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55-517: Lead zirconium titanate was first developed around 1952 at the Tokyo Institute of Technology . Compared to barium titanate , a previously discovered metallic-oxide-based piezoelectric material, lead zirconium titanate exhibits greater sensitivity and has a higher operating temperature. Piezoelectric ceramics are chosen for applications because of their physical strength, chemical inertness and their relatively low manufacturing cost. PZT ceramic

110-433: A 2 and a 3 as Hence zone indices of the direction perpendicular to plane ( hkℓ ) are, in suitably normalized triplet form, simply [ 2 h + k , h + 2 k , ℓ ( 3 / 2 ) ( a / c ) 2 ] {\displaystyle [2h+k,h+2k,\ell (3/2)(a/c)^{2}]} . When four indices are used for the zone normal to plane ( hkℓ ), however,

165-421: A , b and c appropriately: divide by the largest of the three numbers, and then multiply by the least common denominator . Thus, integer Miller indices implicitly include indices with all rational ratios. The reason why planes where the components (in the reciprocal-lattice basis) have rational ratios are of special interest is that these are the lattice planes : they are the only planes whose intersections with

220-454: A higher piezoelectric constant, but larger losses in the material due to internal friction . In hard lead zirconate titanate, domain wall motion is pinned by the impurities, thereby lowering the losses in the material, but at the expense of a reduced piezoelectric constant. One of the commonly studied chemical composition is PbZr 0.52 Ti 0.48 O 3 . The increased piezoelectric response and poling efficiency near to x  = 0.52

275-779: A notation system in crystallography for lattice planes in crystal (Bravais) lattices . In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers h , k , and  ℓ , the Miller indices . They are written ( hkℓ ), and denote the family of (parallel) lattice planes (of the given Bravais lattice) orthogonal to g h k ℓ = h b 1 + k b 2 + ℓ b 3 {\displaystyle \mathbf {g} _{hk\ell }=h\mathbf {b} _{1}+k\mathbf {b} _{2}+\ell \mathbf {b} _{3}} , where b i {\displaystyle \mathbf {b} _{i}} are

330-482: A reciprocal lattice vector. The requirement of lowest terms means that it is the shortest reciprocal lattice vector in the given direction. Equivalently, ( hkℓ ) denotes a plane that intercepts the three points a 1 / h , a 2 / k , and a 3 / ℓ , or some multiple thereof. That is, the Miller indices are proportional to the inverses of the intercepts of the plane, in the basis of the lattice vectors. If one of

385-658: A spontaneous electric polarization ( electric dipole ) that can be reversed in the presence of an electric field. The material features an extremely large relative permittivity at the morphotropic phase boundary (MPB) near x  = 0.52. Some formulations are ohmic until at least 250 kV/cm ( 25 MV/m ), after which current grows exponentially with field strength before reaching avalanche breakdown ; but lead zirconate titanate exhibits time-dependent dielectric breakdown — breakdown may occur under constant-voltage stress after minutes or hours, depending on voltage and temperature, so its dielectric strength depends on

440-499: Is also used in the manufacture of ceramic resonators for reference timing in electronic circuitry. Anti-flash goggles featuring PLZT protect aircrew from burns and blindness in case of a nuclear explosion. The PLZT lenses could turn opaque in less than 150 microseconds. Commercially, it is usually not used in its pure form, rather it is doped with either acceptors, which create oxygen (anion) vacancies, or donors, which create metal (cation) vacancies and facilitate domain wall motion in

495-441: Is applied (useful for actuator applications). The relative permittivity of lead zirconate titanate can range from 300 to 20000, depending upon orientation and doping. Being pyroelectric , this material develops a voltage difference across two of its faces under changing temperature conditions; consequently, lead zirconate titanate can be used as a heat sensor. Lead zirconate titanate is also ferroelectric , which means that it has

550-694: Is due to the increased number of allowable domain states at the MPB. At this boundary, the 6 possible domain states from the tetragonal phase ⟨100⟩ and the 8 possible domain states from the rhombohedral phase ⟨111⟩ are equally favorable energetically, thereby allowing a maximum 14 possible domain states. Like structurally similar lead scandium tantalate and barium strontium titanate , lead zirconate titanate can be used for manufacture of uncooled staring array infrared imaging sensors for thermographic cameras . Both thin film (usually obtained by chemical vapor deposition ) and bulk structures are used. The formula of

605-473: Is important to determine the planes and thus to have a notation system. Ordinarily, Miller indices are always integers by definition, and this constraint is physically significant. To understand this, suppose that we allow a plane ( abc ) where the Miller "indices" a , b and c (defined as above) are not necessarily integers. If a , b and c have rational ratios, then the same family of planes can be written in terms of integer indices ( hkℓ ) by scaling

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660-479: Is marked by Miller indices . By convention, negative integers are written with a bar, as in 3 for −3. The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. Miller indices are also used to designate reflections in X-ray crystallography . In this case the integers are not necessarily in lowest terms, and can be thought of as corresponding to planes spaced such that

715-563: Is the most commonly used piezoelectric ceramic because it has an even greater sensitivity and higher operating temperature than other piezoceramics. Recently, there has been a large push towards finding alternatives to PZT due to legislations in many countries restricting the use of lead alloys and compounds in commercial products. Being piezoelectric, lead zirconate titanate develops a voltage (or potential difference) across two of its faces when compressed (useful for sensor applications), and physically changes shape when an external electric field

770-656: The Meiji Restoration . To accomplish the quick catch-up to the West, the government expected this school to cultivate new modernized craftsmen and engineers. In 1890, it was renamed "Tokyo Technical School". In 1901, it changed name to "Tokyo Higher Technical School". In early days, the school was located in Kuramae, the eastern area of the Greater Tokyo Area, where many craftsmens' workshops had been since

825-700: The Ministry of Education, Culture, Sports, Science and Technology of Japan. Tokyo Tech has been ranked 2nd among the Japanese universities according to The Times Higher Education World University Rankings 2021. Tokyo Tech has also ranked 3rd among the best Japanese universities according to QS World University Rankings 2021. Tokyo Tech has also been ranked 2nd (national) in 2011 in the field of Engineering "Entrance score ranking of Japanese universities-Department of Engineering" by Score-navi. In another ranking, Japanese prep school Kawaijuku ranked Tokyo Tech as

880-419: The basis or primitive translation vectors of the reciprocal lattice for the given Bravais lattice. (Note that the plane is not always orthogonal to the linear combination of direct or original lattice vectors h a 1 + k a 2 + ℓ a 3 {\displaystyle h\mathbf {a} _{1}+k\mathbf {a} _{2}+\ell \mathbf {a} _{3}} because

935-400: The direction : That is, it uses the direct lattice basis instead of the reciprocal lattice. Note that [hkℓ] is not generally normal to the ( hkℓ ) planes, except in a cubic lattice as described below. For the special case of simple cubic crystals, the lattice vectors are orthogonal and of equal length (usually denoted a ), as are those of the reciprocal lattice. Thus, in this common case,

990-546: The Ōokayama Station . Other campuses are located in Suzukakedai and Tamachi . Tokyo Tech was organised into 6 schools, within which there are over 40 departments and research centres. Tokyo Tech enrolled 4,734 undergraduates and 1,464 graduate students for 2015–2016. Tokyo Institute of Technology was founded by the government of Japan as the Tokyo Vocational School on May 26, 1881, 14 years after

1045-480: The 2nd best employment rate in 400 major companies, and the average graduate salary was the 9th best in Japan. École des Mines de Paris ranks Tokyo Tech as 92nd in the world in 2011 in terms of the number of alumni listed among CEOs in the 500 largest worldwide companies. Also, according to the article of The New York Times - Universities with the most employable students ranking 2012, Tokyo Tech ranked 14th place in

1100-563: The 2nd place at the number of patents accepted (284) during 2009 among Japanese Universities. Alumni of Tokyo Tech enjoy their good success in Japanese industries. According to ( Truly Strong Universities -TSU ), the alumni's of Tokyo Tech has been acquiring the highest (1st) employment rate within Japan. According to the Weekly Economist 's 2010 rankings and the PRESIDENT 's article on 2006/10/16, graduates from Tokyo Tech have

1155-538: The 4th best (overall), 2-3rd best in former semester and 1st in latter semester (Department of Engineering) university in Japan (2012). According to QS World University Rankings , Tokyo Tech was ranked 3rd in Japan and internationally ranked 20th in the field of Engineering and Technology, and 51st in Natural science in 2011. The university was ranked 31st worldwide according to Global University ranking and 57th in 2011 according to QS World University Rankings , It

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1210-589: The Bubble Economy of the 1980s, TIT kept providing Japan its leading engineers, researchers, and business persons. Since April 2004, it has been semi-privatized into the National University Incorporation of Tokyo Institute of Technology under a new law which applied to all national universities. Operating the world-class supercomputer Tsubame 2.0 , and making a breakthrough in high-temperature superconductivity , Tokyo Tech

1265-494: The Miller indices ( hkℓ ) and [ hkℓ ] both simply denote normals/directions in Cartesian coordinates . For cubic crystals with lattice constant a , the spacing d between adjacent ( hkℓ ) lattice planes is (from above) Because of the symmetry of cubic crystals, it is possible to change the place and sign of the integers and have equivalent directions and planes: For face-centered cubic and body-centered cubic lattices,

1320-591: The Research Laboratory of Building Materials, the Research Laboratory of Resources Utilization, the Precision and Intelligence Laboratory and the Research Laboratory of Ceramic Industry, and the School of Engineering was renamed the School of Science and Engineering. Throughout the post-war reconstruction of the 1950s, the high economic growth era of the 1960s, and the aggressive economic era marching to

1375-535: The Tokyo Tech's International Graduate Program, the programmes are targeted at international students of high academic potential who are not Japanese speakers. Lectures and seminars are given in English mainly by Tokyo Tech's faculty members. Programme starting dates are October or April. Public fundings for these courses are also available; those students who have academic excellence may apply for scholarships from

1430-431: The [ 1 1 0] directions are really similar. If S is the intercept of the plane with the [ 1 1 0] axis, then There are also ad hoc schemes (e.g. in the transmission electron microscopy literature) for indexing hexagonal lattice vectors (rather than reciprocal lattice vectors or planes) with four indices. However they do not operate by similarly adding a redundant index to the regular three-index set. For example,

1485-445: The corresponding Miller indices, and i is a redundant index. This four-index scheme for labeling planes in a hexagonal lattice makes permutation symmetries apparent. For example, the similarity between (110) ≡ (11 2 0) and (1 2 0) ≡ (1 2 10) is more obvious when the redundant index is shown. In the figure at right, the (001) plane has a 3-fold symmetry: it remains unchanged by a rotation of 1/3 (2 π /3 rad, 120°). The [100], [010] and

1540-438: The crystal are 2d-periodic. For a plane (abc) where a , b and c have irrational ratios, on the other hand, the intersection of the plane with the crystal is not periodic. It forms an aperiodic pattern known as a quasicrystal . This construction corresponds precisely to the standard "cut-and-project" method of defining a quasicrystal, using a plane with irrational-ratio Miller indices. (Although many quasicrystals, such as

1595-461: The direct lattice vectors need not be mutually orthogonal.) This is based on the fact that a reciprocal lattice vector g {\displaystyle \mathbf {g} } (the vector indicating a reciprocal lattice point from the reciprocal lattice origin) is the wavevector of a plane wave in the Fourier series of a spatial function (e.g., electronic density function) which periodicity follows

1650-569: The indices is zero, it means that the planes do not intersect that axis (the intercept is "at infinity"). Considering only ( hkℓ ) planes intersecting one or more lattice points (the lattice planes ), the perpendicular distance d between adjacent lattice planes is related to the (shortest) reciprocal lattice vector orthogonal to the planes by the formula: d = 2 π / | g h k ℓ | {\displaystyle d=2\pi /|\mathbf {g} _{hk\ell }|} . The related notation [hkℓ] denotes

1705-506: The lattice vectors. Both definitions are given below. In either case, one needs to choose the three lattice vectors a 1 , a 2 , and a 3 that define the unit cell (note that the conventional unit cell may be larger than the primitive cell of the Bravais lattice , as the examples below illustrate). Given these, the three primitive reciprocal lattice vectors are also determined (denoted b 1 , b 2 , and b 3 ). Then, given

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1760-406: The left. And, note that for hexagonal interplanar distances, they take the form Crystallographic directions are lines linking nodes ( atoms , ions or molecules ) of a crystal. Similarly, crystallographic planes are planes linking nodes. Some directions and planes have a higher density of nodes; these dense planes have an influence on the behavior of the crystal: For all these reasons, it

1815-463: The literature often uses [ h , k , − h − k , ℓ ( 3 / 2 ) ( a / c ) 2 ] {\displaystyle [h,k,-h-k,\ell (3/2)(a/c)^{2}]} instead. Thus as you can see, four-index zone indices in square or angle brackets sometimes mix a single direct-lattice index on the right with reciprocal-lattice indices (normally in round or curly brackets) on

1870-514: The material used usually approaches Pb 1.1 (Zr 0.3 Ti 0.7 )O 3 (called lead zirconate titanate 30/70). Its properties may be modified by doping it with lanthanum , resulting in lanthanum-doped lead zirconium titanate ( lead zirconate titanate , also called lead lanthanum zirconium titanate ), with formula Pb 0.83 La 0.17 (Zr 0.3 Ti 0.7 ) 0.9575 O 3 (lead zirconate titanate 17/30/70). Tokyo Institute of Technology The Tokyo Institute of Technology ( 東京工業大学 )

1925-496: The material. In general, acceptor doping creates hard lead zirconate titanate, while donor doping creates soft lead zirconate titanate. Hard and soft lead zirconate titanate generally differ in their piezoelectric constants. Piezoelectric constants are proportional to the polarization or to the electrical field generated per unit of mechanical stress, or alternatively is the mechanical strain produced by per unit of electric field applied. In general, soft lead zirconate titanate has

1980-519: The new education system was promulgated in 1949 with the National School Establishment Law , and Tokyo Institute of Technology was reorganized. Many three-year courses were turned into four-year courses with the start of the School of Engineering this year. The university started graduate programmes in engineering in 1953. In the following year, the six research laboratories were integrated and reorganised into four new labs:

2035-505: The number of international research collections was the largest in Japan. It provides around 7,000 registered electronic journals each year. The library was therefore recognised for the outstanding national and international importance and awarded 'Centre of foreign journals' by the government of Japan . Renewal construction of the library was completed in July 2011. Tokyo Tech runs intensive programmes for obtaining master degree or PhD. Named

2090-580: The old Shōgun's era. The buildings in Kuramae campus were destroyed by the Great Kantō earthquake in 1923. In the following year, the Tokyo Higher Technical School moved from Kuramae to the present site in Ōokayama, a south suburb of the Greater Tokyo Area. In 1929, the school became Tokyo University of Engineering, later renamed to Tokyo Institute of Technology around 1946, gaining a status of national university , which allowed

2145-531: The original Bravais lattice, so wavefronts of the plane wave are coincident with parallel lattice planes of the original lattice. Since a measured scattering vector in X-ray crystallography , Δ k = k o u t − k i n {\displaystyle \Delta \mathbf {k} =\mathbf {k} _{\mathrm {out} }-\mathbf {k} _{\mathrm {in} }} with k o u t {\displaystyle \mathbf {k} _{\mathrm {out} }} as

2200-558: The outgoing (scattered from a crystal lattice) X-ray wavevector and k i n {\displaystyle \mathbf {k} _{\mathrm {in} }} as the incoming (toward the crystal lattice) X-ray wavevector, is equal to a reciprocal lattice vector g {\displaystyle \mathbf {g} } as stated by the Laue equations , the measured scattered X-ray peak at each measured scattering vector Δ k {\displaystyle \Delta \mathbf {k} }

2255-558: The primitive lattice vectors are not orthogonal. However, in these cases the Miller indices are conventionally defined relative to the lattice vectors of the cubic supercell and hence are again simply the Cartesian directions. With hexagonal and rhombohedral lattice systems , it is possible to use the Bravais–Miller system, which uses four indices ( h k i ℓ ) that obey the constraint Here h , k and ℓ are identical to

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2310-406: The reciprocal lattice vector ( hkℓ ) as suggested above can be written in terms of reciprocal lattice vectors as h b 1 + k b 2 + ℓ b 3 {\displaystyle h\mathbf {b} _{1}+k\mathbf {b} _{2}+\ell \mathbf {b} _{3}} . For hexagonal crystals this may be expressed in terms of direct-lattice basis-vectors a 1 ,

2365-638: The reflections from adjacent planes would have a phase difference of exactly one wavelength (2 π ), regardless of whether there are atoms on all these planes or not. There are also several related notations: In the context of crystal directions (not planes), the corresponding notations are: Note, for Laue–Bragg interferences Miller indices were introduced in 1839 by the British mineralogist William Hallowes Miller , although an almost identical system ( Weiss parameters ) had already been used by German mineralogist Christian Samuel Weiss since 1817. The method

2420-400: The three Miller indices h , k , ℓ , ( h k ℓ ) {\displaystyle h,k,\ell ,(hk\ell )} denotes planes orthogonal to the reciprocal lattice vector: That is, ( hkℓ ) simply indicates a normal to the planes in the basis of the primitive reciprocal lattice vectors. Because the coordinates are integers, this normal is itself always

2475-435: The time scale over which it is measured. Other formulations have dielectric strengths measured in the 8–16 MV/m range. Lead zirconate titanate-based materials are components of ceramic capacitors and STM / AFM actuators (tubes). Lead zirconate titanate is used to make ultrasound transducers and other sensors and actuators , as well as high-value ceramic capacitors and FRAM chips. Lead zirconate titanate

2530-470: The university to award degrees. The university had the Research Laboratory of Building Materials in 1934, and five years later, the Research Laboratory of Resources Utilisation and the Research Laboratory of Precision Machinery were constructed. The Research Laboratory of Ceramic Industry was made in 1943, and one year before World War Two ended, the Research Laboratory of Fuel Science and the Research Laboratory of Electronics were founded. After World War II ,

2585-753: The world (2nd in Asia, 1st in Japan). Tokyo Tech was one of the most selective universities in Japan. Its entrance examinations are usually considered one of the most difficult in Japan. As of 2009, there was a large population of rose-ringed parakeets residing at the main campus of the Tokyo Institute of Technology in Ookayama. 35°36′18″N 139°41′2″E  /  35.60500°N 139.68389°E  / 35.60500; 139.68389 Miller index#Case of cubic structures Miller indices form

2640-615: The world). Weekly Diamond also reported that Tokyo Tech has the highest research standard in Japan in terms of research fundings per researchers in COE Program . In the same article, it's also ranked 8th in terms of the quality of education by GP funds per student. In addition, according to the September 2012 survey by QS World University Rankings about the general standards in Engineering and Technology field, Tokyo Tech

2695-571: Was a former prime minister . Tokyo Tech has three campuses, Ōokayama campus in Ōokayama Meguro as the main campus, Tamachi campus in Shibaura and Suzukakedai campus, located in Nagatsuta , Midori-ku in Yokohama . Tokyo Tech comprises 6 schools, a number of departments and Institute for Liberal Arts. The main library was the Tokyo Institute of Technology Library in Ookayama. It

2750-531: Was a major centre for supercomputing technology and condensed matter research in the world. In 2011, it celebrated the 130th anniversary of its founding. In 2014, it joined the edX consortium and formed the Online Education Development Office (OEDO) to create MOOCS, which are hosted on the edX website. In its 130 years, Tokyo Tech has provided scientific researchers, engineers and many social leaders, including Naoto Kan who

2805-627: Was a public university in Meguro , Tokyo , Japan . It merged with Tokyo Medical and Dental University to form the Institute of Science Tokyo on 1 October 2024. The Tokyo Institute of Technology was a Designated National University and a Top Type university of Top Global University Project designated by the Japanese government . Tokyo Tech's main campus was located at Ōokayama on the boundary of Meguro and Ota , with its main entrance facing

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2860-472: Was also historically known as the Millerian system, and the indices as Millerian, although this is now rare. The Miller indices are defined with respect to any choice of unit cell and not only with respect to primitive basis vectors, as is sometimes stated. There are two equivalent ways to define the meaning of the Miller indices: via a point in the reciprocal lattice , or as the inverse intercepts along

2915-590: Was also ranked 31st worldwide according to the Global University Ranking in 2009. Tokyo Tech was one of the top research institutions in natural sciences and technology in Japan. According to Thomson Reuters , its research excellence (Pure science only for this information) was especially distinctive in Materials Science (5th in Japan, 24th in the world), Physics (5th in Japan, 31st in the world), and Chemistry (5th in Japan, 22nd in

2970-419: Was placed 19th (world), 2nd (national). The Tsubame 2.0 , which was a large-scale supercomputer in Tokyo Tech, was ranked 5th of the world best-performed computer. 1st in the world as university's owned one, this supercomputer was used for simulation related to the complex systems such as the dynamics of planets or financial systems. As Tokyo Tech has been emphasizing on 'practical' research, Tokyo Tech got

3025-408: Was the home of Japan's largest science and technology library. The library was founded in 1882, and it lost nearly 28,000 books during the Great Kantō earthquake in 1923. Moved to Ookayama in 1936, it has been the national science and technology library of Japan. 1,200 students and staff visit the library each day. It has 674,000 books and 2,500 journals, including 1,600 foreign academic journals;

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