Precision Determination of Lattice Parameter, Coefficient of Thermal Expansion and Atomic Weight of Carbon in Diamond1

1951 ◽  
Vol 73 (12) ◽  
pp. 5643-5646 ◽  
Author(s):  
M. E. Straumanis ◽  
E. Z. Aka
Keyword(s):  
Thermal Expansion ◽  
Coefficient Of Thermal Expansion ◽  
Lattice Parameter ◽  
Atomic Weight ◽  
Precision Determination ◽  
Parameter Coefficient

Determination Of Temperature Dependent Unstressed Lattice Spacings In Crystalline Thin Films On Substrates

1997 ◽  
Vol 505 ◽  
Author(s):  
G. Cornella ◽  
S. Lee ◽  
O. Kraft ◽  
W. D. Nix ◽  
J. C. Bravman
Keyword(s):  
Thin Films ◽  
Thermal Expansion ◽  
Coefficient Of Thermal Expansion ◽  
Strain Analysis ◽  
Lattice Parameter ◽  
Gold Films ◽  
Sample Material ◽  
Temperature Dependent ◽  
X Ray

ABSTRACTX-ray strain analysis via Generalized Focusing Diffractometry (GFD) [1], and the concurrent need for accurate values of the unstrained lattice parameter, are discussed. A new method for determining the unstrained lattice parameter without knowledge of the elastic constants of the sample material is described. Stress measurements at varying temperatures, and extraction of the coefficient of thermal expansion from these measurements, are demonstrated for aluminum and gold films.

Determination of Mechanical Properties of Thin Film on Silicon Wafer

2003 ◽  
Author(s):  
Enboa Wu ◽  
Albert J. D. Yang ◽  
Ching-An Shao ◽  
C. S. Yen
Keyword(s):  
Thin Film ◽  
Mechanical Properties ◽  
Thermal Expansion ◽  
Young’S Modulus ◽  
Silicon Wafer ◽  
Coefficient Of Thermal Expansion ◽  
Young's Modulus ◽  
Poisson Ratio ◽  
Bulk State

Nondestructive determination of Young’s modulus, coefficient of thermal expansion, Poisson ratio, and thickness of a thin film has long been a difficult but important issue as the film of micrometer order thick might behave differently from that in the bulk state. In this paper, we have successfully demonstrated the capability of determining all these four parameters at one time. This novel method includes use of the digital phase-shifting reflection moire´ (DPRM) technique to record the slope of wafer warpage under temperature drop condition. In the experiment, 1-um thick aluminum was sputtered on a 6-in silicon wafer. The convolution relationship between the measured data and the mechanical properties was constructed numerically using the conventional 3D finite element code. The genetic algorithm (GA) was adopted as the searching tool for search of the optimal mechanical properties of the film. It was found that the determined data for Young’s modulus (E), Coefficient of Thermal Expansion (CTE), Poisson ratio (ν), and thickness (h) of the 1.00 um thick aluminum film were 104.2Gpa, 38.0 ppm/°C, 0.38, and 0.98 um, respectively, whereas that in the bulk state were measured to be E=71.4 Gpa, CTE=23.0 ppm/°C, and ν=0.34. The significantly larger values on the Young’s modulus and the coefficient of thermal expansion determined by this method might be attributed to the smaller dislocation density due to the thin dimension and formation of the 5-nm layer of Al2O3 formed on top of the 1-um thick sputtered film. The Young’s Modulus and the Poisson ratio of this nano-scale Al2O3 film were then determined. Their values are consistent with the physical intuition of the microstructure.

scholarly journals Determination of the linear coefficient of thermal expansion in polymer films at the nanoscale: influence of the composition of EVA copolymers and the molecular weight of PMMA

2015 ◽  
Vol 17 (28) ◽  
pp. 18495-18500 ◽  
Author(s):  
J. González-Benito ◽  
E. Castillo ◽  
J. F. Cruz-Caldito
Keyword(s):  
Molecular Weight ◽  
Thermal Expansion ◽  
Methyl Methacrylate ◽  
Polymer Films ◽  
Coefficient Of Thermal Expansion ◽  
Linear Coefficient ◽  
Poly Methyl Methacrylate ◽  
Poly Ethylene ◽  
Eva Copolymers

Nanothermal-expansion of poly(ethylene-co-vinylacetate), EVA, and poly(methyl methacrylate), PMMA, in the form of films was measured to finally obtain linear coefficients of thermal expansion, CTEs.

scholarly journals Determination of the coefficient of expansion of a carbon tube and its assembly for thermal compensation of metrological structures

2019 ◽  
Author(s):  
Salma EL ASMAI ◽  
François HENNEBELLE ◽  
Thierry COOREVITS ◽  
Jean-François FONTAINE
Keyword(s):  
Thermal Expansion ◽  
Composite Materials ◽  
Production Efficiency ◽  
Coefficient Of Thermal Expansion ◽  
Thermal Expansion Coefficients ◽  
Carbon Tube ◽  
Interesting Approach ◽  
Measurement Uncertainties ◽  
3D Metrology

Composite materials are increasingly used in 3D metrology devices. Their use is justified by their interesting mechanical properties including their low density and good rigidity but especially their low coefficient of thermal expansion. In fact, in order to improve production efficiency, companies nowadays integrate more and more control equipment directly in situ. These are then subject to thermal variations. The use of composite materials is an interesting approach. However, in some cases, the lack of knowledge of their coefficient of thermal expansion and their behavior might increase measurement uncertainties. The objective is to study the thermal behavior of a carbon tube alone and the same tube with aluminium fixing elements at its extremities, in order to determine the coefficients of expansion of the carbon alone and to quantify the influence of the fixation with aluminium elements. This experiment makes it possible to directly compensate the dimensional variations of the metrological structure depending on the temperature variations and thus to limit measurement uncertainties. The thermal expansion coefficients of the carbon tube and its assembly are determined by measuring relative variations in height with a ZERODUR® reference bar. The whole is positioned in a climatic chamber. *

Sign in / Sign up

Export Citation Format

Share Document