garcia-ruiz morphology and crystal growth …...a) pure barium seleniate. b) solid solution 50% seo...

Juan Manuel García-Ruiz International School of Crystallization. Granada, May 20-25, 2012

CRYSTAL GROWTH MECHANISMS & MORPHOLOGY

Juan Manuel García-Ruiz

Laboratorio de Estudios CristalográficosCSIC-Universidad de Granada

Juan Manuel García-Ruiz International School of Crystallography for Space Sciences. INAOE, April, 2016

Definitions and notations faces, dendrites,forms, shapes, spherulites,

fractals, morphologies

habits, textures, tabular,

acicular, whiskers,


Definitions and notationsA singular face is a flat surface bounding the crystal in a given direction.



Two non-parallel faces define an edge.




Three or more non-parallel faces define a corner.




Three or more non-parallel faces define a corner.

Three or more faces sharing parallel edges define a zone.


Definitions and notations

FORMA form is a set of all symmetrically equivalentfaces. For instance the cube {100}

100010

001

010- 100-

001-



FORMA form is a set of all symmetrically equivalentfaces. For instance the dodecahedron {110}



FORMA form is a set of all symmetrically equivalentfaces. For instance the tetrahedron {111}

Each form is composed by a number of facescalled its multiplicity.



hkl

Notation:crystal face hkl



{hkl}

Notation:crystal face hklcrystal form {hkl}



[hkl]

Notation:crystal face hklcrystal form {hkl}crystal direction [hkl]



<hkl>

Notation:crystal face hklcrystal form {hkl}crystal direction [hkl]equivalent directions <hkl>


Definitions and notations Triclinic forms

Sphenoid of class 2 Sphenoid of class m Prism

Monoclinic forms


Orthorhombic forms

Rhombic pyramid Rhombic dipyramidRhombic disphenoid



Tetragonal forms

Tetragonal displenoidTetragonal dipyramid Tetragonal pyramidTetragonal trapezohedrom Tetragonal scalenohedrom

Ditetragonal dipyramid Tetragonal prismDitetragonal pyramid Ditetragonal prsm



Hexagonal and trigonal formsDefinitions and notations


Hexagonal formsDefinitions and notations


Cubic formsDefinitions and notations


Why are they not spherical, like soap bubbles ?

Crystals are shapes of minimal energy

Because crystals are anisotropic 3D structures.

Melancholia from Durero


The minimum work required to build a unit interface at a constant volume and temperature in the system is called the specic free-surface energy and denoted gamma

It has units of energy per unit area and is conceptually similar to surface tension, but not identical in the case of solids.

The density and relative strength of bonds in crystals depend on the orientation of the surface. The polyhedral shapes of the crystals result from the anisotropy in specific free-surface energy.


Crystal faces are always parallel to reticular planes. The higher the reticular density of a family of planes, the larger the interplanar distance

001

010

111

100

110


The Wulff plotor gamma plot, as we plot surface energy as a function of direction


The Wulff plotor gamma plot. The minimal convex morphology enclosed within the plot minimizes the surface energy Esurf = Ahkl hkl


Bravais, Friedel, Donnay and Harker BFDH

The larger the interplanar distance dhkl the larger the morphological importance (MI) of a given (hkl) face.

Bravais Friedel law:

Donnay and Harker modificationsdhkl values must be corrected for non-primitive cells, screw axes and glide planes.

The morphological importance (MI) is the relative statistical frequency of occurrence of the face (hkl) on a set of crystals of a given compound or the relative size of the face (hkl) in a statistically representative set of them.


Hartman-Perdok approachThe HP theory is based on the properties of uninterrupted chains of bonds representing strong interactions between growth units. Such a chain is called Periodic Bond Chain (PBC) and, in addition,

PBCs must have an average periodicity [uvw] = ua + vb + wc of the direct primitive lattice (they must be crystallographic directions)

PBCs must be stoichiometric with regard to the unit cell contents (they are representative of the structure in that direction)

Hartman and Perdock Acta Cryst 8 (1955) 49,


Hartman-Perdok theory

In the classical HP theory, three types of faces are distinguished:

F-faces parallel to at least two non parallel intersecting PBCsS-faces parallel to only one PBCK-faces not parallel to any PBC

F

K

S


Hartman-Perdok theory

Hartman and Perdock Acta Cryst 8 (1955) 49,


While the current theories proposed to predict equilibrium and growth morphologies from structural information are not accurate, the information they provided is very useful for the understanding of actual growth morphologies and morphogenesis

There are several software available to calculate equilibrium morphology, such as Materials Studio and Shape. For further information, we refers to the group of Leeds (Prof. K. Roberts), Neimejen (Prof. Elias Vlieg) and Torino (Prof. Dino Aquilano and Prof. Marco Rubbo)


External appearance of a crystalline sample. It includes:

The combination of forms in the crystal

Habit: Definitions and notations


External appearance of a crystalline sample. It includes:

The combination of forms in the crystal

Their relative development or morphological importance

Habit: Definitions and notations

The morphological importance (MI) is the relative statistical frequency of occurrence of the face (hkl) on a set of crystals of a given compound or the relative size of the face (hkl) in a statistically representative set of them.


An inverse relation between dhkl and the growth rate of (hkl) faces is assumed to hold.

The importance of the relative growth rate on morphology

See: H.V. Alexandru, J Crystal Growth 5 (1969) 115

{10}{11}

{10}{11}

R10 = R11 R10 < R11

Juan Manuel Garcia Ruiz (CSIC-‐Universidad de Granada) Institute Laüe-‐Langevin, Grenoble, May 2, 2012

The slowest the growth rate the larger the morphological importanceAt equilibrium, crystals are shaped by the faces with the slowest crystal

growth rates

36

Laser beam direc.on Pathlenght (1.0 mm).

� NaCl at 4.8M, 4.4M, 4.0M in 10µL drops.

� Leave drops to evaporate until dryness.

� Follow in situ by PSI Mach-‐Zehnder Interferometry.

Dynamics of a crystalizing dropA demonstration of the role of gravity

A Phase-Shifting Mach-Zehnder interferometry study

Supersaturation is indicated by colour code

� Density of water (0.998 g/cm3) � Diameter of the drop (3.0 mm) � Viscosity of water (1002 Pa.s) � Average velocity: 0.014 mm/s

Re = 0,40

Laminar flow: parallel layers, with no disruption between them.

1.62 µm/s

1.04 µm/s

Mean growth rate (8 min.)

Top face Lateral faces

0.83 µm/s 1.14 µm/s

Convection greatly increases the rate of solute transport to the growth interface.

Initial concentration: 4.0 M

Durbin, S.D. y Feher, G., J. Cryst. Growth, 76 (1986) 583

110

101

Durbin, S.D. y Feher, G., J. Cryst. Growth, 76 (1986) 583

001011

101210

001

210100

001

210

Crystal habits as a function of the contain inSO42- in the solid solution Ba(SeO4,SO4). a) Pure Barium

Seleniate. b) solid solution 50% SeO42- y SO4

2- in the starting solid solution. c) pure barium sulfate.

Andara A., Heasman D., Prieto M., Fernández-González A., Crystal Growth & Design 7 (2007) 545

210

100

↑ SO42-

Morphological changes of crystal habit of BaSeSO4 as a function of de SO4

2- in the starting water solution.

Andara A., Heasman D., Prieto M., Fernández-González A., Crystal Growth & Design 7 (2007) 545

Crystal Habits

Cubic hopper crystal

Tabular or equant crystals

Aggregate of capillary crystals

Crystal HabitsEquant A crystal that have approximately the same side length in every direction.

Prismatic A crystal elongated in one direction like a prism. When they are vert large, are called columnar crystals

Tabular: Crystals appear tabular or platelike in shape.

Bladed: An elongated, flat crystals suggestive of knife blades.

Crystal Habits

Plumose Acicular Capillary

Botryoidal Mammillary: Reniform: Foliated Micaceous Lamellar or lamelliform

Filiform Fibrous Reticulated Stellated Dendritic Colloform


Calcite with ovotransferrin

Non-singular facesFaces are usually flat and have singular hkl indices. However, sometimes, they may be curved, it means with non-singular indices


Non-singular faces

a b c

a) and b) Calcite, in presence of 128 and 512 µg/ml ovotranferrin respectively and c) vaterite, in presence of 512 µg/ml ovotranferrin.

a b c

a) and b) Calcite with 128 and 512 µg/ml ovalbumin, and c vaterite with 512 µg/ml ovalbumin.

Non-singular facesFaces are usually flat and have singular hkl indices. However, sometimes, they may be curved

010

1k0

García-Ruiz, J.M, Villasuso, R., Ayora, C., Canals, A. & Otálora, F., 2007, Geology 35, 327, Supplementary Information

b

d

Experimental setup of the laser goniometer used for the measurement of angles between mirror reflections belonging to the [001] zone. b) Reflection on the (0 1 0) face as seen from the CCD camera. c-e) Mirror reflections from, respectively, (1 2 0), (1 4 0) and (1 6 0). The angles at

How do crystals grow

Insubria International Summer School Crystallography for Health and Biosciences, Como 2012 Juan Manuel García-Ruiz

Juan Manuel García Ruiz Escola de Altos Estudos em Cristalização e Cristalografia para Latino América (ECRISLA ) November 13-25, 2011 Florianópolis (Brasil)

Movie provided by Peter Vekilov and Georgiou


Crystal Growth MechanismsNormal Growth

(Direct Accretion)

The growth of a rough crystal surface

Growth by direct accretion: Normal growth

Linear trend with supersaturation


Crystal Growth MechanismsTwo-dimensional nucleation

Juan Manuel Garcia Ruiz (CSIC-‐Universidad de Granada) Ciudad de las Artes y las Ciencias de Valencia 2014

Two dimensional nucleation

Juan Manuel García Ruiz Escola de Altos Estudos em Cristalização e Cristalografia para Latino América (ECRISLA ) November 13-25, 2011 Florianópolis (Brasil)

Assuming and S = 1,1, we got:

Growth by two-dimensional nucleation

Crystals could no grow at a supersaturation values of 10% !!!

Parabolic trend with supersaturation


Crystal Growth Mechanisms Screw dislocation

A. McPherson, Y. G. Kuznetsov, A. Malkin & M.Plomp, Macromolecular Crystal Growth As Revealed By Atomic Force Microscopy



Dislocacion helicoidal

Mecanismos de crecimiento cristalino

Parabolic trend at low supersaturation then linear trends

Screw dislocation growth


Juan Manuel García-Ruiz International School of Crystallography for Space Sciences. INAOE, April, 2016 International School on Crystallization, Granada May 25-‐29, 2009 Juan Ma. Garcia-‐Ruiz

Transport and growth


Supersaturation

Growth

r ate

110101

Concentration gradient

Flow of growth units

CrystalSolution

b

a

c d

Crystallization taking place in a diffusive environment yields crystals

of the highest quality

Flow of tranport towards the crystal face

<<<< Flow of integration in the crystal

surface

Dettachment

Attachment


J. M. García-Ruiz and F. Otálora. Macromolecular Crystals: Growth and Characterization. Crystal Growth-From Fundamentals to Technology. G. Müller, J. -J. Métois and P. Rudolph, Ed;. Elsevier, Amsterdam, 2004, pp 369-386.

The Tetris analogy

Arcade games for teaching crystal growth. Journal of Chemical Education 76 (1999) 499-501

J. M. García-Ruiz. "Arcade Games for Teaching Crystal Growth" Journal of Chemical Education 76, 499-501, (1999)

You want to learn how crystals grow?then play CRYSTAL TETRIS


http://www.lec.csic.es/ctetris/

The growth kinetics


The Chemistry of Naica waters

Temperature and pH were measured in situ.

Localiza;on Name T (ºC) pH

XCO. 4544-‐NW Naica-‐01 54 7.6

XCO. 5161-‐NE Naica-‐03 50 7.6

XCO. 77 Naica-‐08 54 7.4

“Rebaje Cincuentenario” Naica-‐13 53 7.6

No significant composi;on differences of water samples was found with sample loca;on

No difference with samples collected in the 70´s

Comparison of the concentrations of the main elements present in water samples collected at Naica at different times. All concentrations were determined by ICP-AES

Water samples collected at the Naica mining complex

The satura;on index was calculated with PHREEQC

It is not possible to determine, unambiguously, when the waters were super-‐ or under-‐saturated

G row t h r a t e o f g i a n t g y p s um c r y s t a l s

Growth mechanisms

(010)

(1kO)(1kO)

(010)

Van Driessche AES, Garcia-‐Ruiz JM, Delgado-‐López JM, Sazaki G (2010) In situ observation of step dynamics on gypsum crystals. Cryst Growth Des 10:3909–3916.

2D nucleation (no spiral growth)

“Hill and valley” surface morphology

Increase of step kinetics with Tª

The growth kinetics

• High-resolution phase-shift interferometry using a white beam light source and modified Linnik-type interference optics.

• To cancel external disturbances: gold nanoparticles attached to the gypsum surface were used as insoluble reference surfaces.

• Long time measurements: A titanium “flow through” cell with a thermo controlled block connected to a HPLC pump

To test our experimental setup, a first run was done at room temperature using milli-Q water. Expansion of etch pits on the {010} face of a gypsum

How to measure slow growth rates

Fitting between 55 -‐60 °C

T (°C) Normal growth rate (nm/s) Fitted Experimental

50 1.6x 10-‐6 ≤3.7x10-‐6

54 1.2x10-‐5

55 (2.1x10-‐5) 1.6±0.3x10-‐5

56 3.5x10-‐5

57 5.8x10-‐5

58 9.6x10-‐5

59 1.6x10-‐4

60 (2.7x10-‐4) 3.5±0.5x10-‐4

50 55 60 65 70 75 80 85 90

0.00

0.05

0.10

0.15

0.20

0.25

0.30

50 55 60

0.0

1.0x10-4

2.0x10-4

3.0x10-4

4.0x10-4

Temperature (ºC)

Nor

mal

gro

wth

rat

e (n

m/s

)

50 55 60 65 70 75 80 85 90

10-5

10-4

10-3

10-2

10-1

Nor

mal

gro

wth

rat

e (n

m/s

)

Temperature (ºC)

Growth ages of the crystals can be estimated

50 1.6x 10-6 <3.7x10-6 -

54 1.2x10-5 13

55 (2.1x10-5) 1.6±0.3x10-5 (0.77) 0.99±0.26

56 3.5x10-5 0,5

57 5.8x10-5 0,3

58 9.6x10-5 0,18

59 1.6x10-4 0,1

60 (2.7x10-4) 3.5±0.5x10-4 (0.06) 0.05±0.01

T (ºC) Fitted growth rate(nm/s)

Experimental growth rate (nm/s)

Growth time of one meter thick crystal

(Ma)

The growth time of the crystals

Normal (010) growth rates from Naica’s present day waters versus temperature

Caves of Crystals: typical diameter of the crystal beams : 1 meter 0.55 ± 0.25 million yearsdepending on the growth temperature

The crystal morphologyof

giant crystals of gypsum


Why two different morphologies?

Single crystals displaying a morphology closer to the equilibrium morphology

The crystal beams The blocky crystals

{010}

Crystals highly elongated in the c direction

Two different nucleation event under different conditions?

Two different growth kinetics due to impurities?

Screw dislocations scarce and only observed on 010

Actually, two different growth geometries

Reentrant twin angle. Beams are twinned crystals and show reentrant angles!

Why two different morphologies?

Reentrant Twin Angles

“It is well known that twinned crystals often grow larger than the co-existing single crystals and also exhibit different morphology from single crystals.

Twinned crystals often exhibit flattened or elongated morphology, as compared to the co-existing single crystals.

They grow much larger than the co-existing single crystals.

They sometimes show crystal faces uncommon for single crystals.”

Kitamura, Hosoya & Sunagawa (1979). J. Crystal Growth 47, 93 The twinned crystals feature a

reentrant angle where four {111} faces (two from each individual) meet.

REENTRANT ANGLES AS STEP SOURCES

011 111

100 contact twin in gypsum produces elongated crystals that grow faster on the side of the reentrant angle.

Crystal B

The reentrant twin angle increases growth rate by a factor of 30!

Transition concave/convexComplex events at the tip

Different reentrant angles exist, but only the 011/011 seems to be active, producing an increase of growth rate by a factor of 10-30.

The existence of two types of crystal morphology can be explained without external changes in the chemistry or physics of the water.

J. M. Garcia-Ruiz (text) J. Trueba (pictures). National Geographic, November 2007

If you wish to know more

F. Otálora & J. M. García-Ruiz, Chem. Soc. Rev. 43 (2014) 20132026

García-Ruiz, J.M, Villasuso, R., Ayora, C., Canals, A. & Otálora, F., 2007, Geology 35, 327;

Van Driessche, A.E.S., García-Ruiz, J.M., Tsukamoto, K., Patiño-López, L.D. and Satoh, H. (2011). Proc. Nat. Acad. of Sciences, 108, 15721–15726.

and references therein


Thank You

garcia-ruiz morphology and crystal growth …...a) pure barium seleniate. b) solid solution 50% seo...

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