Neutron Powder Diffraction Research Articles

Low-temperature crystal structures of the solvent dimethyl carbonate

Dimethyl carbonate (DMC) is an important industrial solvent but is additionally a common component of liquid lithium-ion battery electrolytes. Pure DMC has a melting point of 277 K, so encountering solidification under outdoor climatic conditions is very likely in many locations around the globe. Even eutectic, ethylene carbonate:dimethyl carbonate commercial LiPF6 salt electrolyte formulations can start to solidify at temperatures around 260 K with obvious consequences for their performance. No structures for crystalline DMC are currently available which could be a hindrance for in situ battery studies at reduced temperatures. A time-of-flight neutron powder diffraction study of the phase behavior and crystal structures of deuterated DMC was undertaken to help fill this knowledge gap. Three different orthorhombic crystalline phases were found with a previously unreported low-temperature phase transition around 50–55 K. The progression of Pbca → Pbcm → Ibam space groups follow a sequence of group–subgroup relationships with the final Ibam structure being disordered around the central carbon atom.

Temperature Dependent Crystal Structure of Nd2CuTiO6: An In Situ Low Temperature Powder Neutron Diffraction Study

Herein we reported the crystal structure and crystal chemistry of orthorhombic perovskite type Nd2CuTiO6 in between 2 K and 290 K as observed from the in situ temperature-dependent powder neutron diffraction (PND) studies. It is observed that the cations in octahedral sites are statistically occupied, and the ambient temperature orthorhombic structure is retained throughout the temperature range of the study. Absence of any long-range magnetic ordering down to 2 K is confirmed by both low-temperature PND and magnetization studies. The lattice shows strong anisotropic thermal expansion with increasing temperature, viz. almost no or feeble negative expansion along the a-axis while appreciably larger expansion along the other two axes (αb = 10.6 × 10−6 K−1 and αc = 9.8 × 10−6 K−1). A systematic change in the rotation of octahedral units with temperature was observed in the studied temperature range, while the expansion of unit cells is predominantly associated with the polyhedral units around the Nd3Ions. The temperature-dependent relative change in unit cell parameters as well as coefficients of axial thermal expansion show anomalous behavior at lower temperatures, and that seems to be related to the electronic contributions to lattice expansion.

Polyhedral Distortions and Unusual Magnetic Order in Spinel FeMn2O4.

Spinel compounds AB2X4 consist of both tetrahedral (AX4) and octahedral (BX6) environments with the former forming a diamond lattice and the latter a geometrically frustrated pyrochlore lattice. Exploring the fascinating physical properties and their correlations with structural features is critical in understanding these materials. FeMn2O4 has been reported to exhibit one structural transition and two successive magnetic transitions. Here, we report the polyhedral distortions and their correlations to the structural and two magnetic transitions in FeMn2O4 by employing the high-resolution neutron powder diffraction. The cation distribution is found to be (Mn0.92+Fe0.13+)A(Mn3+Fe0.93+Mn0.12+)BO4. While large trigonal distortion is found even in the high-temperature cubic phase, the first-order cubic-tetragonal structural transition associated with the elongation of both tetrahedra and octahedra with shared oxygen atoms along the c axis occurs at TS ≈ 750 K, driven by the Jahn-Teller effect of the orbital active B-site Mn3+ cation. Strong magnetoelastic coupling is unveiled at TN1 ≈ 400 K as manifested by the appearance of Néel-type collinear ferrimagnetic order, an anomaly in both tetrahedral and octahedral distortions, as well as an anomalous decrease of the lattice constants c and a weak anomaly of a. Upon cooling to TN2 ≈ 65 K, it evolves to a noncollinear ferrimagnetic order accompanied by the different moments at the split magnetic sites B1 and B2. Only one-half of the B-site Mn3+/Fe3+ spins, i.e., the B2-site spins in the pyrochlore lattice, are canted, which is a unique magnetic order among spinels. The canting angle between A-site and B2-site moments is ∼25°, but the B1-site moment stays antiparallel to the A-site moment even at 10 K. This noncollinear order is accompanied by a modification of the O-B-O bond angles in the octahedra without significant change in lattice constants or tetrahedral/octahedral distortion parameters, indicating a distinct magnetoelastic coupling. We demonstrate distinct roles of the A-site and B-site magnetic cations in the structural and magnetic properties of FeMn2O4. Our study indicates that FeMn2O4 is a wonderful platform to unveil interesting magnetic order and to investigate their correlations with polyhedral distortions and lattice.

Noncoplanar antiferromagnetism induced zero thermal expansion behavior in the antiperovskite Mn3Sn0.5Zn0.5Cx

Zero thermal expansion (ZTE) is one of the most fascinating phenomena in condensed-matter physics due to its strong correlation essence and great application prospect. However, the origin of ZTE remains elusive and it becomes an overwhelming challenge to realize the controllable design for which magnetic interaction plays a key role. In this work, with the help of neutron powder diffraction analysis, a noncoplanar $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ antiferromagnetic (AFM) phase is experimentally obtained in the antiperovskite system ${\mathrm{Mn}}_{3}{\mathrm{Sn}}_{0.5}{\mathrm{Zn}}_{0.5}{\mathrm{C}}_{x}$. It shows ZTE behavior in a particularly wide temperature range from 10 to 162 K with linear thermal expansion coefficient 9.3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$. Herein, the theoretical spin model is combined with the experimental results to well understand the strong spin-lattice correlation between AFM ordering and ZTE behavior. The ZTE in the noncoplanar antiferromagnetic ordered system is attributed to the fierce competition between the nearest AFM direct exchange and ferromagnetic superexchange interaction, which is effectively tuned by C occupation. Our work not only paves the way toward understanding the physical origin of ZTE, but it also provides a feasible strategy for the ZTE design, which is also of great significance for promoting the study of a strong correlation system.

Enhanced Li‐ion conductivity of strontium doped Li‐excess garnet‐type Li7+xLa3‐xSrxZr2O12

AbstractThe mechanism underlying the enhancement of the conductivity of Li7La3Zr2O12 (LLZO), an oxide‐based solid electrolyte that contains excess Li, was experimentally investigated through subvalent cation substitution. We prepared Sr‐substituted Li‐rich LLZO with high conductivity of the order of 10−4 S/cm by using a solid‐state method. We investigated the mechanism underlying the conductivity enhancement via detailed structural analysis through Sr K‐edge X‐ray absorption near edge spectroscopy and X‐ray diffraction and neutron powder diffraction analyses. The results suggested that the conductivity enhancement is due to the change in Li+ arrangement caused by the incorporation of excess Li into the LLZO lattice.

Antiferromagnetism and Structure of Sr1−xBaxFeO2F Oxyfluoride Perovskites

Recently, a series of oxyfluorides, Sr1−xBaxFeO2F with x = 0, 0.25, 0.50, and 0.75 obtained through a novel synthesis route, were characterized by X-ray and neutron powder diffraction (NPD), magnetization measurements, and 57Fe Mössbauer spectroscopy (MS). The diffraction data revealed random occupancy of Sr and Ba atoms at the A-cation site, and a statistical distribution of O and F at the anionic sublattice of the perovskite-like structure specified in space group Pm-3m. MS spectra analysis consistently indicated the presence of Fe3+ ions at B-site, confirming the Sr1−xBaxFeO2F stoichiometry. Magnetic structure determination from the NPD data at room temperature established G-type antiferromagnetic arrangement in all compositions with Fe3+ moments of about 3.5 μB oriented along the c axis. In this study, we present and analyze additional NPD data concerning the low-temperature chemical and magnetic structure of Sr0.5Ba0.5FeO2F (x = 0.5) and SrFeO2F (x = 0). Basically, the three-dimensional G-type magnetic structure is maintained down to 2 K, where it is fully developed with an ordered magnetic moment of 4.25(5) μB/Fe at this temperature for x = 0.5 and 4.14(3) μB/Fe for x = 0. The data processing is complemented with a new approach to analyze the temperature dependence of the magnetic order TN on the lattice parameters, based on the magnetic hyperfine fields extracted from the temperature-dependent MS data.

Structure Determination and Analysis of the Ceramic Material La0.987Ti1.627Nb3.307O13 by Synchrotron and Neutron Powder Diffraction and DFT Calculations

In this paper, the ternary system La2O3-TiO2-Nb2O5 is studied to find new ternary phases with useful electrical properties. The solid solution La3−xTi5−3xNb10−2xO39.5−12.5x was recently identified, and this study focuses on the structural characterization of this solid solution with x = 0.04. The crystal structure, representing a new structural type, was determined from synchrotron and neutron powder diffraction data. The unit cell parameters are a = 7.332 Å, b = 7.421 Å, c = 10.673 Å, α = 84.15°, ß = 80.16°, γ = 60.37°, and space group P1¯. The titanium and niobium atoms are disordered in five different crystallographic sites coordinated octahedrally by oxygen atoms. The eight-coordinated La atoms are embedded in the octahedral framework. Ti and Nb preferentially occupy different sites, and this feature was studied using periodic density functional theory methods. Energies of possible Ti/Nb distributions were calculated and the results agree well with the site occupancies obtained by combined Rietveld refinement of synchrotron and neutron powder diffraction patterns. The geometries optimized by DFT also agree well with the structural parameters determined by diffraction. The general agreement between the theoretical calculations and the experimental data justifies the quantum chemical methods as reliable complementary tools for the structural investigation of ceramic materials.

Combined X-ray and Neutron Powder Diffraction Study on B-Site Cation Ordering in Complex Perovskite La2(Al1/2MgTa1/2)O6

Complex perovskite La2(Al1/2MgTa1/2)O6 (LAMT) crystallizes in a monoclinic unit cell with space group P21/n at room temperature. Its B-site cations are ordered in a rock-salt-type arrangement. Previously, the full occupancy of Mg on the 2c-Wyckoff position was deduced from powder X-ray diffraction (PXRD). However, conventional X-rays could not properly resolve the mixed occupation on the B-site, since there is little scattering contrast between the neighbouring elements Mg and Al of the periodic table. Hence, complementary neutron diffraction studies were carried out to verify the exact B-site cation ordering in the unit cell. In this specific configuration of the B-cations, with its occupancy ratio and the presence of a heavy element Ta as well as neighbouring elements Mg and Al, only the strategy of a combined Rietveld analysis using both the X-ray and neutron diffraction data simultaneously succeeded in elucidating an accurate B-site cation ordering in this complex perovskite system. A full occupancy of Mg on the 2c-Wyckoff position and each a half occupancy of Al and Ta on the 2d-Wyckoff position could be resolved for the rock-salt-type ordering of the B-site cations in the monoclinic unit cell of LAMT.

Control of the pore chemistry in metal-organic frameworks for efficient adsorption of benzene and separation of benzene/cyclohexane

Control of the pore chemistry in metal-organic frameworks for efficient adsorption of benzene and separation of benzene/cyclohexane

Canting Angle Behavior of Magnetic Moments in Y‐Substituted Tb2BaNiO5 and Its Relevance for Magnetoelectric Coupling

The Haldane‐spin chain compound, Tb2BaNiO5, has been known to be an exotic multiferroic system, exhibiting antiferromagnetic anomalies at T N1 = 63 K and T N2 = 25 K, with ferroelectricity appearing below T N2 only. Previous reports in addition have established that, interestingly, Tb ions play a direct and decisive role to lead to multiferroic properties with a critical canting angle of magnetic moments, unlike other well‐known multiferroics. Herein, the results of temperature‐dependent neutron powder diffraction studies on Tb2–x Y x BaNiO5 are reported, to get an insight into the critical canting angle for multiferroic behavior. While multiferroic transition temperature decreases linearly with Y concentration, there is an abrupt drop of relative canting angle (of Tb and Ni magnetic moments) with respect to that in the parent compound for an initial substitution of x = 0.5 in the multiferroic region, without any notable change thereafter. Therefore, it is inferred that this critical canting angle is made up of two components—cooperative (long‐range) and local (short‐range) contributions.

Metal-to-Insulating Transition in the Perovskite System YSr2Cu2FeO8-δ (0 < δ < 1) Modeled by DFT Methods.

Progress in the design of functional perovskite oxides relies on advances in density functional theory (DFT) methods to efficiently and effectively model complex systems composed of several transition-metal ions. This work reports the application of DFT methods to investigate the electronic structure of the YSr2Cu2FeO8-δ (0 < δ < 1) family in which the insulating, metal, or superconducting behaviors and even anion conductivity can be tuned by modifying the oxygen content. In particular, we assess the performance of the generalized gradient approximation (GGA), its Hubbard-U correction (GGA + U), and the strongly constrained and appropriately normed (SCAN) to model the metallic (idealized YSr2Cu2FeO8) and insulating (idealized YSr2Cu2FeO7) phases of the system. The analysis of the DFT results is supported by DC resistivity measurements that denote the metal character of the synthesized YSr2Cu2FeO7.86 and the semiconducting character of YSr2Cu2FeO7.08 prepared under reducing conditions. In addition, the band gap of YSr2Cu2FeO7.08, in the range of 0.73-1.2 eV, has been extracted from diffuse reflectance spectroscopy (DRS). While the three methodologies (GGA, GGA + U, SCAN) permit the reproduction of the crystal structures of the synthetized oxides (determined here in the case of YSr2Cu2FeO7.08 by neutron powder diffraction (NPD)), the SCAN emerges as the only one capable to predict the basic electronic and magnetic properties across the YSr2Cu2FeO8-δ (0 < δ < 1) series. The picture that emerges for the metal (δ = 0) to insulating (δ = 1) transition is the one in which oxygen vacancies contribute electrons to the filling of the Cu/Fe-3dx2-y2 states of the conduction band. These results validate the SCAN functional for future DFT investigations of complex functional oxides that combine several transition metals.

Search for octupolar order in NpO2 by neutron powder diffraction

The magnetic structure of neptunium dioxide (NpO2) remains a mystery despite decades of research. We revisited the search for magnetic ordering in NpO2 by performing a powder neutron diffraction experiment at low temperatures and relatively large values of Q. Diffraction data were collected for 300 ​mK, 15 ​K, and 35 ​K to understand the phase transition near 25 ​K. However, no significant changes in the neutron diffraction pattern were identified. Using the octupolar magnetic form factor j6, the maximum theoretical expected value of the magnetic moment (3.27 μB), the calculated magnetic Bragg peak intensities would not be observable in neutron powder diffraction data. This value is much larger than the previously estimated magnetic moment of ∼0.1 μB. Supported by experimental results, these calculations suggest that unpolarized neutron powder diffraction is unsuitable for measuring octupolar ordering in NpO2.

Magnetoelastic effect in R2Ni2In (R = Tb and Tm) investigated by neutron powder diffraction

ABSTRACT Magnetoelastic effect in R2Ni2In (R = Tb, Tm), associated with the antiferro- to paramagnetic phase transition at the Néel temperature TN equal to 40 K (R = Tb) or 4.8 K (R = Tm), has been investigated by neutron powder diffraction. Rietveld refinement reveals that the orthorhombic crystal structure, reported at room temperature, is stable down to low temperatures, including magnetically ordered state. Based on the diffraction data, thermal evolution of the lattice parameters a, b and c and the unit cell volume V have been determined. Both the lattice parameters as well as the unit cell volume show distinct jumps in the vicinity of the respective Néel temperatures, indicating presence of the magnetoelastic effect. The values of the lattice strains Δa, Δb, Δc and change of the unit cell volume ΔV, associated with the antiferro- to paramagnetic phase transition, are reported.

Long-range A-site cation disorder in NaA(MO4)2 (M = Mo, W) double scheelite oxides

Synchrotron X-ray and neutron powder diffraction methods have been used to obtain accurate long-range average structures of some double scheelite compounds of the type NaA(BO4)2 (A ​= ​La, Pr, Nd, Sm, Lu, and Bi; B = Mo, W) at room temperature. Phase pure samples were synthesized using standard solid-state methods. Rietveld refinements using combined synchrotron X-ray diffraction (SXRD) and neutron diffraction (NPD) revealed a random distribution of the Na and A-type cations regardless of the presence of 6s2 lone pairs (such as Bi3+) and the difference in oxidation states and ionic radii between the cations. The NaA(BO4)2 (A ​= ​La, Pr, Nd, Sm, Lu, and Bi) series displayed linear trends in lattice parameters and AO8 polyhedra volume with the ionic radius of the A-type cation for the lanthanoids, but a deviation from the trend was observed for A ​= ​Bi3+. The NaBi(BO4)2 structure has a smaller than expected unit cell volume than based on extrapolation from the corresponding NaLn(BO4)2 series, possibly due to short-range ordering of the 6s2 lone pair electrons.

Insights into thermodynamic destabilization in Mg-In-D hydrogen storage system: A combined synchrotron X-ray and neutron diffraction study

In this study, ultrafine Mg(In) solid-solution particles were successfully prepared through an arc plasma method and their deuterium uptake/release performances were systematically estimated with respect to the identically processed pure Mg particles. Thermodynamic destabilization and kinetic enhancement of Mg-In-D system were achieved simultaneously with lower deuterium ab/desorption enthalpies and decreased desorption temperatures. For the first time, an in-situ synchrotron X-ray diffraction (ISXRD) coupled with neutron powder diffraction (NPD) technique and density functional theory (DFT) calculations clearly substantiated that an indium diffusion-dominated phase transition is the driving force for the evolution from mixture of MgD2 and Mg-In intermetallic to Mg-based solid solution during the deuterium release (DR). The ISXRD results clarified the real-time phase transition from MgIn to Mg3In at 515 K and the interreaction of MgD2 and Mg3In at 640 K, by which the matrix could be destabilized to trigger an indium-diffusion governed DR reaction in deuteride. Moreover, with the aid of NPD experiment, the microstructure evolution of Mg-In-D system demonstrated the continuous diffusion of indium into Mg/MgD2 upon desorption. The solubilized indium in MgD2 effectively reduced the D-migration energy barrier and stabilized the lattice structure to restrain the constriction of Mg-D bonds, through which the noticeable improvement on both thermodynamic and kinetic performances of the Mg-In system was achieved. The combination of synchrotron X-ray and neutron diffraction offers a high-efficiency strategy to fathom the hydrogen discharging mechanism from the viewpoint of real-time phase transitions and crystalline structure evolutions.

One-dimensional quantum magnetism in the S=12 Mo(V) system KMoOP2O7

We present a comprehensive experimental and ab-initio study of the $S=1/2$ Mo$^{5+}$ system, KMoOP$_2$O$_7$, and show that it realizes the $S = 1/2$ Heisenberg chain antiferromagnet model. Powder neutron diffraction reveals that KMoOP$_2$O$_7$ forms a magnetic network comprised of pairs of Mo$^{5+}$ chains within its monoclinic $P2_1/n$ structure. Antiferromagnetic interactions within the Mo$^{5+}$ chains are identified through magnetometry measurements and confirmed by analysis of the magnetic specific heat. The latter reveals a broad feature centred on $T_\textrm{N} = 0.54$ K, which we ascribe to the onset of long-range antiferromagnetic order. No magnetic Bragg scattering is observed in powder neutron diffraction data collected at 0.05 K, however, which is consistent with a strongly suppressed ordered moment with an upper limit $\mu_\textrm{ord} < 0.15 \mu_\textrm{B}$. The one-dimensional character of the magnetic correlations in KMoOP$_2$O$_7$ is verified through analysis of inelastic neutron scattering data, resulting in a model with $J_\textrm{1} \approx 34$ K and $J_\textrm{2} \approx -2$ K for the intrachain and interchain exchange interactions, respectively. The origin of these experimental findings are addressed through density-functional theory calculations.

Topological magnetic structures in MnGe: Neutron diffraction and symmetry analysis

From new neutron powder diffraction experiments on the chiral cubic ($P2{_1}3$) magnet manganese germanide MnGe, we analyse all of the possible crystal symmetry-allowed magnetic superstructures that are determined successfully from the data. The incommensurate propagation vectors $k$ of the magnetic structure are found to be aligned with the [100] cubic axes, and correspond to a magnetic periodicity of about 30 $\r{A}$ at 1.8 K. Several maximal crystallographic symmetry magnetic structures are found to fit the data equally well and are presented. These include topologically non-trivial magnetic hedgehog and "skyrmion'' structures in multi-$k$ cubic or orthorhombic 3+3 and orthorhombic 3+2 dimensional magnetic superspace groups respectively, with either potentially responsible for topological Hall effect. The presence of orthorhombic distortions in the space group $P2_12_12_1$ caused by the transition to the magnetically ordered state does not favour the cubic magnetic hedgehog structure, and leave both orthorhombic hedgehog and "skyrmion'' models as equal candidates for the magnetic structures. We also report on a new combined mechanochemical and solid-state chemical route to synthesise MnGe at ambient pressures and moderate temperatures, and compare with samples obtained by the traditional high pressure synthesis.

Reducing the Cobalt Content in SrCo0.95Ti0.05O3-δ-Based Perovskites to Produce Cleaner Cathodes for IT-SOFCs

Recent studies have demonstrated the possibility of stabilizing the cubic or tetragonal perovskite phases in the SrCoO3-δ system at room temperature by partially replacing Co atoms with small amounts of highly charged cations like Ti4+ in SrCo0.95Ti0.05O3-δ. This material gives extraordinary performances as a cathode for solid oxide fuel cells (SOFCs) at intermediate temperatures (800–850 °C). In this work, we have tried to still improve this cathode in a cleaner and low-priced material by reducing its Co content, since Co is a high-cost and toxic element, additionally reducing its thermal expansion coefficient (TEC), to make it more mechanically compatible with the rest of the components of a SOFC. SrCo0.50Fe0.45Ti0.05O3-δ perovskite has been obtained by the citrate method, introducing 45% of Fe in the Co and Ti positions. Its crystalline structure has been studied by X-ray diffraction (XRD) and neutron powder diffraction (NPD) and has been correlated with mechanical and electrical properties. A chemical compatibility study between SrCo0.50Fe0.45Ti0.05O3-δ and the electrolyte La0.8Sr0.2Ga0.83Mg0.17O3-δ (LSGM) revealed that both materials do not interact at high temperatures. TEC measurements show a linear expansion over the entire temperature range. Finally, the perovskite showed good electrical conductivity and an encouraging power density value of 667 mW/cm2 at 850 °C, which indicate that this material is a promising cathode for SOFCs at intermediate temperatures.

Relationship between magnetoresistance behavior and magnetic states in intercalated compounds FexTiS2

Temperature and field-dependent neutron powder diffraction (NPD) measurements have been performed to reveal the nature of the unusual evolution of the magnetoresistance behavior with increasing Fe content in the intercalated compounds ${\mathrm{Fe}}_{x}{\mathrm{TiS}}_{2}$ (with $x=0.25,0.33,0.50,0.55$) synthesized by solid-phase reaction method with prolonged homogenization heat treatment. As derived from neutron diffraction measurements, both the ${\mathrm{Fe}}_{0.25}{\mathrm{TiS}}_{2}$ and the ${\mathrm{Fe}}_{0.50}{\mathrm{TiS}}_{2}$ compound exhibit an antiferromagnetic (AFM) order below their respective N\'eel temperatures ${T}_{N}\ensuremath{\approx}52$ K and ${T}_{N}\ensuremath{\approx}140\phantom{\rule{4pt}{0ex}}\mathrm{K}$, which results in the presence of a large magnetoresistance accompanying the field-induced phase transition from AFM to the ferromagnetic (FM) state. At low temperatures, this AFM-FM transition is irreversible, confirmed by the irreversibility of changes in the NPD patterns and the presence of remnant magnetoresistance. In contrast, ${\mathrm{Fe}}_{0.33}{\mathrm{TiS}}_{2}$ shows short-range magnetic order at ${T}_{f}\ensuremath{\approx}44$ K due to a triangular network of intercalated Fe atoms and frustrations of exchange interactions with a field-induced FM alignment of Fe magnetic moments in an applied magnetic field as revealed by NPD measurements. The field-induced transformations of the cluster glass magnetic state in this compound lead to a significant decrease in electrical resistivity. According to NPD data, a reduced impact of an external magnetic field on the electrical resistivity of the compound ${\mathrm{Fe}}_{0.55}{\mathrm{TiS}}_{2}$ can be ascribed to the presence of ferromagnetic or ferrimagnetic order in compounds with the Fe concentrations above $x=0.50$. The results obtained indicate that the distribution of the Fe atoms, along with their concentration in ${\mathrm{Fe}}_{x}{\mathrm{TiS}}_{2}$ layered compounds, plays a decisive role in the formation of the magnetic state and the behavior of the magnetoresistance.

Evolution of the magnetic structure in overdoped antiferromagnetic La1−xCaxMnO3(0.51≤x≤0.69) manganites: A neutron diffraction study

The ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{MnO}}_{3}$ series of compounds with antiferromagnetic ground states ($x\ensuremath{\ge}1/2$) have been extensively studied due to the novel spin, orbital, and charge-ordering states observed when the calcium concentration is a simple fraction ($x=1/2,\phantom{\rule{0.28em}{0ex}}2/3$, and 3/4). The ground states of these compositions have been explained by the Goodenough charge, orbital, and spin ordering model. An important issue remaining is the elucidation of how the ground state changes when $x$ is not a simple number. Here we study the magnetic structure of ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{MnO}}_{3}$ for $0.51\ensuremath{\le}x\ensuremath{\le}0.69$ using powder neutron diffraction measurements supported by magnetization data. For compositions with $0.51\ensuremath{\le}x\ensuremath{\le}0.56$, the magnetic structure, which we term as an incommensurate charge exchange (CE) structure can be described by two propagation vectors ${\mathbf{k}}_{\mathrm{C}}=[1/2,0,1/2]$ and ${\mathbf{k}}_{\mathrm{E}}=[{\ensuremath{\varepsilon}}_{\mathrm{E}},0,1/2]$. In the second one, the component parallel to the ${\mathbf{a}}^{*}$ axis of the reciprocal lattice changes with the ${\mathrm{Mn}}^{4+}$ concentration $x$ as ${\ensuremath{\varepsilon}}_{\mathrm{E}}\ensuremath{\approx}x\ensuremath{-}1/2$ providing, thus, an unambiguous signature of the adoption of an incommensurate magnetic structure. As $x$ gradually increases, the diffraction data reveal that two magnetic phases---one adopting the incommensurate CE, and one adopting the commensurate ``2/3'' magnetic structure--co-exist in the concentration regime of $0.57\ensuremath{\le}x\ensuremath{\le}0.61$. Around the simple fraction $x=2/3$, the magnetic structure can be also described by three propagation vectors, the commensurate ${\mathbf{k}}_{\mathrm{E}}=[0,0,1/2]$, ${\mathbf{k}}_{\mathrm{C}}=[1/2,0,1/2]$, and an incommensurate ${\mathbf{k}}_{2/3}=[1/3+{\ensuremath{\varepsilon}}_{2/3},0,1/2]$ propagation vector with ${\ensuremath{\varepsilon}}_{2/3}$ taking negative/zero/positive values for $x$ smaller than/equal to/larger than 2/3, respectively. Our experimental results for $0.51\ensuremath{\le}x\ensuremath{\le}0.56$ are neither in favor of a stripe structure consisting of a fine mixture of $x=1/2$ and $x=2/3$ phases (phase separation) nor of a defect structure in which an appropriate amount of ${\mathrm{Mn}}^{3+}$-O sheets have been replaced by ${\mathrm{Mn}}^{4+}$-O sheets (defect structure). A sinusoidal modulated structure has been used as a possible candidate in explaining the experimental neutron diffraction magnetic Bragg peaks. This result may be linked to the presence of a mixed orbital state of the manganese ions.