Anisotropic shrinkage of cordierite-type glass powder cylindrical compacts
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I. INTRODUCTION Pronounced differences in vertical (along compact axis) and horizontal shrinkage are generally observed during and after the sintering of powder compacts. Well-documented examples are found in the literature for metal powder pressed and sintered under varying conditions1"9 and for glass powders. 1011 The shrinkage anisotropy was related to a number of parameters (particle size and shape and their distribution, amount and direction of pressure applied during pressing, direction of gravity during sintering), and a number of mechanisms were discussed in order to explain the results. In this article we will use data reported earlier for milled, i.e., irregularly shaped, l0 and spheroidized1' cordieritetype glass powders in order to study the anisotropy of shrinkage as a function of total (volume) shrinkage and to relate it to the anisotropy of the pore/solid interface in the compacts. II. EXPERIMENTAL Details on the powders used as well as on compact preparation and sintering conditions were given in Refs. 10 and 11 for the milled and the spheroidized powders, respectively. Polished cross sections of the sintered cylinders were prepared in the axial direction for a few selected samples, and photographs were taken in a scanning electron microscope (SEM) at 1500 and 4000 X magnification. In order to measure the mean linear intercept length in the axial direction (corresponding to the direction of applied pressure and the vertical direction during sintering) and in the radial direction, a grid of two perpendicular sets of parallel straight lines was superimposed on the micrographs. Three hundred pore intercepts were counted for each direction (correo)
On leave from Max Planck Institut fur Metallforschung, Institut fur Werkstoffwissenschaften, D7000 Stuttgart, Federal Republic of Germany.
122
J. Mater. Res. 3 (1), Jan/Feb 1988
http://journals.cambridge.org
sponding to 600 intersection points between the sampling lines and the perimeter of the pore sections) requiring a total line length of approximately 2000//m for the highly porous samples and up to 5000/xm for highdensity samples. From these counts, the total surface density as well as the isotropic and oriented parts of it can be determined. The stereological equations for a preferred orientation in radial direction are (see, for example, Ref. 12) Sv = S
lvs)
N{LH\
(1) (2) (3)
where SyJS ysy and 5 (^or) are the total surface of the solid/pore interface per unit volume and the isotropic and the oriented parts of it, and TV £"' and TV(LH)are the number of intersection points of the straight lines and the perimeters of the pore sections per unit length of the sampling lines counted in the horizontal (diametrical) and vertical (height) direction, respectively. The mean linear intercepts (linear pore sizes) in these directions
where Vv is the volume fraction of pores (or the porosity). The anisotropy of the pore/solid interface can be characterized by the ratio of the linear pore sizes 0 = I
(H)/L
iD)
= NlLDVNlLm
(6)
or by the orientation param
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