Quantum entanglement plays a pivotal role in a number of communication protocols, like secret sha... more Quantum entanglement plays a pivotal role in a number of communication protocols, like secret sharing and quantum cryptography. We consider a scenario where more than two parties are involved in a protocol and they share a multipartite entangled state. In particular, we introduce the protocol of cooperative quantum key distribution (CoQKD). In this protocol, two parties, Alice and Bob establish a key with the cooperation of other parties. Other parties control whether Alice and Bob can establish the key, its security and the key rate. We discuss the case of three parties in detail and find the necessary suitable resource states. We discuss the controlling power of the third party, Charlie. We also examine the usefulness of this new resource state for generating conference key and for cooperative teleportation. In the case of conference key, we find that recently introduced Bell inequalities can be useful to establish the security. We also generalize the scenario to more than three p...
Non-trivial facet inequalities play important role in detecting and quantifying the nonolocality ... more Non-trivial facet inequalities play important role in detecting and quantifying the nonolocality of a state -- specially a pure state. Such inequalities are expected to be tight. Number of such inequalities depends on the Bell test scenario. With the increase in the number of parties, dimensionality of the Hilbert space, or/and the number of measurements, there are more nontrivial facet inequalities. By considering a specific measurement scenario, we find that for any multipartite qubit state, local polytope can have only one nontrivial facet. Therefore there exist a possibility that only one Bell inequality, and its permutations, would be able to detect the nonlocality of a pure state. The scenario involves two dichotomic measurement settings for two parties and one dichotomic measurement by other parties. This measurement scenario for a multipartite state may be considered as minimal scenario involving multipartite correlations that can detect nonlocality. We present detailed resu...
Abstract Three new water soluble dimetallic copper(II) complexes, [Cu(H2O)5][Cu2(cpdp)(µ-O2As(CH3... more Abstract Three new water soluble dimetallic copper(II) complexes, [Cu(H2O)5][Cu2(cpdp)(µ-O2As(CH3)2)]2Br2·13.83H2O·0.67CH3OH (1), [Cu2(Hcpdp)(µ-SO4)]·5H2O (2) and [Cu2(cpdp)(µ-pz)]·16H2O (3) (H3cpdp = N,N′-Bis[2-carboxybenzomethyl]-N,N′-Bis[2-pyridylmethyl]-1,3-diaminopropan-2-ol; (CH3)2AsO2− = cacodylate; SO42− = sulfate; pz− = pyrazolate) have been successfully synthesized and characterized for the investigation of coordination/binding aspects with biologically significant monosaccharide, d -glucosamine. Preparation of 1, 2 and 3 has been achieved by carrying out reaction of H3cpdp with stoichiometric quantities of CuCl2·2H2O/NaO2As(CH3)2·3H2O, CuSO4·5H2O and CuCl2·2H2O/1H-pyrazole, respectively, in the presence of NaOH in MeOH/H2O at ambient temperature. Diverse analytical methods, for example, microanalysis, FTIR, UV–Vis and mass spectral techniques, including single crystal X-ray crystallography, have been utilized to characterize these complexes. Temperature dependant (2–300 K) magnetic susceptibility measurements reveal the presence of antiferromagnetic interactions between the copper(II) centers in 1 and 2. Thermogravimetric analysis of 1–3 indicates that they are stable on average up to ~ 214 °C. We have employed the UV–Vis spectroscopic technique to study the 1:1 interactions of the complexes with d -glucosamine in alkaline aqueous solution. The UV–Vis titration spectra clearly indicate the binding-induced steady decrease of the absorption intensities of 1–3, with a substantial blue shift of absorption maxima of the complexes upon addition of increasing amounts of d -glucosamine. The binding constant values between the complexes and d -glucosamine have been evaluated from the experimentally obtained UV–Vis titration data. Fukui functions at the metal sites, including HOMOs and LUMOs in 1–3 have been calculated by DFT method to forecast the possible metal centers engaged in the binding process with d -glucosamine. To the best of our knowledge, to date, neither the substrate interaction nor the mode of interaction with respect to d -glucosamine using any metal complex of any nuclearity has been documented in the literature.
Quantum entanglement plays a pivotal role in many communication protocols, like secret sharing an... more Quantum entanglement plays a pivotal role in many communication protocols, like secret sharing and quantum cryptography. We consider a scenario where more than two parties are involved in a protocol and share a multipartite entangled state. In particular, we considered the protocol of Controlled Quantum Key Distribution (CoQKD), introduced in the Ref. Chin. Phys. Lett. 20, 183-185 (2003), where, two parties, Alice and Bob establish a key with the cooperation of other parties. Other parties control/supervise whether Alice and Bob can establish the key, its security and key rate. We discuss the case of three parties in detail and find suitable resource states. We discuss the controlling power of the third party, Charlie. We also examine the usefulness of the new resource states for generating conference key and for cooperative teleportation. We find that recently introduced Bell inequalities can be useful to establish the security of the conference key. We also generalize the scenario to more than three parties.
Monthly Notices of the Royal Astronomical Society, 2021
The observations of high-redshifts quasars at z ≳ 6 have revealed that supermassive black holes (... more The observations of high-redshifts quasars at z ≳ 6 have revealed that supermassive black holes (SMBHs) of mass $\sim 10^9\, \mathrm{M_{\odot }}$ were already in place within the first ∼Gyr after the big bang. Supermassive stars (SMSs) with masses $10^{3-5}\, \mathrm{M_{\odot }}$ are potential seeds for these observed SMBHs. A possible formation channel of these SMSs is the interplay of gas accretion and runaway stellar collisions inside dense nuclear star clusters (NSCs). However, mass-loss due to stellar winds could be an important limitation for the formation of the SMSs and affect the final mass. In this paper, we study the effect of mass-loss driven by stellar winds on the formation and evolution of SMSs in dense NSCs using idealized N-body simulations. Considering different accretion scenarios, we have studied the effect of the mass-loss rates over a wide range of metallicities Z* = [.001–1]Z⊙ and Eddington factors $f_{\rm Edd}=L_\ast /L_{\mathrm{Edd}}=0.5,0.7,\, \,\mathrm{ an...
Monthly Notices of the Royal Astronomical Society, 2021
More than 200 supermassive black holes (SMBHs) of masses $\gtrsim 10^9\, \mathrm{M_{\odot }}$ hav... more More than 200 supermassive black holes (SMBHs) of masses $\gtrsim 10^9\, \mathrm{M_{\odot }}$ have been discovered at z ≳ 6. One promising pathway for the formation of SMBHs is through the collapse of supermassive stars (SMSs) with masses $\sim 10^{3}{-}10^{5} \, \mathrm{M_{\odot }}$ into seed black holes which could grow upto few times $10^9\, \mathrm{M_{\odot }}$ SMBHs observed at z ∼ 7. In this paper, we explore how SMSs with masses $\sim 10^{3}{-}10^{5} \, \mathrm{M_{\odot }}$ could be formed via gas accretion and runaway stellar collisions in high-redshift, metal-poor nuclear star clusters (NSCs) using idealized N-body simulations. We explore physically motivated accretion scenarios, e.g. Bondi–Hoyle–Lyttleton accretion and Eddington accretion, as well as simplified scenarios such as constant accretions. While gas is present, the accretion time-scale remains considerably shorter than the time-scale for collisions with the most massive object (MMO). However, overall the time-sca...
To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fide... more To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fidelity of a teleported state depends on the resource state purity and entanglement, as characterized by concurrence. Concurrence and purity are functions of state parameters. However, it turns out that a state with larger purity and concurrence, may have comparatively smaller fidelity. By computing teleportation fidelity, concurrence and purity for two-qubit X-states, we show it explicitly. We further show that fidelity changes monotonically with respect to functions of parameters-other than concurrence and purity. A state with smaller concurrence and purity, but larger value of one of these functions has larger fidelity. These functions, thus characterize nonlocal classical and/or quantum properties of the state that are not captured by purity and concurrence alone. In particular, concurrence is not enough to characterize the entanglement properties of a two-qubit mixed state.
Certain correlations in Quantum Mechanics are not compatible with local-realistic theory, first s... more Certain correlations in Quantum Mechanics are not compatible with local-realistic theory, first shown by John Bell 1 ; those correlations must violate a inequality-Bell inequality. Gisin's theorem 2 tells us that all pure bipartite entangled states violate the CHSH inequality 3. But, the violation of Bell inequality is only sufficient criteria for certifying entanglement but not a necessary one even for the case of two qubit states. Example : Werner state. Unlike pure bipartite case, the relationship between entanglement and nonlocality is not simple even for pure multipartite states. Using Hardy's argument it was shown that all pure entangled states violate a single Bell inequality 4 .
Employing the Pauli matrices, we have constructed a set of operators, which can be used to distin... more Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under SLOCC (stochastic local operation and classical communication) for three-qubit pure states. These operators have very simple structure and can be obtained from the Mermin's operator with suitable choice of directions. Moreover these operators may be implemented in an experiment to distinguish the types of entanglement present in a state. We show that the measurement of only one operator is sufficient to distinguish GHZ class from rest of the classes. It is also shown that it is possible to detect and classify other classes by performing a small number of measurements. We also show how to construct such observables in any basis. We also consider a few mixed states to investigate the usefulness of our operators. Furthermore, we consider the teleportation scheme of Lee et al. [19] and show that the partial tangles and hence teleportation fidelity can be measured. We have also shown that these partial tangles can also be used to classify genuinely entangled state, biseparable state and separable state.
One of the ideas to explain the existence of supermassive black holes (SMBH) that are in place by... more One of the ideas to explain the existence of supermassive black holes (SMBH) that are in place by z ∼ 7 is that there was an earlier phase of very rapid accretion onto direct collapse black holes (DCBH) that started their lives with masses ∼ 10 4−5 M. Working in this scenario, we show that the mass function of SMBH after such a limited time period with growing formation rate paired with super-Eddington accretion can be described as a broken power-law with two characteristic features. There is a power-law at intermediate masses whose index is the dimensionless ratio α ≡ λ/γ, where λ is the growth rate of the number of DCBH during their formation era, and γ is the growth rate of DCBH masses by super-Eddington accretion during the DCBH growth era. A second feature is a break in the power law profile at high masses, above which the mass function declines rapidly. The location of the break is related to the dimensionless number β = γ T , where T is the duration of the period of DCBH growth. If the SMBH continue to grow at later times at an Eddington-limited accretion rate, then the observed quasar luminosity function can be directly related to the tapered power-law function derived in this paper.
A carboxylate containing polydentate ligand in combination with exogeneous succinate (suc) has be... more A carboxylate containing polydentate ligand in combination with exogeneous succinate (suc) has been used to stabilize heterometallic octanuclear [Li 2 Na 2 Cu 4 (cpdp) 2 (suc) 2 (CH 3 OH) 2 (H 2 O) 4 ]Cl 2 Á6H 2 O (1) and decanuclear Na(H 3 O) 2 [Li 2 Zn 8 (cpdp) 4 (suc) 2 (H 2 O) 4 ]Cl 2 Br 3 Á6MeOHÁ19H 2 O (2) complexes. The reaction of ligand H 3 cpdp (H 3 cpdp = N,N'-bis[2-carboxybenzomethyl]-N,N'-bis[2-pyridylmethyl]-1,3-diaminopropan-2-ol) with stoichiometric amounts of CuCl 2 /sodium succinate, and ZnCl 2 /sodium succinate, allowed isolation of complexes 1 and 2, respectively. Analyses of single crystal X-ray structures indicate that complex 1 is capped by two [Cu 2 (cpdp)] + molecular building units and two succinate linkers, while complex 2 is overlaid by four [Zn 2 (cpdp)] + molecular building units and two succinate linkers. Whereas complex 1 shows monodentate terminal and tridentate l 3 :g 2 :g 1 :g 1 bridging coordination of carboxylate, and l 4 :g 2 :g 1 :g 1 :g 1 bridging mode of succinate, complex 2 displays monodentate terminal and anti-anti l 2 :g 1 :g 1 bidentate bridging coordination of carboxylate, and l 4 :g 1 :g 1 :g 1 :g 1 bridging mode of succinate. To our knowledge, 1 is the first example of copper/lithium/sodium-based hetero-octanuclear complex with any class of bridging or non-bridging ligand showing three different binding modes of carboxylates. Again, 2 is also the first example of a hetero-decanuclear metallomacrocyclic complex with any class of bridging or non-bridging ligand combining both lithium and zinc. Variable temperature magnetic investigation of 1 discloses sensible antiferromagnetic interactions intermediated among the copper centers. Thermal behavior of 1 and 2 has been examined by thermogravimetric analysis indicating that the complexes are stable up to $430°C.
Fracture surface retains an imprint of the entire deformation history undergone in a material. He... more Fracture surface retains an imprint of the entire deformation history undergone in a material. Hence, it is possible to derive the approximate deformation and fracture properties of a material from a systematic quantitative fractographic analysis when the microstructure is known. In this research, the deformation behaviour and fracture characteristics of a spinodal decomposed copper alloy at various ageing conditions have been investigated thoroughly. Systematic changes in microstructure are implemented in this alloy through the alteration of ageing time at an elevated temperature on different specimens. As a result, the wavelength and amplitude of modulated spinodal structures have been varied, while those of initial inclusion content, other second phase particles' volume/distribution, initial crystallographic texture and grain size were kept unaltered. Spinodal decomposition results from the coherency strains, hence the zone of mismatch of strain/ stress between phases/interfaces acts as micro/nano void nucleation sites under tensile deformation. The twodimensional tensile fracture features were correlated with the deformation and fracture properties of the alloy under constant strain rate at different ageing conditions at ambient environment. The results obtained bring novel and smart fractographic information to the mechanical engineers and nuclear scientists investigating ductile fracture micromechanisms of spinodal decomposed alloys. This is a novel technique to characterise the material from an analysis of the fracture surface features.
Quantum entanglement plays a pivotal role in a number of communication protocols, like secret sha... more Quantum entanglement plays a pivotal role in a number of communication protocols, like secret sharing and quantum cryptography. We consider a scenario where more than two parties are involved in a protocol and they share a multipartite entangled state. In particular, we introduce the protocol of cooperative quantum key distribution (CoQKD). In this protocol, two parties, Alice and Bob establish a key with the cooperation of other parties. Other parties control whether Alice and Bob can establish the key, its security and the key rate. We discuss the case of three parties in detail and find the necessary suitable resource states. We discuss the controlling power of the third party, Charlie. We also examine the usefulness of this new resource state for generating conference key and for cooperative teleportation. In the case of conference key, we find that recently introduced Bell inequalities can be useful to establish the security. We also generalize the scenario to more than three p...
Non-trivial facet inequalities play important role in detecting and quantifying the nonolocality ... more Non-trivial facet inequalities play important role in detecting and quantifying the nonolocality of a state -- specially a pure state. Such inequalities are expected to be tight. Number of such inequalities depends on the Bell test scenario. With the increase in the number of parties, dimensionality of the Hilbert space, or/and the number of measurements, there are more nontrivial facet inequalities. By considering a specific measurement scenario, we find that for any multipartite qubit state, local polytope can have only one nontrivial facet. Therefore there exist a possibility that only one Bell inequality, and its permutations, would be able to detect the nonlocality of a pure state. The scenario involves two dichotomic measurement settings for two parties and one dichotomic measurement by other parties. This measurement scenario for a multipartite state may be considered as minimal scenario involving multipartite correlations that can detect nonlocality. We present detailed resu...
Abstract Three new water soluble dimetallic copper(II) complexes, [Cu(H2O)5][Cu2(cpdp)(µ-O2As(CH3... more Abstract Three new water soluble dimetallic copper(II) complexes, [Cu(H2O)5][Cu2(cpdp)(µ-O2As(CH3)2)]2Br2·13.83H2O·0.67CH3OH (1), [Cu2(Hcpdp)(µ-SO4)]·5H2O (2) and [Cu2(cpdp)(µ-pz)]·16H2O (3) (H3cpdp = N,N′-Bis[2-carboxybenzomethyl]-N,N′-Bis[2-pyridylmethyl]-1,3-diaminopropan-2-ol; (CH3)2AsO2− = cacodylate; SO42− = sulfate; pz− = pyrazolate) have been successfully synthesized and characterized for the investigation of coordination/binding aspects with biologically significant monosaccharide, d -glucosamine. Preparation of 1, 2 and 3 has been achieved by carrying out reaction of H3cpdp with stoichiometric quantities of CuCl2·2H2O/NaO2As(CH3)2·3H2O, CuSO4·5H2O and CuCl2·2H2O/1H-pyrazole, respectively, in the presence of NaOH in MeOH/H2O at ambient temperature. Diverse analytical methods, for example, microanalysis, FTIR, UV–Vis and mass spectral techniques, including single crystal X-ray crystallography, have been utilized to characterize these complexes. Temperature dependant (2–300 K) magnetic susceptibility measurements reveal the presence of antiferromagnetic interactions between the copper(II) centers in 1 and 2. Thermogravimetric analysis of 1–3 indicates that they are stable on average up to ~ 214 °C. We have employed the UV–Vis spectroscopic technique to study the 1:1 interactions of the complexes with d -glucosamine in alkaline aqueous solution. The UV–Vis titration spectra clearly indicate the binding-induced steady decrease of the absorption intensities of 1–3, with a substantial blue shift of absorption maxima of the complexes upon addition of increasing amounts of d -glucosamine. The binding constant values between the complexes and d -glucosamine have been evaluated from the experimentally obtained UV–Vis titration data. Fukui functions at the metal sites, including HOMOs and LUMOs in 1–3 have been calculated by DFT method to forecast the possible metal centers engaged in the binding process with d -glucosamine. To the best of our knowledge, to date, neither the substrate interaction nor the mode of interaction with respect to d -glucosamine using any metal complex of any nuclearity has been documented in the literature.
Quantum entanglement plays a pivotal role in many communication protocols, like secret sharing an... more Quantum entanglement plays a pivotal role in many communication protocols, like secret sharing and quantum cryptography. We consider a scenario where more than two parties are involved in a protocol and share a multipartite entangled state. In particular, we considered the protocol of Controlled Quantum Key Distribution (CoQKD), introduced in the Ref. Chin. Phys. Lett. 20, 183-185 (2003), where, two parties, Alice and Bob establish a key with the cooperation of other parties. Other parties control/supervise whether Alice and Bob can establish the key, its security and key rate. We discuss the case of three parties in detail and find suitable resource states. We discuss the controlling power of the third party, Charlie. We also examine the usefulness of the new resource states for generating conference key and for cooperative teleportation. We find that recently introduced Bell inequalities can be useful to establish the security of the conference key. We also generalize the scenario to more than three parties.
Monthly Notices of the Royal Astronomical Society, 2021
The observations of high-redshifts quasars at z ≳ 6 have revealed that supermassive black holes (... more The observations of high-redshifts quasars at z ≳ 6 have revealed that supermassive black holes (SMBHs) of mass $\sim 10^9\, \mathrm{M_{\odot }}$ were already in place within the first ∼Gyr after the big bang. Supermassive stars (SMSs) with masses $10^{3-5}\, \mathrm{M_{\odot }}$ are potential seeds for these observed SMBHs. A possible formation channel of these SMSs is the interplay of gas accretion and runaway stellar collisions inside dense nuclear star clusters (NSCs). However, mass-loss due to stellar winds could be an important limitation for the formation of the SMSs and affect the final mass. In this paper, we study the effect of mass-loss driven by stellar winds on the formation and evolution of SMSs in dense NSCs using idealized N-body simulations. Considering different accretion scenarios, we have studied the effect of the mass-loss rates over a wide range of metallicities Z* = [.001–1]Z⊙ and Eddington factors $f_{\rm Edd}=L_\ast /L_{\mathrm{Edd}}=0.5,0.7,\, \,\mathrm{ an...
Monthly Notices of the Royal Astronomical Society, 2021
More than 200 supermassive black holes (SMBHs) of masses $\gtrsim 10^9\, \mathrm{M_{\odot }}$ hav... more More than 200 supermassive black holes (SMBHs) of masses $\gtrsim 10^9\, \mathrm{M_{\odot }}$ have been discovered at z ≳ 6. One promising pathway for the formation of SMBHs is through the collapse of supermassive stars (SMSs) with masses $\sim 10^{3}{-}10^{5} \, \mathrm{M_{\odot }}$ into seed black holes which could grow upto few times $10^9\, \mathrm{M_{\odot }}$ SMBHs observed at z ∼ 7. In this paper, we explore how SMSs with masses $\sim 10^{3}{-}10^{5} \, \mathrm{M_{\odot }}$ could be formed via gas accretion and runaway stellar collisions in high-redshift, metal-poor nuclear star clusters (NSCs) using idealized N-body simulations. We explore physically motivated accretion scenarios, e.g. Bondi–Hoyle–Lyttleton accretion and Eddington accretion, as well as simplified scenarios such as constant accretions. While gas is present, the accretion time-scale remains considerably shorter than the time-scale for collisions with the most massive object (MMO). However, overall the time-sca...
To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fide... more To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fidelity of a teleported state depends on the resource state purity and entanglement, as characterized by concurrence. Concurrence and purity are functions of state parameters. However, it turns out that a state with larger purity and concurrence, may have comparatively smaller fidelity. By computing teleportation fidelity, concurrence and purity for two-qubit X-states, we show it explicitly. We further show that fidelity changes monotonically with respect to functions of parameters-other than concurrence and purity. A state with smaller concurrence and purity, but larger value of one of these functions has larger fidelity. These functions, thus characterize nonlocal classical and/or quantum properties of the state that are not captured by purity and concurrence alone. In particular, concurrence is not enough to characterize the entanglement properties of a two-qubit mixed state.
Certain correlations in Quantum Mechanics are not compatible with local-realistic theory, first s... more Certain correlations in Quantum Mechanics are not compatible with local-realistic theory, first shown by John Bell 1 ; those correlations must violate a inequality-Bell inequality. Gisin's theorem 2 tells us that all pure bipartite entangled states violate the CHSH inequality 3. But, the violation of Bell inequality is only sufficient criteria for certifying entanglement but not a necessary one even for the case of two qubit states. Example : Werner state. Unlike pure bipartite case, the relationship between entanglement and nonlocality is not simple even for pure multipartite states. Using Hardy's argument it was shown that all pure entangled states violate a single Bell inequality 4 .
Employing the Pauli matrices, we have constructed a set of operators, which can be used to distin... more Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under SLOCC (stochastic local operation and classical communication) for three-qubit pure states. These operators have very simple structure and can be obtained from the Mermin's operator with suitable choice of directions. Moreover these operators may be implemented in an experiment to distinguish the types of entanglement present in a state. We show that the measurement of only one operator is sufficient to distinguish GHZ class from rest of the classes. It is also shown that it is possible to detect and classify other classes by performing a small number of measurements. We also show how to construct such observables in any basis. We also consider a few mixed states to investigate the usefulness of our operators. Furthermore, we consider the teleportation scheme of Lee et al. [19] and show that the partial tangles and hence teleportation fidelity can be measured. We have also shown that these partial tangles can also be used to classify genuinely entangled state, biseparable state and separable state.
One of the ideas to explain the existence of supermassive black holes (SMBH) that are in place by... more One of the ideas to explain the existence of supermassive black holes (SMBH) that are in place by z ∼ 7 is that there was an earlier phase of very rapid accretion onto direct collapse black holes (DCBH) that started their lives with masses ∼ 10 4−5 M. Working in this scenario, we show that the mass function of SMBH after such a limited time period with growing formation rate paired with super-Eddington accretion can be described as a broken power-law with two characteristic features. There is a power-law at intermediate masses whose index is the dimensionless ratio α ≡ λ/γ, where λ is the growth rate of the number of DCBH during their formation era, and γ is the growth rate of DCBH masses by super-Eddington accretion during the DCBH growth era. A second feature is a break in the power law profile at high masses, above which the mass function declines rapidly. The location of the break is related to the dimensionless number β = γ T , where T is the duration of the period of DCBH growth. If the SMBH continue to grow at later times at an Eddington-limited accretion rate, then the observed quasar luminosity function can be directly related to the tapered power-law function derived in this paper.
A carboxylate containing polydentate ligand in combination with exogeneous succinate (suc) has be... more A carboxylate containing polydentate ligand in combination with exogeneous succinate (suc) has been used to stabilize heterometallic octanuclear [Li 2 Na 2 Cu 4 (cpdp) 2 (suc) 2 (CH 3 OH) 2 (H 2 O) 4 ]Cl 2 Á6H 2 O (1) and decanuclear Na(H 3 O) 2 [Li 2 Zn 8 (cpdp) 4 (suc) 2 (H 2 O) 4 ]Cl 2 Br 3 Á6MeOHÁ19H 2 O (2) complexes. The reaction of ligand H 3 cpdp (H 3 cpdp = N,N'-bis[2-carboxybenzomethyl]-N,N'-bis[2-pyridylmethyl]-1,3-diaminopropan-2-ol) with stoichiometric amounts of CuCl 2 /sodium succinate, and ZnCl 2 /sodium succinate, allowed isolation of complexes 1 and 2, respectively. Analyses of single crystal X-ray structures indicate that complex 1 is capped by two [Cu 2 (cpdp)] + molecular building units and two succinate linkers, while complex 2 is overlaid by four [Zn 2 (cpdp)] + molecular building units and two succinate linkers. Whereas complex 1 shows monodentate terminal and tridentate l 3 :g 2 :g 1 :g 1 bridging coordination of carboxylate, and l 4 :g 2 :g 1 :g 1 :g 1 bridging mode of succinate, complex 2 displays monodentate terminal and anti-anti l 2 :g 1 :g 1 bidentate bridging coordination of carboxylate, and l 4 :g 1 :g 1 :g 1 :g 1 bridging mode of succinate. To our knowledge, 1 is the first example of copper/lithium/sodium-based hetero-octanuclear complex with any class of bridging or non-bridging ligand showing three different binding modes of carboxylates. Again, 2 is also the first example of a hetero-decanuclear metallomacrocyclic complex with any class of bridging or non-bridging ligand combining both lithium and zinc. Variable temperature magnetic investigation of 1 discloses sensible antiferromagnetic interactions intermediated among the copper centers. Thermal behavior of 1 and 2 has been examined by thermogravimetric analysis indicating that the complexes are stable up to $430°C.
Fracture surface retains an imprint of the entire deformation history undergone in a material. He... more Fracture surface retains an imprint of the entire deformation history undergone in a material. Hence, it is possible to derive the approximate deformation and fracture properties of a material from a systematic quantitative fractographic analysis when the microstructure is known. In this research, the deformation behaviour and fracture characteristics of a spinodal decomposed copper alloy at various ageing conditions have been investigated thoroughly. Systematic changes in microstructure are implemented in this alloy through the alteration of ageing time at an elevated temperature on different specimens. As a result, the wavelength and amplitude of modulated spinodal structures have been varied, while those of initial inclusion content, other second phase particles' volume/distribution, initial crystallographic texture and grain size were kept unaltered. Spinodal decomposition results from the coherency strains, hence the zone of mismatch of strain/ stress between phases/interfaces acts as micro/nano void nucleation sites under tensile deformation. The twodimensional tensile fracture features were correlated with the deformation and fracture properties of the alloy under constant strain rate at different ageing conditions at ambient environment. The results obtained bring novel and smart fractographic information to the mechanical engineers and nuclear scientists investigating ductile fracture micromechanisms of spinodal decomposed alloys. This is a novel technique to characterise the material from an analysis of the fracture surface features.
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