Abstract:Experimental measurements of alpha quartz thermal expansion as reported in the literature have been critically analyzed. A recommended set of best measured values over the temperature range -50 degrees C to +150 degrees C have been determined, as have values for the coefficient of thermal linear expansion (CTE) and the thermoelastic coefficients. The impact of using the coefficients on determinations of quartz material temperature coefficients and on the calculation of temperature coefficients of frequency for… Show more
“…For quartz, we used the thermal expansion reported in Ref. [21], which is valid in the entire temperature region and agrees well with a more recent analysis of the expansion in a narrower temperature region [22]. To be consistent with the experimental geometry, we used the aand b-axis values for the expansion (which are identical).…”
Section: B Modeling Using Continuum Elasticity Theorymentioning
The thermal response of nanoscale cylindrical inclusions of amorphous SiO 2 embedded in crystalline quartz (c-SiO 2) is investigated by means of small-angle x-ray scattering. The inclusions are generated by swift heavy-ion irradiation that leads to the formation of amorphous ion tracks along the ion trajectories. During in situ annealing between room temperature and 620°C, we observe an irreversible expansion of the track cylinders followed by a reversible contraction. The reversible "elastic" response of the tracks can be modeled using the temperature-dependent elastic properties of bulk amorphous and crystalline SiO 2 for the inclusions and the matrix, respectively. A high initial interface pressure of the nanocylinders is apparent from the calculations.
“…For quartz, we used the thermal expansion reported in Ref. [21], which is valid in the entire temperature region and agrees well with a more recent analysis of the expansion in a narrower temperature region [22]. To be consistent with the experimental geometry, we used the aand b-axis values for the expansion (which are identical).…”
Section: B Modeling Using Continuum Elasticity Theorymentioning
The thermal response of nanoscale cylindrical inclusions of amorphous SiO 2 embedded in crystalline quartz (c-SiO 2) is investigated by means of small-angle x-ray scattering. The inclusions are generated by swift heavy-ion irradiation that leads to the formation of amorphous ion tracks along the ion trajectories. During in situ annealing between room temperature and 620°C, we observe an irreversible expansion of the track cylinders followed by a reversible contraction. The reversible "elastic" response of the tracks can be modeled using the temperature-dependent elastic properties of bulk amorphous and crystalline SiO 2 for the inclusions and the matrix, respectively. A high initial interface pressure of the nanocylinders is apparent from the calculations.
“…The IP thermal mismatch strain ε x = −ε z /2 is determined by the product of the difference in thermal expansion coefficients and the temperature change. Garnet films on Si will experience tensile strain after cooling from 800 °C, with ε x ≈ 6 × 10 –3 (neglecting temperature dependence of the thermal expansion coefficients), whereas for films on crystalline quartz with an IP thermal expansion coefficient of 13.7 × 10 –6 , the films will experience compressive strain, , ε x ≈ −3 × 10 –3 . These thermal mismatch strains, combined with the positive magnetostriction, would suggest that the films on Qz would be easier to magnetize in the OP direction than those on Si, but the OP saturation field, H K , was higher for the films on Qz not lower.…”
Photonic integrated circuits require magneto-optical (MO) materials for making nonreciprocal devices such as isolators and circulators. The most successful MO materials are rare-earth-substituted iron garnets, but these can be challenging to grow on silicon without a seed layer, which introduces spacing loss between the waveguide and the MO cladding. A pulsed-laser deposition (PLD) method is used for making MO Ce:YIG (Ce 1 Y 2 Fe 5 O 12 )/YIG (Y 3 Fe 5 O 12 ) bilayer or trilayer films on different substrates, including silicon, quartz, and Gd 3 Ga 5 O 12 (GGG), in which a multilayer film is deposited in one run and then annealed. A YIG seed layer grown above the MO Ce:YIG facilitates recrystallization during ex situ rapid thermal annealing, which results in a reduced thermal budget and simplified deposition process. A monolithically integrated optical isolator was demonstrated by direct deposition of a bilayer Ce:YIG/YIG capping layer onto a siliconon-insulator resonator. The device exhibited an insertion loss of 7.4 ± 1.8 dB and an isolation ratio of 13.0 ± 2.2 dB within the telecommunication window (λ = 1564.4 nm), which outperforms previously reported monolithic isolators.
“…Therefore, the certified lattice parameters are a = 0.491 406 ± 0.000 020 nm and c = 0.540 554 ± 0.000 020 nm. The certified lattice parameters were adjusted using the coefficient of thermal expansion values found in Kosinski et al (1992) to values at 22.5 °C. Figure 2. (Color online) The difference in lattice parameter values for SRM 676a obtained from a FPA Rietveld refinement using the NIST Python-based FPA code and those from a profile-fitting analysis of X-ray powder diffraction data.…”
Section: Discussionmentioning
confidence: 99%
“…Therefore, the certified lattice parameters are a = 0.491 406 ± 0.000 020 nm and c = 0.540 554 ± 0.000 020 nm. The certified lattice parameters were adjusted using the coefficient of thermal expansion values found in Kosinski et al (1992) to values at 22.5°C. Figure 2.…”
Section: Assessment Of Type B Errors In Lattice Parametersmentioning
The National Institute of Standards and Technology (NIST) certifies a suite of Standard Reference Materials (SRMs) to address specific aspects of the performance of X-ray powder diffraction instruments. This report describes SRM 1878b, the third generation of this powder diffraction SRM. SRM 1878b is intended for use in the preparation of calibration standards for the quantitative analyses of α-quartz by X-ray powder diffraction in accordance to National Institute for Occupational Safety and Health Analytical Method 7500, or equivalent. A unit of SRM 1878b consists of approximately 5 g of α-quartz powder bottled in an argon atmosphere. It is certified with respect to crystalline phase purity, or amorphous phase content, and lattice parameter. Neutron powder diffraction, both time of flight and constant wavelength, was used to certify the phase purity using SRM 676a as an internal standard. A NIST-built diffractometer, incorporating many advanced design features was used for certification measurements for lattice parameters.
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