Thermal Expansion and Relaxation of W-Cu Multilayers

1992 ◽  
Vol 286 ◽  
Author(s):  
Wen-C. Chiang ◽  
Soo-Kil Kim ◽  
David V. Baxter
Keyword(s):  
Thermal Expansion ◽  
High Temperature ◽  
Heat Treatments ◽  
Irreversible Change ◽  
Thermally Induced ◽  
Temperature Range ◽  
Thermal Expansion Coefficients ◽  
Induced Stresses ◽  
Expansion Coefficients ◽  
Bulk Behavior

ABSTRACTWe have studied the structure of W-Cu multilayers with modulation wavelengths between 65 and 110 xsÅ over the temperature range 25-400° C. Using a high temperature diffractometer stage specifically designed for low angle work, thermal expansion coefficients were measured and found to be marginally greater than would be expected from bulk behavior even when interaction with the substrate is taken into account. Upon annealing at temperature as low as 180° C, increased intensity of the low angle superlattice peaks is observed. Heat treatments above 180° C result in an irreversible change in the multilayer associated with the migration of Cu atoms to cracks produced by thermally induced stresses.

scholarly journals Organizing Cells Within Non-Periodic Microarchitectured Materials That Achieve Graded Thermal Expansions

2015 ◽  
Author(s):  
Jonathan B. Hopkins ◽  
Lucas A. Shaw ◽  
Todd H. Weisgraber ◽  
George R. Farquar ◽  
Christopher D. Harvey ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Thermal Expansion ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Element Analysis ◽  
Thermal Expansion Coefficients ◽  
Large Lattice ◽  
Unit Cells ◽  
Expansion Coefficients ◽  
Bulk Behavior

The aim of this paper is to introduce an approach for optimally organizing a variety of different unit cell designs within a large lattice such that the bulk behavior of the lattice exhibits a desired Young’s modulus with a graded change in thermal expansion over its geometry. This lattice, called a graded microarchitectured material, can be sandwiched between two other materials with different thermal expansion coefficients to accommodate their different expansions or contractions caused by changing temperature while achieving a desired uniform stiffness. First, this paper provides the theory necessary to calculate the thermal expansion and Young’s modulus of large multi-material lattices that consist of periodic (i.e., repeating) unit cells of the same design. Then it introduces the theory for calculating the graded thermal expansions of a large multimaterial lattice that consists of non-periodic unit cells of different designs. An approach is then provided for optimally designing and organizing different unit cells within a lattice such that both of its ends achieve the same thermal expansion as the two materials between which the lattice is sandwiched. A MATLAB tool is used to generate images of the undeformed and deformed lattices to verify their behavior and various examples are provided as case studies. The theory provided is also verified and validated using finite element analysis and experimentation.

Variations of lattice constants and thermal expansion coefficients of indium at high pressure and high temperature

2018 ◽  
Vol 38 (4) ◽  
pp. 406-413 ◽  
Author(s):  
Yusaku Takubo ◽  
Hidenori Terasaki ◽  
Tadashi Kondo ◽  
Shingo Mitai ◽  
Seiji Kamada ◽  
...  
Keyword(s):  
High Pressure ◽  
Thermal Expansion ◽  
High Temperature ◽  
Lattice Constants ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients

Thermal Expansion of SrZr4-xTix(PO4)6 Ceramics

2018 ◽  
Vol 281 ◽  
pp. 169-174
Author(s):  
Yang Wang ◽  
Yuan Yuan Song ◽  
Yuan Yuan Zhou ◽  
Lu Ping Yang ◽  
Fu Tian Liu
Keyword(s):  
Thermal Expansion ◽  
Relative Density ◽  
Thermophysical Properties ◽  
Sintering Temperature ◽  
Temperature Range ◽  
Thermal Expansion Coefficients ◽  
High Relative Density ◽  
Low Thermal Expansion ◽  
Expansion Coefficients

Low thermal expansion ceramics have been widely applied in multiple fields. In this paper, a series of low thermal expansion ceramics SrZr4-xTix(PO4)6 was prepared and characterized. The SrZr4-xTix(PO4)6 ceramics could be well sintered in the temperature range of 1400~1500 °C. The effect of the addition of Ti substituting Zr and the sintering temperature was studied. The Ceramic with x =0.1 sintered at 1450 °C, the SrZr4-xTix(PO4)6 had a high relative density. The thermal expansion coefficients were about 3.301×10-6 °C-1. It was demonstrated that the microstructure of the SrZr4-xTix(PO4)6 could be altered by adding varying amount of Ti to tailor the thermophysical properties of the material.

Negative Thermal Expansion of Yb2Mo3O12 and Lu2Mo3O12

2008 ◽  
Vol 368-372 ◽  
pp. 1662-1664 ◽  
Author(s):  
X.L. Xiao ◽  
M.M. Wu ◽  
J. Peng ◽  
Y.Z. Cheng ◽  
Zhong Bo Hu
Keyword(s):  
Thermal Expansion ◽  
Solid State ◽  
Solid State Reaction ◽  
Linear Thermal Expansion ◽  
Negative Thermal Expansion ◽  
Orthorhombic Structure ◽  
Conventional Solid State Reaction ◽  
Temperature Range ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients

Compounds Yb2Mo3O12 and Lu2Mo3O12 were prepared by conventional solid-state reaction. Their crystal structures and thermal expansion properties were investigated. It was found that Yb2Mo3O12 and Lu2Mo3O12 adopt orthorhombic structure and show negative thermal expansion (NTE) in the temperature range of 200-800 °C. Their a-axis and c-axis exhibit stronger contraction in the temperature range of 200-800 °C, while b-axis slightly expands in the temperature range of 200-300 °C and then contracts in the temperature range of 300-800 °C. The linear thermal expansion coefficients al of Yb2Mo3O12 and Lu2Mo3O12 are −5.17 × 10−6 °C−1 and −5.67 × 10−6 °C−1, respectively.

Thermal expansion coefficients and Gruneisen parameters of quartz at high temperature by X-ray method

1994 ◽  
Vol 9 (2) ◽  
pp. 148-150
Author(s):  
Nabil N. Rammo ◽  
Saad B. Farid
Keyword(s):  
Thermal Expansion ◽  
High Temperature ◽  
Ambient Temperature ◽  
Least Squares ◽  
Temperature Variation ◽  
Ray Method ◽  
X Ray ◽  
Least Squares Fitting ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients

The temperature variation of the interplanar spacings (101), (112), and (211) of 325 mesh quartz was determined in the range 300–966 °K using X-ray powder diffractometry. The measured lattice parameters have been found to increase nonlinearly with temperature, and the dependence has been expressed by a polynomial of second degree from the least-squares fitting of the data, the results of which are presented herein. Values are given for the thermal expansion coefficients and Gruneisen parameter in the range 300 to 768 °K. In the range 768–966 °K, the expansion is zero. The derivatives dαa/dT, dαc/dT, and dαv/dT at ambient temperature are also given.

Crystal structure and thermal expansion of hexakis(phenylthio)benzene and its CBr4 clathrate

1995 ◽  
Vol 73 (4) ◽  
pp. 513-521 ◽  
Author(s):  
Darek Michalski ◽  
Mary Anne White ◽  
Pradip K. Bakshi ◽  
T. Stanley Cameron ◽  
Ian Swainson
Keyword(s):  
Crystal Structure ◽  
Thermal Expansion ◽  
Neutron Powder Diffraction ◽  
X Ray Diffraction ◽  
Triclinic Space Group ◽  
Space Group ◽  
X Ray ◽  
Temperature Range ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients

The crystal structures of hexakis(phenylthio)benzene (HPTB) and its CBr4 clathrate have been determined by single crystal X-ray diffraction data collected at T = 18 °C and refined to final Rw of 0.036 and 0.047, respectively. Pure HPTB is triclinic, space group [Formula: see text] (No. 2), with a = 9.589(2) Å, b = 10.256(1) Å, c = 10.645(2) Å, α = 68.42(1)°, β = 76.92(2)°, γ = 65.52(1)°, and Z = 1. The CBr4 clathrate of HPTB is rhombohedral, space group [Formula: see text] (No. 148), with a = 14.327(4) Å, b = 20.666(8) Å, and Z = 3. The host–guest mole ratio of HPTB–CBr4 is 1:2. Neutron powder diffraction was carried out on powders of both compounds in the temperature range 25 K < T < 295 K. Thermal expansion coefficients were determined for HPTB and HPTB–CBr4 over this temperature range. Keywords: thermal expansion, crystal structure, clathrate.

Parametric study on the influence of material properties and geometry on the thermally induced bistability of composite laminates

2021 ◽  
pp. 095440622110456
Author(s):  
Samir A Emam ◽  
Tarun Pherwani ◽  
Aravindh Anil ◽  
Aeman Muhammed
Keyword(s):  
Thermal Expansion ◽  
Aspect Ratio ◽  
Material Properties ◽  
Parametric Study ◽  
Composite Laminates ◽  
Thickness Ratio ◽  
Thermally Induced ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients ◽  
Moduli Of Elasticity

This paper presents a parametric study on the key parameters that control the thermally induced bistability of cross-ply laminates. The influence of the material properties including the moduli of elasticity and the thermal expansion coefficients and the laminate’s geometry including the aspect ratio (AR) and the width-to-thickness ratio are investigated. The unsymmetric [Formula: see text] and the antisymmetric [Formula: see text] cross-ply laminates are investigated. Five key parameters are varied: the number of plies, the width-to-thickness ratio, the laminate’s aspect ratio, the ratio of the moduli of elasticity, and the ratio of the thermal expansion coefficients of the lamina. The laminate is assumed flat at the cured temperature and a uniform temperature gradient is applied until it is reduced to the room temperature. For each set of parameters, the stable equilibrium shapes of the laminate are obtained using a Ritz model. The ABAQUS finite element package is used to validate the model and an excellent agreement is obtained. Results that show the variation of the curvatures with the width-to-thickness ratio and the onset of the bistability for a variety of parameters are presented. The ratio of the moduli of elasticity and the thermal expansion coefficients significantly affect the critical width-to-thickness ratio at which the laminates become bistable. The unsymmetric laminates show bistability at a lower width-to-thickness ratio compared with the antisymmetric laminates. The results also show that the higher the aspect ratio, the lower the critical width-to-thickness ratio for stability for both laminates.

Behaviors of the Zr–1.0Sn–0.39Nb–0.31Fe–0.05Cr Alloy at High Temperature

2011 ◽  
Vol 399-401 ◽  
pp. 80-84
Author(s):  
Yi Yuan Tang ◽  
Jie Li Meng ◽  
Kai Lian Huang ◽  
Jian Lie Liang
Keyword(s):  
Thermal Expansion ◽  
Phase Transformation ◽  
High Temperature ◽  
Oxide Film ◽  
Room Temperature ◽  
X Ray Diffraction ◽  
X Ray ◽  
Thin Oxide Film ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients

Phase transformation of the Zr-1.0Sn-0.39Nb-0.31Fe-0.05Cr alloy was investigated by high temperature X-ray diffraction (XRD). The XRD results revealed that the alloy contained two precipitates at room temperature, namely β-Nb and hexagonal Zr(Nb,Fe,Cr,)2. β-Nb was suggested to dissolve into the α-Zr matrix at the 580oC. Thin oxide film formed at the alloy’s surface was identified as mixture of the monoclinic Zr0.93O2and tetragonal ZrO2, when the temperature reached to 750oC and 850 oC. The thermal expansion coefficients of αZr in this alloy was of αa = 8.39×10-6/°C, αc = 2.48×10-6/°C.

A time-resolved x-ray diffraction study of Ti5Si3 product formation during combustion synthesis

1997 ◽  
Vol 12 (12) ◽  
pp. 3230-3240 ◽  
Author(s):  
C. R. Kachelmyer ◽  
I. O. Khomenko ◽  
A. S. Rogachev ◽  
A. Varma
Keyword(s):  
Thermal Expansion ◽  
High Temperature ◽  
Product Formation ◽  
X Ray Diffraction ◽  
Temperature Synthesis ◽  
Time Resolved ◽  
X Ray ◽  
Thermal Expansion Coefficients ◽  
High Temperature Synthesis ◽  
Expansion Coefficients

Time-resolved x-ray diffraction (TRXRD) was performed during Ti5Si3 synthesis by the self-propagating high-temperature synthesis mode for different Ti size fractions. It was determined that the time for product formation (ca. 15 s) was independent of Ti particle size. However, the formation of Ti5Si4 phase occurred when relatively large titanium particles were used. A simultaneous measurement of the temperature and TRXRD allowed us to attribute the shifting of XRD peaks at high temperature to thermal expansion of the Ti5Si3 product. The thermal expansion coefficients differ for different crystal planes, and their numerical values compare well with those reported previously in the literature.

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