Interpretation of X-ray Powder Diffraction Patterns . By H. Lipson and H. Steeple. Pp. viii + 335 + 3 plates. (Mac-millan: London; St Martins Press: New York, May 1970.) £4.

X-Ray Diffraction

Der speziellen Relativitatstheorie liegt folgendes Postulat zugrunde, welchem auch durch die Galilei-Newtonsche Mechanik Genuge geleistet wird: Wird ein Koordinatensystem K so gewahlt, das in bezug auf dasselbe die physikalischen Gesetze in ihrer einfachsten Form gelten, so gelten dieselben Gesetze auch in Bezug auf jedes andere Koordinatensystem K′, das relativ zu K in gleichformiger Translationsbewegung begriffen ist. Dieses Postulat nennen wir „spezielles Relativitatsprinzip“. Durch das Wort „speziell“ soll angedeutet werden, das das Prinzip auf den Fall beschrankt ist, das K′ eine gleichformige Translationsbewegung gegen K ausfuhrt, das sich aber die Gleichwertigkeit von K′ und K nicht auf den Fall ungleichformiger Bewegung von K′ gegen K erstreckt.

Die Grundlage der allgemeinen Relativitätstheorie

Current interferometric gravitational wave detectors use test masses with mirror coatings formed from multiple layers of dielectric materials, most commonly alternating layers of SiO2 (silica) and Ta2O5 (tantala). However, mechanical loss in the Ta2O5/SiO2 coatings may limit the design sensitivity for advanced detectors. We have investigated sources of mechanical loss in the Ta2O5/SiO2 coatings, including loss associated with the coating-substrate interface, with the coating-layer interfaces, and with the bulk material. Our results indicate that the loss is associated with the bulk coating materials and that the loss of Ta2O5 is substantially larger than that of SiO2.

Mechanical Loss in Tantala/Silica Dielectric Mirror Coatings

A Treatise on Electricity and Magnetism, Vol. 1

Reducing thermal noise from optical coatings is crucial to reaching the required sensitivity in next generation interferometric gravitational-waves detectors. Here we show that adding TiO$_2$ to Ta$_2$O$_5$ in Ta$_2$O$_5$/SiO$_2$ coatings reduces the internal friction and in addition present data confirming it reduces thermal noise. We also show that TiO$_2$-doped Ta$_2$O$_5$/SiO$_2$ coatings are close to satisfying the optical absorption requirements of second generation gravitational-wave detectors.

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Titania-doped tantala/silica coatings for gravitational-wave detection

Albert Einstein in 1916 predicted the existence of a Gravitational Wave in his General Theory of Relativity. These waves, which propagate at the speed of light transmit gravitational information through the Universe. Since its prediction by Einstein, astronomers and physicists have searched for them and developed method to detect them. Though so far unsuccessful, the search of Gravitational waves goes on and great efforts are being made to develop the most sensitive detectors yet in the hope of that first detection. 
Currently ground based detectors are limited by coating Brownian thermal noise due to excitation of the reflective coatings applied to the test masses. Through measurement of mechanical loss of a material the magnitude of the Brownian thermal noise can be determined. It is necessary to determine the root cause of mechanical loss in current coatings (Ta2O5¬ and SiO2). Work towards this goal is taking place on multi paths, directly, through characterisation of mechanical loss and indirectly through microscopy studies to determine the structural cause. In this thesis, the effect of TiO2 doping and heat treatment of Ta2O5 has been investigated. It has been previously shown that a TiO2 doping of Ta2O5 reduces the mechanical loss and that, that reduction is at a maximum at 30% TiO2. It has been determined through Electron Diffraction experiments that the structure of TiO2 doped Ta2O5 becomes more homogenous up to 30% doping. Through computation modelling of these structures using Density Functional Theory it has also been determined that the abundance of TiTaO2 ring formations also maximises at 30% doping. Further modelling has also determined that the TiTaO2 rings are more flexible that their counter parts of Ta2O2 and Ti2O2. From this it has been hypothesised that the overall flexibility of a structure is a strong component of the mechanical response of the structure. Hence by increasing the flexibility through TiO2 doping the mechanical loss (as Thermal Noise) is decreased similarly and this response would also be expected using similarly flexibility improving dopants.

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Keith Lee Evans

Papers

Computational Modelling of Amorphous mirror coatings for use in Advanced Gravitational wave detectors