Pb 17Li Research Articles

Anomalous behavior of liquid K–Pb alloys: Excess stability, entropy, and heat capacity

Electromotive force measurements of the potassium activity in liquid K–Pb alloys are reported as a function of composition for T=640, 723, and 879 K and also as a function of temperature for compositions ranging from 2–70 at.% potassium. Thermodynamic mixing properties derived from these measurements indicate anomalous behavior around the equiatomic composition. The Darken excess stability function (or its equivalent the Bhatia–Thornton concentration fluctuations) shows only one well-defined extremum, which occurs at XK=0.52. Contrary to the case of both the Li–Pb and Na–Pb systems, no peak is detected in the excess stability function of K–Pb at the composition corresponding to A4Pb, where A refers to the alkali metal. The variations of the total entropy of mixing with composition exhibit features characteristic of ordered solutions with a sharp negative minimum at about 52 at. % potassium. These results are in consonance with published measurements of electrical conductivity and its temperature coefficient which indicate ordering in the liquid phase around the potassium–lead equiatomic composition. At this composition, in a temperature interval close to the melting point of the corresponding compound K⋅Pb, the composition dependence of the changes in the average heat capacity upon mixing goes through a maximum with a magnitude of about 62 J mol−1 K−1, which is atypical of metallic systems. This unexpected result provides a surprising contrast to prior work on other alkali–lead alloys.

Investigations of binary lithium-zinc, lithium-cadmium and lithium-lead alloys as negative electrodes in organic solvent-based electrolyte

The thermodynamic properties of the binary LiZn, LiCd and LiPb alloy systems were investigated in an organic solvent-based electrolyte at ambient temperature. Titration curves showed several intermediate phases existing in each lithium alloy system. There was a wide composition range in Li y Cd (1.5 ⩽ y ⩽ 3), which showed a very low equilibrium potential (below 60 mV) against pure lithium. There was a longer potential plateau in the LiPb system corresponding to Li y Pb (1 ⩽ y ⩽ 3) at about 450 mV against pure lithium. The preliminary charge-discharge and polarization results showed rather fast kinetics for Li y Zn (0.67 ⩽ y ⩽ 1), Li y Cd (1.5 < y < 2.0), and Li y Pb (1 < y < 3).

A chemical theory analysis of the solution thermodynamics of oxygen, nitrogen and hydrogen in lead-rich LiPb mixtures

The large non-idealities which are seen in LiPb solution thermodynamics are treated by postulating the existence of stable LiPb molecules in solution and strong surface tension effects around all dissolved impurity compounds. The equilibrium constant for LiPb formation obeys the following temperature dependence: In K eq = −1.44+ 7000 T Formulations which derive from these assumptions are used to calculate cold-trap solubilities for hydrogen, nitrogen and oxygen. The minimum cold-trap concentrations (mole fraction) in LiPb eutectic are 4.8 × 10 −5 for hydrogen, 2.5 × 10 −4 for nitrogen and 5.1 × 10 −6 for oxygen; these values are rather lower than the solubilities observed in pure lithium. The same formulations are used to calculate the Sieverts constants for hydrogen and nitrogen in lead-rich LiPb solution; these results agree with the experimentally observed constants. The surface tension interactions are assumed to equal the sum of the energy required to form a hole in the fluid and the energy which is released when the impurity compound is inserted within that hole. The method used here for estimating the latter energy is, I believe, exceptional in its rigor and its predictive capacity. Its use, however, is limited to liquid alloys of metals which, like LiPb, do not form heterometallic oxides and nitrides.

Transient thermal-hydraulics considerations of tandem mirror LiPb cooled blankets during start-up/shutdown operations

The operational aspects of fusion reactors are being recognized as important ingredients of the design process. In this paper, we present analyses and modeling relevant to the understanding of blanket performance during transients. The use of LiPb as a blanket coolant is considered in this paper from the viewpoint of transient operation during initial start-up. When LiPb is first introduced into the blanket tubes in the form of a molten metal, freezing/blockage and thermal shock to the tubes may occur. We first model the transient thermal behavior of the coolant (LiPb)-tube system. We then proceed to analyze the thermal shock to the blanket tubes upon contact with the hot LiPb. It is shown that freezing/blockage due to excessive heat losses from the LiPb coolant is not a major design consideration. However, thermal stresses caused by differential expansion during transients should be mitigated by appropriate pre-heating of blanket modules.

Transient thermal-hydraulics considerations of tandem mirror LiPb cooled blankets during start-up/shutdown operations

The operational aspects of fusion reactors are being recognized as important ingredients of the design process. In this paper, we present analyses and modeling relevant to the understanding of blanket performance during transients. The use of LiPb as a blanket coolant is considered in this paper from the viewpoint of transient operation during initial start-up. When LiPb is first introduced into the blanket tubes in the form of a molten metal, freezing/blockage and thermal shock to the tubes may occur. We first model the transient thermal behavior of the coolant (LiPb)-tube system. We then proceed to analyze the thermal shock to the blanket tubes upon contact with the hot LiPb. It is shown that freezing/blockage due to excessive heat losses from the LiPb coolant is not a major design consideration. However, thermal stresses caused by differential expansion during transients should be mitigated by appropriate pre-heating of blanket modules.

Primary loop conditioning and design constraints of LiPb cooled tandem mirror reactors during start-up/shutdown operations

Engineering considerations during start-up/shutdown operations, and during transients induced by power level variations are considered in this paper. Flooding of cold blanket modules with hot LiPb results in severe strain transients that may lead to fatigue failure. The entire primary system, including blanket modules, must therefore be pre-conditioned. We first analyze, and present results of design, for a pre-heat system for the Mirror Advanced Reactor Study (MARS). The pre-heat system is based on helium gas pre-heating for the primary piping and blanket modules. Operational transients induced by partial power variations, or by loss of fusion power are then considered. It is found that the response of the primary loop system is dictated by how fast pumps can accommodate power fluctuations. Pump transients are modeled with a focus on the time dependent power balance through the pump system. Time constants for a representative pump are also derived. Finally, the situation of a total loss of pump power is investigated. In this case, natural circulation due to boyancy pressure differences is shown to be sufficient for the removal of decay afterheat immediately after a loss of pump power.

Primary loop conditioning and design constraints of LiPb cooled tandem mirror reactors during start-up/shutdown operations

Engineering considerations during start-up/shutdown operations, and during transients induced by power level variations are considered in this paper. Flooding of cold blanket modules with hot LiPb results in severe strain transients that may lead to fatigue failure. The entire primary system, including blanket modules, must therefore be pre-conditioned. We first analyze, and present results of design, for a pre-heat system for the Mirror Advanced Reactor Study (MARS). The pre-heat system is based on helium gas pre-heating for the primary piping and blanket modules. Operational transients induced by partial power variations, or by loss of fusion power are then considered. It is found that the response of the primary loop system is dictated by how fast pumps can accommodate power fluctuations. Pump transients are modeled with a focus on the time dependent power balance through the pump system. Time constants for a representative pump are also derived. Finally, the situation of a total loss of pump power is investigated. In this case, natural circulation due to boyancy pressure differences is shown to be sufficient for the removal of decay afterheat immediately after a loss of pump power.

Thermodynamic properties of liquid Na-VIB alloys

The thermodynamic quantities of mixing such as free energy ΔG, entropy ΔS and enthalpy ΔH of liquid Na-IVb alloys are discussed in view of formation of chemical complex. From these, the excess specific heat ΔC p as a function of temperature, which is resulted from the dissociation of chemical complex, is particularly concerned. The discrepancies in the compound-forming tendencies among liquid NaPb, NaSn and LiPb are also discussed.

Structure of multi-component hard-sphere mixtures application to the liquid LiPb alloy

The general formulae for the partial and the total structure factors of an m-component mixture are obtained and it is shown that the explicit expressions of them can be obtained for the hard-sphere mixture based on the exact solution of the Percus-Yevick equation due to Hiroike. The formulae are applied to the liquid LiPb alloy and the theoretical results for the total structure factor and its temperature dependence are in good agreement with the recent experimental results due to Ruppersberg and Reiter.

Thermodynamic calculations for the liquid systems NaK, KCs and LiPb

The semi-empirical model for the calculation of the Gibbs free energy of mixing via the entropy of mixing, proposed by Visser et al. [1], is used to determine the activity coefficients and the long-wavelength limit of the structure factor, S CC(0). For the liquid alloys systems NaK and KCs the method leads to fairly accurate results, indicating almost ideal behaviour. For the compound-forming liquid alloys systems LiPb the agreement with experiment is less favourable, but the calculations clearly demonstrate the important influence of the volume contraction on the entropy.

Thermodynamic investigation of the LiAl and LiPb systems by the hydrogen titration method

The hydrogen titration method (HTM) constitutes a new technique for investigating the thermodynamic properties and phase relations in binary A-B alloys. It is based on the reaction A( in alloy) + ( x 2 ) H 2( g) ⇌ AH x( s) in which constituent A in the alloy is the material being titrated, hydrogen is the titrant and AH x is the titration product. Equivalence points of the titration are indicated by the steeply rising segments in the isotherms of hydrogen pressure versus alloy composition and correspond to the stoichiometries of the intermediate phases in the alloy. For a given temperature and composition the chemical potential of constituent A can be determined from the corresponding hydrogen pressure and the standard free energy of formation of AH x . The method was tested on two lithium-based systems, LiAl and LiPb. The results verified the validity of the HTM by showing that (1) the hydriding reaction (with A  Li, x = 1) is reversible, (2) the anticipated intermediate phases are correctly identified and (3) there is a good agreement with the available e.m.f. data on the chemical potentials of lithium in these alloys. For the α + β field of the LiAl system the lithium activity, calculated from the combined HTM and e.m.f. data, is represented by In a Li = 2.662−5302 T −1. For the LiPb system, HTM results indicated the existence of a new phase having a stoichiometry between Li 22Pb 5 and Li 7Pb 2. Criteria for applying the HTM to other alloy systems are discussed.

Theory of anomalous thermodynamic properties of liquid semiconducting alloys

A microscopic theory for the isothermal compressibility, the partial volumes, and the stability of liquid alloys with semiconducting behaviour at certain stoichiometric compositions is presented in terms of the low wavenumber limit of the partial structure factors. Using the random phase approximation for the Ornstein Zernike direct correlation functions the quantities can be shown to be composed of a hard core part and a part coming from the long range interatomic potentials. The latter are assumed to be composed of a metallic part treated by pseudopotential theory plus an electronically screened attractive Coulomb interaction due to charge transfer. Under the additional assumption of a reduced electronic density of states near the stoichiometric composition the measured anomalies can be qualitatively explained. In the case of LiPb good agreement with experiment is achieved.

Thermodynamic properties of a quasi-ionic alloy from electromotive force measurements: The Li–Pb system

Electromotive force measurements of the activity of lithium in lithium–lead liquid alloys are reported in the temperature range T=770–932 K. The partial molar excess Gibbs free energies are negative. Variations with composition exhibit an inflection point around an atomic fraction of lead equal to 0.2 which corresponds to the ratio of the valences of Li and Pb. The inflection point, as well as structural data, may be interpreted by assuming an at least partly ionic character of the alloy. A set of partial structure factors defined by Faber and Ziman are calculated as a function of the composition at the long-wavelength limit. Their variations support the hypothesis of a local short-range order around the above-mentioned composition (0.2). Finally, a modeling approach based on an electron transfer from Li to Pb is used to explain some of the characteristics of this class of alloys.

ChemInform Abstract: EXPERIMENTAL EVIDENCE FROM LIQUID SEMICONDUCTORS

AbstractÜbersichtsartikel über 2 allgemeine Grundtypen flüssiger Halbleiter (keine geschmolzenen Festhalbleiter); auf Alkalimetall‐ ( ;z.B. die Systeme Li‐Pb und Cs‐Au) und Chalkogenbasis ( ;z.B. Cu‐Te oder Ni‐Te).

Experimental evidence from liquid semiconductors

Two broad types of liquid semiconducting alloys will be discussed, namely those involving alkali metals (e.g., the Li–Pb and the Cs–Au system) and those in which a chalcogen is involved (e.g., Cu–Te or Ni–Te). It will be argued that relatively simple ionic bonding schemes in alkali metal systems must be replaced by more complicated ones in chalcogen based alloys. The close interaction between atomic structure on one hand, and the electronic structure on the other will be emphasized.

Short-range order in liquid Li–Pb alloys

The neutron diffraction patterns of liquid lithium lead alloys containing 0, 17, 34, 48, 61, 80, and 100 at.% 7Li were measured. The long-wavelength limit of the partial structure factors aij(k) and of the concentration–concentration correlation function SCC(k) is calculated. These values agree well with the values calculated from activity data. For the 80 at.% alloy the total SCC(k) function was measured. It shows a pronounced first peak at the k value of a prepeak observed with x rays. The Fourier tranform of SCC(k) is related to the short-range order-size coefficients which have been introduced by Warren et al. (Ref. 19) to describe the local order of solid solutions. The data for the liquid Li–Pb alloys indicate a preference for unlike nearest neighbors and a reduction of the distance between unlike nearest neighbors as compared with the mean distance of the pure components. This short-range order is probably due to a partially saltlike bonding between lithium and lead ions. The over-all structure of the liquid alloys is similar to the structure of a hard sphere system.

Darstellung und Struktur der Phase Li13Sn5 und die strukturelle Verwandtschaft der Phasen in den Systemen Li-Sn und Li-Pb / The Preparation and Crystal Structure of Li13Sn5 and the Structural Relations Between the Phases of the Systems Li-Sn and Li-Pb

A new compound Li13Sn5 has been prepared and its crystal structure has been determined, It crystallizes trigonal, α = 4.70 ± 0.01 Å, c = 17.12 ± 0.04 Å, c/α = 0.2745, space group P3̅ml-D3 3d, in an ordered bcc derivative structure. Structural relations to other compounds of the systems Li—Sn and Li—Pb with similar atomic arrangements are shown. The Sn—Sn and Pb—Pb-distances are discussed in connection with the valence rule18.

Diffusion of lithium into germanium at low temperatures

The present work describes a technique of diffusing lithium into germanium at low temperatures using a LiPb alloy as an external phase.

Precipitation of lithium in germanium

The precipitation of lithium in solid germanium has been measured: Li is diffused into Ge from an external phase consisting of a molten LiPb alloy; diffusion temperatures extend from 250 to 420°C. Precipitation is measured at 60°C. Results are consistent with Morin and Reiss' theory about the nature of precipitation sites and with Ham's theory of diffusion limited precipitation. Measurements of the rate of nuclei generation are in rough agreement with Lothe's theory of vacancy generation by dislocation climb, but are in substantial disagreement with earlier measurements of Morin and Reiss.

The microstructure of lead-base alloys

An extensive literature search has not revealed any comprehensive publication dealing mainly with the optical metallography of lead-base alloys. During the past four years, Gould-National has conducted systematic studies on pure lead and on seven binary and four ternary systems at various concentrations. The systems are: SbPb, CaPb, LiPb, CdPb, AgPb, AsPb, SnPb, AsSbPb, AgSbPb, CdSbPb, and SnSbPb. Over two thousand lead alloy specimens have been examined metallographically. The objective of our study was to develop lead-base alloys having superior physical and electrochemical corrosion resistance properties. The paper presents observed metallographic structures of the various binary and ternary lead alloys, cast under air or inert atmosphere and with controlled solidification rates. The metallographic structures have been used to reveal the multicrystalline aggregation of phase or phases, to evaluate the grain size and grain growth, to detect grain boundary precipitation during age hardening, to detect microporosity and cracks in cast alloys, and to examine the nature of the corrosion attack mechanism on alloys subjected to anodic corrosion. A detailed description of metallographic sample preparation techniques used on various lead alloys is presented.