Electronic origin of negative thermal expansion in V₂OPO₄

San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55...

The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion, which is the change in size or volume of a given system as its temperature changes. The most visible example is the expansion of hot air. When air is heated, it expands and becomes less dense than the surrounding air, which then exerts an upward force on the hot air to, for example, make steam and smoke rise, and hot air balloons float. The same behavior happens in all liquids and gases,...

Positive regulators allow a cell to advance through cell cycle checkpoints. Negative regulators have an equally important role as they terminate a cell’s progression through the cell cycle—or pause it—until the cell meets specific criteria.

Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...

The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the results of quantum mechanics. It is called the theory of metallic conduction.
In this theory, Newton's second law of motion is used to determine the acceleration of an electron in the presence of an applied electric field. Then, its velocity is expressed via this acceleration.
An electron moves through the crystal, containing positive ions,...