Real space manifestation of the first sharp diffraction peak in the structure factor of liquid and glassy materials

1994 ◽  
Vol 445 (1924) ◽  
pp. 351-365 ◽  
Keyword(s):  
Structure Factor ◽  
Real Space ◽  
Density Fluctuations ◽  
Diffraction Peak ◽  
Minimum Size ◽  
Structural Units ◽  
Structure Factors ◽  
Oscillatory Character ◽  
Glassy Materials ◽  
Total Structure

The problem of those discernible features of the intermediate range order (IRO) which can be attributed to the first sharp diffraction peak (FSDP) observed in the structure factor of many liquid and glassy materials is approached by treating this peak as a distinct feature. It is found, by considering the measured partial structure factors, S αβ ( k ), for molten ZnCl 2 , GeSe 2 , MgCl 2 , NiBr 2 and Nil 2 and the measured total structure factors, F ( k ), for glassy SiO 2 , PS 4 and liquid CCl 4 , that the propensity of the FSDP to have a prominent effect on the underlying features of the IRO depends noticeably on the system type. Specifically, the FSDP confers a marked oscillatory character of periodicity 2π/ k 1 (where k 1 is the FSDP position) on the IRO when the local structural units, which give rise to the density fluctuations on the IRO scale, exist as stable entities for a timescale τ ≫ 5 × 10 -12 s. The FSDP therefore accounts for the discernible features of the underlying IRO for the viscous glass forming liquids ZnCl 2 and GeSe 2 , for the glasses SiO 2 and PS 4 , and for the molecular liquid CCl 4 . The influence of the FSDP on the IRO is less pronounced for molten MgCl 2 and is negligible for molten NiBr 2 and Nil 2 , both of which have a high cation mobility which leads to a relative instability of the Ni 2+ centred structural units. The effect on the FSDP of temperature and pressure are briefly considered as are the development of the FSDP in molten ZnX 2 (when X is changed from Cl to I to Br) and the minimum size of r -space model which is required if the FSDP is to be accurately predicted.

Schallgeschwindigkeitsmessung in Bi-Cu Schmelzen zur Bestimmung der Kompressibilität und der partiellen Strukturfaktoren / Sound Velocity, Compressibility, und Partial Structure Factors (q = 0) in Bi-Cu Melts

1974 ◽  
Vol 29 (12) ◽  
pp. 1890-1897 ◽  
Author(s):  
Helmut Ebert ◽  
Jochen Höhler ◽  
Siegfried Steeb
Keyword(s):  
Sound Velocity ◽  
Linear Combination ◽  
Transition Region ◽  
Density Fluctuations ◽  
Partial Structure ◽  
Cu Alloys ◽  
Structure Factors ◽  
Velocity Of Ultrasound ◽  
Total Structure ◽  
Versus Concentration

The adiabatic velocity of ultrasound in molten Bi-Cu alloys was measured at various concentrations and temperatures. For the alloys with concentrations between 40 and 80 a/0 Cu the μ(T)- curves consist of two linear regions with a transition region. Within the concentration range mentioned ⊿u/⊿T and the compressibility show respectively positive and negative deviations from linearity. The deviations can be detected at temperatures up to 1200 C. The total structure factors I(O) for Bi and Cu as well as the partial structure factors aij(O) were obtained. aCuCu(O) shows rather high values, indicating the existence of inhomogeneities containing mainly Cu-atoms. The slope of ⊿Nj' [which is a linear combination of the aij (O)] versus concentration is negative. From this fact follows that segregation must exist in these melts. This also follows from the rather large density fluctuations given by the partial factors SCC(O) obtained in this work.

X-ray Diffraction Study of Molten Te and Tl-Te Alloys

1975 ◽  
Vol 30 (12) ◽  
pp. 1655-1660 ◽  
Author(s):  
Y. Waseda ◽  
S. Tamaki
Keyword(s):  
Structure Factor ◽  
Molten Metals ◽  
X Ray Diffraction ◽  
Partial Structure ◽  
X Ray ◽  
Partial Structures ◽  
Structure Factors ◽  
Diffraction Patterns ◽  
Total Structure ◽  
Constituent Elements

Abstract X-ray diffraction patterns have been obtained from molten Te at 470, 520 and 570 °C. The heights of the peak maxima in the structure factor were much the same in contrast with those of typical molten metals such as sodium.Molten Tl-Te alloys have been studied by X-ray diffraction for the alloy compositions 25, 33.3, 50, 60 and 75 at% Te at 500 °C and at about 20 °C above the liquidus. The total structure factors for the 25 and 33.3 at% Te alloys were almost the same as that of pure Tl. This implies that the atomic arrangement of these molten alloys is very close to that of pure Tl. Although a drastic change is not found in the general form of the structure factor, the parameter of the range of local atomic order abruptly increases on passing from Tl2Te to more Te-rich alloys. The three partial structures were also evaluated from the observed X-ray intensities assuming that each partial structure is independent of the relative abundance of the constituent elements in the alloys.

Structure of Mn-Si-Melts by Means of X-Ray Diffraction

1983 ◽  
Vol 38 (10) ◽  
pp. 1093-1097 ◽  
Author(s):  
E. Nassif ◽  
P. Lamparter ◽  
B. Sedelmeyer ◽  
S. Steeb
Keyword(s):  
Structure Factor ◽  
Melt Spinning ◽  
Pair Correlation ◽  
X Ray Diffraction ◽  
X Ray ◽  
Coordination Numbers ◽  
Glass Forming ◽  
Structure Factors ◽  
Total Structure Factor ◽  
Total Structure

Abstract The binary molten alloys Mn74Si26 and Mn33.5Si66.5 have been investigated by means of X-ray diffraction. The total structure factors as well as the total pair correlation functions were evaluated. The interatomic distances and total coordination numbers are given. The structural results for Mn74Si26 were compared to those for amorphous Mn74Si23P3 and for a tetrahedral packing model. A pronounced shoulder on the second maximum of the structure factor, which normally is characteristic for the curves obtained with amorphous substances was observed for the Mn74Si26 melt. With the Mn33.5Si66.5 melt, however, this feature cold not be observed. Since with this concentration no glass forming by melt spinning is possible, a correlation between the shape of the second maximum of a total structure factor and the glass forming ability of the corresponding melt is suggested.

The structure of molten and glassy 2:1 binary systems: an approach using the Bhatia—Thornton formalism

1992 ◽  
Vol 437 (1901) ◽  
pp. 591-606 ◽  
Keyword(s):  
Structure Factor ◽  
Binary Systems ◽  
Range Order ◽  
Partial Structure ◽  
Systematic Analysis ◽  
Glass Forming ◽  
Structure Factors ◽  
Total Structure Factor ◽  
Diffraction Patterns ◽  
Total Structure

A systematic analysis of those liquid binary 2:1 systems (denoted MX 2 ), for which experimental partial structure factors are available from the isotopic substitution method in neutron diffraction, is made using the Bhatia-Thornton (BT) formalism.Particular attention is paid to the origin of the first sharp diffraction peak (FSDP ), which occurs in the measured diffraction patterns for some of the MX 2 systems, since it appears, from recent studies, that this feature is a signature of directional bonding. It is found that FSDPS can occur in all three BT partial structure factors S xB (k). A FSDP feature in the concentration-concentration partial structure factor S cc (k) is not, however, pronounced except in the case of MgCl 2 and the glass forming network melts ZnCl 2 and GeSe 2 . To the extent that these systems can be regarded as ionic melts a FSDP in S cc (k) implies a non-uniformity in the charge distribution on the scale of the intermediate-range order (IRO). The structure of molten GeSe 2 is compared with the structures of molten ZnCl 2 , glassy GeS 2 and glassy Si0 2 . Although the GeSe 2 and ZnCl 2 melts have different short-range order, there are similarities in the observed IRO which can be attributed to the arrangement of the electropositive species M. The essential features of the measured total structure factor for glassy GeS 2 can be reproduced by using the molten GeSe 2 S zB (k). This result lends support to the notion that the S zB (k) for liquid GeSe 2 (and ZnCl 2 ) are characteristic of both the liquid and glassy states of other network glass forming systems. The structures of molten GeSe 2 (or ZnCl 2 ) and glassy Si0 2 are, however, found to be different. The observed discrepancies are largest in the region of the FSDP which signifies pronounced differences in the nature of the IRO for these systems.

An X-ray Diffraction Study of the Structure of Vitreous P2O5

1998 ◽  
Vol 53 (3-4) ◽  
pp. 93-104 ◽  
Author(s):  
Uwe Hoppe ◽  
Günter Walter ◽  
Rainer Kranold ◽  
Dörte Stachel
Keyword(s):  
Bond Distance ◽  
Real Space ◽  
Diffraction Peak ◽  
Angle Distribution ◽  
X Ray Diffraction ◽  
X Ray ◽  
Space Resolution ◽  
Structure Factors ◽  
Hole Model ◽  
20 Nm

Abstract Recently, the lengths of the two P-O bonds in the PO4 tetrahedron were obtained by neutron diffraction of high real-space resolution. By use of the present X-ray diffraction experiments, the P-P distance belonging to pairs of corner-linked PO4 units is determined. Using this length of (294 ± 2) pm and taking into account the P-0 bond distance to the bridging oxygen atom of 158 pm, a mean P-O-P angle of 137° ± 3° is calculated. The reverse Monte Carlo simulations fit the neutron and X-ray structure factors. The P-O-P angle distribution obtained this way possesses a mean angle of 141°. An interpretation of the first scattering peaks is presented by analysing the occupancy and the distances of various co-ordination shells by use of model configurations. The low occupancy of the first shells allows the application of the schematic hole model of Dixmier. The first X-ray diffraction peak at 13 nm-1 is related to the P-P2nd shell, the shoulder at 20 nm-1 arises from the P-O2nd shell. The most similar crystalline structure with vitreous P2O5 is the orthorhombic P2O5, form II. But it has more effectively orientated terminal oxygen atoms and, thus, a higher packing than the glass.

scholarly journals Simple Method for Estimating the Contribution of Neighbouring n-beam Interactions to Two-beam Structure Factors

1988 ◽  
Vol 41 (3) ◽  
pp. 469
Author(s):  
HJ Juretschke ◽  
HK Wagenfeld
Keyword(s):  
Experimental Determination ◽  
Structure Factor ◽  
Beam Structure ◽  
Simple Method ◽  
Experimental Configuration ◽  
Structure Factors ◽  
Special Cases ◽  
Better Than

Unless special precautions are taken, the experimental determination of two-beam structure factors to better than 1 % may include contributions from neighbouring n-beam interactions. In any particular experimental configuration, corrections for such contributions are easily carried out using the modified two-beam structure factor formalism developed recently (Juretschke 1984), once the full indexing of the pertinent n-beam interactions is known. The method is illustrated for both weak and strong primary reflections and its applicability in special cases, as well as for less than perfect crystals, is discussed.

Neutron diffraction investigation of copper tellurite glasses with high real-space resolution

2021 ◽  
Vol 54 (6) ◽  
Author(s):  
Navjot Kaur ◽  
Atul Khanna ◽  
Alex C. Hannon
Keyword(s):  
Neutron Diffraction ◽  
Coordination Number ◽  
Diffraction Data ◽  
Fourier Transformation ◽  
Short Range ◽  
Real Space ◽  
Tellurite Glasses ◽  
Space Resolution ◽  
Bond Lengths ◽  
Structure Factors

High real-space resolution neutron diffraction measurements up to 34 Å−1 were performed on a series of xCuO–(100 − x)TeO2 (x = 30, 40 and 50 mol%) glasses that were synthesized by the melt-quenching technique. The Fourier transformation of neutron diffraction structure factors was used to generate the pair distribution functions, with the first peak at 1.90 Å due to the overlapping Te–O and Cu–O atomic pairs. Reverse Monte Carlo (RMC) simulations were performed on the structure factors and the six partial atomic pair distributions of Cu–Cu, Cu–Te, Cu–O, Te–Te, Te–O and O–O were calculated. The Te–O and Cu–O distributions are very similar and asymmetrical, which revealed that there is a significant short-range disorder in the tellurite network due to the existence of a wide range of Te—O and Cu—O bond lengths. A high-Q (magnitude of momentum transfer function) neutron diffraction study revealed that the average Te–O coordination number decreases steadily from 3.45 to 3.18 with an increase in CuO concentration from 30 to 50 mol% in the glass network. Similar coordination number modifications were earlier found by the RMC analysis of neutron diffraction data sets of copper tellurite glasses that were performed up to lower Q maximum values of 9.5 Å−1. The comparison of high-Q and low-Q neutron diffraction studies reveals that RMC is a powerful and possibly the only technique that is available to elucidate the glass short-range and medium-range structural properties when diffraction data are available up to low Q values of, say, 9.5 Å−1, and when cation–oxygen bond lengths are strongly overlapping and cannot be resolved by Fourier transformation. In situ high-temperature (473 K) neutron diffraction studies of 50CuO–50TeO2 glass revealed that significant distortion of the tellurite network occurs with heating.

X-Ray Investigations on Molten Cu-Sb Alloys

1994 ◽  
Vol 49 (4-5) ◽  
pp. 530-534 ◽  
Author(s):  
Th. Halm ◽  
H. Neumann ◽  
W. Hoyer
Keyword(s):  
Electronic Properties ◽  
Structure Factor ◽  
Correlation Functions ◽  
Pair Correlation ◽  
Model Structure ◽  
X Ray Diffraction ◽  
X Ray ◽  
Structure Factors ◽  
Diffraction Structure ◽  
Eutectic Concentration

Abstract Using X-ray diffraction, structure factors and pair correlation functions of several molten Cu-Sb alloys and pure antimony were determined and compared with published structural, thermodynamic and electronic properties. The eutectic concentration Cu37Sb63 was investigated in dependence on temperature, and a model structure factor was calculated applying a segregation model.

X-ray Investigations of Liquid Bismuth-Copper Alloys

2000 ◽  
Vol 55 (3-4) ◽  
pp. 381-389 ◽  
Author(s):  
J. Nomssi Nzali ◽  
W. Hoyer
Keyword(s):  
Copper Alloys ◽  
X Ray Diffraction ◽  
Model Calculations ◽  
Experimental Procedure ◽  
X Ray ◽  
X Ray Scattering ◽  
Structure Factors ◽  
Reverse Monte Carlo Simulation ◽  
Square Well ◽  
Total Structure

Liquid copper, bismuth, and eleven bismuth-copper alloys were investigated at temperatures above the liquidus with X-ray diffraction. The experimental procedure was adjusted to reduce the effects of evaporation. The Faber-Ziman total structure factors S(Q) feature a splitting of the first maximum and negative values for Q around 1 Å -1 in a large concentration range. The results are compared to previous neutron diffraction results by Zaiss and Steeb, to square-well potential model calculations by Gopala Rao and Satpathy and to a simple segregation model. The segregation model reproduces the features qualitatively. Partial structure factors are assessed by fitting both neutron and X-ray scattering results with reverse Monte-Carlo simulation

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