Glossary

Given the novelty of the nano-instrumentation proposed by ELDICO and that electron diffraction is a very recent subject for crystallography, a comprehensive list of scientific terms customarily utilized in relation to ED would prove helpful in setting the ground.

We welcome improvements, addendums, corrections from our scientific community, given how new some of the aspects defined in our glossary are and that many features are still being investigated as we speak. Please do not hesitate to get in contact if you have any comments, questions, or exciting findings to share with us. 

Asymmetric unit

Unité asymétrique (Fr). Asymmetrische Einheit (Ge). Unità asimmetrica (It). Unidad asimétrica (Sp). Мотивная единица (Ru).

An asymmetric unit of a space group is the simply connected smallest group of atoms - closed part of space from which, by application of all symmetry operations of the space group, the whole of space is filled. This implies that:

·     mirror planes must form boundary planes of the asymmetric unit;

·     rotation axes must form boundary edges of the asymmetric unit;

·  inversion centres must either form vertices of the asymmetric unit or be located at the midpoints of boundary planes or boundary edges.[1]

In structures composed of molecules of a single type which have no symmetry themselves, the asymmetric unit is a molecule, or occasionally two or more molecules which differ from one another in orientation or conformation. When the molecule has symmetry, which can conform to crystallographic symmetry, it may occupy a special position, and the asymmetric unit will then be a half molecule or even some smaller fraction.[2] The asymmetric unit may contain multiple molecules of two different types.

References:

1T. Hahn, “International tables for crystallography”, Volume A, 5th Ed., Springer, Dordrecht 2005, 25.

2W. Massa, “Crystal structure determination”, 3rd Ed., Books on Demand, Norderstedt 2016, 79-80.

Bragg’s law

Loi de Bragg (Fr). Bragg-Gesetz (Ge). Legge di Bragg (It). Ley de Bragg  (Sp). Условие Брэгга-Вульфа (Ru).

Bragg’s Law is an equation formulated by Sir W. H. Bragg and his son, which predicts whether diffraction can take place or not[1]. The equation provides the condition for a plane wave to be diffracted by a family of lattice planes:

d sin θn λ

where d is the interplanar spacing, θ the angle between the incident ray and crystal planes, λ its wavelength of the used radiation and n is an integer, the order of the reflection. It is equivalent to the diffraction condition in reciprocal space and to the Laue equations.[2]

Fig. 1 Bragg’s law [3]

The basic idea behind Bragg's Law is that, when it is satisfied, X-ray beams (for example) scattered from successive planes in the crystal will travel distances differing by exactly one wavelength (for the case of n=1); this can be fairly easily proven from a geometrical consideration of the above diagram. In this precise direction, i.e. at the angle θ calculated by Bragg's Law, X-rays scattered from successive planes will interact constructively when they eventually reach the X-ray detector, thus registering the passage of an intense beam which we call the diffracted beam.[4]

Bragg’s Law does not apply only to X-rays, but also neutrons and electrons can be used instead. Because the diffraction pattern is independent of the wavelength used, such principle is very valuable for Electron Diffraction (ED) experiments. This is the underlying issue behind ED for nano-crystallography.

References:

1W. L. Bragg, The Crystalline State: Volume I”, The Macmillan Company, New York 1934.

2“Bragg’s law”, accessed on September 21, 2020https://dictionary.iucr.org/Bragg%27s_law 

3S. Baskaran, “Structure and Regulation of YeastGlycogen Synthase”, PhD thesis, Indiana University, IN, 2010.

4“Bragg’s law”, accessed on September 21, 2020, http://pd.chem.ucl.ac.uk/pdnn/powintro/braggs.html

Cryogenics

Cryogénie (Fr). Kryotechnik (Ge). Criogenia (It). Criogenia (Sp). Криогеника (Ru).

The field of cryogenics studies the regularities of properties alternation of various substances under conditions of extremely low ("cryogenic") temperatures; involves technologies and hardware-methodical means of work at low temperatures. Temperatures below -180°C (93 K; −292 °F) are considered as cryogenic. [1]

Liquefied gases, such as liquid nitrogen and liquid helium, are used in many cryogenic applications. Liquid nitrogen is the most commonly used element in cryogenics and is legally purchasable around the world. Liquid helium is also commonly used and allows for the lowest attainable temperatures to be reached.[2]

Liquid nitrogen is used as part of the cooling system in X-ray diffractometers and (S)TEMs. In the case of EM cooling down organic samples allows them to be irradiated with electrons to minimize the radiation damage effects. It also helps conserve the crystallinity under vacuum for those samples capable of losing solvates.

For a dedicated electron diffractometer, this feature would of great importance, since the beam temperature can cause damage to the samples utilized for diffraction. Using a dedicated electron diffractometer with cryogenic capabilities would ensure that the samples remain intact. 

References:

1R. E. Bilstein, “Stages to Saturn. A Technological History of the Apollo/Saturn Launch Vehicle”, NASA History Office, Washington, DC 1996, 89-91.

2“Cryogenics”, accessed on September 21, 2020, https://en.wikipedia.org/wiki/Cryogenics.

Crystal Lattice

Réseau (Fr). Gitter (Ge). Reticolo (It). Red (Sp). Кристаллическая решётка (Ru).

In order to describe the structure of a crystal, it is only necessary to know the simplest repeating “motif” and the length and directions of the three vectors which together describe its repetition space. The motif can be a molecule or the building block of a network structure. Normally, it consists of several such units, which may be converted into one another by symmetry operations. The three vectors a, b, c, which describe the translations of the motif in space are called the basis vectors. By their operation one upon another, a lattice is generated. Any point in such a lattice may be described by a vector r,

r = n1a + n2b + n3c

where n1, n2 and n3 are integers.[1]

By reading our paper on alpha-Glycine, you can get interesting insights in regards to changes in the crystal lattices visualization patterns from traditional X-ray crystallography to electron diffraction. 

References:

1Werner Massa – Crystal structure determination, 3rd Ed., Books on Demand, Norderstedt 2016, 14-15.

Nanocrystal

Nanocristal (Fr). Nanokristall (Ge). Nanocrystal (It). Nanocristal (Sp). Нанокристалл (Ru).

A material particle having dimensions in the range form 1 – < 1000 nm (i.e, < 1 x 10-6 m) and composed of atoms in either a single- or poly-crystalline arrangement. Nanocrystals of certain substances may have beneficial (or different) chemical and physical properties comparing to larger crystals. Especially if their dimensions range from 1 – 100 nm (quantum dots effects).[1]

In general, the macro physical properties of a material are dictated by the nanocrystalline level. Therefore, being able to analyze nanocrystals is very important for understanding their macro chemical and physical properties. Electron diffraction is a preferred analytical tool for getting the 3D structure of nano-crystalline substance.

References:

1J. L. Burt et al., Journal of Crystal Growth, 2005, 285 (4), 681–691.

2B. D. Fahlman, “Materials Chemistry,” Springer, Berlin 2007, 282-283.

Polymorphism

 Polymorphisme (Fr). Polymorphie (Ge). Polimorfismo (It). Polimorfismo (Sp). Полиморфизм (Ru).

The phenomenon in which the same solid chemical compound can adopt different forms and crystal structures. In 1969, Rosenstein & Lamy propose a definition: ‘‘When a substance can exist in more than one crystalline state it is said to exhibit polymorphism.’’[1] Polymorphs can provide valuable insights into crystal packing and structure-property relationships.[2]

For the Pharmaceutical industry, it is very important to know which polymorph(s) has been produced. Not only because of the different physical properties, but due to IP protection. Polymorphs are normally studied on nano-powders and are characterized by using XRPD techniques.  Electron diffraction is a powerful tool than can detect different polymorphic crystalline systems even on the nanoscale. A dedicated electron diffractometer for such experiments will change in the future the way such systems are characterized, and it could change the way IP protection is done.

Examples:

·       Diamond and graphite are polymorphs of each other: they have the same composition but different structures and properties.[3]

·       5-Methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, known as ROY for its red, orange, and yellow crystals, has seven polymorphs with solved structures, the largest number in the Cambridge Structural Database.[4]

Fig. 7 Polymorphs of ROY

 

References:

1J.-P. Brog, C.-L. Chanez, A. Crochet and K. M. Fromm, RSC Advances, 2013, 3, 16905–16931.

2L. Yu, Accounts of Chemical Research, 2010, 43(9), 1257-1266.

3Ibid. 

4Ibid.

Powder material

Poudre (Fr). Pulver (Ge). Polvere (It). Polvo (Sp). Порошок (Ru).

A powder is a large number of crystallites or particles (grains, agglomerates or aggregates; crystalline or non-crystalline) irrespective of any adhesion* between them and thus can be a loose powder, a solid block, a thin film or even a liquid. An ideal powder is represented by a virtually unlimited number of sufficiently sized, randomly oriented and spherical crystallites.[1]

In the Pharmaceutical industry (for example), an Active Pharmaceutical Ingredient (API) is produced (in general) as a nano powder (crystalline or amorph). Crystalline nano powders are characterized using a widespread technique known as XRPD (X-ray Powder Diffraction). This analytical method provides a fingerprint which is unique for each pure nano powder system. Electron Diffraction (ED) is a new upgrowing technology which indeed is not only able to deliver such a fingerprint, but even more. An electron diffractometer will disrupt in the future the way chemical analysis is done for nano powders.

Professor Mauro Gemmi (IIT Pisa) has highlighted the limitations of present state of research via powder diffraction mode and how the emergence of a dedicated instrument for ED would be a breakthrough

*Adhesion is the tendency of dissimilar particles or surfaces to cling to one another.[2] 

References:

1“Powder”, accessed on September 21, 2020 , https://dictionary.iucr.org/Powder

2“Adhesion”, accessed on September 21, 2020, https://en.wikipedia.org/wiki/Adhesion

Radiation damage

Dommages causés par les radiations (Fr). Strahlenschäden (Ge). Danni da radiazioni (It). Daño por radiación (Sp). Радиационное повреждение (Ru).

Damage caused to the crystals by the X-Ray beam [1], resulting into the change of the ordered structure of crystalline material. Very rarely these changes may be beneficial, but generally they cause harmful modifications of properties. Electrons, which have stronger interaction with matter (as X-rays for example), can produce more radiation damage on organic samples than commonly used sources of X-rays. For electron diffraction applications, cryogenic conditions are very important for those organic molecules which will not survive the e- beam exposure at room temperature. Cryogenic measurements not only minimize radiation damage but often lead to improved resolution owing to decrease in thermal motion in the crystal.[2]

A major obstacle in macromolecular crystallography has been the radiation damage caused by the absorption of the X-ray radiation by the crystals during the diffraction experiments. Free radicals are generated when X-rays are absorbed by macromolecular crystals. These radicals propagate changes that manifest in two ways: as global effects and as site specific structural changes. Global radiation damage is observed as a loss of diffraction intensity, an increase in unit-cell volume, and higher Wilson B-factors, all due to the overall increase in non-isomorphism in the crystal. On the other hand, site specific damage, which also contributes to the global effects, is seen in the electron density maps following structure refinement.[3]

References:

1G. Zaloga & R. Sarma, Nature,1974, 251, 551-552.

2E. Prince, “International tables for crystallography”, Volume C, 3rd Ed., Kluwer Academic publishers, Dordrecht/Boston/London 2004, 166.

3H. Taberman, Crystals, 2018, 8(4), 157-169.

Single crystal

Monocristal (Fr). Einkristall (Ge). Monocristallo (It). Monocrystal (Sp). Монокристалл (Ru).

A single-crystal is a solid material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries.[1] Single crystals are a requirement for X-ray diffraction experiments.

Typically, crystals have flat faces and sharp edges. Also, many crystals will have one or more directions that can be cleaved cleanly.[2] The sufficient single crystal size for an X-ray diffraction measurement is around (0.01 mm)3, for modern X-ray devices. Single crystals bigger than some (0.3 mm)3 can be reduced in size in order to provide satisfactory size for an XRD measurement.[3]

For crystals on the sub-micro and nanometer scale, standard X-ray devices (including Synchrotron facilities) are not capable of producing enough diffraction on these particles to characterize the molecular structure. On the other hand, Electron Diffraction techniques can do that. Furthermore, a dedicated device, like an electron diffractometer, would be the best option fur such regime of samples.

References:

1“Single crystal”, accessed on September 21, 2020, https://en.wikipedia.org/wiki/Single_crystal

2“Symmetry in crystallography”, accessed on September 21, 2020, http://xrayweb.chem.ou.edu/notes/symmetry.html

3W. Massa, “Crystal structure determination”, 3rd Ed., Books on Demand, Norderstedt 2016, 99-100. 

Structure determination

Détermination de la structure (Fr). Strukturbestimmung (Ge). Determinazione della struttura (It). Determinación estructural (Sp). Определение структуры (Ru).

Crystal structure determination is a two-part process: (a) the determination of the size and shape of the unit cell (i.e. the lattice parameters) from the geometry of the diffraction pattern and (b) the determination of the lattice type and distribution of the atoms in the structure from the (relative) intensities of the diffraction spots.[1]

In very simple words, to get a 3D representation of a molecular compound. In fact, it is the process of elaborating the three-dimensional positional coordinates (plus the three-dimensional anisotropic displacement parameters) of the scattering centres in an ordered crystal lattice. Where a crystal is composed of a molecular compound, the term generally includes the three-dimensional description of the chemical structures of each molecular compound present.[2]

Most structure determination techniques involve the diffraction of electromagnetic or matter waves of wavelengths comparable to atomic dimensions.* Bragg's law specifies the condition for plane waves to be diffracted from lattice planes. The diffracted radiation passing through a crystal emerges with intensity varying as a function of scattering angle. This variation arises from constructive and destructive interference of scattered beams from the planes associated with the different atoms present in the lattice. The result is seen by an imaging detector as a pattern of diffraction spots or rings.

Among diffraction-based techniques are:

·       X-ray diffraction (single-crystal, fibre, powder)[3]

·       Electron diffraction (Nano-crystals, selected area, convergent beam)[4]

·       Neutron diffraction (single-crystal, powder)[5]

·       Gamma-ray diffraction

Other techniques for three-dimensional structure determination that are complementary to diffraction methods include

·       transmission electron microscopy (CryoEM for example)

·       nuclear magnetic resonance spectroscopy (used largely for biological macromolecules in solution)

*Atomic diameter range is 62 pm (He) to 520 pm (Cs) (1 picometer (pm) = 1×10−12 m.[6]

Structure determination using electron diffraction techniques has a great advantage over all other diffraction methods. That is, there is no need to grow “bigger” crystals that could produce diffraction conditions under the radiation source used. For 3D-ED experiments it suffice (or even it is necessary) that the nanoparticles are in the range of 20 – < 1000 nm. This range of particles is almost inaccessible with any other kind of diffraction technique.

References:

1C. Hammond, “The Basics of Crystallography and Diffraction”, 3rd Ed., Oxford University Press Inc., New York 2009.

2“Structure determination”, accessed on September 21, 2020, https://dictionary.iucr.org/Structure_determination

3U. Shmueli, “International tables for crystallography”, Volume B, 2nd Ed., Springer, Dordrecht 2006, 534-551.

4Id., 552-556.

5Id., 557-569.

6“Atom”, accessed on September 21, 2020, https://en.wikipedia.org/wiki/Atom

Synchrotron radiation

Rayonnement synchrotron (Fr). Synchrotronstrahlung (Ge). Radiazione di sincrotrone (It). Radiación de sincrotrón (Sp). Синхротронное излучение (Ru).

Electromagnetic energy emitted by charged particles which are accelerated at speeds close to the speed of light in a curved orbit.

Instead of using the characteristic X-radiation produced by X-ray tubes or microfocus sources, it is possible to make use of the radiation produced as a by-product of particle acceleration in a synchrotron. There are several advantages:

·       Very high intensity and very low divergence

·       Tunable wavelength

·       High degree of polarization

Synchrotron sources are widely distributed around the world. They are mostly applied for structure determination of very small crystals and macromolecules (mainly proteins), for high-resolution powder diffraction experiments, and for other special measurements, making use of the highly polarized beam.[1]

An electron diffractometer which uses electrons instead of X-rays has a great advantage even over a synchrotron facility. Smaller crystals can now be analyzed. Normally, and in general, the crystal size of a crystalline substance must be some 5-10 µm in all three dimensions so that even with a synchrotron beam reasonable diffraction patterns can be obtained. Electron Diffraction (ED) experiments have the advantage that they need to be performed in crystals having < 1µm dimensions. In this sense, an electron diffractometer can be seen as a “synchrotron facility in a shoebox”, as previously inaccessible crystalline systems become per se, accessible.

References:

1W. Massa, “Crystal structure determination”, 3rd Ed., Books on Demand, Norderstedt 2016, 29-30.

Twinning

Maclage (Fr). Zwillingsbildung, Verzwillingung (Ge). Geminazione (It). Maclado (Sp). Двойники (Ru).

A twin consists of two or more single crystals of the same species but in different orientation, its twin components. They are intergrown in such a way that at least some of their lattice directions are parallel. The twin law describes the geometrical relation between the twin components. It specifies a symmetry operation, the twin operation, that brings one of the twin components into parallel orientation with the other. The corresponding symmetry element is called the twin element.[1]

Simple twinned crystals may be contact twins or penetration twins:

·       Contact twins share a common surface and often look like mirror images across the boundary. Merohedral twinning occurs when the lattices of the contact twins superimpose in three dimensions, such as by relative rotation of one twin from the other.[2]

·       In penetration twins the individual crystals are passing through each other in a symmetrical manner.[3]

·       If several twin crystal parts are aligned by the same twin law, they are referred to as multiple or repeated twins, where the twin law is the set of twin operations mapping two individuals of a twin.

·       Individuals or domains related by operations, such as reflection, inversion or rotation, form a twin called, respectively, reflection twin, inversion twin or rotation twin.[4]                                                               

Fig. 4 Example of a Quartz twin crystal, Peru.

Obtaining of the crystal structure is not easy, as handling of the twinned crystals in X-ray crystallography is not trivial, as they produce a complex diffraction pattern, which is difficult to solve. On the other hand, the smaller the crystal is, the less chances that the crystal is formed of different domains. In that sense, electron diffraction could be a helpful tool to get the structure of those crystals which repeatedly like to grow as (multi)twin domains. For such nano crystals with a less probability of twinning, ED experiments will be the approach to take.

References:

1E. Prince, “International tables for crystallography”, Volume C, 3rd Ed., Kluwer Academic publishers, Dordrecht/Boston/London 2004, 10-14.

2“Crystal twinning”, accessed on September 21, 2020, https://en.wikipedia.org/wiki/Crystal_twinning

3Ibid.

4“Twinning”, accessed on September 21, 2020, https://dictionary.iucr.org/Twinning

 

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