Open-access and free articles in Acta Crystallographica Section A: Foundations of Crystallography
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Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.en-gbCopyright (c) 2018 International Union of CrystallographyInternational Union of CrystallographyInternational Union of Crystallographyhttps://journals.iucr.orgurn:issn:0108-7673Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.text/htmlOpen-access and free articles in Acta Crystallographica Section A Foundations and Advancestextyearly62002-01-01T00:00+00:00med@iucr.orgActa Crystallographica Section A Foundations and AdvancesCopyright (c) 2018 International Union of Crystallographyurn:issn:0108-7673Open-access and free articles in Acta Crystallographica Section A: Foundations of Crystallographyhttp://journals.iucr.org/logos/rss10a.gif
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Still imageA symmetry roadmap to new perovskite multiferroics
http://scripts.iucr.org/cgi-bin/paper?me6013
Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Woodward, P.M.2018-07-05doi:10.1107/S2053273318009294International Union of CrystallographyThe new approach to the design of technologically important perovskites described by Senn and Bristowe [Acta Cryst. (2018), A74, 303–321] is discussed.enPEROVSKITES; MULTIFERROICS; SYMMETRYtext/htmlA symmetry roadmap to new perovskite multiferroicstext4742018-07-05Acta Crystallographica Section A: Foundations and AdvancesCopyright (c) 2018 International Union of Crystallography2053-2733scientific commentaries291med@iucr.orgJuly 20182922053-2733Ted Janssen (1936–2017)
http://scripts.iucr.org/cgi-bin/paper?es5003
urn:issn:2053-2733Souvignier, B.2018-06-06doi:10.1107/S2053273318007088International Union of CrystallographyObituary for Ted Janssen.enOBITUARY; N-DIMENSIONAL CRYSTALLOGRAPHY; APERIODIC STRUCTURES; SUPERSPACE APPROACHtext/htmlTed Janssen (1936–2017) text4742018-06-06Acta Crystallographica Section A: Foundations and Advances2053-2733obituaries403med@iucr.orgJuly 20184042053-2733Indexing of grazing-incidence X-ray diffraction patterns: the case of fibre-textured thin films
http://scripts.iucr.org/cgi-bin/paper?wo5026
Crystal structure solutions from thin films are often performed by grazing-incidence X-ray diffraction (GIXD) experiments. In particular, on isotropic substrates the thin film crystallites grow in a fibre texture showing a well defined crystallographic plane oriented parallel to the substrate surface with random in-plane order of the microcrystallites forming the film. In the present work, analytical mathematical expressions are derived for indexing experimental diffraction patterns, a highly challenging task which hitherto mainly relied on trial-and-error approaches. The six lattice constants a, b, c, α, β and γ of the crystallographic unit cell are thereby determined, as well as the rotation parameters due to the unknown preferred orientation of the crystals with respect to the substrate surface. The mathematical analysis exploits a combination of GIXD data and information acquired by the specular X-ray diffraction. The presence of a sole specular diffraction peak series reveals fibre-textured growth with a crystallographic plane parallel to the substrate, which allows establishment of the Miller indices u, v and w as the rotation parameters. Mathematical expressions are derived which reduce the system of unknown parameters from the three- to the two-dimensional space. Thus, in the first part of the indexing routine, the integers u and v as well as the Laue indices h and k of the experimentally observed diffraction peaks are assigned by systematically varying the integer variables, and by calculating the three lattice parameters a, b and γ. Because of the symmetry of the derived equations, determining the missing parameters then becomes feasible: (i) w of the surface parallel plane, (ii) the Laue indices l of the diffraction peak and (iii) analogously the lattice constants c, α and ß. In a subsequent step, the reduced unit-cell geometry can be identified. Finally, the methodology is demonstrated by application to an example, indexing the diffraction pattern of a thin film of the organic semiconductor pentacenequinone grown on the (0001) surface of highly oriented pyrolytic graphite. The preferred orientation of the crystallites, the lattice constants of the triclinic unit cell and finally, by molecular modelling, the full crystal structure solution of the as-yet-unknown polymorph of pentacenequinone are determined.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Simbrunner, J.Simbrunner, C.Schrode, B.Röthel, C.Bedoya-Martinez, N.Salzmann, I.Resel, R.2018-07-05doi:10.1107/S2053273318006629International Union of CrystallographyCrystal structure solutions from fibre-textured crystals within thin films are frequently achieved by grazing-incidence X-ray diffraction experiments. In the present work, analytical mathematical expressions are derived for the indexing of experimental diffraction patterns.enGRAZING-INCIDENCE X-RAY DIFFRACTION; THIN FILMS; INDEXING; SPECULAR SCAN; MATHEMATICAL CRYSTALLOGRAPHYCrystal structure solutions from thin films are often performed by grazing-incidence X-ray diffraction (GIXD) experiments. In particular, on isotropic substrates the thin film crystallites grow in a fibre texture showing a well defined crystallographic plane oriented parallel to the substrate surface with random in-plane order of the microcrystallites forming the film. In the present work, analytical mathematical expressions are derived for indexing experimental diffraction patterns, a highly challenging task which hitherto mainly relied on trial-and-error approaches. The six lattice constants a, b, c, α, β and γ of the crystallographic unit cell are thereby determined, as well as the rotation parameters due to the unknown preferred orientation of the crystals with respect to the substrate surface. The mathematical analysis exploits a combination of GIXD data and information acquired by the specular X-ray diffraction. The presence of a sole specular diffraction peak series reveals fibre-textured growth with a crystallographic plane parallel to the substrate, which allows establishment of the Miller indices u, v and w as the rotation parameters. Mathematical expressions are derived which reduce the system of unknown parameters from the three- to the two-dimensional space. Thus, in the first part of the indexing routine, the integers u and v as well as the Laue indices h and k of the experimentally observed diffraction peaks are assigned by systematically varying the integer variables, and by calculating the three lattice parameters a, b and γ. Because of the symmetry of the derived equations, determining the missing parameters then becomes feasible: (i) w of the surface parallel plane, (ii) the Laue indices l of the diffraction peak and (iii) analogously the lattice constants c, α and ß. In a subsequent step, the reduced unit-cell geometry can be identified. Finally, the methodology is demonstrated by application to an example, indexing the diffraction pattern of a thin film of the organic semiconductor pentacenequinone grown on the (0001) surface of highly oriented pyrolytic graphite. The preferred orientation of the crystallites, the lattice constants of the triclinic unit cell and finally, by molecular modelling, the full crystal structure solution of the as-yet-unknown polymorph of pentacenequinone are determined.text/htmlIndexing of grazing-incidence X-ray diffraction patterns: the case of fibre-textured thin filmstext4742018-07-05Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers373med@iucr.orgJuly 20183872053-2733A method to estimate statistical errors of properties derived from charge-density modelling
http://scripts.iucr.org/cgi-bin/paper?ae5043
Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Fournier, B.Guillot, B.Lecomte, C.Escudero-Adán, E.C.Jelsch, C.2018-05-03doi:10.1107/S2053273318004308International Union of CrystallographyErrors on molecular properties including the topology of electron density and electrostatics are estimated from a sample of deviating models generated using the variance–covariance matrix issued at the end of the charge-density refinement.enMONTE CARLO METHODS; ELECTRON DENSITY; UNCERTAINTY; TOPOLOGY; INTERMOLECULAR INTERACTIONSEstimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling.text/htmlA method to estimate statistical errors of properties derived from charge-density modellingtext3742018-05-03Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers170med@iucr.orgMay 20181832053-2733Precise implications for real-space pair distribution function modeling of effects intrinsic to modern time-of-flight neutron diffractometers
http://scripts.iucr.org/cgi-bin/paper?ib5055
Total scattering and pair distribution function (PDF) methods allow for detailed study of local atomic order and disorder, including materials for which Rietveld refinements are not traditionally possible (amorphous materials, liquids, glasses and nanoparticles). With the advent of modern neutron time-of-flight (TOF) instrumentation, total scattering studies are capable of producing PDFs with ranges upwards of 100–200 Å, covering the correlation length scales of interest for many materials under study. Despite this, the refinement and subsequent analysis of data are often limited by confounding factors that are not rigorously accounted for in conventional analysis programs. While many of these artifacts are known and recognized by experts in the field, their effects and any associated mitigation strategies largely exist as passed-down `tribal' knowledge in the community, and have not been concisely demonstrated and compared in a unified presentation. This article aims to explicitly demonstrate, through reviews of previous literature, simulated analysis and real-world case studies, the effects of resolution, binning, bounds, peak shape, peak asymmetry, inconsistent conversion of TOF to d spacing and merging of multiple banks in neutron TOF data as they directly relate to real-space PDF analysis. Suggestions for best practice in analysis of data from modern neutron TOF total scattering instruments when using conventional analysis programs are made, as well as recommendations for improved analysis methods and future instrument design.urn:issn:2053-2733Olds, D.Saunders, C.N.Peters, M.Proffen, T.Neuefeind, J.Page, K.2018-06-06doi:10.1107/S2053273318003224International Union of CrystallographyA systematic overview of the effects of common aberrations in time-of-flight neutron powder diffraction data on real-space pair distribution functions is provided, and methods and best practices to mitigate these effects are discussed.enTOTAL SCATTERING; PAIR DISTRIBUTION FUNCTION; INSTRUMENT RESOLUTION FUNCTION; TIME-OF-FLIGHT PEAK SHAPESTotal scattering and pair distribution function (PDF) methods allow for detailed study of local atomic order and disorder, including materials for which Rietveld refinements are not traditionally possible (amorphous materials, liquids, glasses and nanoparticles). With the advent of modern neutron time-of-flight (TOF) instrumentation, total scattering studies are capable of producing PDFs with ranges upwards of 100–200 Å, covering the correlation length scales of interest for many materials under study. Despite this, the refinement and subsequent analysis of data are often limited by confounding factors that are not rigorously accounted for in conventional analysis programs. While many of these artifacts are known and recognized by experts in the field, their effects and any associated mitigation strategies largely exist as passed-down `tribal' knowledge in the community, and have not been concisely demonstrated and compared in a unified presentation. This article aims to explicitly demonstrate, through reviews of previous literature, simulated analysis and real-world case studies, the effects of resolution, binning, bounds, peak shape, peak asymmetry, inconsistent conversion of TOF to d spacing and merging of multiple banks in neutron TOF data as they directly relate to real-space PDF analysis. Suggestions for best practice in analysis of data from modern neutron TOF total scattering instruments when using conventional analysis programs are made, as well as recommendations for improved analysis methods and future instrument design.text/htmlPrecise implications for real-space pair distribution function modeling of effects intrinsic to modern time-of-flight neutron diffractometerstext4742018-06-06Acta Crystallographica Section A: Foundations and Advances2053-2733feature articles293med@iucr.orgJuly 20183072053-2733Spatial displacement of forward-diffracted X-ray beams by perfect crystals
http://scripts.iucr.org/cgi-bin/paper?sc5112
Time-delayed, narrow-band echoes generated by forward Bragg diffraction of an X-ray pulse by a perfect thin crystal are exploited for self-seeding at hard X-ray free-electron lasers. Theoretical predictions indicate that the retardation is strictly correlated to a transverse displacement of the echo pulses. This article reports the first experimental observation of the displaced echoes. The displacements are in good agreement with simulations relying on the dynamical diffraction theory. The echo signals are characteristic for a given Bragg reflection, the structure factor and the probed interplane distance. The reported results pave the way to exploiting the signals as an online diagnostic tool for hard X-ray free-electron laser seeding and for dynamical diffraction investigations of strain at the femtosecond timescale.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Rodriguez-Fernandez, A.Esposito, V.Sanchez, D.F.Finkelstein, K.D.Juranic, P.Staub, U.Grolimund, D.Reiche, S.Pedrini, B.2018-02-23doi:10.1107/S2053273318001419International Union of CrystallographyThe first experimental observation of transverse spatial echoes generated by forward Bragg diffraction of an X-ray beam propagating through a perfect thin crystal is reported.enX-RAY DYNAMICAL DIFFRACTION; PERFECT CRYSTALS; TRANSVERSE ECHO DISPLACEMENT; HARD X-RAY SELF-SEEDINGTime-delayed, narrow-band echoes generated by forward Bragg diffraction of an X-ray pulse by a perfect thin crystal are exploited for self-seeding at hard X-ray free-electron lasers. Theoretical predictions indicate that the retardation is strictly correlated to a transverse displacement of the echo pulses. This article reports the first experimental observation of the displaced echoes. The displacements are in good agreement with simulations relying on the dynamical diffraction theory. The echo signals are characteristic for a given Bragg reflection, the structure factor and the probed interplane distance. The reported results pave the way to exploiting the signals as an online diagnostic tool for hard X-ray free-electron laser seeding and for dynamical diffraction investigations of strain at the femtosecond timescale.text/htmlSpatial displacement of forward-diffracted X-ray beams by perfect crystalstext742https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2018-02-2375research papers2053-2733March 2018med@iucr.org872053-2733The development of powder profile refinement at the Reactor Centre Netherlands at Petten
http://scripts.iucr.org/cgi-bin/paper?ib5058
With thousands of references to `Rietveld refinement' it is forgotten that the method did not suddenly appear in a flash of inspiration of a single person, but was the result of the work of three individuals working in the 1960s at the Reactor Centre Netherlands at Petten, Loopstra, van Laar and Rietveld. This paper outlines the origins of `profile refinement', as it was called at Petten, and also looks at why it took so long for the scientific community to recognize its importance. With the recent passing of Hugo Rietveld, the death of Bert Loopstra in 1998 and before other pioneers also disappear, it is important to set down a first-hand account.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733van Laar, B.Schenk, H.2018-03-01doi:10.1107/S2053273317018435International Union of CrystallographyAround 1965 at the Reactor Centre Netherlands at Petten, Loopstra, van Laar and Rietveld developed `profile refinement'. Although Loopstra had the idea, van Laar worked it out mathematically and Rietveld wrote the computer program, the essential contributions of the first two are forgotten when using `Rietveld refinement'.enPOWDER PROFILE REFINEMENT; PROFILE REFINEMENT; RIETVELD REFINEMENTWith thousands of references to `Rietveld refinement' it is forgotten that the method did not suddenly appear in a flash of inspiration of a single person, but was the result of the work of three individuals working in the 1960s at the Reactor Centre Netherlands at Petten, Loopstra, van Laar and Rietveld. This paper outlines the origins of `profile refinement', as it was called at Petten, and also looks at why it took so long for the scientific community to recognize its importance. With the recent passing of Hugo Rietveld, the death of Bert Loopstra in 1998 and before other pioneers also disappear, it is important to set down a first-hand account.text/htmlThe development of powder profile refinement at the Reactor Centre Netherlands at Pettentext742https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2018-03-0188scientific comment2053-2733March 2018med@iucr.org922053-2733Quasicrystals: What do we know? What do we want to know? What can we know?
http://scripts.iucr.org/cgi-bin/paper?ib5056
More than 35 years and 11 000 publications after the discovery of quasicrystals by Dan Shechtman, quite a bit is known about their occurrence, formation, stability, structures and physical properties. It has also been discovered that quasiperiodic self-assembly is not restricted to intermetallics, but can take place in systems on the meso- and macroscales. However, there are some blank areas, even in the centre of the big picture. For instance, it has still not been fully clarified whether quasicrystals are just entropy-stabilized high-temperature phases or whether they can be thermodynamically stable at 0 K as well. More studies are needed for developing a generally accepted model of quasicrystal growth. The state of the art of quasicrystal research is briefly reviewed and the main as-yet unanswered questions are addressed, as well as the experimental limitations to finding answers to them. The focus of this discussion is on quasicrystal structure analysis as well as on quasicrystal stability and growth mechanisms.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Steurer, W.2018-01-01doi:10.1107/S2053273317016540International Union of CrystallographyThe state of the art of quasicrystal research is critically reviewed. Fundamental questions that are still unanswered are discussed and experimental limitations are considered.enQUASICRYSTALS; STRUCTURE ANALYSIS; HIGHER-DIMENSIONAL CRYSTALLOGRAPHY; STABILITY OF QUASICRYSTALS; QUASICRYSTAL GROWTHMore than 35 years and 11 000 publications after the discovery of quasicrystals by Dan Shechtman, quite a bit is known about their occurrence, formation, stability, structures and physical properties. It has also been discovered that quasiperiodic self-assembly is not restricted to intermetallics, but can take place in systems on the meso- and macroscales. However, there are some blank areas, even in the centre of the big picture. For instance, it has still not been fully clarified whether quasicrystals are just entropy-stabilized high-temperature phases or whether they can be thermodynamically stable at 0 K as well. More studies are needed for developing a generally accepted model of quasicrystal growth. The state of the art of quasicrystal research is briefly reviewed and the main as-yet unanswered questions are addressed, as well as the experimental limitations to finding answers to them. The focus of this discussion is on quasicrystal structure analysis as well as on quasicrystal stability and growth mechanisms.text/htmlQuasicrystals: What do we know? What do we want to know? What can we know?text741https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2018-01-011topical reviews2053-2733January 2018med@iucr.org112053-2733Small-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements
http://scripts.iucr.org/cgi-bin/paper?vk5021
Small-angle X-ray scattering tensor tomography, which allows reconstruction of the local three-dimensional reciprocal-space map within a three-dimensional sample as introduced by Liebi et al. [Nature (2015), 527, 349–352], is described in more detail with regard to the mathematical framework and the optimization algorithm. For the case of trabecular bone samples from vertebrae it is shown that the model of the three-dimensional reciprocal-space map using spherical harmonics can adequately describe the measured data. The method enables the determination of nanostructure orientation and degree of orientation as demonstrated previously in a single momentum transfer q range. This article presents a reconstruction of the complete reciprocal-space map for the case of bone over extended ranges of q. In addition, it is shown that uniform angular sampling and advanced regularization strategies help to reduce the amount of data required.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Liebi, M.Georgiadis, M.Kohlbrecher, J.Holler, M.Raabe, J.Usov, I.Menzel, A.Schneider, P.Bunk, O.Guizar-Sicairos, M.2018-01-01doi:10.1107/S205327331701614XInternational Union of CrystallographyThe mathematical framework and reconstruction algorithm for small-angle scattering tensor tomography are introduced in detail, as well as strategies which help to reduce the amount of data and therewith the measurement time required. Experimental validation is provided for the application to trabecular bone.enSMALL-ANGLE X-RAY SCATTERING; TENSOR TOMOGRAPHY; SPHERICAL HARMONICS; BONESmall-angle X-ray scattering tensor tomography, which allows reconstruction of the local three-dimensional reciprocal-space map within a three-dimensional sample as introduced by Liebi et al. [Nature (2015), 527, 349–352], is described in more detail with regard to the mathematical framework and the optimization algorithm. For the case of trabecular bone samples from vertebrae it is shown that the model of the three-dimensional reciprocal-space map using spherical harmonics can adequately describe the measured data. The method enables the determination of nanostructure orientation and degree of orientation as demonstrated previously in a single momentum transfer q range. This article presents a reconstruction of the complete reciprocal-space map for the case of bone over extended ranges of q. In addition, it is shown that uniform angular sampling and advanced regularization strategies help to reduce the amount of data required.text/htmlSmall-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirementstext741https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2018-01-0112research papers2053-2733January 2018med@iucr.org242053-2733{\bb Z}-module defects in crystals
http://scripts.iucr.org/cgi-bin/paper?td5044
An analysis is presented of the new types of defects that can appear in crystalline structures where the positions of the atoms and the unit cell belong to the same {\bb Z}-module, i.e. are irrational projections of an N > 3-dimensional (N-D) lattice Λ as in the case of quasicrystals. Beyond coherent irrationally oriented twins already discussed in a previous paper [Quiquandon et al. (2016). Acta Cryst. A72, 55–61], new two-dimensional translational defects are expected, the translation vectors of which, being projections of nodes of Λ, have irrational coordinates with respect to the unit-cell reference frame. Partial dislocations, called here module dislocations, are the linear defects bounding these translation faults. A specific case arises when the Burgers vector B is the projection of a non-zero vector of Λ that is perpendicular to the physical space. This new kind of dislocation is called a scalar dislocation since, because its Burgers vector in physical space is zero, it generates no displacement field and has no interaction with external stress fields and other dislocations.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Sirindil, A.Quiquandon, M.Gratias, D.2017-10-26doi:10.1107/S2053273317013882International Union of CrystallographyNew kinds of defects can appear in crystals where the atoms and unit cell sit on the nodes of {\bb Z}-modules, i.e. on three-dimensional projections of N-dimensional lattices. These defects are the result of the symmetry breaking due to the projection of the structure from N to three dimensions. Examples are given that illustrate the processes. A new kind of dislocation, here called a `scalar dislocation', is expected; it generates no deformation and has no interaction with stress fields.en{\BB Z}-MODULES; INTERMETALLIC ALLOYS; DEFECTS; TWINS; DISLOCATIONSAn analysis is presented of the new types of defects that can appear in crystalline structures where the positions of the atoms and the unit cell belong to the same {\bb Z}-module, i.e. are irrational projections of an N > 3-dimensional (N-D) lattice Λ as in the case of quasicrystals. Beyond coherent irrationally oriented twins already discussed in a previous paper [Quiquandon et al. (2016). Acta Cryst. A72, 55–61], new two-dimensional translational defects are expected, the translation vectors of which, being projections of nodes of Λ, have irrational coordinates with respect to the unit-cell reference frame. Partial dislocations, called here module dislocations, are the linear defects bounding these translation faults. A specific case arises when the Burgers vector B is the projection of a non-zero vector of Λ that is perpendicular to the physical space. This new kind of dislocation is called a scalar dislocation since, because its Burgers vector in physical space is zero, it generates no displacement field and has no interaction with external stress fields and other dislocations.text/html{\bb Z}-module defects in crystalstext736https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2017-10-26427research papers2053-2733November 2017med@iucr.org4372053-2733