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Readers who havearrived at this chapterin a sequential manner will notice that, apart from the phaseproblem,the relationship between the diffraction pattern (reciprocal space) andthe crystal structure (direct space) is mediated by aFouriertransform represented by the electron densityfunction:ρ(xyz), (see the figure below).
Readers will also know that the relationship between these twospaces is "holistic", meaning that the value of this function,at eachpoint in the unit cell of coordinates (xyz),is the result of "adding" the contribution of "all" structure factors[ie diffracted waves in terms of their amplitudes |F(hkl)|and phases Φ(hkl)]contained in the diffractionpattern.
They will also remember that the diffraction patterncontainsmany structural factors (
The "jump" between direct and reciprocalspaces, mediated by a Fourier transform represented by the electrondensity function
Moreover,the number of points in theunit cell, where theρ function has to be calculated, is veryhigh. In a cell of about 100 x 100 x 100 Angstrom3,itwould be necessary to calculate at least 1000 points in every unit celldirection to obtain a resolution of 100/1000,which equals 0.1Angstrom in eachdirection. This means calculating at least 1000 x 1000 x 1000 =1,000,000,000 points (one billion points) and at each point to"add"severalthousand(orhundredsof thousands)structure factorsF(hkl). It should therefore be clear that, regardless of the difficulties ofthe phase problem, solving a crystal structure implies the use ofcomputers. Finally, the analysis of a crystal or molecular structure also impliescalculating manygeometric parameters that define interatomicdistances, bond angles, torsionalangles, molecular surfaces,etc., using the atomic coordinates
It should therefore be clear that, regardless of the difficulties ofthe phase problem, solving a crystal structure implies the use ofcomputers.
Finally, the analysis of a crystal or molecular structure also impliescalculating manygeometric parameters that define interatomicdistances, bond angles, torsionalangles, molecular surfaces,etc., using the atomic coordinates(xyz).
The "hardware" (the evolution)
Forthe reasons described above, since the beginning of the use ofCrystallography as a discipline todetermine molecularand crystal structures, crystallographers have devoted specialattention to the development of calculation tools to facilitatecrystallographic work. With this aim, andeven before theearlycomputers appeared, the crystallographers introduced the so-called"Beevers-Lipsonstrips," which were widely used in all Crystallography laboratories.
The Beevers-Lipson strips
TheBeevers-Lipson strips were strips of paper containing predeterminedvalues of trigonometric functions ofsine and cosine types.These stripswere used in the crystallographiclaboratoriesto speed up the calculations (by hand)oftheFourier transforms (see above: the electron densityfunction, for example). Theelectron density function, among many other periodic functions, can bebroken down into a sum of terms of the sine and cosine type, and hencethe usefulness of these strips.
These strips wereintroduced in 1936 byA.H.Beevers and H. Lipson.In the 1960s, more than 300 boxes were distributed to nearlyall the laboratories in the world. You can also have a look intothedescriptionmade by the International Union of Crystallography. The nightmare was maintaining uprightthisbox, which had a very narrow base,otherwise it was impossible to maintain the strips correctly stored!
As expected, the introduction of early computers (or electro-mechaniccalculators) inspired great hope in crystallographers...
ENIAC (ElectronicNumerical Integrator and Computer, 1945) -- the very first electroniccomputer. Some pictures of the rooms whereitwas installed.
ENIAC, short for ElectronicNumericalIntegratorAndComputer,was the first general-purpose electronic computer, whose design andconstruction were financed by the United States Army during the SecondWorld War. It was the firstdigital computer capable of beingreprogrammed to solve a full range of computing problems, especiallycalculating artillery firing tables for the U.S. Army's BallisticResearch Laboratory.
The ENIAC had immediate importance. When it was announced in 1946, itwas heralded in the press as a "Giant Brain". It boasted speeds onethousand times faster than electro-mechanical machines, a leap incomputing power that no single machine has matched. This mathematicalpower, coupled with general-purpose programmability, excited scientistsand industrialists.
Besides its speed, the most remarkable thing about ENIAC was its sizeand complexity. ENIAC had 17,468 vacuum tubes, 7,200 crystaldiodes, 1,500 relays, 70,000 resistors, 10,000 capacitors and around 5million hand-soldered joints. It weighed27 tons, wasroughly2.6 m by 0.9 m by 26 m, took up63m², andconsumed 150 kW of power.Later, with the development of Electronics and Microelectronics, whichintroduced integrated circuits, computers became accessible tocrystallographers, who flockedto these facilities with largeboxes of "punched cards" (the only means for data storage at thattime), containing the diffraction intensities and theirowncomputer programs.
Apunch card or punched card (or punchcard or Hollerith card or IBMcard), is a piece of stiff paper which contains digital informationrepresented by the presence or absence of holes in predefinedpositions. It was used by crystallographers until the end of the1970s.
Punched paper tape (shown in yellow) anddifferentmagnetic tapes (as well as some small disks) usedfor data storage during the1970s and 1980s.
Around the early 1970s, and for over a decade, crystallographers becameanightmare for the managers and operators of the so-called "computingcenters,'' running in some universities and research centers.
In the 1980s the laboratories of Crystallography became "flooded" withcomputers, which for the first time gavecrystallographers independence from the large computing centers. TheVAX series ofcomputers (sold by the company Digital Equipment Corporation) markedasplendid erafor crystallographic calculations.Theyallowed the use of magnetic tapes and the firsthard diskdrives,withlimited capacity (only a few hundred MB) -- very big and heavy, butthey eliminated the need for the tedious punched cards. Nostalgics shouldhave a look into this link.!!!
A typical computer (of the VAX series)used in many Crystallography laboratories during the 1980s.
Overthe years, crystallographic computing has becomeeasy andaffordable thanks to personal computers (PC), whichmeet nearly all the needs of most conventional crystallographiccalculations, atleast concerning crystals of low and medium complexity (up to hundredsof atoms). Their relative low price and theirability to beassembled into "farms" (for distributed calculation) providecrystallographersthe best solution for almost any type ofcalculation.
Left: A typicalpersonal computer (PC) used inthe 2000s
Right: A typicalPC-farm used in the 2000s
However,the crystallography applied tomacromolecules not onlyneeds what we could call"hard" computing.Themanagement oflarge electron density maps, which are used to build the molecularstructure of proteins, as well as the subsequent structuralanalysis, requiresmore sophisticated computers with powerfulgraphic processors and, if possible, with the capability of displaying3-dimensional images using specialized glasses...
A Silicon Graphicscomputer usedto visualize 3-dimensionalelectrondensitymaps and structures. The processor and the screen are complemented byan infrared transmitter (black box on the screen) and the glasses usedby the crystallographer.
The current computing facilities represent a big jump respect to thecapabilities available during the mid-twentieth century, as it is shownin the representation of the structural model used for the structuraldescription of penicillin, based on three 2-dimensional electrondensity maps... And even 3d maps where also used!...
Left:Three-dimensionalmodel of the structure of penicillin, based on theuse of three 2-dimensional electron density maps, as used by DorothyC. Hodgkin, Nobel laureate in 1964
Right: Representationof 3d electron density maps used until the middle of the1970's. The contours are lines of electron density and show thepositions of individual atoms in the structure
A typical personal computer commonly usedsince 2010 forcrystallographic calculations and also for their graphic capabilities
At present there areenough personal,institutional or commercial computerprogram developments, or even computing facilities through remoteservers,to fulfill nearly all of the needs forcrystallographiccomputing, as well as many sources from which one can download most ofthose programs. In this context, it could be useful to check thefollowing links:
- Ofgeneralinterest: Thecrystallographic software listmaintained by the International Union ofCrystallography - (IUCr)
On the other hand,crystallographic work iscurrentlyunimaginable without having access tocrystallographicdatabases, which contain all the structural information that is beingpublished and which have a clear added value for theresearcher.The typeof structure is what determines its inclusion in any of the existingdatabases. Thus,metals andintermetallic compoundsare madeavailable in the databaseCRYSTMET; inorganic compounds are centralizedin theICSD database (Inorganic Crystal StructureDatabase);organic and organometallic inCSD (CambridgeCrystallographic Database); and proteins in PDB (Protein Data Bank),which is a databank (not a database). Other databases, databanks, etc.,donot necessarily containstructural information in the mostprecise sense,but they can also be very helpful for crystallographers. And this isthe case of WebCitepublished by the Cambridge Crystallographic DataCentre (CCDC),containing over 2000 articles with very importantinformation for structural chemistry research in its broadest sense,and in particular to pharmaceutical drug discovery, materials design ordrug development, among others.
Structuraldatabases and databanks
- CRYSTMET:Metals and intermetallic compounds (no longer exists)
- ICSD:Inorganic compounds(license required)
- CSD:Organic and organometalliccompounds(licenserequired)
- LipidBank: Lipids
- PDB:Proteins,Nucleicacids and large complexes
- NDB:Nucleic acids
During the period 1990-2012,CRYSTMET,ICSD andCSDhave been licensed free ofcharge to all CSICresearch institutes (CRYSTMET andICSD) andto all academic institutions in Spain andLatin Americancountries(CSD). However, due to economic constraints,the CSIC's authoritiesdecided to reduce drastically this program that wasmanagedthrough the Departmentof Crystallography and Structural Biology (at the Institute of PhysicalChemistry "Rocasolano"). Nowadays this program is maintainedin a reduced manner, only for Spanish institutions, as itcan be seen through this link.
What is the concept of crystallography? ›
crystallography, branch of science that deals with discerning the arrangement and bonding of atoms in crystalline solids and with the geometric structure of crystal lattices. Classically, the optical properties of crystals were of value in mineralogy and chemistry for the identification of substances.Is crystallography still used? ›
X-ray crystallography is still the primary method for characterizing the atomic structure of new materials and in discerning materials that appear similar by other experiments.Is it crystallography or crystallography? ›
Crystallography is the science that examines crystals, which can be found everywhere in nature—from salt to snowflakes to gemstones. They are part of a cadre of interdisciplinary scientists that work to understand diverse processes.What branch of science is crystallography? ›
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics).What technology is used in crystallography? ›
As has been mentioned, the three types of diffusion techniques used in crystallography are X-rays, neutrons, and electrons. Many other analytical techniques are also employed in crystallographic studies, such as X-ray fluorescence, spectroscopic techniques, and computer visualization and modeling.What is the basic law of crystallography? ›
The law of the constancy of interfacial angles (or 'first law of crystallography') states that the angles between the crystal faces of a given species are constant, whatever the lateral extension of these faces and the origin of the crystal, and are characteristic of that species.What are the drawbacks of crystallography? ›
Disadvantages of X-ray crystallography include: The sample must be crystallizable. The types of sample that can be analyzed are limited. In particular, membrane proteins and large molecules are difficult to crystallize, due to their large molecular weight and relatively poor solubility.Why is crystallography so important? ›
Crystallographers can work out the atomic structure of almost anything. And they use this knowledge to answer why things behave the way they do. Crystallography reveals why diamonds are hard and shiny and why salt melts in the mouth.What are the any two laws of crystallography? ›
(a) Face centred: When atoms are present in all 8-corners and six face centres in a cubic unit cell then this arrangement is known as FCC. (b) End-Centred: When in addition to particles at the corners, there are particles at the centres of the end faces.What are some uses of crystallography that relate to our everyday lives? ›
Cell phones have become so small and powerful because of our understanding of crystallography. With this understanding, we have created smaller and more powerful batteries, as well as energy-efficient components such as the backlight of the screens in our cell phones.
How many different crystal systems exist in crystallography? ›
The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Informally, two crystals are in the same crystal system if they have similar symmetries (albeit there are many exceptions).Who is known as the father of crystallography? ›
A new biography of William Lawrence Bragg tells a fascinating story, not only of the person but also of the science he initiated, says Ron Lifshitz. William Lawrence Bragg was only 25 when he won the 1915 Nobel Prize in physics, and remains the youngest person ever to win the Nobel Prize.What do you call someone who studies crystals? ›
Crystallographers study diverse substances, from living cells to superconductors, from protein molecules to ceramics. Crystallography began with the study of crystals, like quartz. Today, crystallographers study the atomic architecture of any material that can form an orderly solid - from diamonds to viruses.What are people who study crystals called? ›
What Does a Mineralogist Do? A mineralogist studies rocks, gems and other minerals, including their chemical and crystalline structures.What is the job outlook for a crystallographer? ›
How does Crystallographer job growth stack up to other jobs across the country? By 2024, there will be a change of 3,800 jobs for a total of 40,200 people employed in the career nationwide. This is a 10.4% change in growth over the next ten years, giving the career a growth rate nationwide of Above Average.How is crystallography used today? ›
Crystallographers can work out the atomic structure of almost anything. And they use this knowledge to answer why things behave the way they do. Crystallography reveals why diamonds are hard and shiny and why salt melts in the mouth. But the technique doesn't just look at naturally-occurring crystals.How is crystallography used in medicine? ›
The detailed analysis of crystal structures of protein–ligand complexes allows the study of the specific interactions of a particular drug with its protein target at the atomic level. It is used to design and improve drugs.What is Bragg's law in physics? ›
Bragg law, in physics, the relation between the spacing of atomic planes in crystals and the angles of incidence at which these planes produce the most intense reflections of electromagnetic radiations, such as X-rays and gamma rays, and particle waves, such as those associated with electrons and neutrons.What are three laws of crystallography? ›
laws of crystallography:law of constancy of interfacial angles. law of rational indices . classification of crystal system.What are the basic elements of crystallography? ›
- Elements of symmetry.
- Crystal lattice.
- One-time groups.
- Space groups.
- Use of International Tables of Crystallography.
- Principles of diffraction, reciprocal space.
- Intensity diffracted by a crystal.
- Single crystal diffraction, powder diffraction Experimental methods and instruments.
What is a fun fact about crystallography? ›
In fact, crystallography is the science or discipline directly attributable to winning the most Nobel Prizes, taking the award 28 times. X-ray crystallography has developed at a rapid pace in the last 20 years. Scientists first used the technique over 100 years ago when they determined the crystal structure of salt.What is the difference between crystallography and diffraction? ›
The key difference between X-ray crystallography and X-ray diffraction is that x-ray crystallography is the technique in which single crystals are exposed to x-rays, whereas x-ray diffraction is the technique in which a wide range of forms of the material are used for measurement.How many classes are there in crystallography? ›
The 32 crystal classes represent the 32 possible combinations of symmetry operations. Each crystal class will have crystal faces that uniquely define the symmetry of the class. These faces, or groups of faces are called crystal forms.What is unique reflection in crystallography? ›
The unique reflection number is defined by the resolution of the diffraction data and the size of the unit cell; when combined with the number of amino acids and/or nucleotides that occupy the asymmetric unit, these values set the “observations-to-parameters” ratio for refinement of the model.What are the 7 types of crystals? ›
There are 7 crystals systems and they are named: Triclinic, Monoclinic, Orthorhombic, Tetragonal, Trigonal, Hexagonal, and Cubic.What are the 4 types of crystals? ›
Crystalline substances can be described by the types of particles in them and the types of chemical bonding that take place between the particles. There are four types of crystals: (1) ionic, (2) metallic, (3) covalent network, and (4) molecular.What are the six basic crystal system? ›
Every crystal class is a member of one of the six crystal systems. These systems include the isometric, hexagonal, tetragonal, orthorhombic, monoclinic, and triclinic crystal systems.Who solved the crystal structure of DNA? ›
The 3-dimensional double helix structure of DNA, correctly elucidated by James Watson and Francis Crick.Where does crystallography come from? ›
The word "crystallography" is derived from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write.What is the history of Bragg's law? ›
William Lawrence Bragg proposed a simple but powerful equation – which became known as Bragg's law – showing the connection between the wavelength of the X-rays, the distance between the planes and the angle at which the X-rays are reflected.
What is the ability to control crystals called? ›
|Ability To||Psychically manipulate crystals, minerals and gems|
The ability to manipulate crystalline material. Variation of Earth Manipulation and Mineral Manipulation. Opposite to Amorphous Solid Manipulation.What is the name of Reiki crystals? ›
REIKI CRYSTAL PRODUCTS 12 Tumble Stone Set of Amethyst, Sodalite, Clear Quartz, Labradorite, Lapis Lazuli, Rose Quartz, Green Aventurine,Golden Quartz, Carnelian, Red Jasper, Bloodstone And Smoky Quartz Reiki Healing Gemstones Meditation Chakra Decorative Showpiece - 2.5 cm (Crystal, Stone, Clear)What jobs are related to crystals? ›
- Chemistry Teachers. Chemistry teachers use crystals in classroom demonstrations and lab experiments to teach students about chemical interactions, material compositions, and natural processes. ...
- Geologists. ...
- Materials Engineers. ...
Quartz is the second most abundant mineral in Earth's crust after feldspar. It occurs in nearly all acid igneous, metamorphic, and sedimentary rocks. It is an essential mineral in such silica-rich felsic rocks as granites, granodiorites, and rhyolites.Can I become a chemist without a degree? ›
Chemists and materials scientists typically need a bachelor's degree in chemistry or a related physical science field. Some jobs require a master's degree or Ph. D. and work experience.How high is the demand for geologists? ›
|Quick Facts: Geoscientists|
|Number of Jobs, 2021||24,900|
|Job Outlook, 2021-31||5% (As fast as average)|
|Employment Change, 2021-31||1,200|
Chemists typically work regular hours. A 40-hour work week is usual, but longer hours are not uncommon. Researchers may be required to work odd hours in laboratories or other locations, depending on the nature of their research.What is the objective of crystallography? ›
Objective is to explain the description of a crystal structure in terms of atom positions, unit cells, and crystal symmetry; and to relate the crystal symmetry to the symmetry observed in a diffraction experiment, for symmetries up to and including primitive orthorhombic.What is important about crystallography? ›
Crystallographers can work out the atomic structure of almost anything. And they use this knowledge to answer why things behave the way they do. Crystallography reveals why diamonds are hard and shiny and why salt melts in the mouth. But the technique doesn't just look at naturally-occurring crystals.
What are some fun facts about crystallography? ›
- Crystallography takes the prize. ...
- Around 90 percent of all drugs are crystals. ...
- They're in our eyes and bones. ...
- Chocolate is crystalline. ...
- We owe fireworks to crystals.
Crystallography is the study of atomic and molecular structure. Crystallographers want to know how the atoms in a material are arranged in order to understand the relationship between atomic structure and properties of these materials.What are the six crystallographic elements? ›
Every crystal class is a member of one of the six crystal systems. These systems include the isometric, hexagonal, tetragonal, orthorhombic, monoclinic, and triclinic crystal systems.