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Thermal expansion and Thermal stress: Problem Solving

San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55 °C.
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Related Experiment Video

Updated: Jun 10, 2026

Developing High Performance GaP/Si Heterojunction Solar Cells
10:31

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Published on: November 16, 2018

Transition States Between Pyramids and Domes During Ge/Si Island Growth.

Ross1, Tromp, Reuter

  • 1IBM T. J. Watson Research Center, Post Office Box 218, Yorktown Heights, NY 10598, USA.

Science (New York, N.Y.)
|December 3, 1999
PubMed
Summary

Germanium-silicon islands transition from pyramids to domes during growth on silicon. This shape change, influenced by temperature, occurs via intermediate states and is reversible upon cooling, supporting an anomalous coarsening model.

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Area of Science:

  • Materials Science
  • Surface Science
  • Nanotechnology

Background:

  • Germanium-silicon (GeSi) islands grown on silicon (001) surfaces exhibit complex shape evolution.
  • Understanding island morphology is crucial for semiconductor device fabrication and strain management.

Purpose of the Study:

  • To investigate the real-time shape transformation of GeSi islands from pyramidal to dome structures during growth.
  • To elucidate the intermediate shapes and the role of temperature in this transition.

Main Methods:

  • In-situ real-time observation of GeSi island growth on Si(001).
  • Analysis of island morphology, including facet evolution, during growth and post-growth annealing.
  • Temperature-dependent studies of shape transitions and reversibility.

Main Results:

  • Small GeSi islands are pyramidal, while larger ones adopt dome shapes.
  • The transition involves asymmetric intermediate shapes with increasing numbers of highly inclined facets.
  • Post-growth annealing of pyramids induces a similar shape change, which is temperature-dependent and reversible upon cooling.

Conclusions:

  • The observed pyramid-to-dome shape transition in GeSi islands is mediated by distinct intermediate states.
  • The reversible and temperature-dependent nature of the transition supports an anomalous coarsening model for island growth.
  • These findings provide insights into the fundamental mechanisms governing nanostructure formation on surfaces.