Synthesis,crystal structure,and magnetic properties of K4Mn3(HPO4)4(H2PO4)2

A new layered compound, K₄Mn₃(HPO₄)₄(H₂PO₄)₂ (1), has been synthesized under hydrothermal conditions. It crystallizes in the monoclinic space group P2₁/n with a = 8.874(2) Å, b = 6.554(1) Å, c = 18.075(4) Å, and β = 93.39(3)°. The structure consists of zigzag [Mn₃O₁₄]_n chains of edge-sharing MnO₆ octahedrons and MnO₇ pentagonal bi-pyramids, which form layers of formula [Mn₃(HPO₄)₄(H₂PO₄)₂]^4? in the ab plane via H₂PO₄ and HPO₄ units with vertex-sharing. Potassium ions lie between these layers. Magnetic measurements indicate Curie–Weiss behavior above 6 K for 1. A Heisenberg model, with alternating exchange interactions J₁J₁J₂… within the chain and exchange interactions J₃J₃… between the chains, is proposed to describe the magnetic behavior.     

Crystal structures of Th(OH)PO4, U(OH)PO4 and Th2O(PO4)2. Condensation mechanism of MIV(OH)PO4 (M = Th,U) into M2O(PO4)2

Three new crystal structures, isotypic with β-Zr₂O(PO₄)₂, have been resolved by the Rietveld method. All crystallize with an orthorhombic cell (S.G.: Cmca) with a = 7.1393(2) Å, b = 9.2641(2) Å, c = 12.5262(4) Å, V = 828.46(4) Å³ and Z = 8 for Th(OH)PO₄; a = 7.0100(2) Å, b = 9.1200(2) Å, c = 12.3665(3) Å, V = 790.60(4) Å³ and Z = 8 for U(OH)PO₄; a = 7.1691(3) Å, b = 9.2388(4) Å, c = 12.8204(7) Å, V = 849.15(7) Å³ and Z = 4 for Th₂O(PO₄)₂. By heating, the M(OH)PO₄ (M = Th, U) compounds condense topotactically into M₂O(PO₄)₂, with a change of the environment of the tetravalent cation that lowers from 8 to 7 oxygen atoms. The lower stability of Th₂O(PO₄)₂ compared to that of U₂O(PO₄)₂ seems to result from this unusual environment for tetravalent thorium.     

Synthesis,structure and NMR characterization of a new monomeric aluminophosphate [dl-Co(en)3]2[Al(HPO4)2(H1.5PO4)2(H2PO4)2](H3PO4)4 containing four different types of monophosphates

A new zero-dimensional (0D) aluminophosphate monomer [dl-Co(en)₃]₂[Al(HPO₄)₂(H_1.5PO₄)₂(H₂PO₄)₂](H₃PO₄)₄ (designated AlPO-CJ38) with Al/P ratio of 1/6 has been solvothermally prepared by using racemic cobalt complex dl-Co(en)₃Cl₃ as the template. The Al atom is octahedrally linked to six P atoms via bridging oxygen atoms, forming a unique [Al(HPO₄)₂(H_1.5PO₄)₂(H₂PO₄)₂]^6? monomer. Notably, there exists intramolecular symmetrical O?H?O bonds, which results in pseudo-4-rings stabilized by the strong H-bonding interactions. The structure is also featured by the existence of four different types of monophosphates that have been confirmed by ³¹P NMR and ¹H NMR spectra. The crystal data are as follows: AlPO-CJ38, [dl-Co(en)₃]₂[Al(HPO₄)₂(H_1.5PO₄)₂(H₂PO₄)₂](H₃PO₄)₄, M = 1476.33, monoclinic, C2/c (No. 15), a = 36.028(7) Å, b = 8.9877(18) Å, c = 16.006(3) Å, β = 100.68(3)°, U = 5093.2(18) Å³_, Z = 4, R₁ = 0.0509 (I > 2σ(I)) and wR₂ = 0.1074 (all data). CCDC number 689491.     

Syntheses and crystal structures of new vanadium(IV) oxyphosphates M(VO)2(PO4)2 with M = Co,Ni

We have extended our research interest on titanium oxyphosphates (M^II(TiO)₂(PO₄)₂, with M^II = Mg, Fe, Co, Ni, Cu, Zn) to vanadium oxyphosphates M^II(V^IVO)₂(PO₄)₂ (M^II = Co, Ni). For each compound two phases, named α and β according to synthesis conditions, have been stabilized at room temperature, then characterized. The four crystal structures M(VO)₂(PO₄)₂ (α and β for M = Co, Ni) have been determined in monoclinic P2₁/c space group using X-ray single crystals diffraction data. Structure of the α phase is derived from the Li(TiO)(PO₄) (orthorhombic Pnma) and LiNi_0.50(TiO)₂(PO₄)₂ (monoclinic P2₁/c) types, with cell parameters: a = 6.310(1) Å, b = 7.273(1) Å, c = 7.432(1) Å, β = 90.43(1)° for M = Co, and a = 6.297(2) Å, b = 7.230(2) Å, c = 7.421(2) Å, β = 90.36(2)° for M = Ni. Structure of the β phase is derived from the Ni(TiO)₂(PO₄)₂-type (monoclinic P2₁/c) with cell parameters: a = 7.2742(2) Å, b = 7.2802(2) Å, c = 7.4550(2) Å, β = 120.171(2)° for M = Co, and a = 7.2691(2) Å, b = 7.2366(2) Å, c = 7.4453(2) Å, β = 120.231(2)° for M = Ni. All these structures consist of a three dimensional (3D) framework built up of infinite chains of tilted corner-sharing [VO₆] octahedra, cross-linked by corner-sharing [PO₄] tetrahedra. The M²⁺ ion (M = Co, Ni) is located in a triangular based antiprism which shares faces with two [VO₆] octahedra. Structural filiation is discussed based on a common structural unit, a sheet where divalent cations M²⁺ (M = Co, Ni) are inserted. A thermal study of the α ? β transition is also presented.     

Magnetic properties of hybrid organo-inorganic copper(II) oxovanadate(V) phosphate and phosphonate bridged systems

The hybrid organo-inorganic compounds [Cu₄(bipy)₄V₄O₁₁(PO₄)₂]nH₂O (n ∼ 5) (1), [Cu₂(phen)₂(PO₄)(H₂PO₄)₂(VO₂) · 2H₂O] (2) and [Cu₂(phen)₂(O₃PCH₂PO₃)(V₂O₅) (H₂O)]H₂O (3) which present different bridging forms of the phosphate/phosphonate group, show different bulk magnetic properties. We herein analyze the magnetic behaviour of these compounds in terms of their structural parameters. We also report a theoretical study for compound (1) assuming four different magnetic exchange pathways between the copper centres present in the tetranuclear unit. For compound (1) the following J values were obtained J₁ = +3.29; J₂ = −0.63; J₃ = −2.23; J₄ = −46.14 cm⁻¹. Compound (2) presents a Curie–Weiss behaviour in the whole range of temperature (3–300 K), and compound (3) shows a maximum for the magnetic susceptibility at 64 K, typical for antiferromagnetic interactions. These data where fitted using a model previously reported in the literature, assuming two different magnetic exchange pathways between the four copper(II) centres, with J₁ = −30.0 and J₂ = −8.5 cm⁻¹.     

Jahn–Teller phase transition in Cu0.50TiO(PO4): Powder structural characterization of the β-variety and thermal study

The thermal study of Cu_0.50TiO(PO₄), by X-ray diffraction and DSC, shows a phase transition α → β with a hysteresis (∼600 °C during heating; ∼300 °C during cooling). Single crystals have been obtained for the α-phase but the β-phase can only be stabilised at room temperature as a powder mixture with α. Structural characterization of the β-variety has been done with diffraction data (X-ray Cu Kα₁ and neutrons) using a powder rich in β-phase (α(20%) + β(80%)). A monoclinic cell (a = 7.1134(7) Å; b = 7.7282(7) Å; c = 7.3028(7) Å; β=119.30(1)°; V = 350.1(1) Å³) has been found for β-phase, space group P2₁/c. An “ab initio” structure determination has been done, and the Rietveld refinement leads to cR_wp = 0.150 and R_B = 0.041. The results from the X-ray data were confirmed by refinements from neutron data.Similarly to the α-phase, the structure of β-Cu_0.50TiO(PO₄) can be described as a TiOPO₄ framework constituted of chains of tilted corner-sharing [TiO₆] octahedra running parallel to the c axis and cross linked by [PO₄] tetrahedra. Ti atoms are displaced from the centres of the octahedral units, leading to long (2.27 Å) and short (1.73 Å) Ti–O(1) bonds. The [CuO₆] octahedra exhibit a typical Jahn–Teller distorted coordination with four short equatorial Cu–O bonds (2 × 1.93 Å and 2 × 2.06 Å), and two longer apical Cu–O bonds (2 × 2.33 Å). The two longer Cu–O bonds are almost parallel to the b axis.The transition from the α to the β-phase is characterized by a “rocking” of the Jahn–Teller elongation from the (a,c) plane to the b direction accompanied by a relatively strong expansion of the cell volume.     

Crystal structure and ionic conductivity of AgCr2(PO4)(P2O7)

Single crystals of a new phosphate AgCr₂(PO₄)(P₂O₇) have been prepared by the flux method and its structural and the infrared spectrum have been investigated. This compound crystallizes in the monoclinic system with the space group C2/c and the parameters are, a = 11.493 (3) Å, b = 8.486 (3) Å, c = 8.791 (2) Å, β = 114.56 (2)°, V = 779.8 (3) ųand Z = 4. Its structure consists of CrO₆ octahedra sharing corners with P₂O₇ units to form undulating chains extending infinitely along the [110] direction. These chains are connected by the phosphate tetrahedra giving rise to a 3D framework with six-sided tunnels parallel to the [101] direction, where the Ag⁺ ions are located. The infrared spectrum of this compound was interpreted on the basis of P₂O₇^4? and PO₄^3? vibrations. The appearance of ν_sP–O–P in the spectrum suggests a bent P–O–P bridge for the P₂O₇^4? ions in the compound, which is in agreement with the X-ray data. The electrical measurements allow us to obtain the activation energy of (1.36 eV) and the conductivity measurements suggest that the charge carriers through the structure are the silver captions.     

Ce(H2O)(PO4)3/2(H3O)1/2(H2O)1/2, a second entry in the structural chemistry of cerium(IV) phosphates

A cerium(IV) phosphate has been prepared using precipitation methods and its structure has been solved by single crystal X-ray diffraction (R₁ = 0.0292 for 3092 reflections with I>2σ(I) and wR₂ = 0.0540). Ce(H₂O)(PO₄)_3/2(H₃O)_1/2(H₂O)_1/2 crystallises in the monoclinic space group C2/c (a = 15.7058(17) Å, b = 9.6261(9) Å, c = 10.1632(4) Å, ß = 121.623(7)°, and V = 1308.4 (2) Å³). Its structure is based on a negatively charged 3D framework, made of cerium atoms connected by PO₄ tetrahedra. There are two types of PO₄ units; one shares only corners with the cerium coordination polyhedra while the other one shares edges and corners. This structure also includes hydronium cations, to balance the framework charge, and water molecules. One special feature of this 3D framework is the formation of interconnected tunnels which extend along the c axis and contain the hydronium cations and the water molecules. This open framework and the presence of cationic species in the tunnels are in perfect agreement with the previously reported ion exchange properties.     

Piperazinium dihydrogen phosphate,C4H12N2(H2PO4)2: Synthesis, 31P CP/MAS NMR,structural and thermal investigations

A new piperazinium dihydrogen orthophosphate, C₄H₁₂N₂(H₂PO₄)₂ was discovered and characterized by combining information from X-ray diffraction, ³¹P CP/MAS NMR and thermal analysis (TG/DTA). The compound C₄H₁₂N₂(HPO₄)·H₂O, was also studied in order to compare these two similar materials. The hydrothermal stability is investigated for the system: 1.0 C₄H₁₀N₂: n H₃PO₄: 55–60 H₂O, 0.5 < n < 3. The reaction mixtures with pH in the range 1.6–8.4 were placed at a fixed temperature in the range 20–180 °C for ca. 5 days. C₄H₁₂N₂(H₂PO₄)₂ was obtained when n > ca. 2. A crystal of piperazinium dihydrogen phosphate, C₄H₁₂N₂(H₂PO₄)₂ was structurally investigated using X-ray diffraction: triclinic, space group $P\overline{1}$, a = 7.023(2), b = 7.750(3), c = 12.203(4) Å, α = 84.668(7), β = 81.532(7) and γ = 63.174(6)°, V = 586.0(4) Å³ and Z = 2. The reactivity of C₄H₁₂N₂(H₂PO₄)₂ was investigated by systematic solvothermal syntheses.     

Structure and magnetic properties of a novel copper diphosphonate with pillared layered structure:: Cu2(H2O)2{O3PCH2N(C2H4)2NCH2PO3}

Compound Cu₂(H₂O)₂{O₃PCH₂N(C₂H₄)₂NCH₂PO₃} (1) has a pillared layered structure in which the organic groups of N,N′-piperazinebis(methylenephosphonate) are sandwiched between the inorganic layers. Compared with other copper phosphonates with layered or pillared layered structures, the inorganic layer in 1 is unique in that each {CPO₃} tetrahedron is corner-shared with three {CuO₄N} square pyramids through three oxygen donors. Ferromagnetic interactions are mediated between the metal centers. Crystal data: Pbca, a=10.0830(16) Å, b=9.4517(15) Å, c=13.218(2) Å, V=1259.7(3) Å³, Z=4.     

Raman spectra of Sr3(PO4)2 and Ba3(PO4)2 orthophosphates at various temperatures

The Raman spectra for Sr₃(PO₄)₂ and Ba₃(PO₄)₂ were investigated in the temperature range from 80 to 1623 K at atmospheric pressure. An unexpected melting of each sample was observed around 1573–1583 K in this study. In the temperature range from 80 to 1323 K, the Raman wavenumbers of all observed bands for Sr₃(PO₄)₂ and Ba₃(PO₄)₂ continuously decrease with increasing temperature. A quantitative analysis on the wavenumbers of Raman bands for both samples reveals that the ν₃ antisymmetric stretching vibrations show the strongest temperature dependence and the ν₂ symmetric bending vibration displays the weakest temperature dependence. The effects of cations on Raman bands are discussed. The reason for the unexpected melting of both samples is mainly attributed to the significant contribution from excess surface energy and the grain-boundary energy that has apparently lowered the melting points of the small samples, i.e., Gibbs–Thomson effect.     

Incorporation of 3d-metal ions in the hexagonal channels of the Sr5(PO4)3OH apatite

Strontium phosphate apatites with compositions Sr₅(PO₄)₃Zn_0.15O_0.3(OH)_0.7, Sr₅(PO₄)₃Ni_0.2O_0.4(OH)_0.6, and Sr₅(PO₄)₃Co_0.2O_0.5(OH)_0.4 were synthesized by solid state reaction at 1400 °C in air. The samples were characterized by powder X-ray diffraction, EDX analysis, magnetic measurements and IR spectroscopy. The crystal structures were refined by the Rietveld method in the space group P6₃/m with lattice constants a = 9.7499(1), 9.7722(1), 9.7507(1) Å and c = 7.3066(1), 7.2962(1), 7.2988(1) Å, respectively. The 3d-metal atoms were found randomly distributed in the hexagonal channels formally substituting hydrogen in the initial hydroxyapatite. Zn and Ni atoms were twofold coordinated by oxygen atoms such that the linear O–M–O groups formed in the channel separated by the OH groups. Co atom was shifted from the channel center giving the O–Co–O fragment distorted from a linear geometry probably due to the additional coordination by the oxygen atoms of the phosphate groups.     

New three-dimensional (3,4)-net zincophosphites templated by linear diammonium cations: H3N(CH2)5NH3·Zn3(HPO3)4 and β-H3N(CH2)6NH3·Zn3(HPO3)4

The mild-condition syntheses, single-crystal structures and properties of H₃N(CH₂)₅NH₃·Zn₃(HPO₃)₄ and β-H₃N(CH₂)₆NH₃·Zn₃(HPO₃)₄ are reported. Both are constructed from (3,4)-nets of ZnO₄ tetrahedra and HPO₃ pyramids, sharing vertices to result in three-dimensional anionic open-frameworks. In both materials, the organic species interacts with the framework by way of N–H⋯O bonds. Crystal data: H₃N(CH₂)₅NH₃·Zn₃(HPO₃)₄, M_r = 620.22, orthorhombic, Pccn (No. 56), a = 9.5364 (9) Å, b = 21.8015 (19) Å, c = 9.1118 (7) Å, V = 1894.4 (3) Å³, Z = 4, R(F) = 0.044, wR(F²) = 0.111. β-H₃N(CH₂)₆NH₃·Zn₃(HPO₃)₄, M_r = 634.25, monoclinic, P2₁/n (No. 14), a = 8.7627 (1) Å, b = 13.8117 (2) Å, c = 16.6187 (3) Å, β = 92.680 (1)°, V = 2009.12 (5) Å³, Z = 4, R(F) = 0.072, wR(F²) = 0.187.     

Synthesis and crystal structure of sodium copper tetrametaphosphimate heptahydrate Na2Cu(PO2NH)4·7H2O and sodium potassium copper tetrametaphosphimate heptahydrate KxNa2−xCu(PO2NH)4·7H2O

Na₂Cu(PO₂NH)₄·7H₂O and K_xNa_2−xCu(PO₂NH)₄·7H₂O (x ≈ 0.5) were synthesized by gel crystallization in sodium silicate gels. The crystal structures were solved by single-crystal X-ray methods and found to be isotypic (Pnma, Z = 4; Na₂Cu(PO₂NH)₄·7H₂O: a = 627.5(2) pm, b = 1456.0(3) pm, c = 1900.5(4) pm, R1 = 0.0352; K_0.47Na_1.53Cu(PO₂NH)₄·7H₂O: a = 632.2(2) pm, b = 1460.0(3) pm, c = 1936.4(4) pm, R1 = 0.0345). The P₄N₄ rings of the tetrametaphosphimate anion exhibit a distorted chair-2 conformation with admixtures of saddle and crown conformation. The M⁺ ions are six- and sevenfold coordinated by oxygen atoms, the Cu²⁺ ions are fivefold coordinated, respectively. The MO₇ and the CuO₅ units form pairs of face-sharing polyhedra, which are connected by common corners forming chains and are further interconnected by tetrametaphosphimate anions, forming a three-dimensional network structure with channels along [100] and [010]. The MO₆ units form chains of face-sharing polyhedra, which are situated in the channels along [100]. Extended hydrogen bonding reinforces the three-dimensional framework structure of the compounds. ²³Na-MAS NMR experiments were conducted to verify the K/Na distribution on the M sites derived from the X-ray crystal structure refinement.     

Synthesis and characterization of a novel three-dimensional open-framework: Metal diphosphonate,Zn[HO3PCH2(C6H4)CH2PO3H]

A novel zinc diphosphonate, Zn[HO₃PCH₂(C₆H₄)CH₂PO₃H] (1) was synthesized from tetraethyl para-xylylenediphosphonate, Et₂O₃PCH₂C₆H₄CH₂PO₃Et₂, and Zn (AcO)₂·2H₂O under solvothermal conditions. The structure of compound 1 was determined by single-crystal X-ray diffraction, which reveals that the structure crystallizes in the monoclinic space group C2/c (No. 15), with a = 22.4844(19) Å, b = 6.4361(5) Å, c = 8.1194(7) Å, β = 102.595(2)°, V = 1146.70(16) Å³, T = 298(2) K, Z = 8. The novel three-dimensional (3D) construction is simply built up from linear inorganic chains of corner-sharing four-rings of tetrahedral [ZnO₄] and [PO₃C] which connected adjacent chains by the organophosphorus ligand para-xylylenediphosphonate. The framework has 10 Å × 4 Å (containing the van der Waals radii of atoms) channels running along the b-axis.     

The influence of partial substitution of phosphorus by arsenic in monoclinic CsH2PO4. X-ray single crystal,vibrational and phase transitions in the mixed CsH2(PO4)0.72(AsO4)0.28

Partial substitution of P by As, leading to the solid solution CsH₂(PO₄)_1−x(AsO₄)_x, with x=0.28 (abbreviated as CDAP) has been shown. The structural characteristics of the crystals were analyzed by means of X-ray diffraction, which revealed that the new title compound is nearly isomorphous with the monoclinic phase of CsH₂PO₄ (CDP). The structure was solved from 796 independent reflections with R₁=0.0292 and Rw₂=0.0702, refined with 59 parameters. The following results have been obtained: space group P2₁, a=4.9250(4) Å, b=6.4370(3) Å, c=7.9280(6) Å, β=107.316(3)°, V=239.94(3) Å³, Z=2 and ρ_cal=3.349 g cm⁻³. The hydrogen bonds are clearly distinguished in the electron density maps which display distributions corresponding to order of protons. The shorter bond (2.452(4) Å), links the phosphate–arsenate groups into chains running along the b-axis and the longer bond (2.531(3) Å), crosslinks the chains to form (001) layers. The Raman and infrared spectra of CDAP recorded at room temperature in the frequency ranges 15–1200 cm⁻¹ and 400–4000 cm⁻¹, respectively, confirm the presence of PO³⁻₄ and AsO³⁻₄ groups in the crystal. Differential scanning calorimetry traces show three phase transitions at 333, 449 and 490 K in this material, which are characterized by X-ray powder diffraction at high temperature.     

Study of the ionic conductivity of Ca6La4(PO4)2(SiO4)4F2 and Ca4La6(SiO4)6F2

In order to enhance our knowledge about the Ca_10−xLa_x(PO₄)_6−x(SiO₄)_xF₂ (0 ≤ x ≤ 6) series, whose chemical stability decreases as the substitution degree increases, Ca₆La₄(PO₄)₂(SiO₄)₄F₂ and Ca₄La₆(SiO₄)₆F₂ compounds were prepared through a solid-state reaction. Their ionic conductivity was measured by impedance spectroscopy. The results indicate that the conductivity increases with substitution, and fits the Arrhenius equation over the investigated temperature range. At high temperatures, a change in the activation energy has been observed, which has been related to the nature of the Ca/La–F bond, i.e. to the polarizability of lanthanum.     

Structure cristalline d'un nouvel hydroxyphosphate naturel de strontium,fer et aluminium (lulzacite), Sr2Fe(Fe0,63Mg0,37)2Al4(PO4)4(OH)10

Crystal structure of a new natural strontium, iron and aluminium hydroxyphosphate (lulzacite): Sr₂Fe(Fe_0.63Mg_0.37)₂Al₄(PO₄)₄(OH)₁₀. The crystal structure of a new natural strontium, iron and aluminium hydroxyphosphate (lulzacite) has been solved through an X-ray study of a single crystal:– symmetry: triclinic (P1̄);– unit cell parameters: a=5.457(1) Å, b=9.131(2) Å, c=9.769(2) Å, α=108.47(3)°, β=91.72(3)° and γ=97.44(3);– structural formula: (Sr_0.96Ba_0.04)₂Fe(Fe_0.63Mg_0.37)₂Al₄[(P_0.98V_0.02)O₄]₄(OH)₁₀ (Z=1).The structure presents along the b axis the alternation, on one hand of infinite chains of edge sharing octahedra (one Fe²⁺O₆ and an AlO₆ pair), and, on the other hand, of trimers with a central AlO₆ octahedron framed by two mixed (Fe²⁺,Mg)O₆ octahedra. Trimers and chains are linked by the corners of one AlO₆ octahedron and two PO₄ tetrahedra. Strontium ions are located in the channels of the structure. This structure is isotypic with that of jamesite, a lead arsenate. Similar octahedral building blocks are present in other mineral species: trimers in ludlamite (iron phosphate), chains in various hydroxysalts. © 2000 Académie des sciences / Éditions scientifiques et médicales Elsevier SASlulzacite / hydroxyphosphate / phosphate / strontium / iron / aluminium     

Doping effect of nonmagnetic impurity on the spin-Peierls-like transition in the quasi-one-dimensional (quasi-1D) spin system of 1-(4′-nitrobenzyl)pyridinium bis(maleonitriledithiolato)nickelate

A nonmagnetic compound, [NO₂BzPy][Cu(mnt)₂] (mnt^2? = maleonitriledithiolate; NO₂BzPy⁺ = 1-(4′-nitrobenzyl)pyridinium), is isostructural with [NO₂BzPy][Ni(mnt)₂], which is a quasi-1D spin system and exhibits a spin-Peierls-like transition with J = 192 K in the gapless state and spin energy gap = 738 K in the dimerization state, respectively. Further, five nonmagnetic impurity doped compounds [NO₂BzPy][Cu_xNi_1?x(mnt)₂] (x = 0.04–0.74) were prepared, and their crystal structures as well as magnetic properties were investigated. The nonmagnetic doping causes the suppression of the spin transition with an average rate of 139(13) K/percentage of dopant concentration, and the transition collapse is estimated at around x > 0.5.