Análisis de Puestos de Trabajo

Electromagnetic acoustic transducers (EMATs) are a non-contact generation and detection technique. They induce ultrasound waves in electrically conductive ma- terials through electromagnetic interactions and in ferromagnetic materials through the magnetostriction phenomenon [118]. Ferromagnetic materials are not used here, so magnetostriction is not of interest, though it can be understood as the interac- tion between the magnetic dipoles of a material and a magnetic field, with a more complete description available in the literature [119].

An EMAT consists of a wire coil and, in many cases, a permanent magnet. The magnet is only necessary for detection coils, though generation efficiency is improved by its presence [120], or the presence of a ferrite to strengthen the coil generated field [121]. The coil is then placed close to the surface of the electrically conducting sample, with typical lift-off heights up to a few millimetres [122,123]. For generation, the coil is then driven by a high power source, either with an alternating current at the desired ultrasonic frequency, giving a narrowband output, or with a transient source, generating broadband ultrasound. For detection the coil is attached to a high gain amplifier and the output is measured using standard methods.

Generation by EMATs is achieved through electromagnetic effects described by Maxwell’s equations. Presented here is a summary of the mechanism, though a full mathematical approach can be found elsewhere [119,124]. Any wire containing a current will, according to Ampère’s circuital law, have a magnetic field that encircles the current, as illustrated in figure 1.18(a). As this current is changing with time (being either AC or transient) the resultant magnetic field will also be varying with time. Thus, according to Faraday’s law of induction, it will generate a current in a conductor (in this case the sample) and, according to Lenz’s law, this current will act to oppose the change in magnetic field (by its own generated field). This results in a current being generated within the sample, also known as an eddy current, which mirrors the current in the coil, as illustrated in figure 1.18(b). As this is an alternating current the current density,𝐽, is confined to the sample surface according

to the skin effect,

Generated Magnetic Field Current Carrying Wire a)

Resultant Mirror Current

Conductive Sample b) Permanent Magnet Field From Magnet Lorentz Force c)

Figure 1.18: Simplified schematic for the EMAT generation mechanism. a) Field around a wire containing a changing current. b) Mirror (eddy) current caused by the changing magnetic field. c) Lorentz force from interaction between a field from a permanent wire and the mirror current.

where𝐽𝑆 is the current at the surface, 𝑖=√−1,𝑑is the depth into the sample, and 𝛿 is the skin depth [119, 125]. This means that the amplitude will drop by a factor

of𝑒for each skin depth into the sample, and the imaginary component means that

the phase lag is increased by 1 radian for each skin depth. For a good conductor the skin depth is given by

𝛿 =

√︂ _𝜌

𝜋𝑓 𝜇, (1.35)

where𝑓 is the frequency,𝜌is the resistivity of the sample and𝜇is the permeability of

the sample. For aluminium,𝜇= 1.26×10−6 m·kg·s−2_·A−2 _{and𝜌= 2.42×10}−8 _Ωm

(at 0∘_{C), for which 𝛿 = 0.25 mm at𝑓 = 100 kHz, which is much shorter than the}

wavelength of the ultrasound and thus the current can be considered to be contained within the surface of the sample.

The generated current means that there are moving electrons which interact with the magnetic field,𝐵, of the permanent magnet, or with the field generated by the coil, via the Lorentz force

𝐹 =𝑞(𝑣×𝐵), (1.36)

where𝑣 is the velocity of the electrons and𝑞 is their charge [126]. The velocity of the

electrons is related to the current density by𝑣 = _𝑛𝑞𝐽, where 𝑛is the number density

of electrons. This is illustrated in figure 1.18(c). The force is then transferred to the lattice, resulting in motion and thus generation of ultrasound. The transfer of energy from the electrons to the lattice is not an efficient process due to the difference in mass between the electron and lattice atom, and thus results in a low efficiency for EMAT generation [127]. As the Lorentz force is a cross product the generated motion will be perpendicular to both the current and the magnetic field. The current

is always constrained to be in the plane of the surface and thus the magnetic field direction will determine the motion direction — an out-of-plane field will generate in-plane motion, and an in-plane field will generate out-of-plane motion.

Detection by EMATs is the reverse of this process, though with an improved efficiency as the electrons are already moving and do not need energy to be trans- ferred from the lattice [127]. The motion caused by the ultrasonic waves causes the electrons in the field of the permanent magnet to experience a force. This force causes motion and thus the creation of a current, which then generates a mirror cur- rent within the coil by the same process as eddy currents are created by generation EMATs. As with generation EMATs the orientation of the magnetic field determines the sensitivity to directions of motion — an out-of-plane field EMAT will be sensi- tive to in-plane motion, and an in-plane field EMAT will be sensitive to out-of-plane motion [128–130].

The adaptability of EMATs is a major advantage of their use — through careful consideration of the design of the EMAT, particularly the shape of the coil and direction of the permanent magnetic fields, the generation efficiency and detection sensitivity can be tuned to a variety of different wave types. Additionally, the shape of the design can easily be customised, allowing for directed waves to be generated, as discussed further in section 1.2.3.4.