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Superconductivity is a phenomenon where a material, when cooled below a certain temperature called the critical temperature (T_c), exhibits zero electrical resistance and expulsion of magnetic fields. This means that an electrical current can flow through the material without any energy loss, which has significant potential applications in various industries. Superconducting materials generally need to be cooled down to very low temperatures, making them expensive and challenging to use in practical applications.

In recent years, researchers have discovered materials that display superconductivity at relatively higher temperatures, known as high-temperature superconductors (HTS). Examples include certain copper-oxide-based ceramics called cuprates and iron-based compounds called pnictides. Although their critical temperatures are still low compared to room temperature, they are significantly higher than those of conventional superconductors, meaning they require less cooling and are more practical for certain applications.

The primary limitation of high critical temperature superconductors is their brittleness and difficult processing. Most high-T_c superconductors, such as cuprates, are ceramic materials, which are inherently brittle and challenging to process. This makes it difficult to manufacture them into useful forms such as wires or thin films needed for practical applications like powerful electromagnets, power cables, or energy storage devices. Efforts are ongoing to develop new superconducting materials with high T_c that are easier to form into useful shapes and structures, but this remains a central challenge in making superconductors more widely utilized. In conclusion, the primary limitation of superconducting materials with relatively high critical temperatures is their brittleness and difficult processing, posing a significant challenge for their widespread adoption in practical applications.