Ceramic contraction coefficient

Figure 8-10 The shrinkage process model for copper and ceramic during firing (Sea- ceramic contraction coefficient. So, copper contraction coefficient).

The concept of the matching of firing shrinkage rates of ceramics and conductors was touched upon in Figure 3-1 in Chapter 3. As suggested there, when there is a mismatch in the contraction coefficient between the ceramic and metal materials, defects are formed at their interface [3,4, 5]. 

A third technique to produce tempered ware uses two glasses (or ceramics) formed together (laminated), each with different thermal coefficient of expansion. This is used to make Correll dishes by Coming. For this tableware, a pyrocer-amic material with one type of thermal coefficient of expansion is covered with another pyroceramic with a greater thermal coefficient of expansion and is then baked until the outer layer melts uniformly. Materials with greater thermal coefficients of expansion will expand more when heated and will contract more when cooled. The greater contraction (once cooled) of the outside material causes compression. 

Thermistors are usually made from ceramic metal oxide semiconductors, which have a large negative temperature coefficient of electrical resistance. Thermistor is a contraction of thermal-sensitive-resistor. The recommended temperature range of operation is from -55 to 300°C. The popularity of this device has grown rapidly in recent years. Special thermistors for cryogenic applications are also available [12]. 

Doping the A-sites of PbTiOj with La causes the transition temperature from tetragonal to cubic to fall, and the thermal contraction to diminish steadily, so that at an approximate composition of Pb La TiOj, ceramic samples show a mean thermal expansion coefficient of a=-0.11 x 10 K from room temperature to 130°C. Above this temperature the cubic polymorph has a thermal expansion coefficient of approximately the same value as the undoped material, of 3.82x 10 K , indicating that the substituent influences the distortion of the low-temperature phase rather than other factors. A-site substitution with even modest amounts of Cd has the opposite effect, as a=-2.40x 10 K for ceramic Pb g Cd gTiOj. 

The TCE of most ceramics is isotropic, although for certain crystalline or single-crystal ceramics, the TCE may be anisotropic, and some may even contract in one direction and expand in the other. Ceramics used for substrates do not generally fall into this category, as most are mixed with glasses in the preparation stage and do not exhibit anisotropic properties as a result. The temperature coefficient of expansion of several ceramic materials is shown in Table 4.5. This parameter is linear over the temperature range of interest. 

The sample preparation for a bulk pyroelectric measurement is very similar to what is required for a bulk piezoelectric measurement, namely a well-sintered ceramic disc that has been electrically poled. Determining the pyroelectric coefficient may be divided into two groups - the measurement of the pyroelectric current and the measurement of the charge. We will describe measurement techniques for both groups. In addition, the pyroelectric effect can be subdivided into primary and secondary effects. The primary effect is observed when the material is rigidly clamped under a constant strain to prevent any thermal expansion or contraction. Secondary effects occur when the material is permitted to deform, i.e. the material is under constant stress. Thermal expansion results in a strain that changes the spontaneous polarisation, attributable to the piezoelectric effect. Thus the secondary pyroelectric effect includes contributions caused by piezoelectricity. Exclusively measuring the pyroelectric coefficient under constant strain is experimentally very difficult. What is usually experimentally measured is the total pyroelectric effect exhibited by the material - the sum of the primary and secondary effects. 

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