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Figure 2 The effects of the negative expansion ratio α on the solutions as (pmb{K=0.1}), (pmb{N_{1}=0.1}).
A negative expansion observed in b-direction (in Pbnm setting) below 150 K suggests a magnetoelastic coupling where short-range interactions between Ho3+ magnetic moments are established [24].
Near-zero-CTE and isotropic negative expansion designs are achieved by creating compliant structures where overall expansion is compensated by internal bending deformation.
While the model predicts that microscopic-scale residual stresses are locked into the material after firing (compressive along the negative expansion crystal axis and tensile along the other two positive expansion axes), neutron diffraction provides evidence of this stress.
Despite the NFIB's fierce antigovernment rhetoric, the actual figures in their latest report (July 2010) belies their own argument (and Zuckerman's): Only 12% of respondents based their negative "expansion outlook" on the political climate, while 43% attributed it to "economic conditions".
Both the a-axis and the b-axis of the crystal expand normally on warming (although the b-axis may exhibit a small amount of negative expansion below 100 K), whereas the c-axis contracts.
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The high temperature X-ray diffraction analyses showed that all the peaks ascribe to the ZrW2O8 thin film shifted to higher angle with the increasing temperatures, which demonstrated that the cubic ZrW2O8 thin film exhibited negative thermal expansion and its thermal expansion coefficient was calculated to be − 11.378 × 10−6 K−1 from 20 °C to 600 °C.
The c-axis exhibits negative thermal expansion, but the thermal expansion behaviour of the a and b axes is ormal.
It has negative thermal expansion along the a axis and positive thermal expansion along the c axis, so that the overall expansion is very low or negative.
However, in addition to negative thermal expansion, materials with anisotropic and large positive thermal expansion are also desirable for various applications.
This unique structure is proposed to contribute to the negative thermal expansion, and hence it is a key factor in producing zero thermal expansion alloys.
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