Multiple choice test on A.8 Superconducting metals & X-ray crystallography

Use the following 'quiz' to test your knowledge and understanding of this sub-topic. As this relates to a sub-topic on the options you may need access to the IB data booklet.

What name is given to the phenomenon whereby superconducting metals are able to create a mirror image of an external magnetic field?

The ability of a superconducting metal to repel an external magnetic field by creating a mirror image of the external magnetic field is named after Meissner who first described the effect in 1933. Cooper pairs can be used to explain superconductivity. The Bragg equation is used in X-ray crystallography and resistivity is a measure of the resisting power of a specified material to the flow of an electric current.

Which are best associated with type 2 superconductors?

I. A gradual transition to semiconductivity at temperatures below the critical temperature

II. Extremely low critical temperatures

III. Alloys and metal oxide ceramics

The critical temperature for many type 2 superconductors is not as low as for type 1 superconductors and in some cases is above 0 oC.

The graph below shows how the properties of a type 2 superconductor varies between c1 and c2 as the temperature decreases below the critical temperature, Tc.

What does c1 represent?

The external magnetic field is larger at c2 than c1. Below c1 the superconductor shows zero resistance and the Meissner effect (i.e. perfect diamagnetism). However c1 is the maximum value for the external magnetic field where this can occur. When the external magnetic field has a value greater than c1, even though it is below its critical temperature, the superconductor will begin to show a range of properties between normal and superconducting.

Which are true statements about Cooper pairs of electrons?

I. They are formed due to the distortion that occurs as electrons pass through the lattice of positive ions in a metal.

II. They behave as if they are a single entity as they pass through the lattice.

III. The energy associated with Cooper pairs is quite weak and can be overcome by thermal energy so they only cause superconductivity at and below the critical temperature.

The attraction between the two electrons in a Cooper pair causes them to act as a single entity but is easily overcome by heat so they only form at low temperatures.

Mercury, Hg, has a superconducting critical temperature of 4.1 K. Which are true statements about mercury at 3.9 K?

I. It cannot repel an external magnetic field.

II. It has zero resistance

III. It is diamagnetic

Metals below their critical temperature have zero resistance and repel an external magnetic field (i.e. show perfect diamagnetism) due to their ability to create a mirror image of the magnetic field (the Meissner effect).

What is the coordination number for a body-centred cubic unit cell?

In a body-centred cubic cell each atom or ion has eight nearest neighbours giving it a coordination number of 8.

What is the total number of equivalent atoms in a face-centred cubic unit cell?

The eight corner atoms or ions each contribute 1/8 towards the total number and the six face atoms or ions each contribute 1/2 towards the total number making 4 in all.

What must be true if monochromatic X-rays with a wavelength of λ are reflected from one layer of atoms in a crystal by an angel of θ degrees and also reflected from the next layer at a distance d below so that constructive interference occurs when the X-rays are diffracted?

What technique can be used to determine the precise structures (including bond angles and bond distances) of perovskite type 2 superconductors?

Although information about the structures can be obtained from various techniques, the precise bond angles and bond distances can only be determined by using X-ray crystallography.

Which can be adjusted to obtain maximum constructive interference of the reflected radiation when X-ray crystallography is performed on a crystalline solid?

I. the incident angle

II. the distance between the layers in the crystal

III. the wavelength of the incident X-rays

For constructive interference to occur the X-rays reflected from lower layers must travel a whole number of wavelengths further than those from the layers above. This can be achieved either by altering the incident angle, θ or by altering the wavelength, λ of the incident X-rays. The distance between the layers, d cannot be altered as it is an integral part of the particular crystal structure.

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