CHAPTER 6: CRYSTAL GROWTH & XRD Sarah Lambart
RECAP CHAP. 5 (SEE REVIEW CHAPTER) Crystal twinning Crystal defects Polymorphism and isomorphism
CONTENT CHAP. 6 (2 LECTURES) Part 1: Crystal growing - nucleation and accretion Part 2: Introduction to the XRD method
PART 1- CRYSTAL GROWTH: NUCLEATION AND ACCRETION
CRYSTAL GROWTH Environments: vapor phase, fluid phase, solid phase Volcanic fumaroles (Kilauea) Reaction rim of garnet between plagioclase and hornblende Calcite vein Cooling lava
CRYSTAL GROWTH In order to growth a mineral form a fluid (e.g., magma, water), you need to consider two processes: Nucleation Transport + appropriate P-T conditions
CRYSTAL GROWTH Three possible conditions for a mineral: Stable Metastable Unstable Activation energy: energy required to transform a metastable mineral to a stable mineral
KINETICS Kinetics = study of reaction rates Depend on T, P, composition of the system Reactions tend to occur more quickly at higher T s Different elements will diffuse at different rates, which can cause some minerals to become stable while others remain metastable
CRYSTAL GROWTH Nucleation: the initiation of crystal growth in a fluid (magma, water, etc..)
CRYSTAL GROWTH Nucleation: the initiation of crystal growth in a fluid (magma, water, etc..) In order for the reaction to occur, the energy of the mineral must be lower than the energy of the unbounded ions/atoms in the fluid ( = the mineral must be more stable than the fluid)
CRYSTAL GROWTH Nucleation: the initiation of crystal growth in a fluid (magma, water, etc..) In order for the reaction to occur, the energy of the mineral must be lower than the energy of the unbounded ions/atoms in the fluid ( = the mineral must be more stable than the fluid) The energy of nucleation can be expressed though Gibbs free energy of formation (ΔG f )
CRYSTAL GROWTH Determining the Gibbs free energy of formation for a crystal needs to consider both the volume and surface of the precipitating crystal 1) Volume energy. Consider a crystal of volume V: ΔG v = [ΔG f(crystal) -ΔG f(fluid) ]V If ΔG v <0, the crystal is at lower energy and is stable : it can precipitate.
CRYSTAL GROWTH Determining the Gibbs free energy of formation for a crystal needs to consider both the volume and surface of the precipitating crystal 2) Surface energy (=interfacial energy). Consider a crystal of volume V: ΔG S = γa where γ is the surface energy per unit area, and a is the area of the crystal.
CRYSTAL GROWTH Gibbs free energy of formation: ΔG f = ΔG v + ΔG s Consider a spherical crystal of radius r: ΔG f = ΔG v *(4π/3)*r 3 + ΔG s *πr 2
NUCLEATION r* (or r c ): critical radius ΔG* (or ΔG c ): nucleation energy To form crystal you must overcome the nucleation energy barrier (or add nuclei) r*
NUCLEATION r* (or r c ): critical radius ΔG* (or ΔG c ): nucleation energy ΔG f = ΔG v *(4π/3)*r 3 + ΔG s *πr 2 r 3 r 2 r*
NUCLEATION r* (or r c ): critical radius ΔG* (or ΔG c ): nucleation energy ΔG f = ΔG v + ΔG s Energy required for the nucleation and the growing increase with the surface/ volume ratio. r*
NUCLEATION To form crystal you must overcome the nucleation energy barrier (or add nuclei) homogeneous vs. heterogeneous nucleation The nucleus has to form from a pure fluid reservoir Dust, other nuclei, can serve as support for nucleation: requires less energy
NUCLEATION Supercooling Ex.: Halite in water
NUCLEATION Supercooling nucleation energy
NUCLEATION Supercooling T ΔT Solid + liquid liquid liquidus solid solidus X
CRYSTAL GROWTH Minimize the surface energy Fig. 5.10 in Introduction to mineralogy (Nesse)
CRYSTAL GROWTH Minimize the surface energy Fig. 5.10 in Introduction to mineralogy (Nesse)
CRYSTAL GROWTH Minimize the surface energy Three types of surfaces: F (=flat) S (= Stepped) K (=kinked)
CRYSTAL GROWTH the slow growing faces will tend to dominate in the end
DENDRITIC CRYSTALS Crystal growth limited by transport
ZONED CRYSTALS Change of composition during the growth Element maps showing Ca and Na zonation in plagioclase. source: http:// serc.carleton.edu/details/ images/8598.html
OSTWALD RIPENING This thermodynamically-driven spontaneous process occurs because larger particles are more energetically favored than smaller particles 2h 6h 24h
OSTWALD RIPENING This thermodynamically-driven spontaneous process occurs because larger particles are more energetically favored than smaller particles Log (mean size) Log(t) n t (s)
PART 2: X-RAY DIFFRACTION METHOD
X-RAY DIFFRACTION (XRD) X-rays: discovered in 1895 - powerful tool to "see inside" of crystals Determination of crystal structure and unit cell sizes Identification of minerals: powder diffraction analyse = simple and inexpensive method for identifying minerals, especially fine-grained minerals
X-RAY DIFFRACTION (XRD) X-rays: ability to penetrate the matter depends on density (Z) X-rays: electromagnetic radiation λ= 0.02-100 * 10-10 m λ~ atom size
X-RAY DIFFRACTION (XRD) X-ray Vacuum Tube Cathode (W) electron generator Anode (Mo, Cu, Fe, Co, Cr) electron target, X-ray generator
X-RAY DIFFRACTION (XRD) Continuous spectra (white radiation) range of X-ray wavelengths generated by the absorption (stopping) of electrons by the target Characteristic X-rays particular wavelengths created by dislodgement of inner shell electrons of the target metal; x-rays generated when outer shell electrons collapse into vacant inner shells
X-RAY DIFFRACTION (XRD) Characteristic X-rays Kα peaks created by collapse from L to K shell Kβ peaks created by collapse from M to K shell
BRAGG LAW nλ = 2d sinθ if we know λ of the X-rays going in to the crystal, and we can measure the θ of the diffracted X-rays coming out of the crystal, then we know the spacing between the atomic planes.
POWDER METHOD X-ray intensity plot as function of the angle Comparison with the spectra collections: 70,000 X-ray Tube: can be oriented from 0 to 90 (monochromatic rays) Detector: Can be oriented from 0 to 90 Gionometer: to orient the crystals
POWDER METHOD Ex. Quartz nλ = 2d sinθ θ = arcsin (nλ / 2d) λ(cu) = 1.54Å (anode) d - Qtz [101] = 3.342 θ = 13.32 ; 2θ = 26.64