Thermal diffusivity of garnets at high temperature
Thermal diffusivity of garnets at high temperature
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DOI：
10.1007/s00269-005-0056-8
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发表时间：
2006-01
影响因子：
1.4
通讯作者：
A. Hofmeister
中科院分区：
文献类型：
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作者：
A. Hofmeister
用激光闪光技术测量了不同化学成分的石榴石的热扩散率(D)，该方法准确(±2%)，并将晶格组分与直接辐射传输隔离开来。温度范围从~290℃到~1600℃(除非受到熔融的限制)。研究了7种人工合成的石榴石和15种具有两种离子取代[Ca3(Fe，Al)2Si3O12和(Mg，Fe，Ca)3Al2Si3O12]的天然石榴石和不同数量的OH-。阳离子取代或羟基掺入会降低端元值。一旦温度(T)超过~1,100到1,500℃的临界值(TSAT)，热扩散率就是恒定的。从~290℃到Tsat，测量结果最好用1/D=A+BT+CT2来表示，其中A、B和C是常量。这些常数在不同的化学成分之间几乎没有变化，这表明氧亚晶格控制着热传输。只有当饱和度较低时才需要高阶项，如蚂蚁山石榴石，其中1/D=0.049403+0.0032299T−2.3992T2×10−6+6.0168T3×10−10(1/Din S/mm~2；Tin K)。平均自由程(λ，根据D和声速计算)略大于Tsat上的晶格参数，这与声子-声子相互作用需要非定域模式相一致。在大多数温度下，λ都是纳米大小的。通过外推到几个开尔文，得到了很大的λ值，这表明边界散射只在极端寒冷的温度下才是重要的。观测到的T和化学成分的行为与阻尼谐振子模型一致。声子输运最好地用逆热扩散系数来表示，其中1/D在1和3之间，直到~200K，在适当的T下依赖于二次或三次多项式，但在Tsat以上是常数。1/D的预测和观测的温度响应模拟了众所周知的热容形式，即声学模式控制低温附近的热传输，光学声子在环境温度以上占主导地位，在很高的温度下，由于离散声子态的满布居，达到了类似于Dulong和Petit的极限。
Thermal diffusivity (D) of garnets with diverse chemical compositions was measured using the laser-flash technique, which is accurate (±2%) and isolates the lattice component from direct radiative transfer. Temperatures ranged from ~290 to ~1,600 K (unless limited by melting). Seven synthetic (e.g., YAG, GGG) and 15 natural garnets with two types of ionic substitution [Ca3(Fe,Al)2Si3O12and (Mg,Fe,Ca)3Al2Si3O12] and varying amounts of OH-were examined. Cation substitution or hydroxyl incorporation lowersDfrom end-member values. Thermal diffusivity is constant once the temperature (T) exceeds a critical value (Tsat) of ~1,100 to 1,500 K. From ~290 K toTsat, the measurements are best represented by 1/D=A+BT+CT2where A, B, and C are constants. These constants vary little among diverse chemical compositions, suggesting that the oxygen sublattice controls heat transport. Higher order terms are needed only whenTsatis low, such as Ant Hill garnet wherein 1/D=0.049403+0.0032299T−2.3992T2×10−6+6.0168T3×10−10(1/Din s/mm2;Tin K). The mean free path (λ, computed fromDand sound velocities) is slightly larger than the lattice parameter aboveTsat, in accord with phonon–phonon interactions requiring non-localized modes. At most temperatures, λ is nm-sized. Large values of λ are obtained by extrapolation to a few Kelvins, suggesting that boundary scattering can only be important at extremely cold temperatures. The observed behavior withTand chemical composition is consistent with the damped harmonic oscillator model. Phonon transport is best represented by inverse thermal diffusivity wherein 1/Dgoes asTnwherenis between 1 and 3 up to ~200 K, depends on a quadratic or cubic polynomial at moderateT, but is constant aboveTsat. The predicted and observed temperature response of 1/Dmimics the well-known form for heat capacity, in that acoustic modes control heat transport near cryogenic temperatures, optic phonons dominate above ambient temperature, and a limit analogous to that of Dulong and Petit is reached at very high temperature, due to full population of discrete phonon states.