Fe-rich cordierites from acid volcanic rocks,an optical and x-ray single-crystal structure study

Low-cordierites from volcanic rocks of Tuscany (Italy), Lipari (Italy), and of the Cerberean Cauldron (Australia) were investigated. Both single crystal structure refinements and optical data indicate that the Italian samples contain only low concentrations of volatiles (<0.3 wt.%), whereas in the crystals from the Cerberean Cauldron more than 50% of the structural channels are occupied, preferentially by H₂O (1.6–1.9 wt.%). This high volatile concentration is in qualitative agreement with the estimated p,T-conditions (4–4.5 kbar at 750–780° C) of the magma prior to eruption. In contrast, the Italian cordierites have formed at temperatures above 950° C and pressures below 2 kbars. Low-cordierites of volcanic origin reveal the same high degree of Si, Al-ordering as observed for low-cordierites from metamorphic rocks and pegmatites. The crystals studied possess F(mol)=(Fe+Mn)/(Fe+Mn+Mg)>0.4 and provide additional information about the crystal structure of Fe-rich cordierites. With increasing FeMg substitution the mean T₁1(Al)-O distance decreases slightly, which is probably not caused by substitution of smaller cations on t₁1 but by angular distortion of the tetrahedron.     

Interactions and mixing properties in the (C2/c) clinopyroxene quadrilateral

Excess Gibbs free energy surfaces generated at various pressure and temperature conditions for the C2/c pyroxene quadrilateral compositional space Mg₂Si₂O₆–CaMgSi₂O₆–CaFeSi₂O₆–Fe₂Si₂O₆ with a two-body static interionic potential summation (Ottonello et al. 1992) have been fitted to 4 component extensions of the Wohl and Kohler macroscopic interactions models. The mean precision (272j/mol) and the maximum observed bias (1.19 Kj/mol) are roughly similar for the two macroscopic formulations, but Wohl's extension is preferred due to its relative simplicity.     

Sequential high-pressure transformations of FeGeO3 high-P clinopyroxene (C 2 /c) at temperatures up to 365 ¯C

 In order to elucidate high-pressure transformations of high-P clinopyroxene (C2/c) at kinetically low temperature where atoms are not thermally activated, the transformation processes of FeGeO₃ clinopyroxene (C2/c) have been investigated at pressures up to 20 GPa and 365 °C by powder X-ray diffraction using a synchrotron radiation source and TEM observation. With increasing pressure up to 20 GPa at room temperature, FeGeO₃ high-P clinopyroxene (C2/c) reversibly transforms into a new high-pressure phase, FeGeO₃(II). On increasing the temperature up to 365 °C, this phase rapidly transforms into FeGeO₃ ilmenite within about 2 h. Intensity analysis of the X-ray diffraction pattern reveals that the high-pressure phase of FeGeO₃(II) has an intermediate structure between clinopyroxene and ilmenite: the cation arrangement is similar to that of clinopyroxene and the oxygen arrangement is similar to that of ilmenite. The comparison of the crystal structures of these polymorphs suggests that clinopyroxene to FeGeO₃(II) and FeGeO₃(II) to ilmenite transformations are performed by the slight deformation of the oxygen packing and the short-range movement of cations, respectively. It is shown that this high-P clinopyroxene transforms into ilmenite through a low-activation energy path under the low-temperature condition. Received: 30 August 2000 / Accepted: 10 February 2001     

月球风暴洋地区玄武岩厚度的重力研究

利用剩余布格重力异常进行月球表层玄武岩厚度的推断,为月球地质填图提供了一定的证据。文中利用美国GRAIL卫星660阶布格重力异常,采用巴特沃斯（Butterworth）滤波方法,参考Grant H. Herken等的研究成果（即对月球面向地球一面的玄武岩厚度研究推断）,以此作为控制条件,提取了风暴洋地区的剩余布格重力异常,参考遥感光谱反映出的玄武岩范围,然后利用边界元方法反复模拟修正,最终得出该区的玄武岩厚度分布,玄武岩的厚度不超过1.5 km。     

Relationships between tetrahedral kink angles and site occupations in C2/c pyroxene from volcanic rocks

Summary The relationships between kinking of the T tetrahedral chain and the site configuration of C2/c pyroxenes from volcanic rocks were investigated, and about two hundred samples were examinated.Kink angle (KA) is defined by the equation KA = arccos [1-c ²/(2d ²)], in which c is the cell edge andd the O3A1–O3A2 distance; in the pyroxenes studied here, it varies from about 164° to about 167°.The ratio betweenc cell edge and O3A1–O3A2 distance depends on the various M1, M2 and T site configurations which, in turn, are related to their different mechanisms of cation substitution. Thec/d ratio varies if isomorphic substitutions involve cations with different charge, while it is quite constant if the substitutions involve cations with the same net charge.Thec/d ratio variation is related to the amount of cation substitution in each crystallographic site, and reaches its maximum range in synthetic and natural end-member pyroxenes.

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Beziehungen zwischen dem tetraedrischen kink-Winkel und der Kationenbesetzung in C2/c Pyroxenen aus vulkanischen Gesteinen

Zusammenfassung Die Beziehungen zwischen dem kink-Winkel der tetraedrischen T Kette und der Besetzungskonfiguration der C2/c Pyroxene von vulkanischen Gesteinen wurde an ca. 200 Proben untersucht.Der kink-Winkel (KA) ist durch folgende Gleichung definiert: KA = arccos {1 –c ²/ (2d ²)}, wobei c die Kantenlänge der Einheitszelle und d die Distanz O3A1–O3A2 darstellt. In den hier studierten Pyroxenen variiert dieser Winkel zwischen 164 und 167°.Das Verhältnis zwischen c und der Distanz O3A1–O3A2 hängt von der Besetzung der M1, M2 and T Position im Gitter ab, die ihrerseits wiederum durch verschiedene Substitutions-Mechanismen kontrolliert wird. Das Verhältnisc/d variiert, sobald am Kationenaustausch Kationen verschiedener Ladung involviert sind, und ist ziemlich konstant, wenn gleichgeladene Kationen ausgetauscht werden. Dasc/d Verhältnis ist von der Menge eines Kations, das in eine entsprechende Kristallographische Position eingebaut wird, abhängig und erreicht ein Maximum in synthetischen und natürlich vorkommenden Pyroxenendgliedern.

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Origin of clinopyroxene megacrysts in volcanic rocks from the North China Craton: a comparison study with megacrysts worldwide

ABSTRACT

Clinopyroxene megacrysts in volcanic rocks can provide substantial information on the evolution of the magmatic system at depth. Although considerable attention has been paid to these crystals, their origin is not yet completely resolved. The clinopyroxene megacrysts worldwide can be divided into two major types in general: the green Cr-diopside type and the black Al-augite type. There is a consensus view that the Cr-diopside megacrysts are mantle xenocrysts, whereas two contrasting opinions exist regarding the origin of the black Al-augite megacrysts. One favours a cognate origin, viewing them as crystallization products of the host magmas under high-pressure; while the other argues that they are xenocrysts crystallized from previous alkali basalts or fragments of mantle peridotites, pyroxenites or pegmatite veins. A review study on the clinopyroxene megacrysts in Meso-Cenozoic volcanic rocks from the North China Craton (NCC) and their comparison with those worldwide provides new constraints on their origin, namely, the Cr-diopside megacrysts, as previously thought, are all xenocrysts, representing disaggregated clinopyroxene crystals from clinopyroxene-rich mantle rocks. Contrary to the formerly proposed cognate origin, the Al-augite megacrysts are also xenocrysts, having no direct genetic link to their host rocks. They crystallized from melts that have formed earlier than the host magmas, and probably accumulated in a magma chamber or occurred as sheets or veins filling a fracture network surrounding a magma chamber in the upper mantle. During the subsequent eruption of the host lavas, these previously formed crystals were incorporated into the magma and were brought up to the surface.     

Crystal structure refinement of 13 olivines in the forsterite-fayalite series from volcanic rocks and ultramafic nodules

Summary The results of the present paper confirm the overall dependence of the geometric parameters of olivines on the Mg/(Fe+Mn) ratio. M1 and M2 volumes linearly decrease with increasing forsterite (Fo) content but at different rates. The difference between the volumes of the octahedral sites decreases gradually fromFo 92% toFo 50% and then remains virtually constant down toFo 0.2%.Fe(M1)/Fe(M2) ratios indicate that Fe²⁺ prefers the M1 site in fayalite (Fa)-rich olivines (Fa=39% to 92%; average Fe(M1)/Fe(M2)=1.04±0.02). Instead, in Mg-olivines (Fo=80% to 92%) a Mg-M1 preference (average Mg(M1)/Mg(M2)=0.96±0.05) may exist. Finally, Mn(M1)/Mn(M2) ratios do not indicate a definite Mn preference for M2 in the studied olivines (MnO=0.44% to 4.5 wt.%; average Mn(M1)/Mn(M2)=0.99±0.13).No relevant influence on geometric parameters was observed between Ca-free and Cabearing (maximum CaO=0.66 wt.%) olivines.

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Struktur-Verfeinerung von 13 Olivinen der Forsterit-Fayalit-Serie aus Vulkaniten und ultramafischen Einschlüssen

Zusammenfassung Die Ergebnisse dieser Untersuchung bestätigen die Abhängigkeit der geometrischen Parameter der Olivine vom Verhältnis Mg/(Fe+Mn). Die Volumina M1 und M2 nehmen linear, jedoch jeweils verschieden, mit zunehmenden Forsterit (Fo)-Gehalt ab. Der Unterschied zwischen den Volumina der oktaedrischen Plätze nimmt graduell vonFo 92% bisFo 50% ab und bleibt dann bis zuFo 0.2% konstant.Fe(M1)/Fe(M2)-Verhältnisse zeigen, daß Fe²⁺ vorzugsweise M1 Plätze in fayalitreichen Olivinen (Fa=39% bis 92%; durchschnittliches Fe(M1)/Fe(M2)=1,04±0,02) besetzen. In Mg-Olivinen (Fo=80% bis 92%) hingegen dürfte eine Mg-M1 Präferenz vorliegen (durchschnittliches Mg(M1)/Mg(M2)=0,96±0,05). Mn(M1)/Mn(M2)-Verhältnisse weisen nicht auf eine definitite Mn-Präferenz für M2 in den untersuchten Olivinen hin (MnO=0,44–4,5 wt.%; durchschnittliches Mn(M1)/Mn(M2)-Verhältnis=0,99±0,13).Der Calcium-Gehalt (Maximum, CaO=0,66 wt.%) beeinflußt die geometrischen Parameter der Olivine nicht.

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The olivine — clinopyroxene geobarometer: experimental results in the CaO-FeO-MgO-SiO2 system

The exchange of Ca and Mg between olivine and clinopyroxene has been studied in the CFMS system. Experiments were conducted in a piston-cylinder apparatus in the temperature range of 1,100–1,300° C and the pressure range 10–30 kbar. Results confirm the previous suggestion (Adams and Bishop 1982) that this reaction has a sufficiently large V° to be used as a geobarometer in several basic and ultrabasic systems. Experimental results were corrected for compositional effects using recent activity-composition models for quadrilateral pyroxenes and olivines. The corrected results indicate that the exchange reaction has aH _{1 bar} of 34,900 J, a S° of -7.25J/deg, and a V° of -0.489 J/bar. Corrected results agree well with calculations based on the thermodynamic properties of the endmembers.Application of the olivine-clinopyroxene geobarometer to many systems will require additional calibration of non CFMS components. Preliminary pressure estimates based on simple assumptions about the activity relations of these components have been made for spinel lherzolites from southwestern United States and coarse and porphyroclastic garnet lherzolites from southern Africa. A geotherm calculated from spinel lherzolites near the Rio Grande rift is consistent with a geophysical geotherm based on near-surface heat-flow measurements of 100 mW/m² or greater. Results on garnet lherzolites yield a southern African geotherm with no inflection which falls at somewhat higher temperatures than pyroxene geotherms calculated for the same area.     

Ab initio study of MgSiO3 C2/c enstatite

We have used a newly developed ab initio constant-pressure molecular dynamics with variable cell shape technique to investigate the zero temperature behaviour of high pressure clinoenstatite (MgSiO₃-C2/c) from 0 up to 30 GPa. The optimum structure at 8 GPa, as well as structural trends under pressure, compare very well with experimental data. At this pressure, we find noticeable “fluctuations” in the chain configuration which suggests the structure is on the verge of a mechanical instability. Two distinct compressive behaviours then appear: one below and another above 8 GPa. This phenomenon may be related to the observed transition to a lower symmetry P2₁/c phase which involves a reconfiguration of the silicate chains, and suggests that the C2/c structure at low pressures found here, may be an artifact of the dynamical algorithm which preserves space group in the absence of symmetry breaking fluctuations. Comparison with calculations in other magnesium silicate phases, indicates that the size and shape of the silicate units (isolated and/or linked tetrahedra and octahedra) are generally well described by the local density approximation; however, the weaker linkages provided by the O-Mg-O bonds, are not as well described. This trend suggests that, as in the recently studied case of H₂O-ice, the structural properties of more inhomogeneous systems, like enstatite, may be improved by using gradientcorrected density functionals.     

Average structure and M2 site configurations in C2/c clinopyroxenes along the Di-En join

In order to clarify the structural configurations observed in Di_ss in the Ca-rich region of the Di-En join (in which TEM observations show neither exsolution microstructures nor evidence of spinodal decomposition) single crystals large enough for X-ray diffraction analyses, with composition (Ca_0.66Mg_0.34)MgSi₂O₆, have been equilibrated close to the solvus atT=1350° C for 317 h, and quenched at room temperature. The refinement in C2/c space group shows that in the M2 site Ca and Mg are fully ordered in two split positions (M2_occ: 0.66 Ca; M2_occ: 0.34 Mg). Since the average structure shows a relevant elongation of anisotropic thermal ellipsoids of the O2 and O3 oxygen atoms, the refinement has been carried out according to a split model for O2 and O3 atoms: Ca appears 8-coordinated (as in diopside) and Mg shows a sixfold coordination similar to that of high-pigeonite. This coordination for Mg is significantly different from the fourfold coordination (Zn-like in Zn-cpx) proposed previously and it is a more probable coordination for Mg from a crystalchemical point of view. The same results were obtained refining a Di₈₀En₂₀ cpx, equilibrated atT=1230° C, according to the same O-split model. The data support the coexistence of a Di-like configuration for Ca and of a highPig-like configuration for Mg away from the solvus also. AtT very near toT _solidus the different configurations, observed at room temperature in the quenched samples, should converge and Ca and Mg should retain a single disordered configuration in the M2 site.     

拉萨地块中南部新生代超钾质岩中单斜辉石斑晶的环带成分研究

在青藏高原拉萨地块中南部的米巴勒、麦嘎乡、赛利普地区分布有新生代的超钾质火山岩,这些火山岩的斑晶中广泛发育单斜辉石正环带,其记录了超钾质岩浆的早期结晶历史.这些单斜辉石的正环带核部到边部Mg*和镁、铬的氧化物含量降低,而铁、钠、铝、钛的氧化物含量升高,它反映了岩浆正常结晶的顺序.米巴勒地区超钾质岩中的单斜辉石还出现反环带和少量的韵律环带,可能与该地区所发现的共生钠质过碱性火山岩有关,韵律环带揭示了其可能是相同成分的超钾质母岩浆从岩浆源区多次补给形成,而反环带则可能是与钠质过碱性火山岩岩浆存在一定程度的混合造成的.尽管三个地区超钾质火山岩的喷发时间稍不同,但是三地区的单斜辉石正环带核部成分基本相同,它们具有相似的Al-Ti值,指示出超钾质岩形成在相同的构造环境并具有相同的岩浆成因.     

海南岛玄武岩石粉废渣制备连续纤维实验研究

玄武岩石粉废渣是玄武岩石材破碎加工过程中产生的废料,其粒度细、销路差,尚无成熟的大规模综合利用方法。本文采集海南岛不同地区的8组玄武岩石粉废渣,利用电感耦合等离子体发射光谱仪(ICP-OES)和X射线衍射仪(XRD)分析其化学成分和矿物组分,通过差示扫描量热仪(DSC)、能谱仪(EDS)及熔融实验分析其结晶性能,筛选出最符合玄武岩纤维原料特征的样品进行纤维制备研究。通过扫描电子显微镜(SEM)及XRD分析纤维表面形貌与结晶晶相,将其性能与标准纤维进行对比。结果表明,1 450℃时制得的纤维频繁断丝,表面结晶出大量树枝状及针状的硅灰石、石英、黄长石和磁铁矿;升温至1 480℃并保温1 h后成功制得的连续纤维,仍含有黄长石和磁铁矿,断裂强力略低于标准纤维。研究结果表明利用海南岛玄武岩石粉废渣制备连续纤维具有一定可行性,本研究为海南岛玄武岩石粉废渣的处理提供了导向性建议和理论基础。     

Extraction of hazardous elements by water from contaminated rocks: An experimental study

The interaction of contaminated rocks (loam and clay recovered from depths of 1 and 4 m by a borehole drilled in the territory of a metallurgical plant in Ryazan oblast) was examined experimentally, and the concentrations (C) of twenty elements in solutions after the experiments were analyzed. The concentrations lie within ranges typical of the upper aquifer in the contaminated area, with the Al, As, Mo, Na, S, and W concentrations exceeding the maximum permissible concentration values (MPC). The experiments with clay yielded less stable and unambiguous results because a certain portion of clay particles passed through the filter (0.05 μm) when the rock and water were separated after the experiments and thus may contribute to the concentrations of certain elements in the solutions. The experiments led us to derive two types of dependences for each element: (1) C-t (time) dependences within the range of 1–36 days and (2) C-n (number of acts of rock treatment with fresh water portions) dependences. The both types are presented by various mass ratios of rock and water (r/w = 0.5 and 0.1). The character of the dependences led us to classify the elements into two groups. The concentrations of elements of one of the groups (As, Si, and V) shows no systematic dependences of C on t, n, and r/w, and this corresponds to equilibrium reached by fast adsorption-desorption reactions. These dependences in the other group of elements (almost all other elements) testify that the slow dissolution-precipitation reactions proceed away from equilibrium. The C-n dependences were utilized to evaluate the recovery ratios of elements and to identify easily soluble species of Ca, Mg, Mo, Na, S, and Sr. A fraction of ooliths (goethite + SiO₂) separated from the clay contains elevated concentrations of certain trace elements. Microprobe analyses of the ooliths show that elements whose concentrations are comparable with the detection limits of microprobe analysis are evenly distributed, with elevated concentrations detected only in two instances: (i) Ce and La (in monazite) and (ii) Co and Ni (in MnO). Having a high isomorphic capacity with respect to several elements, goethite can act as a geochemical barrier and thus constrain the migration of these elements. The correlation dependences of elemental concentrations in rock fractions were utilized to derive further information on the speciation of the elements related to common sources in various rocks and the number of concentrator minerals.     

Influence of magma composition and oxygen fugacity on the crystal structure of C2/c clinopyroxenes from a basalt-pantellerite suite

The crystallochemical variations of clinopyroxene in response to changes in f_{O 2} and melt composition have been determined for a basalt-pantellerite suite (Boseti Complex, Main Ethiopian Rift) by crystal structure refinement and microprobe analysis. The pyroxene evolutionary trend has both a “Ca-minimum” and late iron enrichment. During crystallization from basalts to trachytes, clinopyroxene geometry depends mainly on the relationships between T and M2 sites; for example, high SiO₂ activity in the magma causes high Si occupancy in T site, which in turn requires low Ca occupancy in M2 site in order to fulfill the local charge balance requirements. In contrast, clinopyroxene crystallized from acid melts is characterized by high Fe²⁺ (M1) content and therefore by a very large M1 site. Longer 〈M1-O1〉 and M1-O2 bond lengths require shorter T-O1 and T-O2 bond lengths and high Si occupancy in T site. It is concluded that the “Ca-minimum” in the clinopyroxene structure is regarded as the lowest value at which the charge balance requirements are satisfied in a C2/c clinopyroxene structure.     

月球岩浆洋演化的实验岩石学研究进展SCIEI北大核心CSCD

由于缺少直接来自月球深部的岩石样品,实验和计算模拟是认识早期月球演化过程的有效方法和手段。20世纪70年代以来,陆续开展了大量的实验岩石学和实验地球化学工作对月球岩浆洋(lunar magma ocean,LMO)演化模型进行验证和修正。但是,学界对LMO模型中的两个关键性参数,即初始物质组成和熔融深度,仍然存在不同的认识。根据月震和重力探测数据推测的平均月壳厚度的差异、月球样品含水量的研究以及新的遥感数据解译发现月表广泛分布富镁铝尖晶石(Cr#<5)等等,直接影响我们对月球初始物质组成和LMO深度以及月球深部高压矿物相的评估。本文通过整理高温高压实验岩石学和实验地球化学在研究LMO演化方面的一系列研究成果,主要聚焦以下几个科学问题:(1)月球初始物质组成中的难熔元素和挥发分含量,以及LMO深度对月壳厚度、结晶矿物的种类及含量有着决定性的影响;(2)高压矿物相石榴子石在月球深部稳定存在的可能性及其对残余岩浆中微量元素的分配行为的制约;(3)特殊类型的月球样品(包括火山玻璃、镁质岩套等)的成因机制对月球深部物质组成具有指示意义;(4)月核的不同物质组成对LMO模型的初始成分含量,特别是微量元素的限定作用。我们以最新的观测数据和月球样品的分析结果为依据,对已有的LMO演化模型进行重新评估,提出月球深部含有石榴子石的LMO演化模型的可能性,并对该方向亟需开展的工作进行探讨。     

Modification of mineral inclusions in garnet under high-pressure conditions: experimental simulation and application to the carbonate-silicate rocks of Kokchetav massif

Samples of poikoblastic garnets from the Escambray (Cuba), Maksyutov (Russia), and Sambagawa (Japan) eclogite complexes were heated to 700–1100 ºC at 3 to 4 GPa (30–40 kbar). Epidote, amphibole, and chlorite inclusions in the garnets underwent dehydration melting over the entire experimental PT range, which is typical of ultrahigh-pressure (UHP) metamorphic complexes. In the presence of aqueous fluids, carbonate minerals in the inclusions began to melt at 800 ºC and 3 GPa. Melting gave rise to new garnet, with the composition controlled by the chemistry of the primary inclusions and by PT run conditions. Garnet either grew directly from the melt or formed by replacement of host garnet walls leaving residual melt at the substitution front in the latter case. Partial melting of inclusions decreased the mechanical strength of the garnet host and led to local shearing. The experimental results were used to interpret observed features in two samples of a diamond-bearing and a diamond-free carbonate-silicate rocks from the Kumdy-Kol deposit in the Kokchetav Massif. Multiphase inclusions in both samples contain newly formed garnet with morphologies and compositions consistent with those produced experimentally under the given PT conditions. Minerals in the inclusions are compositionally similar to those in matrix, thus suggesting that melting may have occurred on a large scale.     

Formation of shoshonites from calcalkaline basalt magmas: geochemical and experimental constraints from the type locality

Independence volcano, Montana is a major center of the Absaroka volcanic field, from which absarokite, shoshonite, and banakite were originally defined. One magmatic trend at Independence volcano, from high-alumina tholeiitic basalt through shoshonite to high-K dacite, may be modeled by fractional crystallization of observed phenocryst phases (plagioclase, hypersthene, augite, and magnetite). Trace-element and Sr and Nd isotopic compositions of rocks are consistent with this model.Compositions of partial melts from experiments on four rocks at 1 atm and at 10 kbar demonstrate that rock compositions represent a nearly-anhydrous liquid line of descent at a pressure much closer to 10 kbar than to 1 atm. The line of descent involves crystallization of orthopyroxene, not olivine, resulting in strong enrichment in K₂O with little increase in SiO₂. Crystallization at either lower pressures or with water present, involving olivine, results in enrichment in both SiO₂ and K₂O.High-pressure (10 kbar) fractional crystallization of basaltic magma, resulting in formation of shoshonites, may occur at the base of thick crust (e.g., in continental interiors or in very mature arcs). At least a portion of the relationship between K₂O content of arc-related magmas and depth to the Benioff Zone may be attributed to thickening of crust towards the back-arc, resulting in higher pressures of fractionation in Moho-level chambers.     

A model for the υp -pressure function of cracked lunar rocks and some possible seismological consequences

Changes in wave velocity in rocks are mainly caused by pressure and depend on porosity and pore filling. For terrestrial and lunar rocks two formulae can be stated which are comparable with each other and the coefficients of which can be determined from wave velocity and uniaxial stress measurements. The behaviour of rocks may be compared with dynamic phenomena in the earth's crust, and in particular with pre-rupture phenomena (shocks, etc.) in seismic regions. The coefficient K₀ of imperfect bonds in rock increase with the number of shocks and brings about a decrease in wave velocity in seismic regions. The variations in wave velocity are connected with changes in electrical and thermal conductivity and with magnetic variations.