Synthesis and Crystal Structure of α-Ba2ZrF8 and Pb2ZrF8 Determined ab initio from Synchrotron and Neutron Powder Diffraction Data
A. LE BAIL
Laboratoire des Fluorures, CNRS ESA 6010, Université du Maine, Facultédes Sciences, Avenue O. Messiaen, 72085 Le Mans Cedex 9, France
and J.-P. LAVAL
Laboratoire de Matériaux Céramiques et Traitement de Surface, CNRS ESA 6015, Université de Limoges, 123 avenue A. Thomas, 87060 Limoges,
France
ABSTRACT. — α-Ba2ZrF8 is prepared as systematically twinned crystals by hydrothermal synthesis (200°C) or as fine powders either on a sand bath (60°C) (aqueous HF medium) or by solid state reaction at 450°C. Synchrotron radiation was used because of ambiguities in indexations from conventional X-ray (pseudo-hexagonal symmetry). The structure was determined ab initio from synchrotron powder data. Neutron data were used for improving accuracy because some degree of non-stoichiometry was suspected. The cell is orthorhombic, space group Pnma, Z = 4, with a = 9.7401(1) ?, b = 5.6147(1)? and c = 11.8871(1) ? (synchrotron data, 25°C). The final neutron Rietveld refinement led to R P = 8.4 % and R B = 3.5 % for the stoichiometric Ba2ZrF8 formulation (sand bath sample). The structure is built up from [ZrF8] bicapped trigonal prisms isolated in a kinked fluorite matrix. The isostructural Pb2ZrF8 compound prepared in solution is also examined. An unexpected relationship with NaBaZrF7 is discussed.
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INTRODUCTION
Phase equilibria in the BaF2-ZrF4 system were investigated [1] and
reinvestigated [2,3]. Most of the crystallized phases evidenced in this
system, as well as glasses [4], were thoroughly characterized. Among those synthesized by solid state reactions [5], most part were indexed and crystal
structures were determined for α- [6] and β-BaZrF6 [7] ; β-BaZr2F10 [8] and
Ba3ZrF10, isotypic with Pb3ZrF10 [9]. The Ba3Zr2F14 phase reported in
reference [2] was not confirmed in [3], which in turn suggested the
existence of two new modifications of BaZrF6 and BaZr2F10 (however, no powder patterns were published). A compound supposed to have the
Ba0.65Zr0.35F2.70 composition, prepared below 490°C, remained
uncharacterized [5]. Near to this composition, ideally Ba2ZrF8, and at temperature higher than 490°C, a non-stoichiometric phase Ba(4-z)Zr(2+z/2)F16 (0 ≤ z ≤ 0.232) was found. It derives from an anion excess ReO3-type with a tetragonal [10] or an orthorhombic cell depending on the stoichiometry and temperature. For the Ba2ZrF8 composition (z = 0), this high-temperature phase is always orthorhombic (a = 5.608(2) ?, b = 5.644(2) ?, c = 10.425(4) ?, space group Pmmn or P21mn, Z = 2 [5]) and will be referred as β-Ba2ZrF8 in the following.
Some barium fluorozirconates were prepared by hydrothermal methods,
and their structures were determined : γ-BaZrF6 [11] and the dihydrate
BaZr2F10?2H2O transforming reversibly to a monohydrate at 130°C [12]. Finally a compound presenting an X-ray powder pattern similar to that of the solid state phase Ba0.65Zr0.35F2.70 was synthesized and is the subject of the present paper. This low temperature phase is designed hereafter as α-Ba2ZrF8.
EXPERIMENTAL
First investigations were carried out from a 1.5 g sample of a fluoride glass, with a nominal composition BaZr2F10 added to 5 cm3 of a HF 5 M solution in a 15 cm3 hermetic Teflon bucket placed in a metallic container (Parr bomb). The bomb was heated at 200°C for 3 days and then naturally cooled down ; the maximal pressure was close to 15 Mpa (150 atm). Small crystals so obtained were identified by X-ray powder diffraction (Siemens D500, CuKα) as corresponding undoubtedly to the 38-0773 JCPDS-ICDD card (unindexed and classified as questionable with the formula Ba0.65Zr0.35F2.70). Some of these very small crystals had sizes just sufficient for attempting a single crystal diffraction study. Numerous crystals were mounted but unfortunately all were twinned. Further investigations showed that starting from a mixture of BaF2 and ZrF4 in the ratio 1:2 led to the same result (named sample A below). It was concluded that starting from a fluoride glass was useless. Then it was observed that letting the same mixture at 60°C for a few days on a sand bath led to apparently the same compound (sample B, containing an unidentified impurity in very small quantity). The same compound could also be prepared by solid state reaction during ten days at 450°C in a platinum tube sealed under argon (sample C). Traces of BaF2 were detected. It should be noted that the 38-0773 JCPDS-ICDD card clearly shows the presence of some lines characteristic of α-BaZrF6. Later, Rietveld refinement on a similar sample (D) revealed furthermore the presence of a very small quantity of BaF2.
That shows the difficulty to obtain a pure phase by a solid state reaction at relatively low temperature (450°C).
No event was detected on the TGA curve up to 590°C, nor on the DSC curve up to 450°C for both samples A and B. Examining the final product by X-ray powder diffraction revealed a pattern apparently unchanged. Synchrotron-radiation powder diffraction data were collected on the 8.3 station, Daresbury Laboratory, U.K. (sample A), and neutron data were recorded at the ILL, Grenoble, France, on the D2B instrument (samples A in high-flux, low resolution mode and sample B in high resolution mode). Finally, an isostructural compound was prepared in the sand bath conditions replacing BaF2 by PbF2 (sample E). This latter phase was studied exclusively from conventional X-ray data.
TABLE I - Conditions for data recording and Rietveld refinements
_______________________________________________________________________ Space group ; Z Pnma ; 4
Temperature22 ± 2 °C
Sample (see text) A (S) A (N) B (N) D (X) E (X)
Cell parameters (?)a9.7401(1)9.7426(3)9.7401(2)9.7472(2)10.0800(3)
b 5.6147(1) 5.6157(2) 5.6167(1) 5.6173(1) 5.3262(1)
c11.8871(1)11.8877(3)11.8839(3)11.8995(3)11.6637(3) Volume (?3)650.08650.39650.13651.53626.20 Wavelength (?) 1.54072 1.5938 1.5938CuKαCuKα
Data range (°2θ)8-10810-14710-14710-15010-135 Counting step (°2θ)0.010.050.050.020.02 Counting time 2.5 s./pt.3h (total)6h (total)47 s./pt.23 s./pt. Number of reflections442707707738632 Number of refined parameters 4175754436
Zero point (°2θ)0.0136(7)0.079(3)0.003(2)0.282(1)0.176(2) Asymmetry parameters P10.123(7)0.110(8)0.144(5)0.054(4)0.044(5)
P20.0049(9)0.023(3)0.024(1)0.076(1)0.059(1)
η(pseudo-Voigt)0.30(2)0.30(3)0.62(2)0.78(2)0.88(2)
η angular variation0.0069(4)0.0008(5)-0.0007(3)0.0015(3)0.0028(5) Halfwidth parameters U0.0054(6)0.117(5)0.124(4)0.065(4)0.043(3)
V0.0052(5)-0.215(9)-0.157(5)-0.026(3)-0.044(4)
W0.0015(1)0.227(4)0.120(2)0.026(1)0.040(1) Conventional Rietveld reliabilities (background subtracted, peak only) :
R P17.310.48.448.349.64
R WP14.811.18.6210.511.9 %R E11.09.78 5.25 5.14 3.95
χ2 1.79 1.30 2.70 4.199.01
R B 6.80 2.87 3.46 2.84 5.23
R F 4.67 2.03 2.45 2.00 3.36
_______________________________________________________________________ Note : S = Synchrotron data ; N = Neutron data ; X = Conventional X-ray
STRUCTURE DETERMINATION
Indexing without ambiguities the conventional X-ray powder diffraction
data was difficult. Two cell propositions (by TREOR [13], ITO [14] or DICVOL [15] programs) were very close each other : a hexagonal cell with
a = 11.245(2) ?, c = 11.892(2) ? with figures of merit [16, 17] M20 = 29,
F20 = 40, (0.011, 44) and an orthorhombic subcell with a = 9.746(7) ?, b = 5.617(2) ? and c = 11.892(2) ?, M20 = 23, F20 = 33, (0.011, 56). A synchrotron powder pattern was recorded, expecting to increase the resolution. From the synchrotron data, the figures of merit increased to M20 = 106, F20 = 158, (0.0027, 47) for the orthorhombic cell, three times better than for the hexagonal cell. Nevertheless, both unit cells continued to index all lines. Careful examination of the data (reflection splitting) and application of a pattern decomposition method with cell constraints (Le Bail method [18] by iterating the Rietveld [19] decomposition formula) led to definitely choose the orthorhombic cell and to propose two space groups from the extinction conditions : Pnma or Pn21a. Then, 442 structure factors were extracted from the synchrotron powder pattern by Le Bail method and ARITB program [20] choosing the Pnma space group. Application of the SHELXS-86 direct methods [21] allowed to locate three heavy atom sites whose peak height on the Fourier synthesis were 3 or 4 time higher than the height of the next peaks. After refining these heavy atom coordinates by the SHELX-76 program [22] (R = 26.3 %), a Fourier difference synthesis allowed to locate five fluorine sites. From the extracted structure factors, the SHELX-76 refinement with the complete structural model led to the reliability R = 20.4 %. The synchrotron pattern presents a poor statistics due to short measuring time (2.5 sec./pt), so that the final Rietveld refinement by the FULLPROF program [23] could not drop below R P = 17.3 % and R B = 6.8 % with isotropic B-factors. The zirconium thermal parameter was negative. Refining the Zr atom occupancy number (1.19) led to a 2% decrease on reliabilities with R P = 14.6 % and R B = 4.9 %. Trying to explain this anomaly by an hypothesis of non-stoichiometry with a partial replacement of Zr by Ba on the Zr atom site would have led to a Ba:Zr ratio larger than 2, in contradiction with the value previously suggested by Laval (1.86) [9]. However, this result was not confirmed from further conventional X-ray powder diffraction data leading to a Ba:Zr = 2 ratio. Moreover, the measured density of 5.29(6) was very near to the calculated one for a stoichiometric compound (5.278). It was finally decided to record a neutron diffraction pattern which was the only way to really accurately locate the fluorine atoms in presence of heavy atoms (for X-ray) like Ba and Zr ones. The fluorine atom sites should greatly be affected by non-stoichiometry, if any. Two samples were studied (A and B) by neutron diffraction, the Rietveld refinement with isotropic B factors led to R P = 10.4 % and R B = 5.6 % for sample B and to R P = 11.7 and R B = 4.6 %
for sample A, without introduction of cationic non-stoichiometry.
Improvements were obtained with anisotropic B factors, considered as significant according to the Rietveld Refinement Round Robin [24] on
PbSO4, a compound presenting a similar number of independent atoms as α-Ba2ZrF8. Using the Pna21 instead of the Pnma space group did not lead to significant modifications. The final reliabilities are gathered in Table I together with the measurement conditions. Samples C, D and E were examined by Rietveld refinements on conventional X-ray data, but the C sample results are not given hereafter because they are quite similar to those of sample D. Table II gives the atomic coordinates refined for A, B, D and E samples, the anisotropic thermal parameters for samples A and B (neutron data) are listed in Table III and finally Table IV shows the interatomic distances. Some selected plots drawn by the DMPLOT program [25] are shown on figure 1.
TABLE III - Anisotropic temperature factors (Ux104) for α-Ba2ZrF8 (neutron data)
_______________________________________________________________________ Atom Sample U11U22U33U12U13U23
Ba(1) A161(27)62(23)64(22)0-37(20)0 B227(24)68(19)89(19)0-33(18)0
Ba(2) A125(26)125(23)57(22)0-69(20)0 B235(23)85(17)84(23)0-29(18)0
Zr A146(22)88(15)115(16)01(20)0 B147(17)148(13)109(12)02(16)0
F(1) A181(16)131(15)163(16)59(14)-13(16)-18(21) B205(13)127(12)221(14)59(11)-41(13)-40(18)
F(2) A211(18)142(19)183(19)31(20)79(15)14(18) B245(15)163(16)230(15)99(16)58(12)-6(15)
F(3) A331(21)205(20)183(18)-184(16)66(17)4(18) B399(17)268(17)184(14)-210(14)101(22)5(16)
F(4) A349(30)147(27)104(26)075(27)0 B344(24)162(22)164(23)0126(22)0
F(5) A160(27)204(34)168(30)0-28(24)0 B180(22)225(28)200(24)045(19)0
_______________________________________________________________________ STRUCTURE DESCRIPTION AND DISCUSSION
From the neutron and conventional X-ray results, the non-stoichiometry (Ba0.65Zr0.35F2.70), previously announced [5] and suggested by the preliminary synchrotron results, remains undetectable for the samples here examined (A and B). Furthermore, we do not observe any clear dispersion
TABLE IV - Selected interatomic distances (?) for α-Ba2ZrF8 and Pb2ZrF8 (sample E). _______________________________________________________________________
[ZrF8] bicapped trigonal prism
Sample A (S) A (N) B (N) D (X) E (X)
Zr-F(3)x2 2.020(8) 2.072(5) 2.077(4) 2.077(8) 2.159(13) Zr-F(1)x2 2.036(7) 2.067(4) 2.068(3) 2.042(7) 1.972(13) Zr-F(2)x2 2.108(7) 2.130(4) 2.130(4) 2.142(7) 2.207(13) Zr-F(4) 2.180(9) 2.211(6) 2.201(5) 2.229(10) 2.116(17) Zr-F(5) 2.282(9) 2.218(6) 2.229(5) 2.281(10) 2.061(17)
Sample A (S) A (N) B (N) D (X) E (X)
Ba(1)-F(3)x2 2.630(8) 2.677(6) 2.676(4) 2.688(8) 2.550(12) Ba(1)-F(5) 2.667(11) 2.699(7) 2.711(6) 2.736(10) 2.447(16) Ba(1)-F(1)x2 2.779(8) 2.717(6) 2.717(5) 2.735(8) 2.509(12) Ba(1)-F(2)x2 2.794(7) 2.844(6) 2.848(5) 2.865(7) 3.241(12) Ba(1)-F(4)x2 2.838(2) 2.834(1) 2.835(1) 2.832(1) 2.757(4) Ba(1)-F(1)x2 2.892(7) 2.849(6) 2.839(5) 2.875(7) 2.852(13) Ba(1)-F(4) 2.963(11) 2.974(9) 2.982(7) 3.005(11)
_______________________________________________________________________ Ba(2)F13 or Pb(2)F11 polyhedron (replace Ba by Pb for sample E)
Sample A (S) A (N) B (N) D (X) E (X)
Ba(2)-F(3)x2 2.789(8) 2.726(6) 2.712(5) 2.731(8) 2.383(12) Ba(2)-F(1)x2 2.737(8) 2.787(6) 2.793(5) 2.786(1) 3.041(13) Ba(2)-F(2)x2 2.845(7) 2.822(5) 2.826(4) 2.782(7) 2.482(13) Ba(2)-F(2)x2 2.867(7) 2.844(5) 2.821(4) 2.846(7) 2.701(13) Ba(2)-F(5)x2 2.940(3) 2.948(2) 2.952(2) 2.929(3) 3.048(8) Ba(2)-F(4) 3.328(11) 3.297(8) 3.296(6) 3.272(11) 3.014(17) Ba(2)-F(3)x2 3.374(8) 3.367(6) 3.388(5) 3.355(8)
Sample A (S) A (N) B (N) D (X) E (X)
Ba(1)-Zr 3.747(2) 3.746(6) 3.753(5) 3.754(3) 3.621(3) Ba(1)-Zr(x2) 3.817(2) 3.821(4) 3.817(4) 3.818(2) 3.803(2) Ba(1)-Zr 3.841(2) 3.834(7) 3.829(6) 3.844(3) 3.854(4) Ba(2)-Zr 4.095(2) 4.087(6) 4.085(5) 4.087(3) 3.917(3) Ba(2)-Zr(x2) 4.104(2) 4.100(4) 4.115(4) 4.108(2) 3.993(3) Ba(2)-Zr(x2) 4.136(2) 4.147(4) 4.132(4) 4.144(2) 4.216(3) Ba(1)-Ba(1)x24.146(2) 4.142(6) 4.133(5) 4.146(2) 4.162(2) Ba(1)-Ba(2)x24.278(2) 4.272(6) 4.288(5) 4.274(2) 4.341(2) _______________________________________________________________________ Note : S = Synchrotron data ; N = Neutron data ; X = Conventional X-ray
(which would be larger than expected from different patterns of the same
sample [24]) in the cell parameters and atomic coordinates of the various Ba2ZrF8 samples (A, B, C, D). The neutron data from the sand bath
preparation seem to be the more accurate (with longer counting time and
better resolution). Therefore, we will consider only the neutron results from sample B as representative of α-Ba2ZrF8 structure although the most accurate cell parameters are those from the synchrotron data.
The title compound appears as a well ordered material in which [ZrF8]
isolated bicapped trigonal prisms (rather than square antiprisms) are easily detected when examining the structure projection along the b axis (figs. 2 and 3). This short b axis (5.6 ?), very close to the cubic BaF2 cell parameter, immediately suggests a possible relationship between α-Ba2ZrF8 and the fluorite structure. However, the barium anionic polyhedra are far from being cubes in the barium octafluorozirconate. Indeed, the [Ba(1)F12] polyhedron is a quite regular cuboctahedron whereas the [Ba(2)F13] can be considered as a distorted pentagonal prism with two fluorine atoms (F(5)) capping both pentagonal faces and one additional fluorine atom capping a rectangular face (F(4)). Nevertheless, an analogy with the fluorite structure is conceivable because the barium atoms are at y coordinates ? or ?. The relationship becomes obvious when considering the ac plane and selecting the fluorine atoms at y coordinates near of 0 and ? which clearly form parallelepipedic environments around the Ba atoms. In this way, the α-Ba2ZrF8 structure appears in figure 4 as built up from elongated [BaF8] cubes stacked as in the BaF2 fluorite structure by alternating the Ba y coordinates at ? and ? in linear blocks constituted of four such distorted cubes. The linear blocks share one F-F edge of the two extreme [BaF8] distorted cubes with two adjacent blocks forming fluorite strips corrugating in the ab plane. Along 0z, successive strips related by the a glide plane in the ab plane are stacked by sharing F-F edges so forming fluorite corrugated sheets. The zirconium atoms may be considered in this view as occupying holes (triangular prisms) between the sheets, and the remaining fluorine atoms F(4) and F(5) occupy the empty fluorine distorted cubes at ?+y of the barium atoms coordinates. Of course the view is idealized because the [Ba(2)F10] pentagonal prism obtained when removing the F(4) and F(5) atoms is artificially reduced to a pseudo-cube for this purpose. However, this description allows to compare easily the α-Ba2ZrF8 structure to those previously described : NaBaZrF7 and K2ReF8.
NaBaZrF7 [27] crystallizes in the same Pnma space group as α-Ba2ZrF8 with close cell parameters (a = 9.118 ?, b = 5.556 ? and c = 11.236 ?). Moreover, if the cell origin is translated by ? along the b and c axes, then the NaBaZrF7 atomic coordinates become quite similar to the α-Ba2ZrF8 ones (Table V). Consequently, the same fluorite-structure group may be found for the sodium compound (fig. 5) with true [NaF8] cubes. The F(4) site in α-Ba2ZrF8 is vacant in NaBaZrF7 so that the zirconium polyhedron
becomes a monocapped trigonal
prism (by F(4) in Table V).However, comparing F(5) in Table
II and F(4) in Table V shows that
the x coordinates are quite different.Indeed, in NaBaZrF 7, this fluorine
atom is capping the face of the
trigonal prism which is uncapped in the title compound. The next step in
such a series would be a Na 2ZrF 6structure with exclusively [NaF 8]cubes and [ZrF 6] trigonal prisms.
This is unlikely to occur because,
till now, [ZrF 6] polyhedra are always octahedra.
K 2ReF 8 [28] is one of the few structure types with a formula homologous to that of α-Ba 2ZrF 8. Examining possible relationship between both phases (same space group, close cell parameters and [ReF 8] bicapped trigonal prisms) it was found that fluorite blocks could be located in this compound by the same method as for α-Ba 2ZrF 8 (searching for [KF 8] distorted cubes with fluorine atoms at y ≈ 0 and ?, and K atoms at ? and ?). The result is shown in figure 6, leading to a quite different approach of the K 2ReF 8structure relationship with fluorite, than what was previously described by Frit and Laval [29] (including Re and K atoms in a quasi unchanged cationic fluorine network). The present view shows an alternative with small fluorite-related blocks of four [KF 8] pseudo-cubes presenting various orientations. The Re 6+ ions are inserted in the holes (trigonal prisms) created at the connections of two blocks. The same unit block of four pseudo-cubes can be recognized in α-Ba 2ZrF 8, but they are interconnected in sheets which do not interrupt the fluorite net.TABLE V - NaBaZrF 7 coordinates (same origin as for α-Ba 2ZrF 8)______________________________Atom x y z Na 0.8705?0.9448Ba 0.4696?0.1734Zr 0.2472?0.8607F(1)0.07140.48400.8876F(2)0.17270.98400.4823F(3)0.28330.49200.7244F(4)0.9730?0.6668
______________________________
The crystal structures of α-Ba2ZrF8 and Pb2ZrF8 are clearly isotypic.
However, significant differences in both structures have been evidenced resulting from small shifts in cationic and anionic coordinates associated to
an anisotropic contraction of the whole volume from Ba to Pb phase : the b
parameter decreases from 5.2%, the c parameter decreases in less proportion (1.9%) whereas the a parameter increases from 3.5%. This curious behaviour results from the stereochemical influence of Pb2+ lone pair as evident on comparing the Ba and Pb polyhedra represented on fig. 7 with quite the same orientation. The [Ba(1)F12] almost regular cuboctahedron is transformed to a [PbF11] polyhedron by strong elongation of a Pb-F(4) bond (from ~3 ? to 3.503 ?), the F(4) anion being repelled by the lone pair directed toward it. In the same way, the [Ba(2)F13] polyhedron is transformed to a [Pb(2)F11] polyhedron by a repulsion of a F(3)-F(3) edge by the lone pair influence (fig. 7).
Fig. 7 - Comparison of Ba and Pb polyhedra in α-Ba2ZrF8 and Pb2ZrF8 structures, evidencing the distortion and the coordination reduction caused by the stereochemical activity of the Pb2+ lone pair. (a) Ba(1)F12 ; (b) Pb(1)F11+1 ; (c) Ba(2)F13 ;
(d) Pb(2)F11+2.
The hexagonal cell proposition at the indexing stage came from the a/b =
1.735 ratio very close to 3. This appears to be a pure coincidence as no hexagonal subcell can be identified with a common c axis with the
orthorhombic Pnma one. Nevertheless, a pseudo hexagonal cell can be
really found in another direction, taking the b orthorhombic axis as the hexagonal c-axis, with one zirconium at the cell origin.
The possible occurrence of non-stoichiometry in α-Ba2ZrF8 and Pb2ZrF8 phases has been mentioned not only because the first synthesis of the Ba phase at 450°C led to an apparent departure from stoichiometry, unconfirmed in the present work, but also because the similar phases relationship study in the SrF2-ZrF4 system [30] revealed a domain of solid solution between limits MF2.667-MF2.700. Recent investigations [31] by X-ray diffraction and HRTEM show that this domain corresponds in fact to a complex series of microphases of very close compositions. Moreover, two related microphases are obtained by solid state synthesis in the PbF2-ZrF4 system between 500 and 560°C. They are decomposed in a mixture of PbZrF6 and Pb3ZrF10 by long time annealing at temperature below 500°C. Their complex X-ray patterns were indexed with the help of an electron diffraction study which shows the presence of superstructures along the a axis of a common sublattice with parameters very close to those of Pb2ZrF8 studied in the present work. Table VI reports a comparison of the subcell parameters for all these phases. The cell parameters of Pb2ZrF8 obtained by the sand-bath method are closer to those of the micro phase obtained in solid state between 510 and 530°C than to the ones of the higher temperature microphase. But they are not exactly the same. That clearly shows the great plasticity of this new structural family in relation with the conditions and methods of synthesis.
Table VI - Comparison of M2ZrF8 (M = Ba, Pb) and related microphase cell parameters.
CONCLUSION
In the light of the above comparisons, it can be concluded that the same stoichiometric phase α-Ba2ZrF8 is synthesized as well by a solid state
process as by hydrothermal and moderated temperature sand-bath methods.
It corresponds to the crystal structure described in the present paper. This phase has a limited stability at high temperature and transforms to β-Ba2ZrF8 of apparently unrelated structure. The α→β transition was found at 490°C [1] by successive annealings at increasing temperatures, but no
thermal event was detected below 595°C in reference [3] and by DTA
experiments up to 590°C in the present study.
In the PbF2-ZrF4 system, the stoichiometric Pb2ZrF8 phase obtained at 60°C on a sand-bath is distinct from the defective microphases (ordered Pb cationic vacancies) synthesized by solid state reaction.
α-Ba2ZrF8 and Pb2ZrF8 structures provide the basic model allowing to understand the features of the non-stoichiometry in the complex microphases which will be the subject of a forthcoming paper.
Acknowledgments. Most syntheses and thermal analyses were done by A.-M. Mercier with the exception of sample D. The synchrotron pattern was kindly recorded at Daresbury Laboratory by A. Jouanneaux. Thanks are due to the Laue-Langevin Institut for providing neutrons during experiments 5-21-721 and 5-23-421. Drawings were realized with help from the STRUVIR program [33].
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TABLE II - Atomic coordinates, thermal (B) and bond valence parameters (ν) [26] for various samples (A, B, D) of α-Ba2ZrF8 and for Pb2ZrF8 (sample E).
_______________________________________________________________________ Sample A - Hydrothermal α-Ba2ZrF8 - Synchrotron Data
Atom Site x y z B(?2)v
Ba(1)4c0.8612(2)?0.9406(2) 1.05(3) 2.44 Ba(2)4c0.4463(2)?0.1608(2) 1.28(4) 1.90
Zr4c0.2429(2)?0.8593(2) -0.55(3) 4.24
F(1)8d0.0970(8)0.5096(13)0.8579(7) 1.7(2) 1.19
F(2)8d0.1476(8)0.9868(12)0.4637(6) 1.2(2) 1.03
F(3)8d0.3402(8)0.4741(13)0.7529(6) 1.9(2) 1.18
F(4)4c0.1474(12)?0.0252(8) 1.4(2)0.92
F(5)4c0.1369(12)?0.6881(7)0.5(2)0.85
_______________________________________________________________________ Sample A - Hydrothermal α-Ba2ZrF8 - Neutron Data
Atom Site x y z Beq(?2)v
Ba(1)4c0.8618(6)?0.9402(4)0.65(8) 2.42 Ba(2)4c0.4449(5)?0.1607(4)0.70(8) 1.96
Zr4c0.2428(4)?0.8594(3)0.74(5) 3.94
F(1)8d0.0941(3)0.5124(7)0.8640(3) 1.25(5) 1.17
F(2)8d0.1423(4)0.9856(7)0.4636(3) 1.43(6) 1.00
F(3)8d0.3438(4)0.4872(7)0.7546(3) 1.75(6) 1.10
F(4)4c0.1476(6)?0.0282(4) 1.50(8)0.90
F(5)4c0.1381(5)?0.6937(4) 1.19(9)0.88
_______________________________________________________________________ Sample B - Sand Bath α-Ba2ZrF8 - Neutron Data
Atom Site x y z Beq(?2)v
Ba(1)4c0.8624(5)?0.9404(4)0.77(7) 2.42 Ba(2)4c0.4468(4)?0.1603(3)0.91(7) 1.99
Zr4c0.2430(3)?0.8599(3)0.85(5) 3.93
F(1)8d0.0937(2)0.5117(5)0.8639(3) 1.36(5) 1.18
F(2)8d0.1418(3)0.9866(5)0.4634(2) 1.67(5) 1.00
F(3)8d0.3443(3)0.4868(6)0.7544(2) 2.05(5) 1.10
F(4)4c0.1491(5)?0.0284(3) 1.52(7)0.91
F(5)4c0.1372(4)?0.6936(3) 1.36(8)0.86
_______________________________________________________________________ Sample D - Solid State α-Ba2ZrF8 - Conventional X-ray Data
Atom Site x y z B(?2)v
Ba(1)4c0.8613(2)?0.9407(1)0.49(3) 2.31 Ba(2)4c0.4454(2)?0.1603(1)0.87(3) 2.02
Zr4c0.2430(2)?0.8595(2)0.29(3) 3.90
F(1)8d0.0966(7)0.5100(12)0.8623(7)0.86(6) 1.19
F(2)8d0.1394(7)0.9811(13)0.4655(5)0.86(6)0.99
F(3)8d0.3423(8)0.4894(13)0.7543(7)0.86(6) 1.08
F(4)4c0.1495(12)?0.0304(8)0.86(6)0.88
F(5)4c0.1313(12)?0.6911(8)0.86(6)0.82
_______________________________________________________________________ Sample E - Sand Bath Pb2ZrF8 - Conventional X-ray Data
Atom Site x y z B(?2)v
Pb(1)4c0.8714(2)?0.9197(1)0.76(3) 1.94 Pb(2)4c0.4570(2)?0.1565(1) 1.38(3) 2.01
Zr4c0.2498(4)?0.8724(2)0.22(5) 4.16
F(1)8d0.0888(11)0.4601(27)0.8776(11) 3.2(2) 1.17
F(2)8d0.1112(10)0.9998(28)0.4638(10) 3.2(2)0.88
F(3)8d0.3690(12)0.4967(24)0.7677(10) 3.2(2) 1.07
F(4)4c0.1870(16)?0.0455(15) 3.2(2)0.84
F(5)4c0.1779(16)?0.7070(15) 3.2(2) 1.02
_______________________________________________________________________
Sample A : α-Ba2ZrF8
Hydrothermal synthesis
Synchrotron data
Sample B : α-Ba2ZrF8
Sand bath synthesis
Neutron data
Sample E : Pb2ZrF8
Sand bath synthesis
Conventional X-ray data
Fig. 1 - Observed, calculated and difference diffraction patterns of α-Ba2ZrF8 and
Pb2ZrF 8
Fig. 2 - Projection of the α-Ba2ZrF8 structure along the b axis
cuboctahedra and [Ba(2)F13] tricapped pentagonal prisms
Fig. 4 - If F(4) and F(5) atoms are omitted in α-Ba2ZrF8, then distorted [BaF8] cubes appear, evidencing kinked blocks with the fluorine structure. Spheres are the Zr atoms.
Fig. 5 - View of the idealized NaBaZrF7 structure (removing F(4)) with [NaF8] cubes and distorted [BaF8] ones. Spheres are the Zr atoms. In fact, the true Ba atoms environment is
a bicapped pentagonal prism (with one cap less than for Ba(2) in α-Ba2ZrF8).
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目录 1.1创建P ORTAL域 (4) 1.1.1 启动 Configuration Wizard (4) 1.1.2 创建或扩展域 (4) 1.1.3 选择域源 (5) 1.1.4 配置管理员用户名和密码 (6) 1.1.5 指定服务器启动模式和 JDK (7) 1.1.6 自定义环境和服务设置 (9) 1.1.7 创建 WebLogic 域 (9) 1.1.8 创建域 (10) 1.2创建P ORTAL EAR项目 (11) 1.3创建P ORTAL W EB 项目 (16) 1.4创建数据同步项目 (20) 1.5创建P RTAL (23) 1.5.1 创建一个Portal (23) 1.5.2 增加一个页面到你的Portal (25) 1.5.3 发布和查看Portal (27) 1.5.4 创建Portlets (27) 1.5.5 把Portlets添加到Portal (31) 1.6登录管理控制台并创建P ORTAL和桌面 (32) 1.6.1 打开管理控制台 (32) 1.6.2 登录管理控制台 (33) 1.6.3 创建Portal和桌面 (34)
1创建Portal域 ●启动 Configuration Wizard ●创建或扩展域 ●选择域源 ●配置管理员用户名和密码 ●指定服务器启动模式和 JDK ●自定义环境和服务设置 ●创建 WebLogic 域 ●创建域 1.1启动 Configuration Wizard 打开“开始”->“BEA Products”->“Tools”->“Configuration Wizard”。之后将会出现“欢迎”窗口。 1.2创建或扩展域 提示您选择是新建域还是扩展现有域。
基于Crystal Ball 软件对测量不确定度的评定 1240410114 王颖测量结果与被测量真值的一致程度被定义为准确性。但是实际上不存在完全准确无误的测量，因此通常在给出量值结果的同时通常给出适应于实际需要的不确定度。如果没有对不确定度的表述，所进行的测量的被测量对象的质量就无从判断，从而导致测量的结果值不具备充分的实用价值。测量的结果值的准确，是在一定的不确定度、误差允许误差范围内的准确。 一）基本概念 测量不确定度的概念最早是有国外引入，一般译为：与测量结果相联系的参数，用来表示赋予被测量对象值的分散性的特征。它最早跟我们熟悉的误差的概念相似。测量不确定度的前提是当我们在重复性条件下，对具有稳定特征的被测量对象X独立的进行了n次重复测量实验，在这一系列测量实验过程中，通过n个结果按公式计算出的，第i次结果xi的实验标准差E（xi)，xi虽然是指第i 次测量的结果，但是它的实际含义是：任一次的测量结果。表明不确定度s(xi)=u(xi)是这个测量序列中任意一次测量结果的不确定度。如果在相同的相同的、重复条件下再进行测量，得到的结果xi 的标准不确定度仍然是E(xi。 二）测量不确定度评定的步骤
1.识别不确定度来源。对测试结果测量不确定度来源的识别应该首先从分析测量过程开始，并且要对测量方法、测量系统和测量程序作详细研究和熟悉，如果可能要画出测量系统原理图和测量流程图。不确定度来源一般有：对被测量的定义不完善；实现被测量的定义的方法不理想；选取测量样品的典型性不够；对测量过程中受外部环境影响的因素识别不完整等因素引起。 2.建立模型。当被测量对象Y(即我们期望的输出量)由N个其他因素X1，X2，…，XN(即输入量)，通过函数关系f来确定时，则Y = f (X1 , X 2 ,L, X N )称为测量模型或数学模型。式中大写字母表示测量的符号f 为测量函数。如果输入量Xi 的估计值为Xi，被测量对象Y 的估计值为y，则测量模型可建立为：y = f (x1 , x 2 ,L, xN ) 3.标准不确定度A类和B类分量的计算。A类不确定度分量的评估（对观测序列所进行统计分析作出的评估）。a)对输入量Xi进行独立的n 次测量，测量结果为：x1、x2……xn， 单次测量结果的标准差为：估计值的标准不确定 度为：，由于B 类的使用条件与A类不同，因此B 类不确定度分量的评估与A类也不同，B类评估时，输入量的估计量Xi不是由重复观测得到时，其标准偏差可用对Xi的信息来进行评估。B类评估的信息来源可来自：仪器设备的校准证书的说明、生产厂商标示的说明书、使用的检测依据的标准、引用手册的参考数据、以前
Laravel 5.5 入门教程 By IT崖柏图 Mail 973714522@https://www.doczj.com/doc/3c18639070.html, 出自布尔教育PHP高端教育培训 21 章功能细化 21.1 登陆状态 在 view 层 , 判断用户是否登陆 或者我们还可以使用身份快捷认证,如: 21.2 分页功能 中使用 paginate 方法。 代码如下:
如何渲染样式在Blade模板上? 附加参数到分页链接中 方法： ```php {{ $users->fragment('foo')->links() }} 然而，自定义分页视图最简单的方法是通过vendor:publish命令将它们导出到你的resources/views/vendor php artisan vendor:publish --tag=laravel-pagination 这个命令将视图放置在 resources/views/vendor/pagination 目录中。这个目录下的 default.blade.php 文件对应于默认分页视图。你可以简单地编辑这个文件来修改分页的 HTML 。 21.3 JS 验证 以发布借款项目为例 , 做 JS 验证
第22章自动验证自动验证 22.1 验证案例 第1个参数为Request对象,第2个参数为验证规则验证规则 验证规则为关联数组,语法如下: 借款验证案例: 验证未通过的检测,以money为例 22.2 自定义错误信息 如果验证未通过,需要自定义错误信息,只需在第3个参数中传递.
模板中使用 22.3 手动验证 ,也可以手动来创建一个验证对象 22.3 表单授权验证 令来创建表单请求类：
Crystal Ball实验操作过程 实验一： 一、数据录入与导入 双击CB快捷方式图标或直接打开Excel打开软件。前面提到过Crystal Ball软件是在Excel里的一个插件，所以双击打开后是Excel的界面，如下图： 图 1 用户可以在该界面中直接录入数据，也可以左击右上角的符号，选择打开，将原有Excel表格中的数据直接导入到带有Crystal Ball插件的电子表格中。 二、拟合分布 图2 (1)对数据进行标准化处理(减少原数据相互间的距离对拟合分布的影响) 通过Average计算每个分布工程样本数据的均值,然后各个样本数据除以相
应的均值,对数据进行标准化处理。 （2）拟合分布 选取表格区域，点击工具栏上“Run-Tools-Batch Fit”,如图3所示。 图3 在操作对话框中，选择“next”,至图4对话框对相应命令进行选择,可得到拟合过程的相关数据。 图4 注：对于卡方检验，水晶球软件计算p值，p值大于0.5一般表示紧密拟合； 对于科尔莫格洛夫-斯米尔诺夫检验，一般地，小于0.03的K-S值表明良好拟合； 对于安德森-达林检验，小于1.5的计算值一般表明拟合优良。 实验二:
一.按照实验一的操作,先将数据在Crystal Ball软件打开. 二、假设单元格概率分布的定义及相关操作 输入数据后，进行随机变量假设单元格概率分布的定义。这里假设使用悲观时间的单元格来进行概率分布的定义。（注：对于假设单元格的选择，并无太多的限制，因为定义各种概率的分布，是由相应的参数确定的，因此选择的假设单元格不同对结果并没有影响。）有一点需要注意的是，选择假设单元格时，该单元格应当是一确定的数字，而不能是公式. 选定单元格（如单元格I2）后，点击工具栏上的，随即弹出图5，CB 软件中提供22种不同的分布可供选择，根据实验任务书的要求，第一和第二项分部分项工程服从三参数beta分布，因此，选择BtaPERT分布，并填入相应参数，即可完成对“基坑支护挖土方”的定义，如图6所示。同理可完成其它分布的定义。 图5 图6 由于第3~8项同为三角分布，因此当完成第3项的定以后，选定I4单元格
Crystal Ball 介绍 Crystal Ball(CB)是基于PC Windows平台而开发的简单且非常实用的风险分析和评估软件。面向各类商务、科学和技术工程领域，用户界面友好,是基于图表进行预测和风险分析。CB 在微软Excel 应用软件上运行，使用蒙特卡罗（Monte Carlo）模拟法对某个特定状况预测所有可能的结果，运用图表对分析进行总结，并显示每一个结果的概率。除了描述统计量、趋势图和相关变量分配，CB还进行敏感性分析，让用户决定真正导致结果的因素。如今 CB 已是全世界商业风险分析和决策评估软件中的佼佼者。Crystal Ball专业版是市面上以Excel为本的风险分析及预测工具中最全面的套装软件。其功能和特点不仅早已得到广大用户的认同，并获得许多正在考虑购买相关软件产品新用户的青睐和首选。85%<<财富>>评出的全球500强大企业中早已有400家使用 Crystal Ball 软件作为他们进行商务决策，项目投资风险分析的工具。再者,美国前50名最佳MBA 商学院，已有40所也用Crystal Ball作为教研和商业性课题的工具。用户之一世界着名的哈佛大学商学院把 Crystal Ball 列为可用于计划金融的软件 (Project Finance Software)。因为财政计划,金融投资方面的风险分析是CB 软件功能的一部分。 Crystal Ball之前是美国Decisioneering公司的产品，Decisioneering在2007年被Hyperion公司收购，Hyperion 公司之后又被Oracle收购，所以Crystal Ball目前的发行商是Oracle。 Crystal Ball的用途： DFSS，过程研究，过程优化，现有过程的模拟改变，公差分析，设计分析，原料筛选，容量设计，资源分配与存货优化，约束后的项目筛选，预防性维护优化，成本预算，可靠性分析，排队过程分析，建筑项目资金预算的偶然性分析，商业过程模拟，工程设计与预测，供求预测，制造供应链问题的减少与存货控制，新产品商品化的资金模型。 模拟的意义 当我们使用模拟这个字时，代表我们利用分析模型来仿真现实生活的系统。过去仿真软件过于偏重复杂数学造成操作困难。Crystal Ball工作表风险分析结合工作表呈现方式与自动分析模拟，可以清楚的展现因为变量变异造成模型产出的各种情况。如果没有增加仿真功能，那工作表充其量只是揭示单一结果与最一般化的情境。工作表模拟最常用的方法就是蒙特卡洛法，它可随机产生变量在不同情况下的模型结果。 蒙特卡洛模拟 蒙特卡洛模拟一开始主要运作于分析赌博游戏。诸如轮盘、骰子、拉吧等。蒙特卡洛可以模拟这些赌博中的随机行为。当你掷骰子时，你知道共有一至六的数字可能会出现，但是你不知道一个规则。他就像企业主面对问题时，可能知道问题引发的结果与过程，却无法了解每一个变量的严重程度。（例如：利率、员工、股价、存货及来电率） 自行于工作表内选定变量的分配类型 针对每个不确定变数，你可以自行设定相关机率分配。您可以依据该变量所处的环境选择分配的类型，分配类型如下： 您可以将工具栏加入EXCEL工作表中，当然您必须知道这些等式所代表的分配。透过Crystal Ball, 软件可自动为用户计算方程式。Crystal Ball甚至可以藉由过去的历史数据来修正分配。
《微信小程序》教学大纲 课程编码制订人制订日期修订人修订日期审核人审核日期曾建华2021.1 学分：3-4 学时：48-64 适用专业：软件技术专业 一、课程的性质与任务 课程的性质：针对计算机软件类相关专业学生的专业核心课。 课程的任务：通过本课程的学习，学生应能熟练使用微信开发者工具，熟练开发微信小程序，在后台方面，理解后台的开发流程以及微信小程序是如何与后台交互的。 二、教学基本要求 通过本课程的学习，学生应达到下列基本要求： 微信小程序的项目构成 微信小程序页面构成 生命周期函数 WXML 事件 微信小程序如何使用外部API（到此48学时） 使用PHP+MySQL设计自己的API 使用Laravel框架设计自己的API（到此56学时） 系统组件 自定义组件 WeUI组件库（到此64学时） 三、教学条件 机房上课，每个学生有一台电脑。 投影仪等多媒体教学设备。
安装软件：微信开发者工具、HBuilder、xampp。 四、教学内容 各学校可根据实际情况选择： 1-7：48学时 1-9：56学时 1-11：64学时 序号单元主要内容 1 开发环境及第一 个微信小程序 ●了解微信小程序相关技术。 ●掌握微信开发者工具的安装、使用。 ●掌握如何创建微信小程序。 ●掌握微信小程序的项目架构、页面结构。 2 基本页面和底部 导航 ●熟练掌握创建新的页面。 ●熟练编写底部导航代码。 ●理解底部导航各属性的含义。 ●进一步熟悉微信开发者工具界面。 3 js文件●理解app.js中的生命周期函数。 ●掌握app.js中的全局变量。 ●理解page.js中的生命周期函数。 ●掌握page.js中的局部变量。 ●掌握如何创建和引用模块。 4 WXML语法●掌握数据绑定的方法。 ●掌握条件渲染的用法。 ●掌握列表渲染的用法。 ●掌握如何定义模板以及使用import引用模板。 ●掌握include引用方式。 5 事件及数据传递●熟练掌握如何进行事件处理。 ●理解事件冒泡机制。 ●在事件中获取组件绑定的附加信息。 ●熟练掌握路由机制。 ●熟练掌握页面之间如何进行数据传递。 6 常用API及组 件 ●清楚小程序API的类型，熟悉界面交互API。 ●了解地图操作步骤。
Monte-Carlo Simulation with Crystal Ball? To run a simulation using Crystal Ball?: 1. Setup Spreadsheet Build a spreadsheet that will calculate the performance measure ., profit) in terms of the inputs (random or not). For random inputs, just enter any number. 2. Define Assumptions—., random variables Define which cells are random, and what distribution they should follow. 3. Define Forecast—., output or performance measure Define which cell(s) you are interested in forecasting (typically the performance measure, ., profit). 4. Choose Number of Trials Select the number of trials. If you would later like to generate
the Sensitivity Analysis chart, choose “Sensitivity Analysis” under Options in Run Preferences. 5. Run Simulation Run the simulation. If you would like to change parameters and re-run the simulation, you should “reset” the simulation (click on the “Reset Simulation” button on the toolbar or in the Run menu) first. 6. View Results The forecast window showing the results of the simulation appears automatically after (or during) the simulation. Many different results are available (frequency chart, cumulative chart, statistics, percentiles, sensitivity analysis, and trend chart). The results can be copied into the worksheet. Crystal Ball Toolbar: Define Define Run Start Reset Forecast Trend
《PHP网站开发实例教程（第2版）》 教学大纲 （课程英文名称） 课程编号： 学分：5学分 学时：70学时（其中：讲课52学时上机18学时） 先修课程：计算机基础 适用专业：信息技术及其计算机相关专业 开课部门：计算机相关院系 一、课程的性质与目标 《PHP网站开发实例教程（第2版）》是面向计算机相关专业的一门PHP课程，涉及框架基础知识、数据库和模板引擎的使用、框架实现原理、使用框架开发项目等内容。通过本课程的学习，学生能够了解框架的基础使用，如何使用框架进行网站开发，以及市面上流行的Laravel框架的使用。 二、课程设计理念与思路 课程设计理念：高等职业教育的集中实践教学环节需明确必要的理论知识的升华与知识层面的拓展，不能局限于单纯的技能训练。单纯的技能训练不是提高高等职业教育的理想课程。以能力的培养为重点，以就业为导向，培养学生具备职业岗位所需的职业能力，职业生涯发展所需的能力和终身学习的能力，实现一站式教学理念。 课程设计思路：基于工作过程开发课程内容，以行动为导向进行教学内容设计，以学生为主体，以案例（项目）实训为手段，设计出理论学习与技能掌握相融合的课程内容体系。教学整体设计“以职业技能培养为目标，以案例（项目）任务实现为载体、理论学习与实际操作相结合”。
三、教学条件要求 操作系统：Windows 7、W AMP 开发工具：命令行工具（如cmd）、开发工具（如VS Code）、依赖管理工具（如Composer） 四、课程的主要内容及基本要求 第1章开发环境搭建 第2章PHP框架基础（上） 第3章PHP框架基础（下）
第4章数据库和模板引擎 第5章内容管理系统（上）
软件介绍 CrystalMaker：晶体和分子结构可视化软件 探索晶体世界 从金属到沸石，苯到蛋白质, CrystalMaker是了解晶体和分子结构的最简单方法。 什么是CrystalMaker? CrystalMaker软件是一款在创建、显示和操作各种晶体分子结构中屡获好评的软件。CrystalMaker在生产力方面提供了一个流线型的工作流程，您只需把您的数据文件拖拉到程序中便可即时显示照片般逼真的色彩。用鼠标就可以实时操作晶体结构。多视角"bookmarks"和撤销次数鼓励您探索和发现——理想的教学和科研软件。 快速创建晶体和分子结构！ 使用CrystalMaker软件，您可以轻松快速创建任何晶体或分子结构。内置的对称处理和美观的空间群浏览器可得到晶体的日志，并且该程序会自动生成所有的键和多面体。CrystalMaker 提供了广泛的模式类型，包括传统的“ball-and-stick”, space-filling, polyhedral, wireframe 以及thermal ellipsoids模式。使用photo-realistic simpler和line-art display选项，每种模式类型都可以被广泛地定制。 综合数据的输入和输出 负载来自于超过15+ 格式的结构数据，包括Cambridge Structures Database, Protein Data Bank, CIF, GSAS, SHELX等。您可以操作几乎无限的原子数量。使用独特的"Depth Profiling"工具，快速扫描大规模结构中有用的，从而能从计算机模式中得到理想的特征结果。 大量的输出选项使您能跟其他程序共享数据、保存结构数据、键长、协调环境，甚至用您的数据创建网页。 出色的3D图片 深度渐变和视角转换，加上优美的三维立体结构，使您能看到照片质量的图片。高分辨率打印并把图片保存成各种文件格式，同时您还可以定义图片的大小。使用深度剖析和测量处理大规模的结构。完整的误差传递、集群壳和协调网络可视以及强大的输出选项，自动生成键长和多面体。 实时操纵与测量 用鼠标拖拉、键盘或工具栏，便可查看网格矢量或平面矢量。连续绘图范围设置可以设置数百万个原子，健和多面体。 移动、分离、复制、隐藏和删除原子组。隐藏或修复分子片段——分离单个分子。可在任何方位显示平面格。切割晶体结构以便研究其表面或内部平面。或把一个晶体或分子结构置于另一个结构中。 预览协调环境，集群和表面。列出键长和屏幕上的柱状图或保存到磁盘里。在屏幕上测量键长，角度，以及扭转角。在平面和向量间计算角度。
Crystal Ball 模拟基础教程 利用Crystal Ball 进行计算机仿真 学习目标13.2 个案研究：佛莱迪报童问题（13.1节） 13.3–13.19 竞标建设计划（13.2节） 13.20–13.24 项目管理：信用建设公司（13.3节）13.25–13.32 现金流量管理：沼泽地黄金岁月公司（13.4节） 13.33–13.37 财务风险分析：久大发展公司（13.5节）13.38–13.42 运输业收入管理（13.6节）13.43–13.48 选择合适的分配（13.7节）13.49–13.68 利用决策表做决策（13.8节） 13.69–13.84 学习目标 在读完本章后，你应该能够： 1. 描述Crystal Ball在计算机仿真中的角色。 2. 利用Crystal Ball来解决Excel软件包所无法执行的各类基本计算机仿真。 3. 解释利用Crystal Ball于计算机仿真中的结果。 4. 在获得预期的准确度水平后，利用Crystal Ball的特色来停止计算机仿真。 5. 描述当使用Crystal Ball时可以搭配计算机仿真的机率分配之特色。 6. 利用Crystal Ball程序辨识出符合历史数据的连续分配。 7. 利用Crystal Ball的特色来产生一些帮助决策的决策表和趋势图。 报童佛莱迪 佛莱迪在某大城市里主要市区经营一家报摊。 佛莱迪贩卖各类的报纸和杂志，其中最贵的报纸为财经日报。 财经日报相关的成本资料： –每份报纸的成本为1.50美元 –每份报纸的售价为2.50美元 –没售出的报纸，每份报纸可以获得0.50美元的偿还金 财经日报的销售资料： –佛莱迪每天的销售量介于40到70份之间。 –销售数量介于40到70份之间任何数值的频率相同。 运用仿真之电子表格模式 Crystal Ball的应用 利用Crystal Ball来进行计算机仿真有四个步骤： –定义随机输入栏。 –定义输出栏来预测。 –设定执行偏好。 –执行模拟。 步骤1：定义随机输入栏 随机输入栏是拥有随机数值的输入字段。 需要输入储存格的是假设的机率分配而非一永久的数值。 Crystal Ball将每个随机输入栏称作假设栏（assumption cell）。 定义假设栏的步骤 ?点选选定的字段。 ?假如字段没有数值，输入任何一个数字。 ?点选「Crystal Ball」标签（Excel 2007）或工具列（Excel较早版本）的「Define Assumption」
风险管理软件CrystalBall操作指南(英文版)(doc 16页)
Monte-Carlo Simulation with Crystal Ball? To run a simulation using Crystal Ball?: 1. Setup Spreadsheet Build a spreadsheet that will calculate the performance measure (e.g., profit) in terms of the inputs (random or not). For random inputs, just enter any number. 2. Define Assumptions—i.e., random variables Define which cells are random, and what distribution they should follow. 3. Define Forecast—i.e., output or performance measure Define which cell(s) you are interested in forecasting (typically the performance measure, e.g., profit). 4. Choose Number of Trials Select the number of trials. If you would later like to generate the Sensitivity Analysis chart, choose “Sensitivity Analysis” under Options in Run Preferences. 5. Run Simulation Run the simulation. If you would like to change parameters and re-run the simulation, you should “reset” the simulation (click on the “Reset Simulation” button on the toolbar or in the Run menu) first.