked to each other begin to “tremble.”
The law of thermal expansion of bodies is formulated as follows: any body with linear size L in the process of heating by dT (delta T is the difference between the initial and final temperatures), expands by dL (delta L is the derivative of the coefficient of linear thermal expansion by the length of the object and by the difference temperature). This is the simplest version of this law, which by default takes into account that the body expands in all directions at once. But for practical work, much more cumbersome calculations are used, since in reality materials behave differently than modeled by physicists and mathematicians.
Rail thermal expansion
Physics engineers are always involved in laying railway tracks, since they can accurately calculate what distance should be between rail joints so that the tracks do not deform when heated or cooled.
As mentioned above, thermal linear expansion applies to all solids. And the rail was no exception. But there is one detail. Linear change occurs freely if the body is not affected by friction. The rails are rigidly attached to the sleepers and welded to adjacent rails, therefore the law that describes the change in length takes into account overcoming obstacles in the form of linear and butt resistances.
If the rail cannot change its length, then with a change in temperature, thermal stress increases in it, which can either stretch or compress it. This phenomenon is described by Hooke's law.
