EXOTIC METHODS OF GENERATING HIGH PRESSURE PHASES IN SMALL VOLUME ELEMENTS

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EXOTIC METHODS OF GENERATING HIGH PRESSURE PHASES IN SMALL VOLUME

ELEMENTS

H. Schloessin

To cite this version:

H. Schloessin. EXOTIC METHODS OF GENERATING HIGH PRESSURE PHASES IN SMALL VOLUME ELEMENTS. Journal de Physique Colloques, 1984, 45 (C8), pp.C8-387-C8-393.

�10.1051/jphyscol:1984869�. �jpa-00224371�

TOURNAI. DE PHYSIQUE

Colloque C8, supplément au n°l 1, Tome k5, novembre 198<t page C8-387

EXOTIC METHODS OF GENERATING HIGH PRESSURE PHASES IN SMALL VOLUME ELEMENTS

H.H. S c h l o e s s i n

Department of Geophysics, University of Western Ontario, London, Ontario N6A 5B7, Canada

Résumé - On peut observer la formation de variétés allotropiques haute pres- sion de certains métaux déposés par évaporation, du fait des déformations im- posées par le désaccord de paramètres entre le substrat et le dépôt. De même la nucléation de phases haute pression se produit à l'intérieur ou au voisi- nage de précipités au sein de la matrice cristalline de métaux ou lors de la

croissance épitaxique de minéraux. Enfin les conditions favorables à l'appari- tion de phases haute pression peuvent être créées par les champs de contrainte des dislocations.

Abstract - High pressure polymorphs of metals can grow from vapour deposits on substrates due to misfit strains. Nucleations of high pressure phases occur in and outside precipitates in a crystal matrix of metals or in epitaxial overgrowth of minerals. Conditions promoting high pressure phases can be created by the stress fields of dislocations.

Generally, the objectives of high pressure experimental work are to observe and identify high pressure phases and to determine their properties. The production of high pressures can be achieved in various ways by static and dynamic means.

Static, solid medium, high pressure generation usually involves different kinds of contact formation, plastic deformation and flow with the extrusion of matter.

Estimates of achieveable compressions of materials and stresses can be obtained from theories which, in principle, boil down to the basic form of Coulomb's laws.

However, as we shall show in three examples, it is not under all circumstances necessary to have piston-cylinder, opposed anvils, or multi-anvil devices to create conditions suitable for the stability of high pressure phases. The chosen

examples are (i) high pressure phases in crystalline nuclei, deposited from a vapour phase, imposed by the misfit with the substrate on which they grow, (ii) high pressure phases in and in the surroundings of precipitates and nuclei of other inhomogeneous phases under thermal strains in a bulk crystalline matrix, and (iii) specific situations of stress fields at the head of pile-ups of prismatic dislocation loops being punched out under the action of indenter forces applied to a single crystal. Although exotic, these are interesting high pressure situations, which if we are content with the material manifestations and properties observable in very small volume elements may give us insights into the interatomic force functions and furnish us with fundamental data relevant to geophysical and certain industrial processes.

I - HIGH PRESSURE PHASES IN THIN FILMS OR INDIVIDUAL NUCLEI FORMING ON A SUBSTRATE In the process of nucleation and growth of a crystalline phase from a vapour deposition on a solid substrate in high vacuum, the atomic layers building the nuclei of the new phase tend to form in registry with the atomic spacings of the substrate material. The nuclei can exist as thin continuous adsorbed films, but more frequently form discrete 3-dimensional islands of nucleation which may be approximated by hemispherical volumes.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984869

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The misfit at the interface between the substrate and the crystal nuclei causes considerable misfit strains which, over distances of several hundred augstroms, dictate the structure of the overgrowing substances. In the case of a thick substrate with a lattice spacing as which is practically rigid in relation to the thin overgrowing film with lattice spacing a0 the misfit f [ I ] is defined by

In this case the mismatch between as and a. is supposed to be small and the misfit strain is taken up almost entirely by the substrate. If the misfit strains are shared between substrate and nucleus, then

where E is the strain in the interface between substrate and nucleus and 6 is the strain due to misfit dislocations. Misfit dislocations [2,3] accommodate some of the strains in both the substrate and the nucleus. If f is positive, then the strain is tensile and the dislocations are positive Taylor dislocations. A nucleus may at first be free from dislocations or be threaded by dislocations which are propagated into it from dislocations present in the substrate. With increasing interface strains as a result of increasing thickness of the growing film or island, misfit dislocation loops will be generated inside the nucleus and

eventually spread across its dimensions to the periphery. The strains are largest while the nucleus is coherent with the substrate.

The misfit in the case of bi-crystals, i.e. between crystalline phases of similar mechanical strength and lattice parameters as, ao, is defined by [ l ]

In cases where the lattice spacings of the substrate and nucleus materials are very different so that patterns on either side of the interface are in registry only over long periodic distances, i.e. when

with m, n being integers, then the misfit is determined by

Transmission electron microscope studies of thin film nucleation and growth, especially those coming into vogue in the 1960's and 1970's have brought into evidence many examples of poly- and pseudomorphic structures of metals forming on different substrates under vacuum deposition from the vapour phase. Amongst the most beautiful and geophysically interesting examples have been the polymorphic forms of epitaxy of iron (Fe: a(bcc) 2.8612, 0 (bcc) :800°C 2.90

a,

x,

g,

growth mechanism of fcc y-iron and hcp €-iron on Cu, Ni, MoS2 and NaCl were first investigated in great detail by Matthews [4,5], and Jesser and Matthews [6,71 in a series of high vacuum growth experiments with in-situ analyses of beautiful high- resolution images. Interpretations of selected area diffraction and Moire-fringe patterns were used to determine misfit strains and structures of dislocations. The largest coherent island of iron on copper observed was 750A; the theoretically determined radius of a hemispherical nucleus was 8752. The misfit strains in the case of E-iron on MoS2 was found to be greater than those corresponding to hydrostatic pressures of 13 GPa. The misfit structure extended over the entire volume of the nucleus during the stage of coherency. It may also be possible for

hcp iron structures to come into existence as an extrinsic stacking fault subtended between partial dislocations. The latter could be generated by the extension from substrate dislocations which, when propagated through the interface, can split into partial dislocations within the nucleus. Alternatively, the stacking fault could be created by imperfect misfit dislocations nucleating at the interface. An example of the image of iron nuclei on copper is shown in Fig. 1. TEM observations of small phase nuclei offer a very direct method of measuring the small volume changes 6v/v associated with an introduction of a known number of edge dislocations.

Using the bulk modulus K or the derivatives of Johnson potentials for a- and y- iron one can determine values of Grueneisen's

r

where b i, the Burgers vector and R a cut-off radius, or

6w=2TK6v/v (1.7)

Fig. 1. fcc iron on hot (400'~) Cu. (Matthews [ 4 ] ) . I1

-

Definitions of misfit similar to 1.1-5 and the generation of high stresses due to misfit strains, which, in general, will involve curved and polygonized interfaces, apply to the nucleation and growth of crystalline precipitates inside a matrix crystal. The precipitate loses coherency with the matrix when misfit dislocations encircle the periphery of the precipitate, i.e. lie in the interface. Existing dislocations in the matrix may be attracted to the precipitate leaving behind closed loops around the precipitate and thus contribute to the hydrostaticity of the stress in the precipitate. The radial stress at a distance r from a precipitate of radius rp and misfit E in a matrix of shear modulus G is determined by [1,8]

These misfit stresses can be of GPa order. They are capable of punching out, and propagate into the matrix, straits of prismatic dislocation loops. When held up by an obstacle, these arrays may in turn generate stresses which locally

can exceed the elastic strength. The hydrostatic components of edge dislocations play an important part in the nucleation of phase transformations [9].

Epitaxial polymorphs, some corresponding to those only stable at high pressure, are encountered as precipitates in pyroxenes [lo], garnets [ll] and aluminum oxides 1121. In the biosphere some organisms are able to create high pressure modifica- tions; certain kinds of crabs apparently make use of aragonite to strengthen and protect their shins. The precipitates and forms of overgrowth in minerals frequently form as coherent laminae with growth ledges in crystallographic

orientations [9]. Such growth structures can be detected in ~oire/ fringe patterns observed in translation x-ray topographic images. Examples are shown in Figs. 2 and 3.

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There is a persisting interest in the possibility of ferro-paraelectric phase transitions in perovskite-structure silicates [13,14] such as MgSi03 and CaSiO

.

Prom experiments with a few specks of the perovskite-type silicates synthesize2 so far [15], it is not clear whether these high pressure phases are capable of spontaneous polarization or whether they could be anti-ferroelectric. According to Ringwood and Major [16] perovskite-structure silicates, especially those of CaSiO occur in two forms, as precipitates at p>lOGPa and as pure crystalline forms at p > j 2 ~ ~ a . The former offer the possibility of locking in ferroelectric phases by means of epitaxial overgrowth on substrates imposing misfit strains in registry with the spontaneous strains at an undefined Curie temperature. In this connection, studies of the effects of lattice imperfections, line defects and precipitates in

Fig. 2. Clinoenstatite nucleating on orthoenstatite (with doubling of the unit cell).

Fig. 3. Laminar precipitates of A10 (OH) in A1203.

ferroelectric crystals above and below the Curie temperature and on the formation of domain walls have been of particular interest. In T.G.S. (triglycinesulphate) the latter are 180° walls separating regions of reversed polarization with polarization vector in <010> direction, and the Curie temperature of 49'~ is easily transgressed in either direction. For some time separate investigators have tried to account for the image contrast of domain walls in electron and x-ray diffraction. Takahashi [17] proposed that the domain wall was identical with the sites of screw dislocations thus facilitating its mobility. Petrov [18] explained the contrast as being due to the local lattice deformation.

Takahashi and Tarkagi [19] subsequently advocated that the domain wall itself was strain-free and that its image resembled that of a stacking fault. A stacking defect had indeed been identified with the 180' wall of BaTi03 by Malis and Gleiter [20]. The relative displacements on either side of the stacking fault are concomitant with the spontaneous polarization as a result of the inverse piezo- electric effect. Because of the high dielectric constant applied electric fields can amplify the stresses to very high orders of magnitude. X-ray topographic studies of the ferroelectric domain walls [21,22] in T.G.S. confirm the stacking fault contrast and a large wall thickness of >5um. The pinning of domains at dislocations allowing the local preservation of ferroelectric states above the Curie temperature as well as the generation of large strains at precipitates

amounttng to the effects of giant dislocations are promising indicators of conditions favouring ferroelectric states in high pressure phases. Associations of domains with defects and strain lobes of a giant dislocation are illustrated in Figs. 4 and 5.

Fig. 4. Position of domain walls marked by stacking fault contrast at Tc490C.

Fig. 5. Strain lobes at giant dislocations at T>500C.

111 - CAN HEAD STRESSES OF PILE-UPS OF PRISMATIC DISLOCATIONS GENERATE HIGH PRESSURES IN SMALL VOLUME ELEMENTS?

A cubic galena (Pb S) single crystal is most suitable for the generation of pile-ups of square prismatic dislocation loops under the force of an indenter. A force applied to a (100) surface produces dislocation segments in (010) and (001)

segments which intersect to form a rectangular prism. The shear stress at the head of the pile-up [ 2 3 ] under an applied stress T, is given by

where G is the shear modulus, b the Burgers vector and L the length of the pile-up.

n is the number of dislocations which is a function (a hypergeometric series) with the applied stress and the mutual repulsion between dislocations as constant parameters, of the equilibrium ~ositions of all the dislocations in the array. At large distances r c L, the head stress is comparable to that of a giant dis- location with Burgers vector nb at the head of the pile-up

At intermediate distances with ro = L/2n2<<r<<L, the pile-up produces a stress concentration

C8-392 JOURNAL DE PHYSIQUE

similar to that of a Starr crack [ 2 4 ] or twin. However, the most remarkable property of the punched-out pile of dislocations, known for long by mineralogists

[ 2 5 ] and recognized in the case ofthallous oxides as cleavage dislocations par

excellence by Seitz [ 2 6 ] , is that they can be driven right through a crystal slab and made to emerge on the opposite face as a prismatic extrusion. The prism of interstitial dislocation loops thus behaves just like the piston in a cylinder.

It suggests that indentations of small cross section could be used to transmit forces onto a sample, somewhat smaller In cross section, which is supported by a backing block. If two slabs with two opposing indentations were to be used, one side would have to be slightly pre-indented with a smaller diameter punch to prepare the space for the insertion of a small sample. A schematic illustration of loops and indentation is shown in Fig. 6 together with the diagramatic view of its use under lateral constraint inside a cublc press for the purpose of high pressure amplification.

F3i Bismuth probe

Fig. 6(a). Cross section through array of prismatic dislocation loops in galena.

ACKNOWLEDGEMENTS

S Sample

Fig. 6(b). Sample under stress im- pressed by two opposed indentations punched through galena slabs placed face to face inside a BN cube;

sample to be contained in a pre- indented depression on one side of the contacting slabs.

Support of this work by the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.

REFERENCES

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