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91.
Felix Lehmkühler Gerhard Grübel Christian Gutt 《Journal of Applied Crystallography》2014,47(4):1315-1323
The results of a computational X‐ray cross‐correlation analysis (XCCA) study on two‐dimensional polygonal model structures are presented. This article shows how to detect and identify the orientational order of such systems, demonstrates how to eliminate the influence of the `computational box' on the XCCA results and develops new correlation functions that reflect the sample's orientational order only. For this purpose, the dependence of the correlation functions on the number of polygonal clusters and scattering vector magnitude q is studied for various types of polygons, including mixtures of polygons and randomly placed particles. An order parameter that describes the orientational order within the sample is defined. Finally, the influence of detector noise and nonplanar wavefronts on the XCCA data is determined, both of which appear to affect the results significantly and have thus to be considered in real experiments. 相似文献
92.
Martin Rosenthal Denis V. Anokhin Matthieu Defaux Giuseppe Portale Dimitri A. Ivanov 《Journal of Applied Crystallography》2011,44(4):805-811
Small‐angle X‐ray scattering interface distribution function (IDF) analysis is successfully applied to evaluate the two‐ and three‐phase inter‐platelet gallery structure in synthetic montmorillonite (MMT) modified with a mixture of chemically grafted and physically adsorbed chains of a typical organic modifier, octadecyl trimethyl ammonium bromide. Two distinctly different states of adsorbed chains in the inter‐platelet galleries are identified. The first one corresponds to a fully cation‐exchanged structure with an inter‐platelet distance of about 21 Å. In this case the organic modifier is in a liquid‐like state, and the system does not exhibit any structural or thermal transitions between ambient temperature and 433 K. When the number of adsorbed chains exceeds the cation‐exchange capacity of the MMT platelets the inter‐platelet spacing is increased to 43 Å. In this case, the variable‐temperature IDFs reveal partially crystalline order in the inter‐platelet galleries, which vanishes at the melting point of the alkyl tails confined in the galleries. 相似文献
93.
JianFeng Zhang Erich H. Kisi Oliver Kirstein 《Journal of Applied Crystallography》2011,44(5):1062-1070
Orientation distribution functions, essential for making a quantitative connection between single‐crystal and polycrystal properties, have been determined for extruded α‐phase alumina, hot‐pressed Ti3AlC2 and cold isostatically pressed Ti3AlC2 using experimental pole figures recorded on the fixed‐wavelength neutron diffractometer KOWARI. Some practical improvements to the calculation of the pole‐figure density from the raw area‐detector data, and for constructing pole figures on an n×n° hemispherical grid, are presented. The textures give some insight into particle flow during manufacture. Directly measured material textures were compared with one‐dimensional pole density functions, such as the March and Rietveld functions commonly used for the correction of preferred orientation in Rietveld refinements, as a means of assessing the utility of the latter for the computation of diffraction elastic constants and other polycrystal properties from a given set of single‐crystal properties. 相似文献
94.
Katharine Page Taylor C. Hood Thomas Proffen Reinhard B. Neder 《Journal of Applied Crystallography》2011,44(2):327-336
High‐energy X‐ray and spallation neutron total scattering data provide information about each pair of atoms in a nanoparticle sample, allowing for quantitative whole‐particle structural modeling based on pair distribution function analysis. The realization of this capability has been hindered by a lack of versatile tools for describing complex finite structures. Here, the implementation of whole‐particle refinement for complete nanoparticle systems is described within two programs, DISCUS and DIFFEV, and the diverse capabilities they present are demonstrated. The build‐up of internal atomic structure (including defects, chemical ordering and other types of disorder), and nanoparticle size, shape and architecture (including core–shell structures, surface relaxation and ligand capping), are demonstrated using the program DISCUS. The structure refinement of a complete nanoparticle system (4 nm Au particles with organic capping ligands at the surface), based on neutron pair distribution function data, is demonstrated using DIFFEV, a program using a differential evolutionary algorithm to generate parameter values. These methods are a valuable addition to other probes appropriate for nanomaterials, adaptable to a diverse and complex set of materials systems, and extendable to additional data‐set types. 相似文献
95.
Katharine Page Claire E. White Eben G. Estell Reinhard B. Neder Anna Llobet Thomas Proffen 《Journal of Applied Crystallography》2011,44(3):532-539
Nuclear incoherent neutron scattering contributions present a challenge in the structural characterization of many classes of materials. This article introduces methods for the correction of nanoparticle, bulk crystalline and amorphous powder neutron scattering data with significant incoherent contributions from hydrogen, and describes the effects the corrections have on the resulting atomic pair distribution function data sets. The approach is presented in the context of the PDFgetN data‐reduction program [Peterson, Gutmann, Proffen & Billinge (2000). J. Appl. Cryst. 33 , 1192]. 相似文献
96.
P. Juhs L. Granlund S. R. Gujarathi P. M. Duxbury S. J. L. Billinge 《Journal of Applied Crystallography》2010,43(3):623-629
An extension of the Liga algorithm for structure solution from atomic pair distribution functions (PDFs), to handle periodic crystal structures with multiple elements in the unit cell, is described. The procedure is performed in three separate steps. First, pair distances are extracted from the experimental PDF. In the second step the Liga algorithm is used to find unit‐cell sites consistent with these pair distances. Finally, the atom species are assigned over the cell sites by minimizing the overlap of their empirical atomic radii. The procedure has been demonstrated on synchrotron X‐ray PDF data from 16 test samples. The structure solution was successful for 14 samples, including cases with enlarged supercells. The algorithm success rate and the reasons for the failed cases are discussed, together with enhancements that should improve its convergence and usability. 相似文献
97.
Herein, a general method to calculate the scattering functions of polyhedra, including both regular and semi‐regular polyhedra, is presented. These calculations may be achieved by breaking a polyhedron into sets of congruent pieces, thereby reducing computation time by taking advantage of Fourier transforms and inversion symmetry. Each piece belonging to a set or subunit can be generated by either rotation or translation. Further, general strategies to compute truncated, concave and stellated polyhedra are provided. Using this method, the asymptotic behaviors of the polyhedral scattering functions are compared with that of a sphere. It is shown that, for a regular polyhedron, the form factor oscillation at high q is correlated with the face‐to‐face distance. In addition, polydispersity affects the Porod constant. The ideas presented herein will be important for the characterization of nanomaterials using small‐angle scattering. 相似文献
98.
This article discusses the potential problems and currently available solutions in modeling powder‐diffraction‐based pair distribution function (PDF) data from systems where morphological feature information content includes distances in the nanometre length scale, such as finite nanoparticles, nanoporous networks and nanoscale precipitates in bulk materials. The implications of an experimental finite minimum Q value are reviewed by simulation, which also demonstrates the advantages of combining PDF data with small‐angle scattering data. A simple Fortran90 code, DShaper, is introduced, which may be incorporated into PDF data fitting routines in order to approximate the so‐called `shape function' for any atomistic model. 相似文献
99.
In this paper we prove some interesting extensions and generalizations of Enestrom- Kakeya Theorem concerning the location of the zeros of a polynomial in a complex plane. We also obtain some zero-free regions for a class of related analytic functions. Our results not only contain some known results as a special case but also a variety of interesting results can be deduced in a unified way by various choices of the parameters. 相似文献
100.
D. Costarelli & R. Spigler 《分析论及其应用》2013,29(2):169-196
In this paper, a constructive theory is developed for approximating functions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the $L^p$ norm. Results for the simultaneous approximation, with the same order of accuracy, of a function and its derivatives (whenever these exist), are obtained. The relation with neural networks and radial basis functions approximations is discussed. Numerical examples are given for the purpose of illustration. 相似文献