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The birth of quantum physics created a method of investigating materials thousands of times smaller than optical microscopes could ever achieve.
The quantum revolution has not just changed our understanding of the fine structure of matter around us, revealing a world of counter-intuitive rules and behavior, but it has also allowed us to ‘see’ this world in extraordinary detail.
In fact, it is one of the first and most shocking discoveries, arguably the one that created quantum physics as a field, that allows us to use electrons instead of photons to see deeper within matter. That idea is that all matter, not just photons (particles of light ), has a duality of nature and can be modeled as both a particle or a wave depending on the conditions it is found in.
Even before Davisson and Germer had the idea to use electrons instead of photons in Young’s double-slit experiment in 1927, leading to the shocking discovery that matter shared the particle/wave duality of photons, researchers were aware of the limitations of optical microscopes. They were also aware that these limitations were all about wave-size.
In 1873, Ernst Abbe, a German physicist who specialized in optics, published a paper that gave the optical resolution limit of photons and revealed that they are directly tied to the wavelength of the light used.
A microscope cannot produce the image of an object that is smaller than the wavelength of the light it relies upon. Any object that has a size of less than half the wavelength of the microscope’s illumination source simply will not be visible under that microscope.
Fortunately, electrons have a much smaller wavelength associated with them, their de Broglie wavelength — named after Louis de Broglie, the French physicist who first suggested that all particles of matter also have a wave-like nature. Thus, they can be employed to resolve objects in far greater detail than an optical microscope.
This revelation led to a whole new method of imaging, the electron microscope. In the same year that de Broglie reached this conclusion, 1926, it was demonstrated that magnetic or electrostatic fields could serve as lenses for electrons or other charged particles and the first experiments into electron optics began forthwith.
By 1933 the first electron microscope had been created, albeit a very primitive version, and within no more than half a decade the resolution of such devices had already outstripped that of their optical counterparts.
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There are two main types of electron microscope — the scanning electron microscope (SEM) and the transmission electron microscope (TEM). Both use highly concentrated beams of electrons fired from an electron gun to examine their target. Whereas the SEM passes the beam of electrons over the subject, the TEM passes this beam of electrons through a thin sample of the material being examined.
In this way, the TEM is more analogous to a typical optical microscope but using electrons instead of photons as a form of radiation. This method of analyzing an object relies heavily on quantum phenomena.
Magnification with Quantum Mechanics
A TEM can be used in a variety of ways to produce conventional images, diffraction images, and spectroscopic images. Focusing on optical images, the high-resolution capability of TEMs that arises from electrons’ tiny de Broglie wavelengths has allowed researchers to image objects as small as a single line of atoms — thousands of times smaller than anything possible with an optical microscope.
Electrons are fired through the sample, and those that make it through are collected on the other side by a fluorescent screen, creating an image. Some electrons are lost from the beam and never make it through to the other side of the sample and the fluorescent screen that records them.
This is a result of high-angle scattering, essentially them hitting an atomic nucleus head-on and being bounced back, and the fact that some of the electrons are absorbed by atoms within the sample.
The images produced are in black and white and detail is resolved by the change in contrast across them. In contrast, these changes are created by a variety of so-called ‘image contrast mechanisms’, which include characteristics of the sample such as changes in density throughout, its crystalline structure, and its atomic number (represented by the letter Z).
Contrast is also created by other changes induced in the electrons fired through the subject of magnification, such as energy loss and slight phase shifts. These latter two contrast mechanics are directly governed by the rules of quantum mechanics.
In particular, the idea of creating a slight phase shift in a substance relates to the wave nature of matter — the most intrinsic idea in quantum mechanics — and shows that it is far more than a mathematical convenience. This form of contrast mechanism, formally named phase-contrast imaging, gives the highest possible resolution of a TEM.
Making Waves — Phase Shifts in TEMs
The idea of a phase shift relates to the fact that moving particles in quantum mechanics are described as waves, de Broglie waves to be precise, and that the amplitude of these waves represents the probability of finding a particle in any one place.
When the particle is traveling, the wave is intact, it has a non-zero probability of being found anywhere. However, when the particle’s location is determined — when it hits the fluorescent screen for our purposes — the wave-function ‘collapses’ and it can be described as a single point.
As a side note, this is where the infamous Heisenberg’s uncertainty principle arises. As a wave represents momentum, a well-defined wave represents complete knowledge of momentum with no hint of location. A located particle is simply a point with an ill-defined wave or no wave at all remaining — thus a precise location with no idea no momentum.
There is much speculation of exactly what causes the collapse of the wave-function, or indeed whether it collapses at all or grows to envelop the entire Universe, in the process creating many worlds in which the particle is still in a specific place in each but located in an infinity of possible points across them as a whole. However, these interpretations of quantum physics are far beyond the remit of our discussion.
As the electrons pass through the material being magnified, some pass straight through, but those not absorbed that pass close to an atom are subject to inelastic scattering as a result of that atom’s far greater mass and as a result of electrostatic repulsion.
This scattering does not cause wavefunction collapse and because the de Broglie wave amplitude represents the probability, and probability is a conserved quantity in quantum mechanics, the amplitude of the wave cannot be changed, nor can any property of the wave that depends on the amplitude. Yet the phase of the wave can be changed. Thus, the diffracted wave undergoes a phase shift.
You can think of the phase of a wave as the position of the peaks and troughs of a wave. Thus two ‘in-phase’ waves have their peaks aligned. Whilst out of phase waves have their peaks misaligned, everything else about the waves is the same. The amplitudes are unchanged, the space between peaks is the same, but the wave has been wound forward (or backward) by some amount as a result of the scattering.
So how can this phase shift possibly create an image of differing contrast? To give a simple explanation of that we go right back to the beginning: the double-slit experiment.
The Double-Slit Experiment: Constructive and Destructive Interference
Revisiting the double-slit experiment, when electrons or photons are fired through the slits, what researchers find is that the pattern on the far side of the slit is not a build-up of points aligned with the slits as we would find if we replaced the particles with something more macroscopic, say bullets.
Instead what is discovered is a pattern of alternating dark and light bands. This is what first alerted scientists to the wave-like nature of particles, as this banding is characteristic of a phenomenon in waves called constructive and destructive interference.
These bands represent where the de Broglie waves are in phase and out of phase. In phase waves, where two peaks align, cause constructive interference, building points on the receiver, again a fluorescent screen, that form the dark bands. In contrast, where the waves are out of phase, there is destructive interference, no points are created, thus the light bands.
Thus, you can imagine that winding the phase of one of these waves will change that contrast of the banding on the fluorescent screen by decreasing or increasing the amount of constructive interference. This also allows us to see how inelastic scatterings cause a picture of different shades to be built. A picture that reflects the internal structure of the object being examined.
In a way, transmission electron microscopy can be viewed as the child of the double-slit experiment and thus, the advances that it has allowed in nanotechnology, virology, cancer research, and a multitude of other scientific fields are evidence of the extraordinary success of the very weird world of quantum physics.
References and Further Reading
Williams D.B., Carter C.B. ‘Scattering and Diffraction. In: Transmission Electron Microscopy,’ Springer, Boston, MA, (2009).l
Tang. C.Y, Yang. Z, Transmission Electron Microscopy (TEM), Membrane Characterization, (2017).
Griffiths. D. J, ‘Introduction to Quantum Mechanics,’ Cambridge University Press, (2017).
Feynman. R, ‘The Feynman Lectures,’ (1963).