Smart crystals

ABSTRACT
“Smart” crystals have been studied for over a hundred years. There are many different types of smart crystals each with unique properties that have many different possible applications for mechanical, electrical, and optical devices. New properties and types of smart crystals are still being discovered and created in labs. In this paper, I discuss some of the properties of several important types of smart crystals, such as piezoelectric and photochromic crystals. I will comment on the important characteristics that lead to useful devices and some techniques that have been found to maximize their effectiveness. I will then discuss how these led to the discovery and study of diarylethene chromophores and shape changing photoisomeric crystals that are only recently being developed.


INTRODUCTION
Smart crystals are defined as materials that can sense and respond in a controlled or predictable manner to environment stimuli, which can be delivered in mechanical, thermal, chemical, magnetic, or other forms. There exist many different types of these crystals with many different names each corresponding to the type of stimuli they detect and what type of response they exhibit to these stimuli. Two types of crystals that have been of the most interest for researchers and experimenters and that have found many applications are piezoelectric crystals, which can respond to mechanical stress or applied electric fields and photochromic materials which change color in response to light. Later, photochromic materials were discovered to transform in shape as well in response to light. Speed, stability, repeatability, reversibility, and efficiency are important factors for the applicability of all these types of crystals. Recently, crystals which have all these characteristics been developed. These types of crystals and the many derivatives which are being created from them are called diarylethenes and they have good potential to be used optical devices.


PIEZOELECTRIC CRYSTALS
The first type of “smart crystal” which has been around for awhile are known as piezoelectric crystals. Piezoelectrics are materials which exhibit the Piezoelectric Effect. This is where the material will emit an electric field or pulse when mechanical pressure or strain is exerted on the material. These same materials are also shown to exhibit the Converse Piezoelectric Effect, aptly named as the effect which has the opposite effect. When an electric field is applied to the crystal it will then expand and exert an outward mechanical force as shown in the lead zirconate titanate lattice in figure 2. The piezoelectric effect was first observed in 1880 by Pierre Curie and Jacques Curie. Since this time there have been many useful applications discovered such as the submarine sonar, which was the first application developed, and now they are used for such devices as memory cells and tunable capacitors. The piezoelectric equations relate the stress on a ferroelectric crystal to the electric field. , where P is the polarization, Z is the stress, d is the piezoelectric strain constant, E is the electric field, χ is the dielectric susceptibility, e is the electric strain, and s is the elastic compliance constant. From this equation we see that polarization in the ferroelectric crystal can occur as a result of stress and electric field independently. Thus even in the absence of an applied field, E=0, that an applied pressure Z will produce the polarization. This is the piezoelectric effect.
The piezoelectric effect is a result of Weiss Domains. Weiss Domains relate to a property of some ferroelectric crystal lattices to align their dipole moments in portions of the lattice even in the absence of an applied field. The effect comes from areas where seemingly random dipole moments cancel in all but two directions. This creates a lattice of symmetric dipoles while the material remains neutral overall as shown in figure 1 below. An applied field disrupts the symmetry of these dipoles which in turn creates an electric field that disturbs the lattice changing the shape. Or, looking at the opposite effect, applying pressure pressure to crystal moves the orientation of the lattice and thus shift the symmetry of the dipole moments and an electric pulse is emitted. Piezoelectrics are a subclass of ferromagnetic materials and
are classified according to their phase transitions as order-disorder or displacive. Displacive phase transitions are those where the lowest frequency optical phonon modes can propagate in the crystal at the transition whereas, order-disorder cannot. Optical phonons are phonon polariza tion modes with a minimum frequency that occurs in crystals. Piezoelectric crystals are characterized as having a high dielectric constant value. The Lyddane-Sachs Teller relation gives the frequency of the transverse and longitudinal optical phonon modes related to the dielectric constant, , we see that low values of the transverse optical mode correspond to high values of the static dielectric constant. Displacive transitions can also be discussed in terms of the polarization catastrophe. The Polarization catastrophe occurs when at some critical point the polarization gets very large. In plotting the solutions to the dispersion relation for phonons (lattice vibrations) in the First Brillouin Zone, there are several solutions depending how many dimensions you are working in how many different atoms are in the lattice. The solutions are plotted as optical and acoustic branches. Atoms in the acoustic branch all have the same displacement relative to one another and atoms in the optical branch oscillate out of phase proportionate to their masses. The polarization catastrophe occurs when a transverse optical phonon vanishes inside the Brillouin Zone. Kittel describes the effect as follows “ in a polarization catastrophe the local electric field caused by the ionic displacement is larger than the elastic restoring force, thereby giving an asymmetrical shift in the positions of the ions. Higher order restoring forces will limit the shift to a finite displacement.”
Looking at the form for the dielectric constant we can determine the conditions necessary for the polarization catastrophe occur for a piezoelectric.
, is the equation for the dielectric constant (Kittel), where is the electronic plus the ionic polarizability of an ion type i and is the number of ions of type i per unit volume. When the dielelectric constant is infinite and polarization can occur in the absence of an applied field. Thus, the condition is satisfied for the displacive transition. This effect only holds under a critical temperature known as the Curie Temperature where this effect can no longer occur and the material is no longer ferroelectric. Some of the most common piezoelectric crystals include lead zirconate titanate, quartz, Rochelle salt, and PVDF. Some of these are found in nature and others are manmade. The lead zirconate titanate crystal lattice is shown in figure 2 is one of the man made piezoelectric ceramics. Quartz has a silica tetrahedral lattice (Si ) which is rhombohedral in form as shown in figure 3 on the previous page. Quartz is the most common mineral in the Earth’s crust and is a piezoelectric, making it very useful for many applications. One of the first and most common uses is as a crystal oscillator. The crystal oscillator operates by applying a field or voltage to a quartz crystal using an attached electrode. The crystal then expands under the applied voltage. Then when the voltage is turned off the crystal returns to its’ original shape and generates a voltage as is de-excites to a ground state. The resonance effect created can be exploited, for example, as a clock timer in an integrated circuit.


PHOTOCHROMIC CRYSTALS
Another type of smart crystal that is similar to piezoelectrics are crystals that change color and usually isomer in response to electromagnetic radiation (light) often in the ultraviolet wavelength. This effect, that is sometimes referred to as photochromism, has been observed for some time now and recent research has seen much growth in this area. Photochromism is defined as the reversible transformation in a chemical species between two forms having different absorption spectra by photoirradiation (Irie). In these processes A and B can differ from one another in the absorption spectra, index of refraction, dielectric constant, or geometric shape. A simple representation of these optical switches is shown in figure 4. These crystals have several advantages over piezoelectrics in terms of practical applications. The fact that they are light-responsive allows for remote operation and eliminates the need for direct contact (i.e. electrodes, pressure) with the actuator. These crystals also eliminate the need for an applied or emitted electric field which can be difficult to work with in vacuum or in the presence of conducting materials. These crystals have been used in several useful applications and also led to the discovery that some or all photochromic crystals change shape as well as color. Photochromatism was first discovered in 1880 and is seen in organic and inorganic materials. The photochromatic process can be seen in Figure 5 where the commonly studied spiropyran is shown. One can see that when the crystal is photoirradiated with ultraviolet light, the bond is broken between the spiro carbon and oxanine in a unimolecular process. This restructuring changes its’ hybridization as well as other properties of the crystal such as the index of refraction which usually increases. The changing index of refraction accounts for the change in absorption spectra or color. This effect can be seen in figure 7 which shows the two diarylethene samples that change from colorless to colored when radiated with ultraviolet and visible light. Figure 6 also shows the change of the absorption spectra as a function of the wavelength it is irradiated with. In this figure the dark line shows the open ring form and the lighter line shows the closed ring form. The color changing effects of photochromactic materials have been found to have useful applications such as color-changing light-sensitive lenses (sunglasses), and are currently being tested as 3D optical storage devices. The study of photochromatic crystals and the search for better and more useful types led to the development of diarylethenes, which are very effective as photochromic materials. The photochromic properties of diarylethenes are currently being looked at as a possible way to manufacture erasable compact discs. These same materials also led to the discovery of shape changing molecules in response to light which will be discussed later.


REQUIRMENTS FOR PHOTONIC DEVICES
There are several important requirements for piezoelectric, photochromic, and shape changing materials to be useful as photonic devices. First, the process must be reversible. That is the crystal must be able to change its’ shape or color and then also be able to return to its’ original form by the reverse process. Both isomers (different structuring of the same crystal) must the thermally stable. Another important characterization is the response time or speed. This is the time it takes for the molecule to transform its’ shape or react when irradiated. Minimizing the response time is critical for the process to be useful. The sensitivity of the crystal to different wavelengths is another issue and also the work that the crystal can exert as it changes shape. Lastly, many crystals will break or snap during the transformation process. A useful crystal would be able to undergo the transformation many times before wearing out or breaking. The quantum yield for these processes can be shown ideally as , where y is the nondegraded fraction of the product, x is the degree of degredation ( the efficiency of the yield), and n is the number of cycles. In the limit of small x and large n we can approximate this equation to . From this equation we see that for a 99.9% efficiency yield that after cycles 63% the initial system will be lost and that after cycles there will be essentially none. Research is being done on growing and studying photochromatic crystals and finding ways to optimize all these characteristics.


SHAPE-CHANGING “BENDY” CRYSTALS
Recently, studies are being done on crystals that change their shape under photo-irradiation in a process called photoisomerization. Much of the research being done has been pioneered by a researcher in Japan named Masahiro Irie. Irie began doing research in this field during the 1980’s studying photochroic crystals, liquid crystals, and piezoelectrics which led him to the current research on shape changing crystals. In Irie’s earlier research he developed a photochromic compound known as diarylethene. He original studied them for possible useful applications of their photochromic properties and more recently has made some amazing discoveries of their shape changing properties. A diarylethene is a class of Y-shaped compounds that have aromatic groups bonded to each end of a carbon-carbon double bond. Many derivatives of the diarylethene molecule have been developed since its’ creation. One derivative that is commonly used and that Irie himself uses in his experiments is diethienylperfluorocylopenthene. The structure is shown in figure 7 to the left and is similar to that of the spiropyran in figure 5. In fact a common factor of the spiropyran and the diarylethenes is that they are both heterocylic rings and when radiated by with light they go between open-ring and closed-ring forms as shown in figures 5 and 7. This process is called photocyclic or electrocyclic. When ultraviolet is shined on the molecule the ring is closed and then shining visible will return it to the open ring structure in a reversible process.
In his experiment with diethienylperfluorocylopenthene, Irie observed the effect shown in the shaded boxes of figure 7. The molecule originally having a square form transforms to a lozenge (a thin rhombus) shape under light induced transformation. This was the first time that photo induced change in shape and sized was observed. This observation led Irie to perform a new experiment that studied specifically the shape changing properties of diarylethenes with respect its’ characteristics that would make it useful for photonic devices.
In this experiment a single diarylethene crystal was prepared on a slide through sublimation. The crystal was then fixed at one end of the slide and then the irradiated with ultraviolet light. It was observed that the crystal rod bent over a distance of 50 micrometers in response to the light and in fact launched a gold atom that was 90 times heavier (figure 8). Irie ascribes this bending of the rod as “the effect of a gradient in the extent of photoisomerization caused by the high absorbance of the crystal, so that the shrinkage of the irradiated part of the crystal causes bending” (Irie).
Figure 9 shows the molecular packing of the diarylethene lattice Fig. 8
from the (100) and (010) faces (in a. and b. respectively). The change from a square to a lozenge shape indicates that the crystal contracts along the c-axis and expands along the b-axis. The cofacial packing allows the molecules to be stacked one-by-one which results in the contraction along the c-axis which causes the bending of the rod.
The crystal observed to have a response time of 10 picoseconds for the color change and about 25 microseconds for the shape change or bending to Fig. 9 completely take place. This is comparable to the response time for piezoelectric devices. The introduction of aryl groups helps the molecule attain thermal stability. The fatigue for the photochromic effect allows cycles but only around 20 cycles of the bending. The thermal stability, fast response time, and electrocyclic process of diarylethenes indicate that in the near future they will be usuable in a variety of photonic devices such as optical switches. Currently research is being done on increasing the fatigue resistance.

CONCLUSION
In nature there are many biological devices that act similarly to some of the optical and mechanical devices discussed in this paper. The human eye for example has molecules in the retina that undergo cis-trans isomerizations when light radiation shines on them and this induces chemical changes that convert into an electrical signal that get transmitted through nerves to our brain allowing us to see.
Years of research and experimentation have allowed us to use some natural crystals found in nature for the benefit of society and technology. We have also been able to construct molecules that imitate the properties found in nature. The devices have already had a profound impact on electronics, computers, televisions, windows, clothes, and many other devices that are taken for granted. Ongoing research will continue to find new areas where we can implement these photonic devices.

BIBLIOGRAPHY
1.Mason Inman, Crystals Twist About In Response To Light. NewScientistTech. 2007.
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4.Masahiro Irie. Photochromic Diarylethenes for Photonic Devices. Pure & Applied Chemistry (vol. 68, No 7, p1367-1371).1996
5.Kenji Matsuda, Masahiro Irie. Photochromism of Diarylethenes Having Nitronyl Nitroxides. Science Direct. 2000.
6.Charles Kittel. Introduction to Solid State Physics. (p468-480).
7.Organic Photochromism. Pure & Applied Chemisty (vol. 73, No 4, p639-665).2001
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