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1.
This paper examines a model for estimating canopy resistance rc and reference evapotranspiration ETo on an hourly basis. The experimental data refer to grass at two sites in Spain with semiarid and windy conditions in a typical Mediterranean climate. Measured hourly ETo values were obtained over grass during a 4 year period between 1997 and 2000 using a weighing lysimeter (Zaragoza, northeastern Spain) and an eddy covariance system (Córdoba, southern Spain). The present model is based on the Penman–Monteith (PM) approach, but incorporates a variable canopy resistance rc as an empirical function of the square root of a climatic resistance r* that depends on climatic variables. Values for the variable rc were also computed according to two other approaches: with the rc variable as a straight‐line function of r* (Katerji and Perrier, 1983, Agronomie 3 (6): 513–521) and as a mechanistic function of weather variables as proposed by Todorovic (1999, Journal of Irrigation and Drainage Engineering, ASCE 125 (5): 235–245). In the proposed model, the results show that rc/ra (where ra is the aerodynamic resistance) presents a dependence on the square root of r*/ra, as the best approach with empirically derived global parameters. When estimating hourly ETo values, we compared the performance of the PM equation using those estimated variable rc values with the PM equation as proposed by the Food and Agriculture Organization, with a constant rc = 70 s m?1. The results confirmed the relative robustness of the PM method with constant rc, but also revealed a tendency to underestimate the measured values when ETo is high. Under the semiarid conditions of the two experimental sites, slightly better estimates of ETo were obtained when an estimated variable rc was used. Although the improvement was limited, the best estimates were provided by the Todorovic and the proposed methods. The proposed approach for rc as a function of the square root of r* may be considered as an alternative for modelling rc, since the results suggest that the global coefficients of this locally calibrated relationship might be generalized to other climatic regions. It may also be useful to incorporate the effects of variable canopy resistances into other climatic and hydrological models. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

2.
The MacCullagh equation is of key importance in the study of the Earth. It connects the geometrical and the physical properties of the Earth through the geodynamical shape factor J2. This second zonal geopotential coefficient is closely related to the flattening and to the angular spin velocity of the Earth as well as to its equatorial (A) and polar (C) moments of inertia. Through these moments of inertia the gravitational potential V is connected to the mass density distribution within the Earth.The main target of the present study is to obtain a generalized form of the MacCullagh equation for even orders n ≥ 2 by including the higher order zonal coefficients Jn connected with the higher (n ≥ 2) degree moments of inertia Cn and An. The higher the degree n, the higher is the weight of the near-surface (i.e. shallow) mass density distribution in Jn. The second part of this contribution deals with the temporal variations of Jn, dJn/dt for n ≥ 2.  相似文献   

3.
Abstract

Two entities of importance in hydrological droughts, viz. the longest duration, LT , and the largest magnitude, MT (in standardized terms) over a desired time period (which could also correspond to a specific return period) T, have been analysed for weekly flow sequences of Canadian rivers. Analysis has been carried out in terms of week-by-week standardized values of flow sequences, designated as SHI (standardized hydrological index). The SHI sequence is truncated at the median level for identification and evaluation of expected values of the above random variables, E(LT ) and E(MT ). SHI sequences tended to be strongly autocorrelated and are modelled as autoregressive order-1, order-2 or autoregressive moving average order-1,1. The drought model built on the theorem of extremes of random numbers of random variables was found to be less satisfactory for the prediction of E(LT ) and E(MT ) on a weekly basis. However, the model has worked well on a monthly (weakly Markovian) and an annual (random) basis. An alternative procedure based on a second-order Markov chain model provided satisfactory prediction of E(LT ). Parameters such as the mean, standard deviation (or coefficient of variation), and lag-1 serial correlation of the original weekly flow sequences (obeying a gamma probability distribution function) were used to estimate the simple and first-order drought probabilities through closed-form equations. Second-order probabilities have been estimated based on the original flow sequences as well as SHI sequences, utilizing a counting method. The E(MT ) can be predicted as a product of drought intensity (which obeys the truncated normal distribution) and E(LT ) (which is based on a mixture of first- and second-order Markov chains).

Citation Sharma, T. C. & Panu, U. S. (2010) Analytical procedures for weekly hydrological droughts: a case of Canadian rivers. Hydrol. Sci. J. 55(1), 79–92.  相似文献   

4.
《水文科学杂志》2013,58(3):503-518
Abstract

Two parameters of importance in hydrological droughts viz. the longest duration, LT and the largest severity, ST (in standardized form) over a desired return period, T years, have been analysed for monthly flow sequences of Canadian rivers. An important point in the analysis is that monthly sequences are non-stationary (periodic-stochastic) as against annual flows, which fulfil the conditions of stochastic stationarity. The parameters mean, μ, standard deviation, σ (or coefficient of variation), lag1 serial correlation, ρ, and skewness, γ (which is helpful in identifying the probability distribution function) of annual flow sequences, when used in the analytical relationships, are able to predict expected values of the longest duration, E(LT ) in years and the largest standardized severity, E(ST ). For monthly flow sequences, there are 12 sets of these parameters and thus the issue is how to involve these parameters to derive the estimates of E(LT ) and E(ST ). Moreover, the truncation level (i.e. the monthly mean value) varies from month to month. The analysis in this paper demonstrates that the drought analysis on an annual basis can be extended to monthly droughts simply by standardizing the flows for each month. Thus, the variable truncation levels corresponding to the mean monthly flows were transformed into one unified truncation level equal to zero. The runs of deficits in the standardized sequences are treated as drought episodes and thus the theory of runs forms an essential tool for analysis. Estimates of the above parameters (denoted as μav, σav, ρav, and γav) for use in the analytical relationships were obtained by averaging 12 monthly values for each parameter. The product- and L-moment ratio analyses indicated that the monthly flows in the Canadian rivers fit the gamma probability distribution reasonably well, which resulted in the satisfactory prediction of E(LT ). However, the prediction of E(ST ) tended to be more satisfactory with the assumption of a Markovian normal model and the relationship E(ST ) ≈ E(LT ) was observed to perform better.  相似文献   

5.
Abstract

We have contrived a model E(αω) α μ?1ω?p+1(ω 2?ω i 2)?+ for the distribution of internal wave energy in horizontal wavenumber, frequency-space, with wavenumber α extending to some upper limit μ(ω) α ω r-1 (ω 2?ω i 2)½, and frequency ω extending from the inertial frequency ω i to the local Väisälä frequency n(y). The spectrum is portrayed as an equivalent continuum to which the modal structure (if it exists) is not vital. We assume horizontal isotropy, E(α, ω) = 2παE1, α2, ω), with α1, α2 designating components of α. Certain moments of E1, α2, ω) can be derived from observations. (i) Moored (or freely floating) devices measuring horizontal current u(t), vertical displacement η(t),…, yield the frequency spectra F (u,η,…)(ω) = ∫∫ (U 2, Z 2,…)E1, ∞2, ω) dα12, where U, Z,… are the appropriate wave functions. (ii) Similarly towed measurements give the wavenumber spectrum F (…)(α1) = ∫∫… dα2 dω. (iii) Moored measurements horizontally separated by X yield the coherence spectrum R(X, ω) which is related to the horizontal cosine transform ∫∫ E(α1, α2 ω) cos α1 Xdα11. (iv) Moored measurements vertically separated by Y yield R(Y, ω) and (v) towed measurements vertically separated yield R(Y, α1), and these are related to similar vertical Fourier transforms. Away from inertial frequencies, our model E(α, ω) α ω ?p-r for α ≦ μ ω ω r, yields F(ω) ∞ ω ?p, F1) ∞ α1 ?q, with q = (p + r ? 1)/r. The observed moored and towed spectra suggest p and q between 5/3 and 2, yielding r between 2/3 and 3/2, inconsistent with a value of r = 2 derived from Webster's measurements of moored vertical coherence. We ascribe Webster's result to the oceanic fine-structure. Our choice (p, q, r) = (2, 2, 1) is then not inconsistent with existing evidence. The spectrum is E(∞, ω) ∞ ω ?1(ω 2?ω i 2 ?1, and the α-bandwith μ ∞ (ω 2?ω i 2)+ is equivalent to about 20 modes. Finally, we consider the frequency-of-encounter spectra F([sgrave]) at any towing speed S, approaching F(ω) as SS o, and F1) for α1 = [sgrave]/S as SS o, where S o = 0(1 km/h) is the relevant Doppler velocity scale.  相似文献   

6.
Any pair ofm L gz ,m L g b,mmxz andmm x h in the eastern six provinces of China show good linear relation this makes it easy to convert from one scale to another.mm x h may replaceM L (ECH) as the local earthquake magnitude scale for the eastern six provinces, yet retaining the level ofM L (ECH). The scalemm x h is 0.36 magnitude units higher thanM L (SC) for southern California. By comparingRm a x (Δ) withR 3 (Δ) of Yunnan, it is found that the γ-value ofMAX phase of about 1 section in Yunnan region is half as large as that in the eastern six provinces of China. Observation indicates thatmm x hmb for magnitude 4–5. It follows therefore thatmb (ECH)≈mb (WUS). This is supported by the result that the attenuation coefficient, the γ-value in eastern China is the same as in western United States.  相似文献   

7.
In spite of important differences in structural response to near‐fault and far‐fault ground motions, this paper aims at extending well‐known concepts and results, based on elastic and inelastic response spectra for far‐fault motions, to near‐fault motions. Compared are certain aspects of the response of elastic and inelastic SDF systems to the two types of motions in the context of the acceleration‐, velocity‐, and displacement‐sensitive regions of the response spectrum, leading to the following conclusions. (1) The velocity‐sensitive region for near‐fault motions is much narrower, and the acceleration‐sensitive and displacement‐sensitive regions are much wider, compared to far‐fault motions; the narrower velocity‐sensitive region is shifted to longer periods. (2) Although, for the same ductility factor, near‐fault ground motions impose a larger strength demand than far‐fault motions—both demands expressed as a fraction of their respective elastic demands—the strength reduction factors Ry for the two types of motions are similar over corresponding spectral regions. (3) Similarly, the ratio um/u0 of deformations of inelastic and elastic systems are similar for the two types of motions over corresponding spectral regions. (4) Design equations for Ry (and for um/u0) should explicitly recognize spectral regions so that the same equations apply to various classes of ground motions as long as the appropriate values of Ta, Tb and Tc are used. (5) The Veletsos–Newmark design equations with Ta=0.04 s, Tb=0.35 s, and Tc=0.79 s are equally valid for the fault‐normal component of near‐fault ground motions. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

8.
Granger causality (GC) is used in the econometrics literature to identify the presence of one- and two-way coupling between terms in noisy multivariate dynamical systems. Here we test for the presence of GC to identify a soil moisture (S) feedback on precipitation (P) using data from Illinois. In this framework S is said to Granger cause P if F(Ptt−Δt)≠F(Ptt−Δt−St−Δt) where F denotes the conditional distribution of P, Ωt−Δt represents the set of all knowledge available at time t−Δt, and Ωt−Δt−St−Δt represents all knowledge except S. Critical for land–atmosphere interaction research is that Ωt−Δt includes all past information on P as well as S. Therefore that part of the relation between past soil moisture and current precipitation which results from precipitation autocorrelation and soil water balance will be accounted for and not attributed to causality. Tests for GC usually specify all relevant variables in a coupled vector autoregressive (VAR) model and then calculate the significance level of decreased predictability as various coupling coefficients are omitted. But because the data (daily precipitation and soil moisture) are distinctly non-Gaussian, we avoid using a VAR and instead express the daily precipitation events as a Markov model. We then test whether the probability of storm occurrence, conditioned on past information on precipitation, changes with information on soil moisture. Past information on precipitation is expressed both as the occurrence of previous day precipitation (to account for storm-scale persistence) and as a simple soil moisture-like precipitation-wetness index derived solely from precipitation (to account for seasonal-scale persistence). In this way only those fluctuations in moisture not attributable to past fluctuations in precipitation (e.g., those due to temperature) can influence the outcome of the test. The null hypothesis (no moisture influence) is evaluated by comparing observed changes in storm probability to Monte-Carlo simulated differences generated with unconditional occurrence probabilities. The null hypothesis is not rejected (p>0.5) suggesting that contrary to recently published results, insufficient evidence exists to support an influence of soil moisture on precipitation in Illinois.  相似文献   

9.
10.
Abstract

The generation of eddies by a large-scale flow over mesoscale topography is studied with the help of two- and three-layer nonlinear quasi-geostrophic models of the open ocean. The equations are integrated forward in time with no eddies present initially. For a given time, the displacement of the interface between layers two and three (ζ) tends to a well-defined limit (function of the horizontal spatial coordinates) as ρ 3 - ρ 20 (ρr is the density of layer r). Even for values of α[= (ρ 3 - ρ 2)/(ρ 2 - ρ 1)] as small as 0.01 the potential energy due to ζ is not negligible and it can reach, in some cases, a considerable fraction of the total eddy energy.  相似文献   

11.
The state of an Earth surface system (ESS) is determined by three sets of factors: laws, place, and history. Laws ( L = L1, L2, . . . , Ln) are the n general principles applicable to any such system at any time. Place factors ( P = P1, P2, . . . , Pm) are the m relevant characteristics of the local or regional environment. History factors ( H = H1 , H2, . . . , Hq) include the previous evolutionary pathway of the ESS, its stage of development, past disturbance, and initial conditions. Geoscience investigation may focus on laws, place, or history, but ultimately all three are necessary to understand and explain ESS. The LPH triad is useful as a pedagogical device, illustrated here via application to explaining the world's longest cave (Mammoth Cave, KY). Beyond providing a useful checklist, the LPH framework provides analytical traction to some difficult research problems. For example, studies of the avulsions of three southeast Texas rivers showed substantial differences in avulsion regimes and resulting alluvial morphology, despite the proximity and superficial similarity of the systems. Avulsions are governed by the same laws in all cases [ L (A) = L (B) = L (C)], and the three rivers have undergone the same sea‐level, climate, and tectonic histories, as well as the same general anthropic impacts [ H (A) ≈ H (B) ≈ H (C)]. Though regional environmental controls are similar, local details such as the location of the modern main channel relative to Pleistocene meander channels differ, and thus these place factors explain the differences between the rivers. The LPH framework, or similar types of reasoning, is implicit in many types of geoscience analysis. Explicit attention to the triad can help solve or address many specific problems and remind us of the importance of all three sets of factors. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

12.
Ionospheric F2-layer peak height hmF2 variations, as measured over 1986–1995 by the MU radar (34.85°N, 136.1°E) and as calculated with a theoretical model, are discussed. The diurnal variations of the measured peak height for different seasons and levels of solar activity are compared with those estimated from ionosonde M3000F2 and IRI predictions. Also given are the measured ion drift velocities and meridional neutral winds needed to understand the dynamic behavior of the F2-layer. It is found that: (1) hmF2 is generally higher during periods of the solar maximum than during periods of the solar minimum, and higher in summer than in winter; (2) for the solar maximum, hmF2 drops markedly in the morning and in the afternoon, while, for the solar minimum, the hmF2 minimum occurs in the morning during summer and usually in the afternoon during winter. In general, the measured hmF2 is well reproduced by our model when we use the observed drift velocities and plasma temperatures as inputs. Our modeling study shows that the neutral wind contributes strongly to the diurnal variation of hmF2 in winter by lowering the ionization layer by day, particularly for the solar maximum; it also helps to enlarge the day–night difference of hmF2 in summer. The northward electromagnetic drifts that usually cancel the neutral wind effect have only a minor effect for the location of the MU radar. Other features of the observed hmF2 variations, e.g., the solar maximum–minimum difference, the summer–winter difference, and the morning and afternoon drops, are explained by the basic processes of O+ production, loss and diffusion, as influenced by the atomic oxygen concentration and neutral and plasma temperatures.  相似文献   

13.
The catalog of Kamchatka earthquakes is represented as a probability space of three objects {Ω, $ \tilde F $ \tilde F P}. Each earthquake is treated as an outcome ω i in the space of elementary events Ω whose cardinality for the period under consideration is given by the number of events. In turn, ω i is characterized by a system of random variables, viz., energy class ki, latitude φ i , longitude λ i , and depth h i . The time of an outcome has been eliminated from this system in this study. The random variables make up subsets in the set $ \tilde F $ \tilde F and are defined by multivariate distributions, either by the distribution function $ \tilde F $ \tilde F (φ, λ, h, k) or by the probability density f(φ, λ, h, k) based on the earthquake catalog in hand. The probabilities P are treated in the frequency interpretation. Taking the example of a recurrence relation (RR) written down in the form of a power law for probability density f(k), where the initial value of the distribution function f(k 0) is the basic data [Bogdanov, 2006] rather than the seismic activity A 0, we proceed to show that for different intervals of coordinates and time the distribution f elim(k) of an earthquake catalog with the aftershocks eliminated is identical to the distribution f full(k), which corresponds to the full catalog. It follows from our calculations that f 0(k) takes on nearly identical numeral values for different initial values of energy class k 0 (8 ≤ k 0 ≤ 12) f(k 0). The difference decreases with an increasing number of events. We put forward the hypothesis that the values of f(k 0) tend to cluster around the value 2/3 as the number of events increases. The Kolmogorov test is used to test the hypothesis that statistical recurrence laws are consistent with the analytical form of the probabilistic RR based on a distribution function with the initial value f(k 0) = 2/3. We discuss statistical distributions of earthquake hypocenters over depth and the epicenters over various areas for several periods  相似文献   

14.
We present results for the global elastic parameters (k 2, k 3) and (h 2, l 2) derived from the analysis of Satellite Laser Ranging (SLR) data. The SLR data for two satellites, LAGEOS 1 and LAGEOS 2, collected over a period of two years, from 1 January 2005 to 1 January 2007, from 18 globally distributed ground stations are analyzed using different approaches. The analysis is performed for the two satellites jointly, and the four elastic parameters are estimated. We carry out a sequential analysis and study the stability of the estimates as a function of the length of the data set used. The adjusted final values for k 2 (0.3011±0.0001) and k 3 (0.0896±0.0037) and those for h 2 (0.6146±0.0006) and l 2 (0.0883±0.0003) for LAGEOS 1 and LAGEOS 2 tracking data are compared to the estimates derived in other studies.  相似文献   

15.
太湖有色溶解有机物对水体总吸收贡献的遥感估算   总被引:1,自引:0,他引:1  
有色溶解有机物(CDOM)是决定自然水体水色的主要溶解物质,其吸光能力和光化降解产物对水体初级生产力和碳循环过程具有重要影响.以太湖为研究区,2004年10月、2008年10月、2010年4月和2011年1月和3月共5期实测数据,采集了333个有效样点,分析不同时期CDOM对水体总吸收的贡献,并利用遥感技术估算[aCDOM/at](412).结果表明:不同时期[aCDOM/at](412)均值变化明显,2011年[aCDOM/at](412)的均值最大(0.369),高于所有样点[aCDOM/at](412)均值(0.295±0.139);201004期的[aCDOM/at](412)在0.046~0.455之间变化,其均值最小(0.236±0.108);200410和200810两期数据[aCDOM/at](412)均值相差不大.竺山湾、梅梁湾与整个太湖相比,竺山湾[aCDOM/at](412)均值较高,对太湖[aCDOM/at](412)的贡献较大,而梅梁湾[aCDOM/at](412)均值与整个太湖相差较小.利用多元线性模型估算[aCDOM/at](412)精度较高(n=333,RMSE=34.60%).悬浮泥沙和浮游色素是影响[aCDOM/at](412)遥感估算精度的主要原因,浮游色素的吸收造成[aCDOM/at](412)的值被低估,而悬浮泥沙的吸收使得[aCDOM/at](412)的值被高估,并且悬浮泥沙是影响CDOM吸收的主要原因.  相似文献   

16.
Proposed is a new definition of earthquake response spectra, which takes account of the number of response cycles N. The Nth largest amplitude of absolute acceleration response of a linear oscilator with natural period T and damping ratio h, which is subjected to ground motion at its base, is defined as SA(T, h, N). By defining a reduction factor η(T, h, N) as SA(T, h, N)/SA(T, h, 1), characteristics of η(T, h, N) were investigated based on 394 components of strong motion records obtained in Japan. Two practical empirical formulae to assess the reduction factor η(T, h, N) are proposed.  相似文献   

17.
北京市北运河沉积物对氮、磷的吸附/解吸动力学特征   总被引:3,自引:0,他引:3  
选取北运河土沟、榆林庄及和合站3个典型河道断面,进行河道0~60 cm深度沉积物对氨氮、磷酸盐的吸附/解吸批平衡静态试验研究,采用多种动力学模型分析北运河沉积物对氮、磷的吸附/解吸动力学特性,提出适用于北运河沉积物吸附/解吸特性的动力学模型,并对模型参数的主要影响因素进行探讨.结果表明:1)北运河典型断面各深度的沉积物对氨氮和磷酸盐的吸附/解吸过程总体呈现3个阶段:快反应阶段—慢反应阶段—平衡阶段;在0~0.5 h的快反应阶段可完成吸附或解吸总量的60%,且对氮、磷的吸附速率大于解吸速率.2)北运河各断面对氨氮与磷酸盐的平衡吸附量表现为S(榆林庄)S(土沟)S(和合站);对氨氮的平衡解吸量表现为S(土沟)S(榆林庄)S(和合站),对磷酸盐的平衡解吸量表现为S(和合站)S(土沟)S(榆林庄),沉积物对氨氮和磷酸盐的吸附以化学吸附为主,平衡吸附与解吸量随断面深度的增加而减小,0~20 cm表层沉积物对氮、磷的吸附能力较强.3)Lagergren二级动力学模型对各深度沉积物的吸附/解吸过程拟合最优,模型参数公式为k2=S-0.369max+0.163;qe=0.022 Smax+18.077 Kf+41.947.通过模拟得出在400 mg/L氮、磷浓度下吸附于沉积物中的氮、磷污染物会随着解吸过程释放52%~80%的氨氮和6%~42%的磷酸盐,可能不仅二次污染上覆水体,还随河水下渗从而对地下水质形成潜在污染风险.  相似文献   

18.
In this study, the removal of nitrate ions from aqueous solutions with liquid membrane technique has been investigated for different organic solvent types in which solubilized tetradecyl trimethyl ammonium bromide (TDTMABr) as carrier. n-butyl alcohol, chloroform, and mixture of chloroform + n-hexane (n-hexane 85% + chloroform 15%) were used as organic solvent. Kinetic parameters (k 1d, k 2m, k 2a, t max, R mmax, J mmax, J amax) were calculated from obtained data. time R a values of mixture, butyl alcohol, and chloroform are 0.81, 0.78, and 0.55, respectively. Similarly R d, R m, and t max values of the mixture equal to 0.14, 0.04, and 87.92 min, respectively. This behavior of the system shows the organic solvent type is an effective parameter on separation yield. It can be concluded that the mixture is the most effective organic solvent type among the investigated ones, because liquid membrane systems should be operated within the range of having the R m, R d, and t max values are minimum while R a values are maximum.  相似文献   

19.
长江中下游大型湖泊水体固有光学特性:Ⅰ.吸收   总被引:1,自引:0,他引:1  
吸收系数是水体固有光学特性的重要组成部分,也是构建水色参数高精度遥感模型的基础,具有重要的研究意义.本文针对长江中下游三大淡水湖——鄱阳湖(2010 10、2011 08)、太湖(2008 10、2011 08)和巢湖(2009 10)进行5次野外实验,以International Ocean Colour Coordinating Group(IOCCG)2000年报告"Remote Sensing of Ocean Colour in Coastal,and Other Optically-Complex,Waters"为基础,对水体不同光学主导类型进行分类;并根据ad(非色素颗粒物吸收)、aph(浮游植物色素吸收)、ag(有色可溶性有机物吸收)等不同主导类型光谱曲线特征差异,引入ad-g(主导类型adagad-ag的合并类型)和aph-related(主导类型ad-aphad-aph-ag的合并类型)类型,对主导类型进行归纳合并.结果显示:秋季,鄱阳湖、太湖、巢湖的主导类型较为单一,分别为adad-agad-aph-ag;夏季,鄱阳湖和太湖同为两种类型共同主导,分别为adad-ag,ad-aph-agad-aph.总体来说,鄱阳湖夏、秋季和太湖秋季主导类型都属于ad-g类型,而太湖夏季和巢湖秋季则属于aph-related类型.另外,分别针对Gons和Gitelson叶绿素a模型假设条件进行验证,发现不同湖泊水体及不同主导类型下其适用性程度不一致.  相似文献   

20.
Structure refinement of astrophyllite   总被引:1,自引:0,他引:1  
The crystal structure of astrophyllite K2Na(Fe, Mn, Mg,□)7[Ti2(Si4O12)2|O3](OH, F)4 has been refined. The dimensions of the triclinic unit cell are: a = 0.5359(2) nm,b = 1.1614(4) nm, c = 1.1861(4) nm, α= 113.16(2)°, β= 103.04(2)°,γ= 94.56(2)°,V = 0.6495(5) nm3, Z= 1, space group P1, R=0.057 for 5308 reflections |Fo|>3σ|Fo|. According to structural and compositional differences the monoclinic astrophyllite K2NaNa(Fe, Mn)4Mg2Ti2[Si4O12]2(OH)4(OH, F)2 and astrophyllite should be considered as two different mineral species. Astrophyllite, monoclinic astrophyllite, bafertisite and lamprophyllite contain heteropolyhedral sheets which topologically are related with Si, O sheets of mica where one or several SiO4 tetrahedra are replaced by TiO n polyhedra. Therefore this heterophyllotitanosilicate series represents a kind of functional substitution in inorganic crystals.  相似文献   

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