Thermal coefficient of expansion

Most materials expand when heated. However, many fibers contract when heated. This fiber behavior is called thermal contract, or negative thermal expansion. 

The coefficient of linear thermal expansion, a, of a fiber is defined as  

For isotropic materials, these three thermal expansion coefficients are related to each other by  

However, most fibers are anisotropic and they do not follow these two relationships. 

For most fiber applications, the linear thermal expansion coefficient of fibers is the most important one among the three expansion coefficients. Table 17.3 shows the linear thermal expansion coefficients of some fibers and non-fibrous materials. Polymer fibers have negative coefficients of linear thermal expansion although their corresponding non-fibrous materials have positive coefficients. The negative coefficients of polymers fibers are caused by the molecular orientation of polymer chains. Oriented polymer chains have the tendency to increase the entropy of the system and return to coiled conformations. However, oriented polymer chains are frozen at room temperature. When heated, the increased thermal vibrations allow the polymer chaiirs to coil on themselves, resulting in negative coefficients 

The CTE is a measure of the mechanical response of a glass network to an applied thermal load. While of vital importance for bulk optics and their application in optical systems, sensing systems based on planar or fiber forms of similar or dissimilar materials require knowledge of CTE as it impacts the ability to maintain both material geometry and TO behavior. The linear expansion of a system in response to an increase in temperature is thus written as 

As shown in Fig. 7.24, the viscosity/temperature behavior of a ChG glass family varies as a function of the elemental ratios, which is an important design characteristic and can strongly Impact the choice of glass matrix for a given application. 

As shown in the figure, the viscosity/temperature curves for the arsenic selenic glass family shift nearly uniformly to higher temperatures as the molar fraction of arsenic is increased in steps from 10% to 40% in the system, meaning that the higher-selenium-content glasses can be processed via thermal routes at very low temperatures however, the viscosity changes very rapidly with temperatures in these selenium-rich compositions, which makes some fiber fabrication routes very difficult to control accurately. 

Depending on the substrate, the curing temperatures, and the service temperatures that are expected, the adhesive formulator may want to adjust the coefficient of thermal expansion of the adhesive system. This will lessen internal stresses that occur due to differences in thermal expansion between the substrate and the adhesive. These stresses act to degrade the joint strength. 

There are several occasions when the difference in coefficient of thermal expansion between the substrate and adhesive will result in internal stresses in the joint. Common occurrences are (1) when the cured joint is taken to a temperature that is different from the curing temperature and (2) when the joint is exposed to thermal cycling. 

When a liquid adhesive solidifies, the theoretical strength of the joint is reduced because of internal stresses and stress concentrations that usually develop. The most common cause 

There are several possible solutions to the expansion mismatch problem. One is to use a resilient adhesive that deforms with the substrate during temperature change. The penalty here is possible creep of the adhesives, and highly deformable adhesives usually have low cohesive strength. Another approach is to adjust the expansion coefficient of the adhesive to a value that is nearer to that of the substrate. This is generally accomplished by formulating the adhesive with specific fillers to tailor the thermal expansion coefficient. 

The general effect of most fillers is to reduce the coefficient of thermal expansion of the cured epoxy resin in proportion to the degree of filler loading. Certain fillers, such as zirconium silicate and carbon fiber, have a negative coefficient of thermal expansion. These are very effective in lowering the expansion rate of the epoxy, especially at elevated temperatures. 

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Fig. X-14. SEM picture of a drop ot cooled glass on Femico metal (which has the same coefficient of thermal expansion). xl30. (From Ref. 183.)...

This table lists values of /3, the cubical coefficient of thermal expansion, taken from Essentials of Quantitative Analysis, by Benedetti-Pichler, and from various other sources. The value of /3 represents the relative increases in volume for a change in temperature of 1°C at temperatures in the vicinity of 25°C, and is equal to 3 a, where a is the linear coefficient of thermal expansion. Data are given for the types of glass from which volumetic apparatus is most commonly made, and also for some other materials which have been or may be used in the fabrication of apparatus employed in analytical work. 

Below Tg the material is hard and rigid with a coefficient of thermal expansion equal to roughly half that of the liquid. With respect to mechanical properties, the glass is closer in behavior to a crystalline solid than to a... 

Figure 4.14 Behavior of thermodynamic variables at Tg for a second-order phase transition (a) volume and fb) coefficient of thermal expansion a and isothermal compressibility p.

By an assortment of thermodynamic manipulations, the quantities dn/dp and [N (d G/dp )o] can be eliminated from Eq. (10.48) and replaced by the measurable quantities a, /3, and dn/dT the coefficients of thermal expansion, isothermal compressibility, and the temperature coefficient of refractive index, respectively. With these substitutions, Eq. (10.48) becomes... 

Material Properties. The properties of materials are ultimately deterrnined by the physics of their microstmcture. For engineering appHcations, however, materials are characterized by various macroscopic physical and mechanical properties. Among the former, the thermal properties of materials, including melting temperature, thermal conductivity, specific heat, and coefficient of thermal expansion, are particularly important in welding. 

Positive-displacement meters are normally rated for a limited temperature range. Meters can be constmcted for high or low temperature use by adjusting the design clearance to allow for differences in the coefficient of thermal expansion of the parts. Owing to small operating clearances, filters are commonly installed before these meters to minimize seal wear and resulting loss of accuracy. 

The typical mechanical properties that qualify PCTFE as a unique engineering thermoplastic are provided ia Table 1 the cryogenic mechanical properties are recorded ia Table 2. Other unique aspects of PCTFE are resistance to cold flow due to high compressive strength, and low coefficient of thermal expansion over a wide temperature range. 

Coefficient of Linear Thermal Expansion. The coefficients of linear thermal expansion of polymers are higher than those for most rigid materials at ambient temperatures because of the supercooled-liquid nature of the polymeric state, and this applies to the cellular state as well. Variation of this property with density and temperature has been reported for polystyrene foams (202) and for foams in general (22). When cellular polymers are used as components of large stmctures, the coefficient of thermal expansion must be considered carefully because of its magnitude compared with those of most nonpolymeric stmctural materials (203). 

Moleculady mixed composites of montmorillonite clay and polyimide which have a higher resistance to gas permeation and a lower coefficient of thermal expansion than ordinary polyimides have been produced (60). These polyimide hybrids were synthesized using montmorillonite intercalated with the ammonium salt of dodecylamine. When polymerized in the presence of dimethyl acetamide and polyamic acid, the resulting dispersion was cast onto glass plates and cured. The cured films were as transparent as polyimide. 

Hafnium oxide 30—40 mol % titanium oxide ceramics (qv) exhibit a very low coefficient of thermal expansion over the temperature range of 20—1000°C. A 45—50 mol % titanium oxide ceramic can be heated to over 2800°C with no crystallographic change (48). 

In the derivation of equations 24—26 (60) it is assumed that the cylinder is made of a material which is isotropic and initially stress-free, the temperature does not vary along the length of the cylinder, and that the effect of temperature on the coefficient of thermal expansion and Young s modulus maybe neglected. Furthermore, it is assumed that the temperatures everywhere in the cylinder are low enough for there to be no relaxation of the stresses as a result of creep. 

Low Expansion Alloys. Binary Fe—Ni alloys as well as several alloys of the type Fe—Ni—X, where X = Cr or Co, are utilized for their low thermal expansion coefficients over a limited temperature range. Other elements also may be added to provide altered mechanical or physical properties. Common trade names include Invar (64%Fe—36%Ni), F.linvar (52%Fe—36%Ni—12%Cr) and super Invar (63%Fe—32%Ni—5%Co). These alloys, which have many commercial appHcations, are typically used at low (25—500°C) temperatures. Exceptions are automotive pistons and components of gas turbines. These alloys are useful to about 650°C while retaining low coefficients of thermal expansion. Alloys 903, 907, and 909, based on 42%Fe—38%Ni—13%Co and having varying amounts of niobium, titanium, and aluminum, are examples of such alloys (2). 

Aluminum. Some manufacturers also have WORM disks above 5.25 in. on offer with aluminum as substrate material. Eor A1 the same advantages apply as for glass with the exception of a high coefficient of thermal expansion and lacking resistance to aggressive chemical vapors and Hquids. 

The interface region in a composite is important in determining the ultimate properties of the composite. At the interface a discontinuity occurs in one or more material parameters such as elastic moduli, thermodynamic parameters such as chemical potential, and the coefficient of thermal expansion. The importance of the interface region in composites stems from two main reasons the interface occupies a large area in composites, and in general, the reinforcement and the matrix form a system that is not in thermodynamic equiUbhum. 

Thermal Stresses and Properties. In general, ceramic reinforcements (fibers, whiskers, or particles) have a coefficient of thermal expansion greater than that of most metallic matrices. This means that when the composite is subjected to a temperature change, thermal stresses are generated in both components. 

Thermal expansion mismatch between the reinforcement and the matrix is an important consideration. Thermal mismatch is something that is difficult to avoid ia any composite, however, the overall thermal expansion characteristics of a composite can be controlled by controlling the proportion of reinforcement and matrix and the distribution of the reinforcement ia the matrix. Many models have been proposed to predict the coefficients of thermal expansion of composites, determine these coefficients experimentally, and analy2e the general thermal expansion characteristics of metal-matrix composites (29-33). 

Because of its high modulus of elasticity, molybdenum is used in machine-tool accessories such as boring bars and grinding quills. Molybdenum metal also has good thermal-shock resistance because of its low coefficient of thermal expansion combined with high thermal conductivity. This combination accounts for its use in casting dies and in some electrical and electronic appHcations. 

Nitride Stmcture Lattice para-meter, a nm Density, g/cm Micro-hardness Maximum stabiHty tempera-ture, °C Heat con-ductivity, W/(m-K) Coefficient of thermal expansion, /3 X 10- ... 

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