The sparse Blume-Emery-Griffiths model of associative memories

We analyze the Blume-Emery-Griffiths (BEG) associative memory with sparse patterns and at zero temperature. We give bounds on its storage capacity provided that we want the stored patterns to be fixed points of the retrieval dynamics. We compare our results to that of other models of sparse neural networks and show that the BEG model has a superior performance compared to them.Comment: 23 p

Uranyl and/or Rare-Earth Mellitates in Extended Organic–Inorganic Networks: A Unique Case of Heterometallic Cation–Cation Interaction with U^VIO–Ln^III Bonding (Ln = Ce, Nd)

A series of uranyl and lanthanide (trivalent Ce, Nd) mellitates (<i>mel</i>) has been hydrothermally synthesized in aqueous solvent. Mixtures of these 4f and 5f elements also revealed the formation of a rare case of lanthanide–uranyl coordination polymers. Their structures, determined by XRD single-crystal analysis, exhibit three distinct architectures. The pure lanthanide mellitate Ln₂(H₂O)₆(<i>mel</i>) possesses a 3D framework built up from the connection of isolated LnO₆(H₂O)₃ polyhedra (tricapped trigonal prism) through the mellitate ligand. The structure of the uranyl mellitate (UO₂)₃(H₂O)₆(<i>mel</i>)·11.5H₂O is lamellar and consists of 8-fold coordinated uranium atoms linked to each other through the organic ligand giving rise to the formation of a 2D 3⁶ net. The third structural type, (UO₂)₂Ln­(OH)­(H₂O)₃(<i>mel</i>)·2.5H₂O, involves direct oxygen bondings between the lanthanide and uranyl centers, with the isolation of a heterometallic dinuclear motif. The 9-fold coordinated Ln cation, LnO₅(OH)­(H₂O)₃, is linked to the 7-fold coordinated uranyl (UO₂)­O₄(OH) (pentagonal bipyramid) via one μ₂-hydroxo group and one μ₂-oxo group. The latter is shared between the uranyl bonding (UO = 1.777(4)/1.779(6) Å) and a long Ln–O bonding (Ce–O = 2.822(4) Å; Nd–O = 2.792(6) Å). This unusual linkage is a unique illustration of the so-called cation–cation interaction associating 4f and 5f metals. The dinuclear motif is then further connected through the mellitate ligand, and this generates organic–inorganic layers that are linked to each other via discrete uranyl (UO₂)­O₄ units (square bipyramid), which ensure the three-dimensional cohesion of the structure. The mixed U–Ln carboxylate is thermally decomposed from 260 to 280 °C and then transformed into the basic uranium oxide (U₃O₈) together with U–Ln oxide with the fluorite structural type (“(Ln,U)­O₂”). At 1400 °C, only fluorite type “(Ln,U)­O₂” is formed with the measured stoichiometry of U_0.63Ce_0.37O₂ and U_0.60Nd_0.40O_2−δ

Uranyl and/or Rare-Earth Mellitates in Extended Organic–Inorganic Networks: A Unique Case of Heterometallic Cation–Cation Interaction with U^VIO–Ln^III Bonding (Ln = Ce, Nd)

A series of uranyl and lanthanide (trivalent Ce, Nd) mellitates (<i>mel</i>) has been hydrothermally synthesized in aqueous solvent. Mixtures of these 4f and 5f elements also revealed the formation of a rare case of lanthanide–uranyl coordination polymers. Their structures, determined by XRD single-crystal analysis, exhibit three distinct architectures. The pure lanthanide mellitate Ln₂(H₂O)₆(<i>mel</i>) possesses a 3D framework built up from the connection of isolated LnO₆(H₂O)₃ polyhedra (tricapped trigonal prism) through the mellitate ligand. The structure of the uranyl mellitate (UO₂)₃(H₂O)₆(<i>mel</i>)·11.5H₂O is lamellar and consists of 8-fold coordinated uranium atoms linked to each other through the organic ligand giving rise to the formation of a 2D 3⁶ net. The third structural type, (UO₂)₂Ln­(OH)­(H₂O)₃(<i>mel</i>)·2.5H₂O, involves direct oxygen bondings between the lanthanide and uranyl centers, with the isolation of a heterometallic dinuclear motif. The 9-fold coordinated Ln cation, LnO₅(OH)­(H₂O)₃, is linked to the 7-fold coordinated uranyl (UO₂)­O₄(OH) (pentagonal bipyramid) via one μ₂-hydroxo group and one μ₂-oxo group. The latter is shared between the uranyl bonding (UO = 1.777(4)/1.779(6) Å) and a long Ln–O bonding (Ce–O = 2.822(4) Å; Nd–O = 2.792(6) Å). This unusual linkage is a unique illustration of the so-called cation–cation interaction associating 4f and 5f metals. The dinuclear motif is then further connected through the mellitate ligand, and this generates organic–inorganic layers that are linked to each other via discrete uranyl (UO₂)­O₄ units (square bipyramid), which ensure the three-dimensional cohesion of the structure. The mixed U–Ln carboxylate is thermally decomposed from 260 to 280 °C and then transformed into the basic uranium oxide (U₃O₈) together with U–Ln oxide with the fluorite structural type (“(Ln,U)­O₂”). At 1400 °C, only fluorite type “(Ln,U)­O₂” is formed with the measured stoichiometry of U_0.63Ce_0.37O₂ and U_0.60Nd_0.40O_2−δ

Single Crystal Synthesis Methods Dedicated to Structural Investigations of Very Low Solubility Mixed-Actinide Oxalate Coordination Polymers

Two crystal growth methods dedicated to very low solubility actinide coordination polymers have been developed and applied to the synthesis of mixed actinide­(IV)–actinide­(IV) or actinide­(IV)–actinide­(III) oxalate single crystals of a size (typically 100–300 μm) suitable for isolating them and examining their crystal structure. These methods have been optimized on mixed systems composed of U­(IV) and lanthanide (surrogate of trivalent actinides) and then assessed on U­(IV)–Am­(III), Pu­(IV)–Am­(III), and U­(IV)–Pu­(IV) mixtures. Three types of single crystals characterized by different structures have been obtained according to the synthesis and the chemical conditions. This is the first time that these well-known or recently discovered key compounds are formed by crystal growth methods specifically developed for actinide crystal handling (i.e., in glove boxes), thus enabling direct structural studies on transuranium element systems and acquisition of basic data. Characterization by X-ray diffraction, UV–visible solid spectroscopy, thermal ionization mass spectroscopy (TIMS), energy-dispersive X-ray spectroscopy (EDS), and inductively coupled plasma atomic emission spectroscopy (ICP-AES) demonstrates the potentialities and complementarity of the two crystal growth methods for obtaining the targeted mixed oxalates (actinide oxidation state and presence of both metallic ions in the crystal). More generally, this development opens broad prospects for single crystal synthesis of novel actinide organic frameworks and their structural description

Crystal Growth and First Crystallographic Characterization of Mixed Uranium(IV)–Plutonium(III) Oxalates

The mixed-actinide uranium­(IV)–plutonium­(III) oxalate single crystals (NH₄)_0.5[Pu^III_0.5U^IV_0.5(C₂O₄)₂·H₂O]·<i>n</i>H₂O (<b>1</b>) and (NH₄)_2.7Pu^III_0.7U^IV_1.3(C₂O₄)₅·<i>n</i>H₂O (<b>2</b>) have been prepared by the diffusion of different ions through membranes separating compartments of a triple cell. UV–vis, Raman, and thermal ionization mass spectrometry analyses demonstrate the presence of both uranium and plutonium metal cations with conservation of the initial oxidation state, U^IV and Pu^III, and the formation of mixed-valence, mixed-actinide oxalate compounds. The structure of <b>1</b> and an average structure of <b>2</b> were determined by single-crystal X-ray diffraction and were solved by direct methods and Fourier difference techniques. Compounds <b>1</b> and <b>2</b> are the first mixed uranium­(IV)–plutonium­(III) compounds to be structurally characterized by single-crystal X-ray diffraction. The structure of <b>1</b>, space group <i>P</i>4/<i>n</i>, <i>a</i> = 8.8558(3) Å, <i>b</i> = 7.8963(2) Å, <i>Z</i> = 2, consists of layers formed by four-membered rings of the two actinide metals occupying the same crystallographic site connected through oxalate ions. The actinide atoms are nine-coordinated by oxygen atoms from four bidentate oxalate ligands and one water molecule, which alternates up and down the layer. The single-charged cations and nonbonded water molecules are disordered in the same crystallographic site. For compound <b>2</b>, an average structure has been determined in space group <i>P</i>6/<i>mmm</i> with <i>a</i> = 11.158(2) Å and <i>c</i> = 6.400(1) Å. The honeycomb-like framework [Pu^III_0.7U^IV_1.3(C₂O₄)₅]^2.7‑ results from a three-dimensional arrangement of mixed (U_0.65Pu_0.35)­O₁₀ polyhedra connected by five bis-bidentate μ²-oxalate ions in a trigonal-bipyramidal configuration

Crystal Growth and First Crystallographic Characterization of Mixed Uranium(IV)–Plutonium(III) Oxalates

The mixed-actinide uranium­(IV)–plutonium­(III) oxalate single crystals (NH₄)_0.5[Pu^III_0.5U^IV_0.5(C₂O₄)₂·H₂O]·<i>n</i>H₂O (<b>1</b>) and (NH₄)_2.7Pu^III_0.7U^IV_1.3(C₂O₄)₅·<i>n</i>H₂O (<b>2</b>) have been prepared by the diffusion of different ions through membranes separating compartments of a triple cell. UV–vis, Raman, and thermal ionization mass spectrometry analyses demonstrate the presence of both uranium and plutonium metal cations with conservation of the initial oxidation state, U^IV and Pu^III, and the formation of mixed-valence, mixed-actinide oxalate compounds. The structure of <b>1</b> and an average structure of <b>2</b> were determined by single-crystal X-ray diffraction and were solved by direct methods and Fourier difference techniques. Compounds <b>1</b> and <b>2</b> are the first mixed uranium­(IV)–plutonium­(III) compounds to be structurally characterized by single-crystal X-ray diffraction. The structure of <b>1</b>, space group <i>P</i>4/<i>n</i>, <i>a</i> = 8.8558(3) Å, <i>b</i> = 7.8963(2) Å, <i>Z</i> = 2, consists of layers formed by four-membered rings of the two actinide metals occupying the same crystallographic site connected through oxalate ions. The actinide atoms are nine-coordinated by oxygen atoms from four bidentate oxalate ligands and one water molecule, which alternates up and down the layer. The single-charged cations and nonbonded water molecules are disordered in the same crystallographic site. For compound <b>2</b>, an average structure has been determined in space group <i>P</i>6/<i>mmm</i> with <i>a</i> = 11.158(2) Å and <i>c</i> = 6.400(1) Å. The honeycomb-like framework [Pu^III_0.7U^IV_1.3(C₂O₄)₅]^2.7‑ results from a three-dimensional arrangement of mixed (U_0.65Pu_0.35)­O₁₀ polyhedra connected by five bis-bidentate μ²-oxalate ions in a trigonal-bipyramidal configuration

Crystal Growth and First Crystallographic Characterization of Mixed Uranium(IV)–Plutonium(III) Oxalates

The mixed-actinide uranium­(IV)–plutonium­(III) oxalate single crystals (NH₄)_0.5[Pu^III_0.5U^IV_0.5(C₂O₄)₂·H₂O]·<i>n</i>H₂O (<b>1</b>) and (NH₄)_2.7Pu^III_0.7U^IV_1.3(C₂O₄)₅·<i>n</i>H₂O (<b>2</b>) have been prepared by the diffusion of different ions through membranes separating compartments of a triple cell. UV–vis, Raman, and thermal ionization mass spectrometry analyses demonstrate the presence of both uranium and plutonium metal cations with conservation of the initial oxidation state, U^IV and Pu^III, and the formation of mixed-valence, mixed-actinide oxalate compounds. The structure of <b>1</b> and an average structure of <b>2</b> were determined by single-crystal X-ray diffraction and were solved by direct methods and Fourier difference techniques. Compounds <b>1</b> and <b>2</b> are the first mixed uranium­(IV)–plutonium­(III) compounds to be structurally characterized by single-crystal X-ray diffraction. The structure of <b>1</b>, space group <i>P</i>4/<i>n</i>, <i>a</i> = 8.8558(3) Å, <i>b</i> = 7.8963(2) Å, <i>Z</i> = 2, consists of layers formed by four-membered rings of the two actinide metals occupying the same crystallographic site connected through oxalate ions. The actinide atoms are nine-coordinated by oxygen atoms from four bidentate oxalate ligands and one water molecule, which alternates up and down the layer. The single-charged cations and nonbonded water molecules are disordered in the same crystallographic site. For compound <b>2</b>, an average structure has been determined in space group <i>P</i>6/<i>mmm</i> with <i>a</i> = 11.158(2) Å and <i>c</i> = 6.400(1) Å. The honeycomb-like framework [Pu^III_0.7U^IV_1.3(C₂O₄)₅]^2.7‑ results from a three-dimensional arrangement of mixed (U_0.65Pu_0.35)­O₁₀ polyhedra connected by five bis-bidentate μ²-oxalate ions in a trigonal-bipyramidal configuration