We present a methodology based on the Néel model to build a classical spin-lattice Hamiltonian for cubic crystals capable of describing magnetic properties induced by the spin-orbit coupling like magnetocrystalline anisotropy and anisotropic magnetostriction, as well as exchange magnetostriction. Taking advantage of the analytical solutions of the Néel model, we derive theoretical expressions for the parameterization of the exchange integrals and Néel dipole and quadrupole terms that link them to the magnetic properties of the material. This approach allows to build accurate spin-lattice models with the desire magnetoelastic properties. We also explore a possible way to model the volume dependence of magnetic moment based on the Landau energy. This new feature can allow to consider the effects of hydrostatic pressure on the saturation magnetization. We apply this method to develop a spin-lattice model for BCC Fe and FCC Ni, and we show that it accurately reproduces the experimental elastic tensor, magnetocrystalline anisotropy under pressure, anisotropic magnetostrictive coefficients, volume magnetostriction and saturation magnetization under pressure at zero-temperature. This work could constitute a step towards large-scale modeling of magnetoelastic phenomena.
The reported onset temperatures of the flash transition in cubic zirconia single crystals have been analyzed in the present note. The analysis for high-temperature low-field data gives an activation energy of 0.99 eV for the charge transport, which agrees well with the measured ionic conductivity data in cubic zirconia single crystal. Electrical reduction is believed to play an additional role under low-temperature high-field conditions, facilitating electrical/thermal runaway under more modest conditions.
Self-organization on crystal surface is studied as a two dimensional spinodal decomposition in presence of a surface stress. The elastic Green function is calculated for a $(001)$ cubic crystal surface taking into account the crystal anisotropy. Numerical calculations show that the phase separation is driven by the interplay between domain boundary energy and long range elastic interactions. At late stage of the phase separation process, a steady state appears with different nanometric patterns according to the surface coverage and the crystal elastic constants.
Systematic enumeration of crystalline networks with some special topological characters is of considerable interest in both mathematics and crystallography. Based on the restriction of lattice in cubic and inequivalent nodes not exceeding three, a simple method is proposed for systematic searching for three-dimensional crystalline networks with only sp2-configuration nodes (C-sp2-TDTCNs). We systematically scan the cubic space groups from No.195 to No.230 and find many C-sp2-TDTCNs including all the previously proposed cubic ones. These C-sp2-TDTCNs are topologically intriguing and can be cons…
We present diagonal and off-diagonal elements of the permittivity and conductivity tensor up to the second order in magnetization for cubic crystals. We express all tensor elements as a function of a general sample orientation, for arbitrary magnetization direction and for (001), (011) and (111) surface orientations. Finally, we discuss, how to extract values of quadratic elements G of the second order permittivity tensors for different sample surface orientations from both experiment and ab-initio calculations.
Plastic deformations in body-centered-cubic (BCC) crystals have been of critical importance in diverse engineering and manufacturing contexts across length scales. Numerous experiments and atomistic simulations on BCC crystals reveal that classical crystal plasticity models with the Schmid law are not adequate to account for abnormal plastic deformations often found in these crystals. In this paper, we address a continuum mechanical treatment of anomalous plasticity in BCC crystals exhibiting non-Schmid effects, inspired from atomistic simulations recently reported. Specifically, anomalous fea…
The elastostatic Green function tensor approach, which was recently used to treat electrostriction in numerical simulation of domain structure formation in cubic ferroelectrics, is reviewed and extended to the crystals of hexagonal and orthorhombic symmetry. The tensorial kernels appearing in the expressions for effective nonlocal interaction of electrostrictive origin are derived explicitly and their physical meaning is illustrated on simple examples. It is argued that the bilinear coupling between the polarization gradients and elastic strain should be systematically included in the Ginzburg…
Discrete models of dislocations in cubic crystal lattices having one or two atoms per unit cell are proposed. These models have the standard linear anisotropic elasticity as their continuum limit and their main ingredients are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the dislocation size. For these models, conservative and damped equations of motion are proposed. In the latter case, the entropy production and thermodynamic forces are calculated and fluctuation terms obeying the f…
A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the Peierls stress. Explicit expressions are given for crystals with cubic symmetry: sc, fcc and bcc. Numerical simulations of this model with conservative or damped dynamics illustrate static and moving edge and screw dislocations and describe their co…
We have considered the relaxation of transverse thermal and high-frequency phonons for the Landau-Rumer mechanism in the semiconductor cubic crystals. Using the known values of these elastic moduli, the parameters determining the transverse phonon relaxation rates for the Landau-Rumer mechanism have been evaluated for the crystals under consideration. It is shown that the dependence of the relaxation rate on the wave vector of thermal and high-frequency phonons strongly differs from the classical Landau-Rumer relationship both in the isotropic medium and in the cubic crystals studied. In contr…
Interface energy and kinetic coefficient of crystal growth strongly depend on the face of the crystalline lattice. To investigate the kinetic anisotropy and velocity of different crystallographic faces we use the hyperbolic (modified) phase field crystal model which takes into account atomic density (as a slow thermodynamic variable) and atomic flux (as a fast thermodynamic variable). Such model covers slow and rapid regimes of interfaces propagation at small and large driving forces during solidification. In example of BCC crystal lattice invading the homogeneous liquid, dynamical regimes of …
We provide unified phenomenological description of magnetooptic effects being linear and quadratic in magnetization. The description is based on few principal spectra, describing elements of permittivity tensor up to the second order in magnetization. Each permittivity tensor element for any magnetization direction and any sample surface orientation is simply determined by weighted summation of the principal spectra, where weights are given by crystallographic and magnetization orientations. The number of principal spectra depends on the symmetry of the crystal. In cubic crystals owning point …
The transverse ultrasound absorption in cubic crystals with positive and negative anisotropies of the second-order elasticity moduli is analyzed. The scattering of the ultrasound by defects and during anharmonic scattering processes is considered. The transverse ultrasound absorption is analyzed as a function of the wave-vector direction in terms of the anisotropic continuum model. The Landau-Rumer mechanism is considered for anharmonic scattering processes. Known values of the second- and third-order elasticity moduli are used to calculate parameters determining the ultrasound absorption. It …
During past years, a number of reports have been published on synthesis of tetragonal allotrope of boron, t-B52 phase. However, no unambiguous characterization of the crystal structure has been performed to the present time, while remarkable variation of the a/c lattice-parameter ratio raises strong doubts about its uniqueness. Here the Rietveld refinement of the crystal structure of the high pressure - high temperature boron phase synthesized by a direct solid-state transformation of rhombohedral beta-B106 at 20 GPa and 2500 K has been reported for the first time. Although this boron allotrop…
The 300 K equation of state of cubic (zinc-blende) boron phosphide BP has been studied by in situ single-crystal X-ray diffraction with synchrotron radiation up to 55 GPa. The measurements have been performed under quasi-hydrostatic conditions using a Ne pressure medium in a diamond anvil cell. A fit of the experimental p-V data to the Vinet equation of state yields the bulk modulus B0 of 179(1) GPa with its pressure derivative of 3.3(1). These values are in a good agreement with previous elastic measurements, as well as with semiempirical estimations.
We constructed physically stable sp2 negatively curved cubic carbon structures which reticulate a Schwarz P-like surface. The method for constructing such crystal structures is based on the notion of the standard realization of abstract crystal lattices. In this paper, we expound on the mathematical method to construct such crystal structures.
We report the magnetization ($M$) and magnetoresistance (MR) results of HoAl$_2$ single crystals oriented along $<100>$ and $<110>$ directions. Although HoAl$_2$ has cubic Laves phase structure, a large anisotropy is observed in $M$ and MR results below Curie temperature ($T_C$) at 31.5 K. A satisfactory correlation between magnetic entropy change ($ΔS_M$) and MR could be established along $<110>$ direction and in $<100>$ direction except for the temperature ($T$) region, around which spin reorientation takes place. Large inverse magnetocaloric effect is observed at low-$T$ which is associated…
Magnetic symmetry of possible plane domain walls in arbitrary oriented plates of the crystal of hexoctahedral crystallographic class is considered. The symmetry classification is applied for ferro- and ferrimagnets.
Crystallization of pristine cubic ice from liquid at ambient pressure
University College London（伦敦大学学院）；ISIS Neutron and Muon Source, Science and Technology Facilities Council, Rutherford Appleton Laboratory（ISIS中子与μ子源，科学与技术设施委员会，拉瑟福德阿普尔顿实验室）；Uppsala Universitet（乌普萨拉大学）；University of Oxford（牛津大学）；The University of Manchester（曼彻斯特大学）
研究立方冰 Ic 能否从液态直接形成等问题，通过冷却介孔二氧化硅内水溶液在常压下获得原始立方冰 Ic，利用中子散射技术证明其可重复形成且为唯一稳定晶相，揭示该多晶型物在自然和合成过程中作用更重要。
According to classical grain growth laws, grain growth is driven by the minimization of surface energy and will continue until a single grain prevails. These laws do not take into account the lattice anisotropy and the details of the microscopic rearrangement of mass between grains. Here we consider coarsening of body-centered cubic polycrystalline materials in three dimensions using the phase field crystal model. We observe as function of the quenching depth, a cross over between a state where grain rotation halts and the growth stagnates and a state where grains coarsen rapidly by coalescenc…
High-throughput screening has become one of the major strategies for the discovery of novel functional materials. However, its effectiveness is severely limited by the lack of quantity and diversity of known materials deposited in the current materials repositories such as ICSD and OQMD. Recent progress in machine learning and especially deep learning have enabled a generative strategy that learns implicit chemical rules for creating chemically valid hypothetical materials with new compositions and structures. However, current materials generative models have difficulty in generating structura…
To understand the crystal structure of n-diamond, a hydrogen-doped (H-doped) diamond model has been investigated using first principles calculations. In particular, hydrogen concentration dependent elastic constants and lattice parameters for the H-doped diamond have been analyzed. Our results indicate that when the hydrogen concentration is less than 19 at.%, the H-doped diamond is mechanically stable. When the hydrogen concentration is about 4 at.%, the optimized lattice parameter, simulated XRD pattern and electronic properties for the H-doped diamond all agree well with the corresponding e…
When Cubic Is Not Isotropic: Phonon-Exciton Decoupling in CuInSnS$_4$ Single Crystals
Helmholtz-Zentrum Berlin für Materialien und Energie（柏林赫尔姆霍兹中心）；University of Manchester（曼彻斯特大学）；University of Zurich（苏黎世大学）；University of Basel（巴塞尔大学）；University of Cambridge（剑桥大学）；Freie Universität Berlin（柏林自由大学）
Ge$_{2}$Sb$_{2}$Te$_{5}$ (GST) has been widely used as a popular phase change material. In this study, we show that it exhibits high Seebeck coefficients 200 - 300 $μ$V/K in its cubic crystalline phase ($\it{c}$-GST) at remarkably high $\it{p}$-type doping levels of $\sim$ 1$\times$10$^{19}$ - 6$\times$10$^{19}$ cm$^{-3}$ at room temperature. More importantly, at low temperature (T = 200 K), the Seebeck coefficient was found to exceed 200 $μ$V/K for a doping range 1$\times$10$^{19}$ - 3.5$\times$10$^{19}$ cm$^{-3}$. Given that the lattice thermal conductivity in this phase has already been mea…
In this study, we present a novel approach along with the needed computational strategies for efficient and scalable feature engineering of the crystal structure in compounds of different chemical compositions. This approach utilizes a versatile and extensible framework for the quantification of a three-dimensional (3-D) voxelized crystal structure in the form of 2-point spatial correlations of multiple atomic attributes and performs principal component analysis to extract the low-dimensional features that could be used to build surrogate models for material properties of interest. An applicat…
The effect of doping of cubic boron nitride with beryllium, silicon, sulfur and magnesium on the lattice parameters, electrical conductivity and EPR spectra has been studied. It is established that the degree of doping increases significantly in the case of crystallization of cubic boron nitride from BN solutions in supercritical ammonia at 3.9-4.2 GPa and 1100°C in comparison with the conventional synthesis from melts of the Mg-B-N system at 4.2 GPa and 1400°C. Doping with silicon and beryllium results in semiconductor properties of cubic boron nitride.
In a recent work by Jiang et al. [J. Phys. Chem. Solids 67 (2006) 1531-1536], the interrelationship between lattice constant, ionic radii and tolerance factor of cubic perovskites has been established and an empirical equation was obtained. However, the assumption of incorrect ionic coordination led to an incorrect mathematical expression even though the average relative errors between predicted and observed lattice constants of 132 materials were below 1%. Here, corrected coefficients for that empirical expression are obtained, which would likely be useful for investigation of general perovsk…
The phenomenological theory of the flexomagnetoelectric coupling in crystals of the cubic, tetragonal and orthorhombic crystal systems has been suggested. Secondary role of the crystal structure chirality was shown. Oppositely, significant role of the crystallographic point group type (symmetric, alternating, dihedral or cyclic) in the flexomagnetoelectric coupling has been derived. It was shown, that conceptually new features of the flexomagnetoelectric effects are expected in the crystals of the cyclic groups (crystal classes 4/m, 4^- and 4). Proposed verification of the theory is investigat…
Skyrmions are disk-like objects that typically form triangular crystals in two dimensional systems. This situation is analogous to the so-called "pancake vortices" of quasi-two dimensional superconductors. The way in which skyrmion disks or pancake skyrmions pile up in layered centro-symmetric materials is dictated by the inter-layer exchange. Unbiased Monte Carlo simulations and simple stabilization arguments reveal face centered cubic and hexagonal close packed skyrmion crystals for different choices of the inter-layer exchange, in addition to the conventional triangular crystal of skyrmion …
We study what kind of topological crystalline insulator phase emerges from nodal line semimetal phases in the face-centered cubic system which is not indicated by topological indices when spin-orbit coupling (SOC) is introduced. We construct an effective model which hosts two different nodal lines phases, and calculated mirror Chern numbers in it by introducing SOC. As a result, we find that the two nodal line phases with different nodal line configurations are mapped to different topological crystalline insulator phases. This result shows that turning off SOC and checking the nodal line confi…
A study has been performed using a crystal plasticity based finite element method to understand the effect of various stress states and crystal orientations with respect to loading direction for FCC single crystals in both hydrogenated and non-hydrogenated environment. Simulations have been performed for a variety of stress triaxilaities, Lode parmeters, crystal orientations and hydrogen concentrations. It is observed that crystal orientation has a varied effect on the influence hydrogen has on plastic deformation and void growth. Hydrogen in trap distribution at various stages of the deformat…
We report the synthesis of a single-phase sample of the superconducting crystalline approximant Au64.0Ge22.0Yb14.0 and present a structure model refined by Rietveld analysis for X-ray diffraction data.
Explicit expressions for inverse of Young's modulus E, inverse of shear modulus G, and Poisson's ratio for cubic media are considered. All these characteristics of elastic media depend on three components of the compliance tensor S, and on direction cosines of mutually perpendicular vectors m and n with fourfold symmetry axes. These characteristics are studied for all mechanically stable cubic materials for vectors n belonging to the irreducible body angle subtended by three cubic high symmetry directions [001], [111], and [110]. Regions in the stability triangle of in which cubic elastic mate…
The self-organization of a chemi-sorbed mono-layer is studied as a two dimensional ordering process in presence of surface stress. As proved previously for a single phase separation, a steady surface state is yielded from the competition between the domain boundary energy and the surface stress elastic energy. In the present letter, the resulting patterns are shown to depend on the interplay between the symmetries of both the internal layer order and the underlying crystal. For experimental relevance, our study is focussed on a (001) copper surface and we believe to enhance a route to stabiliz…
We use molecular simulation to construct equilibrium phase diagrams for two recently introduced model materials with isotropic, soft-repulsive pair interactions designed to favor diamond and simple cubic lattice ground states, respectively, over a wide range of densities [Jain et al., Soft Matter 9 14 (2013)]. We employ free energy based Monte Carlo simulation techniques to precisely trace the inter-crystal and fluid-crystal coexistence curves. We find that both model materials display rich polymorphic phase behavior featuring stable crystals corresponding to the target ground-state structures…
In this work, Monte Carlo simulation was implemented to study the phase diagrams and magnetic properties of a mixed spin (1-1/2-1) three-layer system with a cubic structure. In particular, the effects of the exchange and coupling parameters on the system compensation temperature were explored. More importantly, the effect of the crystal field on the system compensation, critical temperatures, and magnetic and thermodynamic properties of the system have been explored in detail. The crystal field was found to have a profound impact on the system compensation and critical temperatures. Our result…
In this work, we present a 3D Phase Field Dislocation Dynamics (PFDD) model for body-centered cubic (BCC) metals. The model formulation is extended to account for the dependence of the Peierls barrier on the line-character of the dislocation. Simulations of the expansion of a dislocation loop belonging to the $\left\{110\right\} \left<111\right>$ slip system are presented with direct comparison to Molecular Statics (MS) simulations. The extended PFDD model is able to capture the salient features of dislocation loop expansion predicted by MS simulations. The model is also applied to simulate th…
Theory of $\tilde{J}$-pseudospin for $f$ element in cubic environment is developed. By fulfilling the symmetry requirements and the adiabatic connection to atomic limit, the crystal-field states are uniquely transformed into $\tilde{J}$-pseudospin states. In terms of the pseudospin operators, both the total angular momentum and the crystal-field Hamiltonian contain higher-rank tensor terms than the traditional ones do, which means the present framework naturally include the effects such as the covalency and $J$-mixing beyond the $f$-shell model. Combining the developed theory with {\it ab init…
We address the question of whether three-dimensional crystals are minimizers of classical many-body energies. This problem is of conceptual relevance as it presents a significant milestone towards understanding, on the atomistic level, phenomena such as melting or plastic behavior. We characterize a set of rotation- and translation-invariant two- and three-body energies such that the energy minimum per particle over all n-particle configurations converges to the energy per particle in the face-centered cubic (fcc) lattice as tends to infinity. The proof involves a careful analysis of the symme…
The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values for the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centred-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-c…
Conventional Weyl nodes are twofold band crossings that carry a unit monopole charge, which can exist in condensed matter systems with the protection of translation symmetry. Unconventional Weyl nodes are twofold/multifold band crossings carrying a quantized monopole charge larger than one, and their existence needs the protection of additional crystalline symmetries. Studies on unconventional Weyl nodes are already very comprehensive, such as twofold Weyl nodes with Chern number of C=2/C=3 and fourfold/sixfoldWeyl nodes with C=4. Yet in this paper, we propose a newfound twofold unconventional…
Blackman's diagram of two dimensionless ratios of elastic constants is frequently used to correlate elastic properties of cubic crystals with interatomic bondings. Every's diagram of a different set of two dimensionless variables was used by us for classification of various properties of such crystals. We compare these two ways of characterization of elastic properties of cubic materials and consider the description of various groups of materials, e.g. simple metals, oxides, and alkali halides. With exception of intermediate valent compounds, the correlation coefficients for Every's diagrams o…
While the Born elastic stability criteria are well-known for cubic crystals, there is some confusion in the literature about the form it should take for lower symmetry crystal classes. We present here closed form necessary and sufficient conditions for elastic stability in all crystal classes, as a concise and pedagogical reference to stability criteria in non-cubic materials.
An equation has been derived to predict unit cell volume of high entropy alloys, HEA, by two different methods. Both treatments led to the same equation. For cubic HEA lattice parameters were calculated. The predicted lattice parameters were compared with those reported for 68 HEAs. Lattice parameters were also calculated using the equivalent of Vegards law for these alloys. Average errors were 0.52, and 0.42 when Vegards law, and the equation derived in this work were used, respectively.
Higher-order topological insulators host gapless states on hinges or corners of three-dimensional crystals. Recent studies suggested that even topologically trivial insulators may exhibit fractionally quantized charges localized at hinges or corners. Although most of the previous studies focused on two-dimensional systems, in this work, we take the initial step toward the systematic understanding of hinge and corner charges in three-dimensional insulators. We consider five crystal shapes of vertex-transitive polyhedra with the cubic symmetry such as a cube, an octahedron and a cuboctahedron. W…
Fracture material is seriously problem in daily life, and it has connection with mechanical properties itself. The mechanical properties is belief depend on dislocation movement and crack propagation in the crystal. Information about this is very important to characterize the material. In FCC crystal structure the competition between crack propagation and dislocation wake is very interesting, in a ductile material like copper (Cu) dislocation can be seen in room temperature, but in a brittle material like Si only cracks can be seen observed. Different techniques were applied to material to stu…
High thermal conductivity electronic materials are critical components for high-performance electronic and photonic devices as either active functional materials or thermal management materials. We report an isotropic high thermal conductivity over 500 W m-1K-1 at room temperature in high-quality wafer-scale cubic silicon carbide (3C-SiC) crystals, which is the second highest among large crystals (only surpassed by diamond). Furthermore, the corresponding 3C-SiC thin films are found to have record-high in-plane and cross-plane thermal conductivity, even higher than diamond thin films with equi…
The quasi-harmonic model proposes that a crystal can be modeled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss' law shows that the ion-ion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modeled by springs. We investigate the repercussions of this observation by examining three illustrative regimes: the bare ionic, density tight-binding, and density nearly-free electron models. For the bare ionic model, we demonstrate the zero elements in the force constants matrix an…
The dynamical stability of three-dimensional (3D) Lennard-Jones (LJ) crystals has been studied for many years. The face-centered-cubic and hexagonal close packed structures are dynamically stable, while the body-centered cubic structure is stable only for long range LJ potentials that are characterized by relatively small integer pairs $(m,n)$. Here, we study the dynamical stability of two-dimensional (2D) LJ crystals, where the planar hexagonal, the buckled honeycomb, and the buckled square structures are assumed. We demonstrate that the stability property of 2D and 3D LJ crystals can be clas…
The ordering of the classical Heisenberg model on the pyrochlore lattice with the antiferromagnetic nearest-neighbor interaction J1 and the ferromagnetic next-nearest-neighbour interaction J2 is investigated by means of a mean-field analysis and a Monte Carlo simulation. For a moderate J2/J1-value, the model exhibits a first-order transition into an incommensurate multiple-q ordered state where multiple Bragg peaks coexist in the spin structure factor. We show that there are two types of metastable multiple-q states, a cubic symmetric sextuple-q state and a non-cubic symmetric quadruple-q stat…
Targeting specific technological applications requires the control of nanoparticle properties, especially the crystalline polymorph. Freezing a nanodroplet deposited on a solid substrate leads to the formation of crystalline structures. We study the inherent mechanisms underlying this general phenomenon by means of molecular dynamics simulations. Our work shows that different crystal structures can be selected by finely tuning the solid substrate lattice parameter. Indeed, while for our system, face-centered cubic is usually the most preponderant structure, the growth of two distinct polymorph…
While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). In polymers and biomolecules, NTE originates from the entropic elasticity of an ideal, freely-jointed chain. The origin of NTE in solids has been widely believed to be different. Our neutron scattering study of a simple cubic NTE material, ScF3, overturns this consensus. We observe that the correlation in the positions of the neighboring fluorine atoms rapidly fades on warming, indicating an uncorrelated thermal motion constrained by the rigid Sc-F bonds. This leads us to a quanti…
Based on a simple general relation for the Lorentz field, the precise values are obtained for the energies of ferromagnetic and basic antiferromagnetic states in sc, bcc, fcc, and diamond cubic lattices. Within both the 'nearest-neighbor' and group-theoretic approaches, a large variety of antiferromagnetic states revealed as corresponding to the lowest energies is addressed, with recognizing their spherical spin-orientation degeneracy, which turns out to be rather special in fcc lattices.
The self-assembly of colloidal diamond (CD) crystals is considered as one of the most coveted goals of nanotechnology, both from the technological and fundamental points of view. For applications, colloidal diamond is a photonic crystal which can open new possibilities of manipulating light for information processing. From a fundamental point of view, its unique symmetry exacerbates a series of problems that are commonly faced during the self-assembly of target structures, such as the presence of kinetic traps and the formation of crystalline defects and alternative structures (polymorphs). He…
A smooth path of rearrangement from the body-centered cubic (bcc) to the face-centered cubic (fcc) lattice is obtained by introducing a single parameter to cuboidal lattice vectors. As a result, we obtain analytical expressions in terms of lattice sums for the cohesive energy. This is described by a Lennard-Jones (LJ) interaction potential and the sticky hard sphere (SHS) model with an $r^{-n}$ long-range attractive term. These lattice sums are evaluated to computer precision by expansions in terms of a fast converging series of Bessel functions. Applying the whole range of lattice parameters …
