The lattice parameter of high‐purity silicon is measured as a function of temperature between 300 and 1500 K, and the linear thermal expansion coefficient is accurately determined. Precise measurements are made by the high‐temperature attachment for Bond’s x‐ray method to a few parts per million. It is found that the temperature dependence of the linear thermal expansion coefficient α(t) is empirically given by α(t)=(3.725{1−exp[−5.88×10−3{(t−124)} +5.548×10−4t)×10−6 (K−1), where t is the absolute temperature ranging from 120 to 1500 K. It is shown that the lattice parameter in the above temperature range can be calculated using α(t) and the lattice parameter at 273.2 K (0.5430741 nm). Measured values of the lattice parameter and the thermal expansion coefficient for high‐purity float‐zoned (100 kΩ cm) and Czochralski‐grown (30 Ω cm) single crystals are uniformly distributed within ±1×10−5 nm and ±2×10−7 K−1 with respect to the values obtained from the above empirical formula.

Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K

ElaStic: A tool for calculating second-order elastic constants from first principles

https://sciold.ui.ac.ir/~sjalali/papers/P2014.5.pdf

Elastic constants of cubic crystals

Short, intense laser pulses can be used to access the transition regime between classical and quantum optical responses in dielectrics. In this regime, the relative roles of inter- and intraband light-driven electronic transitions remain uncertain. We applied attosecond transient absorption spectroscopy to investigate the interaction between polycrystalline diamond and a few-femtosecond infrared pulse with intensity below the critical intensity of optical breakdown. Ab initio time-dependent density functional theory calculations, in tandem with a two-band parabolic model, accounted for the experimental results in the framework of the dynamical Franz-Keldysh effect and identified infrared induction of intraband currents as the main physical mechanism responsible for the observations.

/pdf/attosecond-dynamical-franz-keldysh-effect-in-polycrystalline-b24vt70eig.pdf

Attosecond dynamical Franz-Keldysh effect in polycrystalline diamond

The transition from diamond to graphite is a key equilibrium for interpreting ultrahigh-pressure metamorphic rocks. Despite widespread interest, there remain significant systematic differences between the best available experimental determinations of P and T (Kennedy and Kennedy 1976) and numerous thermodynamic calculations of the transition. At temperatures below 1400 K, calculated equilibrium pressures are lower than extrapolations of the experiments by as much as 5 kbar. At 3000 K, calculated pressures vary from more than 8 kbar above to almost 20 kbar below the position of the extrapolated transition. A revised curve based on a critical review of the experimental and thermodynamic data is consistent with expanded experimental brackets and the preferred calorimetric data. It is steeper than the transition proposed by Kennedy and Kennedy (1976) and previous calculations and passes through 16.2 kbar, 298 K; 33.9 kbar, 1000 K; 63.5 kbar, 2000 K; and 98.4 kbar, 3000 K.

The revised curve implies that the minimum pressure for formation of diamond-bearing crustal rocks is 3–4 kbar less than implied by extrapolation of the experiments. Because the revised transition is steeper than most previous calculations, the triple point among graphite, diamond, and liquid carbon may be as much as 40 kbar higher than previously estimated.

A revised diamond-graphite transition curve

The lattice constants of a diamond platelet and of large single, undoped, crystals of silicon and germanium have been determined from measurements of multiple diffraction patterns by the method described in Part I [Post (1975). J. Appl. Cryst. 8, 452–456]. The mean values, based on measurements of eight to twelve reflections, and their standard deviations are: diamond a = 3.566986 A, Aa/a = 2.6 × 10−6; silicon a = 5.430941 A, Aa/a = 2 × 10−6; germanium a = 5.657820 A, Δa/a = 1.6 × 10−6.

T. Hom

Papers

Accurate lattice constants from multiple reflection measurements. II. Lattice constants of germanium silicon, and diamond