Dependent Neutron Research Articles

Systematic derivation of [formula omitted] equations, its discretization using GTIN method and development of a switchable SP3 to [formula omitted] neutron transport solver

The Generalized Simplified Spherical Harmonics (GSPN) method has drawn recent interest owing to the fact that theoretically, it is equivalent to the PN and does not rely on any assumption other than piecewise homogeneity. Its level wise approach to PN offers an agreeable balance between the accuracy and computational efficiency making it a valuable mathematical tool for analyzing neutron transport problems pertaining to nuclear engineering and reactor physics. The lowest level approximation for N = 3, expressed as GSP3(0), offers reducing the complexity while still capturing the essential physics. In the current work, GSP3(0) equations are derived along with the interface and boundary conditions for linear anisotropic scattering. These equations are then discretized using the generalized transverse integration nodal method for a two-dimensional system of piecewise homogeneous rectangular regions. The discretization is done with an option kept for reducing the GSP3(0) formalism to the conventional SP3. Subsequently, a computer code has been developed to solve these discretized equations in the multigroup structure for vacuum, reflective or albedo boundaries. At present, this switchable SP3/GSP3(0) code has the capability of estimating k-eigenvalue and position dependent scalar neutron flux within a given two-dimensional rectangular geometry. The code has been verified by solving SP3, GSP3(0) and other benchmark problems from available literature. The results obtained from our code demonstrate that GSP3(0) is superior to the conventional SP3 and comparable to the recently proposed SDPN (N = 1,2,3) [M. Nazari, A. Zolfaghari, M. Abbasi, Prog. Nucl. Energy, 2023; 166, 104,933] in terms of accuracy as well as computation time.

Re-analysis of temperature dependent neutron capture rates and stellar β-decay rates of 95-98Mo

The neutron capture rates and temperature dependent stellar beta decay rates of Mo isotopes are investigated within the framework of the statistical code TALYS v1.96 and the proton neutron quasi particle random phase approximation (pn-QRPA) model. The Maxwellian average cross-section (MACS) and neutron capture rates for the Mo(n,γ) Mo radiative capture process are analyzed within the framework of the statistical code TALYS v1.96 based on the phenomenological nuclear level density model and gamma strength functions. The present model-based computations for the MACS are comparable to the existing measured data. The sensitivity of stellar weak interaction rates to various densities and temperatures is investigated within the framework of the pn-QRPA model. Particular attention is paid to the impact of thermally filled excited states in the decaying nuclei ( Mo) on electron emission and positron capture rates. Furthermore, we compare the neutron capture rates and stellar beta decay rates. It is found that neutron capture rates are higher than stellar beta decay rates at both lower and higher temperatures.

A re-activation model for 169Yb intensity modulated brachytherapy sources accounting for spatiotemporal isotopic composition.

Intensity modulated brachytherapy based on partially shielded intracavitary and interstitial applicators is possible with a cost-effective 169Yb production method. 169Yb is a traditionally expensive isotope suitable for this purpose, with an average γ-ray energy of 93keV. Re-activating a single 169Yb source multiple times in a nuclear reactor between clinical uses was shown to theoretically reduce cost by approximately 75% relative to conventional single-activation sources. With re-activation, substantial spatiotemporal variation in isotopic source composition is expected between activations via 168Yb burnup and 169Yb decay, resulting in time dependent neutron transmission, precursor usage, and reactor time needed per re-activation. To introduce a generalized model of radioactive source production that accounts for spatiotemporal variation in isotopic source composition to improve the efficiency estimate of the 169Yb production process, with and without re-activation. A time-dependent thermal neutron transport, isotope transmutation, and decay model was developed. Thermal neutron flux within partitioned sub-volumes of a cylindrical active source was calculated by raytracing through the spatiotemporal dependent isotopic composition throughout the source, accounting for thermal neutron attenuation along each ray. The model was benchmarked, generalized, and applied to a variety of active source dimensions with radii ranging from 0.4 to 1.0mm, lengths from 2.5 to 10.5mm, and volumes from 0.31 to 7.85 mm3, at thermal neutron fluxes from 1×1014to1×1015 n cm-2 s-1. The 168Yb-Yb2O3 density was 8.5g cm-3 with 82% 168Yb-enrichment. As an example, a reference re-activatable 169Yb active source (RRS) constructed of 82%-enriched 168Yb-Yb2O3 precursor was modeled, with 0.6mm diameter, 10.5mm length, 3 mm3 volume, 8.5g cm-3 density, and a thermal neutron activation flux of 4 × 1014 neutronscm-2s-1. The average clinical 169Yb activity for a 0.99 versus 0.31 mm3 source dropped from 20.1 to 7.5Ci for a 4×1014ncm-2s-1 activation flux and from 20.9 to 8.7Ci for a 1×1015ncm-2s-1 activation flux. For thermal neutron fluxes ≥2×1014ncm-2s-1, total precursor and reactor time per clinic-year were maximized at a source volume of 0.99 mm3 and reached a near minimum at 3mm3. When the spatiotemporal isotopic composition effect was accounted for, average thermal neutron transmission increased over RRS lifetime from 23.6% to 55.9%. A 28% reduction (42.5 days to 30.6 days) in the reactor time needed per clinic-year for the RRS is predicted relative to a model that does not account for spatiotemporal isotopic composition effects. Accounting for spatiotemporal isotopic composition effects within the RRS results in a 28% reduction in the reactor time per clinic-year relative to the case in which such changes are not accounted for. Smaller volume sources had a disadvantage in that average clinical 169Yb activity decreased substantially below 20Ci for source volumes under 1mm3. Increasing source volume above 3 mm3 adds little value in precursor and reactor time savings and has a geometric disadvantage.

Existence of complex magnetic ground state and topological Hall effect in centrosymmetric silicide DyScSi

Topological Hall effect (THE) originating from non-trivial spin arrangements in magnetic materials has been extensively investigated in recent years. In this context, a centrosymmetric ternary silicide, DyScSi, is explored. Here we show that, a complex magnetic ground state drives THE in a centrosymmetric system. Temperature dependent magnetisation and neutron diffraction results establish the presence of commensurate antiferromagnetic (AFM) phase around 92 K, followed by an incommensurate AFM phase below 40 K. Additionally, two cluster glass transitions near 20 and 8 K, are also noted. These observed features arise due competing AFM and FM interactions. In conjunction with this, a finite contribution of THE is also observed in the intermediate field regime (8–30 kOe), at low temperature in DyScSi. The behaviour of this silicide appears to be fascinating in terms of interplay between complex magnetic ground state and THE in centrosymmetric structure.

Transient analysis of AHWR core using implicit method of NDIFF3D

The knowledge of time dependent behaviour of neutron population is extremely important for any nuclear reactor operation from safety aspect. The reactor transient can be accurately predicted by solving time dependent neutron diffusion equations. A solution scheme based on implicit method has been implemented in NDIFF3D. The loss of regulation (LOR) transient in initial, intermediate and equilibrium core of AHWR has been simulated. The results have shown good agreement with the data calculated with 3DFAST.

A finite volume method based multi-group neutron diffusion model for space-time nuclear reactor kinetics problems in RZ geometry

The transient analysis of Fast Breeder Reactor (FBR) requires the development of high fidelity space-time nuclear reactor kinetics codes for the realistic prediction of spatial and temporal behavior of neutron flux and fission power along with the feedback effects. So, a space-time nuclear reactor kinetics model has been developed for solving the coupled time dependent multi-group neutron diffusion equations and the delayed neutron precursor equations in axi-symmetric cylindrical (r-z) geometry. The numerical model employs an orthogonal mesh finite volume method for spatial discretization and implicit method for time discretization. A computer code named MANDIR-KRZ (Multi-group Analysis of Neutron DIffusion in Reactor for Kinetics problems in RZ geometry) has been developed and employed to reconstruct the keff, transient neutron flux and power results of different benchmark problems. Mathematical formulation of the numerical model and results of the code for Dodds and FBR transient benchmark problems are discussed in this paper.

Identification of low coefficient of thermal expansion in Al23Ce4Ni6 via combinatorial sputtering of Al-Ce-Ni-Mn thin films and upscaling to bulk materials

Al100−x-y-zCexNiyMnz thin films were synthesized via combinatorial sputtering from Al, Al80Ce20, Al91Ni9, and Al93Mn7 targets. The resultant as-deposited films exhibit a continuous composition gradient of the various constituents and form a metastable solid-solution over most of the composition space. Subsequent annealing leads to the formation of the thermodynamically stable systems of Al, and α-Al11Ce3, Al8CeMn4, and Al23Ce4Ni6 intermetallics -- where the phases present and fraction depend on the composition. Temperature dependent x-ray diffraction (TDXRD) was used to determine the coefficients of thermal expansion (CTE) for each phase. The thin film Al and Al11Ce3 temperature dependent CTE values are consistent with previously reported results. The thin film Al8CeMn4 phase reveals a slight decrease in the CTE with a range from 27 × 10−6 oC−1 to 23 × 10−6 oC−1 in the temperature range 25–550 °C. The thin film Al23Ce4Ni6 phase exhibits a CTE value of ≈ 9 × 10−6 oC−1 near room temperature and increases to 14 × 10−6 oC−1 at 550 °C. To confirm the thin film results, bulk stoichiometric Al8CeMn4 and Al23Ce4Ni6 samples were prepared and measured under similar conditions. The Al8CeMn4 bulk sample confirmed the negative CTE trend observed in the thin film sample. Compared to its thin-film counterpart, the Al23Ce4Ni6 bulk sample similarly demonstrated a low CTE value near room temperature of 5 × 10−6 oC−1 and an anomalous minimum in the CTE at ≈ 75 °C, which was confirmed via temperature dependent neutron diffraction. Temperature dependent magnetic and electrical measurements were subsequently taken on Al23Ce4Ni6, and the anomalous minimum in the CTE coincided with an electronic phase transition.

Unveiling the magnetic structure and phase transition of Cr2CoAl using neutron diffraction

We report the detailed analysis of temperature dependent neutron diffraction pattern of the Cr2CoAl inverse Heusler alloy and unveil the magnetic structure up to the phase transition as well as its fully compensated ferrimagnetic nature. The Rietveld refinement of the diffraction pattern using the space group I4¯m2 confirms the inverse tetragonal structure over the large temperature range from 100 to 900 K. The refinement of the magnetic phase considering the wave vector k= (0, 0, 0) reveals the ferrimagnetic nature of the sample below 730±5 K. This transition temperature is obtained from empirical power law fitting of the variation in the ordered net magnetic moment variation in intensity of (110) peak as a function of temperature. The spin configuration of the microscopic magnetic structure suggests the nearly fully compensated ferrimagnetic behavior where the magnetic moments of Cr2 are antiparallel with respect to the Cr1 and Co moments. Moreover, the observed anomaly in the thermal expansion and lattice parameters at 730±5 K suggests that the distortion in the crystal structure may play an important role in the magnetic phase transition.

Bayesian evaluation of energy dependent neutron induced fission yields* *Supported by the National Natural Science Foundation of China (12175064, U2167203) and the Outstanding Youth Science Foundation of Hunan Province, China (2022JJ10031)

From both the fundamental and applied perspectives, fragment mass distributions are important observables of fission. We apply the Bayesian neural network (BNN) approach to learn the existing neutron induced fission yields and predict unknowns with uncertainty quantification. Comparing the predicted results with experimental data, the BNN evaluation results are found to be satisfactory for the distribution positions and energy dependencies of fission yields. Predictions are made for the fragment mass distributions of several actinides, which may be useful for future experiments.

Enhancing transmutation rates of minor actinides using Zr and Y hydride and deuteride coatings in an LFR

The possibility of transmutation of minor actinides (MAs) in lead-cooled fast reactors provides an excellent opportunity to reduce the overall repository of radioactive waste. The present work seeks to augment the transmutation rates of six minor actinides (237Np, 241Am, 243Am, 243Cm, 244Cm, and 245Cm) by increasing neutron capture through the use of moderator coatings around the fuel elements. The reference design for the fuel assembly was based on the design concept of ALFRED, the European Lead Cooled Demonstrator Reactor, and consists of 127 fuel elements loaded with 5 wt.% of minor actinides (MAs) homogeneously mixed with MOX (mixed oxide) fuel. Four different moderators (ZrH1.6, ZrD1.6, YH2, and YD2) with five different coating thicknesses (0.01 cm, 0.02 cm, 0.03 cm, 0.04 cm, and 0.05 cm) were selected for this study and variation in kinf, transmutation rates and fuel cycle parameters (employing the linear reactivity model or LRM) were determined. Results showed that both the addition of a moderator and the increase in moderator thickness improved transmutation rates but had a negative impact on fuel cycle parameters. ZrH1.6 resulted in the highest increase in transmutation rate, but also incurred the largest penalties in fuel burnup, and cycle length. For ZrH1.6 coatings of 0.01 cm, the obtained transmutation rates were 13.57%/y for 237Np, 12.6%/y for 241Am, and 9.26%/y for 243Am. The concentration of Cm isotopes increased over time due to neutron capture of Am, U, and Pu. Deuteride moderators minimized the decrease in fuel cycle parameters but compromised transmutation rates. The fuel temperature coefficient (FTC), energy dependent neutron flux, and relative pin power distribution of the reference design and the models were also determined in order to analyze the effect of moderator addition on these factors. Finally, a suggestion of the best model was put forth in consideration of both transmutation efficiency and fuel cycle parameters.

Evaluation of time dependent neutron transport algorithms using 2D modular ray tracing MOC

Three algorithms for solving the multigroup time dependent neutron transport in two dimensions utilizing the method of characteristics (MOC) are developed in this study. These algorithms are distinguished base on the average angular flux calculation along the characteristic line (track) and the applied approximation to the angular flux time derivative. Since the calculation of the scalar flux in the characteristics method requires the average angular flux along the track, two approaches for implementation of track averaged angular flux are presented. In the first approach, the effect of the angular flux in the previous time step as an extra term added to the source is considered. Second, the average angular flux is applied similar to the common method used in the steady state form. Moreover, two states for the angular flux time derivative in implementing the transient neutron transport solution are considered. First, the angular dependency of the angular flux in time derivative is preserved. Second, isotropic scalar flux approximation is applied to the time derivative.Considering the vital role of ray tracing and improving the non-physical disturbances effect caused by ray tracing methods, the latest modular ray tracing (MRT) method is utilized for the transient calculation. For verification, the well-known TWIGL benchmark is modeled and the results are compared with MPACT and DeCART codes. Additionally, the heterogeneous benchmark problems MOXK_2G and MOXK_7G are simulated and the results are compared with DeCART and VARIANT_K codes.

Two-dimensional short-range spin-spin correlations in the layered spin- 32 maple leaf lattice antiferromagnet Na2Mn3O7 with crystal stacking disorder

We report the nature of magnetic structure, and microscopic spin-spin correlations and their dependence on the underlying crystal structure of the geometrically frustrated layered spin-$\frac{3}{2}$ maple leaf lattice (MLL) antiferromagnet ${\mathrm{Na}}_{2}{\mathrm{Mn}}_{3}{\mathrm{O}}_{7}$ by a comprehensive neutron diffraction study. Crystal structural studies by x-ray and neutron diffraction reveal that the MLL layers (constituted by ${\mathrm{Mn}}_{3}{\mathrm{O}}_{7}{}^{2\ensuremath{-}}$ units) are well separated by nonmagnetic Na layers. The studies also conclude the presence of stacking faults (in-plane sliding of magnetic MLL layers) as well as a distortion in the MLL of ${\mathrm{Mn}}^{4+}$. Temperature dependent magnetic susceptibility, heat capacity, and neutron diffraction data yield a short-range antiferromagnetic (AFM) ordering below $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ without a long-range magnetic ordering down to 1.5 K. The analysis of the diffuse magnetic neutron scattering patterns by the reverse Monte Carlo method reveals two-dimensional (2D) spin-spin correlations within the MLL layers. Additionally, we establish a relation between the correlation length of the short-range magnetic ordering with the stacking faults through a varying synthesis condition. The present study, therefore, explores a microscopic picture of the crystal and spin structures, as well as their correlation; hence it provides experimental insight of the magnetic ordering in a MLL AFM. Further, we have outlined the formation of several 2D frustrated lattice geometries having triangular plaquettes, including the MLL, by crystal engineering of the triangular lattice, and their role in the stabilization of multiple unique chiral spin states which opens up the door for study of unique chiral spin states.

Neutron area monitor for ambient dose equivalent (H*(10)) and effective dose (EAP) using prompt gamma rays induced in high density polyethylene with metallic external layer

Estimations of neutron ambient dose equivalent, H∗(10) and effective dose (anterior-posterior), EAP using measured prompt gamma intensities are theoretically investigated for several prompt gamma generating detection systems, each consisting of a cylindrical high density polyethylene (HDPE) covered with a layer of different materials. The neutron induced prompt gamma intensities are measured using a NaI(Tl) detector with lead as shielding. Materials like cadmium, iron, nickel, zinc, copper and lead are used as an outer layer covering the HDPE cylinder. A linear combination of the distributions of the prompt gamma intensities emitted from these materials at different incident neutron energies are subjected to multiple linear regression analyses to fit the energy dependent neutron fluence to dose conversion coefficients (DCC) as provided by the International Commission on Radiological Protection (ICRP). The aim of the present work is to explore the suitability of other elements to replace boron in the earlier used borated HDPE in the system to overcome certain practical difficulties. Different neutron energy distributions in the energy range from about 0.01 eV to 20 MeV are selected to validate the dose estimation. Among the materials used, iron, nickel, zinc and copper show promising results for the estimation H∗(10) as well as EAP as a replacement of boron for neutron energy distributions with predominant high energy components.

Observation of Anisotropic Thermal Expansion and the Jahn-Teller Effect in Double Perovskites Sr2-xLaxCoNbO6 Using Neutron Diffraction.

We use temperature dependent neutron powder diffraction (NPD) to investigate the structural changes and magnetic interactions in double perovskite Sr2-xLaxCoNbO6 (x = 0.4 and 0.6). A structural phase transition from tetragonal (I4/m) to monoclinic (P21/n) is observed between x = 0.4 and 0.6 samples. Interestingly, the temperature evolution of the unit cell parameters follows the Grüneisen approximation, and the analysis suggests an isotropic thermal expansion in the case of the x = 0.4 sample, whereas the x = 0.6 sample shows the anisotropy where the thermal expansion along the c-axis significantly deviates from the Grüneisen function. We observe the z-out Jahn-Teller distortion in the CoO6 and consequently z-in distortion in the adjacent NbO6 octahedra. With an increase in the La substitution, a decrease in the degree of octahedral distortion is evident from the significant reduction in the local distortion parameter Δ around the B-site atoms.

Magnetic structure of magnetoelectric multiferroic HoFeWO6

The polar magnetic oxide, HoFeWO6, is synthesized, and its crystal structure, magnetic structure, and thermodynamic properties are investigated. HoFeWO6 forms the polar crystal structure (space group Pna21 (#33)) due to the cation ordering of W6+ and Fe3+. An antiferromagnetic transition at TN = 17 K is accompanied by a significant change in magnetic entropy with a value of ≈ 5 J kg−1 K−1 in a 70 kOe applied field. Temperature dependent neutron diffraction and magnetization data indicate that the Fe sublattice orders in a strongly non-collinear and non-coplanar arrangement below TN. The Fe ordering initially leads to induced ordering of the Ho spins such that the Ho spins also show behavior of long-range ordering that is evident from the neutron diffraction measurements. Below T ≈ 4 K, the Ho spins order independently and pull the Fe spins toward the direction of Ho spins. A comparison with the magnetic structures and corresponding ferroelectric properties of other members of RMWO6 (R = Y, Sm-Tm, M = Cr, Fe, V) family indicate that the spontaneous polarization is due to the magnetic structure specific to the Fe sublattice through magnetoelectric coupling whereas the polarization is independent of the Ho sublattice.

Semi wavelet-based improved quasi static method for the analysis of PHWR transients

A new computational method, by incorporating wavelets in the improved quasi static (IQS) scheme, is developed and presented here for the analysis of CANDU PHWR and TWIGL reactor transients. According to this method the time dependent neutron diffusion equation is split into amplitude function and shape function. The amplitude function is solved using the Haar wavelet and its solution is used in the estimation of shape function. The advantage of this computational method is that the concept of micro time step and macro time step, adopted in the IQS scheme, does not arise here at all and the transient can be estimated with only one time step, i.e. single time step. In this method, the transient estimation methodology is different from the improved quasi static scheme. This computational method is applied to estimate the transients in CANDU 3D-PHWR benchmark, CANDU-2D and TWIGL reactors. In TWIGL reactor, a Doppler temperature feedback in introduced and the transient is estimated with feedback. The estimated transients are compared with the reference. From the comparison of results, it is observed that this method is capable of estimating the reactivity initiated transients in heterogeneous reactors to a good accuracy, by adopting only one time step. This computational method is first of its kind in the estimation of reactor transients. It is also shown that as the order of resolution of wavelet is increased, the error in the estimation of transient is reduced.

Strong anharmonicity in tin monosulfide evidenced by local distortion, high-energy optical phonons, and anharmonic potential

Recently, SnSe has been found to possess a remarkable thermoelectric performance. As an isostructural compound to SnSe, SnS contains a more environmentally compatible and earth abundant element, which enables SnS a promising thermoelectric material for commercial application. In this work, we have performed systematic studies of the crystal structures and the lattice vibrations by means of neutron total scattering, Raman scattering measurements, and first-principle calculations. A structural transition has been observed by both temperature dependent neutron diffraction and pressure dependent Raman scattering. The lattice anharmonicity has been revealed by the local distortion induced by the Sn $5{s}^{2}$ lone pair and is also evidenced from the temperature dependent atomic displacement parameter of the Sn atom. By separating the intrinsic anharmonicity and lattice thermal expansion effects, we found that the former plays the primary role in the softening of the Raman active modes. Such anharmonicity has also been observed experimentally by the linewidth broadening of the high-energy optical modes and confirmed by frozen phonon calculations. Furthermore, our frozen phonon calculation reveals the presence of the quartic anharmonicity potential of those high-energy optical modes vibrating along the $b$ axis. Our data will contribute to a better understanding of the thermal conduction in SnS, which will be beneficial for the enhancement of the thermoelectric performance of this material.

Temperature dependent crystal structure re‐determination and electronic properties of UI3

AbstractIn this work, we have re‐investigated the structural and physical properties of UI3 by means of temperature dependent powder neutron diffraction, heat capacity and magnetic measurements. We confirm that UI3 crystallizes in the PuBr3 structure type, space group Cmcm. We did not observe any temperature dependent structural phase transition in the temperature range from 10 to 300 K. We further report the first quantum chemical calculations of UI3 by density functional theory (DFT). The calculated structural and electronic properties demonstrate the pronounced two‐dimensional anisotropic effects present in UI3 due to its layered structure.

An approach for performing resolved and unresolved resonance evaluation based on few or none experimental data available: Application to unstable and short-lived isotopes

Fluctuations in the neutron cross sections resulting from resonance structures have to be accounted for in the calculation of a nuclear system. Regardless of the approach used, deterministic or stochastic, the depression in the neutron flux due to the resonance effects in the cross section must be well understood for the purpose of providing a good understanding of the self-shielding effects and an accurate calculation of any nuclear system. The R-Matrix theory is the mechanism most appropriate to represent the resonance region providing a detailed description of the cross sections thru resonance parameters.The objective of this work is to present an alternative to generate resonance region evaluation on the basis of the R-matrix theory in the resolved and unresolved energy regions. The proposed methodology can be applied to situations where few or none experimental data are available such as the energy dependent neutron cross section. It leverages over the knowledge of information such as thermal cross section values, Westcott factor, resonance integral, coherent and incoherent scattering lengths, scattering radius, and more important, knowledge of average resonance parameters. The approach is demonstrated and validated with applications for an isotope with a well-known resonance evaluation, that is the 103Rh, and afterwards to an isotope with minimum experimental data available. The latter is the 156Eu isotope.

Single-crystal investigations on the multiferroic materialLiFe(WO4)2

The crystal and magnetic structure of multiferroic LiFe(WO$_4$)$_2$ were investigated by temperature and magnetic-field dependent specific heat, susceptibility and neutron diffraction experiments on single crystals. Considering only the two nearest-neighbour magnetic interactions, the system forms a $J_1$, $J_2$ magnetic chain but more extended interactions are sizeable. Two different magnetic phases exhibiting long-range incommensurate order evolve at $T_{\text{N}1}\approx 22.2 \text{ K}$ and $T_{\text{N}2}\approx 19 \text{ K}$. First, a spin-density wave develops with moments lying in the $ac$ plane. In its multiferroic phase below $T_{\text{N}2}$, LiFe(WO$_4$)$_2$ exhibits a spiral arrangement with an additional spin-component along $b$. Therefore, the inverse Dzyaloshinskii-Moriya mechanism fully explains the multiferroic behavior in this material. A partially unbalanced multiferroic domain distribution was observed even in the absence of an applied electric field. For both phases only a slight temperature dependence of the incommensurability was observed and there is no commensurate phase emerging at low temperature or at finite magnetic fields up to $6\text{ T}$. LiFe(WO$_4$)$_2$ thus exhibits a simple phase diagram with the typical sequence of transitions for a type-II multiferroic material.