General Material Aspects

Discordant Doping and Labile Silicon Atoms in Higher Manganese Silicide

“…The crystallization in HMS follows a peritectic reaction, wherein depending on the nominal composition, dopants, and processing condition (such as solidification rate, pressure, temperature, etc. ), , HMS crystallizes with varying stoichiometry primarily resulting from such labile Si atoms and modulated lattice structure. , When the incoming atom cannot adopt the local geometry of the site it occupies, it is referred to as discordant . The solubilities of B and Ge in HMS alloy as reported previously were known to range from 0 to x ∼ 0.04 (B) and x ∼ 0.01 (Ge) .…”

“…The modulated crystal structure of MnSi γ constitutes of a [Si] subsystem, wherein Si atoms may exist in varying oxidation states , and coordination numbers, making them prone to local structural instability by migration or diffusion. The [Si] subsystem constitutes labile Si atoms with dangling bonds, which are more reactive than Si atoms bonded to Mn.…”

“…Silicon-rich manganese silicide (HMS) crystallizes into a degenerate semiconducting crystal with low thermal conductivity and constitutes earth-abundant elements, owing to which they have been extensively explored as prospective p -type material for thermoelectric (TE) applications. , The efficiency of conversion is governed by the TE figure of merit ( zT ), which is evaluated at absolute temperature ( T ) as zT = , wherein S , σ, and κ represent the temperature-dependent Seebeck coefficient, electrical conductivity, and thermal conductivity . Due to the inverse interrelation among these electrical and thermal transport properties, most research efforts in developing TE materials are directed toward optimization of carrier concentration ( n ) and reduction of lattice thermal conductivity (κ L ), wherein to achieve an enhanced performance in HMS, both p-type and n-type dopants were actively studied in the past for their substitution at the [Mn] and/or [Si]-subsystems (≈sublattice). − However, optimization of electrical power factor ( S 2 σ) by doping or reduction in κ L by nanostructuring approaches is often skewed majorly by the inherent structural modulation and undesirable segregation of MnSi as a secondary phase. − …”

Analytical Study of Low Temperature Phase of 3D LGT in the Plaquette Formulation

“…In this section we construct the low-temperature expansion of gauge models in the plaquette formulation. In doing this we follow the strategy developed for the two-dimensional principal chiral models in [10]. The weak-coupling expansion in both models bears many common features.…”

“…k (x) for i ≥ 1 can be computed by making repeated use of the Campbell-Baker-Hausdorff formula. Then, the partition function (7) can be exactly rewritten to the following form [10]…”