Question

(a) What is the superconducting transition temperature, \(T_{c} ?\) (b) The discovery by Müller and Bednorz of superconductivity in a copper oxide ceramic at \(35 \mathrm{~K}\) set off a frantic scramble among physicists and chemists to find materials that exhibit superconductivity at higher temperatures. What is the significance of achieving \(T_{c}\) values above \(77 \mathrm{~K}\) ?

Short answer

The superconducting transition temperature, \(T_c\), is the temperature at which a material's electrical resistance drops to zero, and it becomes a superconductor. For the copper oxide ceramic discovered by Müller and Bednorz, the \(T_c\) is 35 K. Achieving a \(T_c\) value above 77 K is significant because it allows for cooling with relatively inexpensive liquid nitrogen, making the implementation of superconducting technology more accessible and economically viable in various applications, such as medical equipment, transportation, power transmission, and electronic devices.

Step-by-step solution

Understanding Superconducting Transition Temperature

The superconducting transition temperature, \(T_c\), is the temperature at which a superconducting material's electrical resistance drops to zero and it becomes a superconductor. At temperatures below \(T_c\), the material exhibits superconductivity, which means it can conduct electricity without any energy loss due to electrical resistance. The exact value of the transition temperature depends on the specific material.

Part (a): Given Superconducting Transition Temperature

In the given exercise, it is mentioned that Müller and Bednorz discovered superconductivity in a copper oxide ceramic at 35 K. Hence, for the copper oxide ceramic in question, the superconducting transition temperature, \(T_c\), is: \(T_c = 35~K\)

Part (b): Significance of \(T_c\) values above 77 K

77 K is the boiling point of liquid nitrogen, which is a commonly used and relatively inexpensive coolant. If a material has a superconducting transition temperature (\(T_c\)) above 77 K, it can be cooled using liquid nitrogen, making it more economically feasible and practical for various applications. Superconductors with high transition temperatures can allow for more effective, cost-efficient, and energy-saving technologies in various fields, including medical equipment (e.g., MRI machines), transportation (e.g., magnetic levitation trains), power transmission, and electronic devices. In summary, achieving a \(T_c\) value above 77 K is significant as it makes the practical implementation of superconducting technology more accessible and economically viable for a wider range of applications.

Key concepts

Superconductivity

Superconductivity is a quantum mechanical phenomenon that is characterized by the complete absence of electrical resistance in certain materials when they are cooled below a critical temperature known as the superconducting transition temperature, denoted as \(T_c\).

When materials enter this superconducting state, they exhibit remarkable properties, such as the ability to conduct electric current without any loss of energy, and the expulsion of magnetic fields, known as the Meissner effect. This latter property enables superconductors to levitate permanent magnets, a phenomenon that can be used in applications like magnetic levitation (maglev) trains.

Superconductivity was first discovered in 1911 by Heike Kamerlingh Onnes in mercury cooled to 4.2 K. Since then, various materials, including metallic alloys and ceramics, have been found to exhibit superconducting properties at different temperatures.

Electrical Resistance

Electrical resistance is a measure of the opposition to the flow of electric current through a material. It is a fundamental property that impacts how materials conduct electricity, with high resistance materials hindering current flow and low resistance materials allowing it to pass more easily.

In the context of superconductivity, the resistance drops to exactly zero when the material is below its critical temperature \(T_c\). This is in stark contrast to ordinary conductors, where resistance decreases gradually as the temperature is lowered, but never reaches zero. Understanding electrical resistance is essential when examining the efficiency of various materials in electrical and electronic applications since any non-zero resistance results in energy being lost as heat.

Copper Oxide Superconductors

Copper oxide superconductors, also known as high-temperature superconductors (HTS), belong to a class of materials that exhibit superconductivity at temperatures much higher than traditional superconductors, which usually become superconducting at temperatures close to absolute zero.

The discovery in 1986 by Karl Müller and Johannes Georg Bednorz of superconductivity in a lanthanum-based copper oxide compound at temperatures above 30 K was groundbreaking because it defied the established understanding at the time. This discovery not only won them the Nobel Prize in Physics but also triggered an intensive research effort to find materials with even higher \(T_c\) values. These efforts have led to the development of HTS with transition temperatures above the boiling point of liquid nitrogen (77 K), bringing superconductivity closer to practical and widespread use.

Coolant Applications in Superconductors

Coolants play a pivotal role in the operation of superconductors: they are used to achieve and maintain the low temperatures needed for a material to become superconducting. The most common coolants in superconductor applications are liquid helium and liquid nitrogen.

Liquid helium is used to cool materials to within a few degrees of absolute zero, but it is quite expensive and less readily available than liquid nitrogen, which boils at 77 K. Therefore, superconductors that operate at the temperature of liquid nitrogen or higher are particularly valuable because they can be cooled economically and are easier to maintain. This practical cooling requirement makes the significant difference to where and how superconductivity can be applied, such as in medical imaging, electrical power infrastructure, and transportation systems. The less expensive and simpler it is to maintain superconducting systems, the more accessible and widespread their uses become.