The structure of molten ZnCl2

Journal of Non-Crystalline Solids 224 Ž1998. 205–215

The structure of molten ZnCl 2 J. Neuefeind a

a,)

b , K. Todheide , A. Lemke c , H. Bertagnolli ¨

c

Hamburger Synchrotronstrahlungslabor HASYLAB at DESY, Notkestrasse 85, 22603 Hamburg, Germany b Institut fur ¨ Physikalische Chemie, UniÕ. Karlsruhe, Kaiserstr. 12, 76128 Karlsruhe, Germany c Institut fur ¨ Physikalische Chemie, UniÕ. Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany Received 10 June 1997; revised 21 October 1997

Abstract High energy photon diffraction measurements on molten ZnCl 2 have been carried out in the temperature range 623–853 ˚ y1 - Q - 21.6 A˚ y1. The sample is investigated in transmission K. The momentum transfer range covered is 0.15 A geometry. The data are in good agreement with neutron diffraction measurements. A discrepancy at smaller Q values is to be noted, however, with earlier studies using conventional Mo–K a X-rays in reflection geometry. By combining neutron and high energy photon results, the partial distribution functions can be separated to some extent. Almost no change of the first Zn–Cl distance is observed with increasing temperature, whereas the distribution of the first shell Cl–Cl distances increases in width and the first shell Zn–Zn distance decreases. q 1998 Elsevier Science B.V. PACS: 61.20.Q; 61.43.F; 61.10; 07.85.Qe

1. Introduction The chemistry and physics of molten ZnCl 2 is determined by the ambiguity of its description as a molten glass or a molten salt. Molten ZnCl 2 has a viscosity larger than many glass forming compounds and can be supercooled into a glass by normal laboratory methods. Molten ZnCl 2 has been investigated by neutron diffraction by Biggin and Enderby w1x and Allen et al. w2x and by X-ray diffraction by Triolo and Narten w3x and Takagi and Nakamura w4x. In Ref. w1x 35 Clr37Cl isotopic substitution has been used for a complete separation of the partial structure factors. The structure of the glass has been investi-

)

Corresponding author. Tel.: q49-40 8998 2923; fax: q49-40 8998 2787; e-mail: [email protected].

gated by neutron- w5x and by X-ray diffraction w6x. It is accepted that Zn is tetrahedrally coordinated by Cl and that this tetrahedral coordination persists to temperatures well above the melting point. Regarding ZnCl 2 as a glass melt this feature makes it an interesting model system for the ubiquitous SiO 2 based glasses — which also have tetrahedral networks. The SiO 2 liquid is, however, much more inaccessible as the melting point of SiO 2 is 17138C w7x, whereas ZnCl 2 melts at about 3008C. The use of high energy photon diffraction Ži.e. the diffraction of photons in the energy range 80 F E F 200 keV. has been demonstrated earlier for glasses w8x and molecular liquids w9x. The photoelectric absorption cross-section decreases approximately with E 3. Hence, the absorption is reduced by about three orders of magnitude with respect to conventional X-ray tubes and diffraction experiments with high energy photons are in many respects similar to neu-

0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 Ž 9 7 . 0 0 4 8 0 - 8

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tron diffraction experiments — and complementary to them: the interaction mechanism is of course different. The weighing of the partial structure factors in the photon diffraction experiment in this case is similar to a neutron experiment on 37Cl substituted ZnCl 2 : b37 Clrb Zn s 0.542 and fClŽ0.rf ZnŽ0. s 0.567, where b37 Cl rb Zn is the ratio of the coherent scattering length of 37Cl and Zn and fCl Ž0.rf ZnŽ0. the ratio of the atomic scattering factors of Cl and Zn at zero momentum transfer. Using a photon diffraction experiment instead of isotopic substitution has the great advantage that the same, water-free and inexpensive sample can be used.

2. Experimental set-up The experiments have been carried out at the high field wiggler BW5 at the DORIS-III synchrotron in Hamburg. This beam-line is designed for high energy use and is equipped with a 1.5 mm thick Cu absorber in the white beam, cutting off the spectrum below about 60 keV w10x. DORIS-III was running at 4.5 GeV. The magnetic gap being at 20 mm the critical energy of BW5 is 27 keV. The mean positron current at the time of the experiment was about 75 mA, with beam life times of about 20 h. A schema of the set-up is shown in Fig. 1. The beam cross-section is defined at the aperture slit, B0, before the monochromator. It was chosen to be 0.5

Fig. 1. Schema of the instrument set-up Žtop view.. B0–B3 slit system, all slits except B0 are step motor controlled. M: Annealed Ž220. Si monochromator in Laue geometry. BS: Beam stop. Mon: NaI scintillation counter monitoring the intensity of the monochromatic beam. P: Sample, the sample position is marked with a cross. D: N2 Žl. cooled germanium solid state detector, the approximate position of the detector crystal ŽDc. is indicated. For details see text.

mm = 5 mm Žhorizontal= vertical.. The monochromator was an annealed Ž220. Si crystal in Laue geometry with a rocking curve width of 5Y full width at half maximum amplitude ŽFWHM. w11x. The photon flux incident on the sample in this set-up is about 5 = 10 10 sy1 A NaI scintillation counter looking from on top at an air volume illuminated by the monochromatic beam monitors the incoming intensity Žadditionally the DORIS-III beam current is logged into the protocol file.. A step motor controlled guard slit, B1, shields the diffuse scattering from the monochromator. The sample is placed in an evacuated chamber to avoid air scattering from the region near the sample. The dimensions of this vacuum chamber are identical to the D4b spectrometer at the reactor neutron source of the Institut Laue– Langevin, ILL, in Grenoble, allowing us to use the same equipment for neutron and photon scattering. A second step motor controlled guard slit, B2, behind the sample allows control of the region in which the scattered photons are detected. The third slit, B3, determines the solid angle seen by the detector. Detection is done with a liquid nitrogen cooled Ge detector, the detection plane is horizontally in the plane of the positron orbit. The energy of the incoming beam has been determined to be 100.36Ž8. keV. In view of a possible extension of this experiment to high pressure, the sample was contained in a metal cylinder made from Inconel 600 with 7 mm innerand 9 mm outer diameter. The cylinder has two identical compartments, one of which is filled with the sample, the other is empty for the background measurement. The sample container can be moved vertically with a motor, so that either the filled or the empty compartment of the cylinder is in the beam. Inconel 600 is a nickel alloy preserving a high strength up to elevated temperatures. The sample has a quoted purity of 99.999% ŽAldrich.. ZnCl 2 is highly hygroscopic, so the sample was sealed in the container inside a glove-box filled with dry N2 . Temperature control was done with a commercially available controller ŽEurotherm., the temperature was measured with a CrrNi thermocouple at the outer side of the cylinder. The diffraction pattern has been measured at four different temperatures: 623 K, 723 K, 773 K and 853 K. The inconel cylinder generates very strong Debye–Scherrer lines in the diffraction pattern. Within

J. Neuefeind et al.r Journal of Non-Crystalline Solids 224 (1998) 205–215

the region of these powder lines a meaningful measurement is not possible. Consequently the Ž Q y . resolution has to be comparatively high, to reduce the width of the powder lines. Under the conditions of the experiment the first powder line of the empty ˚ y1 at cylinder has a Gaussian width of s s 0.017 A y1 ˚ , with the momentum transfer variable Q s 3.45 A Q s 4 prl sinŽ u ., l is the wavelength and u is the half of the full scattering angle 2 u . The region "0.1 ˚ y1 around the center of the powder lines has then A been rejected from further analysis. Two slightly different set-ups were used for the smaller and the larger Q part of the spectra. At larger Q Ž7.1–21.6 ˚ y1 . the width of the second guard slit B2 was set A to 0.5 mm eliminating most of the scattering from ˚ y1 . The raw data for T s 853 the cylinder for Q R 9 A K are shown in Fig. 2. We decided to measure the attenuation of the monochromatic beam for each temperature ŽThe attenuation of 100 keV photons in 7 mm ZnCl 2 at 853 K is 37%.. The data have been corrected subsequently for dead-time, normalized to monitor counts, corrected for attenuation, the varying sample to detector distance and polarization Žcf. Ref. w12x., and normalized to absolute units using the form-factors tabulated in Ref. w13x. Normalization has been done using the scattering intensity at larger Q, where the oscillations of the structure factor are small.

3. Analysis The data analysis in this study follows the analysis of Ref. w8x. A useful starting point for the structure determination of amorphous materials for photon diffraction data is the reduced interference function, QiŽ Q . defined by Qi Ž Q . s Q

I Ž Q . y Ýuc f i2 y Ýuc Ci

Ž Ýuc f i .

2

,

Ž 1.

where I Ž Q . is the corrected and normalized scattering intensity, f i are the atomic scattering factors, Ci is the Compton scattering intensity and the sums extend over the unit composition, uc. iŽ Q . is a weighted sum of the partial structure functions, si j ,

207

and is completely analogous to the corresponding neutron scattering function SŽ Q .: iŽ Q. s

ÝÝuc f i f j si j

Ž Ýuci f i .

,

2

SŽ Q. s

ÝÝuc bi bj si j

Ž Ýuci bi .

2

,

Ž 2. where bi is the coherent neutron scattering length. In this case we have three different partial structure functions and two equations Žtwo independent experiments.. Linear combinations of iŽ Q . and SŽ Q . can be constructed to eliminate one partial structure siX jX . These linear combinations will be called d iX jX Ž Q . and are defined by 2

uc

d j k Ž Q . s f j fk X X

X

X

žÝ / bi

SŽ Q. y

i

žÝ /

X

X

fi

bjX b k X i Ž Q .

i

Ý Ž f j f k bj b k y bj b k

s

2

uc

X

X

X X

f j f k . s jk .

Ž 3.

jk/j k

In Eq. Ž3. the partial structure factors, s jk , are weighted inter alii with the atomic scattering factors. Consequently the resulting function, d jX k X Ž Q ., is damped with increasing Q. It is useful to normalize the d jX k X Ž Q . so that the weighing of one s jY k Y in the sum becomes a constant in Q 1 : d jX k X Ž Q .

Y Y

d jjX kkX Ž Q . s

f jX f k X bjY b k Y y bjX b k X f jY f k Y

.

Ž 4.

The normalized d jX k X Ž Q . are used in the following. A good knowledge of both the form-factors and the neutron scattering lengths is required. The neutron scattering lengths in this analysis are taken from Ref. w14x, the atomic scattering factors from Ref. w13x. Real space distributions are discussed in terms of T Ž r . which is defined by TŽ r. s

1

Qmax

H 2p r Q

QS Ž Q . sin Ž Qr . dQ q r ,

2

Ž 5.

min

where r is the number density Žreferred to the unit composition.. The density of the liquid has been ˚ y3 at 583 K taken from Ref. w15x to be 0.0110 uc A y3 ˚ at 853 K. T Ž r . is related to g Ž r ., and 0.0105 uc A 1

The weighing factor of the second partial present is then to a sufficient approximation also constant in Q. This would be strictly so, if the atomic scattering factors of Zn and Cl would differ by a constant factor only: fCl s kf Zn .

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J. Neuefeind et al.r Journal of Non-Crystalline Solids 224 (1998) 205–215

the correlation function which is more commonly used in the discussion of the structure of liquids, simply by T Ž r . s rg Ž r .. Whenever a comparison between a model and the experiments is presented, a double Fourier-transform has been carried out, i.e. the model distribution function has been transformed in Q space, multiplied with the weighing factors of the respective partial structure functions, si j , and transformed back in r-space using the same Q cutoffs as used with the experimental data. In short, the model correlation functions are convoluted with a peak shape function comprising the effects of weighing factors being non-constant in Q and truncation errors before comparison. Adopting the technique used for the glasses SiO 2 and GeO 2 in Ref. w8x, the structure of molten ZnCl 2 can be parameterized in four distributions: the Zn–Cl bond length, the Cl–Zn–Cl and the Zn–Cl–Zn bond angle and a Zn–Cl–Zn–Cl dihedral angle distribution. The meaning of these parameters is illustrated in Fig. 3. The left Zn–Cl bond is in the grey plane, the Cl–Zn bond in the middle on the section of the two planes, the right Zn–Cl bond in the white plane.

209

The network continues through the dashed bonds. The model assumes a perfect corner-sharing tetrahedral network. While there are good experimental reasons to assume an almost perfect tetrahedral network for SiO 2 and GeO 2 , the situation is not as clear for ZnCl 2 liquid, where only the tetrahedral coordination of Zn by Cl is well established. However, for sake of comparison the model has been kept in its simple form. Finally, the model is not constrained by the macroscopic density as a reverse Monte Carlo simulation would be. The assumed analytical form of the distributions is given by w8x V Ž r ZnCl . s K r exp y

V Ž a . s K a exp y

Ý exp

2 sa2

y

2

,

Ž 6.

sin Ž a . ,

Ž 7.

2 sr 2

Ž a y a0 .

5

V Ž d . s Kd

Ž r ZnCl y r 0 .

2

d y d 0 Ž i y 2.

is1

2

,

2 sd2

Ž 8.

where sr , sa , sb and sd are the widths of the distributions, r 0 , a 0 , b 0 and d 0 are the equilibrium values and K r , K a , Kb and K d are normalization constants. The analytic form of V Ž b . is identical to V Ž a .. Hence, b and a has to be exchanged in Eq. Ž7. to obtain V Ž b .. Alternatively, the first shell distributions can be assumed to be Gaussian in T Ž r . w20x. This assumption is expressed by Ti j Ž r . s

Fig. 3. Parameters involved in Eqs. Ž6. – Ž8.. Section of the ZnCl 2 network illustrating the meaning of the parameters involved in Eqs. Ž6. – Ž8..

Ni j

si j ri j'2 p

exp y

Ž r y ri j . 2 si 2j

2

,

Ž 9.

where ri j is the mean distance, si j is the RMS deviation and Ni j is the coordination number. With this definition and assuming a perfect corner-sharing tetrahedral network the value for NZnCl , NClCl and NZnZn would be 8, 12 and 4, respectively.

Fig. 2. Diffraction of high energy photons from ZnCl 2 melt at T s 853 K, raw data. Two different set-ups have been used for the low-Q and the high-Q part of the spectrum. At high Qs the scattering from the container is discriminated by a slit system ŽB2 in Fig. 1.. Note the logarithmic scale in Fig. 2b. Ža. Low-Q set-up; diamonds: empty cylinder, crosses: filled cylinder; all points with symbols are kept for further analysis. Žb. High-Q set up. From top to bottom: Filled cylinder, empty cylinder, background Žempty diffractometer..

210

J. Neuefeind et al.r Journal of Non-Crystalline Solids 224 (1998) 205–215 Table 1 Temperature dependence of the first Zn–Cl distance. Results of fitting Eq. Ž9. to the first shell Zn–Cl distance distribution. Almost no change with temperature can be detected. The coordination number has been refined only for the complete data set at 623 K and 853 K

623 K Žl. 723 K Žl. 773 K Žl. 853 K Žl. 623 K Žlqh. 853 K Žlqh.

˚. r ZnCl ŽA

˚. s ZnCl ŽA

NZnCl

2.297Ž5. 2.298Ž4. 2.296Ž5. 2.299Ž4. 2.281Ž3. 2.279Ž4. 2.289Ž4. 2.286Ž4.

0.122Ž5. 0.118Ž5. 0.131Ž5. 0.129Ž4. 0.113Ž3. 0.108Ž3. 0.138Ž3. 0.128Ž4.

8a 8a 8a 8a 8a 7.6Ž2. 8a 7.2Ž2.

˚ y1 ., lqh: All fits in real space, l: low Q data only Ž0.15–11.1 A ˚ y1 .. whole Q range Ž0.15–21.6 A a The coordination number has not been refined.

tributes to T Ž r . in this r-range. This approach has the advantage that the analytic form of the first shell Zn–Cl distance distribution does not need to be known explicitly. Fig. 4. Comparison of the normalized scattering intensity of ZnCl 2 at 623 K obtained with high energy photons in transmission geometry and Mo–K a X-rays w4,16x in reflection geometry. Full line: Result obtained with 100 keV photons in transmission geometry Žthis work.; broken line: Result obtained with Mo–K a X-rays in reflection geometry.

Assuming the weighing factor of the Zn–Cl partial structure function constant Že.g. f Zn fClrŽÝ f . 2 , f Zn Ž0. fClŽ0.rwÝ f Ž0.x 2 . and if the Zn–Cl first shell coordination is separated in r-space from the rest of the structure, NZnCl can be obtained independently by integrating T Ž r .: NZnCl Ž rmax . s

4 pr r Ž Ý uc f i Ž 0 . . f Zn Ž 0 . fCl Ž 0 .

2

rmax

H0

T Ž r. dr,

Ž 10 . where rmax , the upper integration limit, should be chosen such that only the Zn–Cl first shell con-

4. Results Perhaps the most striking result is the complete ˚ y1 , absence of the first diffraction peak at 1.05 A measured in this study, compared to the earlier studies using Mo–K a radiation w3,4x. The resulting I Ž Q . is compared in Fig. 4 to the present data, illustrating that the low Q behavior of the scattering pattern is completely different. The QiŽ Q . have been taken from Ref. w16x, where the data of Ref. w4x are available in digital form. The distribution of distances of the first Zn–Cl coordination shell has been determined assuming a Gaussian distribution in T Ž r . ŽEq. Ž9... The results are collected in Table 1. Using only the data from the low-Q set-up, r ZnCl is constant within a few ˚ well within the experimental uncerthousandth of A, tainty. The Debye–Waller factor and the coordina-

Fig. 5. Combinations of neutron and photon diffraction data of ZnCl 2 at T s 623 K. The Qd iX jX Ž Q . defined in Eqs. Ž3. and Ž4. are shown. In Fig. 5b the contribution of the first Zn–Cl shell in Qd ZnZnŽ Q . and Qd ClClŽ Q . is removed. d ZnZnŽ Q . and d ZnClŽ Q . then become very similar, ClCl Ž . ClCl Ž . ZnZn Ž . since both are dominated by the Cl–Cl contribution. Ža. From top to bottom: Qd ZnZn Q , Qd ZnCl Q and Qd ClCl Q . The contribution of the first Zn–Cl coordination shell is indicated with a solid line where appropriate. Žb. Same as Ža. with the contribution of the first Zn–Cl coordination shell removed.

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J. Neuefeind et al.r Journal of Non-Crystalline Solids 224 (1998) 205–215

212

Table 2 Parameters of the network model described in the main text. The ZnCl 4 tetrahedra at 623 K just above the melting point are almost as regular as the respective tetrahedra in SiO 2 and GeO 2 glass at room temperature. Note also the small decrease in the b angle joining adjacent tetrahedra with increasing temperature

ZnCl 2 Ž623 K. ZnCl 2 Ž853 K. GeO 2 Ž295 K. e SiO 2 Ž295 K. e

rAX

sr

a0

sa

b0

sb

d0

sd

2.281Ž3. a 2.289Ž3. a 1.73 1.605 g

0.113Ž3. a 0.138Ž3. a 0.0415 0.0493 g

120.Ž1. 115.Ž4. 133.0 148.3

13.5Ž14. 17.Ž4. 8.3 7.5

109.47 b 109.47 b 109.47 b 109.47 b

5.3 15.4 4.2 f 4.2

30 c 30 c 30 c 30 c

30 d 30 d 38 27

˚ angles in degree. Distances in A, a Same as Table 1. b Not refined, b 0 is taken from the ideal tetrahedron. c Not refined, d 0 s 308 gives rise to preferentially staggered oriented A–X–A–X chains. d Not refined. e Ref. w8x. f Not refined, taken to be equal to SiO 2 . g Not refined, taken from Ref. w20x.

tion number are also included in Table 1. The coordination number, however, has been refined only for T s 623 K and T s 853 K, where the data are available in the complete Q-range. When the Q-range is too small the resulting Debye–Waller factors and coordination numbers are correlated. The errors given in the tables are conventional statistical errors. The systematic errors are smaller when using high energy photons. These errors are estimated in Ref. w13x and are in the order of 1% on the total scattering intensity. The coordination number can be determined independently by integrating T Ž r . ŽEq. Ž10... The integral reaches eight at somewhat higher r s, but before the Zn–Zn and Cl–Cl correlations start to overlap. The detailed analysis of the first Cl–Cl and Zn–Zn distances is possible only, when combining photon and neutron data w2x and thus separating overlapping partial structures. The first Zn–Zn and the first Cl–Cl coordination shell overlap almost completely, but the Zn–Zn correlation can be determined from d ClClŽ Q . Table 3 The Zn–Zn and the Cl–Cl first shell distance distribution. Result of the fit of Eq. Ž9. to the Zn–Zn and the Cl–Cl first shell distance distribution. rClCl

sClCl

NClCl r ZnZn

T s623 K 3.69Ž1. 0.28Ž1. 12 a T s853 K 3.78Ž2. 0.43Ž3. 12 a a

Not refined.

s ZnZn

NZnZn

3.92Ž6. 0.35Ž3. 4 a 3.78Ž6. 0.36Ž7. 4 a

Žwhere Cl–Cl is absent. and vice versa. The resulting d iX jX Ž Q . for T s 623 K are presented in Fig. 5a, b. When removing the contribution of the first Zn–Cl shell determined above, no structure can be seen ˚ y1 . The Fourier transforms are thus above about 12 A ˚ y1 , to reduce the noise carried out with Q max s 12 A contribution to the transforms. The first Zn–Zn and Cl–Cl coordination shells have been analyzed using the network model described above ŽEqs. Ž6. – Ž8.. This approach gives in addition an approximation for the second shell distributions. Alternatively, the data have been analyzed using a Gaussian distribution Žof distances. in T Ž r . ŽEq. Ž9... The results are presented in Tables 2 and ˚ in TZnZn . 3. A visible structure extends up to 20 A The structure is damped at the higher temperature, which is to be expected.

5. Discussion The discrepancy in the smaller Q behavior of the scattering of ZnCl 2 between this study and the earlier X-ray studies is huge, much larger than the temperature effect and the expected pressure effect. Both studies using conventional X-rays are in good agreement, and both working groups have taken appropriate measures to avoid the contact of ZnCl 2 with atmospheric moisture. As mentioned, the photon diffraction experiment has a weighing of the

J. Neuefeind et al.r Journal of Non-Crystalline Solids 224 (1998) 205–215

213

pothesis is that the surface of ZnCl 2 has a structure different from the bulk. This includes the possibility that a contamination accumulates in the surface. This point merits further study. Related to the smaller Q behavior, it is worthwhile to discuss the extrapolation of the scattering pattern to Q ™ 0. The scattering intensity at Q ™ 0 is related to the isothermal compressibility via w17x uc

I Ž Q ™ 0. s

Fig. 6. Extrapolation of I Ž Q . to Q™0. Extrapolation of the intensity to small momentum transfers. The Mo–K a data have obviously a completely different extrapolation point; plus sign: 623 K, diamonds: 723 K, triangles: 773 K, squares: 853 K; crosses: Mo–K a w4,17x 603 K; full lines: fit of Aq BQ 2 qCQ 4 to the data.

ž / Ý Zi

r kTx T ,

Ž 11 .

where k is the Boltzmann constant and x T is the isothermal compressibility and Zi are the atomic numbers. The isothermal compressibility can be determined from a measurement of the sound velocity, and I Ž Q ™ 0. can be related to measurable quantities via uc

partial structures quite similar to a neutron diffraction experiment on Zn37Cl 2 . Both the peak at 1.05 ˚ y1 and the peak at 2.07 A˚ y1 are resolved in fig. 1c A in Ref. w1x. The overall agreement between the Zn37Cl 2 experiment and the high energy photon diffraction is, however, only qualitative, partly because the statistics of the neutron experiment are worse. Looking for an explanation of the disagreement with the earlier Mo–K a data, an essential point is certainly the larger absorption of ZnCl 2 at 17.4 keV. The Q-range in question corresponds, for the reflection geometry, to an angle of incidence of a few degrees of the incoming and the reflected beam. This angle diminishes the penetration depth, which is, however, still in the order of 1 mm. Correcting the data for systematic errors is consequently especially difficult in this region. If we believe that the Mo–K a data were correct, the most plausible hy-

2

Is Ž Q ™ 0 . s

2

ž / ž Ý Zi

RT

a 2T

1 u s2 M

q Cp

/

,

Ž 12 .

where u s is the sound velocity, a is the thermal expansion coefficient, C p is the molar heat capacity Žall taken from Ref. w19x., M is the molar mass of ZnCl 2 , R is the gas constant and IsŽ Q ™ 0. is the intensity for Q ™ 0 deduced from the sound velocity. Extrapolation of the scattering intensity is often done with an even polynomial of order four w18x, although this is merely an empirical relation. Fig. 6 demonstrates that the data follow this relation. Table 4 illustrates the qualitative agreement of the extrapolated intensity and IsŽ Q ™ 0.; however the extrapolated intensities are systematically less than I Ž Q ™ 0. deduced from the sound velocity. This effect increases with increasing temperature. The extrapolated intensity from Ref. w4x on the other hand is a factor 3.3 larger than IsŽ Q ™ 0..

Table 4 Extrapolation of the normalized intensity scattered from ZnCl 2 at different temperatures to zero momentum transfer with a parabola in Q 2 : A q BQ 2 q CQ 4 . The extrapolation obtained from the Mo–K a data is completely different T

I Ž Q ™ 0. Žel. units.

IsŽ Q ™ 0. Žel. units.

I Ž Q ™ 0.rIsŽ Q ™ 0.

623 K 723 K 773 K 853 K 603 K Žw4x.

178.4Ž4. 196.4Ž4. 212.6Ž4. 232.0Ž4. 697Ž3.

221.6 281.2 314.7 374.5 210.8

0.805 0.698 0.676 0.619 3.3

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The first Zn–Cl coordination remains almost completely unchanged with increasing temperature. There is almost no change in the first peak of T Ž r .. There may be an increase in the Debye–Waller factors. The coordination numbers are quite close to eight 2 in agreement with Ref. w2x. The coordination numbers as given in Table 1 depend on the assumption of a Gaussian distribution of distances ŽEq. Ž9... We assume, the small deficiency of the coordination numbers in Table 1 with respect to the theoretical value is an indication that there is some larger r tailing with respect to a Gaussian, which becomes more important at higher temperatures. It can be noticed, that r ZnCl determined from the full Q-range is slightly smaller compared to the result obtained ˚ y1 . when using the Q-range 0.15–11.1 A The Zn–Cl–Zn angle, a 0 , is quite small compared to the oxidic glasses. The variances, especially sb , are also small at 623 K just above the melting point, given that the temperature is more than twice that for GeO 2 and SiO 2 . The increase in the Cl–Zn– Cl angle variance with increasing temperature is remarkable. The mean Zn–Cl–Zn bond angle decreases with increasing temperature. This decrease corresponds to a decrease of the Zn–Zn distance by ˚ when fitting Eq. Ž9.. ; 0.1 A, As mentioned in the introduction, ZnCl 2 glass has also been investigated by neutron w5x and X-ray diffraction w6x. In these papers different lines of data analysis have been followed. However, it is quite simple to compare the result for the first Zn–Cl ˚ in Ref. coordination. r ZnCl is quoted to be 2.288 A ˚ w5x and 2.278 A in Ref. w6x, indicating that there is no change in the Zn–Cl bond length when supercooling the liquid to the glass. It is further interesting to note, that NClCl increases to 18Ž2. at 623 K if not fixed as in Table 3. This is then comparable to the 2 P 9.5 given in Ref. w5x and 2 P 8.9 in Ref. w6x.

6. Conclusion The low-Q scattering pattern determined with high energy photons in transmission geometry differs from

2

This corresponds to one Zn atom surrounded by four Cl atoms and two Cl atoms surrounded by two Zn atoms.

that determined in earlier studies with Mo–K a radiation in reflection geometry. The measurements presented here are in better agreement with neutron scattering results. The first Zn–Cl coordination shell remains almost completely unchanged with increasing temperature, except for increases in the Debye–Waller factor. Coordination numbers slightly smaller than eight Žcorresponding to a perfect corner-sharing tetrahedral network. are obtained, when assuming a Gaussian distribution in T Ž r . ŽEq. Ž9... Integration of T Ž r . is, however, consistent with a coordination of four Cl atoms around one Zn atom. This effect indicates a large r tailing with respect to a Gaussian. Using a combination of photon and neutron results we have, to some extent, separated the partial structures. This separation enables us to analyze the overlapping Zn–Zn and Cl–Cl first coordination shells. The width of the Cl–Zn–Cl bond angle distribution is small at 623 K and comparable to the width of the O–SiŽGe. –O bond angle distribution found in SiO 2 and GeO 2 glass at room temperature. The width of the Cl–Zn–Cl bond angle distribution increases with temperature and hence the order of the underlying ZnCl 4 tetrahedra is diminished at 853 K. Interestingly, the maximum of the Zn–Cl–Zn bond angle distribution shifts to smaller angles with increasing temperature. The maximum in the first shell Zn–Zn distance distribution shifts correspondingly to smaller r. Oscillations in T Ž r . can be observed up to ˚ most notably in TZnZn . These oscillations are 20 A, more strongly damped at the higher temperature.

Acknowledgements Financial support by the Deutsche Forschungsgemeinschaft under grant Ne-584r1-1 is gratefully appreciated. The authors are further thankful to the BMBF for the financial support Žproject: BE13..

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