Kerr effect

In geometry and crystallography, a Bravais lattice, studied by Template:Harvs, is an infinite array of discrete points generated by a set of discrete translation operations described by:

$𝐑=n_1{𝐚}_1+n_2{𝐚}_2+n_3{𝐚}_3$

where n_i are any integers and a_i are known as the primitive vectors which lie in different directions and span the lattice. This discrete set of vectors must be closed under vector addition and subtraction. For any choice of position vector R, the lattice looks exactly the same.

A crystal is made up of a periodic arrangement of one or more atoms (the basis) repeated at each lattice point. Consequently, the crystal looks the same when viewed from any equivalent lattice point, namely those separated by the translation of one unit cell (the motive).

Two Bravais lattices are often considered equivalent if they have isomorphic symmetry groups. In this sense, there are 14 possible Bravais lattices in three-dimensional space. The 14 possible symmetry groups of Bravais lattices are 14 of the 230 space groups.

Bravais lattices in at most 2 dimensions

In each of 0-dimensional and 1-dimensional space there is just one type of Bravais lattice.

In two dimensions, there are five Bravais lattices. They are oblique, rectangular, centered rectangular (rhombic), hexagonal, and square.

The five fundamental two-dimensional Bravais lattices: 1 oblique, 2 rectangular, 3 centered rectangular (rhombic), 4 hexagonal, and 5 square

Bravais lattices in 3 dimensions

The 14 Bravais lattices in 3 dimensions are obtained by coupling one of the 7 lattice systems (or axial systems) with one of the lattice centerings. Each Bravais lattice refers to a distinct lattice type.

The lattice centerings are:

• Primitive (P): lattice points on the cell corners only.
• Body (I): one additional lattice point at the center of the cell.
• Face (F): one additional lattice point at the center of each of the faces of the cell.
• Base (A, B or C): one additional lattice point at the center of each of one pair of the cell faces.

Not all combinations of the crystal systems and lattice centerings are needed to describe the possible lattices. There are in total 7 × 6 = 42 combinations, but it can be shown that several of these are in fact equivalent to each other. For example, the monoclinic I lattice can be described by a monoclinic C lattice by different choice of crystal axes. Similarly, all A- or B-centred lattices can be described either by a C- or P-centering. This reduces the number of combinations to 14 conventional Bravais lattices, shown in the table below.

The 7 lattice systems	The 14 Bravais lattices
Triclinic	P
Monoclinic	P	C
Orthorhombic	P	C	I	F
	Orthohombic, simple	Orthohombic, base-centred	Orthohombic, body-centred	Orthohombic, face-centred
Tetragonal	P	I
	Tetragonal, simple	Tetragonal, body-centred
Rhombohedral	P
	Rhombohedral
Hexagonal	P
	Hexagonal
Cubic	P (pcc)	I (bcc)	F (fcc)
	Cubic, simple	Cubic, body-centred	Cubic, face-centred

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The volume of the unit cell can be calculated by evaluating a · b × c where a, b, and c are the lattice vectors. The volumes of the Bravais lattices are given below:

Lattice system	Volume
Triclinic	$abc\sqrt{1-{\cos }^2\alpha -{\cos }^2\beta -{\cos }^2\gamma +2\cos \alpha \cos \beta \cos \gamma }$
Monoclinic	$abc\sin \beta$
Orthorhombic	$abc$
Tetragonal	$a^{2}c$
Rhombohedral	$a^3\sqrt{1-3{\cos }^2\alpha +2{\cos }^3\alpha }$
Hexagonal	$\frac{\sqrt{3}{a}^{2}c}{2}$
Cubic	$a^3$

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Individuals all wish to be seen having the identical foresight as the experts in property investment or the massive names in their own fields. Thus the discharge of these tales works to encourage different buyers to observe suit. Bartley Ridge is the most popular new launch in district 13. Irresistible pricing from $1,1xx psf. Bartley Ridge is a ninety nine-12 months leasehold new condominium at Mount Vernon road, good next to Bartley MRT station (CC12). If you want to get more Rehda Johor chairman Koh Moo Hing said potential property consumers in the two areas Http://Modern.Dowatch.Net/Profile/Mic31K/Created/Topics are now adopting a wait-and-see attitude. How can I get the ebrochure and flooring plans of the new launch projects ? The Existing Mortgage on your HDB District 13, Freehold condominium District 11, Freehold Cluster landed house Sea Horizon EC @ Pasir Ris

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To not worry, we'll hold you in our VIP Precedence list for future new launch VIP Preview. We'll contact you to establish your wants and advocate related tasks, both new launch or resale properties that probably match your standards. In case you're looking for resale property, such as these few years old, or just got Short-term Occupation Permit (PRIME), you might click on here right here for fast search and submit your shortlisted listings to us, we'll check and call you for viewing.

Oceanfront Suites, irresistible pricing for a 946 leasehold property with magnificent sea view. Dreaming of basking and feeling the warmth of pure sunlight is now just a click on away. Oceanfront Suites - Seaside residing no longer needs to remain an unattainable This Cambodia new launch, a mega development has also 762 residential models. Additionally located within this Oxley abroad property is a mega shopping center with 627 outlets and also up to 963 available workplace spaces and is surrounded by quite a few Embassy, resorts, Casinos and many vacationer relax space. Belysa EC @ Pasir Ris Esparina EC @ Sengkang Dell Launches World's first Gender-GEDI Female Entrepreneurship Index on 06/04/thirteen by Istanbul, Turkey. Paris Ris EC @ Paris Ris in search of indication of curiosity.

The developer should open a Venture Account with a financial institution or monetary establishment for every housing venture he undertakes, before he's issued with a Sale License (license to sell models in his development). All payments from buyers before completion of the challenge, and construction loans, go into the mission account. New launch rental LA FIESTA, an thrilling new condominium located along Sengkang Square / Compassvale Highway is a brief stroll to the bustling Sengkang City Centre the place the bus interchange, Sengkang MRT and LRT stations are located. Glorious location,Premium rental with Bayfront resort lifestyle theme and views ofwaterscape. Close to EC pricing - Worth for cash! Apr 02, 2013 Sengkang New Rental Launch, La Fiesta- Sengkang MRTstation at your gate.

As The Hillford property launch at Jalan Jurong Kechil may be very close to to beauty world mrt , the environment for the plot of land which belongs to World Class Land remains very upbeat as it is rather close to to Holland Village. Review now by visiting the brand new apartment pages on our website, each displaying complete particulars and the latest information of each new launch. You can even contact us directly to obtain quick & correct answers to all of your questions with high of the road service. An inevitable conclusion is that costs within the property market have just set new highs. The apparent connotation for potential buyers is to take motion now before prices bounce again. tract and points to his property line, marked by a big maple in a sea of Search SG Developersale.com

Centred Unit Cells :

Lattice System	Possible Variations	Axial Distances (edge lengths)	Axial Angles	Examples
Cubic	Primitive, Body-centred, Face-centred	a = b = c	α = β = γ = 90°	NaCl, Zinc Blende, Cu
Tetragonal	Primitive, Body-centred	a = b ≠ c	α = β = γ = 90°	White tin, SnO2, TiO2, CaSO4
Orthorhombic	Primitive, Body-centred, Face-centred, Base-centred	a ≠ b ≠ c	α = β = γ = 90°	Rhombic sulphur, KNO3, BaSO4
Hexagonal	Primitive	a = b ≠ c	α = β = 90°, γ = 120°	Graphite, ZnO, CdS
Rhombohedral	Primitive	a = b = c	α = β = γ ≠ 90°	Calcite (CaCO3, Cinnabar (HgS)
Monoclinic	Primitive, Base-centred	a ≠ b ≠ c	α = γ = 90°, β ≠ 90°	Monoclinic sulphur, Na2SO4.10H2O
Triclinic	Primitive	a ≠ b ≠ c	α ≠ β ≠ γ ≠ 90°	K2Cr2O7, CuSO4.5H2O, H3BO3

Bravais lattices in 4 dimensions

In four dimensions, there are 64 Bravais lattices. Of these, 23 are primitive and 41 are centered. Ten Bravais lattices split into enantiomorphic pairs.

See also

• Translational symmetry
• Lattice (group)
• classification of lattices
• Miller Index

References

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Further reading

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