The concave behaviour of the Porod invariant observed during the calcination of CaCO₃ powder samples suggests the following picture of the evolving internal structure of the samples. The outset sample is formed by a crystalline CaCO₃ phase and a void phase. During the calcination, the first phase shrinks in volume at fixed density since the temperature increase breaks down the crystalline structure at the interface, leading to the formation of an amorphous phase comprising an equal number of CO₂ and CaO atomic groups. The last groups gradually condense, forming a third phase of solid CaO of constant density and increasing volume fraction, while the companion CO₂ groups flow out of the sample. The amorphous phase occupies, with a variable density, all the volume left free by the other two phases. At the end of the calcination, both the volume fraction of the first phase and the density of the amorphous phase vanish so that the sample will again be made up of two phases: the voids and the solid CaO. Best-fitting the resulting theoretical expressions of the Porod invariant and of the Porod law coefficient to the observed values, one can determine the matter densities, volume fractions and specific surface areas of the phases.

中文翻译：

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通过 Porod 不变行为表征 CaCO3 煅烧过程

在 CaCO ₃粉末样品的煅烧过程中观察到的 Porod 不变量的凹面行为表明了样品内部结构演变的以下图片。初始样品由结晶CaCO ₃相和空隙相形成。在煅烧过程中，第一相在固定密度下体积收缩，因为温度升高破坏了界面处的晶体结构，导致形成包含相等数量的 CO ₂和 CaO 原子团的非晶相。最后一组逐渐凝聚，形成密度恒定且体积分数增加的固体 CaO 的第三相，而伴随的 CO ₂群体流出样本。非晶相以可变的密度占据了其他两相留下的所有体积。在煅烧结束时，第一相的体积分数和非晶相的密度都消失了，因此样品将再次由两相组成：空隙和固体 CaO。将所得到的 Porod 不变量和 Porod 定律系数的理论表达式与观测值进行最佳拟合，可以确定各相的物质密度、体积分数和比表面积。